A new Budyko framework extension using time series SARIMAX model

The Budyko framework, used for water balance studies, is an effective tool that estimates the actual evapotranspiration, balancing between energy and water availabilities. In this study, we investigate eight Budyko framework equations as well as the GR1A and GR2M models on the Nile tributary Blue-Nile catchment. On the annual time scale, all investigated models and equations show poor results. Moreover, the resulting errors on the monthly scale show a clear pattern of seasonality and autocorrelation. To overcome such deficiencies, we propose a time series SARIMA model, to fit the error term of the best performing Budyko equation. Building on the time series capabilities, we extend the Budyko framework to allow the incorporation of values of precipitation and potential evapotranspiration from previous months. The selected performance criteria are the Nash-Sutcliffe and Kling-Gupta efficiencies, as well as the coefficient of determination and bias. The novel hybrid SARIMAX-Budyko model exhibits high performance not only on the Blue Nile but also on other five major rivers worldwide. The proposed model outperforms the previously published Budyko equations, as well as the GRIM and GR2A as benchmark models, in almost all performance criteria and especially on the annual time scale.