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Global Sensitivity Analysis (GSA) is key to assisting appraisal of the behavior of hydrological systems through model diagnosis considering multiple sources of uncertainty. Uncertainty sources typically comprise incomplete knowledge in (a) conceptual and mathematical formulation of models and (b) parameters embedded in the models. In this context, there is the need for detailed investigations aimed at a robust quantification of the importance of model and parameter uncertainties in a rigorous multi‐model context. This study aims at evaluating and comparing two modern multi‐model GSA methodologies. These are the first GSA approaches embedding both model and parameter uncertainty sources and encompass the variance‐based framework based on Sobol indices (as derived by Dai & Ye, 2015, https://doi.org/10.1016/j.jhydrol.2015.06.034) and the moment‐based approach upon which the formulation of the multi‐model AMA indices (as derived by Dell'Oca et al., 2020, https://doi.org/10.1029/2019wr025754) is based. We provide an assessment of various aspects of sensitivity upon considering a joint analysis of these two approaches in a multi‐model context. Our work relies on well‐established scenarios that comprise (a) a synthetic setting related to reactive transport across a groundwater system and (b) an experimentally‐based study considering heavy metal sorption onto a soil. Our study documents that the joint use of these GSA approaches can provide different while complementary information to assess mutual consistency of approaches and to enrich the information content provided by GSA under model and parameter uncertainty. While being related to groundwater settings, our results can be considered as reference for future GSA studies coping with model and parameter uncertainty. Key Points Two modern multi‐model Global Sensitivity Analysis (GSA) approaches are evaluated and compared upon considering two groundwater‐related scenarios The results of the two multi‐model GSA methods can be markedly different due to their differing theoretical bases Joint use of the two GSA methods enhances one's ability for model diagnosis and assessment of system behaviors

Power systems are increasingly affected by various sources of uncertainty at all levels. The investigation of their effects thus becomes a critical challenge for their design and operation. Sensitivity Analysis (SA) can be instrumental for understanding the origins of system uncertainty, hence allowing for a robust and informed decision-making process under uncertainty. The SA value as a support tool for model-based inference is acknowledged; however, its potential is not fully realized yet within the power system community. This is due to an improper use of long-established SA practices, which sometimes prevent an in-depth model sensitivity investigation, as well as to partial communication between the SA community and the final users, ultimately hindering non-specialists’ awareness of the existence of effective strategies to tackle their own research questions. This paper aims at bridging the gap between SA and power systems via a threefold contribution: (i) a bibliometric study of the state-of-the-art SA to identify common practices in the power system modeling community; (ii) a getting started overview of the most widespread SA methods to support the SA user in the selection of the fittest SA method for a given power system application; (iii) a user-oriented general workflow to illustrate the implementation of SA best practices via a simple technical example.

Surrogate models are popular tool to approximate the functional relationship of expensive simulation models in multiple scientific and engineering disciplines. Successful use of surrogate models can provide significant savings of computational cost. However, with a variety of surrogate model approaches available in literature, it is a difficult task to select an appropriate one at hand. In this paper, we present an overview of surrogate model approaches with an emphasis of their application for variance-based global sensitivity analysis, including polynomial regression model, high-dimensional model representation, state-dependent parameter, polynomial chaos expansion, Kriging/Gaussian Process, support vector regression, radial basis function, and low rank tensor approximation. The accuracy and efficiency of these approaches are compared with several benchmark examples. The strengths and weaknesses of these surrogate models are discussed, and the recommendations are provided for different types of applications. For ease of implementations, the packages, as well as toolboxes, of surrogate model techniques and their applications for global sensitivity analysis are collected.

Despite the widespread use of transcranial magnetic stimulation (TMS), the precise cortical locations underlying the resulting physiological and behavioral effects are still only coarsely known. To date, mapping strategies have relied on projection approaches (often termed “center of gravity” approaches) or maximum electric field value evaluation, and therefore localize the stimulated cortical site only approximately and indirectly. Focusing on the motor cortex, we present and validate a novel method to reliably determine the effectively stimulated cortical site at the individual subject level. The approach combines measurements of motor evoked potentials (MEPs) at different coil positions and orientations with numerical modeling of induced electric fields. We identify sharply bounded cortical areas, around the gyral crowns and rims of the motor hand area, as the origin of MEPs and show that the magnitude of the tangential component and the overall magnitude of the electric field are most relevant for the observed effect. To validate our approach, we identified the coil location and orientation that produces the maximal electric field at the predicted stimulation site, and then experimentally show that this location produces MEPs more efficiently than other tested locations/orientations. Moreover, we used extensive uncertainty and sensitivity analyses to verify the robustness of the method and identify the most critical model parameters. Our generic approach improves the localization of the cortical area effectively stimulated by TMS and may be transferred to other modalities such as language mapping.

The most general quantities of interest (called “responses”) produced by the computational model of a linear physical system can depend on both the forward and adjoint state functions that describe the respective system. This work presents the Fourth-Order Comprehensive Adjoint Sensitivity Analysis Methodology (4th-CASAM) for linear systems, which enables the efficient computation of the exact expressions of the 1st-, 2nd-, 3rd- and 4th-order sensitivities of a generic system response, which can depend on both the forward and adjoint state functions, with respect to all of the parameters underlying the respective forward/adjoint systems. Among the best known such system responses are various Lagrangians, including the Schwinger and Roussopoulos functionals, for analyzing ratios of reaction rates, the Rayleigh quotient for analyzing eigenvalues and/or separation constants, etc., which require the simultaneous consideration of both the forward and adjoint systems when computing them and/or their sensitivities (i.e., functional derivatives) with respect to the model parameters. Evidently, such responses encompass, as particular cases, responses that may depend just on the forward or just on the adjoint state functions pertaining to the linear system under consideration. This work also compares the CPU-times needed by the 4th-CASAM versus other deterministic methods (e.g., finite-difference schemes) for computing response sensitivities These comparisons underscore the fact that the 4th-CASAM is the only practically implementable methodology for obtaining and subsequently computing the exact expressions (i.e., free of methodologically-introduced approximations) of the 1st-, 2nd, 3rd- and 4th-order sensitivities (i.e., functional derivatives) of responses to system parameters, for coupled forward/adjoint linear systems. By enabling the practical computation of any and all of the 1st-, 2nd, 3rd- and 4th-order response sensitivities to model parameters, the 4th-CASAM makes it possible to compare the relative values of the sensitivities of various order, in order to assess which sensitivities are important and which may actually be neglected, thus enabling future investigations of the convergence of the (multivariate) Taylor series expansion of the response in terms of parameter variations, as well as investigating the range of validity of other important quantities (e.g., response variances/covariance, skewness, kurtosis, etc.) that are derived from Taylor-expansion of the response as a function of the model’s parameters. The 4th-CASAM presented in this work provides the basis for significant future advances towards overcoming the “curse of dimensionality” in sensitivity analysis, uncertainty quantification and predictive modeling.

In the process of parameter identification, sensitivity analysis is mainly used to determine key parameters with high sensitivity in the model. Sensitivity analysis methods include local sensitivity analysis (LSA) and global sensitivity analysis (GSA). The LSA method has been widely used for power system parameter identification for a long time, while the GSA has started to be used in recent years. However, there is no clear conclusion on the impact of different sensitivity analysis methods on parameter identification results. Therefore, this paper compares and studies the roles that LSA and GSA can play in different parameter identification methods, providing clear guidance for the selection of sensitivity analysis methods and parameter identification methods. The conclusion is as follows. If the identification strategy that only identifies key parameters with high sensitivity is adopted, we recommend still using the existing LSA method. If using a groupwise alternating identification strategy (GAIS) for high- and low-sensitivity parameters, either LSA or GSA can be used. To improve the identification accuracy, it is more important to improve the identification strategy than to change the sensitivity analysis method. When the accuracy of the non-key parameters with low sensitivity cannot be confirmed, using the GAIS is an effective method for ensuring identification accuracy. In addition, it should be noted that the high sensitivity of a parameter does not necessarily mean that the parameter is identifiable, which is revealed by the examples used in this paper.

An accurate and objective evaluation of the carbon footprint of rice production is crucial for mitigating greenhouse gas (GHG) emissions from global food production. Sensitivity and uncertainty analysis of the carbon footprint evaluation model can help improve the efficiency and credibility of the evaluation. In this study, we combined a farm-scaled model consisting of widely used carbon footprint evaluation methods with a typical East Asian rice production system comprising two fertilization strategies. Furthermore, we used Morris and Sobol’ global sensitivity analysis methods to evaluate the sensitivity and uncertainty of the carbon footprint model. Results showed that the carbon footprint evaluation model exhibits a certain nonlinearity, and it is the most sensitive to model parameters related to CH 4 emission estimation, including EF c (baseline emission factor for continuously flooded fields without organic amendments), SF w (scaling factor to account for the differences in water regime during the cultivation period), and t (cultivation period of rice), but is not sensitive to activity data and its emission factors. The main sensitivity parameters of the model obtained using the two global sensitivity methods were essentially identical. Uncertainty analysis showed that the carbon footprint of organic rice production was 1271.7 ± 388.5 kg CO 2 eq t –1 year –1 (95% confidence interval was 663.9–2175.8 kg CO 2 eq t –1 year –1 ), which was significantly higher than that of conventional rice production (926.0 ± 213.6 kg CO 2 eq t –1 year –1 , 95% confidence interval 582.5-1429.7 kg CO 2 eq t –1 year –1 ) ( p <0.0001). The carbon footprint for organic rice had a wider range and greater uncertainty, mainly due to the greater impact of CH 4 emissions (79.8% for organic rice versus 53.8% for conventional rice). EF c , t , Y , and SF w contributed the most to the uncertainty of carbon footprint of the two rice production modes, wherein their correlation coefficients were between 0.34 and 0.55 ( p <0.01). The analytical framework presented in this study provides insights into future on-farm advice related to GHG mitigation of rice production.

The absence of electricity is among the gravest problems preventing a nation’s development. Hybrid renewable energy systems (HRES) play a vital role to reducing this issue. The major goal of this study is to use the non-dominated sorting genetic algorithm (NSGA)-II and hybrid optimization of multiple energy resources (HOMER) Pro Software to reduce the net present cost (NPC), cost of energy (COE), and CO2 emissions of proposed power system. Five cases have been considered to understand the optimal HRES system for Kutubdia Island in Bangladesh and analyzed the technical viability and economic potential of this system. To demonstrate the efficacy of the suggested strategy, the best case outcomes from the two approaches are compared. The study’s optimal solution is also subjected to a sensitivity analysis to take into account fluctuations in the annual wind speed, solar radiation, and fuel costs. According to the data, the optimized PV/Wind/Battery/DG system (USD 711,943) has a lower NPC than the other cases. The NPC obtained by the NSGA-II technique is 2.69% lower than that of the HOMER-based system.

Global sensitivity analysis (GSA) enhances our understanding of computational models and simplifies model parameter estimation. VarIance‐based Sensitivity analysis using COpUlaS (VISCOUS) is a variance‐based GSA framework. The advantage of VISCOUS is that it can use existing model input‐output data (e.g., water model parameters‐responses) to estimate the first‐ and total‐order Sobol’ sensitivity indices. This study improves VISCOUS by refining its handling of marginal densities of the Gaussian mixture copula model (GMCM). We then evaluate VISCOUS using three types of generic functions relevant to water system models. We observe that its performance depends on function dimension, input‐output data size, and non‐identifiability. Function dimension refers to the number of uncertain input factors analyzed in GSA, and non‐identifiability refers to the inability to estimate GMCM parameters. VISCOUS proves powerful in estimating first‐order sensitivity with a small amount of input‐output data (e.g., 200 in this study), regardless of function dimension. It always ranks input factors correctly in both first‐ and total‐order terms. For estimating total‐order sensitivity, it is recommended to use VISCOUS when the function dimension is not very high (e.g., less than 20) due to the challenge of producing sufficient input‐output data for accurate GMCM inferences (e.g., more than 10,000 data). In cases where all input factors are equally important (a rarity in practice), VISCOUS faces non‐identifiability issues that impact its performance. We provide a didactic example and an open‐source Python code, pyVISCOUS, for broader user adoption. Plain Language Summary Global sensitivity analysis is a method used to better understand and estimate parameters in computational models. VarIance‐based Sensitivity analysis using COpUlaS (VISCOUS) is a framework for this purpose. It estimates the sensitivity of model outcomes to different uncertain model input factors by using the existing input and output data (e.g., water model parameters and responses). This study improved VISCOUS and tested it with various functions. We found that its performance depends on the number of input factors, the amount of input and output data available, and our ability to determine VISCOUS's parameters. VISCOUS is good at estimating the importance of individual input factors, even with limited data (e.g., 200) and numerous input factors. It always correctly ranks input factor importance, whether individually or collectively. When estimating the importance of input factors together, VISCOUS is recommended when the number of input factors is not very high (e.g., <20), as it is challenging to generate enough input and output data for estimating VISCOUS's parameters. When all input factors hold equal importance (though rare in practice), VISCOUS's performance is impacted due to the difficulty of estimating VISCOUS's parameters. To help people use VISCOUS, we provide an example and an open‐source Python code, pyVISCOUS. Key Points We improve the VarIance‐based Sensitivity analysis using COpUlaS (VISCOUS) global sensitivity analysis framework in its handling of marginal densities of the Gaussian mixture copula model We evaluate VISCOUS and demonstrate how its performance is affected by function dimension, input‐output size, and non‐identifiability We provide a didactic example and an open‐source Python code called pyVISCOUS to make VISCOUS easier to understand and apply

The exposure to uranium (U) in the natural environment is primarily through ingestion (eating contaminated food and drinking water) and dermal (skin contact with U powders/wastes) pathways. This study focuses on the dose assessment for different age-groups using the USEPA model. A total of 156 drinking water samples were tested to know U level in the groundwater of the study region. Different age-groups were selected to determine the human health impact due to uranium exposure in the residing populations. To determine the relative importance of each input, a variance decomposition technique, i.e., Sobol sensitivity analysis, was used. Furthermore, different sample sizes were tested to obtain the optimal Sobol sensitivity indices. Three types of effects were evaluated: first-order effect (FOE), second-order effect (SOE) and total effect. The result of analysis revealed that 17% of the samples had U concentration above 30 µg l−1 of U, which is the recommended level by World Health Organization. The mean hazard index (HI) value for younger age-group was found to be less than 1, whereas the 95th percentile value of HI value exceeded for both age-groups. The mean annual effective dose of U for adults was found to be slightly higher than the recommended level of 0.1 m Sv year−1. This result signified that adults experienced relatively higher exposure dose than the children in this region. Sobol sensitivity analysis of FOE showed that the concentration of uranium (Cw) is the most sensitive input followed by intake rate (IR) and exposure frequency. Moreover, the value of SOE revealed that interaction effect of Cw − IR is the most sensitive input parameter for the assessment of oral health risk. On the other hand, dermal model showed Cw − F as the most sensitive interaction input. The larger value of SOE was also recorded for older age-group than for the younger group.