Abstract:
There has been a recent resurgence of interest in the application of Information Theory to problems
of system identification in the Earth and Environmental Sciences. While the concept of entropy has
found increased application, little attention has yet been given to the practical problems of estimating
entropy when dealing with the unique characteristics of two commonly used kinds of hydrologic data: rainfall
and runoff. In this paper, we discuss four important issues of practical relevance that can bias the computation
of entropy if not properly handled. The first (zero effect) arises when precipitation and ephemeral
streamflow data must be viewed as arising from a discrete-continuous hybrid distribution due to the occurrence
of many zero values (e.g., days with no rain/no runoff). Second, in the widely used bin-counting
method for estimation of PDF’s, significant error can be introduced if the bin width is not carefully selected.
The third (measurement effect) arises due to the fact that continuously varying hydrologic variables can typically
only be observed discretely to some degree of precision. The Fourth (skewness effect) arises when the
distribution of a variable is significantly skewed. Here we present an approach that can deal with all four of
these issues, and test them with artificially generated and real hydrological data. The results indicate that
the method is accurate and robust.
