Entropy theory for derivation of infiltration equations

An entropy theory is formulated for modeling the potential rate of infiltration in unsaturated soils. The theory is composed of six parts: (1) Shannon entropy, (2) principle of maximum entropy (POME), (3) specification of information on infiltration in terms of constraints, (4) maximization of entropy in accordance with POME, (5) derivation of the probability distribution of infiltration, and (6) derivation of infiltration equations. The theory is illustrated with the derivation of six infiltration equations commonly used in hydrology, watershed management, and agricultural irrigation, including Horton, Kostiakov, Philip two-term, Green-Ampt, Overton, and Holtan equations, and the determination of the least biased probability distributions of these infiltration equations and their entropies. The theory leads to the expression of parameters of the derived infiltration equations in terms of measurable quantities (or information), called constraints, and in this sense these equations are rendered nonparametric. Furthermore, parameters of these infiltration equations can be expressed in terms of three measurable quantities: initial infiltration, steady infiltration, and soil moisture retention capacity. Using parameters so obtained, infiltration rates are computed using these six infiltration equations and are compared with field experimental observations reported in the hydrologic literature as well as the rates computed using parameters of these equations obtained by calibration. It is found that infiltration parameter values yielded by the entropy theory are good approximations.