Parameter identification in a soil with constant diffusivity

Abstract

Consider infiltration into a soil with assumed hydraulic conductivity of the form K = Kseαh and water content of the form θ = βK - θr. Here h denotes capillary pressure head while Ks, α, β and θr represent soil specific parameters. These assumptions linearize the flow equation and permit a closed form solution that displays the roles of all the parameters appearing in the hydraulic function K and θ. We assume Ks and θr to be known. A measurement of diffusivity fixes the product of α and β resulting in a parameter identification problem for one parameter. This parameter identification problem, has, in some cases, a unique solution, in other cases it can have multiple solutions, or no solution. Solutions to the parameter identification problem are shown to be very sensitive to small changes in the problem data. -from Authors