A global empirical system for probabilistic seasonal climate prediction

Preparing for episodes with risks of anomalous weather a month to a year ahead is an important challenge for governments, non-governmental organisations, and private companies and is dependent on the availability of reliable forecasts. The majority of operational seasonal forecasts are made using process-based dynamical models, which are complex, computationally challenging and prone to biases. Empirical forecast approaches built on statistical models to represent physical processes offer an alternative to dynamical systems and can provide either a benchmark for comparison or independent supplementary forecasts. Here, we present a simple empirical system based on multiple linear regression for producing probabilistic forecasts of seasonal surface air temperature and precipitation across the globe. The global CO2-equivalent concentration is taken as the primary predictor; subsequent predictors, including large-scale modes of variability in the climate system and local-scale information, are selected on the basis of their physical relationship with the predictand. The focus given to the climate change signal as a source of skill and the probabilistic nature of the forecasts produced constitute a novel approach to global empirical prediction. Hindcasts for the period 1961–2013 are validated against observations using deterministic (correlation of seasonal means) and probabilistic (continuous rank probability skill scores) metrics. Good skill is found in many regions, particularly for surface air temperature and most notably in much of Europe during the spring and summer seasons. For precipitation, skill is generally limited to regions with known El Niño–Southern Oscillation (ENSO) teleconnections. The system is used in a quasi-operational framework to generate empirical seasonal forecasts on a monthly basis.

Data Assimilation and Inverse Methods in Terms of a Probabilistic Formulation

The weak-constraint inverse for nonlinear dynamical models is discussed and derived in terms of a probabilistic formulation. The well-known result that for Gaussian error statistics the minimum of the weak-constraint inverse is equal to the maximum-likelihood estimate is rederived. Then several methods based on ensemble statistics that can be used to find the smoother (as opposed to the filter) solution are introduced and compared to traditional methods. A strong point of the new methods is that they avoid the integration of adjoint equations, which is a complex task for real oceanographic or atmospheric applications. they also avoid iterative searches in a Hilbert space, and error estimates can be obtained without much additional computational effort. the feasibility of the new methods is illustrated in a two-layer quasigeostrophic model.

Willingness-to-pay for a probabilistic flood forecast: a risk-based decision-making game

Probabilistic hydro-meteorological forecasts have over the last decades been used more frequently to communicate forecastuncertainty. This uncertainty is twofold, as it constitutes both an added value and a challenge for the forecaster and the user of the forecasts. Many authors have demonstrated the added (economic) value of probabilistic over deterministic forecasts across the water sector (e.g. flood protection, hydroelectric power management and navigation). However, the richness of the information is also a source of challenges for operational uses, due partially to the difficulty to transform the probability of occurrence of an event into a binary decision. This paper presents the results of a risk-based decision-making game on the topic of flood protection mitigation, called “How much are you prepared to pay for a forecast?”. The game was played at several workshops in 2015, which were attended by operational forecasters and academics working in the field of hydrometeorology. The aim of this game was to better understand the role of probabilistic forecasts in decision-making processes and their perceived value by decision-makers. Based on the participants’ willingness-to-pay for a forecast, the results of the game show that the value (or the usefulness) of a forecast depends on several factors, including the way users perceive the quality of their forecasts and link it to the perception of their own performances as decision-makers.

Quantification of the probability of containment failure caused by an in-vessel steam explosion for the Sizewell B PWR

AEA Technology has provided an assessment of the probability of α-mode containment failure for the Sizewell B PWR. After a preliminary review of the methodologies available it was decided to use the probabilistic approach described in the paper, based on an extension of the methodology developed by Theofanous et al. (Nucl. Sci. Eng. 97 (1987) 259–325). The input to the assessment is 12 probability distributions; the bases for the quantification of these distributions are discussed. The α-mode assessment performed for the Sizewell B PWR has demonstrated the practicality of the event-tree method with input data represented by probability distributions. The assessment itself has drawn attention to a number of topics, which may be plant and sequence dependent, and has indicated the importance of melt relocation scenarios. The α-mode failure probability following an accident that leads to core melt relocation to the lower head for the Sizewell B PWR has been assessed as a few parts in 10 000, on the basis of current information. This assessment has been the first to consider elevated pressures (6 MPa and 15 MPa) besides atmospheric pressure, but the results suggest only a modest sensitivity to system pressure.

Modelling European winter wind storm losses in current and future climate

Severe wind storms are one of the major natural hazards in the extratropics and inflict substantial economic damages and even casualties. Insured storm-related losses depend on (i) the frequency, nature and dynamics of storms, (ii) the vulnerability of the values at risk, (iii) the geographical distribution of these values, and (iv) the particular conditions of the risk transfer. It is thus of great importance to assess the impact of climate change on future storm losses. To this end, the current study employs—to our knowledge for the first time—a coupled approach, using output from high-resolution regional climate model scenarios for the European sector to drive an operational insurance loss model. An ensemble of coupled climate-damage scenarios is used to provide an estimate of the inherent uncertainties. Output of two state-of-the-art global climate models (HadAM3, ECHAM5) is used for present (1961–1990) and future climates (2071–2100, SRES A2 scenario). These serve as boundary data for two nested regional climate models with a sophisticated gust parametrizations (CLM, CHRM). For validation and calibration purposes, an additional simulation is undertaken with the CHRM driven by the ERA40 reanalysis. The operational insurance model (Swiss Re) uses a European-wide damage function, an average vulnerability curve for all risk types, and contains the actual value distribution of a complete European market portfolio. The coupling between climate and damage models is based on daily maxima of 10 m gust winds, and the strategy adopted consists of three main steps: (i) development and application of a pragmatic selection criterion to retrieve significant storm events, (ii) generation of a probabilistic event set using a Monte-Carlo approach in the hazard module of the insurance model, and (iii) calibration of the simulated annual expected losses with a historic loss data base. The climate models considered agree regarding an increase in the intensity of extreme storms in a band across central Europe (stretching from southern UK and northern France to Denmark, northern Germany into eastern Europe). This effect increases with event strength, and rare storms show the largest climate change sensitivity, but are also beset with the largest uncertainties. Wind gusts decrease over northern Scandinavia and Southern Europe. Highest intra-ensemble variability is simulated for Ireland, the UK, the Mediterranean, and parts of Eastern Europe. The resulting changes on European-wide losses over the 110-year period are positive for all layers and all model runs considered and amount to 44% (annual expected loss), 23% (10 years loss), 50% (30 years loss), and 104% (100 years loss). There is a disproportionate increase in losses for rare high-impact events. The changes result from increases in both severity and frequency of wind gusts. Considerable geographical variability of the expected losses exists, with Denmark and Germany experiencing the largest loss increases (116% and 114%, respectively). All countries considered except for Ireland (−22%) experience some loss increases. Some ramifications of these results for the socio-economic sector are discussed, and future avenues for research are highlighted. The technique introduced in this study and its application to realistic market portfolios offer exciting prospects for future research on the impact of climate change that is relevant for policy makers, scientists and economists.

Parameter sensitivity and predictive uncertainty in a new water quality model, Q(2)

A new dynamic model of water quality, Q(2), has recently been developed, capable of simulating large branched river systems. This paper describes the application of a generalized sensitivity analysis (GSA) to Q(2) for single reaches of the River Thames in southern England. Focusing on the simulation of dissolved oxygen (DO) (since this may be regarded as a proxy for the overall health of a river); the GSA is used to identify key parameters controlling model behavior and provide a probabilistic procedure for model calibration. It is shown that, in the River Thames at least, it is more important to obtain high quality forcing functions than to obtain improved parameter estimates once approximate values have been estimated. Furthermore, there is a need to ensure reasonable simulation of a range of water quality determinands, since a focus only on DO increases predictive uncertainty in the DO simulations. The Q(2) model has been applied here to the River Thames, but it has a broad utility for evaluating other systems in Europe and around the world.

Human exposure modelling for chemical risk assessment: a review of current approaches and research and policy implications

A wide variety of exposure models are currently employed for health risk assessments. Individual models have been developed to meet the chemical exposure assessment needs of Government, industry and academia. These existing exposure models can be broadly categorised according to the following types of exposure source: environmental, dietary, consumer product, occupational, and aggregate and cumulative. Aggregate exposure models consider multiple exposure pathways, while cumulative models consider multiple chemicals. In this paper each of these basic types of exposure model are briefly described, along with any inherent strengths or weaknesses, with the UK as a case study. Examples are given of specific exposure models that are currently used, or that have the potential for future use, and key differences in modelling approaches adopted are discussed. The use of exposure models is currently fragmentary in nature. Specific organisations with exposure assessment responsibilities tend to use a limited range of models. The modelling techniques adopted in current exposure models have evolved along distinct lines for the various types of source. In fact different organisations may be using different models for very similar exposure assessment situations. This lack of consistency between exposure modelling practices can make understanding the exposure assessment process more complex, can lead to inconsistency between organisations in how critical modelling issues are addressed (e.g. variability and uncertainty), and has the potential to communicate mixed messages to the general public. Further work should be conducted to integrate the various approaches and models, where possible and regulatory remits allow, to get a coherent and consistent exposure modelling process. We recommend the development of an overall framework for exposure and risk assessment with common approaches and methodology, a screening tool for exposure assessment, collection of better input data, probabilistic modelling, validation of model input and output and a closer working relationship between scientists and policy makers and staff from different Government departments. A much increased effort is required is required in the UK to address these issues. The result will be a more robust, transparent, valid and more comparable exposure and risk assessment process. (C) 2006 Elsevier Ltd. All rights reserved.

Measuring and modelling mixture toxicity of imidacloprid and thiacloprid on Caenorhabditis elegans and Eisenia fetida

While the standard models of concentration addition and independent action predict overall toxicity of multicomponent mixtures reasonably, interactions may limit the predictive capability when a few compounds dominate a mixture. This study was conducted to test if statistically significant systematic deviations from concentration addition (i.e. synergism/antagonism, dose ratio- or dose level-dependency) occur when two taxonomically unrelated species, the earthworm Eisenia fetida and the nematode Caenorhabditis elegans were exposed to a full range of mixtures of the similar acting neonicotinoid pesticides imidacloprid and thiacloprid. The effect of the mixtures on C. elegans was described significantly better (p<0.01) by a dose level-dependent deviation from the concentration addition model than by the reference model alone, while the reference model description of the effects on E. fetida could not be significantly improved. These results highlight that deviations from concentration addition are possible even with similar acting compounds, but that the nature of such deviations are species dependent. For improving ecological risk assessment of simple mixtures, this implies that the concentration addition model may need to be used in a probabilistic context, rather than in its traditional deterministic manner. Crown Copyright (C) 2008 Published by Elsevier Inc. All rights reserved.

Quantifying uncertainty in critical loads: (B) acidity mass balance critical loads on a sensitive site

This paper reports an uncertainty analysis of critical loads for acid deposition for a site in southern England, using the Steady State Mass Balance Model. The uncertainty bounds, distribution type and correlation structure for each of the 18 input parameters was considered explicitly, and overall uncertainty estimated by Monte Carlo methods. Estimates of deposition uncertainty were made from measured data and an atmospheric dispersion model, and hence the uncertainty in exceedance could also be calculated. The uncertainties of the calculated critical loads were generally much lower than those of the input parameters due to a "compensation of errors" mechanism - coefficients of variation ranged from 13% for CLmaxN to 37% for CL(A). With 1990 deposition, the probability that the critical load was exceeded was > 0.99; to reduce this probability to 0.50, a 63% reduction in deposition is required; to 0.05, an 82% reduction. With 1997 deposition, which was lower than that in 1990, exceedance probabilities declined and uncertainties in exceedance narrowed as deposition uncertainty had less effect. The parameters contributing most to the uncertainty in critical loads were weathering rates, base cation uptake rates, and choice of critical chemical value, indicating possible research priorities. However, the different critical load parameters were to some extent sensitive to different input parameters. The application of such probabilistic results to environmental regulation is discussed.

Toward an integrated seasonal forecasting system for South America

This study proposes an objective integrated seasonal forecasting system for producing well-calibrated probabilistic rainfall forecasts for South America. The proposed system has two components: ( i) an empirical model that uses Pacific and Atlantic sea surface temperature anomalies as predictors for rainfall and ( ii) a multimodel system composed of three European coupled ocean - atmosphere models. Three-month lead austral summer rainfall predictions produced by the components of the system are integrated ( i. e., combined and calibrated) using a Bayesian forecast assimilation procedure. The skill of empirical, coupled multimodel, and integrated forecasts obtained with forecast assimilation is assessed and compared. The simple coupled multimodel ensemble has a comparable level of skill to that obtained using a simplified empirical approach. As for most regions of the globe, seasonal forecast skill for South America is low. However, when empirical and coupled multimodel predictions are combined and calibrated using forecast assimilation, more skillful integrated forecasts are obtained than with either empirical or coupled multimodel predictions alone. Both the reliability and resolution of the forecasts have been improved by forecast assimilation in several regions of South America. The Tropics and the area of southern Brazil, Uruguay, Paraguay, and northern Argentina have been found to be the two most predictable regions of South America during the austral summer. Skillful rainfall forecasts are generally only possible during El Nino or La Nina years rather than in neutral years.

How well does the ECMWF Ensemble Prediction System predict blocking?

Forecasting atmospheric blocking is one of the main problems facing medium-range weather forecasters in the extratropics. The European Centre for Medium-Range Weather Forecasts (ECMWF) Ensemble Prediction System (EPS) provides an excellent basis for medium-range forecasting as it provides a number of different possible realizations of the meteorological future. This ensemble of forecasts attempts to account for uncertainties in both the initial conditions and the model formulation. Since 18 July 2000, routine output from the EPS has included the field of potential temperature on the potential vorticity (PV) D 2 PV units (PVU) surface, the dynamical tropopause. This has enabled the objective identification of blocking using an index based on the reversal of the meridional potential-temperature gradient. A year of EPS probability forecasts of Euro-Atlantic and Pacific blocking have been produced and are assessed in this paper, concentrating on the Euro-Atlantic sector. Standard verification techniques such as Brier scores, Relative Operating Characteristic (ROC) curves and reliability diagrams are used. It is shown that Euro-Atlantic sector-blocking forecasts are skilful relative to climatology out to 10 days, and are more skilful than the deterministic control forecast at all lead times. The EPS is also more skilful than a probabilistic version of this deterministic forecast, though the difference is smaller. In addition, it is shown that the onset of a sector-blocking episode is less well predicted than its decay. As the lead time increases, the probability forecasts tend towards a model climatology with slightly less blocking than is seen in the real atmosphere. This small under-forecasting bias in the blocking forecasts is possibly related to a westerly bias in the ECMWF model. Copyright © 2003 Royal Meteorological Society

Efficient tree construction for the multicast problem

A new heuristic for the Steiner Minimal Tree problem is presented here. The method described is based on the detection of particular sets of nodes in networks, the “Hot Spot” sets, which are used to obtain better approximations of the optimal solutions. An algorithm is also proposed which is capable of improving the solutions obtained by classical heuristics, by means of a stirring process of the nodes in solution trees. Classical heuristics and an enumerative method are used CIS comparison terms in the experimental analysis which demonstrates the goodness of the heuristic discussed in this paper.

Efficient tree construction for the multicast problem

A new heuristic for the Steiner minimal tree problem is presented. The method described is based on the detection of particular sets of nodes in networks, the “hot spot” sets, which are used to obtain better approximations of the optimal solutions. An algorithm is also proposed which is capable of improving the solutions obtained by classical heuristics, by means of a stirring process of the nodes in solution trees. Classical heuristics and an enumerative method are used as comparison terms in the experimental analysis which demonstrates the capability of the heuristic discussed

Calibrating flood inundation models: identifying and addressing uncertainty in satellite observed flood extents

Improvements in the resolution of satellite imagery have enabled extraction of water surface elevations at the margins of the flood. Comparison between modelled and observed water surface elevations provides a new means for calibrating and validating flood inundation models, however the uncertainty in this observed data has yet to be addressed. Here a flood inundation model is calibrated using a probabilistic treatment of the observed data. A LiDAR guided snake algorithm is used to determine an outline of a flood event in 2006 on the River Dee, North Wales, UK, using a 12.5m ERS-1 image. Points at approximately 100m intervals along this outline are selected, and the water surface elevation recorded as the LiDAR DEM elevation at each point. With a planar water surface from the gauged upstream to downstream water elevations as an approximation, the water surface elevations at points along this flooded extent are compared to their ‘expected’ value. The pattern of errors between the two show a roughly normal distribution, however when plotted against coordinates there is obvious spatial autocorrelation. The source of this spatial dependency is investigated by comparing errors to the slope gradient and aspect of the LiDAR DEM. A LISFLOOD-FP model of the flood event is set-up to investigate the effect of observed data uncertainty on the calibration of flood inundation models. Multiple simulations are run using different combinations of friction parameters, from which the optimum parameter set will be selected. For each simulation a T-test is used to quantify the fit between modelled and observed water surface elevations. The points chosen for use in this T-test are selected based on their error. The criteria for selection enables evaluation of the sensitivity of the choice of optimum parameter set to uncertainty in the observed data. This work explores the observed data in detail and highlights possible causes of error. The identification of significant error (RMSE = 0.8m) between approximate expected and actual observed elevations from the remotely sensed data emphasises the limitations of using this data in a deterministic manner within the calibration process. These limitations are addressed by developing a new probabilistic approach to using the observed data.

Singular vector ensemble forecasting systems and the prediction of flow dependent uncertainty

The ECMWF ensemble weather forecasts are generated by perturbing the initial conditions of the forecast using a subset of the singular vectors of the linearised propagator. Previous results show that when creating probabilistic forecasts from this ensemble better forecasts are obtained if the mean of the spread and the variability of the spread are calibrated separately. We show results from a simple linear model that suggest that this may be a generic property for all singular vector based ensemble forecasting systems based on only a subset of the full set of singular vectors.