Combining Stochastic Optimization and Monte Carlo Simulation to Deal with Uncertainties in Climate Policy Assessment

In this paper, we explore the impact of several sources of uncertainties on the assessment of energy and climate policies when one uses in a harmonized way stochastic programming in a large-scale bottom-up (BU) model and Monte Carlo simulation in a large-scale top-down (TD) model. The BU model we use is the TIMES Integrated Assessment Model, which is run in a stochastic programming version to provide a hedging emission policy to cope with the uncertainty characterizing climate sensitivity. The TD model we use is the computable general equilibrium model GEMINI-E3. Through Monte Carlo simulations of randomly generated uncertain parameter values, one provides a stochastic micro- and macro-economic analysis. Through statistical analysis of the simulation results, we analyse the impact of the uncertainties on the policy assessment.     

Correlated Parameters Uncertainty Propagation in a Rainfall-Runoff Model,Considering 2-Copula; Case Study: Karoon III River Basin

Hydrological models are widely used to investigate practical issues of water resources. Parametric uncertainty is considered as one of the most important sources of uncertainty in environmental researches. Generally, it is assumed that the parameters are independent mutually, but correlation within the parameter space is an important factor having the potential to cause uncertainty. The objective and innovation of this study was to address the effects of parameters correlation on a continuous hydrological model uncertainty. HEC-HMS with soil moisture accounting (SMA) infiltration method was used to model daily flows and simulate certainty bounds for Karoon III basin, southwest of IRAN, in two scenarios, independent and correlated parameters using 2-copula. The parameters were represented by probability distributions, and the effect on prediction error were evaluated using Latin hypercube sampling (LHS) on Monte Carlo simulation (MCS). Saturated hydraulic conductivity (K), Clark storage-coefficient (R), and time of concentration (tc) were chosen for investigation, based on observed sensitivity analysis of simulated peak over threshold (POT). One hundred runs were randomly generated from 100 parameter sets captured from LHS of parameters distributions in each sub-basin. Using generated parameter sets, 100 continuous hydrographs were simulated and values of certainty bounds calculated. Results showed that when 2-copula correlated R and tc, with 0.656 Kendall’s Tau and 0.818 Spearman’s Rho coefficients, were propagated, decreasing of outputs’ sharpness was more than when considering K and R (K-R), with 0.166 and 0.262; therefore, incorporation of correlations in the MCS is important, especially when the correlation coefficients exceed 0.65. The model was evaluated at the outlet of the basin using daily stream flow data. Model reliability was better for above-normal flows than normal and below-normal. Reliability increases of simulated flow when considering correlated R-tc was more than K-R because of the correlation values. Incorporation of copula for K-tc not only did not improve the model reliability but also decreased it. Results showed improvement of model reliability, by decreasing predicted error of hydrologic modeling, when dealing with correlated parameters in the system.     

Pollution risk assessment based on QUAL2E-UNCAS simulations of a tropical river in Northern India

This paper exemplifies the application of U.S. Environmental Protection Agency's water quality model, QUAL2E-UNCAS in assessing the pollution risk of a tropical river. The rivers selected for study were Hindon (main river) and Kali (its tributary) flowing through Uttar Pradesh district of Northern India. The model application to the two rivers revealed poor water quality in terms of dissolved oxygen (DO), biochemical oxygen demand (BOD), and ammonia concentrations. Monte Carlo simulations were performed on two different data sets that were confirming to marked seasonal variations. The Monte Carlo simulation (MCS) derived 95 % confidence level for these parameters strengthened the fact that all point sources were exploiting the assimilative capacity of the two rivers. In order to ascertain probabilistically the risk at which two rivers were falling short of desired water quality, probability curves based on effluent standards and available water quality were prepared. On mapping the two curves, it was found that at 95 % probability, Hindon River was flowing with 53 to 100 % less of desired DO, up to 100 % more of minimum BOD, and probability with which ammonia concentration would not be more than the desired concentration was found to fall downstream. The Kali headwaters showed better quality during low river temperature but worsened downstream with up to 100 % violation in all the above observed parameters. It is expected that similar studies wherein the dependable levels with which a polluted river can be understood to fall short of desired water quality can prove to be useful in ascertaining the efficacy of effluent standards and/or follow-up of pollution control measures.     

Inexact Fuzzy-Stochastic Programming for Water Resources Management Under Multiple Uncertainties

In this study, an interval-parameter fuzzy-stochastic two-stage programming (IFSTP) approach is developed for irrigation planning within an agriculture system under multiple uncertainties. A concept of the distribution with fuzzy-interval probability (DFIP) is defined to address multiple uncertainties expressed as integration of intervals, fuzzy sets, and probability distributions. IFSTP integrates the interval programming, two-stage stochastic programming, and fuzzy-stochastic programming within a general optimization framework. IFSTP incorporates the pre-regulated water resources management policies directly into its optimization process to analyze various policy scenarios; each scenario has different economic penalty when the promised amounts are not delivered. IFSTP is applied to an irrigation planning in a water resources management system. Solutions from IFSTP provide desired water allocation patterns, which maximize both the system’s benefits and feasibility. The results indicate that reasonable solutions are generated for objective function values and decision variables; thus, a number of decision alternatives can be generated under different levels of stream flows.     

Seasonal changes in the concentrations of nitrogen and phosphorus in farmland drainage and groundwater of the Taihu Lake region of China

Monte Carlo simulations were performed using the GEANT4 code for the investigation of γ-ray absorption in water in different spherical geometries and of the efficiency of a NaI(Tl) detector for different radionuclides in the aquatic environment. In order to test the reliability of these simulations, experimental values of the NaI(Tl) detector efficiency were deduced and seem to be in good agreement with the simulated ones. In addition, using the simulated efficiency, an algorithm was developed to determine the minimum detectable activity in becquerels per cubic meter in situ as a function of energy for typical freshwater and seawater spectra.     

Assessment of groundwater quality: a fusion of geochemical and geophysical information via Bayesian neural networks

Deplorable quality of groundwater arising from saltwater intrusion, natural leaching and anthropogenic activities is one of the major concerns for the society. Assessment of groundwater quality is, therefore, a primary objective of scientific research. Here, we propose an artificial neural network-based method set in a Bayesian neural network (BNN) framework and employ it to assess groundwater quality. The approach is based on analyzing 36 water samples and inverting up to 85 Schlumberger vertical electrical sounding data. We constructed a priori model by suitably parameterizing geochemical and geophysical data collected from the western part of India. The posterior model (post-inversion) was estimated using the BNN learning procedure and global hybrid Monte Carlo/Markov Chain Monte Carlo optimization scheme. By suitable parameterization of geochemical and geophysical parameters, we simulated 1,500 training samples, out of which 50 % samples were used for training and remaining 50 % were used for validation and testing. We show that the trained model is able to classify validation and test samples with 85 % and 80 % accuracy respectively. Based on cross-correlation analysis and Gibb’s diagram of geochemical attributes, the groundwater qualities of the study area were classified into following three categories: “Very good”, “Good”, and “Unsuitable”. The BNN model-based results suggest that groundwater quality falls mostly in the range of “Good” to “Very good” except for some places near the Arabian Sea. The new modeling results powered by uncertainty and statistical analyses would provide useful constrain, which could be utilized in monitoring and assessment of the groundwater quality.     

Severe Wind Hazard Assessment using Monte Carlo Simulation

A Monte Carlo-based model to assess severe wind hazard is presented. Synthetic wind datasets for hazard analysis have been generated using Monte Carlo simulation of the physics of severe wind gust generation, to overcome the limitations of data-based statistical models. These statistical models consider extreme wind gust speeds to calculate the average probability of exceedance of a given wind speed in a single year (return period), and hence the return period is calculated using extreme value distributions. Monte Carlo wind hazard results are shown to be comparable to those produced by data-based statistical methods. They are similar to the results reported by Holmes (Australian Journal of Structural Engineering 4(1):29–40, 2002) and also to the prescribed wind gust speeds of the Australian/NZ standards for wind loading of structures in Region A (non-cyclonic regions) of Australia (AS/NZS 1170.2 2002).     

The use of sensory perception indicators for improving the characterization and modelling of total petroleum hydrocarbon (TPH) grade in soils

This paper proposes a multistep approach for creating a 3D stochastic model of total petroleum hydrocarbon (TPH) grade in potentially polluted soils of a deactivated oil storage site by using chemical analysis results as primary or hard data and classes of sensory perception variables as secondary or soft data. First, the statistical relationship between the sensory perception variables (e.g. colour, odour and oil–water reaction) and TPH grade is analysed, after which the sensory perception variable exhibiting the highest correlation is selected (oil–water reaction in this case study). The probabilities of cells belonging to classes of oil–water reaction are then estimated for the entire soil volume using indicator kriging. Next, local histograms of TPH grade for each grid cell are computed, combining the probabilities of belonging to a specific sensory perception indicator class and conditional to the simulated values of TPH grade. Finally, simulated images of TPH grade are generated by using the P-field simulation algorithm, utilising the local histograms of TPH grade for each grid cell. The set of simulated TPH values allows several calculations to be performed, such as average values, local uncertainties and the probability of the TPH grade of the soil exceeding a specific threshold value.     

Investments in Power Generation Under Uncertainty—a MIP Specification and Large-Scale Application for EU

Investments in power generation constitute a typical budget allocation problem in the context of multiple objectives, while all factors influencing investor’s decisions for power plants are subject to considerable uncertainties. The paper introduces a multi-objective stochastic model designed to optimize budget allocation decisions for power generation in the context of risk aversion taking into account several sources of uncertainty, especially with regard to volatility of fossil fuel and electricity prices, technological costs, and climate policy variability. Probability distributions for uncertain factors influencing investment decisions are directly derived from the stochastic global energy model PROMETHEUS and thus they take into account complex interactions between variables in the systemic context. In order to fully incorporate stochastic characteristics of the problem, the model is specified as an optimization problem in which the probability that an objective exceeds a given threshold is maximized (risk aversion) subject to a set of deterministic and probabilistic constraints. The model is formulated as a mixed integer program providing complete flexibility on the joint distributions of rates of return of technologies competing for investments, as it can handle non-symmetric distributions and take automatically into account complex covariance patterns as emerging from comprehensive PROMETHEUS stochastic results. The analysis shows that risk is a crucial factor for power generation investments with investors not opting for technologies subject to uncertainty related to climate policies and fossil fuel prices. On the other hand, combination of options with negative covariance tends to benefit in the context of risk-hedging behavior.     

Using an Allowance Reserve to Manage Uncertain Costs in a Cap-and-Trade Program for Greenhouse Gases

This paper investigates the design and performance of an allowance reserve in the context of a cap-and-trade program for greenhouse gases. We use a Monte Carlo approach in which the parameters of the marginal abatement cost function, and the supply of offsets, are drawn from specified distributions. Our framework focuses on the potential impact of “medium-run shocks” to abatement cost and offset supply, as opposed to either short-run volatility or permanent shifts in the cost curve. Our model suggests that under reasonable (and even fairly conservative) assumptions about abatement cost and offset supply, an allowance reserve broadly similar to recent proposals for US climate legislation can be effective in containing allowance prices. In our core policy scenario, with a trigger price equal to US $32 in 2015, we estimate that the probability of drawing on the allowance reserve is <25% and the probability of requiring more than 7?GT of reserve tons over 20?years is <5%. We also use the model to explore the trade-off among three features of the reserve that are most relevant to policy makers: the total size of the reserve, the trigger price, and the degree of confidence that the reserve will be large enough to limit allowance prices to the target level. Our essential result is that a lower trigger price, or a higher degree of confidence, requires a larger reserve.     

Factor analysis of trace-element data from tree-bark samples in The Netherlands

Monte Carlo-assisted factor analysis has been applied to a data set of 20 trace-element concentrations in tree-bark samples obtained from 123 locations in The Netherlands, with the aim to investigate the suitability of bark as a biomonitor for air pollution. A Monte Carlo approach was used to give more insight to the uncertainties and significance levels of the factor analysis results. Notwith-standing a rather strong influence of soil material on the concentration levels, factor analysis enabled the identification of five significant pollution source types, all of which corresponded with source types found in an earlier biomonitoring study in The Netherlands using epiphytic lichens. A more detailed comparison with the lichen results showed a remarkable difference in lead concentrations between bark and lichen. It was concluded that bark can be successfully employed as a biomonitor for air pollution. The power of factor analysis to adequately determine the soil contribution may render extensive sample washing procedures superfluous.     

Analysis of the Threshold and Expected Coverage Approaches to the Probabilistic Reserve Site Selection Problem

Two approaches to formulating the reserve site selection problem when species occurrence data is probabilistic were solved for terrestrial vertebrates in a small set of potential reserve sites in Oregon. The expected coverage approach, which maximizes the sum of the occurrence probabilities, yielded solutions that covered more species on average in Monte Carlo simulations than the threshold approach, which maximizes the number of species for which the occurrence probability exceeds some threshold.     

Water and waste load allocation in rivers with emphasis on agricultural return flows: application of fractional factorial analysis

In this paper, a new methodology is developed to handle parameter and input uncertainties in water and waste load allocation (WWLA) in rivers by using factorial interval optimization and the Soil, Water, Atmosphere, and Plant (SWAP) simulation model. A fractional factorial analysis is utilized to provide detailed effects of uncertain parameters and their interaction on the optimization model outputs. The number of required optimizations in a fractional factorial analysis can be much less than a complete sensitivity analysis. The most important uncertain inputs and parameters can be also selected using a fractional factorial analysis. The uncertainty of the selected inputs and parameters should be incorporated real time water and waste load allocation. The proposed methodology utilizes the SWAP simulation model to estimate the quantity and quality of each agricultural return flow based on the allocated water quantity and quality. In order to control the pollution loads of agricultural dischargers, it is assumed that a part of their return flows can be diverted to evaporation ponds. Results of applying the methodology to the Dez River system in the southwestern part of Iran show its effectiveness and applicability for simultaneous water and waste load allocation in rivers. It is shown that in our case study, the number of required optimizations in the fractional factorial analysis can be reduced from 64 to 16. Analysis of the interactive effects of uncertainties indicates that in a low flow condition, the upstream water quality would have a significant effect on the total benefit of the system.     

An Application of the Pump-to-Fill Policy for Management of Urban Stormwater

We consider the management of urban stormwater in two connected dams. Stormwater generated by local rainfall flows into a capture dam and is subsequently pumped into a similar sized holding dam. We assume random gross inflow and constant demand. If we wish to minimise overflow from the system then the optimal management policy is to pump as much water as possible each day from the capture dam to the holding dam without allowing the holding dam to overflow. We shall refer to this policy as the pump-to-fill policy. The model is based on the Parafield stormwater management system in the City of Salisbury (CoS) but assumes constant demand instead of level dependent outflow. If there is insufficient water in the holding dam to meet the desired daily demand then all water in the holding dam is used and the shortfall is obtained from other sources. CoS, in suburban Adelaide in South Australia, is recognised in local government circles as a world leader in urban stormwater management. The water is supplied to local industry to replace regular mains water and is also used to restore and maintain urban wetlands. In mathematical terms the pump-to-fill policy defines a Markov chain with a large transition matrix and a characteristic regular block structure. We use specialised Matrix Analytic Methods to decompose the event space and find simplified equations for the steady state probability vector. In this way we enable an elementary solution procedure which we illustrate by solving the modified Parafield problem. The optimal nature of the pump-to-fill policy is established in a recent paper by Pearce et al. (JIMO 3(2):313–320, 2007). The purpose of the current study is to find optimal management policies for urban stormwater systems. Work supported by the Australian Research Council.     

Climatic Implications of Revised IPCC Emissions Scenarios, the Kyoto Protocol and Quantification of Uncertainties

In December 1997, the United Nations Framework Convention on Climate Change (FCCC) adopted the Kyoto Protocol. This paper describes a framework that models the climatic implications of this international agreement, using Monte Carlo simulations and the preliminary Intergovernmental Panel on Climate Change emissions scenarios (SRES). Emissions scenarios (including intervention scenarios), climate sensitivity, and terrestrial carbon sink are the key sampled model parameters. This framework gives prior probability distributions to these parameters and, using a simple climate model, posterior distributions of global temperature change are determined for the future. Our exercise showed that the Kyoto Protocol's effectiveness will be mostly dependent upon which SRES world evolves. In some worlds the Protocol decreases the warming considerably but in others it is almost irrelevant. We exemplified this approach with a current FCCC issue, namely “hot air”. This modelling framework provides a probabilistic assessment of climate policies, which can be useful for decision-makers involved in global climate change management. This revised version was published online in July 2006 with corrections to the Cover Date.     

Probability of misclassifying biological elements in surface waters

Measurement uncertainties are inherent to assessment of biological indices of water bodies. The effect of these uncertainties on the probability of misclassification of ecological status is the subject of this paper. Four Monte-Carlo (M-C) models were applied to simulate the occurrence of random errors in the measurements of metrics corresponding to four biological elements of surface waters: macrophytes, phytoplankton, phytobenthos, and benthic macroinvertebrates. Long series of error-prone measurement values of these metrics, generated by M-C models, were used to identify cases in which values of any of the four biological indices lay outside of the “true” water body class, i.e., outside the class assigned from the actual physical measurements. Fraction of such cases in the M-C generated series was used to estimate the probability of misclassification. The method is particularly useful for estimating the probability of misclassification of the ecological status of surface water bodies in the case of short sequences of measurements of biological indices. The results of the Monte-Carlo simulations show a relatively high sensitivity of this probability to measurement errors of the river macrophyte index (MIR) and high robustness to measurement errors of the benthic macroinvertebrate index (MMI). The proposed method of using Monte-Carlo models to estimate the probability of misclassification has significant potential for assessing the uncertainty of water body status reported to the EC by the EU member countries according to WFD. The method can be readily applied also in risk assessment of water management decisions before adopting the status dependent corrective actions.     

Interval-Parameter Conditional Value-at-Risk Two-Stage Stochastic Programming Model for Management of End-of-Life Vehicles

The management of end-of-life vehicles conserves natural resources, provides economic benefits, and reduces water, air, and soil pollution. Sound management of end-of-life vehicles is vitally important worldwide thus requiring sophisticated decision-making tools for optimizing its efficiency and reducing system risk. This paper proposes an interval-parameter conditional value-at-risk two-stage stochastic programming model for management of end-of-life vehicles. A case study is conducted in order to demonstrate the usefulness of the developed model. The model is able to provide the trade-offs between the expected profit and system risk. It can effectively control risk at extremely disadvantageous availability levels of end-of-life vehicles. The formulated model can produce optimal solutions under predetermined decision-making risk preferences and confidence levels. It can simultaneously determine the optimal long-term allocation targets of end-of-life vehicles and reusable parts as well as capital investment, production planning, and logistics management decisions within a multi-period planning horizon. The proposed model can efficiently handle uncertainties expressed as interval values and probability distributions. It is able to provide valuable insights into the effects of uncertainties. Compared to the available models, the resulting solutions are far more robust.

     

Representing uncertainty in climate change scenarios: a Monte-Carlo approach

Climate change impact assessment is subject to a range of uncertainties due to both incomplete and unknowable knowledge. This paper presents an approach to quantifying some of these uncertainties within a probabilistic framework. A hierarchical impact model is developed that addresses uncertainty about future greenhouse gas emissions, the climate sensitivity, and limitations and unpredictability in general circulation models. The hierarchical model is used in Bayesian Monte-Carlo simulations to define posterior probability distributions for changes in seasonal-mean temperature and precipitation over the United Kingdom that are conditional on prior distributions for the model parameters. The application of this approach to an impact model is demonstrated using a hydrological example. This revised version was published online in July 2006 with corrections to the Cover Date.     

An Integrated Multicriteria Decision Analysis System for Reducing Air Emissions from Mining Process

The selection of a best alternative method to minimize air pollution and energy consumption for mine sites is a critical task because it encompasses evaluation of different techniques. The aim of this paper is to select most suitable technology for mining system which helps in reducing air pollution and carbon footprints by implementing the multicriteria decision analysis (MCDA) method. The existing methods or frameworks in the mining sector, which have been used in the past to select the sustainable solution, are lacking aid of MCDA, and there is a need to contribute more in this field with a promising decision system. The MCDA method is applied as a probabilistic integrated approach for a mine site in Canada. The analysis involves processing inputs to the Preference Ranking Organization Method for Enrichment Evaluation (PROMETHEE) method which assists in identifying the alternatives, defining the criteria, and thus outranking of the final choice. Moreover, criteria weighting has been determined using analytical hierarchical process (AHP) method. Three categories: reduction of dust/fugitive emission control strategies, reduction in fuel consumption to minimize carbon footprint, and cyanide destruction methods are selected. The probability distributions of criteria weights and output flows are defined by performing uncertainty analysis using the Monte Carlo simulation (MCS). The sensitivity analysis is conducted using Spearman’s rank correlation method and walking criteria weights. The results indicate that the integrated framework provides a reliable way of selecting air pollution control solutions and help in quantifying the impact of different criteria for the selected alternatives.

     

RCRA ground-water monitoring decision procedures viewed as quality control schemes

The problems of developing and comparing statistical procedures appropriate to the monitoring of ground water at hazardous waste sites are discussed. It is suggested that these decision procedures should be viewed as quality control schemes and compared in the same way that industrial quality control schemes are compared. The results of a Monte Carlo simulation study of run-length distribution of a combined Shewhart-CUSUM quality control scheme are reported.