Similarity and length scale for spatially varied overland flow.

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 tr to the time to equilibrium te. Peak discharge distributions change drastically as the dimensionless rainfall duration tr/te 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.

[1]  M. Lighthill,et al.  On kinematic waves I. Flood movement in long rivers , 1955, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[2]  Keith Beven,et al.  Effects of spatial variability and scale with implications to hydrologic modeling , 1988 .

[3]  Juan B. Valdés,et al.  On the influence of the spatial distribution of rainfall on storm runoff , 1979 .

[4]  Brent M. Troutman,et al.  Runoff prediction errors and bias in parameter estimation induced by spatial variability of precipitation , 1983 .

[5]  R. Bras,et al.  Incorporation of Channel Losses in the Geomorphologic IUH , 1986 .

[6]  Elpidio Caroni,et al.  Nonlinearity and Time-variance of the Hydrologic Response of a Small Mountain Creek , 1986 .

[7]  J. Amorocho,et al.  Mathematical Models for the Simulation of Cyclonic Storm Sequences and Precipitation Fields , 1977 .

[8]  David A. Woolhiser,et al.  A Stochastic Model of Dimensionless Thunderstorm Rainfall , 1985 .

[9]  V. Gupta,et al.  A stochastic kinematic study of subsynoptic space‐time rainfall , 1979 .

[10]  Richard H. McCuen,et al.  Hydrologic modeling: Statistical methods and applications , 1986 .

[11]  G. Touzot,et al.  The finite element method displayed , 1984 .

[12]  B. Troutman.  Errors and Parameter Estimation in Precipitation‐Runoff Modeling: 1. Theory , 1985 .

[13]  Peter S. Eagleson,et al.  Effects of spatial variability on annual average water balance , 1987 .

[14]  Approximations of Temporal Rainfall From a Multidimensional Model , 1985 .

[15]  Roger E. Smith,et al.  A Monte Carlo Analysis of the hydrologic effects of spatial variability of infiltration , 1979 .

[16]  Pierre Y. Julien,et al.  Sediment Transport Capacity of Overland Flow , 1985 .

[17]  Roger A. Pielke,et al.  Application of Terrain Height Variance Spectra to Mesoscale Modeling , 1983 .

[18]  Brent M. Troutman,et al.  Errors and Parameter Estimation in Precipitation‐Runoff Modeling: 2. Case Study , 1985 .

[19]  Keith Beven,et al.  On hydrologic similarity: 2. A scaled model of storm runoff production , 1987 .

[20]  P. S. Eagleson,et al.  Mathematical models of rainstorm events in space and time , 1987 .

[21]  Murugesu Sivapalan,et al.  Spatial Heterogeneity and Scale in the Infiltration Response of Catchments , 1986 .

[22]  R. Wooding,et al.  Overland flow and groundwater flow from a steady rainfall of finite duration , 1964 .

[23]  M. Sharma,et al.  An analysis of areal infiltration considering spatial variability , 1981 .

[24]  David A. Woolhiser,et al.  Unsteady, one‐dimensional flow over a plane—The rising hydrograph , 1967 .