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We propose a set of new indices to assist global sensitivity analysis in the presence of data allowing for interpretations based on a collection of diverse models whose parameters could be affected by uncertainty. Our global sensitivity analysis metrics enable us to assess the sensitivity of various features (as rendered through statistical moments) of the probability density function of a quantity of interest with respect to imperfect knowledge of (i) the interpretive model employed to characterize the system behavior and (ii) the ensuing model parameters. We exemplify our methodology for the case of heavy metal sorption onto soil, for which we consider three broadly used (equilibrium isotherm) models. Our analyses consider (a) an unconstrained case, i.e., when no data are available to constrain parameter uncertainty and to evaluate the (relative) plausibility of each considered model, and (b) a constrained case, i.e., when the analysis is constrained against experimental observations. Our moment-based indices are structured according to two key components: (a) a model-choice contribution, associated with the possibility of analyzing the system of interest by taking advantage of multiple model conceptualizations (or mathematical renderings); and (b) a parameter-choice contribution, related to the uncertainty in the parameters of a selected model. Our results indicate that a given parameter can be associated with diverse degrees of importance, depending on the considered statistical moment of the target model output. The influence on the latter of parameter and model uncertainty evolves as a function of the available level of information about the modeled system behavior.

Plain Language Summary The quality and amount of data available in many practical situations justify the interpretation of the system under investigation through a collection of alternative interpretative models. This is reflected by the observation that there is uncertainty about model structure/format. The situation is exacerbated by the observation that parameters associated with each model could also be affected by uncertainty. In this context, quantification of the influence of these multiple sources of uncertainties on environmental quantities of interest is key to increase our understanding and confidence on model(s) functioning and guide further actions (including, e.g., model calibration or collection of new data). We propose an original global sensitivity analysis approach that enables us to quantify the sensitivity of a target quantity with respect to each of the parameters stemming from situations where multiple interpretative models have been formulated. The proposed global sensitivity analysis allows (i) investigating the sensitivity of model outputs through diverse aspects of uncertainty (i.e., focusing on various statistical moments of the probability density function of the target output) as well as (ii) discriminating between contributions to sensitivity due to our lack of knowledge in (a) model format and (b) parameter values.