Estimating epistemic and aleatory uncertainties during hydrologic modeling: An information theoretic approach

With growing interest in understanding the magnitudes and sources of uncertainty in hydrological modeling, the difficult problem of characterizing model structure adequacy is now attracting considerable attention. Here, we examine this problem via a model-structure-independent approach based in information theory. In particular, we (a) discuss how to assess and compute the information content in multivariate hydrological data, (b) present practical methods for quantifying the uncertainty and shared information in data while accounting for heteroscedasticity, (c) show how these tools can be used to estimate the best achievable predictive performance of a model (for a system given the available data), and (d) show how model adequacy can be characterized in terms of the magnitude and nature of its aleatory uncertainty that cannot be diminished (and is resolvable only up to specification of its density), and its epistemic uncertainty that can, in principle, be suitably resolved by improving the model. An illustrative modeling example is provided using catchment-scale data from three river basins, the Leaf and Chunky River basins in the United States and the Chuzhou basin in China. Our analysis shows that the aleatory uncertainty associated with making catchment simulations using this data set is significant (approximate to 50%). Further, estimated epistemic uncertainties of the HyMod, SAC-SMA, and Xinanjiang model hypotheses indicate that considerable room for model structural improvements remain.