A new framework for comprehensive, robust, and efficient global sensitivity analysis: 1. Theory

Abstract

Computer simulation models are continually growing in complexity with increasingly more factors to be identified. Sensitivity Analysis (SA) provides an essential means for understanding the role and importance of these factors in producing 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 special cases of VARS, and that their SA indices can be computed as by-products of the VARS framework. Synthetic functions that resemble actual model response surfaces are used to illustrate the concepts, and show VARS to be as much as two orders of magnitude more computationally efficient than the state-of-the-art Sobol approach. In a companion paper, we propose a practical implementation strategy, and demonstrate the effectiveness, efficiency, and reliability (robustness) of the VARS framework on real-data case studies.

Multicriteria sensitivity analysis as a diagnostic tool for understanding model behaviour and characterizing model uncertainty

“…Perturbation scale can be defined as a prescribed size of neighbourhood around any point in the parameter space (equivalent to the step size, Δ x , for numerical estimation of derivatives) and is shown to be very influential on the assessment of sensitivity of environmental models (Haghnegahdar & Razavi, ). Moreover, VARS can closely reproduce results of the two widely used GSA approaches, derivative‐based (Morris, ) and variance‐based (Sobol', ), while being more efficient (Razavi & Gupta, , b).…”

“…Since IVARS integrates the sensitivity information over all perturbation scales up to H i , it is considered to be a comprehensive measure of the global model sensitivity. Note that h i or H i is ≤50% because, for variograms to remain meaningful, distance between any two points within a given parameter range cannot exceed half of its range (Razavi & Gupta, ). Subsequently, IVARS 50 , Γ ( H i = 50%), can be considered as the most comprehensive metric within the VARS framework to estimate the global sensitivity of a model response to each parameter.…”

Practical experience and framework for sensitivity analysis of hydrological models: six methods, three models, three criteria

“…For comprehensive reviews, please refer to Song et al (2015), and Pianosi and Wagener (2015), and for a relatively recent interesting insight into the SA problem to Razavi and Gupta (2015, 2016a, 2016b.…”

Quantifying Spatial Changes in the Structure of Water Quality Constituents in a Large Prairie River within Two Frameworks of a Water Quality Model

“…Various approaches to sensitivity analysis have been used in the literature, including simple one-factor-at-a-time strategies [36], Monte-Carlo filtering [37], variance-based approaches [38], and a variogram-based framework [39,40]. In this study, a Monte-Carlo Analysis (MOCA) framework was used with many model simulations, each using a different set of parameter values sampled randomly from a certain range of model parameters.…”