Entropy Theory for Groundwater Modeling

Abstract For over two decades entropy theory has been applied to groundwater modeling with particular regard to (1) groundwater head, (2) parameter estimation, and (3) contaminant transport. Entropy theory is formulated in two domains: real domain and frequency domain. In the real domain, the theory comprises (a) Shannon entropy or another form, (2) principle of maximum entropy, (3) relative entropy, and (4) concentration theorem. The theory allows a probabilistic description in each case. In the frequency domain, it comprises Burg entropy, configurational entropy, and relative entropy. The objective of this study to review the potential of entropy theory in groundwater hydrology, point out its limitations, and suggest directions for future work. Observed groundwater depth measured from the land surface were used to evaluate the entropy theories. It was found that hourly groundwater level showed significant daily periodicity. The largest spectral peak happened at 1/24 frequency, which was determined by the relative entropy spectral analysis with the highest resolution among the three entropies. For modeling groundwater level, both configurational entropy and relative entropy fitted observations well, and the errors were much smaller than for the Burg entropy.