Regression model for potential evaporation prediction
Authors:   Ukrainian Hydrometeorological Institute, Oshurok Dmytro , Sidenko Vladyslav 
Published: December 2023

Potential evaporation is one of the key variables in numerous studies, such as water balance calculations or assessment of hydrological impacts on different crops. This parameter represents the maximum evaporation over a certain area under available atmospheric conditions. Thus, potential evaporation/evapotranspiration depends on a number of meteorological variables: solar radiation, air temperature and humidity, wind speed etc. Among all of the factors, thermal and solar radiation characteristics play the most important role. Some methods based only on these parameters can be found in literature as alternatives to simplify estimation of potential evaporation [1, 2]. The aim of this study is to derive a method for calculation of yearly sum of potential evaporation in complex terrain conditions based on regression relationship at points located at different elevation above sea level. For this reason, ERA5 reanalysis data at fifty grid points in Transcarpathia in the domain from 22.25°E to 24.5°E of longitude and from 48°N to 49°N of latitude were used. Three predictors were applied: mean air temperature of the warmest month of the year, mean temperature in June-August and yearly sum of total solar radiation that reaches a horizontal plane at the Earth’s surface. The last one consists of net short-wave radiation and downward long-wave radiation fluxes. The results of the analysis for the period 1961–2020 show the highest Pearson correlation coefficients for the third predictor in range 0.82–0.93 with mean r = 0.88. The first and the second variables have lower relationship with potential evaporation, mean r values equal to 0.64 and 0.78, respectively. The procedure for approximation of obtained relationships revealed strong dependencies of linear regression coefficients on terrain height for all predictors. This allows applying a regression model to approximate coefficients a and b likewise, however quadratic function fits better in this case. Overall, six experiments were conducted in order to calculate yearly sums of potential evaporation using approximated and non-approximated coefficients of regression. Obtained values have been compared to ERA5 actual evaporation. As a measure for results verification, we selected a sum of errors that are negative deviations from potential evaporation. The most accurate estimates were achieved based on total solar radiation without approximation of regression parameters. Approximation leads to larger errors, nevertheless both methods outperform “original” reanalysis estimates on 41% and 11%, respectively. Thermal parameters seem less acceptable to predict potential evaporation. Comparative analysis shows that the usage of mean temperature of summer season is more reasonable if radiation data is unavailable. It is worth noting that the largest errors detected at points located inside the main ridges and in the northeastern part of the Carpathians. We conclude that total solar radiation is the most suitable parameter for potential evaporation prediction. Moreover, it provides some improvement in precision compared to ERA5 potential evaporation. Derived regression relationships are particularly important for hydrological impacts estimations in the near future using climate projections data.