Hydrological Drought Instantaneous Propagation Speed Based on the Variable Motion Relationship of Speed‐Time Process

Abstract

Abstract It is difficult to predict and track the propagation of a hydrological drought because it is hard to determine its propagation speed. We propose a useful framework for calculating the hydrological drought instantaneous propagation speed which includes the instantaneous development speed ( IDS ) and instantaneous recovery speed ( IRS ). First, the run theory was applied to subdivide the propagation of individual hydrological drought events into the development and recovery stages and to determine the individual propagation times (drought development duration and drought recovery duration). Then the hydrological drought instantaneous propagation speed of each hydrological drought event, including the IDS and IRS , were determined based on the variable motion relationship of speed‐time process commonly applied in physics. Finally, the optimal theoretical values of the IDS and IRS were evaluated using a cross‐validation method. Three hydrometric stations, located at the upstream catchment with less human activities influence, were chosen from different countries (China, the United States, and Germany) to demonstrate the satisfactory performance of this proposed framework. The results indicate that the variable motion relationship of speed‐time process can provide an assessment of the overall hydrological drought propagation and perform well for identifying the propagation time in these study areas. The optimal theoretical values of IDS (or IRS ) obtained by the variable motion relationship can simulate the actual drought development duration (or drought recovery duration) of hydrological drought well. The sensitivity of IDS (or IRS ) of hydrological drought is correlated with climate, catchment characteristics, and human activities that should be explored to improve hydrological drought propagation prediction.