**7. Algorithms application and results**

## **7.1. SEBAL algorithm**

vishzadeh et al., (2008) examined the utility of hyper spectral remote sensing in predicting canopy characteristics by using a spectral radiometer. Among the various models investigat‐ ed, they found that canopy chlorophyll content was estimated with the highest accuracy. Some studies used multispectral image sensor system to measure crop canopy characteris‐

Quantification of the canopy leaf area index (LAI) and its spatial distribution provides (Figure 7) an avenue to improve the interpretation of remotely sensed data over vegetat‐ ed areas. The purpose is to test the existing relation between vegetation indices with LAI and crop height and their prediction from remotely sensed data. It allow us to compare, on a consistent basis, the performance of a set of indices found in international litera‐ ture, in the prediction of LAI and CH which are basic parameters in the algorithms of estimating ETc. The method for mapping LAI and Crop Height for specific crops is

**Figure 7.** Production of LAI (B) and CH (C) maps (in pseudo color) using a Landsat image (A) (Papadavid, 2011)

tics (Inoue et al., 2000)

38 Remote Sensing of Environment: Integrated Approaches

shown in Figure 8.

SEBAL is a thermodynamically based model, using the partitioning of sensible heat flux and latent heat of vaporization flux as described by Bastiaanssen et al., (1998) who developed the algorithm. In the SEBAL model, ETc is computed from satellite images and weather data us‐ ing the surface energy balance as illustrated in Figure 9. Remotely sensed data in the visible, near-infrared and thermal infrared bands are used to derive the energy balance components along with ground measured solar radiation, if available. The other ground measurements that are required as model input are air temperature, relative humidity and wind speed at a point within the image.

SEBAL has an internal calibration for removing atmospheric effects using a series of itera‐ tion on Sensible Heat Flux (H) (Baastianssen et al., 2000; 2008). Since the satellite image pro‐ vides information for the overpass time only, SEBAL computes an instantaneous ET flux for the image time. The ET flux is calculated for each pixel of the image as a "residual" of the surface energy budget equation:

$$ET = \mathcal{R}\_u \quad \text{G} \quad H \tag{2}$$

The Reference ET Fraction (ETrF) (Equation 4) is defined as the ratio of the computed instan‐ taneous ET (ETinst) for each pixel to the reference ET (ETr) computed only from weather data:

Remote Sensing for Determining Evapotranspiration and Irrigation Demand for Annual Crops

inst

ET <sup>=</sup> (4)

http://dx.doi.org/10.5772/39305

41

r

**•** ETr is the reference ET at the time of the image from the REF-ET software (mm/hr). ETrF is also known as crop coefficient, Kc. ETrF is used to extrapolate ET from the image time

Finally, to get the daily values of ETc which are more useful than the instantaneous ones, SEBAL computes the ETdaily by assuming that the instantaneous ETrF is the same as the 24-

r r ET F x ET (24h) *<sup>c</sup> ET* = (5)

r

to 24-hour or longer periods. ETrF values usually range from 0 to 1.

**Figure 9.** Energy Balance equilibrium (Source: Waters et al., 2002)

hour average. The daily ETc (mm/day) is computed from Equation 5:

where:

ET ET F

where:


In this equation, the soil heat flux *(G)* and sensible heat flux *(H)* are subtracted from the net radiation flux at the surface *(Rn)* to compute the "residual" energy available for evapotrans‐ piration *(λET)* (Figure 8)*.* Soil heat flux is empirically calculated using vegetation indices, surface temperature and surface albedo. Sensible heat flux is computed using wind speed observations, estimated surface roughness and surface to air temperature differences. SE‐ BAL uses an iterative process to correct for atmospheric instability due to the buoyancy ef‐ fects of surface heating. Once the latent heat flux *(λET)* is computed for each pixel, an equivalent amount of instantaneous ET (mm/hr) is readily calculated by dividing by the la‐ tent heat of vaporization *(λ).* Then, daily ETc is inferred.

When all parameters in Equation (2) are known, an instantaneous estimation of ETc can be conducted. Latent heat flux *(λET)* in Equation (3) is the rate of latent heat loss from the sur‐ face due to evapotranspiration, at the time of the satellite overpass. An instantaneous value of ETcinst in equivalent evaporation depth is computed as:

$$ETc\_{loss.} = 3600 \xrightarrow{ET} \tag{3}$$

where:


The Reference ET Fraction (ETrF) (Equation 4) is defined as the ratio of the computed instan‐ taneous ET (ETinst) for each pixel to the reference ET (ETr) computed only from weather data:

$$\text{ETT}\_{\text{r}}\text{F} = \frac{\text{ET}\_{\text{lrest}}}{\text{ET}\_{\text{r}}} \tag{4}$$

where:

that are required as model input are air temperature, relative humidity and wind speed at a

SEBAL has an internal calibration for removing atmospheric effects using a series of itera‐ tion on Sensible Heat Flux (H) (Baastianssen et al., 2000; 2008). Since the satellite image pro‐ vides information for the overpass time only, SEBAL computes an instantaneous ET flux for the image time. The ET flux is calculated for each pixel of the image as a "residual" of the

In this equation, the soil heat flux *(G)* and sensible heat flux *(H)* are subtracted from the net radiation flux at the surface *(Rn)* to compute the "residual" energy available for evapotrans‐ piration *(λET)* (Figure 8)*.* Soil heat flux is empirically calculated using vegetation indices, surface temperature and surface albedo. Sensible heat flux is computed using wind speed observations, estimated surface roughness and surface to air temperature differences. SE‐ BAL uses an iterative process to correct for atmospheric instability due to the buoyancy ef‐ fects of surface heating. Once the latent heat flux *(λET)* is computed for each pixel, an equivalent amount of instantaneous ET (mm/hr) is readily calculated by dividing by the la‐

When all parameters in Equation (2) are known, an instantaneous estimation of ETc can be conducted. Latent heat flux *(λET)* in Equation (3) is the rate of latent heat loss from the sur‐ face due to evapotranspiration, at the time of the satellite overpass. An instantaneous value

**•** λ is the latent heat of vaporization or the heat absorbed when a kilogram of water evapo‐

. 3600 *inst*

*<sup>n</sup> ET R G H* =åå (2)

*ET ETc* <sup>=</sup> (3)

point within the image.

where:

where:

rates (J/kg)

surface energy budget equation:

40 Remote Sensing of Environment: Integrated Approaches

**•** Rn is the instantaneous net radiation (W.m-2)

**•** G is the instantaneous soil heat flux (W.m-2),

**•** H is the instantaneous sensible heat flux (W.m-2)

**•** λΕΤ is the instantaneous latent heat flux (W.m-2)

tent heat of vaporization *(λ).* Then, daily ETc is inferred.

of ETcinst in equivalent evaporation depth is computed as:

**•** ETcinst is the instantaneous evapotranspiration (mm/hr)

**•** 3600 is the time conversion from seconds to hours

**•** ETr is the reference ET at the time of the image from the REF-ET software (mm/hr). ETrF is also known as crop coefficient, Kc. ETrF is used to extrapolate ET from the image time to 24-hour or longer periods. ETrF values usually range from 0 to 1.

**Figure 9.** Energy Balance equilibrium (Source: Waters et al., 2002)

Finally, to get the daily values of ETc which are more useful than the instantaneous ones, SEBAL computes the ETdaily by assuming that the instantaneous ETrF is the same as the 24 hour average. The daily ETc (mm/day) is computed from Equation 5:

$$ET\_c = \text{ET}\_r\text{F} \times \text{ET}\_r(\text{24h}) \tag{5}$$

where:

**•** ETr (24h) is the total reference evapotranspiration of the day in mm/day.

Daily ETc is the final 'product' of SEBAL algorithm, meaning that satellite images are trans‐ formed into ETc maps where one could retrieve ETc for each pixel, as it is shown in Figure 10.

crop canopy factors (similar to SEBAL), namely albedo, crop height and LAI. It is a method with strong likelihood of correctly predicting the crop evapotranspiration in a wide range of locations and climates and has provision for application in data-sparse situations. The equa‐ tion has a strong theoretical basis, combining an energy balance to account for radiation and sensible heat transfer with an aerodynamic transport function to account for transfer of va‐

Remote Sensing for Determining Evapotranspiration and Irrigation Demand for Annual Crops

( ) ( ) () / 1 / *n p a s a ah s ah*

å å å å+ å <sup>=</sup> å+ + (6)

http://dx.doi.org/10.5772/39305

43

por away from the evaporating surface. The method is described as follows:

or

*ETc* <sup>=</sup> <sup>86400</sup> *λ*

where

*Δ*(*Rn* − *G*) + *c*

**•** *Rn* is the net solar radiation (W/m2

**•** *cp* is the air specific heat (J/kg K)

**•** *rs* is the surface resistance (s/m)

**•** *e*s is the saturated vapor pressure (kPa) **•** *e*a is the actual vapour pressure (kPa) **•** *rah* is the aerodynamic resistance (s/m)

**•** ρ*a* is the air density (kg / m3

**•** G Soil Heat flux (W/m2

*Δ* + *γ*(1 + *r*

**•** ETc is the crop evapotranspiration (mm/day)

)

**•** λ is the latent heat of vaporisation of water (J / kg)

**•** γ is the thermodynamic psychrometric constant (kPa / K)

)

*<sup>p</sup> pa*(*e <sup>s</sup>* − *e <sup>a</sup>*) /*r ah*

> *<sup>s</sup>* /*r ah* )

> > )

*R G cp e e r ETc r r*

**•** *Δ* represents the slope of the saturated vapor pressure temperature relationship (kPa / K1)

This equation is valid under conditions of intense solar irradiance (typical summer condi‐ tion in Mediterranean climate) and for 0,*5 < LAI < 3*, which is the case for Cyprus annual crops. What is important in the specific model is that of its use without the need of the ther‐ mal band of any satellite, contrary to the other Energy Balanced based models which ther‐ mal band is a prerequisite (Papadavid et al., 2011). Another difference that is rising in this model compared to SEBAL, is the need of atmospheric corrections where SEBAL and other models have an internal calibration for compensating atmospheric effects. The parameters Δ, *G*, *u*2, *es*–*ea*, *Rn* and *Δ* are calculated according to the formulae of the method by the con‐ ventional data of the meteorological station situated in the area of interested. The formulae

**Figure 10.** ETc map of the area of interest (Landsat 5 TM image 2/1/2009) using SEBAL (Papadavid, 2011)

#### **7.2.** *Penman-Monteith* **adapted to satellite data algorithm**

*Penman-Monteith* method adapted to satellite data was used to estimate ETc in mm/day (Equation 6). The specific equation needs both meteorological and remotely sensed data to be applied. The equation is used to estimate ETc under some assumptions and depends on the direct application of the Penman-Monteith equation (Monteith, 1965; Rijtema, 1965; Smith, 1992; Allen et al., 1998) also based on EB theory, with canopy parameters estimated from satellite imagery (D'Urso et al., 2006; Minaccapili et al., 2008; Papadavid et al., 2010; 2011). Air temperature, atmospheric pressure, wind speed and other necessary meteorologi‐ cal data were collected from a weather station, located at the Paphos International Airport, very close to our study area. The method also needs empirical equations for describing the crop canopy factors (similar to SEBAL), namely albedo, crop height and LAI. It is a method with strong likelihood of correctly predicting the crop evapotranspiration in a wide range of locations and climates and has provision for application in data-sparse situations. The equa‐ tion has a strong theoretical basis, combining an energy balance to account for radiation and sensible heat transfer with an aerodynamic transport function to account for transfer of va‐ por away from the evaporating surface. The method is described as follows:

$$ETc = \frac{\begin{pmatrix} R\_u & G \end{pmatrix} \cdot \begin{matrix} \star\_p p\_a \begin{pmatrix} e\_s & e\_a \end{pmatrix} / r\_{ah} \\ \cdot & \left( 1 + r\_s / r\_{ah} \right) \end{pmatrix}}{\begin{pmatrix} 1 & + r\_s / r\_{ah} \\ \cdot & 1 \end{pmatrix}} \tag{6}$$

or

where:

42 Remote Sensing of Environment: Integrated Approaches

**•** ETr (24h) is the total reference evapotranspiration of the day in mm/day.

Daily ETc is the final 'product' of SEBAL algorithm, meaning that satellite images are trans‐ formed into ETc maps where one could retrieve ETc for each pixel, as it is shown in Figure 10.

**Figure 10.** ETc map of the area of interest (Landsat 5 TM image 2/1/2009) using SEBAL (Papadavid, 2011)

*Penman-Monteith* method adapted to satellite data was used to estimate ETc in mm/day (Equation 6). The specific equation needs both meteorological and remotely sensed data to be applied. The equation is used to estimate ETc under some assumptions and depends on the direct application of the Penman-Monteith equation (Monteith, 1965; Rijtema, 1965; Smith, 1992; Allen et al., 1998) also based on EB theory, with canopy parameters estimated from satellite imagery (D'Urso et al., 2006; Minaccapili et al., 2008; Papadavid et al., 2010; 2011). Air temperature, atmospheric pressure, wind speed and other necessary meteorologi‐ cal data were collected from a weather station, located at the Paphos International Airport, very close to our study area. The method also needs empirical equations for describing the

**7.2.** *Penman-Monteith* **adapted to satellite data algorithm**

$$ETc = \frac{86400}{\lambda} \left[ \frac{\Delta (R\_n - G) + c\_p \, p\_a (e\_s - e\_a) / r\_{ah}}{\Delta + \gamma \left(1 + r\_s / r\_{ah}\right)} \right]$$

where


This equation is valid under conditions of intense solar irradiance (typical summer condi‐ tion in Mediterranean climate) and for 0,*5 < LAI < 3*, which is the case for Cyprus annual crops. What is important in the specific model is that of its use without the need of the ther‐ mal band of any satellite, contrary to the other Energy Balanced based models which ther‐ mal band is a prerequisite (Papadavid et al., 2011). Another difference that is rising in this model compared to SEBAL, is the need of atmospheric corrections where SEBAL and other models have an internal calibration for compensating atmospheric effects. The parameters Δ, *G*, *u*2, *es*–*ea*, *Rn* and *Δ* are calculated according to the formulae of the method by the con‐ ventional data of the meteorological station situated in the area of interested. The formulae for calculating each parameter can be found extensively in 'FAO Irrigation and Drainage pa‐ per No. 56' by FAO (1998). As in all ETc algorithms the final product is an ETc maps (Figure 11) of the area of interest where users can infer the ETc values for specific crops.

**8. Use of wireless sensors for supporting evapotranspiration measurements and smart management of irrigation demand**

**Figure 12.** Wireless nodes in the Mandria area in Paphos (Papadavid, 2012)

ogy (at the Remote Sensing Laboratory), as shown in Figure 13.

The Wireless Sensor Network (WSN) consisted of a number of wireless nodes (near to 20 nodes) placed at various locations in the surrounding agriculture fields irrigated from the Asprokremmos Dam in Paphos District area in Cyprus (see Figure 12). The WSN acts as a wide area distributed data collection system deployed to collect and reliably transmit soil and air environmental data to a remote base-station hosted at Cyprus University of Technol‐

The micro-sensors were deployed using ad-hoc multi-hop communication protocol and transmit their data to a gateway which is responsible to collect, save and forward them

transpiration results.

Wireless sensors have been used in this study as an extra tool for supporting evapo‐ transpiration measurements in the same area of interest (Hadjimitsis et al., 2008a & 2008b). Such sensors were used as smart meteorological stations (relative humidity, tem‐ perature, wind speed) as well as tools for retrieving soil moisture, soil temperature leaves wetness and temperature. These information can be used to assess our evapo‐

Remote Sensing for Determining Evapotranspiration and Irrigation Demand for Annual Crops

http://dx.doi.org/10.5772/39305

45

**Figure 11.** ETc map of the area of interest (Landsat 7 TM image 2/1/2009) using P-M (Papadavid, 2011)

The results regarding crop water requirements of the different crops can be found on Table 3. The water needs for each crop is average value, for each month, based on the crop evapo‐ transpiration found employing the two algorithms described above, after applying the methodology for modeling crop parameters to satellite data.


**Table 3.** Crop Water Requirements for the different crops (m3/ha/month)
