Variogram Analysis of Response surfaces (VARS): A New Framework for Global Sensitivity Analysis of Earth and Environmental Systems Models

Abstract:

Earth and environmental systems models (EESMs) are continually growing in complexity and dimensionality with continuous advances in understanding and computing power. Complexity and dimensionality are manifested by introducing many different factors in EESMs (i.e., model parameters, forcings, boundary conditions, etc.) to be identified. Sensitivity Analysis (SA) provides an essential means for characterizing the role and importance of such factors in producing the model responses. However, conventional approaches to SA suffer from (1) an ambiguous characterization of sensitivity, and (2) poor computational efficiency, particularly as the problem dimension grows.

Here, we present a new and general sensitivity analysis framework (called VARS), based on an analogy to ‘variogram analysis’, that provides an intuitive and comprehensive characterization of sensitivity across the full spectrum of scales in the factor space. We prove, theoretically, that Morris (derivative-based) and Sobol (variance-based) methods and their extensions are limiting cases of VARS, and that their SA indices can be computed as by-products of the VARS framework. We also present a practical strategy for the application of VARS to real-world problems, called STAR-VARS, including a new sampling strategy, called “star-based sampling”. Our results across several case studies show the STAR-VARS approach to provide reliable and stable assessments of “global” sensitivity across the full range of scales in the factor space, while being at least 1-2 orders of magnitude more efficient than the benchmark Morris and Sobol approaches.