Keywords
shannon entropy, model diagnostics, model uncertainty, rainfall-runoff modelling
Start Date
1-7-2010 12:00 AM
Abstract
Recent papers have called for the development of robust model diagnostics (in addition to traditional “measures of fit”) that provide insights on where model structural components and/or data may be insufficient. The potential of entropy measures to provide these in hydrology has not been adequately explored. Further, flow duration (FD) curves provide a useful visual diagnostic of catchment response, but attempts to quantify the fit of modelled versus observed FD curves to date have relied on using time series measures of fit. We note that Shannon entropy of flow is strongly related to the FD relationship, so suggest it provides a more appropriate quantitative measure of fit. This paper presents initial results from a study calibrating two rainfall-runoff models to 4 years of hourly data from the Mahurangi catchment, NZ. Kling-Gupta efficiency (KGE), Nash-Sutcliffe efficiency (NSE) and two entropy measures were considered. When assessed using a range of model diagnostics, KGE was overall the single best measure, outperforming NSE at all times. Entropy outperformed KGE over particular hydrograph sections, and we show performance may improve further with careful choice of discretisation. We demonstrate entropy’s strong relationship to FD and interrogate the performance of entropy measures in the presence of timing and bias errors. As entropy is insensitive to timing errors but very sensitive to most other errors (in sharp contrast to, e.g., the NSE measure) it potentially provides a useful diagnostic of the types of error present in combination with other OFs.
The Use of Entropy as a Model Diagnostic in Rainfall-Runoff Modelling
Recent papers have called for the development of robust model diagnostics (in addition to traditional “measures of fit”) that provide insights on where model structural components and/or data may be insufficient. The potential of entropy measures to provide these in hydrology has not been adequately explored. Further, flow duration (FD) curves provide a useful visual diagnostic of catchment response, but attempts to quantify the fit of modelled versus observed FD curves to date have relied on using time series measures of fit. We note that Shannon entropy of flow is strongly related to the FD relationship, so suggest it provides a more appropriate quantitative measure of fit. This paper presents initial results from a study calibrating two rainfall-runoff models to 4 years of hourly data from the Mahurangi catchment, NZ. Kling-Gupta efficiency (KGE), Nash-Sutcliffe efficiency (NSE) and two entropy measures were considered. When assessed using a range of model diagnostics, KGE was overall the single best measure, outperforming NSE at all times. Entropy outperformed KGE over particular hydrograph sections, and we show performance may improve further with careful choice of discretisation. We demonstrate entropy’s strong relationship to FD and interrogate the performance of entropy measures in the presence of timing and bias errors. As entropy is insensitive to timing errors but very sensitive to most other errors (in sharp contrast to, e.g., the NSE measure) it potentially provides a useful diagnostic of the types of error present in combination with other OFs.
