**1.2 Background**

In this chapter, Mapping EvapoTranspiration at High Resolution with Internal Calibration (METRIC) was used to produce ET maps in Idaho and Nebraska using Landsat imagery. METRIC is an image processing model for calculating ET as a residual of the surface energy balance. METRIC was developed by the University of Idaho [7, 8, 16] for the application to Landsat satellite imagery to maximize ET product resolution (30 m). METRIC uses as its foundation, the pioneering SEBAL energy balance process developed in the Netherlands by Bastiaanssen et al. [12, 17], where near surface temperature gradients for estimating the sensible heat component of the surface energy balance are an indexed function of radiometric surface temperature, thereby, eliminating the need for absolutely accurate surface temperature and the need for air temperature measurements. The surface energy balance is inversely and internally calibrated in METRIC using ground-based reference ET to reduce computational biases inherent to remote sensing-based energy balance components and to provide congruency with traditional methods for ET [8]. Slope and aspect functions and temperature lapsing are used in applications in mountainous terrain. The primary inputs to the METRIC model are short wave and long wave (thermal) images from satellite (e.g., Landsat or MODIS), a digital elevation model (DEM), and ground-based weather data measured within or near the area of interest. ET "maps" (i.e., images) via METRIC provide the means to quantify ET on a field-by-field basis in terms of both the rate and spatial distribution.

METRIC has significant advantages over conventional methods for estimating ET from crop coefficient curves in that crop development stages do not need to be known with METRIC, nor does the specific crop type need to be known. In addition, the energy balance can detect reduced ET caused by water shortage. For agricultural crops, METRIC takes significant advantage of basing calibration on reference ET, rather than evaporative fraction [18], where reference ET, in the case of METRIC, is the ET from a hypothetical 0.5 m tall vegetation having high leaf area and low bulk surface resistance. The reference ET is estimated from ground-based weather data using the ASCE standardized Penman-Monteith method for the 'tall reference' [19]. The use of reference ET accounts for regional advection effects can cause ET from irrigated and wetland vegetation systems to exceed daily net radiation in many arid or semi-arid locations [16]. Details on the METRIC model are provided in Allen et al. [8].

In the METRIC model, ET is computed from satellite images and weather data using the surface energy balance. Since the satellite image provides information for the overpass time only, METRIC 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 and is expressed as the energy consumed by the evaporation process:

$$\text{LE} = \text{R}\_{\text{n}} - \text{G} - \text{H} \tag{1}$$

**51**

any specific day.

lated as:

*Influence of Landsat Revisit Frequency on Time-Integration of Evapotranspiration…*

where ETinst is produced from the energy balance of METRIC (mm hr<sup>−</sup><sup>1</sup>

is reference ET based on the standardized 0.5 m tall alfalfa reference at the time of the image. ETr represents a near maximum rate of ET based on environmental energy availability and advection of sensible heat and dry air from outside irrigated areas. Generally, only one or two weather stations are required to estimate ETr for a Landsat image that measures 180 km × 180 km. ETrF is 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 because ETr represents a near maximum limit for ET; ETrF values produced by METRIC generally range from 0 to 1.0 [20].

Monthly and seasonal evapotranspiration "maps" are highly useful for water resources management, including water rights litigation, hydrologic water balances, ground water studies, and irrigation depletion analyses. Generally, these maps are derived from the series of ETrF images produced by METRIC by interpolating ETrF between the processed images and then multiplying, on a daily basis, by the ETr for each day. The ETr accounts for day-to-day variation in ET caused by weather fluctuations and the interpolated ETrF from METRIC accounts for the scaling of the weather-based ET according to the effects of vegetation cover, soil water stress, and other localized factors. As mentioned before, the interpolation of ETrF between image dates is not unlike the construction of a seasonal Kc curve, where interpola-

Cumulative ET for any period, for example, a month, season, or year is calcu-

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

between values for ETrF is generally made using a curvilinear interpolation function, for example, a spline function, to follow the typical curvilinearity of ET due to

As a general rule of thumb, one clear satellite image per month is normally considered sufficient to construct an accurate ETrF curve for purposes of integrating ET over time to estimate seasonal ET. During periods of rapid vegetation change, however, a more frequent image interval is highly desirable, as illustrated in **Figure 1**, where the lack of satellite image in mid-July caused an underestimation of the ETrF curve for the dry bean crop in Idaho near the beginning of the midseason,

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. In actuality, ETrF varies substantially from day-to-day due primarily to variability in weather data and surface wetness. Therefore, the continuous ETrF curve, whether constructed from a published curve or table, or estimated from METRIC, is only an approximation of the actual ETrF on

the phenological development of crops during the growing season [25].

[(ETrFi) (ETr24i)] (3)

. The interpolation

i=m n

for day i. Units for ETperiod are in mm, when ETr24 is in mm d<sup>−</sup><sup>1</sup>

when ETrF was interpolated linearly between satellite dates.

ETinst ETr

(2)

) and ETr

*DOI: http://dx.doi.org/10.5772/intechopen.80946*

**1.3 Seasonal evapotranspiration**

tion is done between discrete values for Kc.

ETperiod = ∑

ETrF = \_\_\_\_\_

where LE is the latent heat flux (W/m2 ), Rn is the net radiation flux at the surface (W/m<sup>2</sup> ), G is the soil heat flux (W/m2 ), and H is the sensible heat flux to the air (W/m2 ).

ET produced by METRIC is expressed in the form of a reference ET fraction (ETrF) that is calculated as the ratio of the computed instantaneous ET (ETinst) from a pixel to a reference ET (ETr) that is computed from weather data:

*Influence of Landsat Revisit Frequency on Time-Integration of Evapotranspiration… DOI: http://dx.doi.org/10.5772/intechopen.80946*

$$\mathbf{ET\_{r}F} = \frac{\mathbf{ET\_{int}}}{\mathbf{ET\_{r}}} \tag{2}$$

where ETinst is produced from the energy balance of METRIC (mm hr<sup>−</sup><sup>1</sup> ) and ETr is reference ET based on the standardized 0.5 m tall alfalfa reference at the time of the image. ETr represents a near maximum rate of ET based on environmental energy availability and advection of sensible heat and dry air from outside irrigated areas. Generally, only one or two weather stations are required to estimate ETr for a Landsat image that measures 180 km × 180 km. ETrF is 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 because ETr represents a near maximum limit for ET; ETrF values produced by METRIC generally range from 0 to 1.0 [20].

#### **1.3 Seasonal evapotranspiration**

*Advanced Evapotranspiration Methods and Applications*

In this chapter, Mapping EvapoTranspiration at High Resolution with Internal Calibration (METRIC) was used to produce ET maps in Idaho and Nebraska using Landsat imagery. METRIC is an image processing model for calculating ET as a residual of the surface energy balance. METRIC was developed by the University of Idaho [7, 8, 16] for the application to Landsat satellite imagery to maximize ET product resolution (30 m). METRIC uses as its foundation, the pioneering SEBAL energy balance process developed in the Netherlands by Bastiaanssen et al. [12, 17], where near surface temperature gradients for estimating the sensible heat component of the surface energy balance are an indexed function of radiometric surface temperature, thereby, eliminating the need for absolutely accurate surface temperature and the need for air temperature measurements. The surface energy balance is inversely and internally calibrated in METRIC using ground-based reference ET to reduce computational biases inherent to remote sensing-based energy balance components and to provide congruency with traditional methods for ET [8]. Slope and aspect functions and temperature lapsing are used in applications in mountainous terrain. The primary inputs to the METRIC model are short wave and long wave (thermal) images from satellite (e.g., Landsat or MODIS), a digital elevation model (DEM), and ground-based weather data measured within or near the area of interest. ET "maps" (i.e., images) via METRIC provide the means to quantify ET on a field-by-field basis in terms of both the rate and spatial

METRIC has significant advantages over conventional methods for estimating ET from crop coefficient curves in that crop development stages do not need to be known with METRIC, nor does the specific crop type need to be known. In addition, the energy balance can detect reduced ET caused by water shortage. For agricultural crops, METRIC takes significant advantage of basing calibration on reference ET, rather than evaporative fraction [18], where reference ET, in the case of METRIC, is the ET from a hypothetical 0.5 m tall vegetation having high leaf area and low bulk surface resistance. The reference ET is estimated from ground-based weather data using the ASCE standardized Penman-Monteith method for the 'tall reference' [19]. The use of reference ET accounts for regional advection effects can cause ET from irrigated and wetland vegetation systems to exceed daily net radiation in many arid or semi-arid locations [16]. Details on the METRIC model are

In the METRIC model, ET is computed from satellite images and weather data using the surface energy balance. Since the satellite image provides information for the overpass time only, METRIC 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 and is expressed as the energy consumed by the

LE = Rn − G − H (1)

ET produced by METRIC is expressed in the form of a reference ET fraction (ETrF) that is calculated as the ratio of the computed instantaneous ET (ETinst) from a pixel to a reference ET (ETr) that is computed from weather data:

), Rn is the net radiation flux at the surface

), and H is the sensible heat flux to the air

**1.2 Background**

distribution.

provided in Allen et al. [8].

evaporation process:

where LE is the latent heat flux (W/m2

), G is the soil heat flux (W/m2

**50**

(W/m<sup>2</sup>

(W/m2 ).

Monthly and seasonal evapotranspiration "maps" are highly useful for water resources management, including water rights litigation, hydrologic water balances, ground water studies, and irrigation depletion analyses. Generally, these maps are derived from the series of ETrF images produced by METRIC by interpolating ETrF between the processed images and then multiplying, on a daily basis, by the ETr for each day. The ETr accounts for day-to-day variation in ET caused by weather fluctuations and the interpolated ETrF from METRIC accounts for the scaling of the weather-based ET according to the effects of vegetation cover, soil water stress, and other localized factors. As mentioned before, the interpolation of ETrF between image dates is not unlike the construction of a seasonal Kc curve, where interpolation is done between discrete values for Kc.

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

$$\text{ET}\_{\text{period}} = \sum\_{i=\text{m}}^{\text{n}} \left[ \left( \text{ET}\_{\text{r}} \text{F}\_{i} \right) \left( \text{ET}\_{\text{r24i}} \right) \right] \tag{3}$$

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 are in mm, when ETr24 is in mm d<sup>−</sup><sup>1</sup> . The interpolation between values for ETrF is generally made using a curvilinear interpolation function, for example, a spline function, to follow the typical curvilinearity of ET due to the phenological development of crops during the growing season [25].

As a general rule of thumb, one clear satellite image per month is normally considered sufficient to construct an accurate ETrF curve for purposes of integrating ET over time to estimate seasonal ET. During periods of rapid vegetation change, however, a more frequent image interval is highly desirable, as illustrated in **Figure 1**, where the lack of satellite image in mid-July caused an underestimation of the ETrF curve for the dry bean crop in Idaho near the beginning of the midseason, when ETrF was interpolated linearly between satellite dates.

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. In actuality, ETrF varies substantially from day-to-day due primarily to variability in weather data and surface wetness. Therefore, the continuous ETrF curve, whether constructed from a published curve or table, or estimated from METRIC, is only an approximation of the actual ETrF on any specific day.

#### **Figure 1.**

*Constructed Kc (or ETrF) curve for a bean crop from METRIC (dark symbols) with comparison against a standard Kc curve produced by the US Bureau of Reclamation Agrimet service for a region near Twin Falls, Idaho in year 2000.*
