Correcting Thornthwaite evapotranspiration formula using a global grid of local coefficients to support temperature-based estimations of reference evapotranspiration and aridity indices

Thornthwaite's formula is globally an optimum candidate for large scale applications of potential evapotranspiration and aridity assessment at different climates and landscapes since it has the lower data requirements compared to other methods and especially from the ASCE-standardized reference evapotranspiration (former FAO-56), which is the most data demanding method and is commonly used as benchmark method. The aim of the study is to develop a global database of local coefficients for correcting the formula of monthly Thornthwaite potential evapotranspiration (Ep) using as benchmark the ASCE-standardized reference evapotranspiration method (Er). The validity of the database will be verified by testing the hypothesis that a local correction coefficient, which integrates the local mean effect of wind speed, humidity and solar radiation, can improve the performance of the original Thornthwaite formula. The database of local correction coefficients was developed using global gridded temperature and Er data of the period 1950-2000 at 30 arc-sec resolution (~1 km at equator) from freely available climate geodatabases. The correction coefficients were produced as partial weighted averages of monthly Er/Ep ratios by setting the ratios' weight according to the monthly Er magnitude and by excluding colder months with monthly values of Er or Ep <45 mm month-1 because their ratio becomes highly unstable for low temperatures. The validation of the correction coefficients was made using raw data from 525 stations of Europe, California-USA and Australia including data up to 2020. The validation procedure showed that the corrected Thornthwaite formula Eps using local coefficients led to a reduction of RMSE from 37.2 to 30.0 mm m-1 for monthly and from 388.8 to 174.8 mm y-1 for annual step estimations compared to Ep using as benchmark the values of Er method. The corrected Eps and the original Ep Thornthwaite formulas were also evaluated by their use in Thornthwaite and UNEP (United Nations Environment Program) aridity indices using as benchmark the respective indices estimated by Er. The analysis was made using the validation data of the stations and the results showed that the correction of Thornthwaite formula using local coefficients increased the accuracy of detecting identical aridity classes with Er from 63% to 76% for the case of Thornthwaite classification, and from 76% to 93% for the case of UNEP classification. The performance of both aridity indices using the corrected formula was extremely improved in the case of non-humid classes. The global database of local correction factors can support applications of reference evapotranspiration and aridity indices assessment with the minimum data requirements (i.e. temperature) for locations where climatic data are limited.