All physically based distributed models although with different assump-tions and structures, tend to represent real processes. Real processes are described by more or less complex mathematical relations which translate general physical laws also referred as governing equations. The governing equations are usually partial differential equations (PDEs) at " point-scale " while models refer to finite scale (i.e. the grid cell). A correct integration of the governing equations from the point to the finite dimension of a grid cell, can actually generate relatively scale independent models, which preserve the physical meaning (although as averages) of the model parameters. In order to preserve the essential feature of the rainfall-runoff process from the point scale to the grid cell, only representations that integrate the point equations may correctly reproduce phenomena such as the soil moisture balance and the consequent saturated areas dynamics, which is probably the most important driving mechanism in the formation of surface runoff. Following this aim, it will be shown that a detailed description of the vertical water profile based on the in-tegration of the governing equations is not necessary for the overall representation of the horizontal water flow and that it is actually possible to lump the horizontal flow equations at the grid cell resolution still preserving the physical meaning of the model parameters. The TOPKAPI, a hydrologic model structured according to these approaches has been applied to some numerical experiment in order to find the scale range for the validity of the model physical representativeness.
Martina, M. L. V., & Todini, E. (2008). Watershed Hydrological Modeling: Toward Physically Meaningful Processes Representation. In Hydrological Modelling and the Water Cycle (pp. 229–241). Springer Berlin Heidelberg. https://doi.org/10.1007/978-3-540-77843-1_10