Abstract. We propose new metrics to assist global sensitivity analysis, GSA, of hydrological and Earth systems. Our approach allows assessing the impact of uncertain parameters on main features of the probability density function, pdf, of a target model output, y. These include the expected value of y, the spread around the mean and the degree of symmetry and tailedness of the pdf of y. Since reliable assessment of higher-order statistical moments can be computationally demanding, we couple our GSA approach with a surrogate model, approximating the full model response at a reduced computational cost. Here, we consider the generalized polynomial chaos expansion (gPCE), other model reduction techniques being fully compatible with our theoretical framework. We demonstrate our approach through three test cases, including an analytical benchmark, a simplified scenario mimicking pumping in a coastal aquifer and a laboratory-scale conservative transport experiment. Our results allow ascertaining which parameters can impact some moments of the model output pdf while being uninfluential to others. We also investigate the error associated with the evaluation of our sensitivity metrics by replacing the original system model through a gPCE. Our results indicate that the construction of a surrogate model with increasing level of accuracy might be required depending on the statistical moment considered in the GSA. The approach is fully compatible with (and can assist the development of) analysis techniques employed in the context of reduction of model complexity, model calibration, design of experiment, uncertainty quantification and risk assessment.

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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.

Abstract. We propose new metrics to assist global sensitivity analysis, GSA, of hydrological and Earth systems. Our approach allows assessing the impact of uncertain parameters on main features of the probability density function, pdf, of a target model output, y. These include the expected value of y, the spread around the mean and the degree of symmetry and tailedness of the pdf of y. Since reliable assessment of higher order statistical moments can be computationally demanding, we couple our GSA approach with a surrogate model, approximating the full model response at a reduced computational cost. Here, we consider the generalized Polynomial Chaos Expansion (gPCE), other model reduction techniques being fully compatible with our theoretical framework. We demonstrate our approach through three test cases, including an analytical benchmark, a simplified scenario mimicking pumping in a coastal aquifer, and a laboratory-scale conservative transport experiment. Our results allow ascertaining which parameters can impact some moments of the model output pdf while being uninfluential to others. We also investigate the error associated with the evaluation of our sensitivity metrics by replacing the original system model through a gPCE. Our results indicate that the construction of a surrogate model with increasing level of accuracy might be required depending on the statistical moment considered in the GSA. Our approach is fully compatible with (and can assist the development of) analysis techniques employed in the context of reduction of model complexity, model calibration, design of experiment, uncertainty quantification and risk assessment.

This generates positive density fluctuations, '  , which in turn trigger negative vertical dynamic flow fluctuations, ' dy z v , due to the effect of (reduction in) buoyancy (see Figure 2b). The opposite occurs in the portion of the domain adjacent to the high permeability inclusion. Since ' st z v and ' dy z v are associated with opposite signs, the total vertical flow fluctuation ' z v is smaller than its counterpart evaluated for the constant density scenario (compare Figure 2c and Figure 2a). Note that the stabilizing effect of ' dy z v tends to decrease the intensity of ' z v (with respect to the uniform density case) without altering its sign. This behavior is also observed in the heterogeneous field analyzed in Section 4 for the investigated values of Ng. Ultimately, the velocity field at the solute front is more uniform in the variable density than in the constant density case (compare the velocity fields in Figures 2d and 2e) causing a decreased solute dispersion in the former scenario, as compared against the latter. This observation is further supported by Figures 2f and 2e where the distribution along z of the variance of the vertical velocity, 2 (,) z v z t  , and of ' ' z v C (19) for the constant density case (black curves) are compared against their counterpart associated with variable density (red curves). One can clearly note the reduction of the magnitude of both 2 (,) z v z t  and ' ' z v C under variable density conditions. The basic mechanisms highlighted here for this relatively simple heterogeneous configuration are at '(,) '(,) z z v z t v   and '() '() st st z z v z v  tend to coincide for ξ > z; but '(,) '(,) z z v z t v   becomes significantly smaller, even negative, than '() '() st st z z v z v  for ξ < z. As expected, '(,) '(,) z z v z t v   and '() '() st st z z v z v  tend to coincide when Ng decrease (see Figure 4b). Negative values of the overall covariance '(,) '(,) z z v z t v   for ξ < z are due to the effect of the dynamic and stationary velocity cross-covariances, '(,) '() dy st z z v z t v  and '() '(,) st dy z z v z v   , which are always negative. This result is consistent with (23) and with our discussion in Section 3 arguing that positive values of '() st z v  favor the solute to advance within the domain, thus originating negative dynamic velocity fluctuations, '(,) dy z v z t   , through positive density fluctuations, '(,) z t   . The same holds when '() st z v  is negative, which promotes positive values of '(,) dy z v z t  . We note that '(,) '() dy st z z v z t v  attains its largest (absolute) value for ξ < z and '() '(,) st dy z z v z v   for ξ > z. These findings suggest that the stabilizing dynamic fluctuation '(,) '() dy st z z v z t v  arising at a given space-time location (z, t) displays a strong negative correlation with the stationary velocity fluctuations (i.e., with variations of Y according to (22)), especially those occurring at points ξ < z. This is a result of (i) the coupling between flow and transport (as documented b...