A geostatistics‐informed hierarchical sensitivity analysis method for complex groundwater flow and transport modeling

Abstract

Sensitivity analysis is an important tool for development and improvement of mathematical models, especially for complex systems with a high dimension of spatially correlated parameters. Variance‐based global sensitivity analysis has gained popularity because it can quantify the relative contribution of uncertainty from different sources. However, its computational cost increases dramatically with the complexity of the considered model and the dimension of model parameters. In this study, we developed a new sensitivity analysis method that integrates the concept of variance‐based method with a hierarchical uncertainty quantification framework. Different uncertain inputs are grouped and organized into a multilayer framework based on their characteristics and dependency relationships to reduce the dimensionality of the sensitivity analysis. A set of new sensitivity indices are defined for the grouped inputs using the variance decomposition method. Using this methodology, we identified the most important uncertainty source for a dynamic groundwater flow and solute transport model at the Department of Energy (DOE) Hanford site. The results indicate that boundary conditions and permeability field contribute the most uncertainty to the simulated head field and tracer plume, respectively. The relative contribution from each source varied spatially and temporally. By using a geostatistical approach to reduce the number of realizations needed for the sensitivity analysis, the computational cost of implementing the developed method was reduced to a practically manageable level. The developed sensitivity analysis method is generally applicable to a wide range of hydrologic and environmental problems that deal with high‐dimensional spatially distributed input variables.

Delineating Facies Spatial Distribution by Integrating Ensemble Data Assimilationand Indicator Geostatistics With Level‐Set Transformation

“…Our new ES‐MDA framework of facies delineation is applicable to heterogeneous groundwater aquifers with sharp contrast in their hydraulic properties. A suitable example is the well‐studied IFRC site (Chen et al, , ; Dai et al, ; Zachara et al, ) at the U.S. Department of Energy's Hanford 300 Area. Research activities at this site have focused on understanding the long‐term persistence of a uranium plume resulting from the disposal of nuclear fuels fabrication wastes from 1943 to 1975.…”

Using Bayesian Networks for Sensitivity Analysis of Complex Biogeochemical Models

“…The first‐order sensitivity index is defined as , which quantifies the percentage of output uncertainty contributed by θ i and measures its relative importance compared to other uncertain inputs. The variance decomposition technique has been recursively applied by Dai, Chen, et al () to a three‐layer hierarchical uncertainty framework, from which a new set of sensitivity indices is defined to quantify the uncertainty contributions from three groups of uncertain inputs: scenario, model structure, and parameters. However, the principle of variance decomposition can be applied to a hierarchical structure with more than three layers following the recursive manner.…”

“…Predictive uncertainty is inevitable in Earth system models because of the complexity of natural system processes, physical and chemical heterogeneity in the natural environment, and limited data availability for characterizing the system properties or validating the models (Neuman, ; Refsgaard et al, ; Ye et al, , , ). To effectively and efficiently reduce predictive uncertainty with limited resources, sensitivity analysis is an essential step to rank the importance of different uncertainty sources that contribute to overall predictive uncertainty (Dai, Chen, et al, ; Razavi & Gupta, ; Wainwright et al, ).…”

“…The single‐model, parameter‐oriented sensitivity analysis is insufficient for identifying dominant model processes, each of which usually consists of multiple parameters (Clark et al, , ). Process‐oriented sensitivity analysis has gained increasing attention for improving hydrological models and beyond (Dai, Chen, et al, , Dai, Ye, et al, ; Grayson & Bloschl, ; Sivakumar, , ).…”

“…Dai and Ye () developed a multilayer hierarchical sensitivity analysis framework based on the variance‐based global sensitivity analysis method (Saltelli et al, ; Saltelli, ). Dai, Chen, et al () and Dai et al () further developed a sensitivity framework capable of quantifying relative contribution of uncertainty from multiple, spatially distributed model inputs with relatively low computational cost. However, these frameworks are constrained by a simple three‐layer structure of uncertainty: model parameters, model structures, and forcing scenarios, which may not be sufficient for describing a large number of uncertainty sources involved in multiphysics environmental modeling nor can they adequately characterize the complex relationships between various uncertainty sources.…”