Integrating subgrid connectivity properties of the micro-topography in distributed runoff models, at the interrill scale

SummaryThe spatial configuration of micro-topography affects the runoff connectivity at the interrill scale and, therefore, the shape of the hydrograph. In a previous study, we demonstrated the ability of the so-called Relative Surface Connection (RSC) function to capture, at the grid scale, the evolution of the contributing area as a function of the depression storage filling. However, this function neglects the effect of surface detention, which is proportional to the runoff rate and which must be taken into account if one wants to predict correctly the discharge dynamics. Therefore we tested two corrective procedures in association with the RSC function to integrate, at the grid scale, the effects of both depression storage and surface detention dynamics. The weighted-source corrective procedure consists in weighing the effective supply of water between depression storage and runoff using the RSC function. The weighted-surface corrective procedure consists in splitting a single grid into parallel independent strips whose sizes depend on the RSC function and which activate at various times and then participate to the global runoff production. Those methods allowed to mimic in a simple way and at the grid scale synthetical and experimental hydrographs for complex subgrid micro-topographies.The weighted-source and especially the weighted-surface corrective procedures improved the hydrograph prediction compared to the classical approach where runoff only starts when depression storage capacity is full. In a purely numerical framework with four runoff scenarios on highly contrasted micro-topographies, this improvement was reflected in a significant increase of the median Nash and Sutcliffe coefficients E50 (E50 = 0.29 for the classical approach, E50 = 0.67 for the weighted-source procedure and E50 = 0.94 for the weighted-surface procedure).For the depression storage filling, an alternative to the Linsley equation was found and allowed a better description of surface runoff before maximal depression storage was reached. This was reflected in an increase of the E50 computed for 27 overland flow experiments under laboratory conditions and their equivalent model results (E50 = 0.89 for the Linsley approach, E50 = 0.94 with the proposed ‘uniform’ multiple-compartment conceptual approach, and E50 = 0.85 for the classical approach where runoff only starts when depression storage capacity is full).

► Distributed runoff models may be improved using grid-scale connectivity properties. ► The relative surface connection (RSC) function captures subgrid connectivity. ► A weighted-surface procedure is proposed to account for surface detention. ► The RSC function may be represented by conceptual multiple-compartment topographies. ► A ‘uniform’ multiple-compartment representation performed best.