Estimation of the Nash Model Parameters Based on the Concept of Geomorphologic Dispersion

This study presents a new method to estimate the Nash model parameters on the basis of the concept of geomorphologic dispersion stemming from spatial heterogeneity of flow paths within a catchment. The proposed method is formulated by including physically meaningful characteristic velocities for channel and hillslope and also takes account of the effect of complex interactions between channel and hillslope hydrological behaviors on catchment responses. We applied the proposed formulas to the Bocheong watershed, an experimental area established under the International Hydrological Programme (IHP) in Korea, with several storm events to assess the individual effect of channel and hillslope on hydrological responses in the study site. The characteristic velocities were estimated by topographic data based on a $20\times 20\mathrm{m}$ digital elevation model (DEM) from a $1:25000$-scaled topographic map and statistical features of the historical events. We then calculated the Nash model parameters by substituting the estimated characteristic velocities into the new formulas proposed in this study. The sensitivity analysis results of the Nash model parameters and instantaneous unit hydrograph (IUH) shape of the characteristic velocities indicated that the scale parameter of the Nash model was more sensitive to the hillslope velocity than the channel velocity, whereas all of the Nash model parameters were determined by the relative difference between the hillslope and channel characteristic velocities. The rising limb of IUH and time to peak were dependent mainly on the channel velocity, whereas the recession limb of the IUH reacted very sensitively to the variation of the hillslope velocity. In addition, the skewness of the IUH varied with the ratio of characteristic velocities. Finally, the IUHs, estimated from regional analysis of the characteristic velocities, led to acceptable and constant hydrological responses for the catchment scale. If the improved regional analysis, modeled on hydrodynamic (or physical) approaches, is performed, the proposed formulas for the Nash model in this study can be a useful tool to simulate rainfall-runoff processes in ungauged basins.