Derivation of Rating Curves Using Entropy Theory

Abstract

Using the entropy theory, this study derives the stage‐discharge relation, often called the rating curve, which is based on two simple constraints: (1) the total probability and (2) the mean logarithmic discharge. Parameters of the derived curves are determined with the use of these two constraints. The entropy theory permits a probabilistic characterization of the rating curve and hence the probability density function underlying the curve. It also permits a quantitative assessment of the uncertainty of the rating curve. The derived rating curves are tested using field data and are found to be in agreement with the curves obtained by the least square method.