A novel method based on Landsat 8 and MODIS satellite images to estimate monthly reference evapotranspiration in arid and semi-arid climates

Introduction
Accurate estimation of reference evapotranspiration (ET₀) is essential in water management in the agricultural sector, especially for arid and semi-arid climates. ET₀ plays a vital role in the water and energy cycle and is an essential link between ecological and hydrological processes. Therefore, accurately estimating ET₀ is a major issue for understanding the water cycle in continuous soil-plant-atmosphere systems. The traditional ET₀ estimation methods are mainly based on physical principles, such as Priestley-Taylor, Hargreaves, and Samani, which have many limitations in accurate ET₀ estimation in cases of minimum meteorological parameters (such as radiation solar, wind speed, and air temperature). Numerous studies have focused on ET₀ estimation using terrestrial data. However, in the case of a lack of meteorological stations, the conventional methods of estimating ET₀ using ground data will be inefficient, so remote sensing (RS) provides the possibility to fill such a gap, in such conditions, satellite images are the most effectivefor evaluating ET₀ in large areas. Because satellite images have a suitable spatial and temporal resolution, the time series of satellite images can be used to estimate ET₀. The successful estimation of ET₀ from satellite images paved the way for its prediction using artificial intelligence models. The primary satellite imagery sources can be obtained from Landsat, Moderate Resolution Imaging Spectroradiometer (MODIS), and Global Land Surface Satellite (GLASS). Remote sensing data provides the possibility of recording more information through satellite images. Remote sensing methods can be used to extract vegetation information and different types of radiation, which help estimate ET₀.
 
Materials and Methods
In the current research, two different agro-climatic locations including Ahvaz and Tabriz stations were selected. According to De Martonne classification method, Ahvaz was classified as dry climate and Tabriz as semi-arid climate. In this research, random forest (RF) and multi-layer perceptron (MLP) algorithms have been used to estimate monthly ET₀ in Ahvaz and Tabriz stations. The input parameters were selected from Landsat 8 and MODIS satellite images in the time period of 2014 to 2021. The utilized parameters were the monthly average, Landsat Land Surface Temperature (LST_Land), MODIS Land Surface Temperature (LST_MOD), Landsat Satellite Normalized Difference Vegetation Index (NDVI_Land) and MODIS Normalized Difference Vegetation Index (NDVI_MOD). To evaluate the accuracy of the input parameters and models, the estimated monthly ET₀ was evaluated with the monthly ET₀ of the FAO-Penman-Monteth equation.
 
Results and Discussion
The input parameters for implemented models were Landsat land surface temperature (LST_Land), MODIS land surface temperature (LST_MOD), Landsat Satellite Normalized Difference Vegetation Index (NDVI_Land), and MODIS Normalized Difference Vegetation Index (NDVI_MOD). Six possible scenarios were defined to estimate monthly ET₀. The first two scenarios were considered as a single parameter (scenarios 1 and 2) and other scenarios were evaluated with two input parameters. Scenarios 3 and 4 were evaluated based on the parameters of the Landsat satellite and MODIS sensor, respectively. In scenarios 5 and 6, monthly ET₀ was estimated with Landsat and MODIS NDVI and Landsat and MODIS LST, respectively, to determine the effect of NDVI and LST values on ET₀ estimation. According to the obtained results, for the MLP and RF models in Ahvaz station, the value of R² ranges from 0.440 to 0.972 and 0.271 to 0.983, respectively. In Ahvaz station, the lowest and highest RMSE is 0.279 mm.month^-1 (RF-5 model) and 1.396 mm.month^-1 (RF-4 model), respectively. Additionally, in this station, the highest and lowest values of NS are 0.962 (RF-5 model) and 0.042 (RF-4 model), respectively. According to the obtained results, in estimating the monthly ET₀, the best performance is related to MLP-6 (R²=0.972, RMSE=0.348, and NS=0.940) and RF-4 (R²=0.983, RMSE=0.279, and NS=0.962). The highest and lowest values of R² in Tabriz station were 0.988 and 0.186, respectively. Moreover, MLP-4 and RF-5 models in this station have the lowest and highest RMSE, respectively. The results showed that in Tabriz station, the best performances were related to MLP-4 (R²=0.988, RMSE=0.299, and NS=0.935) and RF-4 (R²=0.979, RMSE=0.302, and NS=0.933). In addition, in this station, the RF-5 model has the weakest performance among all models with R²=0.186, RMSE=1.169, and NS=0.012.
 
Conclusion
The results showed that 1) the accuracy of monthly ET₀ estimation in Ahvaz (arid climate) and Tabriz stations (semi-arid climate) with scenario 4 including LST_MOD and NDVI_MOD was better than other investigated scenarios; 2) in estimating monthly ET₀ using a single input parameter including LST_Land (scenario 1) and LST_MOD (scenario 2), in both Ahvaz and Tabriz stations, scenario 2 had better performance with both MLP and RF models; 3) estimation of monthly ET₀ in Ahvaz and Tabriz stations has performed best with RF-4 and MLP-4 models, respectively, with LST_MOD and NDVI_MOD input parameters (scenario 4); 4) in the comparison of scenario 5 (NDVI_Land, NDVI_MOD) and scenario 6 (LST_Land, LST_MOD) in both RF and MLP models, scenario 6 has the best performance in estimating monthly ET₀; and 5) in the comparison of monthly ET₀ estimation in both arid and semi-arid climates, the best performance with a high correlation coefficient was obtained with the MLP model in semi-arid climates.