Entropy theory for derivation of infiltration equations
Abstract
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.
Subject
Soil water retentionIrrigation management
Entropy
Watershed management
Probabilistic models
Calibration
Unsaturated conditions
Field experimentation
Hydrologic model