Quantitative Assessment Of Uncertainty Research Articles

FAILURE TO ACHIEVE PLANNED ECONOMIC PERFORMANCE OF OIL AND GAS PRODUCTION PROJECTS DUE TO LACK OF RISK ASSESSMENT AND UNCERTAINTY QUANTIFICATION

Quantitative assessment of risks and uncertainty has always played the most important role in the evaluation of oil & gas projects. Any estimated, measurable or evaluable magnitude contains an uncertainty, whether it concerns measuring watercut by means of a multiphase flow meter (MPFM) or to the net present value (NPV) of a major E&P project. Evaluation of project economics, e.g. the calculation of net present value (NPV), internal rate of return (IRR), OPEX and CAPEX shall be probabilistic, i.e. carried out with the quantitative assessment of risks and uncertainty of estimated (predicted) values. Nevertheless probabilistic estimate takes place very rarely. Most commonly, assessment of risks and uncertainty would be intuitive or based on a number of deterministic scenarios mistakenly referred to as pessimistic, optimistic and most probable. This research simulates failure to achieve target economic efficiency of E&P projects with no quantitative assessment of risks and uncertainty, and reviews previous international research conducted to identify the effect of ignoring probabilistic estimates related to the evaluation of E&P projects on their final economic efficiency.

A study of the role of the PDF uncertainty on the LHC -boson mass measurement

The determination of the W-boson mass through an analysis of the decay charged-lepton transverse momentum distribution has a sizable uncertainty due to the imperfect knowledge of the relevant parton distribution functions (PDFs). In this paper, a quantitative assessment of the W-boson mass uncertainty at the LHC resulting from the PDF uncertainty is examined. We use the CT14 NNLO PDFs with a NNLL + NNLO calculation (ResBos) to simulate the W-boson production and decay kinematics. The uncertainty of the W-boson mass determination is then determined as a function of the boson and lepton kinematics. For W+ production using and (GeV) < 45, PDF uncertainties lead (at the 68% CL) to a mass uncertainty for the of MeV, MeV, and MeV, are determined at 7 TeV, 8 TeV and 13 TeV, respectively. The uncertainties of for the same cuts are found to be MeV, MeV and MeV, at 7 TeV, 8 TeV and 13 TeV, respectively.

Application of qualitative and quantitative uncertainty assessment tools in developing ranges of plausible toxicity values for 2,3,7,8-tetrachlorodibenzo-p-dioxin.

Increasing interest in characterizing risk assessment uncertainty is highlighted by recent recommendations from the National Academy of Sciences. In this paper we demonstrate the utility of applying qualitative and quantitative methods for assessing uncertainty to enhance risk‐based decision‐making for 2,3,7,8‐tetrachlorodibenzo‐p‐dioxin. The approach involved deconstructing the reference dose (RfD) via evaluation of the different assumptions, options, models and methods associated with derivation of the value, culminating in the development of a plausible range of potential values based on such areas of uncertainty. The results demonstrate that overall RfD uncertainty was high based on limitations in the process for selection (e.g., compliance with inclusion criteria related to internal validity of the co‐critical studies, consistency with other studies), external validity (e.g., generalizing findings of acute, high‐dose exposure scenarios to the general population), and selection and classification of the point of departure using data from the individual studies (e.g., lack of statistical and clinical significance). Building on sensitivity analyses conducted by the US Environmental Protection Agency in 2012, the resulting estimates of RfD values that account for the uncertainties ranged from ~1.5 to 179 pg/kg/day. It is anticipated that the range of RfDs presented herein, along with the characterization of uncertainties, will improve risk assessments of dioxins and provide important information to risk managers, because reliance on a single toxicity value limits the information needed for making decisions and gives a false sense of precision and accuracy.

Best Practices for Quantification of Uncertainty and Sampling Quality in Molecular Simulations [Article v1.0

The quantitative assessment of uncertainty and sampling quality is essential in molecular simulation. Many systems of interest are highly complex, often at the edge of current computational capabilities. Modelers must therefore analyze and communicate statistical uncertainties so that "consumers" of simulated data understand its significance and limitations. This article covers key analyses appropriate for trajectory data generated by conventional simulation methods such as molecular dynamics and (single Markov chain) Monte Carlo. It also provides guidance for analyzing some 'enhanced' sampling approaches. We do not discuss systematic errors arising, e.g., from inaccuracy in the chosen model or force field.

Simulation-based approach to apply uncertainty evaluation framework, for PSS economic models

PSS offerings are characterized by the presence of uncertainties due to the lack of information, in the design stage of the offer, about future events that the decision makers will face. These uncertainties must be anticipated to validate the profitability of PSS projects. In this paper, an approach to assess uncertainty is presented, then applied to a study case. This approach is an integration of the classical uncertainty management framework together with the quantitative uncertainty assessment framework. In the first part of this article, a literature review on uncertainty identification and assessment in the PSS context is presented. Then, an uncertainty assessment approach is proposed, with the methods and tools to implement it. Finally, the authors describe the results of the application to an industrial case study.

Quantitative Assessment of Epistemic Uncertainties in Tsunami Hazard Effects on Building Risk Assessments

Based on the definition of tsunami risk, we quantitatively evaluated the annual expected tsunami loss ratio (Tsunami Risk Index) and clarified the quantitative effects of epistemic uncertainties in tsunami hazard assessments on the tsunami risk of buildings by combining probabilistic information regarding tsunami inundation depths at target points and tsunami fragility assessments of buildings. For the risk assessment, we targeted buildings with four different structures (reinforced concrete, steel, brick, wood) located in three different areas (Soma, Sendai, Kesennuma). In conclusion, we demonstrated that the expected tsunami risk could vary by approximately two orders of magnitude when considering tsunami hazard uncertainties between the 95th percentile and the 5th percentile. In addition, we quantitatively clarified the fact that we cannot properly understand the tsunami risk by evaluating the tsunami fragility alone. For example, the analysis results indicate that the tsunami risk of a wood building located in Kesennuma is lower than that of a reinforced concrete building located in either Soma or Sendai.

Lithology and fluid prediction from simultaneous seismic inversion over Sandfish field, Niger Delta, Nigeria

Seismic inversion has been widely practiced in the oil and gas industry because it generates broad bandwidth of impedance data which maximizes vertical resolution and minimizes tuning effects. The lack of accurate prediction of lithology and fluid content of subtle features identified in seismic data acquired over the Sandfish field, Niger Delta, Nigeria necessitated the use of seismic inversion. In this paper, simultaneous seismic inversion is adopted to integrate seismic and well data for quantitative interpretation and uncertainty assessment of the subsurface reservoirs in the Sandfish field. Three Sandfish (Sfn) wells with the required petrophysical logs, check-shot data, high quality 3D seismic data of five angle stacks (6–12°, 12–18°, 18–26°, 26–32°, and 32–42°) were used for the analysis. A feasibility study including cross-plots of petrophysical and elastic properties from well data was first carried out to establish rock property relationships in the interval of interest. Biot-Gassmann fluid substitution analysis was also used to reveal sensitivity of rock properties to pore-fill type. Low frequency (0–2 Hz) models were generated from interpolation of high-cut-filtered P-sonic, S-sonic, and density logs guided by interpreted seismic horizons. The low frequency models were used to broaden the spectrum to estimate elastic volumes. The five partial angle stacks were simultaneously inverted using Jason’s Rock-Trace® inversion software which iterated trial inversions until the model sufficiently matched the seismic data. The inverted P-impedance (ZP), Simpedance (ZS), and density (ρ) were used to derive Poisson’s ratio (σ), volume of sand (Vsand), lambda-rho (λρ), and mu-rho (µρ). The cross-plot of λρ with µρ from well data looks similar to that from inverted results. Sands and shales are discriminated on the basis of sands having low values of µρ. Hydrocarbon-bearing sands are differentiated from water-bearing sands and shales on the basis of having lowest values of λρ. The Biot-Gassmann fluid substitution analysis at reservoir N-01 reveals typical class III amplitude variation with angle (AVA) responses for low-impedance hydrocarbon sands. The lithology and fluid prediction maps extracted from Vsand and σ at the N-01 seismic horizon show variation in lithology and fluid types for the entire volume. The inversion products reveal heterogeneities in the reservoirs away from well control validated by a blind well test. Hence, the study shows that rock-property model from a simultaneous inversion is an effective predictive tool for lithology and fluid types which in turn can guide well placement and predict reservoir development in the field of study.

Methane emissions from global wetlands: An assessment of the uncertainty associated with various wetland extent data sets

A wide range of estimates on global wetland methane (CH4) fluxes has been reported during the recent two decades. This gives rise to urgent needs to clarify and identify the uncertainty sources, and conclude a reconciled estimate for global CH4 fluxes from wetlands. Most estimates by using bottom-up approach rely on wetland data sets, but these data sets show largely inconsistent in terms of both wetland extent and spatiotemporal distribution. A quantitative assessment of uncertainties associated with these discrepancies among wetland data sets has not been well investigated yet. By comparing the five widely used global wetland data sets (GISS, GLWD, Kaplan, GIEMS and SWAMPS-GLWD), it this study, we found large differences in the wetland extent, ranging from 5.3 to 10.2 million km2, as well as their spatial and temporal distributions among the five data sets. These discrepancies in wetland data sets resulted in large bias in model-estimated global wetland CH4 emissions as simulated by using the Dynamic Land Ecosystem Model (DLEM). The model simulations indicated that the mean global wetland CH4 emissions during 2000–2007 were 177.2 ± 49.7 Tg CH4 yr−1, based on the five different data sets. The tropical regions contributed the largest portion of estimated CH4 emissions from global wetlands, but also had the largest discrepancy. Among six continents, the largest uncertainty was found in South America. Thus, the improved estimates of wetland extent and CH4 emissions in the tropical regions and South America would be a critical step toward an accurate estimate of global CH4 emissions. This uncertainty analysis also reveals an important need for our scientific community to generate a global scale wetland data set with higher spatial resolution and shorter time interval, by integrating multiple sources of field and satellite data with modeling approaches, for cross-scale extrapolation.

Forecasting Incremental Oil Production of a Polymer-Pilot Extension in the Matzen Field Including Quantitative Uncertainty Assessment

Summary The polymer-pilot project performed in the 8 TH reservoir of the Matzen field showed encouraging incremental oil production. To improve further the understanding of recovery effects resulting from polymer injection, an extension of the pilot is planned by adding a second polymer injector. Forecasting of the incremental oil production needs to take the uncertainty of the geological models and dynamic parameters into account. We propose a work flow that is composed of a geological sensitivity and clustering step followed by a dynamic-calibration step for decreasing the objective function (OF) to improve the reliability of a probabilistic forecast of the incremental oil recovery. For the geological sensitivity, hundreds of geological realizations were generated by taking the uncertainty in the correlation of the sand and shale layers, logs, cores, and geological facies into account. The simulated tracer response was used as dissimilarity distance to classify the geological realizations. Clustering was then applied to select 70 representative realizations (centroids) from a total of 800 to use in the full-physics dynamic simulation. In the dynamic simulation, an OF composed of liquid rate and tracer concentration of the produced fluids was introduced. To improve the calibration further, the P50 value of incremental oil production as derived from simulation was compared with the incremental oil production determined from decline-curve analysis (DCA) from the wells surrounding the polymer-injection well. The mismatch between the P50 and the DCA was improved by adjusting polymer viscosity. The calibrated models were then used for both a probabilistic forecast of incremental oil caused by an additional polymer injector and an estimate of the expected polymer concentration at the producing wells.

Development of probabilistic internal dosimetry computer code

Internal radiation dose assessment involves biokinetic models, the corresponding parameters, measured data, and many assumptions. Every component considered in the internal dose assessment has its own uncertainty, which is propagated in the intake activity and internal dose estimates. For research or scientific purposes, and for retrospective dose reconstruction for accident scenarios occurring in workplaces having a large quantity of unsealed radionuclides, such as nuclear power plants, nuclear fuel cycle facilities, and facilities in which nuclear medicine is practiced, a quantitative uncertainty assessment of the internal dose is often required. However, no calculation tools or computer codes that incorporate all the relevant processes and their corresponding uncertainties, i.e., from the measured data to the committed dose, are available. Thus, the objective of the present study is to develop an integrated probabilistic internal-dose-assessment computer code. First, the uncertainty components in internal dosimetry are identified, and quantitative uncertainty data are collected. Then, an uncertainty database is established for each component. In order to propagate these uncertainties in an internal dose assessment, a probabilistic internal-dose-assessment system that employs the Bayesian and Monte Carlo methods. Based on the developed system, we developed a probabilistic internal-dose-assessment code by using MATLAB so as to estimate the dose distributions from the measured data with uncertainty. Using the developed code, we calculated the internal dose distribution and statistical values (e.g. the 2.5th, 5th, median, 95th, and 97.5th percentiles) for three sample scenarios. On the basis of the distributions, we performed a sensitivity analysis to determine the influence of each component on the resulting dose in order to identify the major component of the uncertainty in a bioassay. The results of this study can be applied to various situations. In cases of severe internal exposure, the causation probability of a deterministic health effect can be derived from the dose distribution, and a high statistical value (e.g., the 95th percentile of the distribution) can be used to determine the appropriate intervention. The distribution-based sensitivity analysis can also be used to quantify the contribution of each factor to the dose uncertainty, which is essential information for reducing and optimizing the uncertainty in the internal dose assessment. Therefore, the present study can contribute to retrospective dose assessment for accidental internal exposure scenarios, as well as to internal dose monitoring optimization and uncertainty reduction.

Concept of Quantitative Assessment of Knowledge Uncertainty in Accident Reconstruction Tasks

Abstract The article substantiates the concept of quantitative assessment of knowledge uncertainty in accident reconstruction tasks based on application of mathematical tools of the fuzzy set theory allowing considering an uncertainty of initial data caused for instance by varying resistance to the motion of investigated objects at the apex stages of the contact–separation processes. The application of the mathematical tools of the fuzzy set theory can substantially expand the potential of applying the methodology to the automobile and technical expertise and provide the enhancement of authenticity and improve the accuracy of making conclusions about the accident reconstruction results.

Imaging Solutions for Harsh Environments

This paper presents a quantitative assessment of uncertainty for the stereo calibration at different cameras angle and control object 3D reconstruction. Stereo-photogrammetry with high resolution commercially available digital cameras is applied to deliver a 3D data from a pair of 2D images. The main goal of the project is the reconstruction of the 3D model from the images obtained underwater in a high vibration manufacturing environment. The crucial step in obtaining high accuracy 3D data is stereo-rig calibration. Robust camera calibration is a critical step in 3D reconstructions in order to extract precise quantitative measurements from 2D images. Two AV 6600 monochrome 29 Megapixels GigE cameras were calibrated at four different angles to ensure that the angle of the stereo rig and variation in image contrast would not influence significantly the final results. All the images were undertaken in the high vibration manufacturing environment. It was shown that calibration of the cameras set at the angle of 15o reduces significantly 3D reconstruction accuracy. However, it does not influence reprojection error, which is less than 0.5 pixels.

Assessing uncertainty in stormwater quality modelling

Designing effective stormwater pollution mitigation strategies is a challenge in urban stormwater management. This is primarily due to the limited reliability of catchment scale stormwater quality modelling tools. As such, assessing the uncertainty associated with the information generated by stormwater quality models is important for informed decision making. Quantitative assessment of build-up and wash-off process uncertainty, which arises from the variability associated with these processes, is a major concern as typical uncertainty assessment approaches do not adequately account for process uncertainty. The research study undertaken found that the variability of build-up and wash-off processes for different particle size ranges leads to processes uncertainty. After variability and resulting process uncertainties are accurately characterised, they can be incorporated into catchment stormwater quality predictions. Accounting of process uncertainty influences the uncertainty limits associated with predicted stormwater quality. The impact of build-up process uncertainty on stormwater quality predictions is greater than that of wash-off process uncertainty. Accordingly, decision making should facilitate the designing of mitigation strategies which specifically addresses variations in load and composition of pollutants accumulated during dry weather periods. Moreover, the study outcomes found that the influence of process uncertainty is different for stormwater quality predictions corresponding to storm events with different intensity, duration and runoff volume generated. These storm events were also found to be significantly different in terms of the Runoff-Catchment Area ratio. As such, the selection of storm events in the context of designing stormwater pollution mitigation strategies needs to take into consideration not only the storm event characteristics, but also the influence of process uncertainty on stormwater quality predictions.

Quantitative Evaluation and Uncertainty Assessment on Geostatistical Simulation of Soil Salinity Using Electromagnetic Induction Technique

Diagnosis of soil salinity and characterizing its spatial variability both vertically and horizontally are needed to establish control measures in irrigated agriculture. In this regard, it is essential that salinity development in varying soil depths be known temporally and spatially. Apparent soil electrical conductivity, measured by electromagnetic induction instruments, has been widely used as an auxiliary variable to estimate spatial distribution of field soil salinity. The main objectives of this paper were adopted a mobile electromagnetic induction (EMI) system to perform field electromagnetic (EM) survey in different soil layers, to evaluate the uncertainty through Inverse Distance Weighted (IDW) and Ordinary Kriging (OK) methods, and to determine which algorithm is more reliable for the local and spatial uncertainty assessment. Results showed that EM38 data from apparent soil electrical conductivity are highly correlated with salinity, more accurate for estimating salinity from multiple linear regression models, which the correlation coefficient of 0 - 20, 20 - 40, 40 - 60 and 60 - 80 cm were 0.9090, 0.9228, 0.896 and 0.9085 respectively. The comparison showed that the prediction accuracy of two methods also displays good performance for soil salinity, the estimation precision of IDW method (with E = 0.8873, 0.9075, 0.8483 and 0.901, RPD = 9.64, 8.01, 8.17 and 11.23 in 0 - 20, 20 - 40. 40 - 60 and 60 - 80 cm soil layers, respectively) was superior to that of OK (with E = 0.8857, 0.872, 0.8744 and 0.8822, RPD = 9.44, 7.83, 8.52 and 10.88, respectively), but differences of two methods in predictions are not significant. The obtained salinity map was helpful to display the spatial patterns of soil salinity and monitor and evaluate the management of salinity.

Integrated assessment of environmental impact of Europe in 2010: data sources and extrapolation strategies for calculating normalisation factors

Assessing comprehensively the overall environmental impacts of a region remains a major challenge. Within life cycle assessment (LCA), this evaluation is performed calculating normalisation factors (NFs) at different scales. Normalisation represents an optional step of LCA according to ISO 14040/44 which may help in understanding the relative magnitude of the impact associated to a product when compared to a reference value. In order to enhance the robustness and comprehensiveness of NFs, this paper presents a methodology for building an extended domestic inventory of emission and resources extraction. The domestic inventory refers to emissions and extractions due to the processes located within a geographical region, Europe (EU 27), in 2010. A robust regional inventory is a fundamental element for supporting the calculation of global factors, often resulting form extrapolation and upscaling from regional ones. The NFs for EU 27 in 2010 are based on extensive data collection and the application of extrapolation strategies for data gaps filling. The inventory is based on domestic emissions into air, water and soil and on resource extracted in EU, adopting a production-based approach. A hierarchy is developed for selection of data sources based on their robustness and quality. Data gap filling is based on several proxy indicators, specific for each impact category, capitalising existing statistics on pressure indicators (e.g. estimating ionising radiation emissions based on data of electricity production from nuclear power plants). To calculate NFs, the inventory is characterised using the International reference Life Cycle Data System (ILCD) Handbook (EC-JRC 2011a) midpoint indicators. The resulting NFs present several added values compared to earlier normalisation exercises based on domestic inventories, namely more complete inventory, based on wide variety of sources; more comprehensive coverage of the flows within each impact category; overall evaluation of the robustness of the final figures; and robustness evaluation of the data sources. Contribution analysis shows that few flows (NO x , SO x , NH4, etc.) are driving the impacts of several impact categories, and the choice of the data sources is particularly crucial, as this may lead to differences in the NFs. A qualitative uncertainty assessment is reported for each impact category. Besides, in order to test the robustness of the NFs, a sensitivity analysis on key choices and assumptions has been advocated. NFs may help identification of the relative magnitude of the impact. Nonetheless, several limitations still exist both at the inventory and at the impact assessment level, e.g., several inventory flows are not characterised as there is no characterisation factor available in current models. Those limitations should be clearly reported and understood by the users of normalisation factors in order to correctly interpret the results of their study as well as when regional NFs are used as basis for building global set of factor. The adoption of domestic NFs may, in fact, result in overestimating the relative magnitude of certain impacts, especially when those impacts are associated with traded goods from or outside the EU 27. Qualitative and quantitative assessment of uncertainties should be conducted from inventory to characterised results. Comprehensive testing is needed on the following: data sources, data mapping, regionalisation as well as models and system boundaries thereof. Strengths and limitations of the current study have implications also in other application contexts, as when indicators are needed to evaluate progress towards environmental policies goals. In fact, environmental impact indicators at regional scale often require data gap filling and estimation methodologies.

Incorporating process variability into stormwater quality modelling

Process variability in pollutant build-up and wash-off generates inherent uncertainty that affects the outcomes of stormwater quality models. Poor characterisation of process variability constrains the accurate accounting of the uncertainty associated with pollutant processes. This acts as a significant limitation to effective decision making in relation to stormwater pollution mitigation. The study undertaken developed three theoretical scenarios based on research findings that variations in particle size fractions <150μm and >150μm during pollutant build-up and wash-off primarily determine the variability associated with these processes. These scenarios, which combine pollutant build-up and wash-off processes that takes place on a continuous timeline, are able to explain process variability under different field conditions. Given the variability characteristics of a specific build-up or wash-off event, the theoretical scenarios help to infer the variability characteristics of the associated pollutant process that follows. Mathematical formulation of the theoretical scenarios enables the incorporation of variability characteristics of pollutant build-up and wash-off processes in stormwater quality models. The research study outcomes will contribute to the quantitative assessment of uncertainty as an integral part of the interpretation of stormwater quality modelling outcomes.

Assessing Landscape Ecological Risk in a Mining City: A Case Study in Liaoyuan City, China

Landscape ecological risk assessment can effectively identify key elements for landscape sustainability, which directly improves human wellbeing. However, previous research has tended to apply risk probability, measured by overlaying landscape metrics to evaluate risk, generally lacking a quantitative assessment of loss and uncertainty of risk. This study, taking Liaoyuan City as a case area, explores landscape ecological risk assessment associated with mining cities, based on probability of risk and potential ecological loss. The assessment results show landscape ecological risk is lower in highly urbanized areas than those rural areas, suggesting that not only cities but also natural and semi-natural areas contribute to overall landscape-scale ecological risk. Our comparison of potential ecological risk in 58 watersheds in the region shows that ecological loss are moderate or high in the 10 high-risk watersheds. The 35 moderate-risk watersheds contain a large proportion of farmland, and the 13 low-risk watersheds are mainly distributed in flat terrain areas. Our uncertainty analyses result in a close range between simulated and calculated values, suggesting that our model is generally applicable. Our analysis has good potential in the fields of resource development, landscape planning and ecological restoration, and provides a quantitative method for achieving landscape sustainability in a mining city.

Robust changes and sources of uncertainty in the projected hydrological regimes of Swiss catchments

AbstractProjections of discharge are key for future water resources management. These projections are subject to uncertainties, which are difficult to handle in the decision process on adaptation strategies. Uncertainties arise from different sources such as the emission scenarios, the climate models and their postprocessing, the hydrological models, and the natural variability. Here we present a detailed and quantitative uncertainty assessment, based on recent climate scenarios for Switzerland (CH2011 data set) and covering catchments representative for midlatitude alpine areas. This study relies on a particularly wide range of discharge projections resulting from the factorial combination of 3 emission scenarios, 10–20 regional climate models, 2 postprocessing methods, and 3 hydrological models of different complexity. This enabled us to decompose the uncertainty in the ensemble of projections using analyses of variance (ANOVA). We applied the same modeling setup to six catchments to assess the influence of catchment characteristics on the projected streamflow, and focused on changes in the annual discharge cycle. The uncertainties captured by our setup originate mainly from the climate models and natural climate variability, but the choice of emission scenario plays a large role by the end of the 21st century. The contribution of the hydrological models to the projection uncertainty varied strongly with catchment elevation. The discharge changes were compared to the estimated natural decadal variability, which revealed that a climate change signal emerges even under the lowest emission scenario (RCP2.6) by the end of the century. Limiting emissions to RCP2.6 levels would nevertheless reduce the largest regime changes by the end of the century by approximately a factor of two, in comparison to impacts projected for the high emission scenario SRES A2. We finally show that robust regime changes emerge despite the projection uncertainty. These changes are significant and are consistent across a wide range of scenarios and catchments. We propose their identification as a way to aid decision making under uncertainty.

Parameter uncertainty of the AWBM model when applied to an ungauged catchment

AbstractIn this study, a quantitative assessment of uncertainty was made in connection with the calibration of Australian Water Balance Model (AWBM) for both gauged and ungauged catchment cases. For the gauged catchment, five different rainfall data sets, 23 different calibration data lengths and eight different optimization techniques were adopted. For the ungauged catchment case, the optimum parameter sets obtained from the nearest gauged catchment were transposed to the ungauged catchments, and two regional prediction equations were used to estimate runoff. Uncertainties were ascertained by comparing the observed and modelled runoffs by the AWBM on the basis of different combinations of methods, model parameters and input data. The main finding from this study was that the uncertainties in the AWBM modelling outputs could vary from −1.3% to 70% owing to different input rainfall data, −5.7% to 11% owing to different calibration data lengths and −6% to 0.2% owing to different optimization techniques adopted in the calibration of the AWBM. The performance of the AWBM model was found to be dominated mainly by the selection of appropriate rainfall data followed by the selection of an appropriate calibration data length and optimization algorithm. Use of relatively short data length (e.g. 3 to 6 years) in the calibration was found to generate relatively poor results. Effects of different optimization techniques on the calibration were found to be minimal. The uncertainties reported here in relation to the calibration and runoff estimation by the AWBM model are relevant to the selected study catchments, which are likely to differ for other catchments. The methodology presented in this paper can be applied to other catchments in Australia and other countries using AWBM and similar rainfall–runoff models. Copyright © 2014 John Wiley &amp; Sons, Ltd.

Bayesian Uncertainty Quantification for Subsurface Inversion Using a Multiscale Hierarchical Model

We consider a Bayesian approach to nonlinear inverse problems in which the unknown quantity is a random field (spatial or temporal). The Bayesian approach contains a natural mechanism for regularization in the form of prior information, can incorporate information from heterogeneous sources and provide a quantitative assessment of uncertainty in the inverse solution. The Bayesian setting casts the inverse solution as a posterior probability distribution over the model parameters. The Karhunen-Loeve expansion is used for dimension reduction of the random field. Furthermore, we use a hierarchical Bayes’ model to inject multiscale data in the modeling framework. In this Bayesian framework, we show that this inverse problem is well-posed by proving that the posterior measure is Lipschitz continuous with respect to the data in total variation norm. Computational challenges in this construction arise from the need for repeated evaluations of the forward model (e.g., in the context of MCMC) and are compounded by high dimensionality of the posterior. We develop two-stage reversible jump MCMC that has the ability to screen the bad proposals in the first inexpensive stage. Numerical results are presented by analyzing simulated as well as real data from hydrocarbon reservoir. This article has supplementary material available online.