A New Multi-Model Difference-Based Sensitivity Analysis Method to Screen Non-Influential Processes with Process Model and Parametric Uncertainty

Abstract:

Multi-model sensitivity analysis has gained increasing attention for advancing our understanding of complex Earth and environmental systems with interacting physical, chemical, and biological processes. We developed a new global sensitivity analysis method, called multi-model difference-based sensitivity analysis (MMDS), which can screen noninfluential system process from further investigation such as model calibration. A unique feature of MMDS is that it considers uncertainty in process presentations and parameters. Specifically speaking, a process may have multiple presentations due to process model uncertainty, and a process parameter may follow a distribution due to parametric uncertainty. The basic idea of MMDS comes from the Morris method, in which elementary effect is evaluated to measure changes of a simulated system state variable due to changes of process model parameter values. MMDS extends the concept to evaluate elementary difference that measures the changes of a simulated system state due to changes of not only process model parameter values but also process representations (process models). The mean and variance of the elementary difference are further calculated by using model averaging and Monte Carlo methods, and a process with small mean and/or variance of elementary difference is considered to be noninfluential and can be screened from further investigation. We evaluated MMDS using three sets of numerical examples with increasing level of complexity as follows: (1) a analytical Sobol-G^* function with analytical solutions, (2) a hypothetical one-dimensional groundwater flow model for which a large number of model simulations are computationally affordable, and (3) a real-world, two-dimensional thermo-hydro-biogeochemical model in the Hanford Site's 300 Area for which a numerical approximation is necessary. Results indicate that MMDS can successfully identify the noninfluential processes within a computationally inexpensive way compared with the variance-based process sensitivity analysis method. MMDS is mathematically general, and can be applied to a wide range of problems in Earth and environmental systems.