127 6 A SCALE TRANSFORM FUNCTION TO COMPUTE SATURATED CONDUCTIVITY FOR MODEL UNITS OF DYNAMIC SPATIAL RAINFALL-RUNOFF MODELS FROM LOCAL SCALE MEASUREMENTS OF INFILTRATION D. Karssenberg Abstract: Dynamic spatial rainfall-runoff models require values of saturated conductivity which are representative for (i.e., effective at) the support size used in these models. The support size is defined as the domain in space and time in which all fluxes are assumed to be homogeneous and constant, respectively. It is defined by the size of the model units and the time step used in the rainfall-runoff model. This chapter describes a scale transform function to upscale local scale values of saturated conductivity to effective values of saturated conductivity at a support corresponding to the size of a model unit of 100 m 2 and a time step of several seconds. The form of the transfer function is derived from a stochastic model simulating the spatial process of runoff and infiltration within a model unit. The three parameters in the transfer function can be found for each model unit in the rainfall-runoff model using a correlation between these parameters and 1) the spatial probability distribution of the saturated conductivity within a model unit, 2) derivatives of the digital elevation model at the scale of the model unit (e.g., slope, curvature), and 3) the pattern of surface runoff in the unit. With field data from a 0.43 km 2 catchment in the Ouvèze river basin, S. France, the transfer function was tested in a simulation with a dynamic spatial rainfall-runoff model, resulting in an effective saturated conductivity that varied for each model unit with the intensity of net rainfall and runon to the model unit. The simulations showed that the application of the transfer function in a dynamic spatial rainfall-runoff model resulted in differences between simulated and measured cumulative discharge from the catchment which were smaller than these found with simulations without the use of the transfer function. This was also the case for a small hillslope in the same area. 6.1 Introduction When it is simulated over a small area (e.g. 10 -2 m 2 ), infiltration is generally considered to be a one dimensional process. A large number of standard infiltration models are available to do such simulations. In most cases these models estimate infiltration as a function of the availability of surface water for infiltration, physical and chemical properties of the soil, water content of the soil, occurrence of macro pores and/or surface sealing. For larger areas, infiltration has to be considered as a spatial process with an interaction between overland flow and infiltration processes in the soil, since the availability of water for infiltration becomes dependent on rain and runon, while runon is determined by the same interaction process in upstream areas. As a result, for larger areas, infiltration can only be modeled when both infiltration processes in the soil and runoff are regarded as interrelated processes with variation in space (Smith and Hebbert,