Development of a temperature-based potential evaporation algorithm for supporting integrated and global-scale climate classifications

Abstract

The assessment of potential evaporation or reference combined evaporation and transpiration is among the most important components for many hydro-climatic applications such as irrigation design and management, water balance assessment studies, and assessment of aridity classification indices. Aridity classification indices such as UNEP, Thornthwaite and others are usually employed at large scale applications and require respective estimations of potential or reference combined evaporation and transpiration. The major problem in such applications is not only the limited availability of stations per se but also the limitation of many stations to provide data for a complete set of parameters (i.e., precipitation, temperature, solar radiation, wind speed, humidity). A complete set of climate parameters is prerequisite for accurate estimations of potential or reference combined evaporation and transpiration using the most advanced methods, which are expressions of energy balance (e.g., ASCE-standardized method, successor method of Penman-Monteith FAO-56). Unfortunately, large scale applications of aridity indices suffer from this limitation and the common solution is to use temperature-based formulas. The most popular and historical temperature-based formula is the one of Thornthwaite, which was developed to support the respective aridity classification index. The popularity of this formula is based on the minimum requirement of mean monthly temperature and latitude at the location of interest. Considering the above, this study aims to develop a global database of local correction factors for the original Thornthwaite formula that will better support all hydro-climatic applications but mostly to support large scale applications of aridity indices, which are highly prone to data limitations. The hypothesis that is tested in this work is that a local correction factor that integrates the local mean effect of wind speed, humidity and solar radiation can improve the performance of the original Thornthwaite formula and to convert it at the same time to a formula of reference combined evaporation and transpiration for short reference crop. The global database of local correction factors was developed using gridded climate data of the period 1950-2000 at 30 arc-sec resolution (~1 km at the equator) from freely available climate geodatabases. The correction factors were produced as partial weighted averages of monthly ratios between the benchmark ASCE-standardized method for short reference crop versus the original formula of Thornthwaite by giving more weight to the warmer months and by excluding colder months of Epr<45 mm month-1 where monthly ratios are highly unstable with unrealistic values. The validation of the correction factors was made using raw data from 525 stations of Europe, California-USA and Australia that cover periods mostly after 2000 and up to 2020. The validation procedure showed significant improvement in the estimations of reference combined evaporation and transpiration using the corrected Thornthwaite formula that led to a 19.4% reduction of RMSE for monthly and a 55% reduction of RMSE for annual estimations compared to the original formula. The variation of the correction factor was also investigated in different major Köppen climate classes and it was found that tends to increase in drier and warmer territories. The five major Köppen groups were ordered as follows B > C > A > D > E considering the magnitude of the correction factors values. The corrected and original Thornthwaite formulas were also evaluated by their use in UNEP and Thornthwaite aridity indices using as a benchmark the respective indices estimated by the ASCE-standardized method. The analysis was made using the validation data of the stations and the results showed that the corrected Thornthwaite formula increased by 18.3% the accuracy of detecting identical aridity classes with ASCE-standardized method for the case of UNEP classification, and by 10.4% for the case of Thornthwaite classification in comparison to the original formula. The performance of the corrected formula was extremely improved especially in the case of non-humid classes of both aridity indices. The overall results showed that the correction factors produced in this study can improve the performance of the original Thornthwaite formula providing better estimations of the aridity classification indices.