What do we mean by sensitivity analysis? The need for comprehensive characterization of “global” sensitivity in Earth and Environmental systems models

Sensitivity analysis is an essential paradigm in Earth and Environmental Systems modeling. However, the term “sensitivity” has a clear definition, based in partial derivatives, only when specified locally around a particular point (e.g., optimal solution) in the problem space. Accordingly, no unique definition exists for “global sensitivity” across the problem space, when considering one or more model responses to different factors such as model parameters or forcings. A variety of approaches have been proposed for global sensitivity analysis, based on different philosophies and theories, and each of these formally characterizes a different “intuitive” understanding of sensitivity. These approaches focus on different properties of the model response at a fundamental level and may therefore lead to different (even conflicting) conclusions about the underlying sensitivities. Here we revisit the theoretical basis for sensitivity analysis, summarize and critically evaluate existing approaches in the literature, and demonstrate their flaws and shortcomings through conceptual examples. We also demonstrate the difficulty involved in interpreting “global” interaction effects, which may undermine the value of existing interpretive approaches. With this background, we identify several important properties of response surfaces that are associated with the understanding and interpretation of sensitivities in the context of Earth and Environmental System models. Finally, we highlight the need for a new, comprehensive framework for sensitivity analysis that effectively characterizes all of the important sensitivity-related properties of model response surfaces.