Scaled forms of the infiltration equation: application to the estimation of the unsaturated soil hydraulic properties

There is a clear need to assess the adequacy of scale matching of soil water dynamics to grid scales relevant for simulation of the vadose zone, aquifers, the land surface and atmospheric interactions. The difficulty of parameterization of soil water movement lies not only in the non-linearity of the saturated/unsaturated flow equations but also in the mismatch between the scale of (point) measurements and the scale ofmodel predictions. Traditionally, the scaling is performed through normalization analyses of static soil properties such as grain size diameter and/or hydraulic soil characteristics. However, the main importance for vadose zone hydrology is the knowledge of the unsaturated flow behavior of a soil, rather than the knowledge of hydraulic soil characteristics, which are just intermediate relationships used to calculate the flow behavior. For that reason we choose, in this paper, to study the problem of scaling directly through the dynamical analysis of the unsaturated flow equations for both Dirichlet concentration type and Neumann flux type boundary conditions. Applying inspectional analysis, a rigorous approach is made to scale Richards ' equation for one-dimensional, isothermal flow in a homogeneous unsaturated soil resulting in a non-dimensional boundary value problem. The case of one-dimensional constant head infiltratio