Correcting Thornthwaite potential evapotranspiration using a global grid of local coefficients to support temperature-based estimations of reference evapotranspiration and aridity indices
Authors: Aschonitis Vassilis , Touloumidis Dimos , ten Veldhuis Marie-Claire , Coenders-Gerrits Miriam 
Published: January 2022

Abstract. 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 lower data
requirements compared to other methods and especially from the
ASCE-standardized reference evapotranspiration (formerly FAO-56), which is the most data-demanding method and is commonly used as the 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, rainfall, and Er data of the period 1950–2000 at 30 arcsec 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 per month
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 step estimations and from 388.8 to 174.8 mm yr−1 for annual step estimations compared to Ep using as a benchmark the values of the 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 a 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 the 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 index assessment
with the minimum data requirements (i.e., temperature) for locations where
climatic data are limited. The global grids of local correction coefficients
for the Thornthwaite formula produced in this study are archived in the PANGAEA
database and can be assessed using the following link: https://doi.org/10.1594/PANGAEA.932638 (Aschonitis et al., 2021).