A Computationally Efficient Method for Estimating Multi-Model Process Sensitivity Index

Identification of important processes of a hydrologic system is critical for improving process-based hydrologic modeling. To identify important processes while jointly considering parametric and model uncertainty, Dai et al. (2017), https://doi.org/10.1002/2016WR019715, developed a multi-model process sensitivity index. Numerical evaluation of the index using a brute force Monte Carlo (MC) simulation is computationally expensive, because it requires a nested structure of parameter sampling and the number of model simulations is on the order of N-2 (N being the number of parameter samples). To reduce computational cost, we develop a new method (here denoted as quasi-MC for brevity) that uses triple sets of parameter samples (generated using quasi-MC sequence) to remove the nested structure of parameter sampling in a theoretically rigorous way. The quasi-MC method reduces the number of model simulations from the order of N-2 to 2N. The performance of the method is assessed against the brute force MC approach and the recent binning method developed by Dai et al. (2017), https://doi.org/10.1002/2016WR019715, through two synthetic cases of groundwater flow and solute transport modeling. Due to its rigorous theoretical foundation, the quasi-MC method overcomes the limitations imposed by the inherently empirical nature of the binning method. We find that the quasi-MC method outperforms both the brute force MC and the binning method in terms of computational requirements and theoretical aspects, thus strengthening its potential for the assessment of process sensitivity indices subject to various sources of uncertainty.