Regional Sensitivity Analysis Research Articles

Moment-independent regional sensitivity analysis: Application to an environmental model

Through several decades of development, global sensitivity analysis has been developed as a very useful guide tool for assessing scientific models and has gained pronounced attention in environmental science. However, standard global sensitivity analysis aims at measuring the contribution of input variables to model output uncertainty on average by investigating their full distribution ranges, but does not investigate the contribution of specific ranges. To deal with this problem, researchers have developed several regional sensitivity analysis techniques such as the contribution to sample mean and variance (CSM and CSV) plots. In this paper, a moment-independent regional sensitivity analysis technique called contribution to delta indices (CDI) plot is developed for assessing the effect of a specific range of an individual input to the uncertainty of model output. The CDI plot can be obtained with the same set of samples used for computing the CSM and CSV. Compared with the CSM and CSV, the CDI plot uses the probability density function shift of model output to describe the uncertainty instead of the mean and variance, thus it is moment-independent. An analytical linear model, the Ishigami function and an environmental model are employed to test the proposed RSA technique.

SENSITIVITY ANALYSIS FOR STUDYING THE RELATION BETWEEN BIOCHEMICAL REACTIONS AND METABOLIC PHENOTYPES

Metabolic models are the most widespread type of models in systems biology and are currently used in several applications, including metabolic engineering and investigations of pathological states in which metabolic disorders play a relevant role. Once a model has been defined and corroborated, sensitivity analysis techniques can be used to study the model behavior in relation to perturbations of the model parameters. Here, we describe how it is possible to combine regionalized sensitivity analysis and response surface methodology to screen and quantitatively characterize the relation between metabolic phenotypes and biochemical reactions rates. By means of this approach, we identified the most important reactions for the citric acid efflux from mitochondria, one of the key metabolic traits of cancer cells.

Global sensitivity analyses for a complex hydrological model applied in an Alpine watershed

AbstractThe increasing complexity of hydrological models results in a large number of parameters to be estimated. In order to better understand how these complex models work, efficient screening methods are required in order to identify the most important parameters. This is of particular importance for models that are used within an operational real‐time forecasting chain such as HQsim. The objectives of this investigation are to (i) identify the most sensitive parameters of the complex HQsim model applied in the Alpine Lech catchment and (ii) compare model parameter sensitivity rankings attained from three global sensitivity analysis techniques. The techniques presented are the (i) regional sensitivity analysis, (ii) Morris analysis and (iii) state‐dependent parameter modelling. The results indicate that parameters affecting snow melt as well as processes in the unsaturated soil zone reveal high significance in the analysed catchment. The snow melt parameters show clear temporal patterns in the sensitivity whereas most of the parameters affecting processes in the unsaturated soil zone do not vary in importance across the year. Overall, the maximum degree day factor (meltfunc_max) has been identified to play a key role within the HQsim model. Although the parameter sensitivity rankings are equivalent between methods for a number of parameters, for several key parameters differing results were obtained. An uncertainty analysis demonstrates that a parameter ranking attained from only one method is subjected to large uncertainty. Copyright © 2012 John Wiley & Sons, Ltd.

Analysis of the behavior of a rainfall–runoff model using three global sensitivity analysis methods evaluated at different temporal scales

The effect of 11 parameters on the discharge of a conceptual rainfall–runoff model was analyzed for a small Austrian catchment. The sensitivities were computed using three methods: Sobol’s indices, the mutual entropy and regional sensitivity analysis (RSA). The calculations were carried out for different temporal scales of evaluation ranging from daily to a multiannual period. A comparison of the methods shows that the mutual entropy and the RSA methods give more robust results than Sobol’s method, which shows a higher variability in the sensitivities when they are calculated using different data sets. While all sensitivity methods are suitable for identifying the most sensitive parameters of a model, there are increasing differences in the results when the parameters become less important and also when shorter temporal scales are considered. A correlation analysis further indicated that the periods in which the parameter sensitivity rankings did not agree between the different methods are characterized by a higher impact of the parameters interactions on the modeled discharge. An analysis of the parameter sensitivity across the scales showed that the number of important parameter decreases when longer evaluation periods are considered. For instance, it was observed that all parameters were important at least during 1 day a daily scale, while at a yearly scale only the parameters characterizing the soil storage and the recession constants for interflow and percolation had high sensitivities. With respect to the impact of the interactions between parameters on the model results, it was observed that the largest effect is related to the parameters describing the size of the soil storage, the interflow and the percolation flow recession constants. Further, it was observed that there is a positive correlation between the importance of the interactions and the measured discharge. While the study focuses on quantitative sensitivity measures, it is also highlighted that graphical RSA analyses provide additional information regarding the parameter ranges associated with different discharge levels. This information can be used for increasing the understanding of the mechanisms by which the parameters affect the model results.

Understanding the metabolism of urban-rural ecosystems

A Multi-sectoral Systems Analysis (MSA) methodology is presented as a tool for identifying the level of importance of flows of energy and materials (water, nitrogen, phosphorus, and carbon) as they pass through an anthropogenically manipulated system. That system comprises a web of processes, across a total of five industrial sectors: water, forestry, food, energy and waste management. Given the heterogeneous nature and quality of data sources, the propagation of data uncertainty is considered through a Regionalized Sensitivity Analysis (RSA) procedure, based on the Monte Carlo simulation approach. The MSA reveals the advantages of studying different material cycles simultaneously, in addition to interpreting them individually, while gaining insight into the magnitude of the associated flows. The proposed framework is illustrated for a case study of the Upper Chattahoochee Watershed, in which parts of Metro Atlanta are located. Results show that natural flows are predominant in the water and energy cycles. Direct human manipulations of water, i.e., withdrawals for public supply and power generation, are less than 25% of the amount received as precipitation. Solar input is 200 times the total demand for electricity. Apart from sun-light, gasoline for transportation is the flow with the largest content of energy; it is responsible for providing 71% of the total demand of fuels for uses other than power generation. In contrast, cycles of nutrients such as N and C are strongly related to the flows of fuels, mainly coal and natural gas. In a second tier, fertilizer use and the poultry industry in the region are significant for the use of nitrogen. Phosphorus fluxes are similarly dominated by the food sector and, as a consequence, to a lesser extent by the water sector, because of water’s role as a waste-conveyance medium.

The use of multiobjective calibration and regional sensitivity analysis in simulating hyporheic exchange

We describe an approach for calibrating a two‐dimensional (2‐D) flow model of hyporheic exchange using observations of temperature and pressure to estimate hydraulic and thermal properties. A longitudinal 2‐D heat and flow model was constructed for a riffle‐pool sequence to simulate flow paths and flux rates for variable discharge conditions. A uniform random sampling approach was used to examine the solution space and identify optimal values at local and regional scales. We used a regional sensitivity analysis to examine the effects of parameter correlation and nonuniqueness commonly encountered in multidimensional modeling. The results from this study demonstrate the ability to estimate hydraulic and thermal parameters using measurements of temperature and pressure to simulate exchange and flow paths. Examination of the local parameter space provides the potential for refinement of zones that are used to represent sediment heterogeneity within the model. The results indicate vertical hydraulic conductivity was not identifiable solely using pressure observations; however, a distinct minimum was identified using temperature observations. The measured temperature and pressure and estimated vertical hydraulic conductivity values indicate the presence of a discontinuous low‐permeability deposit that limits the vertical penetration of seepage beneath the riffle, whereas there is a much greater exchange where the low‐permeability deposit is absent. Using both temperature and pressure to constrain the parameter estimation process provides the lowest overall root‐mean‐square error as compared to using solely temperature or pressure observations. This study demonstrates the benefits of combining continuous temperature and pressure for simulating hyporheic exchange and flow in a riffle‐pool sequence.

Retrieving Spatial Policy Parameters from an Alternative Plan Using Constrained Cellular Automata and Regionalized Sensitivity Analysis

In this paper we propose an approach to identify the spatial policy parameters (termed the implementation intensity reflecting planning controls on corresponding spatial constraint) associated with a predefined alternative plan, namely, a predefined-binary urban form. During plan implementation, the alternative plan cannot be fully realized in some cases due to practical urban growth driven by both institutional forces and market incentives, which are comprehensive and complex. Few researchers have investigated spatial policies appropriate for an alternative plan. We aim to propose a novel approach incorporating constrained cellular automata and regionalized sensitivity analysis, a method for global sensitivity analysis to calculate the realization possibility and identify the spatial policy parameters for an alternative plan. This approach is first tested in a virtual space with four predefined urban forms and various point, line, and polygon spatial constraints, with both positive and negative impacts on urban growth. Finally, the approach is also tested in the Beijing Metropolitan Area to identify the required spatial policy parameters for four alternative plans with seven spatial constraints.

Parameter uncertainty in a highly parameterized model of Lake Okeechobee

The uncertainty in input parameters and management predictions of a complex eutrophication model were defined using a likelihood-based Monte Carlo uncertainty analysis. Results indicate that substantial uncertainty exists in the posterior distributions for model input parameters, despite 18 years of calibration data. Marginal posterior parameter distributions were not significantly different than priors for 95 of the 114 input parameters. The consideration of likelihood did reduce the uncertainty of model predictions of future lake response to nutrient loads by 68–79% compared to predictions based using prior uncertainty alone. These results indicate that consideration of likelihood does provide important information on the necessary correlation structure between inputs, and that selection of an acceptable set of parameters is much more important than the selection of any particular parameter value. Computational requirements were extensive when applying Monte Carlo analysis to a complex model with 18 years of continuous calibration data. Application of a regionalized sensitivity analysis provided close agreement to the full uncertainty analysis with an order of magnitude less computational effort, and is likely a preferred alternative for computationally intensive models with informal likelihood functions and/or poorly defined priors.

Convergence and uncertainty analyses in Monte-Carlo based sensitivity analysis

Sensitivity analysis plays an important role in model development, calibration, uncertainty analysis, scenario analysis, and, hence, decision making. With the availability of different sensitivity analysis techniques, selecting an appropriate technique, monitoring the convergence and estimating the uncertainty of the sensitivity indices are very crucial for environmental modelling, especially for distributed models due to their high non-linearity, non-monotonicity, highly correlated parameters, and intensive computational requirements. It would be useful to identify whether some techniques outperform others with respect to computational requirements, reliability, and other criteria. This paper proposes two methods to monitor the convergence and estimate the uncertainty of sensitivity analysis techniques. One is based on the central limit theorem and the other on the bootstrap technique. These two methods are implemented to assess five different sensitivity analysis techniques applied to an environmental model. These techniques are: the Sobol’ method, the Morris method, Linear Regression (LR), Regionalized Sensitivity Analysis (RSA), and non-parametric smoothing. The results show that: (i) the Sobol’ method is very robust in quantifying sensitivities and ranking parameters despite a large number of model evaluations; (ii) the Morris method is efficient to rank out unimportant parameters at a medium cost; (iii) the non-parametric smoothing is reliable and robust in quantifying the main effects and low-order interactions while requiring a small number of model evaluations; finally (iv) the other two techniques, that is, LR and RSA, should be used with care.

Satellite remote sensing and conceptual cloud modeling for convective rainfall simulation

Motivated by the need for rainfall prediction models in data scarce areas, we adapted a simple storage based cloud model to use routinely available thermal infrared (TIR) data. The data is obtained from the Spinning Enhanced Visible and InfraRed Imager (SEVIRI) of the Meteosat Second Generation (MSG-2) satellite. Model inputs are TIR cloud top temperatures at 15-min intervals and observations of pressure, temperature, and dew point temperatures from ground-based stations at 30-min intervals. The sensitivity of the parsimonious cloud model to its parameters is evaluated by a regional sensitivity analysis (RSA) which suggests that model performance is sensitive to few parameters. The model was calibrated and tested for four convective events that were observed during the wet season in the source basin of the Upper Blue Nile River. The difference between the simulated and the observed depth of the selected rain events varies between 0.2 and 1.8 mm with a root mean square error of smaller than 0.5 mm for each event. It is shown that the updraft velocity characteristic can provide relevant information for rainfall forecasting. The simulation results suggest the effectiveness of the model approach as evaluated by selected performance measures. The various characteristics of the rainfall events as simulated generally match to observed counter parts when ground-based and remote sensing observations are combined.

Structure validation of an integrated waterworks model for trihalomethanes simulation by applying regional sensitivity analysis

A previously developed integrated waterworks model for trihalomethanes simulation was validated by applying a new framework for comprehensive model structure validation. The proposed framework followed the procedure of regional sensitivity analysis and also involved correlation analysis and frequency distribution analysis. Through such an analysis framework, a deep insight into model structure and parameters could be gained besides the traditional focuses on model validation, i.e. model performance and rationality of model parameters. The integrated waterworks model, to which the framework was applied, was proved to give good predictions of the simulated variables, and the identified values of model parameters coincided well with the reported values in the literature. The model was also found to have a large proportion of sensitive parameters, no distinct correlations among parameters, and thus a balanced structure. Moreover, most of the sensitive parameters could be well identified and the associated uncertainties significantly reduced. A detailed investigation into the sensitivity, identifiability, and uncertainty of model parameters showed that the model conceptualization was in good agreement with accepted scientific principles and anticipated system behaviors. All these results, therefore, supported the validity and trustworthiness of the model. In addition, further opportunities for refining the model were also proposed.

Application of a model-based HACCP system to turbidity control in a conventional waterworks

A model-based HACCP system for managing drinking water safety has been proposed by introducing a previously developed Integrated Water Supply System (IWaSS) model for the determination of critical control points (CCPs) and the establishment of critical limits (CLs). In such a HACCP system, hazard analysis is conducted as a quantitative risk assessment through Monte Carlo simulation with the IWaSS model, CCPs are identified through a regional sensitivity analysis, while the CLs for the CCPs are determined through an iterative simulation also with the IWaSS model. The methodology is then applied to a typical conventional waterworks to assess the potential of the waterworks to comply with the standard for turbidity and formulate effective strategies for turbidity control. Coagulation and filtration are found to be the CCPs to improve the performance of the waterworks in turbidity compliance, while source water and sedimentation are the quality control points (QCPs). CLs for the CCPs and QCPs are also quantitatively determined, based on which requirements for monitoring system and corrective actions are proposed.

Modeling of nitrobenzene in the river with ice process in high-latitude regions

To deal with the accidental release of pollutants into frozen rivers, those rivers in high-latitude regions should be treated differently. Pollutants could be stored up in the ice and released when the ice melts in spring, perhaps resulting in secondary pollution in the river. A water quality model of nitrobenzene has been developed in this paper to assess the influence on river water quality due to the freezing process. The model is made up of three modules: thermodynamic module, hydrodynamic module and water quality module. The thermodynamic module considers the complex heat exchange processes between the water body and the atmosphere, the water body and the river bed, the water body and the ice cover, and so on. The growth of the ice cover is simulated in a simplified form whilst taking consideration of heat balance. The hydrodynamic model uses the Saint-Venant equations in non-constant flow and the influence of the ice cover is measured. The degradation, diffusion, absorption and desorption, and the influence of the freezing process are incorporated in the water quality module and the concept of Continuously Stirred Tanked Reactors (CSTRs) model is applied in the model construction. The model has been applied to supporting the management of accidental pollution in the Songhua River. The model was calibrated and validated with monitored data. Regional sensitivity analysis based on a task-based Hornberger-Spear-Young (HSY) algorithm was carried out to examine the model structure and the result showed that the model could describe the system very well. Then the conditioned model was applied to predicting the concentration of nitrobenzene in the water when the ice melted in spring. The predictive result showed that the release of pollutants in the ice could lead to an increase in the concentration of pollutants in the water, but the increase would be very small because there was only a small amount of pollutants stored in the ice. A secondary pollution could therefore be avoided. Also, with necessary modifications, the model established in this study could be applied to the water quality management in rivers that freeze in winter.

Sensitivity analysis of Takagi-Sugeno-Kang rainfall-runoff fuzzy models

Abstract. This paper is concerned with the sensitivity analysis of the model parameters of the Takagi-Sugeno-Kang fuzzy rainfall-runoff models previously developed by the authors. These models are classified in two types of fuzzy models, where the first type is intended to account for the effect of changes in catchment wetness and the second type incorporates seasonality as a source of non-linearity. The sensitivity analysis is performed using two global sensitivity analysis methods, namely Regional Sensitivity Analysis and Sobol's variance decomposition. The data of six catchments from different geographical locations and sizes are used in the sensitivity analysis. The sensitivity of the model parameters is analysed in terms of several measures of goodness of fit, assessing the model performance from different points of view. These measures include the Nash-Sutcliffe criteria, volumetric errors and peak errors. The results show that the sensitivity of the model parameters depends on both the catchment type and the measure used to assess the model performance.

The impact of new developments on river water quality from an integrated system modelling perspective

New housing areas are a ubiquitous feature of modern life in the developing and developed world alike built in response to rising social, demographic and economic pressures. Inevitably, these new developments will have an impact on the environment around them. Empirical evidence confirms the close relationship between urbanisation and ambient water quality. However, what is lacking so far is a detailed and more generalised analysis of environmental impact at a relatively small scale. The aim of this paper is to quantify the impact of new developments on river water quality within an integrated system modelling perspective. To conduct the impact analyses, an existing integrated urban wastewater model was used to predict water flow and quality in the sewer system, treatment plant and receiving water body. The impact on combined sewer overflow (CSO) discharges, treatment plant effluent, and within the river at various reaches is analysed by ‘locating’ a new development on a semi-hypothetical urban catchment. River water quality is used as feedback to constrain the scale of the new development within different thresholds in compliance with water quality standards. Further, the regional sensitivity analysis (RSA) method is applied to reveal the parameters with the greatest impact on water quality. These analyses will help to inform town planners and water specialists who advise them, how to minimise the impact of such developments given the specific context.

Calibration of regional palaeohydrogeology and sensitivity analysis using hydrochemistry data in site investigations

A transient coupled regional model of groundwater flow and solute transport has been developed, which allows the use of hydrochemical data to calibrate the model input parameters. The methodology has been illustrated using examples from the Simpevarp area in south-eastern Sweden which is being considered for geological disposal of spent nuclear fuel. The 3-dimensional model includes descriptions of spatial heterogeneity, density driven flow, rock matrix diffusion and transport and mixing of different water types, and has been simulated between 8000 BC and 2000 AD. Present-day analyses of major elemental ions and stable isotopes have been used to calibrate the model, which has then been cross checked against measured hydraulic conductivities, and against the hydrochemical interpretation of reference water mixing fractions. The key hydrogeological model sensitivities have been identified using the calibrated model and are found to include high sensitivity to the top surface flow boundary condition, the influence of variations in fracture transmissivity in different orientations (anisotropy), spatial heterogeneity in the deterministic regional deformation zones and the spacing between water bearing fractures (in terms of its effect on matrix diffusion).

Nitrate reduction in streambed sediments: Effects of flow and biogeochemical kinetics

The effect of retention time on redox sequences along the hydrological flow path of groundwater discharging through low‐relief coastal stream sediments and the subsequent impact on the fate of NO3− carried in the groundwater was examined in two intact cores. Rates of denitrification were determined for the organic‐rich streambed sediments, and a macroscopic, multispecies, reactive transport model based on multiple Monod kinetics was developed to interpret and extend the experimental results. Regionalized sensitivity analysis and parameter estimation were used to determine a set of parameters that best describe the experimental data for one column. The calibrated model successfully replicated the spatial profiles of nitrate under both steady and transient conditions in the second column operated under different conditions. A dimensionless form of the model was used to examine how coupled biogeochemical reactions and hydrological transport processes operate within the stream sediments could be understood in terms of Peclet (ratio of advection to dispersion) and Damkohler numbers (the ratio of the characteristic time of transport to the characteristic time for reaction). At the study site, the Peclet number and the Damkohler numbers for both oxygen and nitrate are high (Pe = 25, DaN = 47.5, and DaO = 40). When Pe > 5, Damkohler numbers explain observed variations in nitrate removal rates; as the flow rate increases, the solute residence time in the reactive zone is shortened resulting in a lesser extent of reaction, such that more NO3− is delivered to the stream water.

Approaches to Evaluate Water Quality Model Parameter Uncertainty for Adaptive TMDL Implementation1

Abstract: The National Research Council recommended Adaptive Total Maximum Daily Load implementation with the recognition that the predictive uncertainty of water quality models can be high. Quantifying predictive uncertainty provides important information for model selection and decision‐making. We review five methods that have been used with water quality models to evaluate model parameter and predictive uncertainty. These methods (1) Regionalized Sensitivity Analysis, (2) Generalized Likelihood Uncertainty Estimation, (3) Bayesian Monte Carlo, (4) Importance Sampling, and (5) Markov Chain Monte Carlo (MCMC) are based on similar concepts; their development over time was facilitated by the increasing availability of fast, cheap computers. Using a Streeter‐Phelps model as an example we show that, applied consistently, these methods give compatible results. Thus, all of these methods can, in principle, provide useful sets of parameter values that can be used to evaluate model predictive uncertainty, though, in practice, some are quickly limited by the “curse of dimensionality” or may have difficulty evaluating irregularly shaped parameter spaces. Adaptive implementation invites model updating, as new data become available reflecting water‐body responses to pollutant load reductions, and a Bayesian approach using MCMC is particularly handy for that task.

Uncertainty in prediction of disinfection performance

Predicting the disinfection performance of a full-scale reactor in drinking water treatment is associated with considerable uncertainty. In view of quantitative risk analysis, this study assesses the uncertainty involved in predicting inactivation of Cryptosporidium parvum oocysts for an ozone reactor treating lake water. A micromodel is suggested which quantifies inactivation by stochastic sampling from density distributions of ozone exposure and lethal ozone dose. The ozone exposure distribution is computed with a tank in series model that is derived from tracer data and measurements of flow, ozone concentration and ozone decay. The distribution of lethal ozone doses is computed with a delayed Chick–Watson model which was calibrated by Sivaganesan and Marinas [2005. Development of a Ct equation taking into consideration the effect of Lot variability on the inactivation of Cryptosporidium parvum oocysts with ozone. Water Res. 39(11), 2429–2437] utilizing a large number of inactivation studies. Parameter uncertainty is propagated with Monte Carlo simulation and the probability of attaining given inactivation levels is assessed. Regional sensitivity analysis based on variance decomposition ranks the influence of parameters in determining the variance of the model result. The lethal dose model turns out to be responsible for over 90% of the output variance. The entire analysis is re-run for three exemplary scenarios to assess the robustness of the results in view of changing inputs, differing operational parameters or revised assumptions about the appropriate model. We argue that the suggested micromodel is a versatile approach for characterization of disinfection reactors. The scheme developed for uncertainty assessment is optimal for model diagnostics and effectively supports the management of uncertainty.

Estimation of kinetic parameters of a model for deammonification in biofilms and evaluation of the model

A systematic approach to estimate and evaluate parameters for deammonification in biofilms from available experimental data was evaluated. Parameter estimation was based on a regional steady state sensitivity analysis to select relevant parameters and design of experiments based on a local identifiability analysis. The calibrated model was evaluated under different experimental conditions. Nine of the 16 kinetic and stoichiometric parameters had a significant influence on model predictions. Of these nine parameters only six kinetic parameters were identifiable from batch experiments regardless of the experimental design. More parameters were not identifiable due to high correlations between growth rates and the corresponding affinity constant for oxygen. Data from a batch experiment at 2 mg/L dissolved oxygen (DO) were used to estimate inactivation rates and affinity constants for oxygen for ammonium oxidisers (AO), nitrite oxidisers (NO) and anaerobic ammonium oxidisers (AN). In addition, it was found that not only kinetic and stoichiometric parameters but also the external mass transfer resistance significantly affected model predictions. The resulting model was able to reproduce batch test and continuous reactor operation where DO concentrations were similar to those in the batch experiment used for parameter estimation. However, the model overestimated deammonification for a batch experiment at a much higher DO concentration (5 mg/L). Thus, parameter values that are identifiable and are estimated for given environmental conditions may not necessarily be valid for significantly different experimental conditions.