关键词: Nash瞬时单位线, 分数瞬时单位线, 新安江模型, 地表汇流, 长程记忆性,

Abstract: The Nash instantaneous unit hydrograph reflects the short-term memory of the flow routing, while the hydrological responses of natural river systems are characterized as historical dependence and route dependence with long memory feature. Fractional calculus is a non-local operator expressed in differential-integral form, which is very suitable for describing processes with memory and genetic properties. This paper extended the order of differential equations in the routing system from integer order to fractional order, used the Laplace transform to derive the fractional instantaneous unit hydrograph(FIUH), and applied it to describing the long-term memory of the flow routing. A series of experimental data that were not influenced by the runoff yield error were selected to verify the FIUH. Further, the FIUH was applied to the surface runoff routing of the Xin'anjiang model. The results show that the simulation of the high discharges can be improved to a certain extent, thereby improving the overall simulation accuracy, however it may be affected by the runoff yield error, so the simulated effects for flood peaks and total runoff are not improved significantly.

Key words: Nash instantaneous unit hydrograph, fractional instantaneous unit hydrograph, Xin'anjiang model, surface runoff routing, long-term memory