SENSITIVITY ANALYSIS OF NONLINEAR MODELS TO PARAMETER PERTURBATIONS FOR SMALL SIZE ENSEMBLES OF MODEL OUTPUTS

Abstract

A new technique for nonlinear sensitivity analysis of geophysical models for small size ensembles of model outputs has been developed. Such an analysis utilizes the following metrics: (a) Sobol–Saltelli sensitivity indices and cumulative distribution functions if perturbations of model parameters are random, and (b) a Hartley-like measure if perturbations of model parameters are nonrandom and parametrized through fuzzy sets. The indices and the Hartley-like measure allow for ranging model parameters along their significance to the model output. Our calculations demonstrate that accurate estimates of the sensitivity indices are possible even if an ensemble of random perturbations contains considerably less than 100 members. Some calculations were successfully provided for random ensembles with 20–30 members only but, in general 50–100 member ensembles are required to get robust and significant estimations of model sensitivity. The fuzzy set concept allows for robust estimations for small size nonrandom ensembles of model outputs (50–100 members) and accounts for additional a priori information on model sensitivity coming from different sources. The Lorenz 63 model (a few degrees of freedom) and the ocean component (POP) of the Community Climate System Model (CCSM3) (several thousand degrees of freedom) are used to illustrate the sensitivity analysis based on this approach.