Global Sensitivity Analysis Results Research Articles

Identification of parameter importance for benzene transport in the unsaturated zone using global sensitivity analysis

Abstract. One of the greatest threats to groundwater is contamination from fuel derivatives. Benzene, a highly mobile and toxic fuel derivative, can easily reach groundwater from fuel sources and lead to extensive groundwater contamination and drinking water disqualification. Modelling benzene transport in the unsaturated zone can quantify the risk for groundwater contamination and provide needed remediation strategies. Yet, characterization of the problem is often complicated, due to typical soil heterogeneity, numerous unknown site and solute parameters, and the difficulty of distinguishing important from non-important parameters. Thus, sensitivity analysis (SA) methods, such as global SA (GSA), are applied to reduce uncertainty and detect key parameters for groundwater contamination and remediation. Nevertheless, studies devoted to identifying the parameters that determine transport of fuel derivatives in the unsaturated zone are scarce. In this study, we performed GSA to assess benzene transport in the unsaturated zone. First, a simple GSA (Morris) screening method was used for a homogenous sandy vadose zone. Then, a more computationally demanding (Sobol) variance-based GSA was run on the most influential parameters. Finally, the Morris method was tested for a heterogeneous medium containing clay layers. To overcome model crashes during GSA, several methods were tested for imputation of missing data. The GSA results indicate that benzene degradation rate (λk) is the utmost influential parameter controlling benzene mobility, followed by aquifer depth (z). The adsorption coefficient (Kd) and the van Genuchten n parameter of the sandy soil (n1) were also highly influential. The study emphasizes the significance of λk and the presence of clay layers in predicting aquifer contamination. The study also indicates the importance of heterogenous media representation in the GSA. Though identical parameters control the transport in the different soil types, in the presence of both sand and clay, parameters directly affecting the solute concentration like λk and Kd have increased influence in clay, whereas n is more influential for sand comprising most of the profile. Overall, GSA is demonstrated here as an important tool for the analysis of transport models. The results also show that in higher dimensionality models, the radial basis function (RBF) is an efficient surrogate model for missing data imputation.

Global sensitivity analysis for seismic performance of shear wall with high-strength steel bars and recycled aggregate concrete

In terms of bearing lateral loads, a reinforced concrete shear wall (SW) is one of the most crucial structural elements in structures. Despite their significance, recent experimental research and post-earthquake surveys have exposed the inadequate safety margins of the SWs. Significant SW components cannot be accurately identified due to the absence of empirical and mechanistic models. This study introduces a novel paradigm for assessing the SW's crucial elements by using two consecutive modeling strategies. Initially, a finite element model is calibrated to mimic one of the laboratory-experimented SW structures. Then, deep residual neural networks (DRNNs) for non-parametric techniques are used to enhance the Abaqus software prediction skills and comprehensively understand the input parameters' influence on the selected SW structure's displacement value. The suggested DRNNs' design uses residual shortcuts (i.e., connections) that skip several levels in the deep network structure in order to address the issue of training with high accuracy. A thorough global sensitivity analysis (GSA) is done using the Latin Hypercube Simulation. Three distinct GSA techniques are used to emphasize the influence of each input variable on the amount of displacement in real-world applications while limiting the risk of result misinterpretation owing to interactions between input variables. In each GSA approach, an effort would be made to rank, filter, or map the input variables. The performance metrics of the DRNNs prediction models lend confidence to the GSA's results. The diameter of steel stirrups is reported to be the most significant component in the SW structure, while SW's displacement is more sensitive to higher and lower values of the lateral load domain.

A two-stages global sensitivity analysis by using the δ sensitivity index in presence of correlated inputs: application on a tumor growth inhibition model based on the dynamic energy budget theory

Global sensitivity analysis (GSA) evaluates the impact of variability and/or uncertainty of the model parameters on given model outputs. GSA is useful for assessing the quality of Pharmacometric model inference. Indeed, model parameters can be affected by high (estimation) uncertainty due to the sparsity of data. Independence between model parameters is a common assumption of GSA methods. However, ignoring (known) correlations between parameters may alter model predictions and, then, GSA results. To address this issue, a novel two-stages GSA technique based on the δ index, which is well-defined also in presence of correlated parameters, is here proposed. In the first step, statistical dependencies are neglected to identify parameters exerting causal effects. Correlations are introduced in the second step to consider the real distribution of the model output and investigate also the ‘indirect’ effects due to the correlation structure. The proposed two-stages GSA strategy was applied, as case study, to a preclinical tumor-in-host-growth inhibition model based on the Dynamic Energy Budget theory. The aim is to evaluate the impact of the model parameter estimate uncertainty (including correlations) on key model-derived metrics: the drug threshold concentration for tumor eradication, the tumor volume doubling time and a new index evaluating the drug efficacy-toxicity trade-off. This approach allowed to rank parameters according to their impact on the output, discerning whether a parameter mainly exerts a causal or ‘indirect’ effect. Thus, it was possible to identify uncertainties that should be necessarily reduced to obtain robust predictions for the outputs of interest.

Assessment of the parameter sensitivity for the ORYZA model at the regional scale - A case study in the Yangtze River Basin

While global sensitivity analysis (GSA) has been widely implemented for crop models, few studies have assessed the sensitivity of model parameters at the regional scale. To fully understand the overall sensitivity of parameters in a specific area, this study carried out a regional-scale global sensitivity analysis (RGSA) by selecting multiple stations through grids within the study area and integrated GSA results obtained by extended Fourier amplitude sensitivity test (EFAST) from these stations by statistical indicators to quantify parameter sensitivity at the regional scale. Taking the Yangtze River Basin (YRB) as the study area, RGSA was implemented for the ORYZA model for paddy rice under two water and nitrogen situations (WNCs) and four levels of number of stations for sensitivity analysis (NSSA). The results suggested that the applicable area for the results of sensitive and insensitive parameters partitioning, sensitivity ranks and sensitivity indices at a specific station were not larger than grid sizes of 8° × 8°, 4° × 4° and 2° × 2° around it, respectively. Thus, the NSSA needed for sensitive parameter identification, sensitivity ranking and sensitivity indices variability analysis at regional scale increased sequentially. It was recommended that a suitable number of stations should be chosen for analysis according to the sensitivity analysis purpose at the regional scale. Since WNC will affect the results of RGSA, such analysis was recommended to be performed separately for different WNCs. Highly sensitive parameters of the ORYZA model for paddy rice in YZB were screened out through RGSA, which were DVRJ, DVRP and RGRLMX. Model users can adopt the RGSA workflow used in this study for parameter sensitivity assessment of other crop models.

Global Sensitivity Analysis of a Coupled Hydro-Economic Model and Groundwater Restriction Assessment

Assessing impacts on coupled food-water systems that may emerge from water policies, changes in economic drivers and crop productivity requires an understanding of dominant uncertainties. This paper assesses how a candidate groundwater pumping restriction and crop prices, crop yields, surface water price, electricity price, and parametric uncertainties shape economic and groundwater performance metrics from a coupled hydro-economic model (HEM) through a diagnostic global sensitivity analysis (GSA). The HEM used in this study integrates a groundwater depth response, modeled by an Artificial Neural Network (ANN), into a calibrated Positive Mathematical Programming (PMP) agricultural production model. Results show that in addition to a groundwater pumping restriction, performance metrics are highly sensitive to prices and yields of perennial tree crops. These sensitivities become salient during dry years when there is a higher reliance on groundwater. Furthermore, results indicate that performing a GSA for two different water baseline conditions used to calibrate the production model, dry and wet, result in different sensitivity indices magnitudes and factor prioritization. Diagnostic GSA results are used to understand key factors that affect the performance of a groundwater pumping restriction policy. This research is applied to the Wheeler Ridge-Maricopa Water Storage District located in Kern County, California, region reliant on groundwater and vulnerable to surface water shortages.

Comparative energy performance evaluation and uncertainty analysis of two building archetype development methodologies: A case study of high-rise residential buildings in Qatar

Building Archetypes (BAs) are often used in modeling urban-scale building energy consumption profiles to represent the energy consumption behavior of typical buildings within the modeled urban environment. One current approach to the development of BAs involves the creation of Building Energy Models (BEMs) using surveyed data coupled with codes, standards, or engineering experience. Another approach is the modification of existing standardized BEMs using available data to produce a suitable BA for the representation of the building stock. The adoption of either of these methods has been treated as an axiom or a step that did not need much consideration. However, the results produced by BEMs created according to different methodologies present several differences. The discrepancy in the produced results is shown not only in the results of the BEMs developed according to different methodologies but also in the degree to which these results vary when changing input values. Limited studies analyzed the sensitivity of these models to uncertain inputs, even though it is essential for the development of BA libraries. This paper comparatively investigates the Region-Specific (RS) and Department of Energy (DOE)-based BEM creation methods for BA library development. The models are developed by following the two methodologies, and their predictions are compared to the metered data from a high-rise residential building in the Marina district of Lusail City, Qatar. A Global Sensitivity Analysis (GSA) method is used to identify the most influential parameters contributing to the energy consumption variation of these models. Further, a parametric simulation campaign is conducted by varying the inputs determined earlier to quantify the BEMs’ output variability. According to the results, the baseline RS BEM and DOE BEM yield an Energy Use Intensity (EUI) of 211.03 kWh/m2 and 137.9 kWh/m2, respectively. The deviation of these values from the metered EUI of 185,37 kWh/m2 indicates that the RS BEM development methodology is preferable to the DOE BEM for the BA development. Based on the GSA results, regardless of the BEM development methodology used, the most important parameters contributing to output variation are the Cooling Setpoint, the Outdoor Air Requirements, the Equipment Power Density, and the Lighting Power Density. Further, the RS BEM’s parametric simulations produce a mean cooling EUI of 324.83 kWh/m2, closer to the literature benchmarks than the mean cooling EUI of DOE BEM, 341.62 kWh/m2. The results obtained from the baseline model and the uncertainty analysis support the conclusion that a Region-Specific Model developed from the ground up serves to better represent high-rise residential buildings in regions with extreme climate conditions. The impact this work achieves is providing decision-making support for urban scale building energy modelers for future building stock representation efforts in such areas while also providing an expected uncertainty range for the developed high-rise residential archetypes.

Second‐level global sensitivity analysis of numerical simulators with application to an accident scenario in a sodium‐cooled fast reactor

AbstractNumerical simulators are widely used to model physical phenomena and global sensitivity analysis (GSA) aims at studying the global impact of the input uncertainties on the simulator output. To perform GSA, statistical tools based on inputs/output dependence measures are commonly used. We focus here on the Hilbert–Schmidt independence criterion (HSIC). Sometimes, the probability distributions modeling the uncertainty of inputs may be themselves uncertain and it is important to quantify their impact on GSA results. We call it here the second‐level global sensitivity analysis (GSA2). However, GSA2, when performed with a Monte Carlo double‐loop, requires a large number of model evaluations, which is intractable with CPU time expensive simulators. To cope with this limitation, we propose a new statistical methodology based on a Monte Carlo single‐loop with a limited calculation budget. First, we build a unique sample of inputs and simulator outputs, from a well‐chosen probability distribution of inputs. From this sample, we perform GSA for various assumed probability distributions of inputs by using weighted HSIC measures estimators. Statistical properties of these weighted estimators are demonstrated. Subsequently, we define 2nd‐level HSIC‐based measures between the distributions of inputs and GSA results, which constitute GSA2 indices. The efficiency of our GSA2 methodology is illustrated on an analytical example, thereby comparing several technical options. Finally, an application to a test case simulating a severe accidental scenario on nuclear reactor is provided.

Sparse Polynomial Chaos Expansion for Uncertainty Quantification of Composite Cylindrical Shell with Geometrical and Material Uncertainty

The geometrical dimensions and mechanical properties of composite materials exhibit inherent variation and uncertainty in practical engineering. Uncertainties in geometrical dimensions and mechanical properties propagate to the structural performance of composite cylindrical shells under hydrostatic pressure. However, traditional methods for quantification of uncertainty, such as Monte Carlo simulation and the response surface method, are either time consuming with low convergence rates or unable to deal with high-dimensional problems. In this study, the quantification of the high-dimensional uncertainty of the critical buckling pressure of a composite cylindrical shell with geometrical and material uncertainties was investigated by means of sparse polynomial chaos expansion (PCE). With limited design samples, sparse PCE was built and validated for predictive accuracy. Statistical moments (mean and standard deviation) and global sensitivity analysis results were obtained based on the sparse PCE. The mean and standard deviation of critical buckling pressure were 3.5777 MPa and 0.3149 MPa, with a coefficient of variation of 8.801%. Global sensitivity analysis results from Sobol’ indices and the Morris method showed that the uncertainty of longitudinal modulus has a massive influence on the critical buckling pressure of composite cylindrical shell, whereas the uncertainties of transverse modulus, shear modulus, and Poisson’s ratio have a weak influence. When the coefficient of variation of ply thickness and orientation angle does not surpass 2%, the uncertainties of ply thickness and orientation angle have a weak influence on the critical buckling pressure. The study shows that the sparse PCE is effective at resolving the problem of high-dimensional uncertainty quantification of composite cylindrical shell with geometrical and material uncertainty.

Global Sensitivity Analysis of Background Life Cycle Inventories

In recent years many Life Cycle Assessment (LCA) studies have been conducted to quantify the environmental performance of products and services. Some of these studies propagated numerical uncertainties in underlying data to LCA results, and several applied Global Sensitivity Analysis (GSA) to some parts of the LCA model to determine its main uncertainty drivers. However, only a few studies have tackled the GSA of complete LCA models due to the high computational cost of such analysis and the lack of appropriate methods for very high-dimensional models. This study proposes a new GSA protocol suitable for large LCA problems that, unlike existing approaches, does not make assumptions on model linearity and complexity and includes extensive validation of GSA results. We illustrate the benefits of our protocol by comparing it with an existing method in terms of filtering of noninfluential and ranking of influential uncertainty drivers and include an application example of Swiss household food consumption. We note that our protocol obtains more accurate GSA results, which leads to better understanding of LCA models, and less data collection efforts to achieve more robust estimation of environmental impacts. Implementations supporting this work are available as free and open source Python packages.

Implementation of supervised principal component analysis for global sensitivity analysis of models with correlated inputs.

Global Sensitivity Analysis (GSA) plays a significant role in quantifying the tangible impact of model inputs on the uncertainty of response variable. As GSA results are strongly affected by correlated inputs, several studies have considered this issue, but most of them are computationally expensive, labor-intensive, and difficult to implement. Accordingly, this paper puts forward a novel regression-based strategy based on the Supervised Principal Component Analysis (SPCA), benefiting from the Reproducing Kernel Hilbert Space. Indeed, by conducting one kind of variance-based sensitivity analysis, a renowned method exclusively customized for models with orthogonal inputs, on SPCA regression, the impact of the correlation structure of input variables is considered. The ability of the suggested technique is evaluated with five test cases as well as three hydrologic and hydraulic models, and the results are compared with those obtained from the correlation ratio method; Taken as a benchmark solution, which is a robust but quite complicated approach in terms of programming. It is found that the proposed method satisfactorily identifies the sensitivity ordering of model inputs. Furthermore, it is proved in this study that the performance of the proposed approach is also supported by the total contribution index in the derived covariance decomposition equation. Moreover, the proposed method compared with the correlation ratio method, is found to be computationally efficient and easy to implement. Overall, the proposed scheme is appropriate for high dimensional, quite strong nonlinear or expensive models with correlated inputs, whose coefficient of determination between the original model and regression-based SPCA model is larger than 0.33.

Spatio-temporal feature fusion for real-time prediction of TBM operating parameters: A deep learning approach

This research provides a spatio-temporal approach to perform real-time forecasting for the tunnel boring machine (TBM) operating parameters. By extracting the real-time TBM operational data from the data acquisition system, a Long Short-Term Memory (LSTM) based deep learning model is trained for accurate prediction. A global sensitivity analysis (GSA) by adopting the Sobol method is performed for the model to quantify the contribution of input variables. The developed methodology can be a useful tool for TBM performance improvement and it enhances the state of knowledge on underground excavation. The result from the case study indicates that: (1) The proposed spatio-temporal method provides reliable real-time forecasting with mean absolute error (MAE) and root mean squared error (RMSE) of 1.261 mm and 1.955 mm, respectively, and (2) GSA results indicate that TBM's thrust and CHD torque are the 2 most influential spatial factors, while the historical data of penetration rate is critical for accurate forecasting. Further studies could focus on backward optimization to improve TBM's performance based on the prediction.

Is less more? Experimenting with visual stacking of coincident maps for spatial global sensitivity analysis in urban land-use change modeling

Visualization of the outputs from sensitivity analyses of spatially explicit models can potentially enhance the perception of the uncertainty in model outputs. However, spatial global sensitivity analysis (GSA) produces multiple output maps, twice as many as the number of input parameters under investigation, which can result in an overwhelming visual load to interpret. In this research, we tested the visual stacking of coincident maps to handle the visual complexity for an application of an urban land-use change model. The coincident maps were compared with the adjacent representation. Both types of maps were tested using a web-based survey to understand the efficacy in supporting the comprehension of the GSA results. The majority of the questions showed no statistically significant difference between visualization techniques; however, the difficulty of interpreting the adjacent maps was observed among novice users which suggesting the need for an update for the future representations using coincident maps.

Bayesian inference for calibration and validation of uniaxial reinforcing steel models

With ever-advancing structural design and evaluation techniques becoming available for structural engineers, the required level of knowledge about nonlinear material behavior in civil structures has increased accordingly over recent years. In the context of finite element (FE) modeling, constitutive material models play a crucial role in the computation of the structural response. Although significant research has focused on characterizing the stress–strain relationship in reinforcing steel, most of these efforts have considered experimental response data from monotonic tests. In this paper, results from experimental cyclic tests conducted on 36 reinforcing steel coupons obtained from three major manufacturers encompassing two widely used steel grades are employed to gain a deep understanding of the relationship between model formulation and response, for three well-known hysteretic reinforcing steel one-dimensional constitutive stress–strain relationships. Initially, the three models are briefly described. Then, a local sensitivity analysis (LSA) is performed to provide an insight on the influence of each model parameter in model response, followed by a global sensitivity analysis (GSA) performed to further understand the composition of response variability due to parameter uncertainty. Model calibration is then carried out in a probabilistic manner, using the Bayesian estimation (BE) framework through the use of Markov Chain Monte Carlo (MCMC), and informed by LSA and GSA results. Parameter estimation results for each model are discussed, with an emphasis on the level of accuracy of predictions achieved with estimated sets of parameters in each case. The amount of information extracted about each parameter during calibration is assessed, leading to a performance comparison between the three constitutive laws under study.

A coupled framework of variational asymptotic method based homogenization technique and Monte Carlo approach for the uncertainty and sensitivity analysis of unidirectional composites

This article describes a computational framework, based on the variational asymptotic method unit cell homogenization technique coupled with the Monte Carlo method, for carrying out uncertainty and sensitivity analysis of the effective properties of fiber reinforced plastic composites. As an application, univariate and multivariate analysis have been undertaken to investigate the influence of the constituent material properties on the effective properties of the FRP composites. Both bivariate and global sensitivity analysis results are presented to highlight the contribution of the uncertainty in the properties of the constituent materials on the uncertainty in the effective properties. Model predictions are validated by comparing the results with data reported in literature.

Investigation of the importance of different factors of flood inundation modeling applied in urbanized area with variance-based global sensitivity analysis

Flood modeling provides useful information to support flood risk assessment and management and reduce flood impacts in urbanized area. The accuracy of urban flood simulation results is highly dependent on the quality of input data for which the appropriate values are generally difficult to determine for complex urbanized environment and from which various uncertainties are induced into the modeling procedure. In this study, variance-based global sensitivity analysis is applied for the hydrodynamic modeling of urban flood to explore the relative importance of the factors of interest as model inputs and their contributions to the final results of the numerical model for different outputs. The factors include the spatial resolution, the forcing condition and the characteristics of the underlying urbanized surface. The global sensitivity analysis results are examined in both spatially lumped and distributed perspective. Findings indicate that importance of the input factors varies with regard to different model output and the influence of the spatial resolution is more tightly related to the flood flow movements whereas that of the rainfall inputs is more relevant to the flood water volume. Spatial variability in the influence of the input factors is revealed to be hidden by the spatially lumped results and the importance of the factors describing the underlying urban surface is found to be largely dependent on the location of the analyzed model output associated with the land-use type. Improved understanding of sensitivity of hydrodynamic modeling of urban floods may help the modelers to decide which input factors to prioritize on according to which model outputs are assessed and where they are assessed.

Global Sensitivity Analysis Based on BP Neural Network for Thermal Design Parameters

In order to obtain the thermal design parameters that have a great influence on the temperature of the spectrometer frame, the sensitivity of the thermal design parameters of a balloon-borne spectrometer system was analyzed and calculated by the global sensitivity analysis (GSA) method based on the backpropagation neural network (BPNN) surrogate model. Firstly, the BPNN with 12 selected thermal design parameters as input and temperature as output was well trained. Then, two kinds of variance-based GSA methods, the Sobol’ method and the extended Fourier amplitude sensitivity test (EFAST), were used to calculate the values and ranking results of sensitivity indices of 12 parameters based on the established BPNN. Moreover, the GSA results were verified based on the finite element model of the balloon-borne spectrometer system built by I-DEAS/TMG (software developed by Structural Dynamics Research Corporation for space thermal analysis), which indicates that the BPNN surrogate-model-based GSA is reliable. Finally, the sensitivity calculation accuracy and speed of two methods, the Spearman rank correlation coefficient formula and the GSA method based on BPNN, were compared, and the EFAST method based on the BPNN surrogate model has been proved to have obvious advantages in the reliability and speed of calculation results. Also, the GSA method based on a surrogate model like BPNN is of great significance in the thermal analysis of an optical remote sensor.

Considerations and Caveats when Applying Global Sensitivity Analysis Methods to Physiologically Based Pharmacokinetic Models

Three global sensitivity analysis (GSA) methods (Morris, Sobol and extended Sobol) are applied to a minimal physiologically based PK (mPBPK) model using three model drugs given orally, namely quinidine, alprazolam, and midazolam. We investigated how correlations among input parameters affect the determination of the key parameters influencing pharmacokinetic (PK) properties of general interest, i.e., the maximal plasma concentration (Cmax) time at which Cmax is reached (Tmax), and area under plasma concentration (AUC). The influential parameters determined by the Morris and Sobol methods (suitable for independent model parameters) were compared to those determined by the extended Sobol method (which considers model parameter correlations). For the three drugs investigated, the Morris method was as informative as the Sobol method. The extended Sobol method identified different sets of influential parameters to Morris and Sobol. These methods overestimated the influence of volume of distribution at steady state (Vss) on AUC24h for quinidine and alprazolam. They also underestimated the effect of volume of liver (Vliver) for all three drugs, the impact of enzyme intrinsic clearance of CYP2C9 and CYP2E1 for quinidine, and that of UGT1A4 abundance for midazolam. Our investigation showed that the interpretation of GSA results is not straightforward. Dismissing existing model parameter correlations, GSA methods such as Morris and Sobol can lead to biased determination of the key parameters for the selected outputs of interest. Decisions regarding parameters’ influence (or otherwise) should be made in light of available knowledge including the model assumptions, GSA method limitations, and inter-correlations between model parameters, particularly in complex models.Graphical abstract

A surrogate assisted thermal optimization framework for design of pin-fin heat sink for the platform inertial navigation system

ABSTRACT In this study, a thermal optimization framework for the platform inertial navigation system (PINS) is built. To reduce the local high temperature of the PINS, a pin-fin heat sink with staggered arrangement is designed. To reduce the dimension of the inputs and improve the optimization efficiency, a feasible global sensitivity analysis (GSA) based on kriging–high-dimensional model representation with DIviding RECTangles (DIRECT-KG-HDMR) sampling strategy is proposed. According to the GSA results, the filtered structural parameters are used to optimize the thermal performance of the heat sink, and several optimization algorithms (genetic algorithm, differential evolution, teaching–learning-based optimization, particle swarm optimization and efficient global optimization) are used for optimization. The steady thermal response of the PINS with the optimized heat sink is also studied, and the result shows that the maximum temperature of the high-temperature region of the platform is reduced by 1.08°C compared with the PINS without the heat sink.

A Global Sensitivity Analysis of Commonly Used Satellite-Derived Vegetation Indices for Homogeneous Canopies Based on Model Simulation and Random Forest Learning

Remote sensing (RS) provides operational monitoring of terrestrial vegetation. For optical RS, vegetation information is generally derived from surface reflectance (ρ). More generally, vegetation indices (VIs) are built on the basis of ρ as proxies for vegetation traits. At canopy level, ρ can be affected by a variety of factors, including leaf constituents, canopy structure, background reflectivity, and sun-sensor geometry. Consequently, VIs are mixtures of different information. In this study, a global sensitivity analysis (GSA) is made for several commonly used satellite-derived VIs in order to better understand the application of these VIs at large scales. The sensitivities of VIs to different parameters are analyzed on the basis of PROSPECT-SAIL (PROSAIL) radiative transfer model simulations, which apply for homogeneous canopies, and random forest (RF) learning. Specifically, combined factors such as canopy chlorophyll content (CCC) and canopy water content (CWC) are introduced in the RF-based GSA. We find that for most VIs, the leaf area index is the most influential factor, while the broad-band sensor-derived enhanced VI (EVI) exhibits a strong sensitivity to CCC, and the universal normalized VI (UNVI) is sensitive to CWC. The potential and uncertainty for the application of all the considered VIs are analyzed according to the GSA results. The results can help to improve the use of VIs in different contexts, and the RF-based GSA method can be further applied in more sophisticated situations.

Accounting for inter-correlation between enzyme abundance: a simulation study to assess implications on global sensitivity analysis within physiologically-based pharmacokinetics.

Physiologically based pharmacokinetic (PBPK) models often include several sets of correlated parameters, such as organ volumes and blood flows. Because of recent advances in proteomics, it has been demonstrated that correlations are also present between abundances of drug-metabolising enzymes in the liver. As the focus of population PBPK has shifted the emphasis from the average individual to theoretically conceivable extremes, reliable estimation of the extreme cases has become paramount. We performed a simulation study to assess the impact of the correlation between the abundances of two enzymes on the pharmacokinetics of drugs that are substrate of both, under assumptions of presence or lack of such correlations. We considered three semi-physiological models representing the cases of: (1) intravenously administered drugs metabolised by two enzymes expressed in the liver; (2) orally administered drugs metabolised by CYP3A4 expressed in the liver and gut wall; (3) intravenously administered drugs that are substrates of CYP3A4 and OATP1B1 in the liver. Finally, the impact of considering or ignoring correlation between enzymatic abundances on global sensitivity analysis (GSA) was investigated using variance based GSA on a reduced PBPK model for repaglinide, substrate of CYP3A4 and CYP2C8. Implementing such correlations can increase the confidence interval for population pharmacokinetic parameters (e.g., AUC, bioavailability) and impact the GSA results. Ignoring these correlations could lead to the generation of implausible parameters combinations and to an incorrect estimation of pharmacokinetic related parameters. Thus, known correlations should always be considered in building population PBPK models.