H. Mirhashemi

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**Abstract **

Introduction: Potential evaporation is the result of the combined effects of several meteorological elements, including air temperature, relative humidity (or vapor pressure for saturation), wind speed, sunshine hours and air pressure. The amount of potential evaporation depends on how these variables ...
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Introduction: Potential evaporation is the result of the combined effects of several meteorological elements, including air temperature, relative humidity (or vapor pressure for saturation), wind speed, sunshine hours and air pressure. The amount of potential evaporation depends on how these variables interact in each climate region. Potential evaporation response of each of these variables depends on the importance that variable plays in the environment. For example, in windy places, the importance of wind speeds in the potential evaporation rate increases relative to places with calm air. By changing each of these meteorological elements, while the rest of the elements react to the given change, the overall effect of these changes and reactions is reflected in the amount of potential evaporation. It is therefore obvious that the potential evaporation response to meteorological variables due to spatial and time variations of these variables is of a complex nature. Materials and Methods: For this study, monthly data of air temperature, air pressure at sea level, wind speed, relative humidity and sunshine hours were used as independent variables and monthly data of evaporation pan at Tabriz Synoptic Station as response or dependent variable. In this study, firstly, the nonlinear and linear relationship between meteorological elements and potential evaporation were identified through Generalized Additive Model (GAM), MARSplines Model, and Generalized Linear Model (GLM), respectively. In the next step, by applying the simplex algorithm on the MARSplines model, the evaporation response gradient levels were determined individually for the meteorological variables. Also, to understand the process of pure evaporation response to each of these variables under different climatic conditions, first three weather conditions based on Tabriz Synoptic Station data were defined in three scenarios as S-1, S-2 and S-3. Then, by controlling and maintaining the meteorological variables under these three scenarios and combining the simplex algorithm with the MARSplines Model, the net evaporation reaction curves for the meteorological variables changes were evaluated. Results and Discussion: The computational results show that in all combinations, the computational error of the GAM model is less than the GLM model. Also considering the significant variables in each model, the combination of temperature, pressure, wind speed and sunshine are considered as the best subset of the effective variables in the distribution of potential evaporation in both models. On the one hand, relative humidity in these two linear and nonlinear models, in combination with other variables, does not show a significant relationship with potential evaporation. The results of the graphs of Splin smoothing components of the GAM model show that the overall effect of temperature on the evaporation is incremental. But the unit amount of this effect increases with increasing temperature. The individual evaporation reaction against air temperature is similar to its combined reaction. It is thus clear that other meteorological variables do not play a significant role in the influence of air temperature on the evaporation gradient. The overall and hybrid effect of air pressure variations on the amount of evaporation is singular and decreasing. Instead, the individual effect of this variable on evaporation is very intense, decreasing, and partly linear. Therefore, the major influence of air pressure on evaporation in the environment is due to the performance of other variables that interfere with the relationship between these two variables. The evaporation hybrid response to wind velocity was also incremental, although the single and nonlinear evaporation response to wind velocity was not significant, but its tendency was to increase its slope with respect to wind velocity changes. Sunny hours also have a net effect on the amount of evaporation. However, the slope of the solitary effect of this variable, like wind speed, is more than its combined effect. Based on the GLM model results, except for relative humidity, the other variables have a significant linear effect on the potential evaporation. Evaporation response to changes in meteorological variables under S-1, S-2 and S-3 scenarios, while accurately determining the interaction of these variables in plotting absolute evaporation, implicitly implying the synergistic role of these variables in determining absolute evaporation. The lowest distance between the absolute values of evaporation under these three scenarios is related to air temperature, which implies less influence of air temperature than the other variables. That is, the effect of each of the meteorological variables on the amount of evaporation depends to a large extent on the relationship of this variable to other meteorological variables, if such a matter is less weighted for temperature. Conclusion: The results of this study show that, except for air pressure, which has an increment-reducing effect on evaporation, other variables have only an incremental influence on evaporation and the intensity of this relationship has changed. This process has resulted in a nonlinear component in the relation of independent variables to evaporation. Since hybrid spline smoothing graphs determine evapotranspiration response to each of the predictor variables by eliminating the effect of other variables, therefore, consideration of the composition of these meteorological variables provides more accurate information on evaporation behavior against environmental changes. Through individually fitting evaporation against these meteorological elements, one cannot find how evaporation works against environmental changes. Comparing individual and combined evaporation responses to meteorological variables, while identifying the net effect of each of these variables, explains why evaporation responses within a given unit differ from changing meteorological variables over different times and locations.