Estimation of Evapotranspiration Using the METRIC Energy Balance Algorithm (Case Study: Rasht County)
Abstract
Evapotranspiration is a crucial factor in the hydrological cycle and a key determinant of the Earth's surface energy balance. Accurate estimation of evapotranspiration is essential in various fields, including hydrology, agriculture, and water resource management. While direct methods and empirical models offer relatively high accuracy at a point scale, they are not practical or effective across larger spatial and temporal scales. As a result, the use of remote sensing techniques and satellite imagery for evapotranspiration estimation has garnered significant attention in recent years. In this study, the METRIC algorithm and MODIS sensor images were used to estimate the actual daily evapotranspiration in Rasht County. To assess the results, lysimetric data from the paddy fields of the Rice Research Institute in Rasht were utilized. The findings revealed that the METRIC algorithm underestimated the daily evapotranspiration of rice crops by 0.55 mm per day compared to actual values, which, overall, demonstrates suitable and acceptable accuracy for daily scale estimations.
Keywords: Evapotranspiration, Energy Balance, Remote Sensing, METRIC Algorithm
1. Introduction
In the process of evapotranspiration, the energy balance is a crucial aspect in examining energy exchange within environmental systems, particularly in agriculture and hydrology. Evapotranspiration (ET) encompasses the evaporation of water from the soil surface and the transpiration from plant surfaces, collectively acting as a primary process in the water cycle and energy transfer at the Earth's surface (Omidvar et al., 2013). The components of the energy balance refer to the distribution and transfer of energy at the Earth's surface. These components include net radiation, latent heat flux, soil heat flux, and sensible heat flux. By having the values of these components, the amount of ET can be calculated based on the energy balance.
The measurement of energy balance components can be categorized into four methods: the use of meteorological equipment, micrometeorological measurements, empirical models (Bowen ratio and gradient correlation), and remote sensing techniques (Disney et al., 2004). Experimental and micro-meteorological models are regionally highly accurate, but they are not applicable on a large spatial and temporal scale, the existence of such a limitation motivates the use of remote sensing techniques and satellite images to estimate energy balance components. In different conditions (Kim et al. 2010). Amini et al. (2023) investigated soil moisture variations and drought conditions in Kermanshah province, northwest Iran, using data from the Global Land Data Assimilation System (GLDAS). The study involved comparing GLDAS soil moisture data at various depths with observed monthly soil moisture and employing Geographic Information System (GIS) techniques to process the data. Their findings revealed a significant correlation between GLDAS moisture data and extreme wet and dry seasons, demonstrating the effectiveness of GLDAS in reconstructing spatial and temporal moisture patterns.
Remote sensing-based methods that operate on the principles of energy balance are classified into two categories: single-source and dual-source models (Chirouze et al., 2014). Single-source models treat the soil-plant system as a single unit, referred to as a big leaf, and utilize only one aerodynamic resistance (Nishida et al., 2003). Among the single-source models, the SEBAL (Bastiaanssen, 1998) and METRIC (Allen et al., 2007) models can be mentioned, while the dual-source models include the TSEB (Norman et al., 1996) and STSEB (Sánchez et al., 2008) models. In this context, various studies have been conducted on the application of energy balance-based algorithms to estimate evapotranspiration (ET) using satellite imagery.
Singh et al. (2015) evaluated the accuracy of four models: SEBAL, SSEBop, SEBS, and METRIC for estimating evapotranspiration using Landsat images in the western United States. The results indicated that the METRIC model is the most complex among all models, and its accuracy depends on instantaneous evapotranspiration and meteorological data. Lian et al. (2016) conducted a study in China using Landsat images to evaluate ET values derived from three methods: SSEB, METRIC, and TS-VI. The results indicated that the METRIC method performed more reliably.
Wagle et al. (2017) in the United States evaluated five energy balance methods to estimate the ET of sorghum crops. The results showed that the S-SEBI model had the best agreement with lysimeter data.
Grosso et al. (2018) estimated ET using Landsat images and the SEBAL algorithm in a corn field near the Venice Lagoon in Italy and confirmed the suitability of this algorithm. Elkatoury et al. (2019) evaluated the accuracy of three algorithms: SEBAL, METRIC, and SSEBI for estimating ET in a region of Saudi Arabia using Landsat-8 images. The results showed that the METRIC algorithm had the best performance. Asadi and Karami (2020) evaluated evapotranspiration in the eastern part of East Azerbaijan province using Landsat-8 images and the SEBAL algorithm. They found a difference of 0.67 mm/day between the SEBAL algorithm and the FAO Penman-Monteith method, indicating the suitability of this algorithm.
Nisa et al. (2021) evaluated the accuracy of three models: SEBS, METRIC, and the water model for estimating evapotranspiration of fennel, corn, and wheat crops in southern Italy. The results showed that the SEBS and METRIC models performed satisfactorily. Bolhasani et al. (2022) investigated evapotranspiration using Landsat-8 satellite images and the SEBS model in the Bakhtegan-Maharloo watershed in Fars province, and with an error of 0.62 mm/day, confirmed the accuracy and practicality of the model. Rostamizad et al. (2023) estimated ET in north northwestern region of Zanjan using the SEBS model and Landsat-8 images, affirming the suitability of remote sensing methods for ET estimation.
Based on previous studies, this research aims to assess the performance of the METRIC algorithm for estimating evapotranspiration (ET) in a humid climate using MODIS sensor imagery. To evaluate the performance of the algorithm, lysimetric data will be utilized.
2. Materials and Methods
2.1. Study Area
Rasht County is located in Gilan Province in northern Iran. Covering an area of 180 square kilometers, it is situated between latitudes 37°1′ N to 37°27′ N and longitudes 48°35′ E to 49°36′ E (Figure 1). The climate of Rasht County is classified as moderate Caspian and semi-Mediterranean, characterized by hot and humid summers and cold, wet winters. The annual precipitation in this region is approximately 1359 mm (Asadi Oskouei, 2017).
Figure 1: Location of the study area in Rasht County and Iran.
2.2. Data Used
In this study, the ET (Evapotranspiration) was estimated pixel by pixel for the entire Rasht County using the METRIC algorithm along with meteorological and satellite data. To evaluate the accuracy of the METRIC algorithm, lysimetric data from the Rice Research Institute was utilized, which will be explained in detail later (Asadi Oskouei, 2017).
1.2.2. Meteorological Data
The meteorological data utilized in this study include variables such as air temperature, relative humidity, sunshine hours, precipitation, and wind speed, all recorded at a three-hour temporal scale. These data were obtained from the agricultural meteorological station located in Rasht at 37°12' N latitude and 49°39' E longitude. To utilize this data at the time of satellite passage, three-hour values were converted into instantaneous values using linear interpolation. Given that the METRIC algorithm requires hourly data, this study relied on three-hour data from the meteorological station and the REF-ET software to estimate reference evapotranspiration due to the lack of hourly data in the study area. This software estimates evapotranspiration based on user-selected methods using empirical equations (such as the Penman-Monteith method, Priestley-Taylor method, evaporation pan, Hargreaves-Samani method, etc.) with acceptable accuracy on a daily and monthly basis (Rahimi, 2012).
2.2.2. Spatial Data
The MODIS sensor is mounted on the Terra satellite, positioned at an altitude of 705 kilometers above the Earth's surface. It captures reflectance data from various terrestrial phenomena across 36 spectral bands (ranging from 0.4 to 14 micrometers) with a spatial resolution of 250 to 1000 meters and a temporal resolution of one day (Leblon, 2005). In this study, cloud-free 1B-Level calibrated MODIS product images were obtained free of charge from the website http://modis.gsfc.nasa.gov. After downloading the images in HDF format from the aforementioned website, the desired image was converted to a format compatible with ERDAS IMAGINE using ENVI software. This method preserves the coordinates of the satellite images, eliminating the need for further geometric correction (Leblon, 2005). Finally, the maps and final images related to the energy balance equation parameters and evapotranspiration (ET) were prepared as different layers using ArcGIS software.
3.2.2. Lysimetric Data
A lysimeter is a controlled, enclosed system comprising soil, water, and plants, used for the precise measurement of water consumption by plants (Amini et al., 2023). In this study, as shown in Figure (3), a lysimeter located in a 1.5-hectare field at the Rice Research Institute in the country was utilized. This field is situated 300 meters from the meteorological and agricultural research station in Rasht County. To measure the daily evapotranspiration (ET) during the growth period of the rice plants, 220-liter metal barrels were employed as lysimeters. For this purpose, the barrels were cut in half at their midsection, resulting in metal cylinders with a height and diameter of 60 centimeters. Then, they were transported to the designated rice paddy locations for installation. In each lysimeter, five rice plants were placed around the perimeter and one plant was positioned in the center, with a distance of 20 centimeters between them. During the growth period of the rice plants, the ET was measured daily in the installed lysimeters. Finally, the ET data obtained from the lysimeters on August 12, 2014, were utilized to evaluate the performance and accuracy of the METRIC algorithm.
Figure 2. Stages of measuring actual evaporation and transpiration in the rice paddy. (a) Placement of the evaporation pan in the field. (b) Setup and planting of seedlings in the lysimeters located in the field. (c) Daily measurement of evaporation and transpiration in the lysimeters. (d) Examination and evaluation of rice plants in the lysimeters at different growth stages.
3.2. METRIC Algorithm
One of the practical algorithms for estimating evapotranspiration (ET) using satellite images, based on the energy balance concept, is the METRIC algorithm. This algorithm calculates ET at instantaneous, daily, and seasonal time scales using satellite imagery and minimal ground data (French et al. 2015). The energy consumed by ET in this method is calculated as the residual from the energy balance equation at the surface, as follows (Allen et al. 2007):
\(LE = R_{n} - G - H\) (1)
where LE represents latent heat flux, \(R_{n}\) is net radiation,\(\ G\) is soil heat flux, and H is sensible heat flux, all expressed in watts per square meter \(w.m^{- 2}.\)
1.3.2. Net Radiation
In the METRIC algorithm, the amount of net radiation (\(R_{n}\)) is calculated from the balance of outgoing and incoming radiation fluxes using the following equation (Bastiaanssen et al. 1998):
\(R_{n} = (1 - \alpha)R_{s \downarrow} + R_{L \downarrow} - R_{L \uparrow} - \left( 1 - \varepsilon_{0} \right)R_{L \downarrow}\) (2)
\(R_{s \downarrow}\), \(R_{L \downarrow}\), and \(R_{L \uparrow}\) represent the incoming shortwave radiation to the Earth's surface, the incoming longwave radiation to the Earth's surface, and the outgoing longwave radiation emitted from the Earth's surface, respectively, expressed in watts per square meter (W·m⁻²).\(\ \alpha\) And \(\varepsilon\) denote the surface albedo and surface thermal emissivity, respectively. The expression (\(1 - \varepsilon_{0}\) (represents the fraction of incoming longwave radiation that is reflected from the surface (Liou et al., 2014). For estimating the surface albedo in MODIS images, equation (3) was used (Liang, 2001).
\(\alpha = 0.16{\ \rho}_{1} + 0.291\ \rho_{2} + 0.243{\ \rho}_{3} + 0.116{\ \rho}_{4} + 0.112{\ \rho}_{5} + 0.081{\ \rho}_{7} - 0.0015\) (3)
Where \(\rho\) the spectral reflectance of bands 1 to 7 of the MODIS sensor.
2.3.2. Soil Heat Flux
The soil heat flux (G) is the portion of the net radiation received by the soil surface that is used for heating the soil depths through the conduction process, and it is estimated using the following relationships (Tasumi, 2003).
\(\frac{G}{R_{n}} = 0.05 + 0.18e^{- 0.521LAI}\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ LAI \geq 0.5\) (4)
\(\frac{G}{R_{n}} = \frac{1.8\ (T_{s} - 273.15)}{R_{n}} + 0.084\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ LAI < 0.5\) (5)
where \(T_{s}\) the land surface temperature in ° K, LAI is the Leaf Area Index, and \(R_{n}\) is the net radiation in\(\ w.m^{- 2}\). In this study, the land surface temperature was calculated using the following equation (Coll & Caselles, 1997):
\(LST = 0.39T_{31}^{2} + 2.34T_{31} - 0.78T_{31}T_{32} - 1.34T_{32} + 0.39T_{32}^{2} + 0.56\) (6)
where \(T_{31}\) and \(T_{32}\ \)are the brightness temperatures in °K for bands 31 and 32 of the MODIS sensor.
The values of the Leaf Area Index (LAI) and the Soil-Adjusted Vegetation Index (SAVI) are also estimated using equations (7) and (8) (Allen et al., 2002):
\(LAI = - \frac{\left( \ln\left( \frac{0.69 - SAVI}{0.59} \right) \right)}{0.91}\) (7)
\(SAVI = \frac{(1 + L)(\rho_{3} - \rho_{2})}{L + \rho_{3} + \rho_{2}}\) (8) where L is a dimensionless correction factor, typically set to 0.5 (Huete, 1988).
3.3.2. Sensible Heat Flux
The sensible heat flux (H) is the portion of the net radiation received by the soil surface that is used for heating the air through convection and conduction processes, and it is calculated using the following equation (Bastiaanssen et al., 2000).
\(H = \frac{\rho_{air}.C_{p}.dT}{r_{ah}}\) (9)
where \(\ \rho_{air}\) is the air density in\(\ kg.m^{- 3}\), \(C_{p}\) is the specific heat of the air in\(\ j.{kg}^{- 1}.{{^\circ}k}^{- 1}\), \(dT\) is the temperature difference between two heights\({\ Z}_{1}\) \({\ Z}_{2}\) in \({^\circ}k\), and \({\ r}_{ah}\) is the aerodynamic resistance of the air against heat transfer in \(s.m^{- 1}\).
4.3.2. Latent Heat Flux of Evaporation
In this section, the amount of latent heat flux of evaporation (LE) is calculated based on the net radiation (\(R_{n}\)), sensible heat flux (H), and soil heat flux (G). The actual evapotranspiration at the time of satellite passage is then calculated using the following equation (Allen et al., 2011):
\({ET}_{inst} = 3600\frac{LE}{\lambda\ \rho_{w}}\) (10)
where \({ET}_{inst}\) is the instantaneous evapotranspiration in \(mm.h^{- 1}\), \(\lambda\) is the latent heat of evaporation in \(j.{kg}^{- 1}\), \(\rho_{w}\) is the density of water in \(kg.m^{- 3}\), and the number 3600 is the conversion factor from seconds to hours. In the METRIC algorithm, the reference evapotranspiration fraction \(kg.m^{- 3}\) can be estimated using the following equation:
\({ET}_{r}F = \frac{{ET}_{inst}}{{ET}_{r}}\) (11)
The METRIC algorithm calculates daily evapotranspiration using the following equation:
\({ET}_{24} = {ET}_{r}F \times {ET}_{r - 24}\) (12)
Where \({ET}_{r - 24}\) is the sum of \({ET}_{r}\)a 24-hour period for the day of satellite imaging, and its value is obtained by summing the hourly \({ET}_{r}\) values throughout the day the satellite passes over the location.
3. Results and Discussion
1.3. Selection of Cold and Warm Pixels
Considering that one of the most critical steps in the METRIC algorithm is the selection of cold and hot pixels, this study utilized surface temperature, vegetation index, and surface albedo to select these pixels. Specifically, the pixels that numerically exhibited the lowest temperature, the highest vegetation index, and the lowest albedo were chosen as cold pixels, while those with the opposite conditions were selected as hot pixels (Noori, 2010). Given the significant role of the aforementioned parameters in the results obtained from the METRIC algorithm, the variations of these parameters in the study area on the date on August 12, 2014, are presented in Figure (3).
Figure 3. Map of NDVI Index, Albedo, and Surface Temperature in °K on August 12, 2014
According to Figure 3, in the image corresponding to the NDVI index, the majority of the area is shown in green, indicating dense vegetation and forested regions. Residential areas and lands lacking vegetation (shown in red) account for the lowest NDVI values. The results obtained align reasonably well with the NDVI values presented for various surfaces by Helben (1986). In the image related to albedo, the highest albedo values (shown in blue) correspond to rice fields and paddies. The northern part of the image, representing water-covered areas, has the lowest albedo values. The albedo value recorded on the day of data collection was in the range of 0.15 to 0.25, which corresponds closely with the values reported by Guttmann (1988) for rice fields. Based on the LST image, the surface temperature values obtained ranged from 305 to 315 °K, with the highest temperatures corresponding to residential areas and regions lacking vegetation (shown in green), while the lowest surface temperatures were associated with open water bodies and areas with dense vegetation. Overall, the highest temperature and the lowest NDVI and albedo values were found in residential areas, whereas the lowest surface temperature and the highest NDVI and albedo values were observed in forested areas with dense vegetation. According to the findings of the study by Bagheri Harooni et al. (2012), there is an inverse relationship between vegetation cover, albedo, and surface temperature, which is consistent with the results of this research."
2.3. Evaluation of Energy Balance Components
The results obtained from the energy balance components, estimated using the parameters of surface temperature, albedo, and vegetation index, are presented in the final map shown in Figure (4).
Figure 4. Variations
in Net Radiation Flux (Rn), Soil Heat Flux (G), and
Sensible Heat Flux (H) in the Study Area on August 12,
2014.
According to Figure 4, the highest net radiation flux (Rn) is observed in forested areas, while the lowest values are found in residential areas and lands lacking vegetation (shown in red). Similarly, in the maps related to soil heat flux (G) and sensible heat flux (H), residential areas and lands lacking vegetation have the highest values, while forested areas exhibit the lowest values. Dense vegetation minimizes soil heat flux by obstructing light from reaching the soil surface, and as vegetation cover decreases, soil heat flux increases (Rahimi, 2012).
3.3. Evaluation of Instantaneous and Daily Evapotranspiration
Using the energy balance components and the empirical relationships mentioned, the values of \({ET}_{inst}\) and \({ET}_{24}\) were calculated for the study area based on the METRIC algorithm (Figure 5). According to these images, the highest values of instantaneous and daily evapotranspiration are associated with water surfaces (in the northern part of the images) and forested areas with dense vegetation (in the southern part of the images). In general, the highest ET values were obtained in areas with high NDVI and low surface temperatures, which is consistent with the findings of Ghorbani et al. (2014).
Figure 5. Maps of instantaneous and daily evapotranspiration in the study area on August 12, 2014.
4.3. Evaluation of METRIC Algorithm Performance
Finally, to evaluate the results of the study, the daily ET value obtained using the METRIC algorithm was compared with lysimeter data from the Rice Research Institute of Rasht on the day of imaging. A difference of -0.55 mm/day was observed between the calculated and measured values, indicating an underestimation by the METRIC algorithm. One reason for this error in the study is the pixel size and the low spatial resolution of MODIS sensor images. Since the pixel sizes are large, they account for diverse conditions within the study area when evaluating ET, and this heterogeneity within the pixels causes errors (Noori, 2010). Moreover, due to the absence of hourly data, three-hourly data were used to estimate the reference evapotranspiration, which in itself contributes to error and underestimation in the algorithm. Additionally, selecting cold and hot pixels from MODIS images with low spatial resolution is challenging and introduces minor errors (Omidvar et al., 2012).
4. Conclusion
Considering the significance of energy balance components and their impact on assessing various terrestrial phenomena, it is essential to evaluate the accuracy of existing methods for estimating these components. In this study, using MODIS sensor imagery and the METRIC algorithm, the energy balance components for Rasht County were estimated for August 12, 2014. Subsequently, using meteorological data and the aforementioned components, evapotranspiration in the study area was calculated. To assess the performance of the METRIC algorithm, lysimeter data from the Rice Research Institute in Rasht was utilized. The comparison between the estimated data and lysimeter data revealed an error of -0.55 mm/day, indicating an underestimation by the METRIC algorithm. Overall, the results showed that the use of three-hourly data instead of hourly data, inaccuracies in selecting cold and hot pixels, and the use of MODIS images with low spatial resolution could be the primary causes of this discrepancy and underestimation in the study's results. Therefore, it is recommended that future studies employ high-resolution imagery such as Landsat and ASTER, along with hourly meteorological data. Additionally, the accuracy of energy balance-based algorithms using remote sensing should be evaluated across different vegetation covers, plant growth stages, and climates.
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