First-order Uncertainty Research Articles

Sensitivity Analysis and Data Assimilation in a Subcritical Plutonium Metal Benchmark

This work presents the application of first-order adjoint sensitivity analysis, uncertainty quantification, and data assimilation to a subcritical plutonium benchmark experiment using a modified version of the discrete ordinates radiation transport code Denovo. Previous Monte Carlo simulations of this benchmark saw a consistent overprediction of the mean and variance of the measured neutron multiplicity distribution. It was observed that a small scalar reduction in the value of the 239Pu-induced fission neutron multiplicity was capable of significantly reducing the discrepancies. This work extends those results by computing first-order sensitivities to each nuclide, reaction type, energy, and material region in the benchmark. The sensitivities are then used in a data assimilation methodology to simultaneously calibrate all responses and multigroup nuclear data. The resulting best-estimate values for the energy group differential multiplicity ν̄(Eg) are 1σ to 2σ less than the nominal values found in ENDF/B-VII for energies less than ˜1.5 MeV.

Effectiveness of subsurface pressure monitoring for brine leakage detection in an uncertain CO2 sequestration system

This work evaluates the detection sensitivity of deep subsurface pressure monitoring within an uncertain carbon dioxide sequestration system by linking the output of an analytical reduced-order model and first-order uncertainty analysis. A baseline (non-leaky) modeling run was compared against 10 different leakage scenarios, where the cap rock permeability was increased by factors of 2–100 (cap rock permeability from 10−3 to 10−1 millidarcy). The uncertainty variance outputs were used to develop percentile estimates and detection sensitivity for pressure throughout the deep subsurface as a function of space (lateral distance from the injection wells and vertical orientation within the reservoir) and time (years since injection), or P(x, z, t). Conditional probabilities were computed for combinations of x, z, and t, which were then used to generate power curves for detecting leakage scenarios. The results suggest that measurements of the absolute change in pressure within the target injection aquifer would not be able to distinguish small leakage rates (i.e., less than 50 × baseline) from baseline conditions, and that only large leakage rates (i.e., >100 × baseline) would be discriminated with sufficient statistical power (>99 %). Combining measurements, for example by taking the ratio of formation pressure in Aquifer 2/Aquifer 1, provides better statistical power for distinguishing smaller leakage rates at earlier times in the injection program. Detection sensitivity for pressure is a function of space and time. Therefore, design of an adequate monitoring network for subsurface pressure should account for this space–time variability to ensure that the monitoring system performs to the necessary design criteria, e.g., specific false-negative and false-positive rates.

Probabilistic multi-objective optimal design of composite channels using particle swarm optimization

To achieve cost effectiveness and reliability in design, this paper presents a probabilistic multi-objective model for optimal design of composite channels that have a cross-sectional shape of horizontal bottom and parabolic sides. The multiple objectives of channel design include minimizing the cost of channel construction, maximizing the probability of the expected channel capacity being greater than the design flow and minimizing the overtopping probability. In this study, the principles of first-order uncertainty analysis are adopted for handling uncertainty in parameters of the problem. The optimization model is solved using the particle swarm optimization method and Pareto-optimal solutions are generated for various combinations of overtopping probability and exceedance probability of channel capacity. The results show that the presented approach has good potential for exploring different alternative designs of open channels under input parameter uncertainty.

Impact of second-order uncertainty on the efficiency of the 0.5-double auction

This paper studies the impact of second-order uncertainty on the (ex-post) efficiency of the 0.5-double auction. We consider a discrete double auction model in which the seller’s valuation is either v¯s or v¯s and the buyer’s valuation is either v¯b or v¯b with 0=v¯s<v¯b<v¯s<v¯b=1. The buyer’s valuation and the seller’s valuation are private information. We further assume that the buyer’s belief about the seller’s valuation is also private information (i.e., there is second-order uncertainty). We show that if v¯b−v¯s and v¯b−v¯s are sufficiently small, then the efficiency of the 0.5-double auction model with second-order uncertainty is higher than the efficiency of the 0.5-double auction model with first-order uncertainty. Our result thus serves as an example in which the introduction of higher-order uncertainty results in reducing, instead of increasing, the inefficiency of a bargaining model.

A Study on the Effects of Sensitive Parameters Errors on Digital Soil Erosion Simulation

2 Abstract: A combined runoff-sediment model is used to simulated soil erosion processes and predict soil loss of land surface. The Stanford Watershed Model (SWM) is used as runoff generator for this model. Effects of sensitive parameters errors on soil erosion characteristics are investigated. These characteristics include peak erosion and mean monthly erosion rates. Three different methods are used for the analysis, namely; first-order uncertainty analysis method; direct investigation technique and mean-maximum likelihood method. The aim is to quantify sensitive parameters errors propagation and to gain an appreciation of the approximate magnitudes of model output uncertainty caused by different levels of sensitive parameters uncertainty. Model output uncertainty ranges between (4.000-83.115)% for mean monthly erosion against (4.680-83.098)% for peak erosion. Uncertainty in simulated erosion due to sensitive parameters uncertainty is subsequently analyzed. The probability of peak erosion values occurrence due to sensitive parameters error are investigation. Based on the result obtain, high and moderately parameters are identified. Appropriate conclusion are drawn and suggestion for future work are introduced.

Habit Persistence, Currency Competition and Sunspot Equilibria

This paper cites the concept of consumption habit persistence and sunspot equilibria with uncertainty for analyzing the issue of currency competition to discuss the necessity of Gresham's Law and provide a complement of explanation to the euro exchange rate movements. We study the economy in one-good, two-currency Brock model with perfect currency substitution in discrete time. With habit persistence, we show that the optimal holding of currency asset is affected by the elasticity of intertemporal substitution. Besides, the higher-growth-rate currency does not always dominate the other currency in the long run. The Gresham-law result obtained in the deterministic model could not be true in a stationary sunspot equilibrium with a first-order Markov extrinsic uncertainty process. The existence of sunspot equilibria expresses another situation of currency competition depending on the possibility of people's expectations and supports complementally the investor-emotion view of the empirical studies in the currency-asset holding and the euro exchange rate movements.

Modelling Approaches

Schizophrenia is a chronic disease characterized by periods of relative stability interrupted by acute episodes (or relapses). The course of the disease may vary considerably between patients. Patient histories show considerable inter- and even intra-individual variability. We provide a critical assessment of the advantages and disadvantages of three modelling techniques that have been used in schizophrenia: decision trees, (cohort and micro-simulation) Markov models and discrete event simulation models. These modelling techniques are compared in terms of building time, data requirements, medico-scientific experience, simulation time, clinical representation, and their ability to deal with patient heterogeneity, the timing of events, prior events, patient interaction, interaction between co-variates and variability (first-order uncertainty). We note that, depending on the research question, the optimal modelling approach should be selected based on the expected differences between the comparators, the number of co-variates, the number of patient subgroups, the interactions between co-variates, and simulation time. Finally, it is argued that in case micro-simulation is required for the cost-effectiveness analysis of schizophrenia treatments, a discrete event simulation model is best suited to accurately capture all of the relevant interdependencies in this chronic, highly heterogeneous disease with limited long-term follow-up data.

A screening tool for vulnerability assessment of pesticide leaching to groundwater for the islands of Hawaii, USA

This paper describes an updated version of a screening tool for groundwater vulnerability assessment to evaluate pesticide leaching to groundwater, based on a revised version of the attenuation factor. The tool has been implemented in a geographical information system (GIS) covering the major islands of the state of Hawaii, USA. The Hawaii Department of Agriculture currently uses the tool in their pesticide evaluation process as a first-tier screening tool. The basic soil properties and pesticide properties necessary to compute the index, and estimates of their uncertainty, are included in the GIS. Uncertainties in soil and pesticide properties are accounted for using first-order uncertainty analysis. Classifications of pesticides as 'likely', 'uncertain' or 'unlikely' to leach are made on the basis of the uncertainty and a comparison of the revised attenuation factor with values and uncertainties of two reference chemicals. The reference chemicals represent what are considered to be a 'leachable' and a 'non-leachable' pesticide under Hawaii conditions. It is concluded that the tool is suitable for screening new and already used pesticides for the islands of Hawaii. However, the tool is associated with uncertainties that are not accounted for, so a conservative approach with respect to interpretation of the results and selection of pesticide parameters used in the tool is recommended.

Identifying the Potential Loss of Monitoring Wells Using an Uncertainty Analysis

From the mid-1940s through the 1980s, large volumes of waste water were discharged at the Hanford Site in southeastern Washington State, causing a large-scale rise (>20 m) in the water table. When waste water discharges ceased in 1988, ground water mounds began to dissipate. This caused a large number of wells to go dry and has made it difficult to monitor contaminant plume migration. To identify monitoring wells that will need replacement, a methodology has been developed using a first-order uncertainty analysis with UCODE, a nonlinear parameter estimation code. Using a three-dimensional, finite-element ground water flow code, key parameters were identified by calibrating to historical hydraulic head data. Results from the calibration period were then used to check model predictions by comparing monitoring wells' wet/dry status with field data. This status was analyzed using a methodology that incorporated the 0.3 cumulative probability derived from the confidence and prediction intervals. For comparison, a nonphysically based trend model was also used as a predictor of wells' wet/dry status. Although the numerical model outperformed the trend model, for both models, the central value of the intervals was a better predictor of a wet well status. The prediction interval, however, was more successful at identifying dry wells. Predictions made through the year 2048 indicated that 46% of the wells in the monitoring well network are likely to go dry in areas near the river and where the ground water mound is dissipating.

A behavioural model for vague probability assessments

I present an hierarchical uncertainty model that is able to represent vague probability assessments, and to make inferences based on them. This model can be given an interpretation in terms of the behaviour of a modeller in the face of uncertainty, and is based on Walley's theory of imprecise probabilities. It is formally closely related to Zadeh's fuzzy probabilities, but it has a different interpretation, and a different calculus. Through rationality (coherence) arguments, the hierarchical model is shown to lead to an imprecise first-order uncertainty model that can be used in decision making, and as a prior in statistical reasoning.

Stochastic integration of seismic data and geologic scenarios: A West Africa submarine channel saga

Providing quantitative statements about the risk associated with reservoir exploration and production has become increasingly important in modern-day reservoir management. At the exploration or early production stage, with limited well-log and production data in hand, the first-order uncertainty is often dominated by the quality of the seismic data and the accuracy of conceptual geologic models showing facies geometry and connectivity. Seismic may provide quality information on reservoir geometry and large-scale trends of facies such as net-to-gross variations. As a complement to seismic, detailed geologic interpretations of facies association and geometry may provide heterogeneity information at all scales of the reservoir, including the fine-scale lacking in the seismic. However, geologic interpretations may result in competing geologic scenarios. The variability associated with multiple geologic interpretations may result in competing geologic scenarios. The variability associated with multiple geologi...

Uncertainty in Water Surface Profile of Buried Stream Flowing under Coarse Material

Non-Darcy flow occurs when a hydraulic gradient is set up across a matrix of coarse porous media, resulting in turbulence in the void spaces. Buried streams that are formed at open-pit coal mines in mountainous areas (due to the disposal of large quantities of waste rock in valley terrain) are good examples of this phenomenon. An overview of the sources of uncertainty associated with non-Darcy water surface profile computations is presented. Numerical and experimental examples are used to illustrate how the mathematical developments presented in this paper can be used to quantify some of the inherent uncertainties. A model buried stream built as part of this study was used to test these mathematical developments. The performance of an equation for optimizing cross-section spacing is described. Uncertainty equations developed using first-order uncertainty analysis are applied to a rectangular stream. A procedure for quantifying the probable error in the computed depth of flow is illustrated herein by applying a simplified form of the total uncertainty equation to a model buried stream. Based on these results, guidance is provided for the uncertainty analysis of water surface profiles for field-scale buried streams.

Comparison of first-order analysis and fuzzy set approach for the evaluation of imprecision in a pesticide groundwater pollution screening model

The results of a screening model are always approximate, lying within an imprecision range. This paper focuses first on various types of imprecision in such modelling results, introduced either by subjective or state-of-the-art estimates of coefficients or through measurement error, and second on the different types of methods able to take into account imprecision in the input parameters in order to evaluate imprecision in the simulation results. Emphasis is placed on the evaluation of imprecision in potential groundwater contamination by pesticides using the Attenuation Factor (AF) index, the Retardation Factor (RF) index and two different methods of uncertainty analysis: the classical first-order uncertainty analysis and a method based on the fuzzy set approach as an illustration of the basic ideas. The results of this comparison show that the fuzzy set approach is more suitable for evaluating imprecision in screening models than the classical technique. Furthermore, it furnishes a mean value imprecision range and adds a degree of confidence to this range.

An assessment of agrochemical leaching potentials for Tenerife

This paper reports an index-based regional-scale characterization of non-point source groundwater contamination potential for the agricultural areas on the Canary Island of Tenerife. The relative leaching potential for 24 pesticides was quantitatively assessed and ranked using the Leaching index (Li) for the soil, landcover, and recharge conditions in Tenerife. The uncertainty in the Li estimates, due to uncertainties in the soil, recharge, and chemical data, were accounted for using first-order uncertainty analysis. Several of the pesticides considered in this study were assessed to be potential leachers. The soil insecticide Carbofuran (2,3-dihydro-2,2-dimethyl-7-benzofuranyl- n-methylcarbamate) was found to have the greatest leaching potential for the soil, landcover, and recharge conditions across Tenerife.

Second-Order Uncertainty in Accounting Information and Bilateral Bargaining Costs

Bargaining costs have been identified as a key determinant of the organization of economic activity, and accounting information plays a significant role in contracts created through bargaining. Properties of accounting information systems can increase or decrease the uncertainty associated with accounting-based payoffs; we show in a bilateral bargaining setting that increased uncertainty leads to increased delays in reaching agreement and increased premiums for the party bearing the uncertainty. We examine two types of uncertainty: first-order (uncertainty about outcomes) and second-order (uncertainty about the probability distributions of outcomes). At a moderately high level of first-order uncertainty, we find that an accounting information system that lowers second-order uncertainty halves the time bargainers need to reach agreement and decreases the premium paid to the bargainer bearing increased risk by 43 percent. The fact that bargaining efficiency gains can arise from accounting systems that reduce second-order uncertainty can help explain the choices firms make in designing and operating their accounting information systems.

Uncertainty analysis of groundwater flow with DRBEM

The reliability of groundwater flow numerical simulation is affected by the quality of input data of aquifer physical parameters. This paper presents an uncertainty analysis based on a first order approximation of covariances. A two-dimensional steady state groundwater flow problem is carried out by coupling the first-order uncertainty analysis with dual reciprocity boundary element method.

Uncertainty in recharge estimation: impact on groundwater vulnerability assessments for the Pearl Harbor Basin, O'ahu, Hawai'i, U.S.A.

In this paper, uncertainty in recharge estimates is investigated relative to its impact on assessments of groundwater contamination vulnerability using a relatively simple pesticide mobility index, attenuation factor (AF). We employ a combination of first-order uncertainty analysis (FOUA) and sensitivity analysis to investigate recharge uncertainties for agricultural land on the island of O'ahu, Hawai'i, that is currently, or has been in the past, under sugarcane or pineapple cultivation. Uncertainty in recharge due to recharge component uncertainties is 49% of the mean for sugarcane and 58% of the mean for pineapple. The components contributing the largest amounts of uncertainty to the recharge estimate are irrigation in the case of sugarcane and precipitation in the case of pineapple. For a suite of pesticides formerly or currently used in the region, the contribution to AF uncertainty of recharge uncertainty was compared with the contributions of other AF components: retardation factor (RF), a measure of the effects of sorption; soil-water content at field capacity (ΘFC); and pesticide half-life (t1/2). Depending upon the pesticide, the contribution of recharge to uncertainty ranks second or third among the four AF components tested.The natural temporal variability of recharge is another source of uncertainty in AF, because the index is calculated using the time-averaged recharge rate. Relative to the mean, recharge variability is 10%, 44%, and 176% for the annual, monthly, and daily time scales, respectively, under sugarcane, and 31%, 112%, and 344%, respectively, under pineapple. In general, uncertainty in AF associated with temporal variability in recharge at all time scales exceeds AF. For chemicals such as atrazine or diuron under sugarcane, and atrazine or bromacil under pineapple, the range of AF uncertainty due to temporal variability in recharge encompasses significantly higher levels of leaching potential at some locations than that indicated by the AF estimate.

Simultaneous parameter estimation and contaminant source characterization for coupled groundwater flow and contaminant transport modelling

Parameter estimation and contaminant source characterization are key steps in the development of a coupled groundwater flow and contaminant transport simulation model. Here a methodologyfor simultaneous model parameter estimation and source characterization is presented. The parameter estimation/source characterization inverse model combines groundwater flow and contaminant transport simulation with non-linear maximum likelihood estimation to determine optimal estimates of the unknown model parameters and source characteristics based on measurements of hydraulic head and contaminant concentration. First-order uncertainty analysis provides a means for assessing the reliability of the maximum likelihood estimates and evaluating the accuracy and reliability of the flow and transport model predictions. A series of hypothetical examples is presented to demonstrate the ability of the inverse model to solve the combined parameter estimation/source characterization inverse problem. Hydraulic conductivities, effective porosity, longitudinal and transverse dispersivities, boundary flux, and contaminant flux at the source are estimated for a two-dimensional groundwater system. In addition, characterization of the history of contaminant disposal or location of the contaminant source is demonstrated. Finally, the problem of estimating the statistical parameters that describe the errors associated with the head and concentration data is addressed. A stage-wise estimation procedure is used to jointly estimate these statistical parameters along with the unknown model parameters and source characteristics.

Impact of uncertainty in soil, climatic, and chemical information in a pesticide leaching assessment

A simple mobility index, when combined with a geographic information system, can be used to generate rating maps which indicate qualitatively the potential for various organic chemicals to leach to groundwater. In this paper we investigate the magnitude of uncertainty associated with pesticide mobility estimates as a result of data uncertainties. Our example is for the Pearl Harbor Basin, Oahu, Hawaii. The two pesticides included in our analysis are atrazine (2-chloro-4-ethylamino-6-isopropylamino-s-triazine) and diuron [3-(3,4-dichlorophenyul)-1,1-dimethylarea]. The mobility index used here is known as the Attenuation Factor ( AF); it requires soil, hydrogeologic, climatic and chemical information as input data. We employ first-order uncertainty analysis to characterize the uncertainty in estimates of AF resulting from uncertainties in the various input data. Soils in the Pearl Harbor Basin are delineated at the order taxonomic category for this study. Our results show that there can be a significant amount of uncertainty in estimates of pesticide mobility for the Pearl Harbor Basin. This information needs to be considered if future decisions concerning chemical regulation are to be based on estimates of pesticide mobility determined from simple indices.

Uncertainty in a pesticide leaching assessment for Hawaii

In this paper we report the predictive uncertainty associated with using the retardation factor ( RF) as an index to evaluate pesticide leaching in Hawaii soils when uncertainty exists within the soil and chemical data used to excite the RF model. Our analysis takes two separate but ultimately related tacks. First, we assess the uncertainty caused by extrapolating soil properties between taxonomic categories. Second, we characterize the amount of uncertainty for calculated RF values due to data uncertainty by using first-order uncertainty analysis. Our results indicate that the RF index should only be used with soil information from the lowest taxonomic category and that even then considerable uncertainty will exist in the predicted RF values used to screen and rank chemicals.