An Efficient Quasi‐Monte Carlo Method for Concurrent Estimation of First‐Order and Total‐Effect Process Sensitivity Indices

Developing and improving process-based models requires identifying the importance and/or influence of various processes driving system behavior. In our recent studies, important processes are identified using first-order process sensitivity index PSK (Dai et al., 2017, https://doi.org/10.1002/2016wr019715), and non-influential processes are determined using total-effect process sensitivity index PSTK (Yang et al., 2022, https://doi.org/10.1029/2021wr029812), K denoting a given system process. Estimating these indices through the brute force Monte Carlo (MC) method is computationally intensive and often impractical. This study extends the quasi-MC method developed by Dai et al. (2022), https://doi.org/10.1029/2022wr033263 to concurrently estimate PSK and PSTK with reduced computational cost. The concurrent estimation is based on a rigorous theoretical framework that we leverage to provide a robust computational implementation of the quasi-MC method. The number of model executions required for estimating PSK or PSTK associated with system process K is reduced from N2 in brute force MC method to 2N in quasi-MC method, N being the number of samples generated for uncertain parameters. The total model executions required to concurrently estimate PSK and PSTK for all processes of an individual system model are N × (Np + 2), Np being the number of system processes associated with the system model of interest. Convergence, accuracy, and reliability of the quasi-MC method are evaluated through an exemplary one-dimensional groundwater flow example. Results demonstrate that the quasi-MC method converges substantially faster and is more reliable than its brute force MC counterpart. Impacts of process model weights on estimating the two indices and their theoretical and practical limitations are also discussed.