Entropy Theory of Hydrologic Systems

Hydrologic systems are characterized by processes which may occur on, below, and above the land surface. These processes are irreversible, and the irreversibility produces entropy. In thermodynamics, entropy is a measure of the loss of heat energy which is a reflection of disorder. The entropy of a system achieves its maximum at steady state, meaning that the maximum entropy production corresponds to the most probable state. In information theory, entropy is a measure of uncertainty or disorder or information imbued in the random variable describing the hydrologic system. The maximum uncertainty corresponds to maximum entropy or the most probable distribution of the variable which leads to the principle of maximum entropy or the principle of minimum cross entropy, subject to the given constraints. The most probable or maximum entropy-based distribution is confirmed by the theorem of concentration. The form of entropy (Shannon, Tsallis, Renyi, or Kapur), principle of maximum entropy, principle of minimum cross-entropy, and the concentration theorem constitute the theory of entropy. This paper presents a general framework based on the entropy theory, and demonstrates its application for modeling a number of surface and subsurface hydrologic and water quality processes, including hydrometric network evaluation, eco-index, surface runoff, infiltration, soil moisture, velocity distribution, sediment concentration, sediment discharge, sediment yield, channel cross section, rating curve, and debris flow.