Variance-Based Sensitivity Analysis: An Illustration on the Lorenz'63 Model

Sensitivity analysis (SA) generally refers to an assessment of the sensitivity of the output(s) of some complex model with respect to changes in the input(s). Examples of inputs or outputs include initial state variables, parameters of a numerical model, or state variables at some future time. Sensitivity analysis is useful for data assimilation, model tuning, calibration, and dimensionality reduction; and there exists a wide range of SA techniques for each. This paper discusses one special class of SA techniques, referred to as variance based. As a first step in demonstrating the utility of the method in understanding the relationship between forecasts and parameters of complex numerical models, here the method is applied to the Lorenz'63 model, and the results are compared with an adjoint-based approach to SA. The method has three major components: 1) analysis of variance, 2) emulation of computer data, and 3) experimental-sampling design. The role of these three topics in variance-based SA is addressed in generality. More specifically, the application to the Lorenz'63 model suggests that the Z state variable is most sensitive to the b and r parameters, and is mostly unaffected by the s parameter. There is also evidence for an interaction between the r and b parameters. It is shown that these conclusions are true for both simple random sampling and Latin hypercube sampling, although the latter leads to slightly more precise estimates for some of the sensitivity measures.