Sensitivity Analysis of Nonlinear Models for Small Ensembles of Model Outputs

Numerical models especially climate ones are typically complex (have many free parameters), thus, it can be difficult to prioritize parameters that are most promising with respect to system management goals. In the present paper, we discuss a number of methods which allow us to understand model sensitivity when number of model runs is limited and cannot be expanded. We suggest an approach and develop methods to estimate nonlinear sensitivity of models to parameter variations, measure relative importance of each (a group of) parameter[s] and range these parameters along their significance for model output variability. Special focus is on how to construct an ensemble of parameter perturbations when model demonstrates a chaotic behavior or when perturbations are non-random and parameterized through fuzzy sets. Our calculations for Lorenz 63 model (a few degrees of freedom) and the ocean component of CCSM3 (several thousands degrees of freedom) allow us to understand feasibility of the developing techniques and result into the following practical conclusion: accurate estimations of the model sensitivity are possible even when dimensionality of ensembles is about 20-30. However robust and significant estimations require at least 50-100 term ensembles.