Distributed Evaluation of Local Sensitivity Analysis (DELSA), with application to hydrologic models

Abstract

[1] This paper presents a hybrid local-global sensitivity analysis method termed the Distributed Evaluation of Local Sensitivity Analysis (DELSA), which is used here to identify important and unimportant parameters and evaluate how model parameter importance changes as parameter values change. DELSA uses derivative-based ''local'' methods to obtain the distribution of parameter sensitivity across the parameter space, which promotes consideration of sensitivity analysis results in the context of simulated dynamics. This work presents DELSA, discusses how it relates to existing methods, and uses two hydrologic test cases to compare its performance with the popular global, variance-based Sobol' method. The first test case is a simple nonlinear reservoir model with two parameters. The second test case involves five alternative ''bucket-style'' hydrologic models with up to 14 parameters applied to a medium-sized catchment (200 km 2 ) in the Belgian Ardennes. Results show that in both examples, Sobol' and DELSA identify similar important and unimportant parameters, with DELSA enabling more detailed insight at much lower computational cost. For example, in the real-world problem the time delay in runoff is the most important parameter in all models, but DELSA shows that for about 20% of parameter sets it is not important at all and alternative mechanisms and parameters dominate. Moreover, the time delay was identified as important in regions producing poor model fits, whereas other parameters were identified as more important in regions of the parameter space producing better model fits. The ability to understand how parameter importance varies through parameter space is critical to inform decisions about, for example, additional data collection and model development. The ability to perform such analyses with modest computational requirements provides exciting opportunities to evaluate complicated models as well as many alternative models.

Detecting Tipping points in Ecological Models with Sensitivity Analysis

“…Hybrid methodologies of sensitivity analysis give a good overview of the global parameter sensitivities [22]. Furthermore, these methodologies are well-suited for the computation of parameter sensitivities for subregions within the parameter space.…”

“…The distribution of sensitivity indices across a range of parameter space measures the global sensitivity over the region. The delsa methodology [22] converts local sensitivity indices into variance-based sensitivity indices, enabling direct comparison with the Sobol' methodology. Computing the variance of a Taylor expansion of the model output around the point where the local sensitivity index is evaluated yields, [21,22] …”

“…Unlike the Sobol' method, which is properly normalised only for independent parameters, delsa does not assume that the model parameters are independent. In addition, the computational costs have been reported to be lower than the costs of the Sobol' method [22], but nevertheless are still much higher than the costs of local sensitivity analysis.…”

“…Local methodologies quantify the sensitivity at a specific point in parameter space, whereas global quantify it across a range of parameter space. In addition, there are hybrid methodologies [22,33] that apply local methodologies at different points in parameter space to obtain a distribution of local sensitivity indices across a range of parameter space. Local methodologies linearise the output around the point at which they are applied to reveal detailed information limited to the neighbourhood of this point, omitting nonlocal interaction effects.…”

Sensitivity Analysis of Environmental Models: A Systematic Review with Practical Workflow

“…This sensitivity measure is especially suitable for screening since a small value of the measure implies that the input factor is non-influential, while the same authors show that it may give false conclusions if used for ranking. Along a similar line of reasoning is the DELSA approach (Distributed Evaluation of Local Sensitivity Analysis) by Rakovec et al (2014), which also uses the squared finite differences as a measure of sensitivity (scaled by the ratio between the a priori input variance and the total output variance). Here, local sensitivities computed at different sampling points are not aggregated but their full frequency distribution is analysed, and if aggregated, the median value is used rather than the mean.…”