Application of a Fractional Instantaneous Unit Hydrograph in the TOPMODEL: A Case Study in Chengcun Basin, China

The movement of water flow usually has history and path dependence. Fractional calculus is very suitable for describing the process with memory hereditary properties. In this study, order differential equation in Nash confluence system was extended from integer to fractional order. On basis Laplace transform, instantaneous unit hydrograph obtained, which used describe long-term basin system. Furthermore, enhanced TOPMODEL (FTOP) model obtained by applying as surface runoff calculation. Taking Chengcun Basin China an example, FTOP simulate daily 22 floods 1989 1996. simulation results were compared two original models (the NTOP ITOP models). show that simulation, Nash–Sutcliffe efficiency (NSE), relative error (RE), root mean square (RMSE) 0.82, −11.14%, 15.25 m3/s, respectively, being slightly better than other models. According hydrologic frequency curve, measured divided into different levels. It found can improve effect medium-flow (frequency between 10% 50%) low-flow more sections a certain extent. flood average depth (RDRE), peak discharge (PDRE), occurrence time (POTE), NSE 1.99%, 14.06%, −1.27, 0.88, indicating had been improved. Especially NSE, improvement prominent, meaning flooding process. However, not significantly These conclusions indicate method using effect.