Complementary Relationship for Estimating Evapotranspiration Using the Granger-Gray Model: Improvements and Comparison with a Remote Sensing Method

Abstract. The Granger and Gray (GG) model, which uses the complementary relationship for estimating evapotranspiration (ET), is a simple approach requiring only commonly available meteorological data; however, most complementary relationship models decrease in predictive power with increasing aridity. In this study, a previously developed modified GG model using the vegetation index is further improved to estimate ET under a variety of climatic conditions. This updated GG model, GG-NDVI, includes Normalized Difference Vegetation Index (NDVI), precipitation, and potential evapotranspiration using the Budyko framework. The Budyko framework is consistent with the complementary relationship and performs well under dry conditions. We validated the GG-NDVI model under operational conditions with the commonly used remote sensing-based Operational Simplified Surface Energy Balance (SSEBop) model at 60 Eddy Covariance AmeriFlux sites located in the USA. Results showed that the Root Mean Square Error (RMSE) for GG-NDVI ranged between 15 and 20 mm month⁻¹, which is lower than for SSEBop every year. Although the magnitude of agreement seems to vary from site to site and from season to season, the occurrences of RMSE less than 20 mm month⁻¹ with the proposed model are more frequent than with SSEBop in both dry and wet sites. This study also found an inherent limitation of the complementary relationship under moist conditions, indicating the relationship is not symmetrical as previously suggested. A nonlinear correction function was incorporated into GG-NDVI to overcome this limitation. The resulting Adjusted GG-NDVI produced much lower RMSE values, along with lower RMSE across more sites, as compared to measured ET and SSEBop.