Monte Carlo-based Uncertainty Analysis Research Articles

Uncertainty and sensitivity analysis of revised leachate pollution index.

Composite indicators (CIs) are being utilized more frequently to assess and monitor environmental systems. The revised leachate pollution index (r-LPI) is one such composite indicator used to quantify the pollution potential of landfill leachate on a scale of 5-100. The development of CIs involves several steps, and each of these steps has various methodological choices, each of which could lead to different results. Thereby, the reliability of the quantified pollution potential of leachate may be questioned. This study investigated the techniques for developing the r-LPI, examining decisions related to parameter selection, normalization technique, weighting approach, sub-indicator weights, and their aggregation. As the index developer made the decisions, each of these stages was fraught with uncertainty. The uncertainty in the various stages of the development of r-LPI was quantified using the Monte Carlo-based uncertainty analysis and the sensitivity analysis approach. Uncertainty analysis is a helpful but seldom-used step of index development that identifies the model's most dependable sections. Sensitivity analysis was carried out to ascertain the degree of impact the input parameters have on the r-LPI values. The combined use of sensitivity and uncertainty analysis in this study for the formulation of r-LPI affirmed the transparency, credibility, and accuracy of the index.

Investigation of an Indian Site with Mafic Rock for Carbon Sequestration.

The increasing extent of greenhouse gas emissions has necessitated the development of techniques for atmospheric carbon dioxide removal and storage. Various techniques are being explored for carbon storage including geological sequestration. The geological sequestration has various avenues such as depleted oil and gas reservoirs, coal-bed methane reservoirs, and mafic and ultramafic rocks. Different trapping mechanisms are in play in these subsurface storage systems. In these sequestration sites, the mafic and ultramafic rocks are best suited for long-term and effective sequestration as they comprise minerals, conducive for chemical alteration, forming stable carbonates. However, these sites often suffer from distinct disadvantages of injectivity issues due to their low permeability and porosity. This study investigates the potential of sequestration in the rock samples obtained from one such site located in India. The rock samples are first characterized using various techniques including X-ray fluorescence, X-ray diffraction, Raman spectroscopy, and field emission scanning electron microscopy (FESEM). The mineralogical characterization shows that the rock sample contains approximately 10% of diopside. The samples were put in the reactor chamber comprising CO2, which were then investigated using FESEM analysis. Additionally, a reservoir block simulation using commercial software was conducted with the representative minerals in the sample to evaluate the CO2 sequestration potential. The simulation result suggests the formation of magnesite which corresponds to a major part of CO2 mineral trapping. The reduced injectivity due to low porosity and permeability in this rock can be addressed using hydraulic fracturing. The geomechanical behavior of the rock sample for hydraulic fracturing is studied using the Brazilian disc test. The Monte Carlo-based uncertainty analysis was conducted using the tensile strength data of the sample. Results suggest that the most likely fracturing pressure is 2100 psi for this rock sample.

Assessing the attractiveness of chemical and process facilities to terrorism using a situational crime prevention approach

As intentional attacks to industry have been on the rise in the last years, researchers and institutions put effort in addressing risks of industrial assets exposed to acts of interference. One of the key steps of security risk assessment is the evaluation of the attractiveness, i.e. determining which installation or part of it could be of interest to a potential attacker. As security concerns are intrinsically tied to human intention, attractiveness does not only depend on technical characteristics of the facility, but also on the type of threat and its geographic, economic, and socio-political context. Therefore, interdisciplinarity is among the key features of a team tasked with assessing attractiveness. This work is the result of the joint effort of Physical Sciences and Engineering experts and Social Sciences and Humanities experts, and it presents a methodology for the assessment of attractiveness of process facilities to physical terroristic attacks developed using a “terrorist thinking” approach. Technical factors such as plant layout and physical protection systems were combined with modern criminology principles (namely Situational Crime Prevention, i.e. how actors take advantage of situated opportunities to commit a crime) to obtain a comprehensive picture of the possible motives behind a physical terroristic attack to a chemical and process facility (meant as facilities where chemical substances are present and where chemical and/or physical processes occurs). The methodology was applied to a case study featuring facilities located in a critical context; a ranking among facilities was obtained, and the robustness of the results was tested through a Monte Carlo-based uncertainty analysis. The results revealed that it is not possible to obtain a clear ranking of critical facilities accounting only for technical or non-technical factors, but both are necessary. The method developed was demonstrated easy to apply and could be used not only by plant security managers, but also by Institutions and Governments to prioritize critical assets in threatening contexts.

Centralized MPC for Home Energy Management With EV as Mobile Energy Storage Unit

Electric vehicle (EV) is commonly considered as an electric load in a residential energy network. However, the large capacity EV battery can be used as electric storage when the EV is plugged in at home. While model predictive control (MPC) offers an efficient and reliable control mechanism for a home energy management system (HEMS), the uncertainty related to the availability of an EV at home poses an interesting challenge for the MPC optimization strategy. In this article, the thermal comfort and energy management performance of a centralized MPC-based HEMS is presented for such a scenario where an EV is used as a mobile energy storage unit in a home energy network. The MPC-based HEMS simultaneously controls the zone-based heating system consisting of a heat pump and baseboard units along with the energy flow among the different components of the home energy network. This network comprises the home baseload, charging and discharging of the home-battery and the EV battery, in-house solar energy generation and storage. The MPC-based HEMS optimizes the buying/selling of energy from/to the grid based on time of use electricity rates. A Monte-Carlo based uncertainty analysis is presented here to estimate the robustness of the MPC against the randomness in the EV arrival and departure schedule. Finally, the responsiveness of the centralized MPC is showcased using a vehicle to home communication scenario where the owner notifies the home network regarding their arrival within a short interval, along with the preferred indoor temperature upon arrival.

Aboveground biomass estimation in forests with random forest and Monte Carlo-based uncertainty analysis

Estimates of aboveground biomass (AGB) in forests and the associated uncertainty are important pieces of information outlined in the United Nations Framework Convention on Climate Change. Traditional integrated surveying methods require high inputs of manpower and material resources, whereas remote sensing technology can be used to improve the efficiency of forest resources surveying at a lower measurement cost. Previous studies have primarily utilized spectral information and textural features as the main modeling factors for AGB prediction models, however, few studies have examined how different modeling factors affect prediction accuracy in detail. At the same time, uncertainties in AGB are usually determine by a data set producing a single prediction result, ignoring the model uncertainty due by residual variability in the prediction results. To solve the above problems, this study focuses on Milin County of the Tibet Autonomous Region of China as the research area and uses data from the Landsat Operational Land Imager, digital elevation models (DEM), and the national forest inventory (NFI) to extract and analyze spectral information, textural features, and terrain factors. Four regression models based on different combinations of variables were established using a combination of random forest and Monte Carlo simulation methods (RF-MC), and the uncertainties of each model were determined. The purpose of this paper is to study the influence of different types of variable factors on AGB inversion and to measure the model uncertainty resulting from changes in the variable factors. The coefficient of determination (R2), mean absolute error (MAE), and root mean square error (RMSE) were used to evaluate the fit and accuracy of the model, while the relative root mean square error (rRMSE) was used to quantify the uncertainty. The results show that the degree of fitting and accuracy are greatest for the RF-MC model based on three kinds of variables (spectrum and plot data + DEM + texture characteristics) the best (R2 = 0.85, RMSE = 11.76 t/ha, MAE = 8.49 t/ha, rRMSE = 5.97 %), which performed better than the RF-MC model based on two variables (spectrum and plot data + texture characteristics, R2 = 0.78, RMSE = 13.93 t/ha, MAE = 10.01 t/ha, rRMSE = 7.07 % or spectrum and plot data + DEM, R2 = 0.69, RMSE = 16.75 t/ha, MAE = 14.62 t/ha, rRMSE = 8.49 %) and the RF-MC model based on a single variable (spectrum and plot data, R2 = 0.49, RMSE = 21.39 t/ha, MAE = 19.84 t/ha, rRMSE = 10.86 %). The range of the predicted model value is 150.6–227.8 t/ha, which is close to the actual value. The RF-MC method based on multifeature is demonstrated to be effective in the practical application of AGB inversion, and different types of modeling variables have a certain impact on the accuracy of AGB inversion. This study provides a theoretical basis for improving the accuracy of AGB estimates and the selection of modeling variables, while also contributing to continued improvements in remote sensing-based systems for monitoring forest resources.

Recognizing the role of uncertainties in the transition to renewable hydrogen

Achieving the goal of net zero emissions targeted by many governments and businesses around the world will require an economical zero-emissions fuel, such as hydrogen. Currently, the high production cost of zero emission ‘renewable’ hydrogen, produced from electrolysis powered by renewable electricity, is hindering its adoption. In this paper, we examine the role of uncertainties in projections of techno-economic factors on the transition from hydrogen produced from fossil fuels to renewable hydrogen. We propose an integrated framework, linking techno-economic and Monte-Carlo based uncertainty analysis with quantitative hydrogen supply-demand modelling, to examine hydrogen production by different technologies, and the associated greenhouse gas (GHG) emissions from both the feedstock supply and the production process. The results show that the uncertainty around the cost of electrolyser systems, the capacity factor, and the gas price are the most critical factors affecting the timing of the transition to renewable H2. We find that hydrogen production will likely be dominated by fossil fuels for the next few decades if the cost of carbon emissions are not accounted for, resulting in cumulative emissions from hydrogen production of 650 Mt CO2-e by 2050. However, implementing a price on carbon emissions can significantly expedite the transition to renewable hydrogen and cut the cumulative emissions significantly.

Reconstruction of a flash flood event using a 2D hydrodynamic model under spatial and temporal variability of storm

In this paper, the catastrophic flash flood event which occurred in the western part of Attica (Greece) in November 2017 is reconstructed. The flood event hit the town of Mandra, causing 24 fatalities and huge damages in the properties and the infrastructure. The flood hydrograph was derived using the two-dimensional hydrodynamic model FLOW-R2D. Attention was drawn on the uncertainties of the model output due to the uncertainty of the estimated parameters such as infiltration, friction and the uncertainty of input data. Due to the computational burden related to the model, a global sensitivity analysis based on Morris method was performed. Then, a Monte Carlo-based uncertainty analysis was performed on the two most influential factors. It was concluded that even the results of the physically based hydrodynamic models are characterised by uncertainties. However, the capability of the hydrodynamic models to describe in detail the dynamics of the overland flow is the main advantage of these models against the conventional hydrological models. It is concluded that the rational use of physically based models for analysing complex storm phenomena with high variable spatial and temporal distribution can lead to a more accurate range of magnitudes of flood peak.

Application of Bayesian nonparametric models to the uncertainty and sensitivity analysis of source term in a BWR severe accident

A full-scope method is constructed to reveal source term uncertainties and to identify influential inputs during a severe accident at a nuclear power plant (NPP). An integrated severe accident code, MELCOR Ver. 1.8.5, is used as a tool to simulate the accident similar to that occurred at Unit 2 of the Fukushima Daiichi NPP. In order to figure out how much radioactive materials are released from the containment to the environment during the accident, Monte Carlo based uncertainty analysis is performed. Generally, in order to evaluate the influence of uncertain inputs on the output, a large number of code runs are required in the global sensitivity analysis. To avoid the laborious computational cost for the global sensitivity analysis via MELCOR, a surrogate stochastic model is built using a Bayesian nonparametric approach, Dirichlet process. Probability distributions derived from uncertainty analysis using MELCOR and the stochastic model show good agreement. The appropriateness of the stochastic model is cross-validated through the comparison with MELCOR results. The importance measure of uncertain input variables are calculated according to their influences on the uncertainty distribution as first-order effect and total effect. The validity of the present methodology is demonstrated through an example with three uncertain input variables.

Uncertainty Analysis of a Coupled Hydrological-plant Growth Model for Grassland under Elevated CO2

The continuous increase in atmospheric carbon dioxide (CO2) contributes to changes in plant evapotranspiration and terrestrial water budgets in two ways. Firstly, elevated CO2 can result in a water saving effect, since increasing CO2 reduces stomatal opening and therefore decreases transpiration. Secondly, CO2 fertilization increases biomass accumulation and leaf area at plant canopy level, likely increasing transpiration1. Vegetation and hydrological models can be used to investigate the CO2 response and the bidirectional effects outlined above, including their relative contribution to the changes in the water cycle. However, the intrinsic plant-soil interaction and the uncertainty related to model parameterization have rarely been considered.Hence, we coupled a detailed plant growth and soil hydrological model by using the generic model frameworks Plant growth Modelling Framework (PMF)2 and Catchment Modelling Framework (CMF)3. Up to date response mechanisms have been implemented in PMF to simulate the various ways of how plant physiology is influenced by elevated CO2. Both models interact by using the Python computer language. Applying the coupled PMF-CMF model we investigate the effects of elevated CO2 in a number of plant physiological and environmental variables such as biomass, leaf area index and soil moisture using field data of a long-term Free Air Carbon Enrichment (FACE) experiment in Giessen, Germany. In this experiment, various grassland varieties (herbs, legumes, grass) grow under elevated (+20%) and ambient CO2 since 1997.A Monte Carlo based uncertainty analysis (GLUE) is conducted to investigate the coupled PMF-CMF parameter space. The focus will be on the identification of parameters for plant and soil, which are the drivers for the CO2 response of the terrestrial water balance. We will present first results of the simulation of biomass accumulation and transpiration under ambient and elevated CO2 concentrations.

Assessing hydrologic prediction uncertainty resulting from soft land cover classification

Summary For predictions in ungauged basins (PUB), environmental data is generally not available and needs to be inferred by indirect means. Existing technologies such as remote sensing are valuable tools for estimating the lacking data, as these technologies become more widely available and have a high areal coverage. However, indirect estimates of the environmental characteristics are prone to uncertainty. Hence, an improved understanding of the quality of the estimates and the development of methods for dealing with their associated uncertainty are essential to evolve towards accurate PUB. In this study, the impact of the uncertainty associated with the classification of land cover based on multi-temporal SPOT imagery, resulting from the use of the Random Forests classifier, on the predictions of the hydrologic model TOPLATS is investigated through a Monte Carlo simulation. The results show that the predictions of evapotranspiration, runoff and baseflow are hardly affected by the classification uncertainty when area-averaged predictions are intended, implying that uncertainty propagation is only advisable in case a spatial distribution of the predictions is relevant for decision making or is coupled to other spatially distributed models. Based on the resulting uncertainty map, guidelines for additional data collection are formulated in order to reduce the uncertainty for future model applications. Because a Monte Carlo-based uncertainty analysis is computationally very demanding, especially when complex models are involved, we developed a fast indicative uncertainty assessment method that allows for generating proxies of the Monte Carlo-based result in terms of the mean prediction and its associated uncertainty based on a single model evaluation. These proxies are shown to perform well and provide a good indication of the impact of classification uncertainty on the prediction result.

Monte-Carlo based uncertainty analysis: Sampling efficiency and sampling convergence

Monte Carlo analysis has become nearly ubiquitous since its introduction, now over 65 years ago. It is an important tool in many assessments of the reliability and robustness of systems, structures or solutions. As the deterministic core simulation can be lengthy, the computational costs of Monte Carlo can be a limiting factor. To reduce that computational expense as much as possible, sampling efficiency and convergence for Monte Carlo are investigated in this paper. The first section shows that non-collapsing space-filling sampling strategies, illustrated here with the maximin and uniform Latin hypercube designs, highly enhance the sampling efficiency, and render a desired level of accuracy of the outcomes attainable with far lesser runs. In the second section it is demonstrated that standard sampling statistics are inapplicable for Latin hypercube strategies. A sample-splitting approach is put forward, which in combination with a replicated Latin hypercube sampling allows assessing the accuracy of Monte Carlo outcomes. The assessment in turn permits halting the Monte Carlo simulation when the desired levels of accuracy are reached. Both measures form fairly noncomplex upgrades of the current state-of-the-art in Monte-Carlo based uncertainty analysis but give a substantial further progress with respect to its applicability.

Probabilistic ecological risk assessment of DDTs in the Bohai Bay based on a food web bioaccumulation model

The fugacity-based food web model was developed to simulate the bioaccumulation of dichloro-diphenyl-trichloroethanes (DDTs) in the aquatic ecosystem in the Bohai Bay. The internal exposure levels (IELs) of DDTs in various organism categories were calculated. Monte Carlo-based uncertainty analysis was performed to get the of IEL distributions of DDTs in organisms. Probabilistic ecological risk assessment (ERA) was performed based on IEL distributions and internal species sensitivity distributions (SSDs). The results show that fugacities and bioaccumulation factors (BAFs) generally increased with increasing trophic level in the food web. Octanol–water partition coefficient (K ow), DDT levels in water and the lipid contents had the greatest influences on IELs in the organism bodies. The ecological risks of DDTs were relatively high. The risk order was p,p′-DDT > p,p′-DDE > p,p′-DDD. At an internal hazard quotient (HQ int) criterion of 1/5, the risk probabilities were 0.10 (0.055–0.17), 0.079 (0.045–0.13) and 0.053 (0.028–0.092) for p,p′-DDT, p,p′-DDE and p,p′-DDD, respectively. The results from ERA based on the internal exposure approximated those based on external exposure. The food web model is a feasible method to predict the extent of bioaccumulation and IELs of hydrophobic organic pollutants in organisms as a step to evaluate their risk posed on aquatic ecosystems.

Evidence for resource homogenization in 50 trophic ecosystem networks

Connectivity patterns of ecological elements are often the core concern of ecologists working at multiple levels of organization (e.g., populations, communities, ecosystems, and landscapes) because these patterns often reflect the forces shaping the system’s development as well as constraining their operation. One reason these patterns of direct connections are critical is that they establish the pathways through which elements influence each other indirectly. Here, we tested a hypothesized consequence of connectivity in ecosystems: the homogenization of resource distributions in flow networks. Specifically, we tested the generality of the systems ecology hypothesis of resource homogenization in 50 empirically derived trophic ecosystem models representing 35 distinct ecosystems. We applied Network Environ Analysis (NEA) to calculate resource homogenization for these models, where homogenization is defined as the ratio of the coefficient of variation of the direct flow intensity matrix ( C V ( G ) ) to the covariance of the integral flow intensity matrix ( C V ( N ) ). A ratio greater than unity indicates the presence of homogenization. We also tested the hypotheses that homogenization increases with system size, connectance, and cycling. We further evaluated the robustness of our results in two ways. First, we verified the close correspondence between the input- and output-oriented homogenization values to ensure that our results were not biased by our decision to focus on the output orientation. Second, we conducted a Monte Carlo based uncertainty analysis to determine the robustness of our results to ± 5 % error introduced into the original flow matrices for each model. Our results show that resource homogenization occurs universally in the 50 ecosystem models tested, with values ranging from 1.04 to 1.97 and a median of 1.61. However, our results do not support the hypothesized relationship between network homogenization and system size and connectance, as the results of the linear regressions are insignificant. Further, there is only weak support for the positive relationship between homogenization and cycling. We confirm that our results are not biased by using the output-oriented homogenization values instead of the input-oriented values because there is a significant linear regression between the two types of homogenization ( r 2 = 0.38 , p < 0.001 ) and the values are well correlated ( S = 8 , 054 , ρ = 0.61 , p < 0.001 ). Finally, we found that our results are robust to ± 5 % error in the flow matrices. The error in the homogenization values was less than the error introduced into the models and ranged from a minimum of 0.24% to a maximum of 1.5% with a median value of 0.58%. The error did not change the qualitative interpretation of the homogenization values. In conclusion, we found strong support for the resource homogenization hypothesis in 50 empirically derived ecosystem models.

A Monte Carlo-based error propagation analysis of Simulated Moving Bed systems

A Monte Carlo-based uncertainty analysis for the performance assessment of a Simulated Moving Bed (SMB) system, which is widely employed in the petrochemical, sugar, and pharmaceutical industries, is presented. The error propagation analysis is carried out to predict the performance of the SMB system for two different binary separations: (a) glucose–fructose separation in a pilot-scale SMB unit and (b) separation of p-xylene from xylene isomers in an industrial-scale SMB unit. Existing SMB models in literature, which utilize a linear isotherm for the glucose–fructose separation [D.C.S. Azevedo, A.E. Rodrigues, Fructose–glucose separation in a SMB pilot unit: modelling, simulation, design and operation, AIChE J. 47 (2001) 2042–2051] and a nonlinear isotherm for the separation of xylene isomers [M. Minceva, A.E. Rodrigues, Modeling and simulation of a simulated moving bed for the separation of p-xylene, Ind. Eng. Chem. Res. 41 (2002) 3454–3461], are employed for the analysis. While the purity and productivity of glucose and fructose are chosen as the performance (or output) variables in the former case study, the purity and recovery of p-xylene are chosen as those in the latter. In both cases, the isotherm parameters, often obtained from chromatography experiments with appreciable levels of uncertainty, are chosen as the process (or input) variables. From the sensitivity analysis, simple models are developed to predict the variations in the performance of the SMB as a function of the isotherm parameters.

Status of Safety and Environmental Activities for Inertial Fusion Energy

ABSTRACTOver the past several years, significant progress has been made in the analysis of safety and environmental (S–E) issues for inertial fusion energy (IFE). Detailed safety assessments have been performed for the baseline power plant concepts, as well as for a conceptual target fabrication facility. Safety analysis results are helping to drive the agenda for experiments. A survey of the S–E characteristics—both radiological and chemical—of candidate target materials has been completed. Accident initiating events have been identified and incorporated into master logic diagrams, which will be essential to the detailed safety analyses that will be needed in the future. Studies of aerosol generation and transport will have important safety implications. A Monte Carlo-based uncertainty analysis procedure has been developed for use in neutron activation calculations. Finally, waste management issues are receiving increased attention and are deserving of further discussion.

Stochastic simulation modelling of southern Great Barrier Reef green turtle population dynamics

A stochastic simulation model was developed for the southern Great Barrier Reef (sGBR) green sea turtle stock to foster better insight into local population dynamics and to assess the risk of harvesting on long-term stock viability. The model was ageclass-structured with time-varying, nonlinear and stochastic demographic processes that were parameterised using recent findings on sex- and ageclass-specific growth and survivorship and female breeding behaviour subject to environmental stochasticity. Monte Carlo based uncertainty analysis was used to estimate population growth given demographic parameters subject to sampling error and environmental stochasticity. Model validity was based on replication of stock reference behaviours with sensitivity evaluated using parameter perturbation and Monte Carlo simulation within a fractional factorial sampling design. Fertility and adult survival were the most important high level parameters affecting population growth, where fertility is a function of fecundity and temporal variability in breeding likelihood. A dynamic stochastic form of the model was then used to evaluate stock viability given various turtle harvesting scenarios. It was found, given model assumptions, that even limited turtle harvesting would result in the sGBR stock being categorised, as vulnerable under IUCN criteria for listing of threatened species. It is apparent that extensive harvesting of either eggs or turtles is probably not a prudent management policy, if the long-term viability of the sGBR green sea turtle stock is the primary conservation objective.

New QCD sum rules for nucleon axial-vector coupling constants

Two new sets of QCD sum rules for the nucleon axial coupling constants are derived using the external-field technique and generalized interpolating fields. An in-depth study of the predicative ability of these sum rules is carried out using a Monte-Carlo based uncertainty analysis. The results show that the standard implementation of the QCD sum rule method has only marginal predicative power for the nucleon axial coupling constants, as the relative errors are large. The errors range from approximately 50 to 100% compared to the nucleon mass obtained from the same method, which has only 10% to 25% error. The origin of the large errors is examined. Previous analyses of these coupling constants are based on sum rules that have poor OPE convergence and large continuum contributions. Preferred sum rules are identified and their predictions are obtained. We also investigate the new sum rules with an alternative treatment of the problematic transitions which are not exponentially suppressed in the standard treatment. The new treatment provides exponential suppression of their contributions relative to the ground state. Implications for other nucleon current matrix elements are also discussed.

QCD Sum Rules for Skeptics

A new Monte-Carlo based uncertainty analysis is introduced to quantitatively determine the predictive ability of QCD sum rules. A comprehensive analysis of ground stateρ-meson and nucleon spectral properties is performed. Many of the findings contradict the conventional wisdom of both practitioners and skeptics alike. Associations between the phenomenological fit parameters are particularly interesting as they reveal how the sum rules resolve the spectral properties. The use of derivative sum rules for the determination ofρ-meson spectral properties is shown to be a very unfavorable approach. Most prior nucleon sum rule analyses are based on a sum rule which is found to be invalid; the results are suspect, and should be reevaluated. The “Ioffe formula,” argued by many to qualitatively encapsulate a description of the nucleon mass in terms of the chiral symmetry breaking order parameter ⦠qq⦔ is misleading at best. QCD sum rules are found to be self-consistent without contributions from direct instantons. This implies that instanton effects are adequately accounted for in the nonperturbative vacuum condensates. This in-depth examination of QCD sum rule self consistency paints a favorable picture for further quantitative refinements of the QCD sum rule approach.