Optimal analysis of the effect of a surface crust

Recently, experiments have been presented for the horizontal flow of water by soil with a surface crust and compared to an analytical model. It was found that the water content at the surface was consistently less than predicted by about a 1% water content. Such a small discrepancy may seem to be more of theoretical rather than practical interest. In fact, due to the rapid variation of soil properties near saturation, a very small error in water content at the surface implies that the model is unreliable to predict the relationship between cumulative absorption and soil water content at the soil surface, especially in the early stages of infiltration. A new model is developed here, based on an optimal principle.