Ratio Limits of Water Storage and Outflow in Rainfall-runoff Process

Abstract. Through the numerical simulations of the hydrodynamic model, the water storage and discharge are found to be limited to envelope lines and the discharge/water depth process lines during water rising and falling showed a grid-shaped distribution. Furthermore, if a catchment is regarded as a semi-open water storage system, there is a nonlinear relationship between the inside average water depth and the outlet water depth, namely the water storage ratio curve, which resembles the shape of a “plume”. In the case of an open channel without considering spatial variability, the water storage ratio curve is limited to three values (i.e., the upper, the steady, and the lower limit), which are found to be independent of meteorological (rainfall intensity), vegetation (Manning’s coefficient), and terrain (slope gradient) conditions. Meteorological, vegetation, and terrain conditions only affect the size of the “plume” without changing its shape. Rainfall, especially weak rain (rainfall intensity is less than 5.0 mm h^-1) significantly affects the fluctuations of water storage ratio, which can be divided into three modes, that is Mode Ⅰ during rainfall beginning stage, Mode Ⅱ during rainfall duration stage, and Mode Ⅲ during rainfall end stage. Results indicate that the determination of the nonlinear relationship of the water storage ratio curve under different geographical scenarios will provide new ideas for simulation and early warning of floods.