A universal triangle method for evapotranspiration estimation with MODIS products and routine meteorological observations: Algorithm development and global validation

The surface temperature (Ts) and vegetation index (VI) triangle method is one of the most famous and widely applied methods for regional evapotranspiration (ET) estimation. However, no robust validation has been performed yet to evaluate its accuracy on a global scale, making its accuracy unclear when compared with other global ET models. The main reason behind it is that most traditional triangle models depend on the Ts-VI feature space within a certain spatial domain to parameterize their boundary conditions. The domain dependency makes it impossible to derive universal boundaries for continental or global application. Under this background, this study presented a universal triangle method for ET estimation with Moderate Resolution Imaging Spectroradiometer (MODIS) products and routine meteorological observations. The solution for boundary conditions was performed pixel by pixel without the consideration of spatial domain based configuration. Specifically, the dry boundary was solved theoretically based on the surface energy balance equation, and the wet boundary was substituted by wet-bulb temperature estimated from dew point temperature and air temperature. The validation against ground observations collected from 33 flux towers worldwide shows that this universal triangle method achieved evaporative fraction (EF) estimation with the correlation coefficient of 0.65, the mean absolute error of 0.17, the root-mean-square-error of 0.20, and the bias of 0.13. These four metrics of daily ET estimation were 0.83, 0.71 mm/d, 0.90 mm/d, and 0.41 mm/d, respectively. This analysis is the first comprehensive validation of the triangle method on a global scale. The comparison with early work suggests that our universal triangle method on a global scale has reached a comparable accuracy to traditional triangle models at regional scale. However, the universal triangle method has the capacity to monitor ET continuously pixel by pixel without domain dependency. This is just what most traditional triangle methods do not possess.