A New Sensitivity Analysis Approach Using Conditional Nonlinear Optimal Perturbations and Its Preliminary Application

Simulations and predictions using numerical models show considerable uncertainties, and parameter uncertainty is one of the most important sources. It is impractical to improve the simulation and prediction abilities by reducing the uncertainties of all parameters. Therefore, identifying the sensitive parameters or parameter combinations is crucial. This study proposes a novel approach: conditional nonlinear optimal perturbations sensitivity analysis (CNOPSA) method. The CNOPSA method fully considers the nonlinear synergistic effects of parameters in the whole parameter space and quantitatively estimates the maximum effects of parameter uncertainties, prone to extreme events. Results of the analytical g-function test indicate that the CNOPSA method can effectively identify the sensitivity of variables. Numerical results of the theoretical five-variable grassland ecosystem model show that the maximum influence of the simulated wilted biomass caused by parameter uncertainty can be estimated and computed by employing the CNOPSA method. The identified sensitive parameters can easily change the simulation or prediction of the wilted biomass, which affects the transformation of the grassland state in the grassland ecosystem. The variance-based approach may underestimate the parameter sensitivity because it only considers the influence of limited parameter samples from a statistical view. This study verifies that the CNOPSA method is effective and feasible for exploring the important and sensitive physical parameters or parameter combinations in numerical models.