Sensitivity Analysis of Inverse Problems Solved by Singular Value Decomposition

Local sensitivity analysis can provide considerable insight into models commonly used for resource management, risk assessment, and so on. The local sensitivity analysis methods used in this work require fewer than 50 model runs; global methods would have required 10,000 runs or more model runs. Here we consider methods of diagnosing inverse model convergence problems caused by parameter insensitivity and(or) parameter interdependence (correlation), understanding what aspects of the model and data contribute to measures of uncertainty, and identifying new data are likely to reduce model uncertainty. We consider sensitivity statistics relevant to models in which the process model parameters are transformed using singular value decomposition (SVD) to create SVD parameters for model calibration.  The statistics considered include the Doherty-Hunt identifiability (ID) statistic, combined use of the process-model parameter statistics composite scaled sensitivities and parameter correlation coefficients (CSS and PCC), and the inverse of the parameter coefficient of variation (b/SD).  The statistics are complimentary in that graphs of ID clearly show what process-model parameters contribute to a set of SVD parameters, b/SD statistics identify parameters likely to be well and poorly estimated, and CSS and PCC indicate whether parameters are poorly estimated due to lack of sensitivity, parameter interdependence, or both. The statistics are demonstrated using a USDA Root Zone Water Quality Model in which nitrogen fate and transport is simulated through the unsaturated zone.