Analysis of Climatic Factors Affecting Actual Evapotranspiration through Weighted Regression Model. Case study: Eastern Towns of Uremia Lake

Introduction
For the first time, Faddingham presented a geographic weight regression model. He tried to study the aspects of space heterogeneity. After that, Bronson examined the relationship between housing prices and areas. Which encountered a number of issues in relation to the model, which included the selection of variables, bandwidth and spatial correlation errors. Using the GWR, Franklin analyzed the spatial characteristics of the rainfall along with the elevation changes. Elvi also used this model to study the spatial factors that affect land prices. The GWR produces spatial information that expresses spatial variations between variables' relationships. Therefore, the maps produced from these analyzes play a key role in the spatial non-static description and interpretation of variables (Mennis 2006) and an equation Generates a separate regression for each observation instead of calibrating an equation, so it allows the parameter values ​​to be continuously changed in the geographic space. Each of the equations is calibrated using a different weight of the observations contained in the total data. And more relative weights are assigned to closer observations and less or zero weights to those who are far away. 
Data and Method
The Surface Energy Balance Algorithm for Land (SEBAL) calculates the surface heat flux instantaneously as well as 24-hour. The latent heat flux shows the energy required for true evapotranspiration and is calculated as the remainder of the equilibrium energy equation (Mobasheri, 2005). In remote sensing estimates of surface Albedo, surface temperature and surface leakage in the thermal infrared region, reflectance is used to calculate spatial variations in short-wave radiation and long-wave radiation emitted from the surface of the earth. A combination of short-wave and long-wave radiation combines the ability to calculate the pure absorbed surface radiation for each image pixel. Each of the equations is calibrated using a different weight of the observations contained in the total data. And more relative weights are assigned to closer observations and less or zero weights to those who are far away. In other words, the GWR only uses geographically close observations to estimate local coefficients. This method of weighting is based on the idea that the use of geographically close observations is the best way to estimate local coefficients. The GWR method not only does not consider the effects of self-variables on the independent variable, but also the effects of neighboring situations. The values ​​of the geographic weighting model can be used to describe the spatial correlation of the factors used. Therefore, we extend the study area to several sections We divide the values ​​of the geographic weight coefficients in each of the sections in relation to each of the environmental parameters. Unlike regular regression models, they provide an equation for describing general relationships between variables. GWR allows the parameter values ​​to be changed continuously in the geographic space. Each of the equations is obtained using a different weight of the observations contained in the total data.
Results and Discussion
The analysis of the relationships between selected indices by geographic weighted regression model and the classification of output values ​​through the normalization of data in seven categories. The values ​​obtained vary between 1 and 1, and the smaller the index, the spatial disjunction is variable, and the larger it shows the presence of spatial clusters. It was found that all three indexes of evapotranspiration, surface temperature and vegetation index have cluster spatial pattern. Therefore, the null hypothesis is based on the spatial correlation itself, and as a result, three of the above indicators can be used for spatial analysis of the actual evaporation. Based on the correlation between the factors affecting the macroeconomic factors, the factor of vegetation index has the most effect on the magnitude of the spatial distribution in the studied area (53% with an area of ​​471782864 square meters). However, as the results are clear, this number is an overall number and covers the overall situation in the area. And does not refer to spatial features of the area. In the results of weighted regression, the effect of elements can be observed spatially. Accordingly, according to the geographic weighted regression method, the relationship between evapotranspiration and surface temperature was negatively affected and negatively affected. The relationship between dehiscence and vegetation index was studied in different years. The highest digit on the seventh floor is 13/99 and in the area of ​​266611500, which shows a high positive effect. The relationship between evapotranspiration and the Albedo shows the highest value in the first and second classes. The values ​​of 18 and 10 in the area of ​​490428000 and 1170753300 m 2, respectively, show a very negative impact and a significant negative effect.
Conclusion
Geographic weighted regression method is a statistical method that is adapted to study local patterns. This method is, in fact, a technical technique that analyzes the relationship between spatial variables in a hypothetical unpopular space. In this research, we tried to express the effect of several indicators on actual evaporation. These indicators are not all indicators that have had an impact on actual evapotranspiration Because actual evapotranspiration is closely related to other climatic factors. Because of the unique ability of spatial weighted regression to identify and analyze the relationships between variables, it is recommended to use it in quantitative analyzes. The Z classes resulting from the GWR analysis of the actual evapotranspiration in different years have different states that indicate the spatial effect of the surface temperature in different conditions.