WATER RESOURCES RESEARCH, VOL. 23, NO. 12, PAGES 2266-2278, DECEMBER 1987 2, On Hydrologic Similarity A Scaled Model of Storm Runoff Production M. SIVAPALAN Department of Civil Engineering and Operations Research, Princeton University, Princeton, New Jersey KEITH BEVEN Department of Environmental Science, University of Lancaster, Lancaster, United Kingdom ERIC F. WOOD Department of Civil Engineering and Operations Research, Princeton University, Princeton, New Jersey The paper describes a simple physically based conceptual model of runoff production based on catchment topography and the spatial variablity of rainfall and soil properties. Both infiltration excess (Horton type) and saturationexcess (Dunne type) runoff productionmechanisms are considered. The effectof topography is modeled usingthe In (a/tan fi)-topographic index method of Bevenand Kirkby (1979). The effects of the spatial variability of soil propertiesand rainfall on areal averageinfiltration rates are handled using a quasi-analytical approach.The interaction between the two mechanisms of runoff productionand the effectof a finite water table on the infiltration excess mechanism are explicitly considered. The model equations are cast in a dimensionless form to clarify the interrelationships involved in hydrological responses and to identifymeasures of similaritybetween different heterogeneous catchments.The dimensionless formulation has led to the identification of five similarity parameters and three dimensionless variables representing initial conditions and storm characteristics. Finally, a number of experiments were performedto study the sensitivity of the runoff production response to someof these similarity parameters. INTRODUCTION In this sequenceof papers our aim is to provide a greater understanding of the interrelationships that underlie the storm response of catchments of different scales and physicalcharac- teristics by focusing on concepts of similarity. In the first paper Wood and Hebson [1986] make a first attempt to for- mulate the similarity relationshipsinvolved in flood frequency characteristics. They provide a dimensionless flood frequency curve under the assumptions of spatially homogeneousrain- falls and a constant contributing area during the flood pro- ducing events. This paper represents a step toward relaxing those assump- tions. We provide a model of storm runoff production due to spatially variable rainfalls on heterogeneous catchments taking accountof the effects of catchment form on the within- storm dynamics of runoff contributing areas. The model can be expressed in dimensionless form. The inclusion of the ef- fects of variability in rainfalls, soil characteristics, and topog- raphy on contributing area dynamicsrepresents a major ad- vance over previous models based on "point" hydrological response modelsassumed to apply at the catchment scale. However, many simplifying assumptionshave been made regarding the hydrologic processes taking place at the catch- ment scale: rainfall has been assumed to be constant in time during the storm event while being spatially variable; down- slope redistribution of moisture during the storm has been neglected;and spatial correlations in soils and rainfall are ignored. Also, the effects of microtopography on infiltration Copyright 1987 by the American GeophysicalUnion. Paper number 7W4850. 0043-1397/87/007W-4850505.00 rates are neglected. Although these assumptions have been necessary to keep the model simple,it is expected that in time, many of thesecan be relaxed while retaining the concept of similarity betweendisparatecatchments. Mechanisms of Runoff Production Based on hydrological experience, it is evident that runoff in actual catchments is produced by a numberof different mech- anisms. These have been reviewed by Freeze [1974, 1980], Dunne[1978], and Beven[1983a]. Accordingto Dunne [1978] (see also Freeze [1980]), the primary sources of runoff pro- duced on hillslopes during storm runoff events is overland flow. Overland flow is produced at any location in a catch- ment due to the surface soil layers being saturated.Basedon extensive field evidence Dunne has established that this sur- face saturation occursdue to two quite distinct mechanisms. The first mechanism, first espoused by Horton [1933], is for a rainfall intensity that exceeds the saturated hydraulic con- ductivity of the soil. The moisture content at the surfacein- creases as a function of time and, at some point in time, the surface becomes saturated and an inverted zone of saturation begins to propagate downwardinto the soil. At this time the infiltration rate drops below the rainfall rate and overland flow is produced. As originally presented, Horton's infiltration excess mechanism inferred that most rainfall events exceed infiltration capacitiesand that overland flow is common and areally widespread. Analysis of catchment response by Betson [1964], however, suggested that generallyonly part of a catch- ment would contribute to overland flow. Recent work has shown that the great heterogeneity in soil types over a catch- ment and the very irregular patterns of rainfall in time and space create a very complex hydrologic responseat the land 2266