Sensitivity analysis of correlated outputs and its application to a dynamic model

Risk assessment and decision making in ecology, hydrology and biology often employ dynamic models with multiple calibrations. The global sensitivity analysis of models is usually completed at each time step of a single output. However, due to the enormous volume of data and model complexity, a single index cannot give a full-scale analysis of such models. The purposes of this paper are: (1) to apply T-pooling for analysing multiple outputs at a lower computational cost; (2) to consider the influence of the correlations among the outputs and the output dimensions on sensitivity analysis; and (3) to propose a procedure that combines the Sobol' index for a single output and the generalised sensitivity method and T-pooling index for multiple outputs to analyse dynamic models comprehensively. The proposed procedure and index are applied to a Hydrologiska Byråns Vattenbalansavdelning (HBV) model with three calibrations to provide an uncertainty analysis across time periods ranging from a single time step to the entire time period.