Parameter identification in a soil with constant diffusivity

Consider infiltration into a soil with assumed hydraulic conductivity of the form K = K_se^αh and water content of the form θ = βK - θ_r. Here h denotes capillary pressure head while K_s, α, β and θ_r 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 K_s and θ_r 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