**Possibilities of Deriving Crop Evapotranspiration from Satellite Data with the Integration with Other Sources of Information**

Gheorghe Stancalie and Argentina Nertan *National Meteorological Administration 97, Soseaua Bucuresti-Ploiesti, Bucharest Romania* 

## **1. Introduction**

16 Will-be-set-by-IN-TECH

436 Evapotranspiration – Remote Sensing and Modeling

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*and Remote Sensing* 44: 1885–1898.

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*dc9f9298946f723c196b3*

After precipitation, evapotranspiration is one of the most significant components in terrestrial water budgets.

Evapotranspiration (ET) describes the transport of water into the atmosphere from surfaces (including soil - soil evaporation) and from vegetation (transpiration). Those are often the most important contributors to evapotranspiration. Other contributors to evapotranspiration are the e from wet canopy surface (wet-canopy evaporation) and evaporation from vegetation-covered water surface in wetlands the process of evapotranspiration is one of the main consumers of solar energy at the Earth's surface. The energy used for evapotranspiration is generally referred to as latent heat flux. The term latent heat flux includes other related processes unrelated to transpiration including condensation (e.g., fog, dew), and snow and ice sublimation.

There are several factors that affect the evapotranspiration processes: energy availability; the humidity gradient away from the surface(the rate and quantity of water vapor entering into the atmosphere are higher in drier air); the wind speed at the soil level (wind affects evapotranspiration by bringing heat energy into an area); Water availability (it is well known that the evapotranspiration cannot occur if water is not available); Vegetation biophysical parameters (many physical parameters of the vegetation, like cover plant height, leaf area index and leaf shape and the reflectivity of plant surfaces can affect evapotranspiration); Stomatal resistance (the transpiration rate is dependent on the diffusion resistance provided by the stomatal pores, and also on the humidity gradient between the leaf's internal air spaces and the outside air); soil characteristics which includes its heat capacity, and soil chemistry and albedo. For a given climatic region the evapotranspiration follows the seasonal declination of solar radiation and the resulting air temperatures: minimum evapotranspiration rates generally occur during the coldest months of the year and maximum rates generally coincide with the summer season (Burba, 2010). Even so evapotranspiration depends on solar energy; the availability of soil moisture and plant maturity, the seasonal maximum evapotranspiration actually may precede or follow the seasonal maximum solar radiation and air temperature by several weeks (Burba, 2010). If the moisture is available, evapotranspiration is dependent mainly on the availability of solar energy to vaporize water: evapotranspiration varies with latitude, season, time of day, and cloud cover. Most of the evapotranspiration of water at the Earth's surface level occurs in the subtropical regions (Fig.1). In these areas, high quantities of solar radiation provide the energy necessary to convert liquid water into a gas. Usually, evapotranspiration exceeds precipitation on middle and high latitude large areas during the summer season. As a result of climate change it is expected to induce a further intensification of the global water cycle, including ET (Huntington, 2006). Therefore accurate estimates of evapotranspiration are needed for weather forecasting and projecting the long-term effects of land use change and global climate change, irrigation scheduling and watershed management.

Fig. 1. Mean Annual Potential Evapotranspiration (UNEP World Atlas of Desertification)

In this regard, remote sensing data with the increasing imagery resolution is a useful tool to provide ET information over different temporal and spatial scales. During the last decades important progresses were made in the determination of ET using remote sensing techniques. Some studies have classified the methods of ET estimation in two categories: semi- empirical methods - use empirical relationship and a minimum set of meteorological data; analytical methods – consist in the establishment of the physical process at the scale of interest. A study done by Courault (2007) proposed a few methods which can be classified as follows: empirical direct methods, residual methods of the energy budget, deterministic methods, and vegetation index methods.

In agriculture, an accurate quantification of ET is important for effective and efficient irrigation management. When evaporative demand exceeds precipitation, plant growth and quality may be unfavorably affected by soil water deficit. A large part of the irrigation water applied to agricultural lands *(Fig. 2)* is consumed by evaporation and transpiration. In a given crop, evapotranspiration process is influenced by several factors: plant species,

seasonal maximum solar radiation and air temperature by several weeks (Burba, 2010). If the moisture is available, evapotranspiration is dependent mainly on the availability of solar energy to vaporize water: evapotranspiration varies with latitude, season, time of day, and cloud cover. Most of the evapotranspiration of water at the Earth's surface level occurs in the subtropical regions (Fig.1). In these areas, high quantities of solar radiation provide the energy necessary to convert liquid water into a gas. Usually, evapotranspiration exceeds precipitation on middle and high latitude large areas during the summer season. As a result of climate change it is expected to induce a further intensification of the global water cycle, including ET (Huntington, 2006). Therefore accurate estimates of evapotranspiration are needed for weather forecasting and projecting the long-term effects of land use change and

global climate change, irrigation scheduling and watershed management.

Fig. 1. Mean Annual Potential Evapotranspiration (UNEP World Atlas of Desertification)

methods, and vegetation index methods.

In this regard, remote sensing data with the increasing imagery resolution is a useful tool to provide ET information over different temporal and spatial scales. During the last decades important progresses were made in the determination of ET using remote sensing techniques. Some studies have classified the methods of ET estimation in two categories: semi- empirical methods - use empirical relationship and a minimum set of meteorological data; analytical methods – consist in the establishment of the physical process at the scale of interest. A study done by Courault (2007) proposed a few methods which can be classified as follows: empirical direct methods, residual methods of the energy budget, deterministic

In agriculture, an accurate quantification of ET is important for effective and efficient irrigation management. When evaporative demand exceeds precipitation, plant growth and quality may be unfavorably affected by soil water deficit. A large part of the irrigation water applied to agricultural lands *(Fig. 2)* is consumed by evaporation and transpiration. In a given crop, evapotranspiration process is influenced by several factors: plant species, canopy characteristics, plant population, degree of surface cover, plant growth stage, irrigation regime (over irrigation can increase ET due to larger evaporation), soil water availability, planting date, tillage practice, etc. As it can be observed from Fig. 2 the movement of the water vapor from the soil and plant surface, a t a field level is influenced mainly by wind speed and direction although other climatic factors also can play a role. Evapotranspiration increases with increasing air temperature and solar radiation. Wind speed can cause ET increasing. For high wind speed values the plant leaf stomata (the small pores on the top and bottom leaf surfaces that regulate transpiration) close and evapotranspiration is reduced. There are situations when wind can cause mechanical damage to plants which can decrease ET due to reduced leaf area. Hail can reduce also leaf area and evapotranspiration. Higher relative humidity decreases ET as the demand for water vapor by the atmosphere surrounding the leaf surface decreases. If relative humidity (dry air) has lower values, the ET increases due to the low humidity which increases the vapor pressure deficit between the vegetation surface and air. On rainy days, incoming solar radiation decreases, relative humidity increases, and air temperature usually decreases, generation ET decreasing. But, depending on climatic conditions, actual crop water use usually increases in the days after a rain event due to increased availability of water in the soil surface and crop root zone.

Fig. 2. Evaporation and transpiration and the factors that impact these processes in an irrigated crop.

## **2. Evapotranspiration and energy budget**

The estimation of ET parameter, corresponding to the latent heat flux (E) from remote sensing is based on the energy balance evaluation through several surface properties such as albedo, surface temperature (Ts), vegetation cover, and leaf area index (LAI). Surface energy balance (SEB) models are based on the surface energy budget equation. To estimate regional crop ET, three basic types of remote sensing approaches have been successfully applied (Su, 2002).

*The first approach* computes a surface energy balance (SEB) using the radiometric surface temperature for estimating the sensible heat flux (H), and obtaining ET as a residual of the energy balance. The single-layer SEB models implicitly treat the energy exchanges between soil, vegetation and the atmosphere and compute latent heat flux (E) by evaluating net (allwave) radiant energy (Rn), soil heat flux (G) and H. For instantaneous conditions, the energy balance equation is the following:

$$
\lambda E = R\_n - H - G \tag{1}
$$

where: Rn = net radiant energy (all-wave); G = soil heat flux; H = sensible heat flux (Wm-2); E = latent energy exchanges (E = the rate of evaporation of water (kg m-2 s-1) and = the latent heat of vaporization of water (J kg-1)). E is obtained as the residual of the energy balance contain biases from both H and (Rn - G). There are several factors which affect the performance of single-source approaches, like the uncertainties about atmospheric and emissivity effects. LST impacts on all terms of the energy balance in particular on long wave radiation. The radiative surface temperatures provided by an infrared radiometer from a space borne platform are measured by satellite sensors such as LANDSAT, AVHRR, MODIS and ASTER. Converting radiometric temperatures to kinetic temperature requires considerations about surface emissivity (E), preferably from ground measurements. Remotely LST is subject to atmospheric effects which are primarily associated with the absorption of infrared radiation by atmospheric water vapor and which lead to errors of 3–5 K. A wide range of techniques have been developed to correct for atmospheric effects, including: single-channel methods; split-window techniques; multi-angle methods and combinations of split-window and multi-channel methods. Radiant and convective fluxes can be described: by considering the observed surface as a single component (single layer approaches); by separating soil and vegetation components with different degrees of canopy description in concordance with the number of vegetation layers (multilayer approaches). Net radiant energy depends on the incident solar radiation (Rg), incident atmospheric radiation over the thermal spectral domain (Ra), surface albedo (αs), surface emissivity (εs) and surface temperature (Ts), according to the following equation:

$$R\_n = (1 - a\_s)R\_g + \varepsilon\_s R\_a - \varepsilon\_s \sigma T\_s^4 \tag{2}$$

For single layer models, Rn is related to the whole surface and in the case of multiple layer models, *Rn* is linked with both soil and vegetation layers. For single approaches, sensible heat flux H is estimated using the aerodynamic resistance between the surface and the reference height in the lower atmosphere (usually 2 m) above the surface. Aerodynamic resistance (ra) is a function of wind speed, atmospheric stability and roughness lengths for momentum and heat. For multiple layer models, H is characterized taking into account the soil and canopy resistance, with the corresponding temperature:

$$H = \ \rho c\_p \frac{(T\_s - T\_a)}{r\_a} \tag{3}$$

Eq. (3) shows that the estimation of E parameter can be made using the residual method, which induces that E is linearly related to the difference between the surface temperature (Ts) and air temperature (Ta) at the time of Ts measurement if the second order dependence of ra on this gradient is ignored.

$$
\lambda E = \, R\_n - G - \, \rho c p \frac{(\tau\_t - \tau\_a)}{r\_a} \tag{4}
$$

energy balance. The single-layer SEB models implicitly treat the energy exchanges between soil, vegetation and the atmosphere and compute latent heat flux (E) by evaluating net (allwave) radiant energy (Rn), soil heat flux (G) and H. For instantaneous conditions, the energy

where: Rn = net radiant energy (all-wave); G = soil heat flux; H = sensible heat flux (Wm-2); E = latent energy exchanges (E = the rate of evaporation of water (kg m-2 s-1) and = the latent heat of vaporization of water (J kg-1)). E is obtained as the residual of the energy balance contain biases from both H and (Rn - G). There are several factors which affect the performance of single-source approaches, like the uncertainties about atmospheric and emissivity effects. LST impacts on all terms of the energy balance in particular on long wave radiation. The radiative surface temperatures provided by an infrared radiometer from a space borne platform are measured by satellite sensors such as LANDSAT, AVHRR, MODIS and ASTER. Converting radiometric temperatures to kinetic temperature requires considerations about surface emissivity (E), preferably from ground measurements. Remotely LST is subject to atmospheric effects which are primarily associated with the absorption of infrared radiation by atmospheric water vapor and which lead to errors of 3–5 K. A wide range of techniques have been developed to correct for atmospheric effects, including: single-channel methods; split-window techniques; multi-angle methods and combinations of split-window and multi-channel methods. Radiant and convective fluxes can be described: by considering the observed surface as a single component (single layer approaches); by separating soil and vegetation components with different degrees of canopy description in concordance with the number of vegetation layers (multilayer approaches). Net radiant energy depends on the incident solar radiation (Rg), incident atmospheric radiation over the thermal spectral domain (Ra), surface albedo (αs), surface emissivity (εs)

and surface temperature (Ts), according to the following equation:

soil and canopy resistance, with the corresponding temperature:

of ra on this gradient is ignored.

�� = (�� ��)�� � ���� � �����

� = ���

(��� ��) ��

��

Eq. (3) shows that the estimation of E parameter can be made using the residual method, which induces that E is linearly related to the difference between the surface temperature (Ts) and air temperature (Ta) at the time of Ts measurement if the second order dependence

�� = �� � � � ��� (��� ��) 

For single layer models, Rn is related to the whole surface and in the case of multiple layer models, *Rn* is linked with both soil and vegetation layers. For single approaches, sensible heat flux H is estimated using the aerodynamic resistance between the surface and the reference height in the lower atmosphere (usually 2 m) above the surface. Aerodynamic resistance (ra) is a function of wind speed, atmospheric stability and roughness lengths for momentum and heat. For multiple layer models, H is characterized taking into account the

� = �� � � � � (1)

� (2)

 (3)

(4)

balance equation is the following:

Equation (4) is usually used to estimate E. At midday, it provides a good indicator regarding the plant water status for irrigation scheduling. For E estimation over longer periods (daily, monthly, seasonal estimations), the use of ground-based ET from weather data is necessary to make temporal interpolation. Some studies have used the trend for the evaporative fraction (EF), such as the ratio of latent heat flux to available energy for convective fluxes, to be almost constant during the daytime. This allows estimating the daytime evaporation from one or two estimates only of EF at midday, for example at the satellite acquisition time (Courault et al., 2005).

$$EF = \frac{\lambda E}{R\_n - G} \quad ET\_{24} = EF \ast R\_{n24} \tag{5}$$

ET can be estimated from air vapor pressure (pa) and a water vapor exchange coefficient (hs) according to the following equation:

$$
\lambda E = \rho c\_p h\_s (p\_s^\*(T\_s) - e\_a) \tag{6}
$$

Usually this method is used in models simulating Soil–Vegetation–Atmosphere Transfers (SVAT). ps <sup>∗</sup>(Ts) represent the saturated vapor pressure at the surface temperature Ts and hs is the exchange coefficient which depends on the aerodynamic exchange coefficient (1/ra), soil surface and stomatal resistances of the different leaves in the canopy. Katerji & Perrier (1985) estimated a global canopy resistance (rg) including both soil and canopy resistances (equation 6)

$$r\_g = \frac{1}{\frac{1}{r\_{\text{reg}} + r\_{\text{w}}} + \frac{1}{r\_0 + r\_s}}\tag{7}$$

where: rveg is the resistance due to the vegetation structure, rw the resistance of the soil layer depending on the soil water content, r0 the resistance due to the canopy structure and rs the bulk stomatal resistance. To calculate this parameters it necessary to have information regarding the plant structure like LAI and fraction of vegetation cover (FC), the minimum stomatal resistance (rsmin). Many studies proposed various parameterizations of the stomatal resistance taking into account climatic conditions and soil moisture (Jacquemin & Noilhan, 1990). This proves that the (Ts − Ta) is related to ET term, and that Ts can be estimated using thermal infrared measurements (at regional or global scale using satellite data, and at local scale using ground measurements).

*The second approach* uses vegetation indices (VI) derived from canopy reflectance data to estimate basal crop coefficient (Kcb) that can be used to convert reference ET to actual crop ET, and requires local meteorological and soil data to maintain a water balance in the root zone of the crop. The VIs is related to land cover, crop density, biomass and other vegetation characteristics. VIs such as the Normalized Difference Vegetation Index (NDVI), the Soil Adjusted Vegetation Index (SAVI), the Enhanced Vegetation Index (EVI) and the Simple Ratio (SR), are measures of canopy greenness which may be related to physiological processes such as transpiration and photosynthesis. Among the relatively new satellite sensors it has to be mentioned the advantages of using MODIS/Aqua that offer improved spectral and radiometric resolution for deriving surface temperatures and vegetation indices, as well as increased frequency of evaporative fraction and evaporation estimates when compared with other sensors. The observed spatial variability in radiometric surface temperature is used with reflectance and/or vegetation index observations for evaporation estimation. For ET estimation from agricultural crops the most direct application is to substitute the VIs for crop coefficients (defined as the ratio between actual crop water use and reference crop evaporation for the given set of local meteorological conditions). Negative observing correlations between the NDVI and radiometric surface temperature could be linked to evaporative cooling, although for most landscapes variations in fractional vegetation cover, soil moisture availability and meteorological conditions will cause considerable scatter in those relationships. The methods associated with this approach generate spatially distributed values of Kcb that capture field-specific crop development and are used to adjust a reference ET (ETo) estimated daily from local weather station data.

*The third approach* uses remotely sensed LST with Land Surface Models (LSMs) and Soil– Vegetation–Atmosphere (SVAT) models, developed to estimate heat and mass transfer at the land surface. LSMs contain physical descriptions of the transfer in the soil–vegetation– atmosphere continuum, and with proper initial and boundary conditions provide continuous simulations when driven by weather and radiation data. The energy-based LSMs are of particular interest because these approaches allow for a strong link to remote sensing applications. The use of the spatially distributed nature of remote sensing data as a calibration source has been limited, with the focus placed on data assimilation approaches to update model states, rather than inform the actual model structure. Data assimilation is the incorporation of observations into a numerical model(s) with the purpose of providing the model with the best estimate of the current state of a system. There are two types of data assimilation: (i) sequential assimilation which involves correcting state variables (e.g. temperature, soil moisture) in the model whenever remote sensing data are available; and (ii) variation assimilation when unknown model parameters are changed using data sets obtained over different time windows. Remotely sensed LSTs have been assimilated at point scales into various schemes for estimating land surface fluxes by comparing simulated and observed temperatures and adjusting a state variable (e.g. soil moisture) or model parameters in the land surface process model. Such use of remote sensing data has highlighted problems of using spatial remote sensing data with spatial resolutions of tens or hundreds of kilometers with point-scale SVAT models and has led to the search for ''effective'' land surface parameters. There exist no effective means of evaluating ET spatially distributed outputs of either remote sensing based approaches or LSMs at scales greater than a few kilometers, particularly over non-homogeneous surfaces. The inability to evaluate remote sensing based estimates in a distributed manner is a serious limitation in broader scale applications of such approaches. It must be noted here that ET evaluation of remote sensing based approaches with ground based data tends to favour those few clear sky days when fluxes are reproduced most agreeably, and on relatively flat locations. In this case the radiation budget is given by the following equation (Kalma et al., 2008):

$$R\_n = K \downarrow \ -K \uparrow \ +L \downarrow \ -L \uparrow \tag{8}$$

where K is the down-welling shortwave radiation and it depends on atmospheric transmissivity, time of the day, day of the year and geographic coordination. K represents the reflected shortwave radiation which depends on K and surface albedo (a), L is the down-welling long wave radiation and L is the up-welling long wave radiation. L depends on the atmospheric emissivity (which in turn is influenced by amounts of atmospheric water vapor, carbon dioxide and oxygen) and by air temperature. L si influenced by land surface temperature and emissivity

temperature is used with reflectance and/or vegetation index observations for evaporation estimation. For ET estimation from agricultural crops the most direct application is to substitute the VIs for crop coefficients (defined as the ratio between actual crop water use and reference crop evaporation for the given set of local meteorological conditions). Negative observing correlations between the NDVI and radiometric surface temperature could be linked to evaporative cooling, although for most landscapes variations in fractional vegetation cover, soil moisture availability and meteorological conditions will cause considerable scatter in those relationships. The methods associated with this approach generate spatially distributed values of Kcb that capture field-specific crop development and are used to adjust a reference ET (ETo) estimated daily from local weather station data. *The third approach* uses remotely sensed LST with Land Surface Models (LSMs) and Soil– Vegetation–Atmosphere (SVAT) models, developed to estimate heat and mass transfer at the land surface. LSMs contain physical descriptions of the transfer in the soil–vegetation– atmosphere continuum, and with proper initial and boundary conditions provide continuous simulations when driven by weather and radiation data. The energy-based LSMs are of particular interest because these approaches allow for a strong link to remote sensing applications. The use of the spatially distributed nature of remote sensing data as a calibration source has been limited, with the focus placed on data assimilation approaches to update model states, rather than inform the actual model structure. Data assimilation is the incorporation of observations into a numerical model(s) with the purpose of providing the model with the best estimate of the current state of a system. There are two types of data assimilation: (i) sequential assimilation which involves correcting state variables (e.g. temperature, soil moisture) in the model whenever remote sensing data are available; and (ii) variation assimilation when unknown model parameters are changed using data sets obtained over different time windows. Remotely sensed LSTs have been assimilated at point scales into various schemes for estimating land surface fluxes by comparing simulated and observed temperatures and adjusting a state variable (e.g. soil moisture) or model parameters in the land surface process model. Such use of remote sensing data has highlighted problems of using spatial remote sensing data with spatial resolutions of tens or hundreds of kilometers with point-scale SVAT models and has led to the search for ''effective'' land surface parameters. There exist no effective means of evaluating ET spatially distributed outputs of either remote sensing based approaches or LSMs at scales greater than a few kilometers, particularly over non-homogeneous surfaces. The inability to evaluate remote sensing based estimates in a distributed manner is a serious limitation in broader scale applications of such approaches. It must be noted here that ET evaluation of remote sensing based approaches with ground based data tends to favour those few clear sky days when fluxes are reproduced most agreeably, and on relatively flat locations. In this case the radiation budget is given by the following equation (Kalma et al., 2008):

ܴ ൌ ܭ ՝ െܭ ՛ ܮ ՝ െܮ ՛ (8)

where K is the down-welling shortwave radiation and it depends on atmospheric transmissivity, time of the day, day of the year and geographic coordination. K represents the reflected shortwave radiation which depends on K and surface albedo (a), L is the down-welling long wave radiation and L is the up-welling long wave radiation. L depends on the atmospheric emissivity (which in turn is influenced by amounts of atmospheric water vapor, carbon dioxide and oxygen) and by air temperature. L si

influenced by land surface temperature and emissivity

## **3. Direct methods using difference between surface and air temperature**

Mapping daily evapotranspiration over large areas considering the surface temperature measurements has been made using a simplified relationship which assumes that it is possible to directly relate the daily (Ed) to the difference (Trad – Ta)i between (near) mid-day observations (i) of surface temperature and near-surface air temperature (Ta) measured at midday as follows:

$$
\lambda E\_d = \langle R\_n \rangle\_d - B(T\_{rad} - T\_a)\_l^n \tag{9}
$$

B is a statistical regression coefficient which depends on surface roughness. n depends on atmospheric stability. Equation 9 was derived from Heat Capacity Mapping Mission (HCMM) observations over fairly homogeneous irrigated and non-irrigated land surfaces, with areas between 50 and 200 km2 (Seguin et al. 1982a, b). Some authors as Carlson et al. (1995a) proposed a simplified method based on Eq. 9 which uses the difference (Trad – Ta) at 50 m at the time of the satellite overpass. They showed that B coefficient and n are closely related to fractional cover fc that can be obtained from the NDVI–Trad plots. B values vary from 0.015 for bare soil to 0.065 for complete vegetation cover and n decreased from 1.0 for bare soil to 0.65 for full cover.

## **4. Surface energy balance models**

Surface energy balance models (SEBAL) assume that the rate of exchange of a quantity (heat or mass) between two points is driven by a difference in potential (temperature or concentration) and controlled by a set of resistances which depend on the local atmospheric environment and the land surface and vegetation properties. In the review made by Overgaard et al. (2006) regarding the evolution of land surface energy balance models are described the following approaches: the combination approach by Penman (1948) which developed an equation to predict the rate of ET from open water, wet soil and well-watered grass based on easily measured meteorological variables such as radiation, air temperature, humidity, and wind speed; the Penman–Monteith ''one-layer'', ''one-source'' or ''big leaf'' models (Monteith 1965) which recognize the role of surface controls but do not distinguish between soil evaporation and transpiration; this approach estimates ET rate as a function of canopy and boundary layer resistances; ''two-layer'' or ''two-source'' model such as described by Shuttleworth and Wallace (1985) which includes a canopy layer in which heat and mass fluxes from the soil and from the vegetation are allowed to interact; multi-layer models which are essentially extensions of the two-layer approach.

### **4.1 The Penman–Monteith, ''one-source'' SEB models**

The Penman–Monteith (PM) approach combines energy balance and mass transfer concepts (Penman, 1948) with stomatal and surface resistance (Monteith, 1981). Most "one source" SEB models compute E by evaluating Rn, G and H and solve for E as the residual term in the energy balance equation (see Eq. 10). The sensible heat flux (H) is given by:

$$H = \rho \mathcal{C}\_p \left[ \frac{(T\_{ad} - T\_a)}{r\_a} \right] \tag{10}$$

Where: = air density (kg\*m-3); Cp = specific heat of air at constant pressure (J kg-1 K-1); Tad = aerodynamic surface temperature at canopy source height (K); Ta = near surface air temperature (K); ra = aerodynamic resistance to sensible heat transfer between the canopy source height and the bulk air at a reference height above the canopy (s m-1). The ra term is usually calculated from local data on wind speed, surface roughness length and atmospheric stability conditions. According to Norman and Becker (1995), the aerodynamic surface temperature (Tad) represent the temperature that along with the air temperature and a resistance calculated from the log-profile theory provides an estimate H. The key issue of PM approach is to estimate an accurately sensible heat flux. Tad is obtained by extrapolating the logarithmic air temperature profile to the roughness length for heat transport (zoh) or, more precisely, to (d + zoh) where d = zero-plane displacement height. Usually, due to the fact that Tad cannot be measured using remote sensing, it is replaced with Trad. As it is demonstrated by Troufleau et al. (1997), for dense canopy Trad and Tad may differ with 1-2 K and much more for sparse canopy. Surface temperature (Trad) is related to the kinetic temperature by the surface emissivity () (Eq, 11) and it depends on view angle () (Norman et. al, 2000). On the other hand Tad and aerodynamic resistance are fairly difficult to obtain for non-homogenous land surfaces.

$$T\_{rad} = \ \varepsilon^{1/4} \ast \ T\_k \tag{11}$$

The aerodynamic resistance ra can be calculated with the following equation:

$$r\_a = \frac{1}{k^2} u \left[ \ln \frac{z - d}{z\_{oh}} - \left. \Psi\_h \frac{z - d}{L} \right| \right] \left[ \ln \frac{z - d}{z\_{om}} - \left. \Psi\_m \frac{z - d}{L} \right| \right] \tag{12}$$

where: k = 0.4 (von Karman's constant); u = wind speed at reference height z (m s-1); d = zero-plane displacement height (m); zoh and zom = roughness lengths (m) for sensible heat and momentum flux, respectively; h and m = stability correction functions for sensible heat and momentum flux, respectively; L = Monin-Obukhov length L (m). The h = 0 and m = 0 if near surface atmospheric conditions are neutrally stable. Usually, the aerodynamic resistance is estimated from local data, even that area averaging of roughness lengths is highly non-linear (Boegh et al. 2002). Several studies, such as Cleugh at al. (2007) used these equations for evapotranspiration landscape monitoring. Their approach estimates E at 16 day intervals using 8-day composites of 1 km MODIS Trad observations and was tested with 3 years of flux tower measurements and was obtained significant discrepancies between observed and simulated land surface fluxes, generated by the following factors: the estimation of H with Eqs. 9 and 10 is not constrained by the requirement for energy conservation; errors in zoh determination; use of unrepresentative emissivities; using timeaverages of instantaneous Trad, Ta and Rn, the non-linearity of Eq. 9 may cause significant errors; standard MODIS data processing eliminates all cloud-contaminated pixels in the composite period. Bastiaanssen et al. (1998a) developed a calibration procedure using image data to account for the differences between Taero and Trad, which are important, mainly for incomplete vegetation covers. Other authors, such as Stewart et al. (1994) and Kustas et al. (2003a), made empirical adjustments to aerodynamic resistance, related to zoh (eq. 13).

$$H = \rho \mathcal{C}\_p \left[ \frac{T\_{rad} \left( \Theta \right) - T\_a}{r\_a - r\_{ex}} \right] \tag{13}$$

where: Trad () =radiometric surface temperature (K) at view angle derived from the satellite brightness temperature; rex = excess resistance (s m-1) (reflects differences between

temperature (K); ra = aerodynamic resistance to sensible heat transfer between the canopy source height and the bulk air at a reference height above the canopy (s m-1). The ra term is usually calculated from local data on wind speed, surface roughness length and atmospheric stability conditions. According to Norman and Becker (1995), the aerodynamic surface temperature (Tad) represent the temperature that along with the air temperature and a resistance calculated from the log-profile theory provides an estimate H. The key issue of PM approach is to estimate an accurately sensible heat flux. Tad is obtained by extrapolating the logarithmic air temperature profile to the roughness length for heat transport (zoh) or, more precisely, to (d + zoh) where d = zero-plane displacement height. Usually, due to the fact that Tad cannot be measured using remote sensing, it is replaced with Trad. As it is demonstrated by Troufleau et al. (1997), for dense canopy Trad and Tad may differ with 1-2 K and much more for sparse canopy. Surface temperature (Trad) is related to the kinetic temperature by the surface emissivity () (Eq, 11) and it depends on view angle () (Norman et. al, 2000). On the other hand Tad and aerodynamic resistance are fairly difficult to obtain

The aerodynamic resistance ra can be calculated with the following equation:

� = ��� �

����(Θ) − �� �� − ���

where: Trad () =radiometric surface temperature (K) at view angle derived from the satellite brightness temperature; rex = excess resistance (s m-1) (reflects differences between

− Ψ�

�−�

where: k = 0.4 (von Karman's constant); u = wind speed at reference height z (m s-1); d = zero-plane displacement height (m); zoh and zom = roughness lengths (m) for sensible heat and momentum flux, respectively; h and m = stability correction functions for sensible heat and momentum flux, respectively; L = Monin-Obukhov length L (m). The h = 0 and m = 0 if near surface atmospheric conditions are neutrally stable. Usually, the aerodynamic resistance is estimated from local data, even that area averaging of roughness lengths is highly non-linear (Boegh et al. 2002). Several studies, such as Cleugh at al. (2007) used these equations for evapotranspiration landscape monitoring. Their approach estimates E at 16 day intervals using 8-day composites of 1 km MODIS Trad observations and was tested with 3 years of flux tower measurements and was obtained significant discrepancies between observed and simulated land surface fluxes, generated by the following factors: the estimation of H with Eqs. 9 and 10 is not constrained by the requirement for energy conservation; errors in zoh determination; use of unrepresentative emissivities; using timeaverages of instantaneous Trad, Ta and Rn, the non-linearity of Eq. 9 may cause significant errors; standard MODIS data processing eliminates all cloud-contaminated pixels in the composite period. Bastiaanssen et al. (1998a) developed a calibration procedure using image data to account for the differences between Taero and Trad, which are important, mainly for incomplete vegetation covers. Other authors, such as Stewart et al. (1994) and Kustas et al. (2003a), made empirical adjustments to aerodynamic resistance, related to zoh (eq. 13).

� � ��� �−� ���

���� =��� �� ���� (11)

�−�

� � (12)

� (13)

− Ψ�

for non-homogenous land surfaces.

�� <sup>=</sup> <sup>1</sup>

�� � ��� �−� ���

$$r\_{\rm ex} = \frac{kB^{-1}}{ku^\*} = \ln \frac{\mathbf{z\_{om}}/\mathbf{z\_{oh}}}{ku^\*} \tag{14}$$

where kB-1 = dimensionless ratio determined by local calibration. Eq. 14 assumes that the ratio zom/zoh may be treated as constant for uniform surfaces, although kB-1 has been found to be highly variable (Brutsaert 1999).

In the case of the one source Surface Energy Balance System (SEBS) (Su, 2002) the surface heat fluxes are estimated from satellite data and available meteorological data. There are three sets of input data in SEBS: the first set includes the following parameters: , , Trad, LAI, fractional vegetation coverage and the vegetation height (if the vegetation information is not explicitly available, SEBS can use as input data the Normalized Difference Vegetation Index (NDVI)); the second set includes Ta, u, actual vapour pressure (ea) at a reference height as well as total air pressure; the third set of data consists of measured (or estimated) K and L. For Rn, G, and the partitioning of (Rn - G) into H and E, SEBS use different modules (Fig. 3): H is estimated using Monin–Obukhov similarity theory; in the case of u and vegetation parameters (height and LAI) is used the Massman (1997) model to to estimate the displacement height (d) and the roughness height for momentum (zom); the equations proposed by Brutsaert (1982, 1999) are used when only the height of the vegetation is available. The SEBS was successfully tested for agricultural areas, grassland and forests, across various spatial scales. Several studies used flux tower method and data from Landsat, ASTER ad Modis sensors (Su et al. 2005, 2007, McCabe and Wood 2006).

The Fig. 4 shows the time series, determined during the Soil Moisture Atmosphere Coupling Experiment 2002 (SMACEX-02) (Kustas et al. 2005). These time series illustrates latent heat fluxes and sensible heat fluxes measured with in situ eddy-covariance equipment (closed) together with SEBS model (open) over a field site (corn) from Iowa. The gaps in the time series are caused either the missing ancillary data or absence of flux measurements. Many factors influence the single-source approach: there are uncertainties due to atmospheric and emissivity effects; because of the vegetation properties and of the angle view, the relationship between Tad and Ta is not unique; this approach requires representative nearsurface Ta and other meteorological data measured (or estimated) at the time of the satellite overpass at a location closely with the Trad observation. This can generate errors in defining meteorological parameter for each satellite pixel from a sparse network of weather stations (at the time of satellite overpass), mainly for areas with high relative relief and slopes. Another important factor is that the accuracy of any of the estimates depends on the performance of the algorithm used for temperature retrieval.

The major advantages of SEBS are: uncertainty due to the surface temperature or meteorological variables can be limited taking into account the energy balance at the limiting cases; through the SEBS was formulated a new equation for the roughness height for heat transfer, using fixed values; a priori knowledge of the actual turbulent heat fluxes is not required. Another single-source energy balance models, developed based on the conception of SEBAL, are S-SEBI (Simplified-SEBI), METRIC (Mapping EvapoTranspiration at high Resolution with Internalized Calibration), etc. The main difference between such kinds of models is the difference in how they calculate the sensible heat, i.e. the way to define the dry (maximum sensible heat and minimum latent heat) and wet (maximum latent heat and minimum sensible heat) limits and how to interpolate between the defined upper and lower limits to calculate the sensible heat flux for a given set of boundary layer parameters of remotely sensed data (Ts, albedo, NDVI, LAI) and ground-based air temperature, wind speed, humidity. The assumptions in all these models are that there are few or no changes in atmospheric conditions (especially the surface available energy) in space and sufficient surface horizontal variations are required to ensure dry and wet limits existed in the study area.

Fig. 3. Schematic representation of SEBS (after Su, 2008)

Fig. 4. Reproduction of surface flux development with a one-source model (SEBS) (after Kalma, 2008)

#### **4.2 Two-source SEB models**

The equations 10 and 13 make no difference between evaporation soil surface and transpiration from the vegetation and from this reason the resistances are not well defined.

heat and minimum sensible heat) limits and how to interpolate between the defined upper and lower limits to calculate the sensible heat flux for a given set of boundary layer parameters of remotely sensed data (Ts, albedo, NDVI, LAI) and ground-based air temperature, wind speed, humidity. The assumptions in all these models are that there are few or no changes in atmospheric conditions (especially the surface available energy) in space and sufficient surface horizontal variations are required to ensure dry and wet limits

existed in the study area.

Kalma, 2008)

**4.2 Two-source SEB models** 

Fig. 3. Schematic representation of SEBS (after Su, 2008)

Fig. 4. Reproduction of surface flux development with a one-source model (SEBS) (after

The equations 10 and 13 make no difference between evaporation soil surface and transpiration from the vegetation and from this reason the resistances are not well defined. To solve this problem two-source models have been developed for use with incomplete canopies (e.g. Lhomme et al. 1994; Norman et al. 1995; Jupp et al. 1998; Kustas and Norman 1999). These models consider the evaporation as the sum of evaporation from the soil surface and transpiration from vegetation. For example, Norman et. Al. (1995) developed a two-source model (TSM) based on single-time observations which eliminate the need for rex as used in equations 13 and 14. They reformulated the equation 10 as:

$$H = \rho C\_p \frac{T\_{rad}(\theta) - T\_a}{r\_r} \tag{15}$$

where: Trad = directional radiometric surface temperature obtained at zenith view angle ; rr = radiometric-convective resistance (s m-1). The radiometric convective resistance is calculated according to the following formula:

$$r\_r = \frac{T\_{rad}(\theta) - T\_a}{\left[\frac{(T\_c - T\_a)}{r\_a} + \left(\frac{(T\_s - T\_a)}{r\_a + r\_s}\right)\right]}\tag{16}$$

where: Tc = canopy temperature; Ts = soil surface temperature; Rs = soil resistance to heat transfer (s m-1). To estimate the Tc and Ts variables, Norman et al. used fractional vegetation cover (fc) which depends on sensor view angle (Eq. 17):

$$T\_{rad}(\theta) \approx \left[ f\_c(\theta) T\_c^4 + \{1 - f\_c(\theta)\} T\_s^4 \right]^{\frac{1}{4}} \tag{17}$$

H variable is divided in vegetated canopy (Hc) and soil (Hs) influencing the temperature in the canopy air-space. Other revisions of TSM compared flux estimates from two TSM versions proved that thermal imagery was used to constrain Trad and H and microwave remote sensing was employed to constrain near surface soil moisture. The estimations resulting from those two models were compared with flux tower observations. The results showed opposing biases for the two versions that it proves a combination between microwave and thermal remote sensing constraints on H and E fluxes from soil and canopy. Compared to other types of remote sensing ET formulations, dual-source energy balance models have been shown to be robust for a wide range of landscape and hydrometeorological conditions.

## **5. Spatial variability methods using vegetation indices**

Visible, near-infrared and thermal satellite data has been used to develop a range of vegetation indices which have been related to land cover, crop density, biomass or other vegetation characteristics (McVicar and Jupp 1998). Several vegetation indices as the Normalized Difference Vegetation Index (NDVI), the Soil Adjusted Vegetation Index (SAVI), the Enhanced Vegetation Index (EVI) and the Simple Ratio (SR), are indicators of canopy greenness which can be related to physiological processes such as transpiration and photosynthesis (Glenn et al., 2007).

#### **5.1 Vegetation indices, reflectance and surface temperature**

The SEBAL approach used remotely sensed surface temperature, surface reflectivity and NDVI data. It has been developed for the regional scale and it requires few ground level observations from within the scene. K and L are computed using a constant atmospheric transmissivity, an appropriate atmospheric emissivity value and an empirical function of Ta, respectively. G is calculated as a fraction of Rn depending on Trad, NDVI and (Bastiaanssen 2000). The instantaneous values of sensible heat flux are calculated in three main steps. First step makes the difference between Tad and Trad and assumes that the relationship between Trad and the near-surface temperature gradient (T = Tad - Ta) is quasi-linear. Therefore wet and dry extremes can be identified from the image. These extremes fix the quasi-linear relationship relating T to Trad, allowing T to be estimated for any Trad across the image. In the second step, a scatter plot is obtained for all pixels in the entire image of broadband values versus Trad. Low temperature and low reflectance values correspond to pixels with large evaporation rates, while high surface temperatures and high reflectance values correspond to the areas with little or no evaporation rates. Scatter plots for large heterogeneous regions frequently show an ascending branch controlled by moisture availability and evaporation rate, and a radiation-controlled descending branch where evaporation rate is negligible. The ascending branch indicates that the temperatures increase with increasing values as water availability is reduced and evaporation rate becomes more limited. For the descending branch the increasing of induce a decreasing of surface temperature. If the radiation-controlled descending branch is well defined, ra may be obtained from the (negative) slope of the reflectance–surface temperature relationship. The last step use the local surface roughness (zom) based on the NDVI; is assumed that the zom/zoh ratio has a fix value and H can be calculated for every pixel with E as the residual term in Eq. 1. The SEBAL models have been used widely with satellite data in the case of relatively flat landscapes with and without irrigation.

The Mapping EvapoTranspiration with high Resolution and Internalized Calibration (METRIC) models, derived from SEBAL are used for irrigated crops (Allen et al. 2007a, b). METRIC model derive ET from remotely sensed data (LANDSAT TM) in the visible, nearinfrared and thermal infrared spectral regions along with ground-based wind speed and near surface dew point temperature. In this case extreme pixels are identified with the cool/wet extreme comparable to a reference crop, the evaporation rates being computed wit Penman-Monteith method. The ET from warm/dry pixel is calculated using soil water budget having local meteorological data as input parameters. METRIC model can be used to produce high quality and accurate maps of ET for areas smaller than a few hundred kilometers in scale and at high resolution (Fig. 5). In their study, Boegh et al. (1999) presented an energy balance method for estimating transpiration rates from sparse canopies based on net radiation absorbed by the vegetation and the sensible heat flux between the leaves and the air within the canopy. The net radiation absorbed by the vegetation is estimated using remote sensing and regular meteorological data by merging conventional method for estimation of the land surface net radiation with a groundcalibrated function of NDVI.

SEBAL and METRIC methods assume that the temperature difference between the land surface and the air (near-surface temperature difference) varies linearly with land surface temperature. Bastiaanssen et al. (1998) and Allen and al. (2007) derive this relationship based on two anchor pixels known as the hot and cold pixels, representing dry and bare agricultural fields and wet and well-vegetated fields, respectively. Both methods use the linear relationship between the near-surface temperature difference and the land surface temperature to estimate the sensible heat flux which varies as a function of the near-surface temperature difference, by assuming that the hot pixel experiences no latent heat, i.e., ET = 0.0, whereas the cold pixel achieves maximum ET.

transmissivity, an appropriate atmospheric emissivity value and an empirical function of Ta, respectively. G is calculated as a fraction of Rn depending on Trad, NDVI and (Bastiaanssen 2000). The instantaneous values of sensible heat flux are calculated in three main steps. First step makes the difference between Tad and Trad and assumes that the relationship between Trad and the near-surface temperature gradient (T = Tad - Ta) is quasi-linear. Therefore wet and dry extremes can be identified from the image. These extremes fix the quasi-linear relationship relating T to Trad, allowing T to be estimated for any Trad across the image. In the second step, a scatter plot is obtained for all pixels in the entire image of broadband values versus Trad. Low temperature and low reflectance values correspond to pixels with large evaporation rates, while high surface temperatures and high reflectance values correspond to the areas with little or no evaporation rates. Scatter plots for large heterogeneous regions frequently show an ascending branch controlled by moisture availability and evaporation rate, and a radiation-controlled descending branch where evaporation rate is negligible. The ascending branch indicates that the temperatures increase with increasing values as water availability is reduced and evaporation rate becomes more limited. For the descending branch the increasing of induce a decreasing of surface temperature. If the radiation-controlled descending branch is well defined, ra may be obtained from the (negative) slope of the reflectance–surface temperature relationship. The last step use the local surface roughness (zom) based on the NDVI; is assumed that the zom/zoh ratio has a fix value and H can be calculated for every pixel with E as the residual term in Eq. 1. The SEBAL models have been used widely with satellite data in the case of

The Mapping EvapoTranspiration with high Resolution and Internalized Calibration (METRIC) models, derived from SEBAL are used for irrigated crops (Allen et al. 2007a, b). METRIC model derive ET from remotely sensed data (LANDSAT TM) in the visible, nearinfrared and thermal infrared spectral regions along with ground-based wind speed and near surface dew point temperature. In this case extreme pixels are identified with the cool/wet extreme comparable to a reference crop, the evaporation rates being computed wit Penman-Monteith method. The ET from warm/dry pixel is calculated using soil water budget having local meteorological data as input parameters. METRIC model can be used to produce high quality and accurate maps of ET for areas smaller than a few hundred kilometers in scale and at high resolution (Fig. 5). In their study, Boegh et al. (1999) presented an energy balance method for estimating transpiration rates from sparse canopies based on net radiation absorbed by the vegetation and the sensible heat flux between the leaves and the air within the canopy. The net radiation absorbed by the vegetation is estimated using remote sensing and regular meteorological data by merging conventional method for estimation of the land surface net radiation with a ground-

SEBAL and METRIC methods assume that the temperature difference between the land surface and the air (near-surface temperature difference) varies linearly with land surface temperature. Bastiaanssen et al. (1998) and Allen and al. (2007) derive this relationship based on two anchor pixels known as the hot and cold pixels, representing dry and bare agricultural fields and wet and well-vegetated fields, respectively. Both methods use the linear relationship between the near-surface temperature difference and the land surface temperature to estimate the sensible heat flux which varies as a function of the near-surface temperature difference, by assuming that the hot pixel experiences no latent heat, i.e., ET =

relatively flat landscapes with and without irrigation.

calibrated function of NDVI.

0.0, whereas the cold pixel achieves maximum ET.

Fig. 5. (a) Landsat color infrared image of T3NR1E of the Boise Valley; (b) Land use/land cover polygons in T3NR1E of the Boise Valley; (c) ET image of T3NR1E the Boise Valley (after R.G. Allen et al., 2007)

The sensible heat flux is assessed like a linear function of the temperature difference between vegetation and mean canopy air stream. The surface temperature recorded by satellite comprises information from soil and from vegetation; therefore the vegetation temperature is estimated taking into account the linear relationship between NDVI and surface temperature. The difference between the surface temperature and the mean canopy air stream temperature is linearly related to the difference between surface temperature and the air temperature above the canopy with the slope coefficient which depend on the canopy structure. This relationship was used to evaluate the mean canopy air stream temperature. The method was used in the Sahel region for agricultural crops, natural vegetation, forest vegetation, with ground based, airborne and satellite remote sensing data and validated with sapflow and latent heat flux measurements. Agreement between remote sensing based estimates and ground based measurements of E rates is estimated to be better than 30–40 W m-2.

#### **5.2 Reflectance and surface temperature**

The Simplified Surface Energy Balance Index (S-SEBI) proposed by Roerink et al. (2000) estimate the instantaneous latent heat flux (Ei) with (Kalma, 2008):

$$
\lambda E\_l = \Lambda\_l (R\_{nl} - G\_l) \tag{18}
$$

where: (Rni – Gi) = available energy at the time of the satellite overpass; i = the evaporative fraction. The S-SEBI algorithm has two limitations: the atmospheric conditions have to be almost constant across the image and the image has to contain borh dry and wet areas. <sup>i</sup> was obtained from a scatter plot of observed surface temperature (Trad) and Landsat TM derived broadband a values across the single scene. i is with:

$$
\Lambda\_l = \frac{T\_H - T\_{rad}}{T\_H - T\_{rad}} \tag{19}
$$

where: Trad = observed surface temperature for a given pixel; TH = temperature for the upper boundary (dry radiation controlled conditions - all radiation is used for surface heating and decreases with increasing surface temperature (TH - where E = 0 (W m-2)); TE = temperature at the lower boundary (evaporation controlled wet conditions - all energy is used for E and increases with an increase of surface temperature (TE -where H = 0 W m-2)). This method does not need any additional meteorological data.

Fig. 6. Flowchart of the proposed methodology to obtain ET from NOAA–AVHRR data (after Sobrino et al., 2007)

Sobrino et. al (2007) use S-SEBI algorithm to estimate the daily evapotranspiration from NOAA-AVHRR images for the Iberian Penisnula. The Figure 6 present the flowchart used by Sobrino et al. (2007) to obtain ET from NOAA-AVHRR. Daily evapotranspiration (ETd) is given by:

$$ET\_d = \frac{\Lambda\_l \mathcal{C}\_{dl} R\_{nl}}{L} \tag{20}$$

where: Rnd = daily net radiation; Rni = instantaneous net radiation: L = 2.45 MJ kg-1 = latent heat vaporization; Cdi=Rnd /Rni. In this case the daily ground heat flux was considered close to 0. There are several studies which proposed methods for Cdi calculation. For example Seguin and Itier (1983) proposed a constant value for Cdi = (0.30±0.03). Wassenaar et al. (2002) showed that this ratio have a seasonal variation 0.05 in winter to 0.3 in summer, following a sine law. In the Sobrino et al. (2007) study, Cdi was calculated using net radiation fluxes measured at the meteorological station of located on the East coast of the Iberian Peninsula (El Saler area). The ET estimation from high spectral and spatial resolution data (5 m) was adapted to the low resolution data NOAA-AVHRR (1 km spatial resolution) based on the evaporative fraction concept proposed by Roerink et al. (2007). The main

is used for E and increases with an increase of surface temperature (TE -where H = 0 W

Fig. 6. Flowchart of the proposed methodology to obtain ET from NOAA–AVHRR data

Sobrino et. al (2007) use S-SEBI algorithm to estimate the daily evapotranspiration from NOAA-AVHRR images for the Iberian Penisnula. The Figure 6 present the flowchart used by Sobrino et al. (2007) to obtain ET from NOAA-AVHRR. Daily evapotranspiration (ETd) is

> ��� <sup>=</sup> ������� �

where: Rnd = daily net radiation; Rni = instantaneous net radiation: L = 2.45 MJ kg-1 = latent heat vaporization; Cdi=Rnd /Rni. In this case the daily ground heat flux was considered close to 0. There are several studies which proposed methods for Cdi calculation. For example Seguin and Itier (1983) proposed a constant value for Cdi = (0.30±0.03). Wassenaar et al. (2002) showed that this ratio have a seasonal variation 0.05 in winter to 0.3 in summer, following a sine law. In the Sobrino et al. (2007) study, Cdi was calculated using net radiation fluxes measured at the meteorological station of located on the East coast of the Iberian Peninsula (El Saler area). The ET estimation from high spectral and spatial resolution data (5 m) was adapted to the low resolution data NOAA-AVHRR (1 km spatial resolution) based on the evaporative fraction concept proposed by Roerink et al. (2007). The main

(20)

(after Sobrino et al., 2007)

given by:

m-2)). This method does not need any additional meteorological data.

advantage of the Sobrino et al. (2007) methodology is that the method requires only satellite data to estimate ET.

Fig. 7. Monthly evolution (from June 1997 to November 2002) of the daily evapotranspiration (ETd) in the eight selected zones. There is represented also the temporal mean for the six years of analyzing (after Sobrino et al., 2007).

Its major disadvantage is represented by the requiring that satellite images must have extreme surface temperatures. The method was tested over agricultural area using high resolution values, with errors lower than 1.4 mm d-1. As it can be observed from Fig. 7, regarding the monthly and seasonal evolution of ET the highest values (∼6 mm d−1) were obtained in the West of the Iberian Peninsula, which is the most vegetated area. Taking into account the impact of incoming solar energy the higher values of ET was obtained in spring and summer and the lower values in autumn and winter. Seasonal ET was obtained by averaging daily ET over the season. Figure 8 shows as an example the monthly ET maps obtained from the NOAA-AVHRR images acquired in 1999. Fig. 9 also indicates that the highest ET values were obtained in the summer and spring, in the north and west of Iberian Peninsula. To map land surface fluxes and surface cover and surface soil moisture, Gillies and Carlson (1995) combined two model, SVAT and ABL and run it for vegetative cover with the maximum known NDVI and for bare soil conditions with the minimum known NDVI in the scene for a range of soil moisture values until AVHRR observed (Trad) and simulated (Tad) surface temperatures corrected, at which stage the actual fractional vegetation cover (fc) and surface soil moisture were estimated.

Fig. 8. Monthly mean for the daily evapotranspiration obtained from NOAA–AVHRR data over the Iberian Peninsula in 1999. Pixels in black color correspond to sea and cloud masks and red correspond to higher value of ET (after Sobrino et al., 2007).

#### **5.3 Vegetation indices and surface temperature**

Several studies shown the efficiency of ''triangle method'' (Carlson et al. (1995a, b); Gillies et al. 1997; Carlson 2007) to estimate soil moisture from the NDVI–Trad relationship. The major advantages of the remotely sensed VI-Ts triangle method are that: the method allows an accurate estimation of regional ET with no auxiliary atmospheric or ground data besides the remotely sensed surface temperature and vegetation indices; is relatively insensitive to the correction of atmospheric effects. Its limitations are: determination of the dry and wet edges requires a certain degree of subjectivity; to make certain that the dry and wet limits exist in the VI-Trad triangle space most of pixels over a flat area with a wide range of soil wetness and fractional vegetation cover are required. So, the boundaries of this triangle are limiting conditions for H and E. Other studies suggest the dependence of Trad variability on the remote sending data resolution, thus higher resolution data means that the variations of Trad and NDVI is more related to the land cover type. Lower resolution data show the dependency of the NDVI and Trad variations to agricultural practices and rainfall. Jiang and Islam (2001) proposed a triangle method based on the interpolation of the Priestley–Taylor method (Priestley and Taylor, 1972) using the triangular (Trad, NDVI) spatial variation. The Priestley–Taylor expression for equilibrium evaporation from a wet surface under conditions of minimal advection (EPT) is given by:

$$
\lambda E\_{PT} = \alpha\_{PT} (R\_n - G) \frac{\Delta}{\Delta + \gamma} \tag{21}
$$

Fig. 8. Monthly mean for the daily evapotranspiration obtained from NOAA–AVHRR data over the Iberian Peninsula in 1999. Pixels in black color correspond to sea and cloud masks

Several studies shown the efficiency of ''triangle method'' (Carlson et al. (1995a, b); Gillies et al. 1997; Carlson 2007) to estimate soil moisture from the NDVI–Trad relationship. The major advantages of the remotely sensed VI-Ts triangle method are that: the method allows an accurate estimation of regional ET with no auxiliary atmospheric or ground data besides the remotely sensed surface temperature and vegetation indices; is relatively insensitive to the correction of atmospheric effects. Its limitations are: determination of the dry and wet edges requires a certain degree of subjectivity; to make certain that the dry and wet limits exist in the VI-Trad triangle space most of pixels over a flat area with a wide range of soil wetness and fractional vegetation cover are required. So, the boundaries of this triangle are limiting conditions for H and E. Other studies suggest the dependence of Trad variability on the remote sending data resolution, thus higher resolution data means that the variations of Trad and NDVI is more related to the land cover type. Lower resolution data show the dependency of the NDVI and Trad variations to agricultural practices and rainfall. Jiang and Islam (2001) proposed a triangle method based on the interpolation of the Priestley–Taylor method (Priestley and Taylor, 1972) using the triangular (Trad, NDVI) spatial variation. The Priestley–Taylor expression for equilibrium evaporation from a wet surface under

���� �����(�� � �) �

���� (21)

and red correspond to higher value of ET (after Sobrino et al., 2007).

**5.3 Vegetation indices and surface temperature** 

conditions of minimal advection (EPT) is given by:

where: = slope of the saturated vapour pressure curve at the prevailing Ta ((Pa K-1); = psychrometric constant (Pa K-1); PT = Priestley-Taylor parameter defined as the ratio between actual E and equilibrium E. For wet land surface conditions, PT = 1.26. Its value is affected by global changes in air temperature, humidity, radiation and wind speed. Jiang and Islam (2001) replaced PT with parameter which varies for a wide range of ra and rc values. The warm edge of the (Trad, NDVI) scatter plot represents pixels with the highest Trad and minimum evaporation from the bare soil component, while Ea can vary function of the vegetation type. Linear interpolation between the sides of the triangular distribution of Trad - NDVI allows to derive for each pixel using the spatial context of remotely sensed Trad and NDVI. The values are related to surface wetness, rs and Trad. Therefore, the minimum value of is 0 for the driest bare soil pixel and the maximum value is 1.26 for a densely vegetated, well-watered pixel. Thus the actual value for each pixel in a specified NDVI interval is obtained from the observed (Trad)obs with the following:

$$\phi = \phi\_{\max} \frac{\langle T\_{rad} \rangle\_{\max} - \langle T\_{rad} \rangle\_{obs}}{\langle T\_{rad} \rangle\_{\max} - \langle T\_{rad} \rangle\_{\min}} \tag{22}$$

where (Trad)min and (Trad)max are the lowest and highest surface temperatures for each NDVI class, corresponding to the highest and lowest evaporation rates, respectively. The evaporative fraction can be calculated with:

$$
\Lambda = \left. \phi \frac{\Delta}{\Delta + \Upsilon} \right. \tag{23}
$$

Based on the Jiang and Islam (2001) approach, Wang et al. (2006) obtained better results using the spatial variation (Trad, NDVI), where Trad represent the day–night difference in Trad, obtained from MODIS data. However, to convert into E, the method described above still requires estimation/ measurement of net radiation (Rn) and soil heat flux (G). In a later work, Jiang and Islam (2003) consider the fractional vegetative cover (fc) as a more suitable generalized vegetation index calculated from the normalized NDVI with (Kalma et al. 2008):

$$f\_c = \left(\frac{NDVI - NDVI\_{min}}{NDVI\_{max} - NDVI\_{min}}\right)^2\tag{24}$$

They assumed that the evaporative fraction = E/(Rn - G) is linearly related to T = Trad - Ta, inside a certain class fc. The reason for this assumption is that theT is more representative for sensible heat flux H. Thus the evaporative fraction can be estimated from fc and T, for a given set of Tmax, Te (Te = Tmax for fc = 1) and a stress factor (). In their study, they used NOAA-AVHRR data and obtained better results using the aerodynamic resistance-energy balance method represented by Eq. 13, this equation including atmospheric stability corrections and using an iterative procedure to reach the most appropriate kB-1 value.

Serban et al. (2010) used the Priestly-Taylor equation modified by Jiang and Islam (2001) in their study to estimate the evapotranspiration using remote sensing data and Grid Computing. The most advantage of Priestly-Taylor equation is that the all terms can be calculated using remotely sensed data. Grid computation procedure has two major advantages: strong data processing capacity and the capability to use distributed computing resources to process the spatial data offered by a satellite image. According to Jiang and Islam (2001) the parameter αPT parameter is obtained by two-step linear interpolation: in the

$$\alpha\_{PT} = \left(\frac{\Delta + \gamma}{\Delta}\right) \left(\frac{LST\_l^{max} - LST}{LST\_l^{max} - LST\_l^{min}}\right) \left(\frac{NDVI\_l^{max} - NDVI\_l^{min}}{NDVI\_l^{max}}\right) + \left(\frac{\Delta + \gamma}{\Delta}\right) \left(\frac{NDVI\_l^{min}}{NDVI\_l^{max}}\right) \tag{25}$$

$$
\lambda E\_{daily} = \alpha\_{PT} \frac{2DL(R\_l - G\_l)}{\pi \sin\left(\pi \frac{t}{DL}\right)}\tag{26}
$$

$$LST = \sqrt{\left[LSE^{-1}(\psi\_1 L\_{sensor} + \psi\_2) + \psi\_3\right]} + \delta \tag{27}$$

$$\chi = \left[ \frac{c^2 L\_{sensor}}{T\_{sensor}^2} \left( \frac{\lambda^4}{c\_1} L\_{sensor} + \lambda^{-1} \right) \right] \tag{28}$$

$$
\mathcal{S} = \mathcal{Y}L\_{sensor} + T\_{sensor} \tag{29}
$$

$$L\_{sensor} = gain \, \* \, DN + bias - spectral \, radiance \tag{30}$$

$$T\_{sensor} = \frac{K\_2}{\ln\left(\frac{K\_1}{L\_{sensor}} + 1\right)}\tag{31}$$

processes. The main weather parameters influencing evapotranspiration are radiation, air temperature, humidity and wind speed. Several algorithms have been developed to estimate the evaporation rate from these parameters. The evaporation power of the atmosphere is expressed by the reference crop evapotranspiration (ETo) which represents the evapotranspiration from a standardized vegetated surface (Allen et al., 1998). The reference surface is a hypothetical grass reference crop with specific characteristics. Because ETo is affected by only climatic parameters, it is a climatic parameter and may be computed from weather data. Thus ETo is the evaporating power of the atmosphere at a specific location and time of the year and does not take into account the crop characteristics and soil factors.

Crop water requirement is defined as the amount of water required to compensate the evapotranspiration loss from the cropped field. Even the values for crop evapotranspiration are identical with crop water requirement (CWR), crop evapotranspiration refers to the amount of water that is lost by evapotranspiration, while CWR refers to the amount of water that needs to be supplied. Thus, the irrigation water requirement represents the difference between the crop water requirement and effective precipitation and also includes additional water for leaching of salts and to compensate for non-uniformity of water application (Allen et al., 1998). Several empirical methods have been developed over the last five decades in order to estimate the evapotranspiration from different climatic variables. Testing the accuracy of the methods under a new set of conditions is laborious, time-consuming and costly, and yet evapotranspiration data are frequently needed at short notice for project planning or irrigation scheduling design. To meet this need, guidelines were developed and published in the FAO Irrigation and Drainage Paper No. 24 'Crop water requirements'. From different data availability, four methods are usually used to estimate the reference crop evapotranspiration (ETo): the Blaney-Criddle, radiation, modified Penman and pan evaporation methods. From these four methods, the modified Penman-Monteith method offer the best results with minimum possible error in relation to a living grass reference crop. The radiation method can be used for areas where available climatic data include measured air temperature and sunshine, cloudiness or radiation, but not measured wind speed and air humidity. The Blaney-Criddle method is better to be applying for areas where available climatic data cover air temperature data only. The pan method gives acceptable estimates, depending on the location of the pan. Based on the original Penman- FAO proposed a standard parameterization of the Penman–Monteith method for estimating the evaporation from a -irrigated, homogenous, 0.12 m grass cover considered as a ''reference crop'' (Allen et al., 1998) (Fig. 11).

Fig. 11. Characteristics of the hypothetical reference crop (after Allen et al., 1998)

processes. The main weather parameters influencing evapotranspiration are radiation, air temperature, humidity and wind speed. Several algorithms have been developed to estimate the evaporation rate from these parameters. The evaporation power of the atmosphere is expressed by the reference crop evapotranspiration (ETo) which represents the evapotranspiration from a standardized vegetated surface (Allen et al., 1998). The reference surface is a hypothetical grass reference crop with specific characteristics. Because ETo is affected by only climatic parameters, it is a climatic parameter and may be computed from weather data. Thus ETo is the evaporating power of the atmosphere at a specific location and

time of the year and does not take into account the crop characteristics and soil factors.

m grass cover considered as a ''reference crop'' (Allen et al., 1998) (Fig. 11).

Fig. 11. Characteristics of the hypothetical reference crop (after Allen et al., 1998)

Crop water requirement is defined as the amount of water required to compensate the evapotranspiration loss from the cropped field. Even the values for crop evapotranspiration are identical with crop water requirement (CWR), crop evapotranspiration refers to the amount of water that is lost by evapotranspiration, while CWR refers to the amount of water that needs to be supplied. Thus, the irrigation water requirement represents the difference between the crop water requirement and effective precipitation and also includes additional water for leaching of salts and to compensate for non-uniformity of water application (Allen et al., 1998). Several empirical methods have been developed over the last five decades in order to estimate the evapotranspiration from different climatic variables. Testing the accuracy of the methods under a new set of conditions is laborious, time-consuming and costly, and yet evapotranspiration data are frequently needed at short notice for project planning or irrigation scheduling design. To meet this need, guidelines were developed and published in the FAO Irrigation and Drainage Paper No. 24 'Crop water requirements'. From different data availability, four methods are usually used to estimate the reference crop evapotranspiration (ETo): the Blaney-Criddle, radiation, modified Penman and pan evaporation methods. From these four methods, the modified Penman-Monteith method offer the best results with minimum possible error in relation to a living grass reference crop. The radiation method can be used for areas where available climatic data include measured air temperature and sunshine, cloudiness or radiation, but not measured wind speed and air humidity. The Blaney-Criddle method is better to be applying for areas where available climatic data cover air temperature data only. The pan method gives acceptable estimates, depending on the location of the pan. Based on the original Penman- FAO proposed a standard parameterization of the Penman–Monteith method for estimating the evaporation from a -irrigated, homogenous, 0.12

Monteith equation and the equations of the aerodynamic and surface resistance, the FAO Penman-Monteith method to estimate ETo is the following:

$$ET\_0 = \frac{0.408\Delta (R\_n - G) + \chi \left(\frac{900}{T + 273}\right) u\_2 (e\_s - e\_a)}{\Delta + \chi (1 + 0.34u\_2)}\tag{32}$$

where: ET0 = reference evapotranspiration [mm day-1]; Rn = net radiation at the crop surface [MJ m-2 day-1]; G = soil heat flux density [MJ m-2 day-1]; T = mean daily air temperature at 2 m height [°C]; u2 = wind speed at 2 m height [m s-1]; es = saturation vapour pressure [kPa]; ea = actual vapour pressure [kPa]l; es - ea = saturation vapour pressure deficit [kPa]; = slope vapour pressure curve [kPa °C-1]; γ = psychrometric constant [kPa °C-1]. The equation uses standard climatological records of solar radiation (sunshine), air temperature, humidity and wind speed. To obtain correct estimations of ET0, the weather measurements should be made at 2 m (or converted to that height) above an extensive surface of green grass, shading the ground and not short of water. The psychrometric constant, γ, is calculated with:

$$
\gamma = \frac{c\_p p}{\varepsilon \lambda} = 0.665 \ast 10^{-3} \tag{33}
$$

Where: P = atmospheric pressure [kPa]; λ = latent heat of vaporization, 2.45 [MJ kg-1]; cp = specific heat at constant pressure, 1.013 10-3 [MJ kg-1 °C-1]; ε = ratio molecular weight of water vapour/dry air = 0.622. For standardization, Tmean for 24 hour is defined as the mean of the daily maximum (Tmax) and minimum temperatures (Tmin) rather than as the average of hourly temperature measurements.

$$T\_{mean} = \frac{\tau\_{max} - \tau\_{mtn}}{2} \tag{34}$$

The temperature is given in degrees Celsius (°C), Fahrenheit (°F) or in Kelvin (K =C + 273,16).

$$P = 101.3 \left( \frac{^{293 - 0.00652}}{^{293}} \right)^{526} \tag{35}$$

where: z = elevation above sea level [m].

#### **6.2 CROPWAT model**

CROPWAT is a decision support system developed by the Land and Water Development Division of FAO for planning and management of irrigation. The main functions of CROPWAT model are: to calculate the reference evapotranspiration, crop water requirements and crop irrigation requirements; to develop irrigation schedules under different management conditions and water supply schemes; to estimate the rainfed production and drought effects; to evaluate the efficiency of irrigation practices.

The input data of the model are the following climatic, crop and soil data: reference crop evapotranspiration: (ETo) values measured or calculated using the FAO Penman–Montieth equation based on monthly climatic average data of the minimum and maximum air temperature (C), relative humidity (%), sunshine duration (h) and wind speed (m/s); rainfall data: (daily/monthly data); monthly rainfall is divided for each month into a number of rainstorms; a cropping pattern: crop type, planting date, crop coefficient data files (including Kc values, stage days, root depth, depletion fraction, Ky values) and the area planted (0– 100% of the total area); a set of typical crop coefficient data files are provided in the program; soil type: total available soil moisture, maximum rain infiltration rate, maximum rooting depth, and initial soil moisture depletion (% of the total available moisture);scheduling criteria: several options can be selected regarding the calculation of the application timing and application depth.

The output parameters for each crop are crop reference crop evapotranspiration Et0 (mm/period), crop Kc (average values of crop coefficient for each time step, effective rain (mm/period) (the amount of water that enters in the soil); water requirements (CWR) or ETm (mm/period); irrigation requirements (IWR - mm/period); actual crop evapotranspiration (ETc - mm); effective rain (mm/period) which represents the amount of water that enters into the soil; daily soil moisture deficit (mm); estimated yields reduction due to crop stress (when ETc/ETm falls below 100%).

The CROPWAT model can compute the actual evapotranspiration using the FAO Penman– Monteith equation or using directly the evapotranspiration measurements values. The crop water requirements (CWR) or maximum evapotranspiration (ETm) (mm/period) are calculated as:

$$CWR = ET\_0 \* CompK\_c \tag{36}$$

This means that the peak CWR in mm/day can be less than the peak Eto value when less than 100% of the area is planted in the cropping pattern.

The average values of the crop coefficient (Kc) for each time step are estimated by linear interpolation between the Kc values for each crop development stage. The ''Crop Kc" values are calculated as:

$$GroupK\_{\mathcal{C}} = K\_{\mathcal{C}} \* GroupArea \tag{37}$$

where CropArea is the area covered by the crop. So, if the crop covers only 50% of the area, the "Crop Kc" values will be half of the Kc values in the crop coefficient data file.

The CROPWAT model operates in two modes: computing the actual evapotranspiration using climatic parameters and using directly the evapotranspiration measurements values.

Possibilities to use the satellite-based data as input into the CROPWAT model are limited, because this model was not developed to use satellite-derived information directly. But this information can be useful for the comparison/validation procedures of some model input/output data, as precipitation, sunshine duration and evapotranspiration. Satellite based data can be used by CROPWAT model in different ways: measured evapotranspiration may be replaced with estimations derived from satellite data; for comparison and validation procedures; satellite-derived evapotranspiration values may bring better accuracy for the specialization of the punctual computing values; satellite information may be used for the assessment of the some reference parameters of the actual evapotranspiration (e.g. Land surface temperature, vegetation indexes, etc.).

#### **6.3 Using earth observation data and CROPWAT model to estimate the actual crop evapotranspiration**

There is a strong dependence between evapotranspiration and surface temperature on the, thus thermal images meteorological satellites (METEOSAT, NOAA, MODIS, LANDSAT) adequate for mapping of regional evapotranspiration. Several works have been done to determine regional evapotranspiration from satellite data (Batra et al., 2006; Courault et al., 2005; Wood et al., 2003). The application of NOAA AVHRR data seems to be more successful because of the higher spatial and spectral resolution (Stancalie et al., 2010). Multichannel algorithms are routinely used for atmospheric correction of the AVHRR data.

maximum rooting depth, and initial soil moisture depletion (% of the total available moisture);scheduling criteria: several options can be selected regarding the calculation of the

The output parameters for each crop are crop reference crop evapotranspiration Et0 (mm/period), crop Kc (average values of crop coefficient for each time step, effective rain (mm/period) (the amount of water that enters in the soil); water requirements (CWR) or ETm (mm/period); irrigation requirements (IWR - mm/period); actual crop evapotranspiration (ETc - mm); effective rain (mm/period) which represents the amount of water that enters into the soil; daily soil moisture deficit (mm); estimated yields reduction

The CROPWAT model can compute the actual evapotranspiration using the FAO Penman– Monteith equation or using directly the evapotranspiration measurements values. The crop water requirements (CWR) or maximum evapotranspiration (ETm) (mm/period) are

This means that the peak CWR in mm/day can be less than the peak Eto value when less

The average values of the crop coefficient (Kc) for each time step are estimated by linear interpolation between the Kc values for each crop development stage. The ''Crop Kc" values

where CropArea is the area covered by the crop. So, if the crop covers only 50% of the area,

The CROPWAT model operates in two modes: computing the actual evapotranspiration using climatic parameters and using directly the evapotranspiration measurements values. Possibilities to use the satellite-based data as input into the CROPWAT model are limited, because this model was not developed to use satellite-derived information directly. But this information can be useful for the comparison/validation procedures of some model input/output data, as precipitation, sunshine duration and evapotranspiration. Satellite based data can be used by CROPWAT model in different ways: measured evapotranspiration may be replaced with estimations derived from satellite data; for comparison and validation procedures; satellite-derived evapotranspiration values may bring better accuracy for the specialization of the punctual computing values; satellite information may be used for the assessment of the some reference parameters of the actual

the "Crop Kc" values will be half of the Kc values in the crop coefficient data file.

evapotranspiration (e.g. Land surface temperature, vegetation indexes, etc.).

**6.3 Using earth observation data and CROPWAT model to estimate the actual crop** 

There is a strong dependence between evapotranspiration and surface temperature on the, thus thermal images meteorological satellites (METEOSAT, NOAA, MODIS, LANDSAT) adequate for mapping of regional evapotranspiration. Several works have been done to determine regional evapotranspiration from satellite data (Batra et al., 2006; Courault et al., 2005; Wood et al., 2003). The application of NOAA AVHRR data seems to be more successful because of the higher spatial and spectral resolution (Stancalie et al., 2010). Multichannel algorithms are routinely used for atmospheric correction of the AVHRR data.

��� � ��� � ������ (36)

������ � �� � �������� (37)

application timing and application depth.

calculated as:

are calculated as:

**evapotranspiration** 

due to crop stress (when ETc/ETm falls below 100%).

than 100% of the area is planted in the cropping pattern.

Efforts are directed towards the estimation of surface temperatures by considering the effects of emissivity (Lagouarde and Brunet, 1991; Li and Becker, 1993). The method used for the estimation of the daily crop actual evapotranspiration, ETcj, is based on the energy balance of the surface. The method uses the connection between evapotranspiration, net radiation and the difference between surface and air temperatures measured around 14:00 h (the time of the satellite passage), local time. The first version of the method used a simplified linear relationship as:

$$ET\_{cj} - R\_{nj} = A - B \* (T\_s - T\_{
alpha}) \tag{38}$$

where Rnj is the daily net radiation; Ts and Tamax is the surface and air maximum temperature; A, B are coefficients which depend on the surface type and the daily mean wind speed. Coefficients A and B may be determined either analytically, on the basis of the relationships given by Lagouarde and Brunet (1991), or statistically. The coefficients A and B are stable in the case of mature crop vegetation cover and in clear sky conditions. The coefficient B vary considerably, function of the land vegetation cover percent. In case of soil with great thermal inertia, the heat flux changed by conduction at the soil-atmosphere interface can be neglected and the computing relationship for daily actual crop evapotranspiration can be expressed in a version 2 of the proposed method:

$$ET\_{cj} = \,^rR\_{nj} - B' \ast \left(T\_s - T\_{amax}\right) \tag{39}$$

$$B'=0.0253+\left[\frac{1.0016}{\log 2^{\left(2/2\text{h}\right)}}\right] \upsilon\tag{40}$$

$$zh = \begin{bmatrix} 1 - \exp(-LAI) \end{bmatrix} \begin{bmatrix} \exp\left(-\frac{LAI}{2}\right) \end{bmatrix} \tag{41}$$

where: v = daily average wind speed; zh = vegetation roughness and LAI the foliar index. One possible use of satellite information is to replace the measured evapotranspiration by estimations made from satellite information. Because the estimations made from satellite information are available only for clear sky conditions, it was not possible to estimate the monthly average evapotranspiration, as input data in the CROPWAT model. For this reason, the satellite-derived data have been used for comparison/validation procedures of the CROPWAT model output data, like evapotranspiration. Fig. 12 presents the comparison between daily crop evapotranspiration values computed by the CROPWAT model and those computed through the energy balance method (Version 1), using remotely sensed data at the Alexandria and Craiova test-areas (situated in the south-western part of Romania), in the conditions of the year 2000 (Stancalie et al., 2010, 2010).

Analysis of model results concerning comparison of daily actual crop evapotranspiration calculated by using climatic data vs. satellite estimations based on the surface energetic balance (Version 1) showed that ETc values from satellite information are in general higher than those simulated by the model, the differences being from +0.45 - 1.9 mm/day. Preliminary results highlighted a good correlation between the simulated values (CROPWAT) and those derived from the satellite data; with relative errors from +20% - 18% at Craiova site and from +13% -17% at Alexandria site (Stancalie et al., 2010).

Fig. 13 shows a comparison between ETc simulated daily by the CROPWAT model over the whole maize-growing season and by the energy balance method (Version 2) respectively, using satellite data, at Alexandria and Craiova test-areas. The ETc calculated by the model is very similar to the estimated one. The results obtained can constitute the premise of an ETc data validation process, determined by the CROPWAT model (Stancalie et al., 2010).

Fig. 12. Comparison between daily crop evapotranspiration values computed by the CROPWAT model and by the energy balance method (Version 1) using satellite data at the Alexandria and Craiova test-areas (after Stancalie et al., 2010)

Fig. 13. Comparison between daily crop et values computed by the CROPWAT model and by the energy balance method (Version 2) using satellite data, at Alexandria (A) and Craiova (B) test-areas, for the maize vegetative development period in 2000 (Stancalie et al., 2010).

## **7. Conclusions**

460 Evapotranspiration – Remote Sensing and Modeling

Fig. 12. Comparison between daily crop evapotranspiration values computed by the CROPWAT model and by the energy balance method (Version 1) using satellite data at the

Fig. 13. Comparison between daily crop et values computed by the CROPWAT model and by the energy balance method (Version 2) using satellite data, at Alexandria (A) and Craiova (B) test-areas, for the maize vegetative development period in 2000 (Stancalie et al., 2010).

Alexandria and Craiova test-areas (after Stancalie et al., 2010)

The use of the multispectral satellite data can improve the classical methods applied in determining the agrometeorological parameters, including evapotranspiration.

Estimating evapotranspiration using remote sensing methodologies have a significant role in irrigation management and crop water demand assessment, for plant growth, carbon and nutrient cycling and for production modeling in dry land agriculture and forestry. Also it can have an important role in catchment hydrology, and larger scale meteorology and climatology applications. In the last years, due to the exceptional developments of satellite technology, a wide range of remote sensing-based evapotranspiration (ET) methods/models have been developed and evaluated. The use of remote sensing data for ET estimation is mainly based on land surface temperature (LST) and reflectivity (using different spectral regions) due to satellite ability to spatially integrate over heterogeneous surfaces at a range of resolutions and to routinely generating areal products once long time-series data availability issues are overcome. The chapter reviews some main methods for estimating crop evapotranspiration based on remotely sensed data, and highlights uncertainties and limitations associated with those estimation methods. This paper is focused on Surface Energy Balance models (SEB), spatial variability methods using vegetation indices and ET estimation using meteorological data through CROPWAT model. The analysis and critical issues are supported by the dedicated literature and specific case-studies. This review provides information of temporal and spatial scaling issues associated with the use of optical and thermal remote sensing for estimating evapotranspiration. Improved temporal scaling procedures are required to extrapolate estimates to daily and longer time periods and gap-filling procedures are needed when temporal scaling is affected by intermittent satellite coverage. It is also noted that analysis of multi-resolution data from different satellite/sensor systems is able to assist the development of spatial scaling and aggregation approaches. Approaches differ in: (i) type and spatial extent of application (e.g. irrigation, dry-land agriculture); (ii) type of remote sensing data; and (iii) use of ancillary (micro-) meteorological and land cover data. The integration of remotely sensed data into methods/models of ET facilitates the estimation of water consumption across agricultural regions. There are important limitations for using remote sensing data in estimating evapotranspiration.

Usually evapotranspiration is computed using land surface temperature and air temperatures. All this methods are affected by errors induced by estimation or measurements of those temperatures. The accuracy of Trad observations is influenced by atmospheric factors, surface emissivity or view angle. Emissivity information is useful in estimating of the radiative temperature of the land surface. Several direct methods (which atmospheric variables are coupled with radiative transfer models) or indirect algorithms (use only remote sensing data) to make atmospheric corrections in order to obtain the brightness temperature that represents the temperature of a black body that would have the same radiance as that observed by the radiometer. The uncertainties of surface temperature have a strong influence in determination of sensible heat flux H. The difference between surface and air temperatures depends on many factors, including vegetation type, fractional cover fc and view angle. Another important limitation of various spatial variability methods is considered the fact according to the highest and lowest surface temperatures observed in the one scene are assumed to represent very dry and very wet pixels. Usually the available energy (Rn - G) is obtained from ground based point observations of Rn: Rn is estimated based on observations of K, , LAI, emissivity of land surface and atmosphere, and Trad. Such kind of estimation generates errors in the calculation of long and short wave components. G can be estimated for example as function of NDVI. An alternative method would be to assume that soil heat flux is a constant fraction of net radiation flux, but this estimation doesn't take into account the diurnal variation. Many models for ET estimation need ground based meteorological data, mainly air temperature and wind speed. For that models which based on computing the difference between Tad and Ta, the time and location of air temperature (Ta) observations and their spatial representativeness are very important).

Incomplete vegetation cover generates also errors in evapotranspiration estimation. The two source models require parameterizations for the segmentation of the computed surface temperature between vegetation and soil, for the turbulent exchange of heat and mass between soil and atmosphere and between vegetation and atmosphere. Also, these models require some assumptions regarding solar transmittance, extinction coefficients and canopy emissivity in order to compute the variation of net radiation flux inside the canopy.

Another important limitation, regarding the spatial variability methods is that a large number of pixels are required over the area of interest with a wide range of soil wetness and fractional vegetation cover. The identification of vegetation limits for bare soil or full vegetation cover can be easily done using high resolution images which display a wide range in surface wetness conditions and land cover conditions

Remote sensing data is a useful tool that provides input data in land surface model (NDVI, LAI, fc – fraction cover) and can be used to correct the state variables of the models.

The frequency of spatial resolution imagery is also very significant: satellites which provide high resolution data usually have lower temporal frequency while low spatial resolution images have higher temporal frequency. Some applications require different spatial and temporal coverage rates and need different ''turn-around'' times. If acquiring the satellite data and ET estimation method are more time consuming, the method are not very convenient for operational applications like determining water requirements for irrigated agriculture.

Another significant limitation for using remote sensing is the presence of clouds that generates intermittent coverage. Cloudy days are characterized by a diffuse light, whereas while direct light is dominant on clear days when most TIR data are acquired for use in modeling applications. Most SEB models have been developed for use in cloud-free conditions and do not makes difference between direct and diffuse radiation; they use only daytime data obtained for clear-sky conditions. For a continuously monitoring of water balance, the effects of an increased diffuse fraction should be taking into account, because the diffuse radiation is used by vegetation more efficiently than direct radiation. For water use efficiency, to ignore difference between direct and diffuse radiation can induce significant differences in ET estimations.

### **8. References**

Allen RG, Pereira LS, Raes D, Smith M (1998), Crop evapotranspiration - guidelines for computing crop water requirements. FAO irrigation and drainage paper 56, Rome, Italy http://www.fao.org/docrep/X0490E/X0490E00.htm

based on observations of K, , LAI, emissivity of land surface and atmosphere, and Trad. Such kind of estimation generates errors in the calculation of long and short wave components. G can be estimated for example as function of NDVI. An alternative method would be to assume that soil heat flux is a constant fraction of net radiation flux, but this estimation doesn't take into account the diurnal variation. Many models for ET estimation need ground based meteorological data, mainly air temperature and wind speed. For that models which based on computing the difference between Tad and Ta, the time and location of air temperature (Ta) observations and their spatial representativeness are very

Incomplete vegetation cover generates also errors in evapotranspiration estimation. The two source models require parameterizations for the segmentation of the computed surface temperature between vegetation and soil, for the turbulent exchange of heat and mass between soil and atmosphere and between vegetation and atmosphere. Also, these models require some assumptions regarding solar transmittance, extinction coefficients and canopy

Another important limitation, regarding the spatial variability methods is that a large number of pixels are required over the area of interest with a wide range of soil wetness and fractional vegetation cover. The identification of vegetation limits for bare soil or full vegetation cover can be easily done using high resolution images which display a wide

Remote sensing data is a useful tool that provides input data in land surface model (NDVI,

The frequency of spatial resolution imagery is also very significant: satellites which provide high resolution data usually have lower temporal frequency while low spatial resolution images have higher temporal frequency. Some applications require different spatial and temporal coverage rates and need different ''turn-around'' times. If acquiring the satellite data and ET estimation method are more time consuming, the method are not very convenient for operational applications like determining water requirements for

Another significant limitation for using remote sensing is the presence of clouds that generates intermittent coverage. Cloudy days are characterized by a diffuse light, whereas while direct light is dominant on clear days when most TIR data are acquired for use in modeling applications. Most SEB models have been developed for use in cloud-free conditions and do not makes difference between direct and diffuse radiation; they use only daytime data obtained for clear-sky conditions. For a continuously monitoring of water balance, the effects of an increased diffuse fraction should be taking into account, because the diffuse radiation is used by vegetation more efficiently than direct radiation. For water use efficiency, to ignore difference between direct and diffuse radiation can induce

Allen RG, Pereira LS, Raes D, Smith M (1998), Crop evapotranspiration - guidelines for

Italy http://www.fao.org/docrep/X0490E/X0490E00.htm

computing crop water requirements. FAO irrigation and drainage paper 56, Rome,

emissivity in order to compute the variation of net radiation flux inside the canopy.

LAI, fc – fraction cover) and can be used to correct the state variables of the models.

range in surface wetness conditions and land cover conditions

important).

irrigated agriculture.

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## **Operational Remote Sensing of ET and Challenges**

Ayse Irmak1, Richard G. Allen2, Jeppe Kjaersgaard2, Justin Huntington3, Baburao Kamble4, Ricardo Trezza2 and Ian Ratcliffe1 *1School of Natural Resources University of Nebraska–Lincoln, HARH, Lincoln NE 2University of Idaho, Kimberly, ID 3Desert Research Institute, Raggio Parkway, Reno, NV 4University of Nebraska-Lincoln, Lincoln, NE USA* 

## **1. Introduction**

466 Evapotranspiration – Remote Sensing and Modeling

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Satellite imagery now provides a dependable basis for computational models that determine evapotranspiration (ET) by surface energy balance (EB). These models are now routinely applied as part of water and water resources management operations of state and federal agencies. They are also an integral component of research programs in land and climate processes. The very strong benefit of satellite-based models is the quantification of ET over large areas. This has enabled the estimation of ET from individual fields among populations of fields (Tasumi et al. 2005) and has greatly propelled field specific management of water systems and water rights as well as mitigation efforts under water scarcity. The more dependable and universal satellite-based models employ a surface energy balance (EB) where ET is computed as a residual of surface energy. This determination requires a thermal imager onboard the satellite. Thermal imagers are expensive to construct and more a required for future water resources work. Future moderate resolution satellites similar to Landsat need to be equipped with moderately high resolution thermal imagers to provide greater opportunity to estimate spatial distribution of actual ET in time. Integrated ET is enormously valuable for monitoring effects of water shortage, water transfer, irrigation performance, and even impacts of crop type and variety and irrigation type on ET. Allen (2010b) showed that the current 16-day overpass return time of a single Landsat satellite is often insufficient to produce annual ET products due to impacts of clouds. An analysis of a 25 year record of Landsat imagery in southern Idaho showed the likelihood of producing annual ET products for any given year to increase by a factor of NINE times (from 5% probability to 45% probability) when two Landsat systems were in operation rather than one (Allen 2010b).

Satellite-based ET products are now being used in water transfers, to enforce water regulations, to improve development and calibration of ground-water models, where ET is a needed input for estimating recharge, to manage streamflow for endangered species management, to estimate water consumption by invasive riparian and desert species, to estimate ground-water consumption from at-risk aquifers, for quantification of native American water rights, to assess impacts of land-use change on wetland health, and to monitor changes in water consumption as agricultural land is transformed into residential uses (Bastiaanssen et al., 2005, Allen et al., 2005, Allen et al. 2007b).

The more widely used and operational remote sensing models tend to use a 'CIMEC' approach ("calibration using inverse modeling of extreme conditions") to calibrate around uncertainties and biases in satellite based energy balance components. Biases in EB components can be substantial, and include bias in atmospheric transmissivity, absolute surface temperature, estimated aerodynamic temperature, surface albedo, aerodynamic roughness, and air temperature fields. Current CIMEC models include SEBAL (Bastiaanssen et al. 1998a, 2005), METRIC (Allen et al., 2007a) and SEBI-SEBS (Su 2002) and the process frees these models from systematic bias in the surface temperature and surface reflectance retrievals. Other models, such as the TSEB model (Kustas and Norman 1996), use absolute temperature and assumed air temperature fields, and so can be more susceptible to biases in these fields, and often require multiple times per day imagery. Consequently, coarser resolution satellites must be used where downscaling using finer resolution reflectance information is required.

Creating 'maps' of ET that are useful in management and in quantifying and managing water resources requires the computation of ET over monthly and longer periods such as growing seasons or annual periods. Successful creation of an ET 'snapshot' on a satellite overpass day is only part of the required process. At least half the total effort in producing a quantitative ET product involves the interpolation (or extrapolation) of ET information between image dates. This interpolation involves treatment of clouded areas of images, accounting for evaporation from wetting events occurring prior to or following overpass dates, and applying a grid of daily reference ET with the relative ET computed for an image, or a direct Penman-Monteith type of calculation, over the image domain for periods between images to account for day to day variation in weather. The particular methodology for estimating these spatial variables substantially impacts the quality and accuracy of the final ET product.

## **2. Model overview**

Satellite based models can be separated into the following classes, building on Kalma et al. (2008):

	- Full energy balance for the satellite image: *E = Rn G H*
	- Water stress index based on surface temperature and vegetation amounts
	- Application of a continuous Land Surface Model (LSM) that is partly initialized and advanced, in time, using satellite imagery

where *E* is latent heat flux density, representing the energy 'consumed' by the evaporation of water, *Rn* is net radiation flux density, *G* is ground heat flux density and *H* is sensible heat flux density to the air.

American water rights, to assess impacts of land-use change on wetland health, and to monitor changes in water consumption as agricultural land is transformed into residential

The more widely used and operational remote sensing models tend to use a 'CIMEC' approach ("calibration using inverse modeling of extreme conditions") to calibrate around uncertainties and biases in satellite based energy balance components. Biases in EB components can be substantial, and include bias in atmospheric transmissivity, absolute surface temperature, estimated aerodynamic temperature, surface albedo, aerodynamic roughness, and air temperature fields. Current CIMEC models include SEBAL (Bastiaanssen et al. 1998a, 2005), METRIC (Allen et al., 2007a) and SEBI-SEBS (Su 2002) and the process frees these models from systematic bias in the surface temperature and surface reflectance retrievals. Other models, such as the TSEB model (Kustas and Norman 1996), use absolute temperature and assumed air temperature fields, and so can be more susceptible to biases in these fields, and often require multiple times per day imagery. Consequently, coarser resolution satellites must be used where downscaling using finer resolution reflectance

Creating 'maps' of ET that are useful in management and in quantifying and managing water resources requires the computation of ET over monthly and longer periods such as growing seasons or annual periods. Successful creation of an ET 'snapshot' on a satellite overpass day is only part of the required process. At least half the total effort in producing a quantitative ET product involves the interpolation (or extrapolation) of ET information between image dates. This interpolation involves treatment of clouded areas of images, accounting for evaporation from wetting events occurring prior to or following overpass dates, and applying a grid of daily reference ET with the relative ET computed for an image, or a direct Penman-Monteith type of calculation, over the image domain for periods between images to account for day to day variation in weather. The particular methodology for estimating these spatial variables substantially impacts the quality and accuracy of the

Satellite based models can be separated into the following classes, building on Kalma et al.

Application of a continuous Land Surface Model (LSM) that is partly initialized

Simplified correlations or relationships between surface temperature extremes in an

where *E* is latent heat flux density, representing the energy 'consumed' by the evaporation of water, *Rn* is net radiation flux density, *G* is ground heat flux density and *H* is sensible heat

Water stress index based on surface temperature and vegetation amounts

Full energy balance for the satellite image: *E = Rn – G – H* 

Statistical methods using differences between surface and air temperature

Vegetation-based relative ET that is multiplied by a weather-based reference ET

and advanced, in time, using satellite imagery

image and endpoints of anticipated ET

uses (Bastiaanssen et al., 2005, Allen et al., 2005, Allen et al. 2007b).

information is required.

final ET product.

(2008):

**2. Model overview** 

flux density to the air.

Surface Energy Balance

Except for the LSM applications, none of the listed energy balance methods, in and of themselves, go beyond the creation of a 'snapshot' of ET for the specific satellite image date. Large periods of time exist between snapshots when evaporative demands and water availability (from wetting events) cause ET to vary widely, necessitating the coupling of hydrologically based surface process models to fill in the gaps. The surface process models employed in between satellite image dates can be as simple as a daily soil-surface evaporation model based on a crop coefficient approach (for example, the FAO-56 model of Allen et al. 1998) or can involve more complex plant-air-water models such as SWAT (Arnold et al. 1994), SWAP (van Dam 2000), HYDRUS (Šimůnek et al. 2008), Daisy (Abrahamsen and Hansen 2000) etc. that are run on hourly to daily timesteps.

### **2.1 Problems with use of absolute surface temperature**

Error in surface temperature (*Ts*) retrievals from many satellite systems can range from 3 – 5 K (Kalma et al. 2008) due to uncertainty in atmospheric attenuation and sourcing, surface emissivity, view angle, and shadowing. Hook and Prata (2001) suggested that finely tuned *Ts* retrievals from modern satellites could be as accurate as 0.5 K. Because near surface temperature gradients used in energy balance models are often on the order of only 1 to 5 K, even this amount of error, coupled with large uncertainties in the air temperature fields, makes the use of models based on differences in absolute estimates of surface and air temperature unwieldy.

Cleugh et al. (2007) summarized challenges in using near surface temperature gradients (*dT*) based on absolute estimates of *Ts* and air temperature, *Tair*, attributing uncertainties and biases to error in *Ts* and *Tair*, uncertainties in surface emissivity, differences between radiometrically derived *Ts* and the aerodynamically equivalent *Ts* required as a sourcing endpoint to *dT*.

The most critical factor in the physically based remote sensing algorithms is the solution of the equation for sensible heat flux density:

$$\mathbf{H} = \rho\_a \mathbf{c}\_p \frac{T\_{aero} - T\_a}{r\_{ahi}} \tag{1}$$

where a is the density of air (kg m-3), *cp* is the specific heat of air (J kg-1 K-1), *rah* is the aerodynamic resistance to heat transfer (s m-1), *Taero* is the surface aerodynamic temperature, and *Ta* is the air temperature either measured at standard screen height or the potential temperature in the mixed layer (K) (Brutsaert et al., 1993). The aerodynamic resistance to heat transfer is affected by wind speed, atmospheric stability, and surface roughness (Brutsaert, 1982). The simplicity of Eq. (1) is deceptive in that *Taero* cannot be measured by remote sensing. Remote sensing techniques measure the radiometric surface temperature *Ts* which is not the same as the aerodynamic temperature. The two temperatures commonly differ by 1 to 5 C, depending on canopy density and height, canopy dryness, wind speed, and sun angle (Kustas et al., 1994, Qualls and Brutsaert, 1996, Qualls and Hopson, 1998). Unfortunately, an uncertainty of 1 C in *Taero* – *Ta* can result in a 50 W m-2 uncertainty in *H* (Campbell and Norman, 1998) which is approximately equivalent to an evaporation rate of 1 mm day-1. Although many investigators have attempted to solve this problem by adjusting *rah* or by using an additional resistance term, no generally applicable method has been developed.

Campbell and Norman (1998) concluded that a practical method for using satellite surface temperature measurements should have at least three qualities: (i) accommodate the difference between aerodynamic temperature and radiometric surface temperature, (ii) not require measurement of near-surface air temperature, and (iii) rely more on differences in surface temperature over time or space rather than absolute surface temperatures to minimize the influence of atmospheric corrections and uncertainties in surface emissivity.

#### **2.2 CIMEC Models (SEBAL and METRIC)**

The SEBAL and METRIC models employ a similar inverse calibration process that meets these three requirements with limited use of ground-based data (Bastiaanssen et al., 1998a,b, Allen et al., 2007a). These models overcome the problem of inferring *Taero* from *Ts* and the need for near-surface air temperature measurements by directly estimating the temperature difference between two near surface air temperatures, *T1* and *T2*, assigned to two arbitrary levels *z1* and *z2* without having to explicitly solve for absolute aerodynamic or air temperature at any given height. The establishment of the temperature difference is done via inversion of the function for H at two known evaporative conditions in the model using the CIMIC technique. The temperature difference for a dry or nearly dry condition, represented by a bare, dry soil surface is obtained via *H=Rn – G- λE* (Bastiaanssen et al., 1998a):

$$T\_1 - T\_2 = \Delta T\_a = \frac{H \, r\_{\text{alt}\_{1-2}}}{\rho\_a \, \text{c}\_p} \tag{2}$$

where *rah,1-2* is the aerodynamic resistance to heat transfer between two heights above the surface, *z1* and *z2*. At the other extreme, for a wet surface, essentially all available energy *Rn - G* is used for evaporation *E.* At that extreme, the classical SEBAL approach assumes that *H*  ≈ 0, in order to keep requirements for high quality ground data to a minimum, so that *Ta* ≈ 0. Allen et al. (2001, 2007a) have used reference crop evapotranspiration, representing wellwatered alfalfa, to represent *E* for the cooler population of pixels in satellite images of irrigated fields in the METRIC approach, so as to better capture effects of regional advection of *H* and dry air, which can be substantial in irrigated desert. METRIC calculates *H* = *Rn - G* – k1*ETr* at these pixels, where *ETr* is alfalfa reference ET computed at the image time using weather data from a local automated weather station, and *Ta* from Eq. (2) , where k1 ~ 1.05. In typical SEBAL and METRIC applications, *z1* and *z2* are taken as 0.1 and 2 m above the zero plane displacement height (*d*). *z1* is taken as 0.1 m above the zero plane to insure that *T1* is established at a height that is generally greater than *d* + *zoh (zoh* is roughness length for heat transfer). Aerodynamic resistance, *rah*, is computed for between *z1* and *z2* and does not require the inclusion and thus estimation of *zoh*, but only *zom*, the roughness length for momentum transfer that is normally estimated from vegetation indices and land cover type. *H* is then calculated in the SEBAL and METRIC CIMEC-based models as:

$$H = \rho\_a c\_p \frac{\Delta T\_a}{r\_{ab\_{1-2}}} \tag{3}$$

One can argue that the establishment of *Ta* over a vertical distance that is elevated above *d*  + *zoh* places the *rah* and established *Ta* in a blended boundary layer that combines influences

Campbell and Norman (1998) concluded that a practical method for using satellite surface temperature measurements should have at least three qualities: (i) accommodate the difference between aerodynamic temperature and radiometric surface temperature, (ii) not require measurement of near-surface air temperature, and (iii) rely more on differences in surface temperature over time or space rather than absolute surface temperatures to minimize the influence of atmospheric corrections and uncertainties in surface emissivity.

The SEBAL and METRIC models employ a similar inverse calibration process that meets these three requirements with limited use of ground-based data (Bastiaanssen et al., 1998a,b, Allen et al., 2007a). These models overcome the problem of inferring *Taero* from *Ts* and the need for near-surface air temperature measurements by directly estimating the temperature difference between two near surface air temperatures, *T1* and *T2*, assigned to two arbitrary levels *z1* and *z2* without having to explicitly solve for absolute aerodynamic or air temperature at any given height. The establishment of the temperature difference is done via inversion of the function for H at two known evaporative conditions in the model using the CIMIC technique. The temperature difference for a dry or nearly dry condition, represented by a bare, dry soil surface is obtained via *H=Rn – G- λE* (Bastiaanssen et al.,

1 2

*H* is then calculated in the SEBAL and METRIC CIMEC-based models as:

*TT T*

1 2

(2)

(3)

*ah*

*H r*

*c*

1 2 *<sup>a</sup> a p ah*

*<sup>T</sup> H c r*

One can argue that the establishment of *Ta* over a vertical distance that is elevated above *d*  + *zoh* places the *rah* and established *Ta* in a blended boundary layer that combines influences

*a p*

*a*

where *rah,1-2* is the aerodynamic resistance to heat transfer between two heights above the surface, *z1* and *z2*. At the other extreme, for a wet surface, essentially all available energy *Rn - G* is used for evaporation *E.* At that extreme, the classical SEBAL approach assumes that *H*  ≈ 0, in order to keep requirements for high quality ground data to a minimum, so that *Ta* ≈ 0. Allen et al. (2001, 2007a) have used reference crop evapotranspiration, representing wellwatered alfalfa, to represent *E* for the cooler population of pixels in satellite images of irrigated fields in the METRIC approach, so as to better capture effects of regional advection of *H* and dry air, which can be substantial in irrigated desert. METRIC calculates *H* = *Rn - G* – k1*ETr* at these pixels, where *ETr* is alfalfa reference ET computed at the image time using weather data from a local automated weather station, and *Ta* from Eq. (2) , where k1 ~ 1.05. In typical SEBAL and METRIC applications, *z1* and *z2* are taken as 0.1 and 2 m above the zero plane displacement height (*d*). *z1* is taken as 0.1 m above the zero plane to insure that *T1* is established at a height that is generally greater than *d* + *zoh (zoh* is roughness length for heat transfer). Aerodynamic resistance, *rah*, is computed for between *z1* and *z2* and does not require the inclusion and thus estimation of *zoh*, but only *zom*, the roughness length for momentum transfer that is normally estimated from vegetation indices and land cover type.

**2.2 CIMEC Models (SEBAL and METRIC)** 

1998a):

of sparse vegetation and exposed soil, thereby reducing the need for two source modeling and problems associated with differences between radiative temperature and aerodynamic temperature and problems associated with estimating *zoh* and specific air temperature associated with the specific surface.

Evaporative cooling creates a landscape having high *Ta* associated with high *H* and high radiometric temperature and low *Ta* with low H and low radiometric temperature. For example, moist irrigated fields and riparian systems have much lower *Ta* and much lower *Ts* than dry rangelands. Allen et al. (2007a) argued, and field measurements in Egypt and Niger (Bastiaanssen et al., 1998b), China (Wang et al., 1998), USA (Franks and Beven, 1997), and Kenya (Farah, 2001) have shown the relationship between *Ts* and *Ta* to be highly linear between the two calibration points

$$
\Delta T\_a = \mathbf{c}\_1 \ T\_s - \mathbf{c}\_2 \tag{4}
$$

where *c1* and *c2* are empirical coefficients valid for one particular moment (the time and date of an image) and landscape. By using the minimum and maximum values for *Ta* as calculated for the nearly wettest and driest (i.e., coldest and warmest) pixel(s), the extremes of *H* are used, in the CIMEC process to find coefficients *c1* and *c2*. The empirical Eq. (4) meets the third quality stated by Campbell and Norman (1998) that one should rely on differences in radiometric surface temperature over space rather than absolute surface temperatures to minimize the influence of atmospheric corrections and uncertainties in surface emissivity.

Equation (3) has two unknowns: *Ta* and the aerodynamic resistance to heat transfer *rah,1-2* between the z1 and z2 heights, which is affected by wind speed, atmospheric stability, and surface roughness (Brutsaert, 1982). Several algorithms take one or more field measurements of wind speed and consider these as spatially constant over representative parts of the landscape (e.g. Hall et al., 1992; Kalma and Jupp, 1990; Rosema, 1990). This assumption is only valid for uniform homogeneous surfaces. For heterogeneous landscapes a unique wind speed near the ground surface is required for each pixel. One way to meet this requirement is to consider the wind speed spatially constant at a blending height about 200 m above ground level, where wind speed is presumed to not be substantially affected by local surface heterogeneities. The wind speed at blending height is predicted by upward extrapolation of near-surface wind speed measured at an automated weather station using a logarithmic wind profile. The wind speed at each pixel is obtained by a similar downward extrapolation using estimated surface momentum roughness *z0m* determined for each pixel.

Allen et al. (2007a) have noted that the inverted value for *Ta* is highly tied to the value used for wind speed in its CIMEC determination. Therefore, they cautioned against the use of a spatial wind speed field at some blending height across an image with a single *Ta* function. The application of the image-specific *Ta* function with a blending height wind speed in a distant part of the image that is, for example, double that of the wind used to determine coefficients *c1* and *c2* can estimate higher *H* than is possible based on energy availability. In those situations, the 'calibrated' *Ta* would be about half as much to compensate for the larger wind speed. Therefore, if wind fields at the blending height (200 m) are used, then fields of *Ta* calibrations are also needed, which is prohibitive. The single *Ta* function of SEBAL and METRIC, coupled with a single wind speed at blending height, transcends these problems. Gowda et al., (2008) presented a summary of remote sensing based energy balance algorithms for mapping ET that complements that by Kalma et al. (2008).

*Aerodynamic Transport*. The value for *rah,1,2* is calculated between the two heights z1 and z2 in SEBAL and METRIC. The value for *rah,1,2* is strongly influenced by buoyancy within the boundary layer driven by the rate of sensible heat flux. Because both *rah,1,2* and *H* are unknown at each pixel, an iterative solution is required. During the first iteration, *rah,1,2* is computed assuming neutral stability:

$$r\_{al\_{1-2}} = \frac{\ln\left(\frac{z\_2}{z\_1}\right)}{u\_\* \cdot k} \tag{5}$$

where *z1* and *z2* are heights above the zero plane displacement of the vegetation where the endpoints of *dT* are defined, *u\** is friction velocity (m s-1), and *k* is von Karman's constant (0.41). Friction velocity *u\** is computed during the first iteration using the logarithmic wind law for neutral atmospheric conditions:

$$
\mu^\* = \frac{k \text{ } \mu\_{200}}{\ln\left(\frac{200}{z\_{om}}\right)}\tag{6}
$$

where *u200* is the wind speed (m s-1) at a blending height assumed to be 200 m, and *zom* is the momentum roughness length (m). *zom* is a measure of the form drag and skin friction for the layer of air that interacts with the surface. *u\** is computed for each pixel inside the process model using a specific roughness length for each pixel, but with *u200* assumed to be constant over all pixels of the image since it is defined as occurring at a "blending height" unaffected by surface features. Eq. (5) and (6) support the use of a temperature gradient defined between two heights that are both above the surface. This allows one to estimate *rah,1-2* without having to estimate a second aerodynamic roughness for sensible heat transfer (*zoh*), since height *z1* is defined to be at an elevation above *zoh*. This is an advantage, because *zoh* can be difficult to estimate for sparse vegetation.

The wind speed at an assumed blending height (200 m) above the weather station, u200, is calculated as:

$$\mu\_{200} = \frac{\mu\_{w} \ln\left(\frac{200}{z\_{comw}}\right)}{\ln\left(\frac{z\_{\chi}}{z\_{comw}}\right)}\tag{7}$$

where *uw* is wind speed measured at a weather station at *zx* height above the surface and *zomw* is the roughness length for the weather station surface, similar to Allen and Wright (1997). All units for *z* are the same. The value for *u200* is assumed constant for the satellite image. This assumption *is required* for the use of a constant relation between *dT* and *Ts* to be extended across the image (Allen 2007a).

The effects of mountainous terrain and elevation on wind speed are complicated and difficult to quantify (Oke, 1987). In METRIC, *zom* or wind speed for image pixels in mountains are adjusted using a suite of algorithms to account for the following impacts (Allen and Trezza, 2011):

*Aerodynamic Transport*. The value for *rah,1,2* is calculated between the two heights z1 and z2 in SEBAL and METRIC. The value for *rah,1,2* is strongly influenced by buoyancy within the boundary layer driven by the rate of sensible heat flux. Because both *rah,1,2* and *H* are unknown at each pixel, an iterative solution is required. During the first iteration, *rah,1,2* is

> 2 1 \*

(5)

(6)

(7)

 

*<sup>z</sup> ln z*

*u k*

where *z1* and *z2* are heights above the zero plane displacement of the vegetation where the endpoints of *dT* are defined, *u\** is friction velocity (m s-1), and *k* is von Karman's constant (0.41). Friction velocity *u\** is computed during the first iteration using the logarithmic wind

<sup>200</sup> \* <sup>200</sup>

where *u200* is the wind speed (m s-1) at a blending height assumed to be 200 m, and *zom* is the momentum roughness length (m). *zom* is a measure of the form drag and skin friction for the layer of air that interacts with the surface. *u\** is computed for each pixel inside the process model using a specific roughness length for each pixel, but with *u200* assumed to be constant over all pixels of the image since it is defined as occurring at a "blending height" unaffected by surface features. Eq. (5) and (6) support the use of a temperature gradient defined between two heights that are both above the surface. This allows one to estimate *rah,1-2* without having to estimate a second aerodynamic roughness for sensible heat transfer (*zoh*), since height *z1* is defined to be at an elevation above *zoh*. This is an advantage, because *zoh* can

The wind speed at an assumed blending height (200 m) above the weather station, u200, is

*w*

*u ln z*

> *<sup>z</sup> ln z*

where *uw* is wind speed measured at a weather station at *zx* height above the surface and *zomw* is the roughness length for the weather station surface, similar to Allen and Wright (1997). All units for *z* are the same. The value for *u200* is assumed constant for the satellite image. This assumption *is required* for the use of a constant relation between *dT* and *Ts* to be

The effects of mountainous terrain and elevation on wind speed are complicated and difficult to quantify (Oke, 1987). In METRIC, *zom* or wind speed for image pixels in mountains are adjusted using a suite of algorithms to account for the following impacts

200

 

*omw x omw*

200

*u*

*ln z* 

*k u*

*om*

1 2

*ah*

*u*

*r*

computed assuming neutral stability:

law for neutral atmospheric conditions:

be difficult to estimate for sparse vegetation.

extended across the image (Allen 2007a).

(Allen and Trezza, 2011):

calculated as:


These algorithms have been developed for western Oregon and are being tested in Idaho, Nevada and Montana and are described in an article in preparation (Allen and Trezza, 2011). Allen and Trezza (2011) also refined the estimation of diffuse radiation on steep mountainous slopes.

*Iterative solution for rah,1-2.* During subsequent iterations for the solution for H, a corrected value for *u\** is computed as:

$$
\mu\_\* = \frac{\mu\_{200}k}{\ln\left(\frac{200}{z\_{0m}}\right) - \Psi\_{m(200m)}}\tag{8}
$$

where *m(200m)* is the stability correction for momentum transport at 200 meters. A corrected value for *rah,1-2* is computed each iteration as:

$$r\_{\rm alt,1,2} = \frac{\ln\left(\frac{z\_2}{z\_1}\right) - \Psi\_{\rm h(z\_2)} + \Psi\_{\rm h(z\_1)}}{\mu\_\* \times k} \tag{9}$$

where *h(z2)* and *h(z1)* are the stability corrections for heat transport at *z2* and *z1* heights (Paulson 1970 and Webb 1970) that are updated each iteration.

*Stability Correction functions.* The Monin-Obukhov length (*L*) defines the stability conditions of the atmosphere in the iterative process. *L* is the height at which forces of buoyancy (or stability) and mechanical mixing are equal, and is calculated as a function of heat and momentum fluxes:

$$L = -\frac{\rho\_{\rm air} \, \mathcal{C}\_p \, \mu \star^3 T\_s}{k \text{g}H} \tag{10}$$

where *g* is gravitational acceleration (= 9.807 m s-2) and units for terms cancel to m for *L*. Values of the integrated stability corrections for momentum and heat transport (*m* and *h*) are computed using formulations by Paulson (1970) and Webb (1970), depending on the sign of *L*. When *L* < 0, the lower atmospheric boundary layer is unstable and when *L* > 0, the boundary layer is stable. For *L*<0:

$$\Psi\_{m(200m)} = 2ln\left(\frac{1+\chi\_{(200m)}}{2}\right) + ln\left(\frac{1+\chi\_{(200m)}}{2}\right) - 2ARCTAN\left(\chi\_{(200m)}\right) + 0.5\pi\tag{11}$$

$$\Psi\_{h(2m)} = 2ln\left(\frac{1 + \chi\_{(2m)}}{2}\right) \tag{12a}$$

$$\Psi\_{h(0.1m)} = 2ln\left(\frac{1 + \chi\_{(0.1m)}\,^2}{2}\right) \tag{12b}$$

where

$$\mathbf{x}\_{\text{(200m)}} = \left(\mathbf{1} - \mathbf{1}\mathbf{6}\frac{200}{L}\right)^{0.25} \tag{13a}$$

$$\propto\_{\text{(2m)}} = \left(1 - 16\frac{2}{L}\right)^{0.25} \tag{13b}$$

$$\mathbf{x}\_{\text{(0.1m)}} = \left(\mathbf{1} - \mathbf{1} \mathbf{6} \frac{\mathbf{0} \mathbf{1}}{L}\right)^{0.25} \tag{14}$$

Values for *x(200m)*, *x(2m)*, and *x(0.1m)* have no meaning when *L* 0 and their values are set to 1.0. For *L* > 0 (stable conditions):

$$\Psi\_{m(200m)} = -5\left(\frac{2}{L}\right) \tag{15}$$

$$\Psi\_{h(2m)} = -5 \left(\frac{2}{L}\right) \tag{16a}$$

$$\Psi\_{h\text{(0.1m)}} = -\mathfrak{S}\left(\frac{0.1}{L}\right) \tag{16b}$$

When *L* = 0, the stability values are set to 0. Equation (15) uses a value of 2 m rather than 200 m for *z* because it is assumed that under stable conditions, the height of the stable, inertial boundary layer is on the order of only a few meters. Using a larger value than 2 m for *z* can cause numerical instability in the model. For neutral conditions, *L* = 0, *H* = 0 and *m* and *<sup>h</sup>* = 0.

#### **2.2.1 The use of inverse modeling at extreme conditions during calibration (CIMEC)**

In METRIC, the satellite-based energy balance is internally calibrated at two extreme conditions (dry and wet) using locally available weather data. The auto-calibration is done for each image using alfalfa-based reference *ET* (*ETr*) computed from hourly weather data. Accuracy and dependability of the *ETr* estimate has been established by lysimetric and other studies in which we have high confidence (ASCE-EWRI, 2005). The internal calibration of the sensible heat computation within SEBAL and METRIC and the use of the indexed temperature gradient eliminate the need for atmospheric correction of surface temperature (*Ts*) and reflectance (albedo) measurements using radiative transfer models (Tasumi et al., 2005b). The internal calibration also reduces impacts of biases in estimation of aerodynamic stability correction and surface roughness.

The calibration of the sensible heat process equations, and in essence the entire energy balance, to *ETr* corrects the surface energy balance for lingering systematic computational biases associated with empirical functions used to estimate some components and uncertainties in other estimates as summarized by Allen et al. (2005), including:


474 Evapotranspiration – Remote Sensing and Modeling

1

1

 

2 *m*

> 2 *m*

*L* 

*L* 

*L* 

2

*L*

0.25

0.25

*x*

 

*x*

(2 )

*ln*

*h m*

(0.1 )

2

cause numerical instability in the model. For neutral conditions, *L* = 0, *H* = 0 and

0.1

200

*ln*

*h m*

where

For *L* > 0 (stable conditions):

stability correction and surface roughness.

2

2

<sup>200</sup> 1 16 *<sup>m</sup> <sup>x</sup>*

<sup>2</sup> 1 16 *<sup>m</sup> <sup>x</sup>*

0.1 1 16 *<sup>m</sup> <sup>x</sup>*

(200 )

 2 <sup>2</sup> <sup>5</sup> *h m <sup>L</sup>*

 0.1 0.1 <sup>5</sup> *h m <sup>L</sup>*

*m m* 5

When *L* = 0, the stability values are set to 0. Equation (15) uses a value of 2 m rather than 200 m for *z* because it is assumed that under stable conditions, the height of the stable, inertial boundary layer is on the order of only a few meters. Using a larger value than 2 m for *z* can

**2.2.1 The use of inverse modeling at extreme conditions during calibration (CIMEC)**  In METRIC, the satellite-based energy balance is internally calibrated at two extreme conditions (dry and wet) using locally available weather data. The auto-calibration is done for each image using alfalfa-based reference *ET* (*ETr*) computed from hourly weather data. Accuracy and dependability of the *ETr* estimate has been established by lysimetric and other studies in which we have high confidence (ASCE-EWRI, 2005). The internal calibration of the sensible heat computation within SEBAL and METRIC and the use of the indexed temperature gradient eliminate the need for atmospheric correction of surface temperature (*Ts*) and reflectance (albedo) measurements using radiative transfer models (Tasumi et al., 2005b). The internal calibration also reduces impacts of biases in estimation of aerodynamic

Values for *x(200m)*, *x(2m)*, and *x(0.1m)* have no meaning when *L* 0 and their values are set to 1.0.

2 (2 )

2 (0.1 )

0.25

(12a)

(12b)

(13a)

(13b)

(14)

(15)

(16a)

(16b)

*m* and *<sup>h</sup>* = 0.


This list of biases plagues essentially all surface energy balance computations that utilize satellite imagery as the primary spatial information resource. Most polar orbiting satellites orbit about 700 km above the earth's surface, yet the transport of vapor and sensible heat from land surfaces is strongly impacted by aerodynamic processes including wind speed, turbulence and buoyancy, all of which are essentially invisible to satellites. In addition, precise quantification of albedo, net radiation and soil heat flux is uncertain and potentially biased. Therefore, even though best efforts are made to estimate each of these parameters as accurately and as unbiased as possible, some biases do occur and calibration to *ETr* helps to compensate for this by introducing a bias correction into the calculation of *H*. The end result is that biases inherent to *Rn*, *G*, and subcomponents of *H* are essentially cancelled by the subtraction of a bias-canceling estimate for *H*. The result is an *ET* map having values ranging between near zero and near *ETr*, for images having a range of bare or nearly bare soil and full vegetation cover.

#### **2.3 Calculation of evapotranspiration**

*ET* at the instant of the satellite image is calculated for each pixel by dividing *LE* from *LE* = *Rn - G* – *H* by latent heat of vaporization:

$$ET\_{inst} = 3600 \frac{LE}{\lambda \, \rho\_w} \tag{17}$$

where *ETinst* is instantaneous *ET* (mm hr-1), 3600 converts from seconds to hours, *<sup>w</sup>* is the density of water [~1000 kg m-3], and is the latent heat of vaporization (J kg-1) representing the heat absorbed when a kilogram of water evaporates and is computed as:

$$
\dot{\lambda} = \left[2.501 - 0.00236(T\_s - 273.15)\right] \times 10^6\tag{18}
$$

The reference *ET* fraction (*ETrF*) is calculated as the ratio of the computed instantaneous *ET* (*ETinst*) from each pixel to the reference *ET* (*ETr*) computed from weather data:

$$ET\_rF = \frac{ET\_{inst}}{ET\_r} \tag{19}$$

where *ETr* is the estimated instantaneous rate (interpolated from hourly data) (mm hr-1) for the standardized 0.5 m tall alfalfa reference at the time of the image. Generally only one or two weather stations are required to estimate *ETr* for a Landsat image that measures 180 km x 180 km, as discussed later. *ETrF* is the same as the well-known crop coefficient, *Kc*, when used with an alfalfa reference basis, and is used to extrapolate *ET* from the image time to 24 hour or longer periods.

One should generally expect *ETrF* values to range from 0 to about 1.0 (Wright, 1982; Jensen et al., 1990). At a completely dry pixel, *ET* = 0 and therefore *ETrF* = 0. A pixel in a well established field of alfalfa or corn can occasionally have an *ET* slightly greater than *ETr* and therefore *ETrF* 1, perhaps up to 1.1 if it has been recently wetted by irrigation or precipitation. However, *ETr* generally represents an upper bound on *ET* for large expanses of well-watered vegetation. Negative values for *ETrF* can occur in METRIC due to systematic errors caused by various assumptions made earlier in the energy balance process and due to random error components so that error should oscillate about *ETrF* = 0 for completely dry pixels. In calculation of *ETrF* in Equation (19), each pixel retains a unique value for *ETinst* that is derived from a common value for *ETr* derived from the representative weather station data.

*24-Hour Evapotranspiration (ET24).* Daily values of *ET* (*ET24*) are generally more useful than the instantaneous *ET* that is derived from the satellite image. In the METRIC process, *ET24* is estimated by assuming that the instantaneous *ETrF* computed at image time is the same as the average *ETrF* over the 24-hour average. The consistency of *ETrF* over a day has been demonstrated by various studies, including Romero (2004), Allen et al., (2007a) and Collazzi et al., (2006).

The assumption of constant *ETrF* during a day appears to be generally valid for agricultural crops that have been developed to maximize photosynthesis and thus stomatal conductance. In addition, the advantage of the use of *ETrF* is to account for the increase in 24-hour *ET* that can occur under advective conditions. The impacts of advection are represented well by the Penman-Monteith equation. However, the *ETrF* may decrease during afternoon for some native vegetation under water short conditions where plants endeavor to conserve soil water through stomatal control. In addition, by definition, when the vegetation under study is the same as or similar to the vegetation for the surrounding region and experiences similar water inputs (natural rainfall, only), then (by definition) no advection can occur. This is because as much sensible heat energy is generated by the surface under study as is generated by the region. Therefore, the net advection of energy is nearly zero. Therefore, under these conditions, the estimation by *ETr* that accounts for impacts of advection to a *wet* surface do not occur, and the use of *ETrF* to estimate 24-hour ET may not be valid. Instead, the use of evaporative fraction, *EF*, that is used with SEBAL applications may be a better time-transfer approach for rainfed systems. Various schemes of using *EF* for rainfed portions of Landsat images and *ETrF* for irrigated, riparian or wetland portions were explored by Kjaersgaard and Allen (2010). When used, the *EF* is calculated as:

$$EF = \frac{ET\_{inst}}{R\_n - G} \tag{20}$$

where *ETinst* and *Rn* and *G* have the same units and represent the same period of time. Finally, the *ET24* (mm/day) is computed for each image pixel in SEBAL as:

$$ET\_{24} = \left(EF\right) \left(R\_{n\_{-24}}\right) \tag{21}$$

and in METRIC as:

476 Evapotranspiration – Remote Sensing and Modeling

two weather stations are required to estimate *ETr* for a Landsat image that measures 180 km x 180 km, as discussed later. *ETrF* is the same as the well-known crop coefficient, *Kc*, when used with an alfalfa reference basis, and is used to extrapolate *ET* from the image time to 24-

One should generally expect *ETrF* values to range from 0 to about 1.0 (Wright, 1982; Jensen et al., 1990). At a completely dry pixel, *ET* = 0 and therefore *ETrF* = 0. A pixel in a well established field of alfalfa or corn can occasionally have an *ET* slightly greater than *ETr* and therefore *ETrF* 1, perhaps up to 1.1 if it has been recently wetted by irrigation or precipitation. However, *ETr* generally represents an upper bound on *ET* for large expanses of well-watered vegetation. Negative values for *ETrF* can occur in METRIC due to systematic errors caused by various assumptions made earlier in the energy balance process and due to random error components so that error should oscillate about *ETrF* = 0 for completely dry pixels. In calculation of *ETrF* in Equation (19), each pixel retains a unique value for *ETinst* that is derived from a common value for *ETr* derived from the representative

*24-Hour Evapotranspiration (ET24).* Daily values of *ET* (*ET24*) are generally more useful than the instantaneous *ET* that is derived from the satellite image. In the METRIC process, *ET24* is estimated by assuming that the instantaneous *ETrF* computed at image time is the same as the average *ETrF* over the 24-hour average. The consistency of *ETrF* over a day has been demonstrated by various studies, including Romero (2004), Allen et al., (2007a) and Collazzi

The assumption of constant *ETrF* during a day appears to be generally valid for agricultural crops that have been developed to maximize photosynthesis and thus stomatal conductance. In addition, the advantage of the use of *ETrF* is to account for the increase in 24-hour *ET* that can occur under advective conditions. The impacts of advection are represented well by the Penman-Monteith equation. However, the *ETrF* may decrease during afternoon for some native vegetation under water short conditions where plants endeavor to conserve soil water through stomatal control. In addition, by definition, when the vegetation under study is the same as or similar to the vegetation for the surrounding region and experiences similar water inputs (natural rainfall, only), then (by definition) no advection can occur. This is because as much sensible heat energy is generated by the surface under study as is generated by the region. Therefore, the net advection of energy is nearly zero. Therefore, under these conditions, the estimation by *ETr* that accounts for impacts of advection to a *wet* surface do not occur, and the use of *ETrF* to estimate 24-hour ET may not be valid. Instead, the use of evaporative fraction, *EF*, that is used with SEBAL applications may be a better time-transfer approach for rainfed systems. Various schemes of using *EF* for rainfed portions of Landsat images and *ETrF* for irrigated, riparian or wetland portions were

explored by Kjaersgaard and Allen (2010). When used, the *EF* is calculated as:

Finally, the *ET24* (mm/day) is computed for each image pixel in SEBAL as:

where *ETinst* and *Rn* and *G* have the same units and represent the same period of time.

*inst n ET EF*

*R G* (20)

*ET EF R* <sup>24</sup> *<sup>n</sup>* \_ 24 (21)

hour or longer periods.

weather station data.

et al., (2006).

$$ET\_{24} = C\_{rdd} \left( ET\_r F \right) \left( ET\_{r\_-24} \right) \tag{22}$$

where *ETrF* (or *EF*) is assumed equal to the *ETrF* (or *EF*) determined at the satellite overpass time, *ETr-24* is the cumulative 24-hour *ETr* for the day of the image and *Crad* is a correction term used in sloping terrain to correct for variation in 24-hr vs. instantaneous energy availability. *Crad* is calculated for each image and pixel as:

$$\mathbf{C}\_{rad} = \frac{\mathbf{R}\_{\text{so(inst)}} \mathbf{H}\_{\text{Horizontal}}}{\mathbf{R}\_{\text{so(inst)}} \text{Pixel}} \cdot \frac{\mathbf{R}\_{\text{so(24)}} \text{Pixel}}{\mathbf{R}\_{\text{so(24)}} \text{Holar}} \tag{23}$$

where *Rso* is clear-sky solar radiation (W m-1), the "*(inst)*" subscript denotes conditions at the satellite image time, "*(24)*" represents the 24-hour total, the "*Pixel*" subscript denotes slope and aspect conditions at a specific pixel, and the "*Horizontal*" subscript denotes values calculated for a horizontal surface representing the conditions impacting *ETr* at the weather station. For applications to horizontal areas, *Crad* = 1.0.

The 24 hour *Rso* for horizontal surfaces and for sloping pixels is calculated as:

$$R\_{so(24)} = \int\_0^{24} R\_{so\\_i} \tag{24}$$

where *Rso\_i* is instantaneous clear sky solar radiation at time *i* of the day, calculated by an equation that accounts for effects of slope and aspect. In METRIC, *ETr 24* is calculated by summing hourly *ETr* values over the day of the image.

After *ET* and *ETrF* have been determined using the energy balance, and the application of the single *dT* function, then, when interpolating between satellite images, a full grid for *ETr* is used for the extrapolation over time, to account for both spatial and temporal variation in *ETr*. The *ETr* grid is generally made on a 3 or 5 km base using as many quality-controlled weather stations located within and in the vicinity of the study area as available. Depending on data availability and the density of the weather stations various gridding methods including krieging, inverse-distance, and splining can be used.

*Seasonal Evapotranspiration (ETseasonal)*. Monthly and seasonal evapotranspiration "maps" are often desired for quantifying total water consumption from agriculture. These maps can be derived from a series of *ETrF* images by interpolating *ETrF* on a pixel by pixel basis between processed images and multiplying, on a daily basis, by the *ETr* for each day. The interpolation of *ETrF* between image dates is not unlike the construction of a seasonal *Kc* curve (Allen et al., 1998), where interpolation is done between discrete values for *Kc*.

The METRIC approach assumes that the *ET* for the entire area of interest changes in proportion to change in *ETr* at the weather station. This is a generally valid assumption and is similar to the assumptions used in the conventional application of *Kc* x *ETr*. This approach is effective in estimating *ET* for both clear and cloudy days in between the clear-sky satellite image dates. Tasumi et al., (2005a) showed that the *ETrF* was consistent between clear and cloudy days using lysimeter measurements at Kimberly, Idaho. *ETr* is computed at a specific weather station location and therefore may not represent the actual condition at each pixel. However, because *ETr* is used only as an index of the relative change in weather, specific information at each pixel is retained through the *ETrF*.

Cumulative *ET* for any period, for example, month, season or year is calculated as:

$$ET\_{period} = \sum\_{i=m}^{n} \left[ \left( ET\_r F\_i \right) \left( ET\_{r24i} \right) \right] \tag{25}$$

where *ETperiod* is the cumulative *ET* for a period beginning on day m and ending on day *n*, *ETrFi* is the interpolated *ETrF* for day *i*, and *ETr24i* is the 24-hour *ETr* for day *i*. Units for *ETperiod* will be in mm when *ETr24* is in mm d-1. The interpolation between values for *ETrF* is best made using a curvilinear interpolation function, for example a spline function, to better fit the typical curvilinearity of crop coefficients during a growing season (Wright, 1982). Generally one satellite image per month is sufficient to construct an accurate *ETrF* curve for purposes of estimating seasonal *ET* (Allen et al., 2007a). During periods of rapid vegetation change, a more frequent image interval may be desirable. Examples of splining *ETrF* to estimate daily and monthly ET are given in Allen et al. (2007a) and Singh et al. (2008).

If a specific pixel must be masked out of an image because of cloud cover, then a subsequent image date must be used during the interpolation and the estimated *ETrF* or *Kc* curve will have reduced accuracy.

*Average ETrF over a period.* An average *ETrF* for the period can be calculated as:

$$ET\_rF\_{period} = \frac{\sum\_{i=m}^{n} \left[ \left( ET\_rF\_i \right) \left( ET\_{r24i} \right) \right]}{\sum\_{i=m}^{n} ET\_{r24i}} \tag{26}$$

Moderately high resolution satellites such as Landsat provide the opportunity to view evapotranspiration on a field by field basis, which can be valuable for water rights management, irrigation scheduling, and discrimination of *ET* among crop types (Allen et al., 2007b). The downside of using high resolution imagery is less frequent image acquisition. In the case of Landsat, the return interval is 16 days. As a result, monthly ET estimates are based on only one or two satellite image snapshots per month. In the case of clouds, intervals of 48 days between images can occur. This can be rectified by combining multiple Landsats (5 with 7) or by using data fusion techniques, where a more frequent, but more coarse system like MODIS is used as a carrier of information during periods without quality Landsat images (Gao et al., 2006, Anderson et al., 2010).

#### **2.4 Reflectance based ET methods**

Reflectance based ET methods typically estimate relative fractions of reference ET (ETrF, synonymous with the crop coefficient) based on some sort of vegetation index, for example, the normalized difference vegetation index, NDVI, and multiply the ETrF by daily computed reference ETr (Groeneveld et al., 2007). NDVI approaches don't directly or indirectly account for evaporation from soil, so they have difficulty in estimating evaporation associated with both irrigation and precipitation wetting events, unless operated with a daily evaporation process model. The VI-based methods are therefore largely blind to the treatment of both irrigation and precipitation events, except on an average basis. In contrast, thermally based models detect the presence of evaporation from

*period ri r i i m ET ET F ET* 

where *ETperiod* is the cumulative *ET* for a period beginning on day m and ending on day *n*, *ETrFi* is the interpolated *ETrF* for day *i*, and *ETr24i* is the 24-hour *ETr* for day *i*. Units for *ETperiod* will be in mm when *ETr24* is in mm d-1. The interpolation between values for *ETrF* is best made using a curvilinear interpolation function, for example a spline function, to better fit the typical curvilinearity of crop coefficients during a growing season (Wright, 1982). Generally one satellite image per month is sufficient to construct an accurate *ETrF* curve for purposes of estimating seasonal *ET* (Allen et al., 2007a). During periods of rapid vegetation change, a more frequent image interval may be desirable. Examples of splining *ETrF* to estimate daily and monthly ET are given in Allen et al. (2007a) and Singh et al.

If a specific pixel must be masked out of an image because of cloud cover, then a subsequent image date must be used during the interpolation and the estimated *ETrF* or *Kc* curve will

<sup>24</sup>

*ET F ET*

*ET*

*ri r i*

24

*r i*

*i m*

Moderately high resolution satellites such as Landsat provide the opportunity to view evapotranspiration on a field by field basis, which can be valuable for water rights management, irrigation scheduling, and discrimination of *ET* among crop types (Allen et al., 2007b). The downside of using high resolution imagery is less frequent image acquisition. In the case of Landsat, the return interval is 16 days. As a result, monthly ET estimates are based on only one or two satellite image snapshots per month. In the case of clouds, intervals of 48 days between images can occur. This can be rectified by combining multiple Landsats (5 with 7) or by using data fusion techniques, where a more frequent, but more coarse system like MODIS is used as a carrier of information during periods without quality

Reflectance based ET methods typically estimate relative fractions of reference ET (ETrF, synonymous with the crop coefficient) based on some sort of vegetation index, for example, the normalized difference vegetation index, NDVI, and multiply the ETrF by daily computed reference ETr (Groeneveld et al., 2007). NDVI approaches don't directly or indirectly account for evaporation from soil, so they have difficulty in estimating evaporation associated with both irrigation and precipitation wetting events, unless operated with a daily evaporation process model. The VI-based methods are therefore largely blind to the treatment of both irrigation and precipitation events, except on an average basis. In contrast, thermally based models detect the presence of evaporation from

*Average ETrF over a period.* An average *ETrF* for the period can be calculated as:

*ET F*

Landsat images (Gao et al., 2006, Anderson et al., 2010).

**2.4 Reflectance based ET methods** 

*n*

*i m r period n*

<sup>24</sup>

(25)

(26)

Cumulative *ET* for any period, for example, month, season or year is calculated as:

*n*

(2008).

have reduced accuracy.

soil, during the snapshot, at least, via evaporative cooling. VI-based methods also do not pick up on acute water stress caused by drought or lack of irrigation, which is often a primary reason for quantifying ET. These models can be run with a background daily evaporation process model, similar to the EB-based models, to estimate evaporation from precipitation between satellite overpass dates.

## **2.5 Challenges with snapshot models**

The SEBAL, METRIC, and other EB models, that can be applied at the relatively high spatial resolution of Landsat and similar satellites, despite their different relative strengths and weaknesses, all suffer from the inability to capture evaporation signals from episodic precipitation and irrigation events occurring between overpass dates. In the case of irrigation events, which are typically unknown to the processer in terms of timing and location, the random nature of these events in time can be somewhat accommodated via the use of multiple overpass dates during the irrigation season (Allen et al. 2007a). In this manner, the ET retrieval for a specific field may be biased high when the overpass follows an irrigation event, but may be biased low when the overpass just precedes an irrigation event. Allen et al. (2007a) suggested that monthly overpass dates over a seven month growing season, for example, can largely compensate for the impact of irrigation wetting on individual fields, especially when it is total growing season ET that is of most interest. The variance of the error in ET estimate caused by unknown irrigation events should tend to decrease with the square root of the number of images processed during the irrigation season.

The impact by precipitation events is a larger problem in converting the 'snapshot' ET images from energy balance models or other methods into monthly and longer period ET. Precipitation timing and magnitudes tend to be less random in time and have much larger variance in depth per wetting event than with irrigation. Because of this, the use of snapshot ET models to construct monthly and seasonal ET maps is more likely to be biased high (if a number of images happen to be 'wet' following a recent precipitation event) or low (if images happen to be 'dry', with precipitation occurring between images). The latter may often be the case since the most desired images for processing are cloud free.

One important use of ET maps is in the estimation of ground water recharge (Allen et al., 2007b). Ground water recharge is often uncertain due to uncertainty in both precipitation and ET, and is usually computed using the difference between P and ET, with adjustment for runoff. It is therefore important to maintain congruency between ET and P data sets or 'maps'. Lack of congruency can cause very large error in estimated recharge, especially in the more arid regions.

## **3. Adjusting for background evaporation**

Often a Landsat or other image is processed on a date where antecedent rainfall has caused the evaporation from bare soil to exceed that for the surrounding monthly period. Often, for input to water balance applications, it is desirable that the final ET image represent the average evaporation conditions for the month. In that case, one approach is to adjust the 'background' evaporation of the processed image to better reflect that for the month or other period that it is to ultimately represent. This period may be a time period that is half way between other adjacent images.

An example of a sequence of Landsat images processed using the METRIC surface energy balance model for the south-western portion of the Nebraska Panhandle (Kjaersgaard and Allen, 2010a) is shown in Figure 1 along with daily precipitation from the Scottsbluff High Plains Regional Climate Center (HPRCC) weather station. The August 13 image date was preceded by a wet period and followed by a very dry period, thus the evaporation from non-irrigated areas at the satellite image date is not representative for the month.

Fig. 1. Image dates of nearly cloud free Landsat 5 path 33 row 31 images from the Nebraskan Panhandle in 1997 (black vertical bars) and precipitation recorded at the Scottsbluff HPRCC weather station (red bars). After Kjaersgaard and Allen (2010).

In making the adjustment for background evaporation, the background evaporation on the overpass date is subtracted out of the image and the average background evaporation is substituted in. Full adjustment is made for areas of completely bare soil, represented by NDVI = NDVIbare soil, with no adjustment to areas having full ground covered by vegetation, represented by NDVI = NDVIfull cover, and with linear adjustment in between.

The following methodology is taken from a white paper developed by the University of Idaho during 2008 and 2009 (Allen 2008, rev. 2010). The ETrF of the Landsat image is first adjusted to a 'basal' condition, where the evaporation estimate is free of rainfall induced evaporation, but still may contain any irrigation induced evaporation:

$$\left(\left(ET\_rF\_i\right)\_b = ET\_rF\_i - \left(ET\_rF\_{\text{background}}\right)\_i \left(\frac{\text{NDVI}\_{full\,\text{cover}} - \text{NDVI}\_i}{\text{NDVI}\_{full\,\text{cover}} - \text{NDVI}\_{all\,\text{resources}}}\right) \tag{27}$$

where (ETrFbackground)i is the background evaporation on the image date (i) for bare soil, computed using a gridded FAO-56 two-stage evaporation model of Allen et al. (1998) with modification to account for 'flash' evaporation from the soil skin (Allen 2010a) or some other soil evaporation model such as Hydrus or DAISY. The soil evaporation model is on a daily timestep using spatially distributed precipitation, reference ET, and soil properties. (ETrFi)b is the resulting 'basal' ET image for a particular image date, representing a condition having NDVI amount of vegetation and a relatively dry soil surface. This parameter represents the foundation for later adjustment to represent the longer period.

An example of a sequence of Landsat images processed using the METRIC surface energy balance model for the south-western portion of the Nebraska Panhandle (Kjaersgaard and Allen, 2010a) is shown in Figure 1 along with daily precipitation from the Scottsbluff High Plains Regional Climate Center (HPRCC) weather station. The August 13 image date was preceded by a wet period and followed by a very dry period, thus the evaporation from

Fig. 1. Image dates of nearly cloud free Landsat 5 path 33 row 31 images from the Nebraskan Panhandle in 1997 (black vertical bars) and precipitation recorded at the Scottsbluff HPRCC

In making the adjustment for background evaporation, the background evaporation on the overpass date is subtracted out of the image and the average background evaporation is substituted in. Full adjustment is made for areas of completely bare soil, represented by NDVI = NDVIbare soil, with no adjustment to areas having full ground covered by vegetation,

The following methodology is taken from a white paper developed by the University of Idaho during 2008 and 2009 (Allen 2008, rev. 2010). The ETrF of the Landsat image is first adjusted to a 'basal' condition, where the evaporation estimate is free of rainfall induced

*r i r i r background <sup>b</sup> <sup>i</sup> full er baresoil*

where (ETrFbackground)i is the background evaporation on the image date (i) for bare soil, computed using a gridded FAO-56 two-stage evaporation model of Allen et al. (1998) with modification to account for 'flash' evaporation from the soil skin (Allen 2010a) or some other soil evaporation model such as Hydrus or DAISY. The soil evaporation model is on a daily timestep using spatially distributed precipitation, reference ET, and soil properties. (ETrFi)b is the resulting 'basal' ET image for a particular image date, representing a condition having NDVI amount of vegetation and a relatively dry soil surface. This parameter represents the

cov

*NDVI NDVI*

*full er i*

*NDVI NDVI*

represented by NDVI = NDVIfull cover, and with linear adjustment in between.

cov

evaporation, but still may contain any irrigation induced evaporation:

*ET F ET F ET F*

foundation for later adjustment to represent the longer period.

weather station (red bars). After Kjaersgaard and Allen (2010).

non-irrigated areas at the satellite image date is not representative for the month.

#### **3.1 Adjustment for cases of riparian vegetation**

For riparian vegetation and similar systems, where soil water stress is not likely to occur due to the frequent presence of shallow ground water, an adjusted ETrF is computed for the image date that reflects background evaporation averaged over the surrounding period in proportion to the amount of ground cover represented by NDVI:

$$\left(\left(ET\_rF\_i\right)\_{afusted} = \left(ET\_rF\_i\right)\_b + \overline{\left(ET\_rF\_{background}\right)} \left(\frac{\text{NDVI}\_{full\,cover} - \text{NDVI}\_i}{\text{NDVI}\_{full\,cover} - \text{NDVI}\_{threshold}}\right) \tag{28}$$

where *ET Fr background* is the average evaporation from bare soil due to precipitation over the averaging period (e.g., one month), calculated as:

$$\frac{1}{\left(ET\_rF\_{background}\right)} = \frac{\sum\_{1}^{n} \left(ET\_rF\_{background}\right)\_i}{n} \tag{29}$$

Equations 5 and 6 can be combined as:

(27)

$$\left(\left(ET\_rF\_i\right)\_{\text{adjusted}} = ET\_rF\_i + \left(\overline{\left(ET\_rF\_{\text{background}}\right)} - \left(ET\_rF\_{\text{background}}\right)\_i\right)\left(\frac{\text{NDVI}\_{\text{full cover}} - \text{NDVI}\_i}{\text{NDVI}\_{\text{full cover}} - \text{NDVI}\_{\text{threshold}}}\right) \tag{30}$$

with limits NDVIbare soil ≤ NDVIi ≤ NDVIfull cover.

The outcome of this adjustment is to preserve any significant evaporation stemming from irrigation or ground-water and any transpiration stemming from vegetation, with adjustment only for evaporation stemming from precipitation to account for differences between the image date and that of the surrounding time period. In other words, if the initial ETrFi, prior to adjustment is high due to evaporation from irrigation or from high ground-water condition, much of that evaporation would remain in the adjusted ETrFi estimate.

#### **3.2 Adjustments for non-riparian vegetation**

The following refinement to Eq. 30 is made for application to non-riparian vegetation, to account for those situations where, during long periods (i.e., months), soil moisture may have become limited enough that even transpiration of vegetation has been reduced due to moisture stress. If the Landsat image is processed during that period of moisture stress, then the ETrF value for vegetated or partially vegetated areas will be lower than the potential (nonstressed) value. This can happen, for example, during early spring when winter wheat may go through stress prior to irrigation or a rainy period, or in desert and other dry systems.

This causes a problem in that the method of Eq. 8 attempts to 'preserve' the ETrF of the vegetated portion of a pixel that was computed by METRIC on the image date. However, when a rain event occurs following the image date, not only will the ETrF of exposed soil increase, but any stressed vegetation will equally 'recover' from moisture stress and the ETrF of the vegetation fraction of the surface will increase. This situation may occur for rangeland and dryland agricultural systems. It is therefore assumed that the ETrF of nonstressed vegetation will be at least as high as the ETrF of bare soil over the same time period, since it should have equal access to shallow water. An exception would be if the vegetation were sufficiently stressed to not recover transpiration potential. However, this amount of stress should be evidenced by a reduced NDVI. A minimum limit is therefore

placed, using the background ETrF *ET Fr background* for the period.

To derive a modified Eq. 8, it is useful to first isolate the 'transpiration' portion of the ETrF. On the satellite image date, the bulk ETrF computed by METRIC for a pixel, is decomposed to:

$$ET\_rF\_i = (1 - f\_c) \left( ET\_rF\_{background} \right)\_i + f\_c \left( ET\_rF\_{transposition} \right)\_i \tag{31}$$

where ETrFtranspiration is the apparent transpiration from the fraction of ground covered by vegetation, fc. The fc is estimated as 1 – fs, where fs is the fraction of bare soil, and for consistency with equations 30, fs is estimated as:

$$f\_s = \left(\frac{\text{NDVI}\_{full\,\text{cover}} - \text{NDVI}\_i}{\text{NDVI}\_{full\,\text{cover}} - \text{NDVI}\_{pure\,\text{oil}}}\right) \tag{32a}$$

so that:

$$f\_c = 1 - \left(\frac{NDVI\_{full\,cover} - NDVI\_i}{NDVI\_{full\,cover} - NDVI\_{threshold}}\right) \tag{32b}$$

Eq. 31 is not used as is, since ETrFi comes from the energy balance-based ET image (i.e., from METRIC, etc.). However, one can rearrange Eq. 31 to solve for ETrFtranspiration :

$$\left(f\_c \left(ET\_rF\_{transposition}\right)\_i\right)\_i = ET\_rF\_i - (1 - f\_c)\left(ET\_rF\_{background}\right)\_i\tag{33}$$

Now, if ETrFtranspiration is limited to the maximum of the ETrFtranspiration on the day of the image, or the *ET Fr background* for the period, then:

$$\left(\left(ET\_rF\_{transposition}\right)\_{adjusted}\right)\_{adjusted} = \max\left[\left(ET\_rF\_{transposition}\right)\_i, \sqrt{\left(ET\_rF\_{background}\right)\_i}\right] \tag{34}$$

Then the new ETrF adjusted value becomes:

$$\begin{aligned} \left( \left( ET\_r F\_i \right)\_{\text{adjusted}} = (1 - f\_c) \overline{\left( ET\_r F\_{\text{background}} \right)} + f\_c \left( ET\_r F\_{\text{transjunction}} \right)\_{\text{adjusted}} \\ \text{or} \\ \left( ET\_r F\_i \right)\_{\text{adjusted}} = (1 - f\_c) \overline{\left( ET\_r F\_{\text{background}} \right)} + f\_c \max \left[ \left( ET\_r F\_{\text{transjunction}} \right)\_i , \overline{\left( ET\_r F\_{\text{background}} \right)} \right] \end{aligned} \tag{35}$$

where *ET Fr background* is the average evaporation from bare soil due to precipitation over the averaging period (e.g., one month) and ETrFtranspiration is the original transpiration computed from Eq. 33. Eq. 33 and 35 can be combined so that:

period, since it should have equal access to shallow water. An exception would be if the vegetation were sufficiently stressed to not recover transpiration potential. However, this amount of stress should be evidenced by a reduced NDVI. A minimum limit is therefore

To derive a modified Eq. 8, it is useful to first isolate the 'transpiration' portion of the ETrF. On the satellite image date, the bulk ETrF computed by METRIC for a pixel, is

where ETrFtranspiration is the apparent transpiration from the fraction of ground covered by vegetation, fc. The fc is estimated as 1 – fs, where fs is the fraction of bare soil, and for

> cov cov

*<sup>f</sup> NDVI NDVI* 

*<sup>f</sup> NDVI NDVI* 

METRIC, etc.). However, one can rearrange Eq. 31 to solve for ETrFtranspiration :

*ET F f ET F f ET F*

*r i adjusted c r background c r transpiration adjusted*

*NDVI NDVI*

cov cov 1 *full er <sup>i</sup>*

Eq. 31 is not used as is, since ETrFi comes from the energy balance-based ET image (i.e., from

Now, if ETrFtranspiration is limited to the maximum of the ETrFtranspiration on the day of the

max , *r transpiration r transpiration r background adjusted <sup>i</sup>*

*ET F f ET F f ET F ET F*

(1 ) max ,

*r i c r background c r transpiration r background adjusted <sup>i</sup>*

where *ET Fr background* is the average evaporation from bare soil due to precipitation over the averaging period (e.g., one month) and ETrFtranspiration is the original transpiration computed

*NDVI NDVI*

*full er i*

*full er baresoil*

*full er baresoil*

*c r trans piration r i c r back* (1 ) *ground i i f ET F ET F f ET F* (33)

*ET F ET F ET F* (34)

*r i c r back* (1 ) *ground c r trans piration i i ET F f ET F f ET F* (31)

(32a)

(32b)

(35)

placed, using the background ETrF *ET Fr background* for the period.

consistency with equations 30, fs is estimated as:

*s*

*c*

image, or the *ET Fr background* for the period, then:

(1 )

from Eq. 33. Eq. 33 and 35 can be combined so that:

Then the new ETrF adjusted value becomes:

*or*

decomposed to:

so that:

$$\begin{aligned} \left(ET\_rF\_i\right)\_{\text{adjusted}} &= \left(1 - f\_c\right)\left(ET\_rF\_{\text{background}}\right) + \\ &+ \max\left[\left(ET\_rF\_i - \left(1 - f\_c\right)\left(ET\_rF\_{\text{background}}\right)\_i\right)\_i, f\_c\left(\overline{ET\_rF\_{\text{background}}}\right)\_i\right] \end{aligned} \tag{36}$$

Only areas with bare soil or partial vegetation cover are adjusted. Pixels having full vegetation cover, defined as when NDVI > 0.75, are not adjusted. An example of an image date where the adjustment increased the ETrF for bare soil and partially vegetated areas is shown in Figure 2. Figure 3 shows an example of an image date where the ETrF from bare soil and partial vegetation cover was decreased by the adjustment.

Fig. 2. ETrF in western Nebraska from May 9 1997 before (left) and after (right) adjustment for background evaporation representing the time period (~month) represented by that image. After Kjaersgaard and Allen (2010).

Fig. 3. ETrF in western Nebraska on August 13 1997 before (left) and after (right) adjustment to reflect soil evaporation occurring over the time period (~ 1 month) represented by that image. Note that irrigated fields with full vegetation cover having a substantial transpiration component were not affected by the adjustment. After Kjaersgaard and Allen (2010).

Fig. 4. Average ETrF from ten rangeland locations in western Nebraska before and after adjustment. Also shown is the precipitation from the Scottsbluff HPRCC weather station (after Kjaersgaard and Allen 2010).

Fig. 5. Schematic representation of the linear cloud gap filling and the cubic spline used to interpolate between image dates for a corn crop. The green points represent image dates and the black line is the splined interpolation between points; the red point represents the value of ETrF that is interpolated linearly from the two adjacent image dates had the field had cloud cover on September 10.

Fig. 4. Average ETrF from ten rangeland locations in western Nebraska before and after adjustment. Also shown is the precipitation from the Scottsbluff HPRCC weather station

Fig. 5. Schematic representation of the linear cloud gap filling and the cubic spline used to interpolate between image dates for a corn crop. The green points represent image dates and the black line is the splined interpolation between points; the red point represents the value of ETrF that is interpolated linearly from the two adjacent image dates had the field had

(after Kjaersgaard and Allen 2010).

cloud cover on September 10.

Average ETrF on image dates before and after adjustment for background evaporation is shown in Figure 4 from ten rangeland locations in western Nebraska. For some image dates, such as early and late in the season, the adjusted ETrF values are "wetter" than that represented by the original image. Similarly, for other images dates, such as in the middle of the growing season, the images were "drier". The adjustment for one image in August reduced the estimated ET for the month of August by nearly 50%, which is considerable.

It is noted, that the images no longer represent the ET from the satellite overpass dates after the adjustment for background evaporation. The images are merely an intermediate product that is used as the input into an interpolation procedure when producing ET estimates for monthly or longer time periods.

## **4. Dealing with clouded parts of images**

Satellite images often have clouds in portions of the images. ETrF cannot be directly estimated for these areas using surface energy balance because cloud temperature masks surface temperature and cloud albedo masks surface albedo. Generally ETrF for clouded areas must be filled in before application of further integration processes so that those processes can be uniformly applied to an entire image. The alternative is to directly interpolate ETrF between adjacent (in time) image dates or to run some type of daily ET process model that is based on gridded weather data.

In METRIC applications (Allen et al. 2007b), ETrF for clouded areas of images is usually filled in prior to interpolating ETrF for days between image dates (and multiplying by gridded ETr for each day to obtain daily ET images). A linear interpolation, as shown in Figure 5, is used to fill in ETrF for clouded portions of images rather than curvilinear interpolation that is used to interpolate ETrF between nonclouded image portions because some periods between cloud-free pixel locations can be as long as several months. Often, the change in crop vegetation amount and thus ETrF is uncertain during that period. Thus, the use of curvilinear interpolation can become speculative.

Image processing code can be created to conduct the 'filling' of cloud masked portions of images. The code used with METRIC accommodates up to eight image dates and corresponding ETrF, with conditionals used to select the appropriate set of images to interpolate between, depending on the number of consecutive images that happen to be cloud masked for any specific location. Missing (clouded) ETrF for end-member images (those at the start or end of the growing season) must be estimated by extrapolation of the nearest (in time) image having valid ETrF, or alternatively, for end-member images, a 'synthetic' image can be created, based on daily soil water balance or other methods, to be used to substitute for cloud-masked areas. Often, the availability of images for early spring is limited due to clouds. In these cases, the ETrF values in the synthetic image are based on a soil-water balance–weather data model, such as the FAO-56 evaporation model or Hydrus or DAISY, applied over the month of April, for example, to provide an improved estimate of ETrF over the early season. The synthetic image(s) are strategically placed, date-wise, so that the cloud-filling process and the subsequent cubic spline process used to interpolate final ETrF has end-points early enough in the year to provide ETrF for all days of interest during the growing period.

Examples of cloud masking for a METRIC application in western Nebraska are shown in Figure 6. Black portions within each image are the areas masked for clouds. ETrF for cloud masked areas was filled in for individual Landsat dates prior to splining ETrF between images. The cloud mask gap filling and interpolation of ET between image dates entails interpolating the ETrF for the missing area from the previous and following images that have ETrF for that location.

Fig. 6. Maps of cloud masked ETrF from seven 1997 images dates. The geographical extent of the North Platte and South Platte Natural Resource Districts boundaries and principal cities is shown on the image in the top left corner (after Kjaersgaard and Allen 2010).

In current METRIC applications, gaps in the ETrF maps occurring as a result of the cloud masking are filled in using linear time-weighted interpolation of ETrF values from the previous image and the nearest following satellite image date having a valid ETrF estimate, adjusted for vegetation development. The NDVI is used to indicate change in vegetation amount from one image date to the next. The principle is sketched in Figure 7, where a location in the two nearest images (i-1 and i+1) happen to be clouded. During the gap filling, the interpolated values for the clouded and cloud-shadowed areas are adjusted for differences in residual soil moisture between the image dates occurring as a result of heterogeneities in precipitation (such as by local summer showers) in inverse proportion to NDVI and by adding an interpolated 'basal' ETrF from the previous and following satellite image dates. This procedure is needed to remove artifacts of this precipitation-derived evapotranspiration that are unique to specific image dates but that may not be representative of the image date that is to be represented by the ETrF from the previous and

masked areas was filled in for individual Landsat dates prior to splining ETrF between images. The cloud mask gap filling and interpolation of ET between image dates entails interpolating the ETrF for the missing area from the previous and following images that

Fig. 6. Maps of cloud masked ETrF from seven 1997 images dates. The geographical extent of the North Platte and South Platte Natural Resource Districts boundaries and principal cities

In current METRIC applications, gaps in the ETrF maps occurring as a result of the cloud masking are filled in using linear time-weighted interpolation of ETrF values from the previous image and the nearest following satellite image date having a valid ETrF estimate, adjusted for vegetation development. The NDVI is used to indicate change in vegetation amount from one image date to the next. The principle is sketched in Figure 7, where a location in the two nearest images (i-1 and i+1) happen to be clouded. During the gap filling, the interpolated values for the clouded and cloud-shadowed areas are adjusted for differences in residual soil moisture between the image dates occurring as a result of heterogeneities in precipitation (such as by local summer showers) in inverse proportion to NDVI and by adding an interpolated 'basal' ETrF from the previous and following satellite image dates. This procedure is needed to remove artifacts of this precipitation-derived evapotranspiration that are unique to specific image dates but that may not be representative of the image date that is to be represented by the ETrF from the previous and

is shown on the image in the top left corner (after Kjaersgaard and Allen 2010).

have ETrF for that location.

the following images. A comparison between cloud gap filling without and with adjustment for background evaporation is shown in Figure 8. An additional example from Singh et al. (2008) is shown in Figure 9 for central Nebraska, where filled in areas that were clouded are difficult to detect due to the adjustment for background evaporation via a daily process model.

Fig. 7. Principle of cloud gap filling. "i" is the image having cloud masked areas to be filled; "i-1" and "i-2" are the two earlier images than image I; "i+1" and "i+2" are the two following images.

Fig. 8. Maps of ETrF from Landsat 5, July 12 1997, in western Nebraska after cloud masking (left) (black indicate areas removed during cloud masking or background); and after cloud gap filling without (center) and with (right) adjustment for vegetation amount and background evaporation from antecedent rainfall. The August 13 image from which part of the ETrF data was borrowed was quite wet from precipitation, and thus had high ETrF for low-vegetated areas, and therefore created substantially overestimated ETrF for July 12 in the filled areas (center). After Kjaersgaard and Allen (2010).

Fig. 9. ETrF product for August 20, 2007 over the Central Platte Natural Resources District, Nebraska, with clouded areas masked (top) and filled (bottom) using a procedure that adjusted for background evaporation from antecedent precipitation events (after Singh et al., 2008).

## **5. Other remaining challenges with operational models for spatial ET**

In addition to challenges in producing daily time series of spatial ET, as described in the previous section, other challenges remaining with all models, snapshot and process models alike include the following. These were described by Allen et al., (2010) and include estimation of aerodynamic roughness at 30 m scale; aerodynamic roughness and wind speed variation in complex terrain and in tall, narrow vegetation systems such as riparian systems; and estimation of hemispherical reflectance from bi-direction reflectance in deep vegetation canopies from nadir-looking satellites such as Landsat. Other remaining challenges include estimation of soil heat and aerodynamic sensible heat fluxes in sparse desert systems and in playa and estimation of ET over 24-hour periods using one-time of day observation (for example ~1000 solar time for Landsat) based on energy balance, especially where substantial stomatal control exists (desert and forest). METRIC capitalizes on using weather-based reference ET to make this transfer over time, which has been shown

to work well for irrigated crops, especially in advective environments (Allen et al. 2007a). However, the evaporative fraction, as used in early SEBAL (Bastiaanssen et al. 1998a) and other models may perform best for rainfed systems where, by definition, advection can not exist. Therefore, a mixture of ETrF and EF may be optimal, based on land-use class.

## **6. Conclusions**

488 Evapotranspiration – Remote Sensing and Modeling

Fig. 9. ETrF product for August 20, 2007 over the Central Platte Natural Resources District, Nebraska, with clouded areas masked (top) and filled (bottom) using a procedure that adjusted for background evaporation from antecedent precipitation events (after Singh et

In addition to challenges in producing daily time series of spatial ET, as described in the previous section, other challenges remaining with all models, snapshot and process models alike include the following. These were described by Allen et al., (2010) and include estimation of aerodynamic roughness at 30 m scale; aerodynamic roughness and wind speed variation in complex terrain and in tall, narrow vegetation systems such as riparian systems; and estimation of hemispherical reflectance from bi-direction reflectance in deep vegetation canopies from nadir-looking satellites such as Landsat. Other remaining challenges include estimation of soil heat and aerodynamic sensible heat fluxes in sparse desert systems and in playa and estimation of ET over 24-hour periods using one-time of day observation (for example ~1000 solar time for Landsat) based on energy balance, especially where substantial stomatal control exists (desert and forest). METRIC capitalizes on using weather-based reference ET to make this transfer over time, which has been shown

**5. Other remaining challenges with operational models for spatial ET** 

al., 2008).

Satellite-based models for determining evapotranspiration (ET) are now routinely applied as part of water and water resources management operations of state and federal agencies. The very strong benefit of satellite-based models is the quantification of ET over large areas. Strengths and weaknesses of common EB models often dictate their use. The more widely used and operational remote sensing models tend to use a 'CIMEC' approach ("calibration using inverse modeling of extreme conditions") to calibrate around uncertainties and biases in satellite based energy balance components. Creating 'maps' of ET that are useful in management and in quantifying and managing water resources requires the computation of ET over monthly and longer periods such as growing seasons or annual periods. This requires accounting for increases in ET from precipitation events in between images. An approach for estimating the impacts on ET from wetting events in between images has been described. This method is empirical and can be improved in the future with more complex, surface conductance types of process models, such as used in Land surface models (LSM's). Interpolation processes involve treatment of clouded areas of images, accounting for evaporation from wetting events occurring prior to or following overpass dates, and applying a grid of daily reference ET with the relative ET computed for an image, or a direct Penman-Monteith type of calculation. These approaches constitute a big step forward in computing seasonal ET over large areas with relatively high spatial (field-scale) definition, where impacts of intervening wetting events and cloud occurrence are addressed.

## **7. References**


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## **Adaptability of Woody Plants in Aridic Conditions**

Viera Paganová and Zuzana Jureková *Slovak University of Agriculture in Nitra Slovak Republic* 

## **1. Introduction**

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assess within-population variance of crop coefficient curves, *J. Irrig. and Drain.* 

parameters in the oasis-desert systems of Northwest China. *Hydr. Processes* 12:2133-

Ecological conditions and sources such as water, temperature, solar radiation, and carbon dioxide concentration are factors that limit plant growth, development, and reproduction. Deviations from the optimal values of these factors can cause stress. Plants are subjected to multiple abiotic and biotic stresses that adversely influence plant survival and growth by inducing physiological dysfunctions (Kozlowski & Pallardy, 2002). On the other hand, plants use different strategies for survival that are important for their distribution throughout various regions. Plants differ widely in their ability to adjust to a changing environment and the associated stress (Itail et al., 2002), including the ability to cope with drought (Kozlowski Pallardy 1997).

Water deficiency is the most significant stress factor for plant growth and reproduction. Drought is mostly associated with the dieback of trees within various regions and throughout the world (Mc Dowel et al., 2008). However, physiological mechanisms of woody plant survival have not yet been described. According to Passioura (2002a), all mechanisms that support physiological functions of plants under conditions of limited water availability are mechanisms of stress resistance. These mechanisms have developed over a long period of time as part of plant adaptability. According to Jones (1993), there are three mechanisms for plant drought resistance. The first mechanism consists of avoiding water deficit and involves the limitation of transpiration and maximisation of root uptake. The second mechanism involves the tolerance to water deficit (Passioura, 2002b; Gielen et al., 2008), and the third mechanism optimises the utilisation of water (Jones 2004).

Plant water stress is the result of a disproportionate balance between the amount of received and released water through various interactions with plant growth, development, and biomass production. The interactions are modified by genetic properties of the specimen and by the character and degree of plant adaptation. The amount of water that a plant can receive depends on the water supply in the soil and on eco-physiological characteristics of plant roots. The transport of water enables for a potential water gradient between the atmosphere and soil, and depends on the hydraulic resistance of the root and stem vascular system. Another component of the water regime of plants – release through transpiration – is a function of the physiological availability and mobility of the water. Plant regulation of the stomata opening and transpiration depend on the pressure potential and other influencing factors. Maintenance of a positive pressure potential is therefore conditional for the survival of plants under drought. The water regime of plants is therefore an ensemble of the physical and physiological rules of the water transport within the soil-plant-atmosphere continuum.

## **2. Distribution of the wild pear** *Pyrus pyraster* **(L.) Burgsd. and service tree** *Sorbus domestica* **L. in Slovakia**

The wild pear and service tree are members of the rare woody plants in Slovakia. The wild pear often grows in the scattered vegetation of the landscape, but also on the forest margins mainly in communities of oak stands. The service tree appears mostly in the rural landscape, and mainly in vineyards and fruit orchards. In many European countries, wild pear and service tree are often sought after by landscape designers and foresters, because both species have aesthetic influence in the landscape, a good growth rate, and provide valuable timber.

The vertical distribution of wild pear has been documented mainly at lower altitudes up to 400 m (Hofmann, 1993; Schmitt, 1998; Wilhelm, 1998). The highest location found was at an altitude of 754 m in bundesland Süd-Niedersachsen und Nordhessen (Schmitt, 1998).

In Slovakia, wild pear grows in the lowlands to sub-mountain areas, up to an approximate altitude of 950 m (Peniašteková, 1992), and in some cases up to an altitude of 1163 m (Blattný & Šťastný, 1959). A detailed study on the environmental conditions of stands where wild pear naturally occurs was conducted in 1994-1999 (Paganová, 2003). The basic data were obtained from 64 locations (Fig. 1).

Stands with wild pear were located mostly on grazing lands, meadows, and in the scattered woodlands. Wild pear populations were also found along a dry stream channel (locality 8) and in a thin forest (location 21). Wild pear often grows on the forest edge (locations 30, 34, 41, and 48), or on former grazing land that gradually changed to woodlands (location 42, 55, and 56).

The majority of stands with wild pear (80%) were found at altitudes up to 500 m. The lowest location in Slovakia was at an altitude of 100 m (12 Solnička), and the highest analysed stand was at an altitude of 800 m (19 Jezersko) (Paganová, 2003).

Fig. 1. Distribution of the wild pear *(Pyrus pyraster)* populations in the territory of Slovakia (Paganová, 2003).

the physical and physiological rules of the water transport within the soil-plant-atmosphere

The wild pear and service tree are members of the rare woody plants in Slovakia. The wild pear often grows in the scattered vegetation of the landscape, but also on the forest margins mainly in communities of oak stands. The service tree appears mostly in the rural landscape, and mainly in vineyards and fruit orchards. In many European countries, wild pear and service tree are often sought after by landscape designers and foresters, because both species have aesthetic influence in the landscape, a good growth rate, and provide valuable timber. The vertical distribution of wild pear has been documented mainly at lower altitudes up to 400 m (Hofmann, 1993; Schmitt, 1998; Wilhelm, 1998). The highest location found was at an

**2. Distribution of the wild pear** *Pyrus pyraster* **(L.) Burgsd. and service** 

altitude of 754 m in bundesland Süd-Niedersachsen und Nordhessen (Schmitt, 1998).

In Slovakia, wild pear grows in the lowlands to sub-mountain areas, up to an approximate altitude of 950 m (Peniašteková, 1992), and in some cases up to an altitude of 1163 m (Blattný & Šťastný, 1959). A detailed study on the environmental conditions of stands where wild pear naturally occurs was conducted in 1994-1999 (Paganová, 2003). The basic data

Stands with wild pear were located mostly on grazing lands, meadows, and in the scattered woodlands. Wild pear populations were also found along a dry stream channel (locality 8) and in a thin forest (location 21). Wild pear often grows on the forest edge (locations 30, 34, 41, and 48), or on former grazing land that gradually changed to woodlands (location 42,

The majority of stands with wild pear (80%) were found at altitudes up to 500 m. The lowest location in Slovakia was at an altitude of 100 m (12 Solnička), and the highest analysed stand

Fig. 1. Distribution of the wild pear *(Pyrus pyraster)* populations in the territory of Slovakia

continuum.

55, and 56).

(Paganová, 2003).

**tree** *Sorbus domestica* **L. in Slovakia** 

were obtained from 64 locations (Fig. 1).

was at an altitude of 800 m (19 Jezersko) (Paganová, 2003).

The service tree is one of the rare autochthonous woody plants in the entire area of natural distribution. The area of natural distribution of the service tree reaches the northern part of Asia Minor and Africa as well as the northern border crosses of North Rhine-Westphalia, Lower Saxony, Saxony-Anhlat, and Thüringen, Bavaria. The northernmost occurrence is located in the Federal Republic of Germany at approximate latitude 51º of north width (Haeupeler & Schönfelder, 1988), and then continues to South Moravia and Slovakia, Hungary, Romania, and Crimea Mt.

According to Májovský (1992), the service tree has higher demands for light and high temperatures. In Slovakia, it is cultivated in the uplands on sunny south and southwest exposed stands. The vertical distribution of this woody plant occurs at an altitude of 109 m (Benčať, 1995) or 175 m (Michalko, 1961) up to an altitude of 610 m (Michalko, 1961; Benčať, 1995).

In 1996-2000, the environmental conditions of 24 locations of the service tree were analysed (Paganová, 2008). In Slovakia, the service tree appears in the southern regions in warmer stands at lower altitudes (Fig. 2). The distribution of the analysed stands containing the service tree confirmed its occurrence mainly at lower altitudes. The lowest stand with the service tree was found at an altitude of 200 m (location 23 - Vinné), and the highest stand was found at an altitude of 490 m (location 1 - Predpoloma) (Fig. 2).

The majority of the analysed stands containing the service tree (50%) were located in an open landscape near vineyards and fruit orchards (location 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 21, and 22). The service tree was frequently (46% of analysed stands) found in abandoned fruit orchards or on grazing lands as well (location 1, 2, 3, 4, 5, 6, 7, 19, and 20). Only a few plants were found in woodlands (location 23 and 24) and one stand of service tree (location 8) was located in an oak forest.

According to the analysis of the vertical distribution (Fig. 3), the service tree grows mainly on uplands in Slovakia. Approximately 66% of the analysed stands were found at an

Fig. 2. Location of the stands with a higher number of service trees (*Sorbus domestica*) in Slovakia (Paganová, 2008).

Fig. 3. Distribution of wild pear (*Pyrus pyraster*) and service tree (*Sorbus domestica*) in Slovakia according to stand altitude.

altitude of 201–300 m, and 26% of the stands were at an altitude of 301–400 m. One location was at altitudes of 450 m and 490 m. Compared to the wild pear (Fig. 3), the service tree is absent from the lowlands, and the occurrence of this woody plant at altitudes above 400 m is rare. According to Kárpáti (1960), the service tree is frequently found within communities of oak forests at lower altitudes and on fertile soils in communities of *Lithospermo*-*Quercetum*, *Melico* (*uniflorae*)-*Quercetum petraeae,* and others. Michalko (1961) confirmed the findings by Kárpáti, but according to his opinion, the service tree grows at higher altitudes only in extreme communities of *Corneto-Quercetum* (*pubescentis* and *petraeae*), and can even be found in the beech woodland *Corneto*-*Fagetum* and in relict pinewoods growing on limestone and dolomite parent rock.

Similar to the data mentioned above, very similar findings regarding the range of altitudinal distribution were found in Switzerland. In this country, the service tree was found within an altitude of 384 m in the Basel region and 675 m in the Schaffhausen region (Brütsch & Rotach, 1993). In the southeast section of the Wiener Wald in the area of Merkenstein, the service tree has been found up to an altitude of 550 m (Steiner, 1995). At the northern border of its natural distribution in Germany in the region of Sachsen-Anhalt, the service tree is distributed from 140 m to 310 m, and predominantly within an altitude of 161-240 m (Steffens, 2000). On the Plateau of Lorraine, the service tree appears in forest crops at an altitude of 200-400 m (Wilhelm, 1998).

In southern regions of the natural distribution, the service tree grows at higher altitudes than in Slovakia. For example, in Spain, it grows at altitudes up to 1400 m, in Greece up to 1350 m, in Turkey up to 1300 m, and in southern Bulgaria from 300 to 800 m (Kausch, 2000). In southern Italy (Mt. Vesuvius), the service tree grows from the banks of the sea up to an altitude of 800 m (Bignami, 2000).

Fig. 3. Distribution of wild pear (*Pyrus pyraster*) and service tree (*Sorbus domestica*) in

*Pyrus pyraster Sorbus domestica*

altitude of 201–300 m, and 26% of the stands were at an altitude of 301–400 m. One location was at altitudes of 450 m and 490 m. Compared to the wild pear (Fig. 3), the service tree is absent from the lowlands, and the occurrence of this woody plant at altitudes above 400 m is rare. According to Kárpáti (1960), the service tree is frequently found within communities of oak forests at lower altitudes and on fertile soils in communities of *Lithospermo*-*Quercetum*, *Melico* (*uniflorae*)-*Quercetum petraeae,* and others. Michalko (1961) confirmed the findings by Kárpáti, but according to his opinion, the service tree grows at higher altitudes only in extreme communities of *Corneto-Quercetum* (*pubescentis* and *petraeae*), and can even be found in the beech woodland *Corneto*-*Fagetum* and in relict pinewoods growing on limestone and

100-200 201-300 301-400 401-500 501-600 601-700 701-800 **altitude (m)**

Similar to the data mentioned above, very similar findings regarding the range of altitudinal distribution were found in Switzerland. In this country, the service tree was found within an altitude of 384 m in the Basel region and 675 m in the Schaffhausen region (Brütsch & Rotach, 1993). In the southeast section of the Wiener Wald in the area of Merkenstein, the service tree has been found up to an altitude of 550 m (Steiner, 1995). At the northern border of its natural distribution in Germany in the region of Sachsen-Anhalt, the service tree is distributed from 140 m to 310 m, and predominantly within an altitude of 161-240 m (Steffens, 2000). On the Plateau of Lorraine, the service tree appears in forest crops at an

In southern regions of the natural distribution, the service tree grows at higher altitudes than in Slovakia. For example, in Spain, it grows at altitudes up to 1400 m, in Greece up to 1350 m, in Turkey up to 1300 m, and in southern Bulgaria from 300 to 800 m (Kausch, 2000). In southern Italy (Mt. Vesuvius), the service tree grows from the banks of the sea up to an

Slovakia according to stand altitude.

altitude of 200-400 m (Wilhelm, 1998).

altitude of 800 m (Bignami, 2000).

dolomite parent rock.

0

10

20

30

40

50

60

70

**(%)**

## **3. Ecological characteristics of the stands with** *Pyrus pyraster* **(L.) Burgsd. and** *Sorbus domestica* **L.**

The wild pear is considered to be a light-demanding woody plant, which prefers warm stands with a sufficient amount of sunlight (Namvar & Spethman 1986; Hofmann, 1993; Wagner, 1995; Kleinschmit & Svolba 1998; Schmitt, 1998; Rittershoffer, 1998; Roloff, 1998; Wilhelm, 1998). Hofmann (1993) previously created a diagram for the occurrence of 300 wild pear plants according to the stand exposure. The plants were predominantly in locations with south and southwest exposures. In support of these findings, Roloff (1998) also found that the most frequent occurrence of wild pear plants was on slopes with a south or west exposure.

The service tree is explicitly regarded as a light-demanding woody plant (Michalko, 1961; Májovský, 1992; Brütsch & Rotach, 1993; Pagan, 1996; Wilhelm, 1998). In Slovakia, 96% of stands with the service tree were found in the open landscape with solitary trees. Two stands were on the margin of woodlands with a few service trees in the crop, and only one location was an oak forest, with service trees found in the upper tree canopy or slightly above it. In all of these stands, the individual service trees grew under nearly full light without competition from other woody plants (Paganová, 2008). The service tree is intolerant to shading at an early age, and similar to the wild pear, will die quickly without a minimum light supply (Wilhelm, 1998).

Based on data obtained on the distribution of 507 wild pear plants in Slovakia, the majority of stands (80%) had a south, southeast, or southwest exposure. However, a limited number of stands (14%) containing wild pears were also found to have west, east, or northwest exposures, and four locations (6%) were on a plain stand (Fig. 4).

Fig. 4. The distribution of locations with wild pear (*Pyrus pyraster*) and service tree (*Sorbus domestica*) in Slovakia according to stand exposure.

In comparison to the wild pear, a majority of stands with service trees (38%) had a southern exposure, and many locations also had southeast (33%) and southwest (25%) exposures. One location (4%) had a western exposure. According to measurements by Geiger (1961), slopes with northern exposure obtain just half of the absolute total light emission as slopes with southern exposure. The prevalent distribution of service trees in southern-exposed stands supports the hypothesis regarding their high demand of light and warm climate. In Slovakia, none of the analysed locations had northern exposure. In Switzerland, 74% of the locations with service trees had southern exposure (Brütsch & Rotach, 1993).

The ecological-climatic amplitude of the wild pear locations in Slovakia is relatively wide. In stands with wild pear plants, the conditions range from plain and fold climates, to a mountain climate (Paganová, 2003). Stands were classified to climate-geographic types and subtypes according to Tarábek (1980) and Špánik et al. (1999).

Within the analysed scale of the wild pear stands in Slovakia, the average January temperatures range from -1.4ºC to -5.8ºC and the average July temperatures range from 13.5ºC to 20.4ºC. The annual sum of precipitation reaches values ranging from 570 mm to 900 mm. The majority of the pear locations (53%) fall within the climate-geographic type of mountain climate (Fig. 5), which is humid or very humid with rare temperature inversion. These stands were most frequently found in the warm and moderately warm subtypes of the mountain climate at an altitude of 250-550 m. The average January temperatures range from -1.4ºC to -5.0ºC, the average July temperatures range from 17.0ºC to 20.4ºC, and the annual sum of precipitation for these stands ranges from 580 mm to 790 mm.

Stands within the warm subtype of the fold climate are observed quite frequently. The fold climate is semi-humid to semi-arid with a remarkable inversion of temperatures. These locations are at altitudes of 210-450 m. The average January temperatures range from -2.0ºC to -4.0ºC, the average July temperatures range from 18.0ºC to 19.2ºC, and the annual sum of precipitation ranges from 628 mm to 765 mm in the respective locations.

The lowest number of wild pear locations was documented for stands in the warm or mostly warm subtypes of the plane climate, which is arid and semi-arid. Locations were registered at altitudes of 120-400 m. The average January temperatures in these stands range from -1.5ºC to -3.3ºC, and the average July temperatures range from 17.2ºC to 20.1ºC. The annual sum of precipitation is 570-700 mm.

The climate–geographic characteristics of stands with service trees are slightly different than stands containing wild pears (Fig. 5). The climate with the highest number of locations (42%) belongs to the mostly warm subtype of the plane climate, which is arid or semi-humid with a mild inversion of air temperatures. These stands are at an altitude of 200-300 m. The average annual temperature ranges from 8.3°C to 9.0°C, and the annual sum of precipitation is 610–650 mm.

A high number of stands (33%) were classified in the mountain climate with a mild inversion of air temperatures (the climate is rather humid). These stands are at an altitude of 220-490 m. The average annual temperature is 8.3°C and the annual sum of precipitation ranges from 650 to 620 mm.

The climate with the fewest locations of service trees was the fold climate (25%), which has a markedly high inversion of air temperatures (with an arid or even humid climate). The stand altitude ranges from 250 m to 380 m, the annual average temperature ranges between 8.1–8.5°C, and the annual sum of precipitation is 620–700 mm.

According to a recent climatic evaluation (Škvarenina et al., 2004), the annual average temperature of the majority of locations with service trees is above 8°C, with the exception

In comparison to the wild pear, a majority of stands with service trees (38%) had a southern exposure, and many locations also had southeast (33%) and southwest (25%) exposures. One location (4%) had a western exposure. According to measurements by Geiger (1961), slopes with northern exposure obtain just half of the absolute total light emission as slopes with southern exposure. The prevalent distribution of service trees in southern-exposed stands supports the hypothesis regarding their high demand of light and warm climate. In Slovakia, none of the analysed locations had northern exposure. In Switzerland, 74% of the

The ecological-climatic amplitude of the wild pear locations in Slovakia is relatively wide. In stands with wild pear plants, the conditions range from plain and fold climates, to a mountain climate (Paganová, 2003). Stands were classified to climate-geographic types and

Within the analysed scale of the wild pear stands in Slovakia, the average January temperatures range from -1.4ºC to -5.8ºC and the average July temperatures range from 13.5ºC to 20.4ºC. The annual sum of precipitation reaches values ranging from 570 mm to 900 mm. The majority of the pear locations (53%) fall within the climate-geographic type of mountain climate (Fig. 5), which is humid or very humid with rare temperature inversion. These stands were most frequently found in the warm and moderately warm subtypes of the mountain climate at an altitude of 250-550 m. The average January temperatures range from -1.4ºC to -5.0ºC, the average July temperatures range from 17.0ºC to 20.4ºC, and the

Stands within the warm subtype of the fold climate are observed quite frequently. The fold climate is semi-humid to semi-arid with a remarkable inversion of temperatures. These locations are at altitudes of 210-450 m. The average January temperatures range from -2.0ºC to -4.0ºC, the average July temperatures range from 18.0ºC to 19.2ºC, and the annual sum of

The lowest number of wild pear locations was documented for stands in the warm or mostly warm subtypes of the plane climate, which is arid and semi-arid. Locations were registered at altitudes of 120-400 m. The average January temperatures in these stands range from -1.5ºC to -3.3ºC, and the average July temperatures range from 17.2ºC to 20.1ºC. The

The climate–geographic characteristics of stands with service trees are slightly different than stands containing wild pears (Fig. 5). The climate with the highest number of locations (42%) belongs to the mostly warm subtype of the plane climate, which is arid or semi-humid with a mild inversion of air temperatures. These stands are at an altitude of 200-300 m. The average annual temperature ranges from 8.3°C to 9.0°C, and the annual sum of precipitation

A high number of stands (33%) were classified in the mountain climate with a mild inversion of air temperatures (the climate is rather humid). These stands are at an altitude of 220-490 m. The average annual temperature is 8.3°C and the annual sum of precipitation

The climate with the fewest locations of service trees was the fold climate (25%), which has a markedly high inversion of air temperatures (with an arid or even humid climate). The stand altitude ranges from 250 m to 380 m, the annual average temperature ranges between

According to a recent climatic evaluation (Škvarenina et al., 2004), the annual average temperature of the majority of locations with service trees is above 8°C, with the exception

locations with service trees had southern exposure (Brütsch & Rotach, 1993).

annual sum of precipitation for these stands ranges from 580 mm to 790 mm.

precipitation ranges from 628 mm to 765 mm in the respective locations.

8.1–8.5°C, and the annual sum of precipitation is 620–700 mm.

annual sum of precipitation is 570-700 mm.

is 610–650 mm.

ranges from 650 to 620 mm.

subtypes according to Tarábek (1980) and Špánik et al. (1999).

Fig. 5. Wild pear (*Pyrus pyraster*) and service tree (*Sorbus domestica*) stand classification in Slovakia according to climate-geographic types.

of two of the analysed locations (1 and 5), where the annual average temperature ranges from 7.5°C to 7.7°C. The average annual sum of precipitation for the majority of the stands is 610–700 mm, with the exception of the two mentioned locations, where this parameter reaches 790 mm and 750 mm, respectively. The potential evapotranspiration amount in the majority of the analysed stands was 600–750 mm during one year. Considering that the annual average sum of precipitation is 610–700 mm, it is possible that the service tree has to obtain enough moisture during the main growing season predominantly from water resources in soil. The deficit of rain during the summer occurs in the majority of the stands with this woody plant.

Warm and arid (southeast, south, southwest, and even west) stand exposures play an important role in the formation of the arid microclimate and mezzo-climate of the mentioned locations. According to climate classification in Slovakia (Špánik et al., 1999), the analysed locations with service trees were in warm and even moderately warm as well as semi-humid and even semi-arid climates. Compared to the wild pear, the service tree prefers stands at lower altitudes and is prevalent in warm and arid climates. The wild pear has wider ecological amplitude and grows at higher altitudes in stands with different water regimes and climate extremes.

Based on the brief pedology characteristics of our experimental plots, we can hypothesize that these soils are very well fertile (Chernozem, Fluvi-mollic soils, Cambisols, and Orthic Luvisols) or well supplied with nutrients (Luvisols, Pararendzinas, and Fluvisols). In addition, browned Rendzinas can be considered as relatively favourable soils.

According to the ecological scheme of Ellenberg (1978), the wild pear is a woody plant with broad ecological amplitude that grows in nearly all soil types, with the exception of extreme acidic soils. Rittershoffer (1998) found that mildly acidic or mildly alkaline soils were optimal for wild pear growth. According to information from Westfalen-Lippe (Germany), the wild pear prefers soils developed on limestone or on the rich nutrient parent rocks (80% of stands) (Schmitt, 1998). In the area of Süd-Niedersachsen und Nordhessen (Germany), the wild pear frequently grows in shallow rendzinas from mussel limestone or from lime sandstone, and very rarely appears on deeper brown forest soils. More than 92% of all natural stands were on rich basic rocks (Hofmann, 1993). In the forest on the Plateau Lorraine, the wild pear grows mainly on parent rock of the mussel limestone and on keuper sediments. There are deep terra fusca soils and shallow Rendzinas (Wilhelm, 1998). The colective data from different areas of the natural distribution indicate that suitable growth conditions for the wild pear are mainly basic and rich nutrient soils with occasional water deficits.

In Slovakia, the wild pear grows on fertile soils (Chernozem, Fluvi-mollic soils, Cambisols, and Orthic Luvisols), or soils well supplied with nutrients (Albic Luvisol, Pararendzina, and Fluvisol). In addition, in some stands it grows on soils that are rich in minerals but under conditions of unbalanced soil chemistry with little fertility (Paganová, 2003).

In general, Fluvi-mollic and Cambisol soils have a sufficient water supply. At lower altitudes, the water deficit appears mainly in Rendzinas. The water deficit in Luvisols is usually a result of a lower amount of precipitation and higher evaporation. Orthic Luvisols have a lower water supply, and therefore the possibility of their aridization is higher. In addition, a fluctuating water regime appears within the Planosols and Fluvisols (Šály, 1988).

According to the ecological scheme by Ellenberg (1978), the wild pear has optimal growth conditions on fresh basic soils (its potential optimum). Another more frequent existence optimum of this woody plant is near the xeric forest limit, where the wild pear grows in arid soils rich in bases as well as in moderately acidic soils. Some authors have placed the wild pear among xerophytic woody plants according to its lower demands on soil humidity (Bouček, 1954). When under competition with some woody plants, it grows on its synecological optimum in extreme arid stands - rocky hilltops, stands of the xeric forest limit close to steppe communities, and in the sparse xerophytic oak woodlands (Rittershoffer, 1998). However, another existence optimum of this woody plant occurs in the hydric forest boundary in stands of the hardwood floodplain forests, where wild pear growth is limited by inundation (Rittershoffer, 1998). Based on these findings, the wild pear is a flexible woody plant with tolerance to a large range of soil humidity.

In Slovakia, stands with the service tree have favourable physical characteristics, good saturation, and are very fertile (Orthic-Luvisols and Cambisols), or have soils that are well supplied with nutrients (Rendzinas). However, under conditions of unbalanced soil chemistry, there is little fertility, and the pH of this soil is moderately acidic, neutral, or moderately alkaline. Cambisols generally have a sufficient water supply, and Orthic-Luvisols have a lower water supply with the possibility of aridization. Water deficiency can appear in Rendzinas as a result of the water penetration, so the water supply in this soil is usually low (Šály, 1988).

According to Wilhelm (1998), the service tree grows on mussel limestone and on keuper sediments on the Plateau Lorraine. These soils are well or very well supplied with nutrients. On slopes based with mussel limestones are deep terra fusca soils, and in the upper parts of the slopes are shallow Rendzinas. On the keuper, there are abundant, deep Vertic Cambisols with water deficiency during summer.

In east Austria, the service tree grows in the oak forest communities and is considered to be a woody plant of the uplands with less demands on soil humidity, but with quite high demands on the nutrient content of the soils (Kirisits, 1992). In the Wiener Wald (Steiner, 1995), the service tree appears on limestone and dolomite parent rock with prevalence in

parent rocks (80% of stands) (Schmitt, 1998). In the area of Süd-Niedersachsen und Nordhessen (Germany), the wild pear frequently grows in shallow rendzinas from mussel limestone or from lime sandstone, and very rarely appears on deeper brown forest soils. More than 92% of all natural stands were on rich basic rocks (Hofmann, 1993). In the forest on the Plateau Lorraine, the wild pear grows mainly on parent rock of the mussel limestone and on keuper sediments. There are deep terra fusca soils and shallow Rendzinas (Wilhelm, 1998). The colective data from different areas of the natural distribution indicate that suitable growth conditions for the wild pear are mainly basic

In Slovakia, the wild pear grows on fertile soils (Chernozem, Fluvi-mollic soils, Cambisols, and Orthic Luvisols), or soils well supplied with nutrients (Albic Luvisol, Pararendzina, and Fluvisol). In addition, in some stands it grows on soils that are rich in minerals but under

In general, Fluvi-mollic and Cambisol soils have a sufficient water supply. At lower altitudes, the water deficit appears mainly in Rendzinas. The water deficit in Luvisols is usually a result of a lower amount of precipitation and higher evaporation. Orthic Luvisols have a lower water supply, and therefore the possibility of their aridization is higher. In addition, a fluctuating water regime appears within the Planosols and Fluvisols (Šály, 1988). According to the ecological scheme by Ellenberg (1978), the wild pear has optimal growth conditions on fresh basic soils (its potential optimum). Another more frequent existence optimum of this woody plant is near the xeric forest limit, where the wild pear grows in arid soils rich in bases as well as in moderately acidic soils. Some authors have placed the wild pear among xerophytic woody plants according to its lower demands on soil humidity (Bouček, 1954). When under competition with some woody plants, it grows on its synecological optimum in extreme arid stands - rocky hilltops, stands of the xeric forest limit close to steppe communities, and in the sparse xerophytic oak woodlands (Rittershoffer, 1998). However, another existence optimum of this woody plant occurs in the hydric forest boundary in stands of the hardwood floodplain forests, where wild pear growth is limited by inundation (Rittershoffer, 1998). Based on these findings, the wild pear

In Slovakia, stands with the service tree have favourable physical characteristics, good saturation, and are very fertile (Orthic-Luvisols and Cambisols), or have soils that are well supplied with nutrients (Rendzinas). However, under conditions of unbalanced soil chemistry, there is little fertility, and the pH of this soil is moderately acidic, neutral, or moderately alkaline. Cambisols generally have a sufficient water supply, and Orthic-Luvisols have a lower water supply with the possibility of aridization. Water deficiency can appear in Rendzinas as a result of the water penetration, so the water supply in this soil is

According to Wilhelm (1998), the service tree grows on mussel limestone and on keuper sediments on the Plateau Lorraine. These soils are well or very well supplied with nutrients. On slopes based with mussel limestones are deep terra fusca soils, and in the upper parts of the slopes are shallow Rendzinas. On the keuper, there are abundant, deep Vertic Cambisols

In east Austria, the service tree grows in the oak forest communities and is considered to be a woody plant of the uplands with less demands on soil humidity, but with quite high demands on the nutrient content of the soils (Kirisits, 1992). In the Wiener Wald (Steiner, 1995), the service tree appears on limestone and dolomite parent rock with prevalence in

conditions of unbalanced soil chemistry with little fertility (Paganová, 2003).

is a flexible woody plant with tolerance to a large range of soil humidity.

usually low (Šály, 1988).

with water deficiency during summer.

and rich nutrient soils with occasional water deficits.

semi-humid and arid Rendzinas. In addition, the service trees in Switzerland are found mainly in arid soil with less skeleton that is rich in bases (Landolt, 1977; Brütsch & Rotach, 1993), as determined from detailed studies of the service tree stands in Canton Genf, which refer to the medium deep and deep skeletal Cambisols and Luvisols with slower water penetration and possible water logging. In the Bassel region, the service tree also grows on Rendzinas or Lithosols, which are shallow and extreme skeletal soils that have a very low water capacity. In the Schaffhausen, approximately 92% of the service tree plants grow on limestones, and the rest of the stands grow on gravels of the high terrace that belong to Riss. In the deeper strata, there are limestones that are part of the morena and gravels. Various soils, even acidic soils, can appear randomly on small areas of the parent rocks . These data document quite a broad range of soil conditions for the stands containing service trees, and tolerance of the taxon to periodic or rare occurrences of water deficit in the soils is evident. On some stands within the area of its natural distribution, the service tree grows under conditions of a soil drought.

## **4. Potential adaptability of the analysed woody plants to progressive drought**

Drought can be considered in meteorological, agricultural, hydrological, and socio-economic terms (Wilhite & Glantz, 1985). Meteorological drought reflects one of the primary causes of drought. It is usually defined as precipitation less than a long-term average (defined as normal) over a specific period of time. Agricultural drought is expressed in terms of the moisture availability at a particular time during the growing season for a particular crop. Hydrological drought is usually expressed as a deficiency in surface and subsurface suppliers, and refers to a period when stream flows are unable to supply the established users under a given water management system. Socio-economic definitions of drought relate to the supply and demand of specific goods. Importantly, humans can create a drought situation through land-use choices or an excess demand for water (Wilhite & Glantz, 1985).

According to Škvarenina et al. (2009a), drought is a temporary aberration that differs from aridity, which is restricted to low rainfall regions and is a permanent feature of the climate. The altitude and topography are significant climate-differentiating factors. In Slovakia, a considerably broken topography plays an important role in the variability of climate conditions. The increase in altitude causes changes in solar radiation as well as thermal and water balance of the land (Škvarenina et al., 2009a). Vertical differentiation of the climate conditions has a significant influence on species structure of the natural vegetation. The biogenocenoses can be classified into nine vegetation stages described by Zlatník (1976) based on altitude, exposure, and topography, which are named after woody plants that are dominant in the area.

Škvarenina et al. (2009a) analysed trends in the occurrence of dry and wet periods in altitudinal vegetation stages in Slovakia between 1951 and 2005. The authors considered relative evapotranspiration (E/E0), which is defined as the rate of the actual evapotranspiration (E) to potential evapotranspiration (E0), as an excellent measure of water sufficiency for vegetation. According to their findings, the smallest annual values of (E/E0) were recorded in the Danube lowland (1st Oak vegetation stage) with relatively high totals of potential evapotranspiration (E0) above 700 mm and with annual precipitation totals below (P) 550 mm. The lowest value of the relative evapotranspiration (approximately 60%) was recorded in the lowest areas of Slovakia with an altitude up to 200 m. Relative evapotranspiration reached higher values towards higher vegetation stages (above 90% in the 4th Beech vegetation stage at altitudes above 650 m).

In addition to relative evapotranspiration, the drought index (E0/P) has also been used to describe the relationship between the energy and precipitation (P) inputs within particular vegetation stages. Warm forest-steppe stands in Slovakia with oak communities have drought index values (E0/P) of approximately 1. The predominant areas of Slovak forests are stands with drought index values up to 0.3. Moreover, the vegetation stages with E0/P < 0.3 are within the mountain climate (Škvarenina et al., 2009b).

In Slovakia, wild pear stands are distributed from lowlands up to an altitude of 800 m. Specimens also appear in 1st (oak) and 2nd (beech-oak) vegetation stages with a water deficit during the growing season. The stands in these vegetation stages are classified as a territory with a dry (arid) climate according to the relative evapotranspiration and drought index. On the other hand, the wild pear is also distributed in stands at higher altitudes in the 4th (beech) and 5th (fir-beech) vegetation stages, which have a higher humidity (higher relative evapotranspiration). This type of distribution shows that the wild pear is tolerant to different conditions of water sufficiency.

The service tree is predominantly distributed in the 1st (oak), 2nd (beech oak), and 3rd (oakbeech) vegetation stages in Slovakia, avoids lowland stands, and appears mainly on slope terrain of the forest steppe stands. This taxon often grows in conditions of warm oak communities with an arid climate. At higher altitudes, the service tree most likely avoids the consequences of a strong beech competition. In the Slovak lowlands, the absence of the service tree is most likely due to the higher underground water level and the intensive agricultural utilization of the land.

According to Škvarenina et al. (2009a), a markedly severe drought between 1951 and 2005 was only identified in the Danube Lowland (1st Oak vegetation stage) and in the Záhorská lowland (2nd Beech-oak vegetation stage) of Slovakia. Considering the natural distribution of the wild pear and tolerance to a wider range of water supply, this woody plant has the potential to adapt to the decreasing humidity of the Danube Lowland. The service tree has similar qualities and the potential to grow in arid conditions; however, this taxon is mainly found on the slopes of forest-steppe stands.

According to a drought analysis of the Slovak territory conducted on the climatic data obtained from 1960-1990, agricultural regions become more sensitive to conditions of climate change upon drought occurrence (Šiška & Takáč, 2009). The authors used two indices for spatial evaluation of drought conditions in Slovakia: the climatic index of drought and the evapotranspiration deficit. The climatic index of drought (K) was applied for the entire growing season (GS10 period) and KGS10 = ∆E, where E0 is the potential evapotranspiration during GS10 and R is the rainfall during GS10. The evapotranspiration deficit ∆E during the growing season was calculated as ∆E GS10 = E0 – E, where E0 is the potential evapotranspiration during the main growing season (GS10) and E is the actual evapotranspiration during the main growing season.

Two very dry and hot regions were classified in Slovakia, the Danubian and east Slovakian lowlands, which represent maize production areas with a water deficit that exceeds 250 mm during the growing season. These evapotranspiration deficit values will most likely be present in river valleys up to altitudes of 300 m as well (Šiška & Takáč, 2009).

The findings described here support the hypothesis that a higher frequency of drought occurs in agroclimatic regions of the Slovak Republic. In the future, it is important to elaborate on several concepts of the stabilization of agricultural production against water

evapotranspiration reached higher values towards higher vegetation stages (above 90% in

In addition to relative evapotranspiration, the drought index (E0/P) has also been used to describe the relationship between the energy and precipitation (P) inputs within particular vegetation stages. Warm forest-steppe stands in Slovakia with oak communities have drought index values (E0/P) of approximately 1. The predominant areas of Slovak forests are stands with drought index values up to 0.3. Moreover, the vegetation stages with E0/P <

In Slovakia, wild pear stands are distributed from lowlands up to an altitude of 800 m. Specimens also appear in 1st (oak) and 2nd (beech-oak) vegetation stages with a water deficit during the growing season. The stands in these vegetation stages are classified as a territory with a dry (arid) climate according to the relative evapotranspiration and drought index. On the other hand, the wild pear is also distributed in stands at higher altitudes in the 4th (beech) and 5th (fir-beech) vegetation stages, which have a higher humidity (higher relative evapotranspiration). This type of distribution shows that the wild pear is tolerant to

The service tree is predominantly distributed in the 1st (oak), 2nd (beech oak), and 3rd (oakbeech) vegetation stages in Slovakia, avoids lowland stands, and appears mainly on slope terrain of the forest steppe stands. This taxon often grows in conditions of warm oak communities with an arid climate. At higher altitudes, the service tree most likely avoids the consequences of a strong beech competition. In the Slovak lowlands, the absence of the service tree is most likely due to the higher underground water level and the intensive

According to Škvarenina et al. (2009a), a markedly severe drought between 1951 and 2005 was only identified in the Danube Lowland (1st Oak vegetation stage) and in the Záhorská lowland (2nd Beech-oak vegetation stage) of Slovakia. Considering the natural distribution of the wild pear and tolerance to a wider range of water supply, this woody plant has the potential to adapt to the decreasing humidity of the Danube Lowland. The service tree has similar qualities and the potential to grow in arid conditions; however, this taxon is mainly

According to a drought analysis of the Slovak territory conducted on the climatic data obtained from 1960-1990, agricultural regions become more sensitive to conditions of climate change upon drought occurrence (Šiška & Takáč, 2009). The authors used two indices for spatial evaluation of drought conditions in Slovakia: the climatic index of drought and the evapotranspiration deficit. The climatic index of drought (K) was applied for the entire growing season (GS10 period) and KGS10 = ∆E, where E0 is the potential evapotranspiration during GS10 and R is the rainfall during GS10. The evapotranspiration deficit ∆E during the growing season was calculated as ∆E GS10 = E0 – E, where E0 is the potential evapotranspiration during the main growing season (GS10) and E is the actual

Two very dry and hot regions were classified in Slovakia, the Danubian and east Slovakian lowlands, which represent maize production areas with a water deficit that exceeds 250 mm during the growing season. These evapotranspiration deficit values will most likely be

The findings described here support the hypothesis that a higher frequency of drought occurs in agroclimatic regions of the Slovak Republic. In the future, it is important to elaborate on several concepts of the stabilization of agricultural production against water

present in river valleys up to altitudes of 300 m as well (Šiška & Takáč, 2009).

the 4th Beech vegetation stage at altitudes above 650 m).

0.3 are within the mountain climate (Škvarenina et al., 2009b).

different conditions of water sufficiency.

agricultural utilization of the land.

found on the slopes of forest-steppe stands.

evapotranspiration during the main growing season.

deficit and soil aridity. With the exception of breeding programs that focus on developing new crop varieties that can tolerate the changed climatic conditions and development of integrated irrigation systems, there are also possibilities for landscape stabilization using non-forest woodlands. These types of woodlands should be established with woody plants that are tolerant to water deficit and that are adaptable to dynamic changes of water regimes. The taxa analysed here, including the wild pear and service tree, belong among the prospective woody plant species that are suitable for planting in regions potentially endangered by droughts.

The described research focused on an analysis of the physiological parameters of two woody plant species (wild pear and service tree) under conditions of a regulated water regime and water stress. The aims of the study were to verify the adaptive potential of both taxa to drought, and to obtain information on the mechanisms used by these woody plants under conditions of water deficit.

## **5. Interspecific differences of the selected physiological parameters of woody plants**

Woody plants make different ecological adjustments to water deficit, and can modify their physiological functions and anatomical structures for adaptation. Adaptability is a rather complex quality, and the explicit function of a typical plant response to water deficit is very difficult to define. Therefore, we established experiments that regulated the water regime of juvenile (two-year old) wild pear and service tree plants under semi-controlled conditions.

The plants were planted in pots (content 2 L) with mixed peat substrate enriched with clay (content of clay 20 kg.m-3; pH 5.5-6.0; fertilizer 1.0 kg.m-3). The potted plants were placed under a polypropylene cover with 60% shading. The plants were regularly watered and maintained on 60% of the full substrate saturation for 28 days. In the phenological stage of shoot elongation (at the beginning of June), the plants of both taxa were divided in two variants according to a differentiated water regime. Variant "stress" was supplied with water at 40% of full substrate saturation and "control" at 60% of full substrate saturation. The model of the differentiated water regime was maintained for 126 days (to the end of September). Sampling was performed at 14 day periods for both conditions.

The size of the leaf area (A) and leaf water content (LWC) were measured, and a determination of fresh weight (FW) and dry weight (DW) was done gravimetrically. The size of leaf area (A) was calculated from leaf scans using ImageJ software (http://rsbweb.nih.gov/ij/). The LWC and specific leaf area (SLA) were calculated according to the methods described by Larcher (2003). For metabolic characteristics, the total chlorophyll and carotenoid content were determined according to the methods described by Šesták & Čatský (1966).

Data were analysed from three growing seasons in 2008-2010 for each taxon under two variations of water regimes (40% and 60% substrate saturation). The relationship between SLA and LWC of the plants under stress and control conditions as well as changes in the assimilatory pigments during water stress were also analysed. A statistical assessment of these parameters was conducted by regression analysis using the statistical software Statgraphics Centurion XV (StatPoint Technologies, USA). A P < 0.05 was consisted statistically significant.

#### **5.1 The influence of water stress on the production of leaf dry mass**

The different reactions of the analysed taxa (wild pear and service tree) to water stress were confirmed by the dry mass (DM) measurements taken under controlled and stress experimental conditions (Table 1). Under control conditions, the increment of leaf dry mass of the wild pear was 14.67 mg p-1 d-1 and the increment of leaf dry mass of the service tree was 18.37 mg p-1 d-1. Under conditions of water deficit (stress), the increment of the leaf dry mass of wild pear plants was 12.78 mg p-1 d-1 and the increment of leaf dry mass for the service tree plants decreased to 3.04 mg p-1 d-1. The impact of water stress on the wild pear was less significant, and this plant is probably more tolerant to drought. Importantly, the relationship to photosynthesis economy depends on the leaf structure. The wild pear is a typical taxon of sunny and arid stands, and contains heterobaric leaves. Parenchyma (or sclerenchyma) cells without chloroplasts accompany the vascular system, and similar to ribs, lead to the top (adaxial) or bottom (abaxial) epidermis (Essau, 1977; Fahn, 1990; Terashima, 1992). The tips (ribs) of the vascular bundles divide leaf mesophyll hermetically into compartments that are reciprocally isolated against gas exchange. In the compartments, the intercellular space is relatively small with low chlorophyll content. The compartments are similar to "open windows", which transmit visible light into the internal layers of the mesophyll (Liakoura et al., 2009). Heterobaric leaf structures are also significant because they allow for easier transport of water to the epidermis due to increased hydraulic conductivity. One predominant factor that limits plant transpiration is leaf area. The reduction of leaf area during water deficit is typical for plants from arid stands. Several authors (Reich et al., 2003, Wright et al., 2004; Niclas & Cobb, 2008) have confirmed the narrow relationship between leaf structure and function. Our comparison of the leaf area ratio to dry weight of the leaves (SLA) of the analysed species confirmed the interspecific differences (Table 1). Wild pear leaves with higher values of SLA were thinner than leaves of the service tree under control conditions. The leaf water content per unit of dry weight in pear leaves was higher than service tree leaves. In experiments with fast growing woody plants, Dijkstra (1989) confirmed the thinner leaves of these species as well as the presence of larger vacuoles in the cells, which accumulate a larger amount of water per unit of dry mass. In our experiments with wild pear, the values of SLA decreased after 70 days under both conditions (stress and control), and the pear leaves became xeromorphous. There were no significant differences in SLA values of the pear leaves after 70 days under the differentiated water regime or due to water stress (Table 1).

The different functional qualities of the leaves can be effected by 1) changes in the leaf structure, and 2) different compositions of the leaf, including sclerenchyma elements and organic compounds (lignins and phenols), which increase leaf dry mass as described by Mooney & Gulmon (1982) and Lin & Harnly (2008).

Interspecific differences in the reaction to water deficit were not confirmed in the analysed taxa of this study. However, at the beginning of the experiments and after 70 days of cultivation, the values of LWC of the wild pear and service tree plants were different, and these values did not change under conditions of water stress (Table 1).

Based on our analysis of the relationship between SLA and LWC, both of the analysed taxa maintained higher LWC with increasing values of the specific leaf area, regardless of the level of substrate saturation (Fig. 6, 7, 8, and 9). In addition, a significant linear correlation was observed between SLA and LWC under control and stress conditions without interspecific differences.

The different reactions of the analysed taxa (wild pear and service tree) to water stress were confirmed by the dry mass (DM) measurements taken under controlled and stress experimental conditions (Table 1). Under control conditions, the increment of leaf dry mass of the wild pear was 14.67 mg p-1 d-1 and the increment of leaf dry mass of the service tree was 18.37 mg p-1 d-1. Under conditions of water deficit (stress), the increment of the leaf dry mass of wild pear plants was 12.78 mg p-1 d-1 and the increment of leaf dry mass for the service tree plants decreased to 3.04 mg p-1 d-1. The impact of water stress on the wild pear was less significant, and this plant is probably more tolerant to drought. Importantly, the relationship to photosynthesis economy depends on the leaf structure. The wild pear is a typical taxon of sunny and arid stands, and contains heterobaric leaves. Parenchyma (or sclerenchyma) cells without chloroplasts accompany the vascular system, and similar to ribs, lead to the top (adaxial) or bottom (abaxial) epidermis (Essau, 1977; Fahn, 1990; Terashima, 1992). The tips (ribs) of the vascular bundles divide leaf mesophyll hermetically into compartments that are reciprocally isolated against gas exchange. In the compartments, the intercellular space is relatively small with low chlorophyll content. The compartments are similar to "open windows", which transmit visible light into the internal layers of the mesophyll (Liakoura et al., 2009). Heterobaric leaf structures are also significant because they allow for easier transport of water to the epidermis due to increased hydraulic conductivity. One predominant factor that limits plant transpiration is leaf area. The reduction of leaf area during water deficit is typical for plants from arid stands. Several authors (Reich et al., 2003, Wright et al., 2004; Niclas & Cobb, 2008) have confirmed the narrow relationship between leaf structure and function. Our comparison of the leaf area ratio to dry weight of the leaves (SLA) of the analysed species confirmed the interspecific differences (Table 1). Wild pear leaves with higher values of SLA were thinner than leaves of the service tree under control conditions. The leaf water content per unit of dry weight in pear leaves was higher than service tree leaves. In experiments with fast growing woody plants, Dijkstra (1989) confirmed the thinner leaves of these species as well as the presence of larger vacuoles in the cells, which accumulate a larger amount of water per unit of dry mass. In our experiments with wild pear, the values of SLA decreased after 70 days under both conditions (stress and control), and the pear leaves became xeromorphous. There were no significant differences in SLA values of the pear leaves after 70 days under the

**5.1 The influence of water stress on the production of leaf dry mass** 

differentiated water regime or due to water stress (Table 1).

these values did not change under conditions of water stress (Table 1).

Mooney & Gulmon (1982) and Lin & Harnly (2008).

interspecific differences.

The different functional qualities of the leaves can be effected by 1) changes in the leaf structure, and 2) different compositions of the leaf, including sclerenchyma elements and organic compounds (lignins and phenols), which increase leaf dry mass as described by

Interspecific differences in the reaction to water deficit were not confirmed in the analysed taxa of this study. However, at the beginning of the experiments and after 70 days of cultivation, the values of LWC of the wild pear and service tree plants were different, and

Based on our analysis of the relationship between SLA and LWC, both of the analysed taxa maintained higher LWC with increasing values of the specific leaf area, regardless of the level of substrate saturation (Fig. 6, 7, 8, and 9). In addition, a significant linear correlation was observed between SLA and LWC under control and stress conditions without


Table 1. Physiological characteristics of leaves taken from 2-year old potted plants of wild pear (*Pyrus pyraster)* and service tree (*Sorbus domestica)* grown in conditions of differentiated water regime - control (60% of the full substrate saturation) and stress (40% of the full substrate saturation) conditions.

Plot of Fitted Model for Pyrus pyraster with 40% saturation of the substrate LWC = 41,5452 + 1,03154 \* SLA

Fig. 6. Positive linear correlation between SLA (mm2.mg-1) and LWC (%) of wild pear (*Pyrus pyraster*) leaves under conditions of water stress. Correlation coefficient (r) = 0.760432, p value = 0.0000.

Plot of Fitted Model for Pyrus pyraster with 60% saturation of the substrate LWC = 42,5661 + 1,06149 \* SLA

Fig. 7. Positive linear correlation between SLA (mm2.mg-1) and LWC (%) of wild pear (*Pyrus pyraster*) leaves under control conditions. Correlation coefficient (r) = 0.704177, p value = 0.0002.

Fig. 8. Positive linear correlation between SLA(mm2.mg-1) and LWC (%) parameters of service tree (*Sorbus domestica*) leaves under water stress. Correlation coefficient (r) = 0.669898, p value = 0.0009.

Plot of Fitted Model for Pyrus pyraster with 60% saturation of the substrate LWC = 42,5661 + 1,06149 \* SLA

Fig. 7. Positive linear correlation between SLA (mm2.mg-1) and LWC (%) of wild pear (*Pyrus pyraster*) leaves under control conditions. Correlation coefficient (r) = 0.704177, p value =

Plot of Fitted Model for Sorbus domestica with 40% saturation of the substrate

LWC = 8,9215 + 2,46979 \* SLA

SLA (mm2.mg-1)

11 13 15 17 19 21 23

Fig. 8. Positive linear correlation between SLA(mm2.mg-1) and LWC (%) parameters of service tree (*Sorbus domestica*) leaves under water stress. Correlation coefficient (r) =

SLA (mm2.mg-1)

13 15 17 19 21 23

0.0002.

LWC (%)

LWC (%)

54

58

62

66

70

0.669898, p value = 0.0009.

35

39

43

47

51

55

59

Plot of Fitted Model for Sorbus domestica with 60% saturation of the substrate

Fig. 9. Positive linear correlation between SLA (mm2.mg-1) and LWC (%) parameters of service tree (*Sorbus domestica*) leaves under control conditions. Correlation coefficient (r) = 0.76925, p value = 0.0000.

#### **5.2 Changes in the assimilatory pigment content in leaves under conditions of water stress**

The content of assimilatory pigments is an important factor that has a significant influence on thermal characteristics of the leaves. Leaves with lower chlorophyll content have higher reflexion, and the leaf surface temperature can have relatively lower values than the temperature of leaves with a higher content of assimilatory pigments. In addition, leaves with a higher content of carotenoids should have a relatively higher resistance against water stress. On the other hand, the ability of a plant to maintain a higher content of assimilatory pigments during stress can be very important for the functional activity of the leaves. Our analysis confirmed a different content profile of assimilatory pigments (chlorophyll a and chlorophyll b), -carotene, and neoxantine in the leaves of the wild pear and service tree. There was a significant positive linear correlation between carotenoid and chlorophyll content in the leaves of both analysed taxa, regardless of the level of water saturation of the substrate (Table 2). This relationship is illustrated in Figure 10 for the wild pear plants at 40% substrate saturation. The results of the regression analysis for the wild pear under the control condition as well as for the service tree under both conditions are shown in Table 2. The SLA values of the service tree leaves did not change significantly under the differentiated water regime or under conditions of water stress (Table 1). The values of SLA in wild pear leaves decreased during the differentiated water regime under both conditions (control and stress). The decrease of SLA was most likely influenced by the specific quality of the taxon, which produces so called "summer leaves" during twig elongation. Two-year old plants of the service tree created leaves on terminal shoots only, and the values of SLA were not significantly changed in both variants of the water regime (control and stress) within the analysed period of time. During summer, the chlorophyll content in leaves of the wild pear increased under control and water stress conditions. The chlorophyll content in


Table 2. Results of a simple regression between total chlorophyll content and carotenoid content in leaves of the analysed taxa wild pear (*Pyrus pyraster)* and service tree (*Sorbus domestica*) under two conditions of substrate saturation. Legend: 40 – conditions of water stress (40% substrate saturation); 60 – control conditions (60 % of substrate saturation).

Plot of Fitted Model for Pyrus pyraster with 40% saturation of the substrate CAR = 47,0357 + 0,131496 \* CC

Fig. 10. Positive linear regression between total chlorophyll content (CC) and carotenoid content (CAR) in leaves of wild pear (*Pyrus pyraster*) plants growing under conditions of water stress. The correlation is quite close, with a correlation coefficient (r) = 0.973681 and statistically significant p value = 0.0002.

service tree leaves also increased; however, under water stress conditions, the chlorophyll content was lower than in the leaves of the control plants.

We confirmed a statistically significant relationship between SLA values and chlorophyll content in the leaves of the service tree under conditions of water stress, and this relationship was described by a polynomial curve of the second order (Figure 11). These data showed that the service tree maintained a balanced content of chlorophyll in leaves with a lower specific leaf area. In the stress variant, the chlorophyll concentration in service tree leaves varied between 340-470 mg.mm-2 within a 95% confidence level.

The relationship between SLA and chlorophyll content in the leaves of the wild pear under water stress conditions was also described as a polynomial function of the second order (Figure 12). However, this relationship was not significant. The leaf chlorophyll concentration ranged between 490-610 mg.mm-2 in the wild pear plants under conditions of lower substrate saturation (water stress).

**taxon/substrate saturation wild pear/40 wild pear/60 service tree/40 service tree/60**  correlation coefficient r 0.973681 0.964724 0.982228 0.974045

Table 2. Results of a simple regression between total chlorophyll content and carotenoid content in leaves of the analysed taxa wild pear (*Pyrus pyraster)* and service tree (*Sorbus domestica*) under two conditions of substrate saturation. Legend: 40 – conditions of water stress (40% substrate saturation); 60 – control conditions (60 % of substrate saturation).

Fig. 10. Positive linear regression between total chlorophyll content (CC) and carotenoid content (CAR) in leaves of wild pear (*Pyrus pyraster*) plants growing under conditions of water stress. The correlation is quite close, with a correlation coefficient (r) = 0.973681 and

CC (mg.mm-2)

500 540 580 620 660 700 740

service tree leaves also increased; however, under water stress conditions, the chlorophyll

We confirmed a statistically significant relationship between SLA values and chlorophyll content in the leaves of the service tree under conditions of water stress, and this relationship was described by a polynomial curve of the second order (Figure 11). These data showed that the service tree maintained a balanced content of chlorophyll in leaves with a lower specific leaf area. In the stress variant, the chlorophyll concentration in service

The relationship between SLA and chlorophyll content in the leaves of the wild pear under water stress conditions was also described as a polynomial function of the second order (Figure 12). However, this relationship was not significant. The leaf chlorophyll concentration ranged between 490-610 mg.mm-2 in the wild pear plants under conditions of

tree leaves varied between 340-470 mg.mm-2 within a 95% confidence level.

statistically significant p value = 0.0002.

CAR (mg.mm-2)

110

120

130

140

150

lower substrate saturation (water stress).

content was lower than in the leaves of the control plants.

p value 0.0002 0.0004 0.0005 0.0001

Plot of Fitted Model for Pyrus pyraster with 40% saturation of the substrate CAR = 47,0357 + 0,131496 \* CC

Plot of Fitted Model for Sorbus domestica with 40% saturation of the substrate

Fig. 11. Polynomial regression of the second order between specific leaf area (SLA) and chlorophyll content (CC) in the leaves of service tree (*Sorbus domestica)* plants grown under conditions of water stress. R2 = 30.92%; p = 0.0358.

Plot of Fitted Model for Pyrus pyraster with 40% saturation of the substrate

Fig. 12. Polynomial regression of second order between specific leaf area (SLA) and chlorophyll content (CC) in the leaves of wild pear (*Pyrus pyraster)* plants growing under conditions of water stress. R2 = 18.3086%; p = 0.1324

According to the results obtained from experiments with the differentiated water regime, we found a non-significant influence of low substrate saturation on the metabolic processes related to chlorophyll production in both of the analysed woody plant species.

## **6. Conclusion**

With regard to progressive aridization, the research of resistant autochthonous woody plants that survive in extreme drought conditions is considerable. We have studied two taxa that naturally grow in the cultural landscape of Slovakia – the wild pear and service tree. Both species are light-demanding woody plants and occur in similar stands. Compared to the wild pear, the service tree prefers stands at lower altitudes, and is prevalent in warm and arid climates. The wild pear has wider ecological amplitude, and also grows at higher altitudes in stands with a different water regime and climate extremes.

Two-year old plants of the studied taxa were used in experiments with a regulated water regime. The plant material was grown from seeds collected directly from original stands in Slovakia, and the plants were maintained under semi-controlled conditions with 60% and 40% substrate saturation. Under these conditions, we analysed the following parameters: leaf dry mass, size of leaf area, leaf water content, specific leaf area, and the complex of assimilatory pigments.

Assessment of the analysed parameters confirmed interspecific differences in the physiological reactions of the woody plants under regulated conditions of a water regime. Each of the studied taxa utilized unique drought tolerance strategies. Under a differentiated water regime, the wild pear produced and increased leaf dry mass regardless of the level of substrate saturation (water regime). Based on these findings, the wild pear uses this mechanism to resist drought conditions.

Interspecific differences between the wild pear and service tree were confirmed by measuring the specific leaf area (SLA) and leaf water content (LWC). Compared to the service tree, the wild pear had higher SLA values when provided with a sufficient water supply. The SLA values of both taxa had a positive linear correlation with the leaf water content (LWC). Under water stress conditions, the wild pear reduced SLA, which was influenced not only by water deficit, but also by different morphogensis of the assimilation apparatus. During the experiment with the regulated water regime, the service tree had lower values of SLA than the wild pear and maintained them without significant changes, even under conditions of water stress.

A statistically significant relationship was confirmed between SLA values and chlorophyll concentration in the leaves of the service tree under conditions of water stress. This relationship was described as a polynomial curve of the second order. The relationship between SLA and chlorophyll concentration in the leaves of the wild pear under water stress conditions was also described as a polynomial function of the second order; however, this relationship was not significant. The low level of substrate saturation did not significantly influence metabolic processes related to chlorophyll production in both of the analysed taxa. The water regime of the analysed woody plants is the decisive factor that affects their distribution and survival in conditions of progressive aridization. Considering the natural distribution of these woody plants and their tolerance to a wide range of water supply, the wild pear exhibits good adaptability to decreasing humidity. The service tree has similar qualities and the potential to adapt to arid conditions; however, it is generally found on slopes of forest-steppe stands.

In the future, studies will focus on strategies of water utilization used by xerotermic woody plants under conditions of aridization. The photosynthetic activity and transpiration of woody plants will also be analysed under conditions of limited water supply. The research will focus on the photosynthesis, transpiration, stomatal resistance, structural leaf elements, and root system of woody plants.

### **7. Acknowledgment**

The research was supported by research grant project VEGA 1/0426/09 "Plant adaptability and vitality as criteria of their utilization in urban environment and in the landscape" from the Slovak Grant Agency for Science.

### **8. References**

510 Evapotranspiration – Remote Sensing and Modeling

According to the results obtained from experiments with the differentiated water regime, we found a non-significant influence of low substrate saturation on the metabolic processes

With regard to progressive aridization, the research of resistant autochthonous woody plants that survive in extreme drought conditions is considerable. We have studied two taxa that naturally grow in the cultural landscape of Slovakia – the wild pear and service tree. Both species are light-demanding woody plants and occur in similar stands. Compared to the wild pear, the service tree prefers stands at lower altitudes, and is prevalent in warm and arid climates. The wild pear has wider ecological amplitude, and also grows at higher

Two-year old plants of the studied taxa were used in experiments with a regulated water regime. The plant material was grown from seeds collected directly from original stands in Slovakia, and the plants were maintained under semi-controlled conditions with 60% and 40% substrate saturation. Under these conditions, we analysed the following parameters: leaf dry mass, size of leaf area, leaf water content, specific leaf area, and the complex of

Assessment of the analysed parameters confirmed interspecific differences in the physiological reactions of the woody plants under regulated conditions of a water regime. Each of the studied taxa utilized unique drought tolerance strategies. Under a differentiated water regime, the wild pear produced and increased leaf dry mass regardless of the level of substrate saturation (water regime). Based on these findings, the wild pear uses this

Interspecific differences between the wild pear and service tree were confirmed by measuring the specific leaf area (SLA) and leaf water content (LWC). Compared to the service tree, the wild pear had higher SLA values when provided with a sufficient water supply. The SLA values of both taxa had a positive linear correlation with the leaf water content (LWC). Under water stress conditions, the wild pear reduced SLA, which was influenced not only by water deficit, but also by different morphogensis of the assimilation apparatus. During the experiment with the regulated water regime, the service tree had lower values of SLA than the wild pear and maintained them without significant changes,

A statistically significant relationship was confirmed between SLA values and chlorophyll concentration in the leaves of the service tree under conditions of water stress. This relationship was described as a polynomial curve of the second order. The relationship between SLA and chlorophyll concentration in the leaves of the wild pear under water stress conditions was also described as a polynomial function of the second order; however, this relationship was not significant. The low level of substrate saturation did not significantly influence metabolic processes related to chlorophyll production in both of the analysed taxa. The water regime of the analysed woody plants is the decisive factor that affects their distribution and survival in conditions of progressive aridization. Considering the natural distribution of these woody plants and their tolerance to a wide range of water supply, the wild pear exhibits good adaptability to decreasing humidity. The service tree has similar qualities and the potential to adapt to arid conditions; however, it is generally found on

related to chlorophyll production in both of the analysed woody plant species.

altitudes in stands with a different water regime and climate extremes.

**6. Conclusion** 

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## *Edited by Ayse Irmak*

This edition of Evapotranspiration - Remote Sensing and Modeling contains 23 chapters related to the modeling and simulation of evapotranspiration (ET) and remote sensing-based energy balance determination of ET. These areas are at the forefront of technologies that quantify the highly spatial ET from the Earth's surface. The topics describe mechanics of ET simulation from partially vegetated surfaces and stomatal conductance behavior of natural and agricultural ecosystems. Estimation methods that use weather based methods, soil water balance, the Complementary Relationship, the Hargreaves and other temperature-radiation based methods, and Fuzzy-Probabilistic calculations are described. A critical review describes methods used in hydrological models. Applications describe ET patterns in alpine catchments, under water shortage, for irrigated systems, under climate change, and for grasslands and pastures. Remote sensing based approaches include Landsat and MODIS satellitebased energy balance, and the common process models SEBAL, METRIC and S-SEBS. Recommended guidelines for applying operational satellite-based energy balance models and for overcoming common challenges are made.

Evapotranspiration - Remote Sensing and Modeling

Evapotranspiration

Remote Sensing and Modeling

*Edited by Ayse Irmak*

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