We present general optimal results in two dimensions and check their validity by comparison with exact results for a diffusivity obeying a power law. Because of the existence of a first integral of the diffusion equation, these exact results are obtained without iterations. The optimal results form the basis of a new method to estimate the soil-water diffusivity, by measuring the wetting front position when water is injected in the soil at different fluxes. The method is illustrated by analyzing earlier experiments.