Probabilistic climate change predictions applying Bayesian model averaging

This study explores the sensitivity of probabilistic predictions of the twenty-first century surface air temperature (SAT) changes to different multi-model averaging methods using available simulations from the Intergovernmental Panel on Climate Change fourth assessment report. A way of observationally constrained prediction is provided by training multi-model simulations for the second half of the twentieth century with respect to long-term components. The Bayesian model averaging (BMA) produces weighted probability density functions (PDFs) and we compare two methods of estimating weighting factors: Bayes factor and expectation-maximization algorithm. It is shown that Bayesian-weighted PDFs for the global mean SAT changes are characterized by multi-modal structures from the middle of the twenty-first century onward, which are not clearly seen in arithmetic ensemble mean (AEM). This occurs because BMA tends to select a few high-skilled models and down-weight the others. Additionally, Bayesian results exhibit larger means and broader PDFs in the global mean predictions than the unweighted AEM. Multi-modality is more pronounced in the continental analysis using 30-year mean (2070-2099) SATs while there is only a little effect of Bayesian weighting on the 5-95% range. These results indicate that this approach to observationally constrained probabilistic predictions can be highly sensitive to the method of training, particularly for the later half of the twenty-first century, and that a more comprehensive approach combining different regions and/or variables is required.     

How uncertain are climate model projections of water availability indicators across the Middle East?

The projection of robust regional climate changes over the next 50 years presents a considerable challenge for the current generation of climate models. Water cycle changes are particularly difficult to model in this area because major uncertainties exist in the representation of processes such as large-scale and convective rainfall and their feedback with surface conditions. We present climate model projections and uncertainties in water availability indicators (precipitation, run-off and drought index) for the 1961-1990 and 2021-2050 periods. Ensembles from two global climate models (GCMs) and one regional climate model (RCM) are used to examine different elements of uncertainty. Although all three ensembles capture the general distribution of observed annual precipitation across the Middle East, the RCM is consistently wetter than observations, especially over the?mountainous areas. All future projections show decreasing precipitation (ensemble median between -5 and -25%) in coastal Turkey and parts of Lebanon, Syria and Israel and consistent run-off and drought index changes. The Intergovernmental Panel on Climate Change (IPCC) Fourth Assessment Report (AR4) GCM ensemble exhibits drying across the north of the region, whereas the Met Office Hadley Centre work Quantifying Uncertainties in Model ProjectionsAtmospheric (QUMP-A) GCM and RCM ensembles show slight drying in the north and significant wetting in the south. RCM projections also show greater sensitivity (both wetter and drier) and a wider uncertainty range than QUMP-A. The nature of these uncertainties suggests that both large-scale circulation patterns, which influence region-wide drying/wetting patterns, and regional-scale processes, which affect localized water availability, are important sources of uncertainty in these projections. To reduce large uncertainties in water availability projections, it is suggested that efforts would be well placed to focus on the understanding and modelling of both large-scale processes and their teleconnections with Middle East climate and localized processes involved in orographic precipitation.     

Ensemble climate predictions using climate models and observational constraints

Two different approaches are described for constraining climate predictions based on observations of past climate change. The first uses large ensembles of simulations from computationally efficient models and the second uses small ensembles from state-of-the-art coupled ocean-atmosphere general circulation models. Each approach is described and the advantages of each are discussed. When compared, the two approaches are shown to give consistent ranges for future temperature changes. The consistency of these results, when obtained using independent techniques, demonstrates that past observed climate changes provide robust constraints on probable future climate changes. Such probabilistic predictions are useful for communities seeking to adapt to future change as well as providing important information for devising strategies for mitigating climate change.     

Issues in the interpretation of climate model ensembles to inform decisions

There is a scientific consensus regarding the reality of anthropogenic climate change. This has led to substantial efforts to reduce atmospheric greenhouse gas emissions and thereby mitigate the impacts of climate change on a global scale. Despite these efforts, we are committed to substantial further changes over at least the next few decades. Societies will therefore have to adapt to changes in climate. Both adaptation and mitigation require action on scales ranging from local to global, but adaptation could directly benefit from climate predictions on regional scales while mitigation could be driven solely by awareness of the global problem; regional projections being principally of motivational value. We discuss how recent developments of large ensembles of climate model simulations can be interpreted to provide information on these scales and to inform societal decisions. Adaptation is most relevant as an influence on decisions which exist irrespective of climate change, but which have consequences on decadal time-scales. Even in such situations, climate change is often only a minor influence; perhaps helping to restrict the choice of 'no regrets' strategies. Nevertheless, if climate models are to provide inputs to societal decisions, it is important to interpret them appropriately. We take climate ensembles exploring model uncertainty as potentially providing a lower bound on the maximum range of uncertainty and thus a non-discountable climate change envelope. An analysis pathway is presented, describing how this information may provide an input to decisions, sometimes via a number of other analysis procedures and thus a cascade of uncertainty. An initial screening is seen as a valuable component of this process, potentially avoiding unnecessary effort while guiding decision makers through issues of confidence and robustness in climate modelling information. Our focus is the usage of decadal to centennial time-scale climate change simulations as inputs to decision making, but we acknowledge that robust adaptation to the variability of present day climate encourages the development of less vulnerable systems as well as building critical experience in how to respond to climatic uncertainty.     

The use of the multi-model ensemble in probabilistic climate projections

Recent coordinated efforts, in which numerous climate models have been run for a common set of experiments, have produced large datasets of projections of future climate for various scenarios. Those multi-model ensembles sample initial condition, parameter as well as structural uncertainties in the model design, and they have prompted a variety of approaches to quantify uncertainty in future climate in a probabilistic way. This paper outlines the motivation for using multi-model ensembles, reviews the methodologies published so far and compares their results for regional temperature projections. The challenges in interpreting multi-model results, caused by the lack of verification of climate projections, the problem of model dependence, bias and tuning as well as the difficulty in making sense of an 'ensemble of opportunity', are discussed in detail.     

Accounting for Parameter Uncertainty in Simulation Input Modeling

We formulate and evaluate a Bayesian approach to probabilistic input modeling for simulation experiments that accounts for the parameter and stochastic uncertainties inherent in most simulations and that yields valid predictive inferences about outputs of interest. We use prior information to construct prior distributions on the parameters of the input processes driving the simulation. Using Bayes' rule, we combine this prior information with the likelihood function of sample data observed on the input processes to compute the posterior parameter distributions. In our Bayesian simulation replication algorithm, we estimate parameter uncertainty by independently sampling new values of the input-model parameters from their posterior distributions on selected simulation runs; and we estimate stochastic uncertainty by performing multiple (conditionally) independent runs with each set of parameter values. We formulate performance measures relevant to both Bayesian and frequentist input-modeling techniques, and we summarize an experimental performance evaluation demonstrating the advantages of the Bayesian approach.     

Data-based stochastic subgrid-scale parametrization: an approach using cluster-weighted modelling

A new approach for data-based stochastic parametrization of unresolved scales and processes in numerical weather and climate prediction models is introduced. The subgrid-scale model is conditional on the state of the resolved scales, consisting of a collection of local models. A clustering algorithm in the space of the resolved variables is combined with statistical modelling of the impact of the unresolved variables. The clusters and the parameters of the associated subgrid models are estimated simultaneously from data. The method is implemented and explored in the framework of the Lorenz '96 model using discrete Markov processes as local statistical models. Performance of the cluster-weighted Markov chain scheme is investigated for long-term simulations as well as ensemble prediction. It clearly outperforms simple parametrization schemes and compares favourably with another recently proposed subgrid modelling scheme also based on conditional Markov chains.     

Model complexity versus ensemble size: allocating resources for climate prediction

A perennial question in modern weather forecasting and climate prediction is whether to invest resources in more complex numerical models or in larger ensembles of simulations. If this question is to be addressed quantitatively, then information is needed about how changes in model complexity and ensemble size will affect predictive performance. Information about the effects of ensemble size is often available, but information about the effects of model complexity is much rarer. An illustration is provided of the sort of analysis that might be conducted for the simplified case in which model complexity is judged in terms of grid resolution and ensemble members are constructed only by perturbing their initial conditions. The effects of resolution and ensemble size on the performance of climate simulations are described with a simple mathematical model, which is then used to define an optimal allocation of computational resources for a range of hypothetical prediction problems. The optimal resolution and ensemble size both increase with available resources, but their respective rates of increase depend on the values of two parameters that can be determined from a small number of simulations. The potential for such analyses to guide future investment decisions in climate prediction is discussed.     

Hierarchical asphalt pavement deterioration model for climate impact studies

Quantification of the impacts of projected climate change on road pavement performance is possible using predictive models that correctly consider key causal factors of pavement deterioration. These factors include climate, traffic, properties of materials and the design of pavements. This paper presents a new model developed to predict rutting in asphalt surfacing. In addition to the key causal factors of road deterioration, the developed model takes into account several sources of uncertainties, particularly those inherent in future climate change predictions and model input parameters. The asphalt surfacing rut depth progression model was developed from a hierarchical road network data structure using a Bayesian regression approach resulting in a model for each surfacing group. The model was applied within a Monte Carlo simulation framework to derive probabilistic outputs of pavement rut depth progression and maintenance costs under the pre-determined future climate scenarios. This model is useful for application at both the network and project levels to develop road management strategies and policies.     

Uncertainty propagation in a multiscale model of nanocrystalline plasticity

We characterize how uncertainties propagate across spatial and temporal scales in a physics-based model of nanocrystalline plasticity of fcc metals. Our model combines molecular dynamics (MD) simulations to characterize atomic-level processes that govern dislocation-based-plastic deformation with a phase field approach to dislocation dynamics (PFDD) that describes how an ensemble of dislocations evolve and interact to determine the mechanical response of the material. We apply this approach to a nanocrystalline Ni specimen of interest in micro-electromechanical (MEMS) switches. Our approach enables us to quantify how internal stresses that result from the fabrication process affect the properties of dislocations (using MD) and how these properties, in turn, affect the yield stress of the metallic membrane (using the PFMM model). Our predictions show that, for a nanocrystalline sample with small grain size (4 nm), a variation in residual stress of 20 MPa (typical in today's microfabrication techniques) would result in a variation on the critical resolved shear yield stress of approximately 15 MPa, a very small fraction of the nominal value of approximately 9 GPa.     

Performance updating of concrete bridges using proactive health monitoring methods

Uncertainties associated with modelling of deteriorating bridges strongly affect management decisions, such as inspection, maintenance and repair actions. These uncertainties can be reduced by the effective use of health monitoring systems, through which information regarding in situ performance can be incorporated in the management of bridges.The objectives of this paper are twofold; first, an improved chloride induced deterioration model for concrete bridges is proposed that can quantify degradation in performance soon after chlorides are deposited on the bridge, rather than when initiation of corrosion at the reinforcement level takes place. As a result, the implications of introducing proactive health monitoring can be assessed using probabilistic durability criteria. Thus, the second objective of the paper is to present a methodology for performance updating of deteriorating concrete bridges fitted with a proactive health monitoring system.This methodology is illustrated via a simple example of a typical bridge element, such as a beam or a part of a slab. The results highlight the benefits from introducing ‘smart’ technology in managing bridges subject to deterioration, and quantify the reduction in uncertainties and their subsequent effect on predictions of future bridge performance.     

Reliability prediction of pipes and valves

A methodology for predicting the reliability of pipes and valves and for assessing the impact of testing and inspection policy on the safe life of a component is described. The method is based on the stress-strength interference model and enables a combination of physical models and engineering experience to be used to estimate means, variances and associated uncertainties in the life of a component. Particular attention is paid to modelling failures arising from underlying degradation processes. Bayesian routines are used to update the model parameters and to reduce uncertainties using inspection, monitoring or test data. The paper describes the principles of the method together with examples related to subsea gate valves and pipelines.     

Dynamic response of structures with uncertain parameters: A comparative study of probabilistic and fuzzy sets models

This paper presents the results of a study on the response of structures with uncertain properties such as mass, stiffness and damping. The effect of the uncertain parameters on the response and the effect of the modelling of the uncertainties on the response are investigated. In particular, two types of uncertainties are distinguished: random and fuzzy uncertainties. Two kinds of models are studied: probabilistic and fuzzy set models. The two approaches to uncertainty modelling are compared with regard to their impacts on the analysis and on the uncertain structural response obtained. The study considers free vibration, forced vibration with deterministic excitation, and forced vibration with Gaussian white noise excitation. It is concluded that, in general, fuzzy models are much easier to implement and the associated analysis easier to perform than their probabilistic counterparts. When the available data on the structural parameters are crude and do not support a rigorous probabilistic model, the fuzzy set approach should be considered in view of its simplicity.     

Predictive maintenance of complex system with multi-level reliability structure

Onboard sensors, which constantly monitor the states of a system and its components, have made the predictive maintenance (PdM) of a complex system possible. To date, system reliability has been extensively studied with the assumption that systems are either single-component systems or they have a deterministic reliability structure. However, in many realistic problems, there are complex multi-component systems with uncertainties in the system reliability structure. This paper presents a PdM scheme for complex systems by employing discrete time Markov chain models for modelling multiple degradation processes of components and a Bayesian network (BN) model for predicting system reliability. The proposed method can be considered as a special type of dynamic Bayesian network because the same BN is repeatedly used over time for evaluating system reliability and the inter-time–slice connection of the same node is monitored by a sensor. This PdM scheme is able to make probabilistic inference at any system level, so PdM can be scheduled accordingly.     

Introduction. Stochastic physics and climate modelling

Finite computing resources limit the spatial resolution of state-of-the-art global climate simulations to hundreds of kilometres. In neither the atmosphere nor the ocean are small-scale processes such as convection, clouds and ocean eddies properly represented. Climate simulations are known to depend, sometimes quite strongly, on the resulting bulk-formula representation of unresolved processes. Stochastic physics schemes within weather and climate models have the potential to represent the dynamical effects of unresolved scales in ways which conventional bulk-formula representations are incapable of so doing. The application of stochastic physics to climate modelling is a rapidly advancing, important and innovative topic. The latest research findings are gathered together in the Theme Issue for which this paper serves as the introduction.     

A Bayesian probabilistic framework for avalanche modelling based on observations

Applied avalanche models are based on parameters which cannot be measured directly. As a consequence, these models are associated with large uncertainties, which must be addressed in risk assessment. To this end, we present an integral probabilistic framework for the modelling of avalanche hazards. The framework is based on a deterministic dynamic avalanche model, which is combined with an explicit representation of the different parameter uncertainties. The probability distribution of these uncertainties is then determined from observations of avalanches in the area under investigation through Bayesian inference. This framework facilitates the consistent combination of physical and empirical avalanche models with the available observations and expert knowledge. The resulting probabilistic spatial model can serve as a basis for hazard maping and spatial risk assessment. In this paper, the new model is applied to a case study in a test area located in the Swiss Alps.     

Introducing two hyperparameters in Bayesian estimation of wave spectra

An estimate of the on-site wave spectrum can be obtained from measured ship responses by use of Bayesian modelling, which means that the wave spectrum is found as the optimum solution from a probabilistic viewpoint. The paper describes the introduction of two hyperparameters into Bayesian modelling so that the prior information included in the modelling is based on two constraints: the wave spectrum must be smooth directional-wise as well as frequency-wise. Traditionally, only one hyperparameter has been used to control the amount of smoothing applied in both the frequency and directional ranges. From numerical simulations of stochastic response measurements, it is shown that the optimal hyperparameters, determined by use of ABIC (a Bayesian Information Criterion), correspond to the best estimate of the wave spectrum, which is not always the case when only one hyperparameter is included in the Bayesian modelling. The paper includes also an analysis of full-scale motion measurements where wave spectra estimated by the Bayesian modelling are compared with results from ocean surface measurements by satellite and from a wave radar. The agreement is found to be reasonable.     

Progress towards the development of a model for predicting human reliability

A methodology for predicting the probability of human task reliability during a task sequence is described. The method is based on a probabilistic performance requirement–resource consumption model. This enables error-promoting conditions in accident scenarios to be modelled explicitly and a time-dependent probability of error to be estimated. Particular attention is paid to modelling success arising from underlying human learning processes and the impact of limited resources. The paper describes the principles of the method together with an example related to safety and risk of a diver in the wreck scenario. © 1998 John Wiley & Sons, Ltd.     

Updating robust reliability using structural test data

The concept of robust reliability is defined to take into account uncertainties from structural modeling in addition to the uncertain excitation that a structure will experience during its lifetime. A Bayesian probabilistic methodology for system identification is integrated with probabilistic structural analysis tools for the purpose of updating the assessment of the robust reliability based on dynamic test data. Methods for updating the structural reliability for both identifiable and unidentifiable models are presented. Application of the methodology to a simple beam model of a single-span bridge with soil-structure interaction at the abutments, including a case with a tuned-mass damper attached to the deck, shows that the robust reliabilities computed before and after updating with “measured” dynamic data can differ significantly.     

A nested modelling approach to infrastructure performance characterisation

Reliable and accurate predictions of infrastructure condition can save significant amounts of money for infrastructure management agencies through better planned maintenance and rehabilitation activities. Infrastructure deterioration is a complicated, dynamic and stochastic process affected by various factors such as design, environmental conditions, material properties, structural capacities and some unobserved variables. Previous researchers have explored different types of modelling techniques, ranging from simple deterministic models to sophisticated probabilistic models, to characterise the deterioration process of infrastructure systems; however, these models have limitations in various aspects. Traditional deterministic models are inadequate to capture the uncertainties associated with infrastructure deterioration processes. State-based probabilistic models can only predict conditions at fixed time points. Time-based probabilistic models require frequent observations that, in practice, are not easy to perform. The goal of this research is to develop a new probabilistic model that is capable of capturing the stochastic nature of infrastructure deterioration, while at the same time avoiding the limitations of previous modelling efforts. The proposed nested model is based on discrete choice model theory. It can be used to predict the probability of an infrastructure system staying at defined condition states by relating an index representing the performance of the infrastructure to a number of explanatory variables that characterise the structural adequacy, traffic loading and environmental conditions of the infrastructure. The proposed model includes different possible implementation paths (sequential versus multinomial) depending on the considered explanatory variables and the available data. In the case study, the proposed probabilistic model is implemented with pavement performance data collected in Texas, yielding promising preliminary results.