Entropy as a measure of hydrologic data uncertainty and model performance

Abstract

This paper extends the original use of entropy by Amorocho and Espildora as a measure of uncertainty in hydrologic data and the reduction in that uncertainty due to application of a model. In many situations calculations of entropy are better based on a proportional rather than a fixed class interval. General equations are given for the proportional class interval, are solved for assumed log-normal and gamma distributions, and extended to data series with zero values. The solutions are shown to be independent of the units of measurement of the original data. The results are applied to comparative evaluation of hydrologic models using the same and different data sets, and a new criterion of model performance is suggested for the latter case.