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. SA can be useful for data assimilation, model tuning, and dimensionality reduction. However, many commonly employed implementations of SA involve inadequate practices, such as simply varying the inputs and observing the effect on the outputs. This paper reviews some of the latest SA techniques, pointing out their pros and cons. Central to the discussion is the experimental design. Two methods are considered for sampling the input values: simple random, and space-filling designs, and it is shown that different measures of sensitivity have different properties under these sampling schemes. The methodology is illustrated on a few toy examples as well as on the Lorenz ’63 model.