USE OF INFORMATIONAL ENTROPY-BASED METRICS TO DRIVE MODEL PARAMETER IDENTIFICATION

摘要

Calibration of rainfall-runoff models is made complicated by uncertainties in data, and by the arbitrary emphasis placed on various magnitudes of the model residuals by most traditional measures of fit. Current research highlights the importance of driving model identification by assimilating information from the data. Information theory can help by providing powerful tools to examine the fundamental gaps in relating data to process understanding. Information theoretic computations ultimately rely on quantities such as entropy, which has been applied in a wide spectrum of areas, including environmental and water resources. However, its potential to perform model diagnostics and identify fundamental inconsistencies between data, system understanding and hydrological models has received little investigation to date.In this paper, we evaluate the potential use of entropy-based measures as objective functions or as model diagnostics in hydrological modelling, with particular interest in providing an appropriate quantitative measure of fit to the flow duration curve (FDC). We propose an estimation of entropy metrics capable of characterising the information in the flow frequency distribution and thereby driving the model calibration in such a way as to learn from information in the data. Four years of hourly data from the 46.6 km2 Mahurangi catchment, NZ, are used to calibrate the 6-parameter Probability Distributed Moisture model, and results are analysed using three measures: an informational entropy measure, the Nash-Sutcliffe (NSE), and the recently proposed Kling-Gupta efficiency (KGE). We also examine a conditioned entropy metric that trades-off and re-weights different segments of the FDC to drive model calibration in a way that is based on modelling objectives.Overall, we find that use of the entropy measure for model calibration results in good performance in terms of NSE but poor performance in terms of KGE. Entropy is strongly sensitive to the shape of the flow distribution and is, from some viewpoints, the single best descriptor of the FDC. However, the lack of statistically significant sample at high flow ranges has an effect on the estimation of entropy. Further, entropy is completely insensitive to the timing of hydrological events, which limits its potential as a stand-alone performance measure. Nonetheless, its inclusion in a multi-objective study would provide a useful diagnostic to decouple timing and other errors. By conditioning entropy to respect multiple segments of the FDC, we can re-weight entropy to respect those parts of the flow distribution of most interest to the modelling application. This approach constrains the behavioural parameter space so as to better identify parameters that represent both the "fast" and "slow" runoff processes.