Similarity and length scale for spatially varied overland flow

Abstract

One‐dimensional finite element models enable physically based investigations of overland flow generated under spatially varied surface slope, width, roughness, and excess rainfall intensity. Simulated results of 8400 dimensionless hydrographs under spatially varied input parameters indicate that runoff discharge variations depend primarily on the ratio of rainfall duration t r to the time to equilibrium t e . Peak discharge distributions change drastically as the dimensionless rainfall duration t r / t e approaches unity. Similarity conditions exist for all four parameters regardless of whether the spatial variability is correlated or uncorrelated. A length scale function of not only the spatially averaged values of surface parameters but also depending on rainstorm duration and intensity delineates similarity conditions for spatially varied surface runoff. For surface runoff lengths much shorter than this length scale, the rainfall‐runoff relationship becomes nearly independent of the spatial variability in hydrologic parameters. Conversely, for surface runoff lengths exceeding the length scale, the rainfall‐runoff relationship is sensitive to spatial variability. This length scale can serve as a basis for the determination of grid sizes in hydrologic models.