Use of regional sensitivity analysis for diagnosing parsimony of models: A water model case study

Abstract

Sensitivity analysis is usually carried out to examine how the variation in the output of a model can be attributed to variations of its input variables or model parameters. In this study, classical regional sensitivity analysis (RSA) is used in a novel way to determine parameter dependency in a model and subsequently to make the model more parsimonious. Parameter dependencies are identified through visual inspection of pairwise correlations and quantified using the mutual information index (MII) within the behavioural region of RSA. The dependence information is then used to reduce the number of parameters in the model. This approach was demonstrated through a case study with the WAPABA model, a monthly water balance model with five parameters: α₁ and α₂, which represent catchment consumption and evapotranspiration curve parameters; β, which governs the proportion of catchment yield that becomes groundwater; S_max, the maximum water-holding capacity of the soil store; and K, the groundwater store time constant that controls baseflow recession. Application of this approach resulted in a more parsimonious model with only three parameters (β, S_max, K), while α₁ and α₂ were shared and fixed using predefined values due to their dependency on other parameters. In addition, robustness of the model was investigated by calibrating the model using different lengths of historical data, and it was found that the model can be used reliably even with very short length of historical data. Although illustrated with WAPABA, the proposed approach is general and can be applied to other hydrological and system models where parameter parsimony is desirable.