An extended time-varying Budyko framework for quantifying the hydrological effect of vegetation restoration under climate variations at watershed scale

The Budyko framework, widely used to quantify the watershed hydrological response to the watershed characteristics and climate variabilities, is continuously refined to overcome the disadvantages of steady state assumption. However, dynamic variations in vegetations and climate variables are not fully integrated including coverages and precipitation regimes of intensity, frequency, and duration. To address this, we developed an innovative approach for determining the parameter ω in the Budyko framework to quantify the hydrological effects of vegetation restoration in a mesoscale watershed located in northern China. We found that fractional vegetation coverage (FVC), heavy precipitation amount (95pTOT), and the number of precipitation days (R01mm) are significant variables for estimating ω to improve the predictive capability of the watershed response. This extended time-varying Budyko framework can rigorously capture the temporal variations and underlying mechanisms of interactions between vegetation dynamic and precipitation regime partitioning precipitation (P) to R. Under the Budyko-Fu framework, compared to constant ω (ω‾) or ω that only considers FVC (ω^P) or precipitation regimes (ω^FVC) for simulating R, using ω that integrated FVC and precipitation regimes (ω^P-FVC) can improve Nash-Sutcliffe efficiency coefficient (NSE) by 24.81%, while reduced the root mean squared error (RMSE) and relative error (RE) by 64.08% and 65.77%, respectively. Although the increase in climatic dryness (PET/P) resulted in decreased R, the increase in FVC has also a significant contribution to this decrease due to vegetation restoration. We highlight that decrease precipitation intensity (95pTOT) and frequency (R01mm) amplified the hydrological effects of vegetation restoration, causing a 79.09∼100.31% increase in R compared to the independent impact of changes in FVC. We conclude that the extended time-varying Budyko framework by precipitation regime is more rigorous for quantifying the hydrological effects of ecological restoration under climate change and providing more reliable approach for adaptive watershed management.