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Windstorms are the most damaging natural hazard across western Europe. Risk modellers are limited by the observational data record to only ∼60 years of comprehensive reanalysis data that is dominated by considerable inter-annual variability. This makes estimating return periods of rare events difficult and sensitive to choice of historical period used. This study proposes a novel statistical method for estimating wind gusts across Europe based on observed windstorm footprints from the WISC project. Estimates of the 10-year and 200-year return levels are provided. The North Atlantic Oscillation (NAO) is particularly important for modulating lower return levels and setting the tail location parameter, with a less detectable influence on rarer extremes and the tail scale parameter. The optimal length of historical data required to make an accurate return level estimation is quantified using both observed and simulated timeseries of the historical NAO. For estimating 200-year return levels, a data catalogue of at least 20 years is required. For lower return levels the NAO has a stronger influence on estimated return levels and so there is more variability in estimates. Using recent estimates of plausible future NAO states, return levels are largely outside the historical uncertainty, indicating significant increases in risk potential from windstorms in the next 100 years. Our method presents a framework for assessing high return period losses across a range of hazards without the additional complexities of a full catastrophe model.

Climate trends over multiple decades are important drivers of regional climate change that need to be considered for climate resilience. Of particular importance are extreme trends that society may not be expecting and is not well adapted to. This study investigates approaches to assess the likelihood of maximum moving window trends in historical records of climate indices by making use of simulations from climate models and stochastic time series models with short- and long-range dependence. These approaches are applied to assess the unusualness of the large positive trend that occurred in the North Atlantic Oscillation (NAO) index between the 1960s to 1990s. By considering stochastic models, we show that the chance of extreme trends is determined by the variance of the trend process, which generally increases when there is more serial correlation in the index series. We find that the Coupled Model Intercomparison Project (CMIP5 + 6) historical simulations have very rarely (around 1 in 200 chance) simulated maximum trends greater than the observed maximum. Consistent with this, the NAO indices simulated by CMIP models were found to resemble white noise, with almost no serial correlation, in contrast to the observed NAO which exhibits year-to-year correlation. Stochastic model best fits to the observed NAO suggest an unlikely chance (around 1 in 20) for there to be maximum 31-year NAO trends as large as the maximum observed since 1860. This suggests that current climate models do not fully represent important aspects of the mechanism for low frequency variability of the NAO.

Reliable estimates of historical effective radiative forcing (ERF) are important for understanding the causes of past climate change and for constraining predictions of future warming. This study proposes a new linear-filtering method for estimating historical radiative forcing from time series of global mean surface temperature (GMST), using energy-balance models (EBMs) fitted to GMST from CO2-quadrupling general circulation model (GCM) experiments. We show that the response of any k-box EBM can be represented as an ARMA(k, k−1) (autoregressive moving-average) filter. We show how, by inverting an EBM's ARMA filter representation, time series of surface temperature may be converted into radiative forcing. The method is illustrated using three-box EBM fits to two recent Earth system models from CMIP5 and CMIP6 (Coupled Model Intercomparison Project). A comparison with published results obtained using the established ERF_trans method, a purely GCM-based approach, shows that our new method gives an ERF time series that closely matches the GCM-based series (correlation of 0.83). Time series of estimated historical ERF are obtained by applying the method to a dataset of historical temperature observations. The results show that there is clear evidence of a significant increase over the historical period with an estimated forcing in 2018 of 1.45±0.504 W m−2 when derived using the two Earth system models. This method could be used in the future to attribute past climate changes to anthropogenic and natural factors and to help constrain estimates of climate sensitivity.

This study has developed a rigorous and efficient maximum likelihood method for estimating the parameters in stochastic energy balance models (with any k > 0 number of boxes) given time series of surface temperature and top-of-the-atmosphere net downward radiative flux. The method works by finding a state-space representation of the linear dynamic system and evaluating the likelihood recursively via the Kalman filter. Confidence intervals for estimated parameters are straightforward to construct in the maximum likelihood framework, and information criteria may be used to choose an optimal number of boxes for parsimonious k-box emulation of atmosphere–ocean general circulation models (AOGCMs). In addition to estimating model parameters the method enables hidden state estimation for the unobservable boxes corresponding to the deep ocean, and also enables noise filtering for observations of surface temperature. The feasibility, reliability, and performance of the proposed method are demonstrated in a simulation study. To obtain a set of optimal k-box emulators, models are fitted to the 4 × CO2 step responses of 16 AOGCMs in CMIP5. It is found that for all 16 AOGCMs three boxes are required for optimal k-box emulation. The number of boxes k is found to influence, sometimes strongly, the impulse responses of the fitted models.

Categorical probabilistic prediction is widely used for terrestrial and space weather forecasting as well as for other environmental forecasts. One example is a warning system for geomagnetic disturbances caused by space weather, which are often classified on a 10-level scale. The simplest approach assumes that the transition probabilities are stationary in time – the Homogeneous Markov Chain (HMC). We extend this approach by developing a flexible Non-Homogeneous Markov Chain (NHMC) model using Bayesian non-parametric estimation to describe the time-varying transition probabilities. The transition probabilities are updated using a modified Bayes’ rule that gradually forgets transitions in the distant past, with a tunable memory parameter. The approaches were tested by making daily geomagnetic state forecasts at lead times of 1-4 days and verified over the period 2000-2019 using the Rank Probability Score (RPS). Both HMC and NHMC models were found to be skilful at all lead times when compared with climatological forecasts. The NHMC forecasts with an optimal memory parameter of ~100 days were found to be substantially more skilful than the HMC forecasts, with an RPS skill for the NHMC of 10.5% and 5.6% for lead times of 1 and 4 days ahead, respectively. The NHMC is thus a viable alternative approach for forecasting geomagnetic disturbances, and could provide a new benchmark for producing operational forecasts. The approach is generic and applicable to other forecasts including discrete weather regimes or hydrological conditions, e.g. wet and dry days.

Quantifying the risk of global warming exceeding critical targets such as 2.0 ◦ C requires reliable projections of uncertainty as well as best estimates of Global Mean Surface Temperature (GMST). However, uncertainty bands on GMST projections are often calculated heuristically and have several potential shortcomings. In particular, the uncertainty bands shown in IPCC plume projections of GMST are based on the distribution of GMST anomalies from climate model runs and so are strongly determined by model characteristics with little influence from observations of the real-world. Physically motivated time-series approaches are proposed based on fitting energy balance models (EBMs) to climate model outputs and observations in order to constrain future projections. It is shown that EBMs fitted to one forcing scenario will not produce reliable projections when different forcing scenarios are applied. The errors in the EBM projections can be interpreted as arising due to a discrepancy in the effective forcing felt by the model. A simple time-series approach to correcting the projections is proposed based on learning the evolution of the forcing discrepancy so that it can be projected into the future. This approach gives reliable projections of GMST when tested in a perfect model setting. When applied to observations this leads to projected warming of 2.2 ◦ C (1.7 ◦ C to 2.9 ◦ C) in 2100 compared to pre-industrial conditions, 0.4 ◦ C lower than a comparable IPCC anomaly estimate. The probability of staying below the critical 2.0 ◦ C warming target in 2100 more than doubles to 0.28 compared to only 0.11 from a comparably IPCC estimate.

Extratropical cyclones and their associated extreme precipitation and winds can have a severe impact on society and the co-occurrence between the two extremes is important when assessing risk. In this study the extremal dependency measure, χ , is used to quantify the co-occurrence of extreme precipitation and wind gusts, and is investigated at individual grid points and spatially over Europe. Results using three observational datasets and a higher spatial and temporal resolution version of ERA5 than previously used confirm previous studies. Over Europe high co-occurrence is found over western coasts and low co-occurrence is found over eastern coasts. All datasets have qualitatively similar spatial patterns over most regions of Europe excluding some regions of high topography where ERA5 χ values are much larger. ERA5 represents the timings of daily extreme co-occurring events well, compared to observations. The differences in precipitation accumulation timescales are also accounted for by considering hourly, 6, 24 and 48 hourly co-occurrence. In a few regions co-occurrence changes with longer accumulations, indicating the different speeds and sizes of weather systems affecting these regions. χ in most regions has little increase by allowing a 24 h lag and lead between the precipitation and wind, with a few exceptions where χ is increased by up to 24%. Regions with the larger of these increases are on or around elevated topography. Using an objective feature tracking method, insight into the spatial pattern of extreme precipitation and wind within cyclones over Europe is given. As well as suggesting how many hours apart the extremes occur from one another in a particular location. Extreme co-occurring events are associated with cyclones far more of the time than non extreme events. Given an extreme co-occurring event the chance of a cyclone being within 1110 km is more than 70% for much of Europe. Regions with low co-occurrence have extremes caused by different weather systems and regions with large co-occurrence have both extremes caused by the same weather system. Cyclones linked to extreme events, particularly co-occurring and extreme wind, have larger intensity than those not and for most of Europe these cyclones also have faster mean speed.

Since the 1970s, scientists have developed statistical methods intended to formalize detection of changes in global climate and to attribute such changes to relevant causal factors, natural and anthropogenic. Detection and attribution (D&A) of climate change trends is commonly performed using a variant of Hasselmann’s “optimal fingerprinting” method, which involves a linear regression of historical climate observations on corresponding output from numerical climate models. However, it has long been known in the field of time series analysis that regressions of “non-stationary” or “trending” variables are, in general, statistically inconsistent and often spurious. When non-stationarity is caused by “integrated” processes, as is likely the case for climate variables, consistency of least-squares estimators depends on “cointegration” of regressors. This study has shown, using an idealized linear-response-model framework, that if standard assumptions hold then the optimal fingerprinting estimator is consistent, and hence robust against spurious regression. In the case of global mean surface temperature (GMST), parameterizing abstract linear response models in terms of energy balance provides this result with physical interpretability. Hypothesis tests conducted using observations of historical GMST and simulation output from 13 CMIP6 general circulation models produced no evidence that standard assumptions required for consistency were violated. It is therefore concluded that, at least in the case of GMST, detection and attribution of climate change trends is very likely not spurious regression. Furthermore, detection of significant cointegration between observations and model output indicates that the least-squares estimator is “superconsistent”, with better convergence properties than might previously have been assumed. Finally, a new method has been developed for quantifying D&A uncertainty, exploiting the notion of cointegration to eliminate the need for pre-industrial control simulations.

This is the author accepted manuscript. The final version is available from Wiley / The Royal Meteorological Society via the DOI in this record.

Extreme precipitation and winds can have a severe impact on society, particularly when they occur at the same place and time. Studies have investigated the frequency of co-occurring extreme precipitation and wind using observational data. However, due to the rarity of very extreme events, these results are limited, since a large number of samples is needed to get robust estimates. Additionally, it is very difficult for estimates based on observations alone to help us understand the risk of future unprecedented events. Using the UNSEEN method (UNprecedented Simulated Extremes using ENsembles) this risk can be estimated from large ensembles of climate simulations. The Met Office's Global Seasonal forecast system version 5 (GloSea5) model ensembles are evaluated against ERA5 reanalysis data to find out how well they represent extreme precipitation, extreme wind and extreme co-occurring events over Europe. This model has not been evaluated in such a way before and this is needed before the model can be used to estimate the likelihood of unprecedented events using the UNSEEN method. We find that although the intensity of precipitation and wind extremes differ between the model and observations (by up to 12 mm and 9 m/s), the frequency of co-occurring events is well represented. The extremal dependency measure, χ, which measures co-occurrence, compares well spatially over Europe between GloSea5 and ERA5. However, significant differences in χ are found over areas of high topography, over the North Atlantic, Western Europe and the Norwegian Sea. Generally, GloSea5 underestimates χ over the ocean, and performs better over land. Mean sea level pressure anomaly composites for co-occurring extreme events show that at a number of selected locations, the co-occurring extremes are produced by very similar synoptic situations in the model and reanalysis. This gives increased confidence in the model. The model ensembles can then be used to assess the present day likelihood of unprecedented 3 hourly compound precipitation and wind extremes for winter over Europe, and to find out how the NAO index influences the frequency of co-occurring events over Europe.

Convection-permitting models (CPMs) provide a better representation of sub-daily precipitation statistics and convective processes, both on climate and NWP time scales, mainly thanks to the possibility to switch off the parameterisation of convection. The improved realism of these models gives us greater confidence in their ability to project future changes in short-duration precipitation extremes.The first 12-member ensemble of convection-permitting climate simulations over the UK was completed within the latest updates to the UK Climate Projections (UKCP). The 20-year long CPM simulations for present-day and end of century periods are nested in an ensemble of regional climate model (RCM) simulations over Europe driven by a global climate model ensemble. In the driving ensembles, uncertain parameters in the model physics are varied within plausible bounds to sample uncertainty. Although no perturbations are applied directly to the CPMs, this project allow us to provide a first-ever estimate of uncertainty at convection-permitting scale and thus provide UK risk assessment studies with more reliable climate change projections at local and hourly scales.Here we will present results looking at the uncertainty in future changes in hourly precipitation extremes across the CPM ensemble, and how this differs from the driving RCM ensemble.

Seasonal forecasts of variables like near-surface temperature or precipitation are becoming increasingly important for a wide range of stakeholders. Due to the many possibilities of recalibrating, combining, and verifying ensemble forecasts, there are ambiguities of which methods are most suitable. To address this we compare approaches how to process and verify multi-model seasonal forecasts based on a scientific assessment performed within the framework of the EU Copernicus Climate Change Service (C3S) Quality Assurance for Multi-model Seasonal Forecast Products (QA4Seas) contract C3S 51 lot 3. Our results underpin the importance of processing raw ensemble forecasts differently depending on the final forecast product needed. While ensemble forecasts benefit a lot from bias correction using climate conserving recalibration, this is not the case for the intrinsically bias adjusted multi-category probability forecasts. The same applies for multi-model combination. In this paper, we apply simple, but effective, approaches for multi-model combination of both forecast formats. Further, based on existing literature we recommend to use proper scoring rules like a sample version of the continuous ranked probability score and the ranked probability score for the verification of ensemble forecasts and multi-category probability forecasts, respectively. For a detailed global visualization of calibration as well as bias and dispersion errors, using the Chi-square decomposition of rank histograms proved to be appropriate for the analysis performed within QA4Seas., The research leading to these results is part of the Copernicus Climate Change Service (C3S) (Framework Agreement number C3S_51_Lot3_BSC), a program being implemented by the European Centre for Medium-Range Weather Forecasts (ECMWF) on behalf of the European Commission. Francisco Doblas-Reyes acknowledges the support by the H2020 EUCP project (GA 776613) and the MINECO-funded CLINSA project (CGL2017-85791-R).

There is a pressing need for simple and reliable risk transfer mechanisms that can pay out quickly after natural disasters without delays caused by loss estimation, and the need for long historical claims records. One such approach, known as parametric insurance, pays out when a key hazard variable exceeds a predetermined threshold. However, this approach to catastrophe risk, based on making deterministic binary predictions of loss occurrence, is susceptible to basis risk (mismatch between payouts and realized losses). A more defensible approach is to issue probabilistic predictions of loss occurrence, which then allows uncertainty to be properly quantified, communicated, and evaluated. This study proposes a generic probabilistic framework for parametric trigger modeling based on logistic regression, and idealized modeling of potential damage given knowledge of a hazard variable. We also propose various novel methods for evaluating the quality and utility of such predictions as well as more traditional trigger indices. The methodology is demonstrated by application to flood-related disasters in Jamaica from 1998 to 2016 using gridded precipitation data as the hazard variable. A hydrologically motivated transformation is proposed for calculating potential damage from daily rainfall data. Despite the simplicity of the approach, the model has substantial skill at predicting the probability of occurrence of loss days as demonstrated by traditional goodness-of-fit measures (i.e., pseudo-R2 of 0.55) as well as probabilistic verification diagnostics such as receiver operating characteristics. Using conceptual models of decisionmaker expenses, we also demonstrate that the system can provide considerable utility to involved parties, e.g., insured parties, insurers, and risk managers.

Extreme precipitation and winds can have a severe impact on society, particularly when they occur at the same place and time. In this study the Met Office’s Global Seasonal forecast system version 5 (GloSea5) model ensembles are evaluated against the reanalysis dataset ERA5, to find out how well they represent three hourly extreme precipitation, extreme wind and extreme co-occurring events over Europe. Although substantial differences in magnitude are found between precipitation and wind extremes between the datasets, the conditional probability of exceedance above the 99th percentile, which measures the co-occurrence between the two extremes, compares well spatially over Europe. However, significant differences in frequency are found around and over some areas of high topography. Generally GloSea5 underestimates this co-occurrence over sea. The model’s co-occurring events at individual locations investigated occur with very similar synoptic patterns to ERA5, indicating that the compound extremes are produced for the correct reasons.

The skill of weather and climate forecast systems is often assessed by calculating the correlation coefficient between past forecasts and their verifying observations. Improvements in forecast skill can thus be quantified by correlation differences. The uncertainty in the correlation difference needs to be assessed to judge whether the observed difference constitutes a genuine improvement, or is compatible with random sampling variations. A widely used statistical test for correlation difference is known to be unsuitable, because it assumes that the competing forecasting systems are independent. In this paper, appropriate statistical methods are reviewed to assess correlation differences when the competing forecasting systems are strongly correlated with one another. The methods are used to compare correlation skill between seasonal temperature forecasts that differ in initialization scheme and model resolution. A simple power analysis framework is proposed to estimate the probability of correctly detecting skill improvements, and to determine the minimum number of samples required to reliably detect improvements. The proposed statistical test has a higher power of detecting improvements than the traditional test. The main examples suggest that sample sizes of climate hindcasts should be increased to about 40 years to ensure sufficiently high power. It is found that seasonal temperature forecasts are significantly improved by using realistic land surface initial conditions.

Since numerical models of the climate system are only imperfect approximations of the real world, their forecasts often do not agree with real-world observations. This discrepancy often necessitates a statistical postprocessing step, called forecast recalibration, to better fit the climate model forecasts to future observations. In this chapter, we discuss forecast recalibration from the point of view of statistical modeling. We consider numerical model forecasts as explanatory variables in a statistical model of the real world. We focus on well known regression methods, particularly model output statistics and nonhomogeneous Gaussian regression, for their simplicity, interpretability, and good performance to correct common forecast errors. In situations where more than one climate model forecast is available for the same prediction target, it is necessary to produce an optimal combination of multiple forecasts into a single forecast. We show that forecast recalibration and forecast combination are closely related, and discuss a Bayesian regression method to combine multiple forecasts. The method can assign higher combination weights to models that better correlate with the real world, while avoiding overfitting by controlling the overall variability of the combination weights. All methods are illustrated on seasonal temperature forecasts over the Nino-3.4 region.

International audience

Late Holocene sea-level changes can be reconstructed from salt-marsh sediments with decimetre-scale precision and decadal-scale resolution. These records of relative sea-level changes comprise the net sea-level contributions from mechanisms that act across local, regional and global scales. Recent efforts help to constrain the relative significance of these mechanisms that include sediment dynamics and isostasy, which cause relative sea-level changes via vertical land motion, ocean-atmosphere processes that influence regional-scale ocean mass redistribution, and ocean-cryosphere and steric interactions that drive global scale ocean-volume changes. There remains a paucity of high-resolution Late Holocene sea-level data from eastern Canada. This precludes an interrogation of the mechanisms that define sea-level changes over recent centuries and millennia in a region sensitive to oceanic (Atlantic Multidecadal Variability, Atlantic Meridional Overturning Circulation), atmospheric (North Atlantic Oscillation, Arctic Oscillation) and cryospheric (ice-mass balance) changes. We present new relative sea-level data that span the past three millennia from Baie des Chaleurs in the Gulf of St. Lawrence generated using salt-marsh foraminifera supported with plant macrofossil analyses. The accompanying chronology is based on radiocarbon and radionuclide analyses, which are independently verified using trace metal and microcharcoal records. Relative sea level has risen at a mean rate of 0.93 ± 1.25 mm yr−1 over the past ∼1500 years. Residual structure within the reconstruction (‘internal variability’) has contributed up to an additional 0.61 ± 0.46 mm yr−1 of short-lived RSL rise prior to 1800 CE. Following a sea-level low stand during the Little Ice Age, acceleration in relative sea-level rise is identified between 1800 and 1900 CE within the estimates of internal variability and from 1950 CE to present in both the secular and residual trends. Phases of relative sea-level changes in the Gulf of St. Lawrence are concomitant with periods of glacier mass loss following the Little Ice Age, phase periods of the North Atlantic Oscillation and the Atlantic Meridional Overturning Circulation and Northern Hemisphere warming. Quantifying the individual effects of these different mechanisms is important for understanding how ocean-atmosphere processes redistribute ocean-mass upon larger scale background ocean-volume changes.

For climate services to be relevant and informative for users, scientific data definitions need to match users’ perceptions or beliefs. This study proposes and tests novel yet simple methods to compare beliefs of timing of recurrent climatic events with empirical evidence from multiple historical time series. The methods are tested by applying them to the onset date of the monsoon in Bangladesh, where several scientific monsoon definitions can be applied, yielding different results for monsoon onset dates. It is a challenge to know which monsoon definition compares best with people’s beliefs. Time series from eight different scientific monsoon definitions in six regions are compared with respondent beliefs from a previously completed survey concerning the monsoon onset. Beliefs about the timing of the monsoon onset are represented probabilistically for each respondent by constructing a probability mass function (PMF) from elicited responses about the earliest, normal, and latest dates for the event. A three-parameter circular modified triangular distribution (CMTD) is used to allow for the possibility (albeit small) of the onset at any time of the year. These distributions are then compared to the historical time series using two approaches: likelihood scores, and the mean and standard deviation of time series of dates simulated from each belief distribution. The methods proposed give the basis for further iterative discussion with decision-makers in the development of eventual climate services. This study uses Jessore, Bangladesh, as an example and finds that a rainfall definition, applying a 10 mm day−1 threshold to NCEP–NCAR reanalysis (Reanalyis-1) data, best matches the survey respondents’ beliefs about monsoon onset.

This study describes a systematic approach to selecting optimal statistical recalibration methods and hindcast designs for producing reliable probability forecasts on seasonal-to-decadal time scales. A new recalibration method is introduced that includes adjustments for both unconditional and conditional biases in the mean and variance of the forecast distribution and linear time-dependent bias in the mean. The complexity of the recalibration can be systematically varied by restricting the parameters. Simple recalibration methods may outperform more complex ones given limited training data. A new cross-validation methodology is proposed that allows the comparison of multiple recalibration methods and varying training periods using limited data. Part I considers the effect on forecast skill of varying the recalibration complexity and training period length. The interaction between these factors is analyzed for gridbox forecasts of annual mean near-surface temperature from the CanCM4 model. Recalibration methods that include conditional adjustment of the ensemble mean outperform simple bias correction by issuing climatological forecasts where the model has limited skill. Trend-adjusted forecasts outperform forecasts without trend adjustment at almost 75% of grid boxes. The optimal training period is around 30 yr for trend-adjusted forecasts and around 15 yr otherwise. The optimal training period is strongly related to the length of the optimal climatology. Longer training periods may increase overall performance but at the expense of very poor forecasts where skill is limited.

The inclusion of carbon cycle processes within CMIP5 Earth system models provides the opportunity to explore the relative importance of differences in scenario and climate model representation to future land and ocean carbon fluxes. A two-way analysis of variance (ANOVA) approach was used to quantify the variability owing to differences between scenarios and between climate models at different lead times. For global ocean carbon fluxes, the variance attributed to differences between representative concentration pathway scenarios exceeds the variance attributed to differences between climate models by around 2025, completely dominating by 2100. This contrasts with global land carbon fluxes, where the variance attributed to differences between climate models continues to dominate beyond 2100. This suggests that modeled processes that determine ocean fluxes are currently better constrained than those of land fluxes; thus, one can be more confident in linking different future socioeconomic pathways to consequences of ocean carbon uptake than for land carbon uptake. The contribution of internal variance is negligible for ocean fluxes and small for land fluxes, indicating that there is little dependence on the initial conditions. The apparent agreement in atmosphere–ocean carbon fluxes, globally, masks strong climate model differences at a regional level. The North Atlantic and Southern Ocean are key regions, where differences in modeled processes represent an important source of variability in projected regional fluxes.

Summary Floods pose multi-dimensional hazards to critical infrastructure and society and these hazards may increase under climate change. While flood conditions are dependent on catchment type and soil conditions, seasonal precipitation extremes also play an important role. The extreme precipitation events driving flood occurrence may arrive non-uniformly in time. In addition, their seasonal and inter-annual patterns may also cause sequences of several events and enhance likely flood responses. Spatial and temporal patterns of extreme daily precipitation occurrence are characterized across the UK. Extreme and very heavy daily precipitation is not uniformly distributed throughout the year, but exhibits spatial differences, arising from the relative proximity to the North Atlantic Ocean or North Sea. Periods of weeks or months are identified during which extreme daily precipitation occurrences are most likely to occur, with some regions of the UK displaying multimodal seasonality. A Generalized Additive Model is employed to simulate extreme daily precipitation occurrences over the UK from 1901 to 2010 and to allow robust statistical testing of temporal changes in the seasonal distribution. Simulations show that seasonality has the strongest correlation with intra-annual variations in extreme event occurrence, while Sea Surface Temperature (SST) and Mean Sea Level Pressure (MSLP) have the strongest correlation with inter-annual variations. The north and west of the UK are dominated by MSLP in the mid-North Atlantic and the south and east are dominated by local SST. All regions now have a higher likelihood of autumnal extreme daily precipitation than earlier in the twentieth century. This equates to extreme daily precipitation occurring earlier in the autumn in the north and west, and later in the autumn in the south and east. The change in timing is accompanied by increases in the probability of extreme daily precipitation occurrences during the autumn, and in the number of days with a very high probability of an extreme event. These results indicate a higher probability of several extreme occurrences in succession and a potential increase in flooding.

Sensitivity Analysis (SA) investigates how the variation in the output of a numerical model can be attributed to variations of its input factors. SA is increasingly being used in environmental modelling for a variety of purposes, including uncertainty assessment, model calibration and diagnostic evaluation, dominant control analysis and robust decision-making. In this paper we review the SA literature with the goal of providing: (i) a comprehensive view of SA approaches also in relation to other methodologies for model identification and application; (ii) a systematic classification of the most commonly used SA methods; (iii) practical guidelines for the application of SA. The paper aims at delivering an introduction to SA for non-specialist readers, as well as practical advice with best practice examples from the literature; and at stimulating the discussion within the community of SA developers and users regarding the setting of good practices and on defining priorities for future research. We present an overview of SA and its link to uncertainty analysis, model calibration and evaluation, robust decision-making.We provide a systematic review of existing approaches, which can support users in the choice of an SA method.We provide practical guidelines by developing a workflow for the application of SA and discuss critical choices.We give best practice examples from the literature and highlight trends and gaps for future research.

This paper applies time series modeling methods to paleoclimate series for temperature, ice volume, and atmospheric concentrations of CO2 and CH4. These series, inferred from Antarctic ice and ocean cores, are well known to move together in the transitions between glacial and interglacial periods, but the dynamic relationship between the series is open to question. A further unresolved issue is the role of Milankovitch theory, in which the glacial/interglacial cycles are correlated with orbital variations. We perform tests for Granger causality in the context of a vector autoregression model. Previous work with climate series has assumed nonstationarity and adopted a cointegration approach, but in a range of tests, we find no evidence of integrated behavior. We use conventional autoregressive methodology while allowing for conditional heteroscedasticity in the residuals, associated with the transitional periods. Copyright © 2015 John Wiley & Sons, Ltd.

A decline in damaging European windstorms has led to a reduction in insured losses in the 21st century. This decline is explored by identifying a damaging windstorm characteristic and investigating how and why this characteristic has changed in recent years. This novel exploration is based on 6103 high-resolution model-generated historical footprints (1979–2014), representing the whole European domain. The footprint of a windstorm is defined as the maximum wind gust speed to occur at a set of spatial locations over the duration of the storm. The area of the footprint exceeding 20 ms−1 over land, A20, is shown to be a good predictor of windstorm damage. This damaging characteristic has decreased in the 21st century, due to a statistically significant decrease in the relative frequency of windstorms exceeding 20 ms−1 in north-western Europe, although an increase is observed in southern Europe. This is explained by a decrease in the quantiles of the footprint wind gust speed distribution above approximately 18 ms−1 at locations in this region. In addition, an increased variability in the number of windstorm events is observed in the 21st century. Much of the change in A20 is explained by the North Atlantic Oscillation (NAO). The correlation between winter total A20 and winter-averaged mean sea-level pressure resembles the NAO pattern, shifted eastwards over Europe, and a strong positive relationship (correlation of 0.715) exists between winter total A20 and winter-averaged NAO. The shifted correlation pattern, however, suggests that other modes of variability may also play a role in the variation in windstorm losses.

Uncertainties in natural hazard risk assessment are generally dominated by the sources arising from lack of knowledge or understanding of the processes involved. There is a lack of knowledge about frequencies, process representations, parameters, present and future boundary conditions, consequences and impacts, and the meaning of observations in evaluating simulation models. These are the epistemic uncertainties that can be difficult to constrain, especially in terms of event or scenario probabilities, even as elicited probabilities rationalized on the basis of expert judgements. This paper reviews the issues raised by trying to quantify the effects of epistemic uncertainties. Such scientific uncertainties might have significant influence on decisions that are made for risk management, so it is important to communicate the meaning of an uncertainty estimate and to provide an audit trail of the assumptions on which it is based. Some suggestions for good practice in doing so are made.

This chapter reviews how Event Loss Tables (ELTs) produced by catastrophe models are used to simulate insurance losses due to natural hazards. A formal statistical interpretation is presented in terms of a static mixture of compound processes and implications for clustering of losses are discussed. The consistency of this approach is then critiqued on the basis of physical understanding of natural hazard processes. A more dynamic nonstationary approach is demonstrated using various idealized dynamical mixing models and results are compared for an artificial ELT typical of windstorm losses. The tail of the aggregate loss distribution is found to be highly sensitive to the modeling choices.

Numerical climate models are used to project future climate change due to both anthropogenic and natural causes. Differences between projections from different climate models are a major source of uncertainty about future climate. Emergent relationships shared by multiple climate models have the potential to constrain our uncertainty when combined with historical observations. We combine projections from 13 climate models with observational data to quantify the impact of emergent relationships on projections of future warming in the Arctic at the end of the 21st century. We propose a hierarchical Bayesian framework based on a coexchangeable representation of the relationship between climate models and the Earth system. We show how emergent constraints fit into the coexchangeable representation, and extend it to account for internal variability simulated by the models and natural variability in the Earth system. Our analysis shows that projected warming in some regions of the Arctic may be more than 2C lower and our uncertainty reduced by up to 30% when constrained by historical observations. A detailed theoretical comparison with existing multi-model projection frameworks is also provided. In particular, we show that projections may be biased if we do not account for internal variability in climate model predictions., Revised manuscript 6 figures, 2 tables

We develop Bayesian state space methods for modelling changes to the mean level or temporal correlation structure of an observed time series due to intermittent coupling with an unobserved process. Novel intervention methods are proposed to model the effect of repeated coupling as a single dynamic process. Latent time-varying autoregressive components are developed to model changes in the temporal correlation structure. Efficient filtering and smoothing methods are derived for the resulting class of models. We propose methods for quantifying the component of variance attributable to an unobserved process, the effect during individual coupling events, and the potential for skilful forecasts. The proposed methodology is applied to the study of winter-time variability in the dominant pattern of climate variation in the northern hemisphere, the North Atlantic Oscillation. Around 70% of the inter-annual variance in the winter (Dec-Jan-Feb) mean level is attributable to an unobserved process. Skilful forecasts for winter (Dec-Jan-Feb) mean are possible from the beginning of December., 27 pages, 8 figures, 4 tables

Synoptic observations are often treated as error-free representations of the true state of the real world. For example, when observations are used to verify numerical weather prediction (NWP) forecasts, forecast–observation differences (the total error) are often entirely attributed to forecast inaccuracy. Such simplification is no longer justifiable for short-lead forecasts made with increasingly accurate higher-resolution models. For example, at least 25% of t + 6 h individual Met Office site-specific (postprocessed) temperature forecasts now typically have total errors of less than 0.2 K, which are comparable to typical instrument measurement errors of around 0.1 K. In addition to instrument errors, uncertainty is introduced by measurements not being taken concurrently with the forecasts. For example, synoptic temperature observations in the United Kingdom are typically taken 10 min before the hour, whereas forecasts are generally extracted as instantaneous values on the hour. This study develops a simple yet robust statistical modeling procedure for assessing how serially correlated subhourly variations limit the forecast accuracy that can be achieved. The methodology is demonstrated by application to synoptic temperature observations sampled every minute at several locations around the United Kingdom. Results show that subhourly variations lead to sizeable forecast errors of 0.16–0.44 K for observations taken 10 min before the forecast issue time. The magnitude of this error depends on spatial location and the annual cycle, with the greater errors occurring in the warmer seasons and at inland sites. This important source of uncertainty consists of a bias due to the diurnal cycle, plus irreducible uncertainty due to unpredictable subhourly variations that fundamentally limit forecast accuracy.

In this study, the relationship between the frequency and intensity of extratropical cyclones over the North Atlantic is investigated. A cyclone track database of extended October–March winters was obtained from the National Centers for Environmental Prediction and National Center for Atmospheric Research (NCEP–NCAR) reanalysis. A large positive correlation is found between winter cyclone counts and local sample mean vorticity over the exit region of the North Atlantic storm track in this cyclone track database. Conversely, a negative correlation is found over the Gulf Stream. Possible causes for the dependence are investigated by regressing winter cyclone counts and local sample mean vorticity on teleconnection indices with Poisson and linear models. The indices for the Scandinavian pattern, North Atlantic Oscillation and East Atlantic Pattern are able to account for most of the observed positive correlation over the North Atlantic. To consider the implications of frequency intensity dependence for the insurance industry, an aggregate risk metric was used as a proxy for the annual aggregate insured loss. Here, the aggregate risk is defined as the sum of the intensities of all events occurring within a season. Assuming independence between the frequency and intensity results in large biases in the variance and the extremes of the aggregate risk, especially over Scandinavia. Therefore including frequency intensity dependence in extratropical cyclone loss models is necessary to model the risk of extreme losses.

This study has investigated serial (temporal) clustering of extratropical cyclones simulated by 17 climate models participating in CMIP5. Clustering was estimated by calculating the dispersion (ratio of variance to mean) of 30 December–February counts of Atlantic storm tracks passing near each grid point. Results from single historical simulations of 1975–2005 were compared to those from historical ERA40 reanalyses from 1958 to 2001 and single future model projections of 2069–2099 under the RCP4.5 climate change scenario. Models were generally able to capture the broad features in reanalyses reported previously: underdispersion/regularity (i.e. variance less than mean) in the western core of the Atlantic storm track surrounded by overdispersion/clustering (i.e. variance greater than mean) to the north and south and over Western Europe. Regression of counts onto North Atlantic Oscillation (NAO) indices revealed that much of the overdispersion in the historical reanalyses and model simulations can be accounted for by NAO variability. Future changes in dispersion were generally found to be small and not consistent across models. The overdispersion statistic, for any 30-year sample, is prone to large amounts of sampling uncertainty which obscures the climate change signal. For example, the projected increase in dispersion for storm counts near London in the CNRMCM5 model is 0.1 compared to a standard deviation of 0.25. Projected changes in the mean and variance of NAO are insufficient to create changes in overdispersion that are discernible above natural sampling variations.

This paper discusses how epistemic uncertainties are considered in a number of different natural hazard areas including floods, landslides and debris flows, dam safety, droughts, earthquakes, tsunamis, volcanic ash clouds and pyroclastic flows, and wind storms. In each case it is common practice to treat most uncertainties in the form of aleatory probability distributions but this may lead to an underestimation of the resulting uncertainties in assessing the hazard, consequences and risk. It is suggested that such analyses might be usefully extended by looking at different scenarios of assumptions about sources of epistemic uncertainty, with a view to reducing the element of surprise in future hazard occurrences. Since every analysis is necessarily conditional on the assumptions made about the nature of sources of epistemic uncertainty it is also important to follow the guidelines for good practice suggested in the companion Part 2.

There is a pressing need for simple and reliable risk transfer mechanisms that can pay out quickly after natural disasters without delays caused by loss estimation, and the need for long historical claims records. One such approach, known as parametric insurance, pays out when a key hazard variable exceeds a predetermined threshold. However, this approach to catastrophe risk, based on making deterministic binary predictions of loss occurrence, is susceptible to basis risk (mismatch between payouts and realized losses). A more defensible approach is to issue probabilistic predictions of loss occurrence, which then allows uncertainty to be properly quantified, communicated, and evaluated. This study proposes a generic probabilistic framework for parametric trigger modeling based on logistic regression, and idealized modeling of potential damage given knowledge of a hazard variable. We also propose various novel methods for evaluating the quality and utility of such predictions as well as more traditional trigger indices. The methodology is demonstrated by application to flood-related disasters in Jamaica from 1998 to 2016 using gridded precipitation data as the hazard variable. A hydrologically motivated transformation is proposed for calculating potential damage from daily rainfall data. Despite the simplicity of the approach, the model has substantial skill at predicting the probability of occurrence of loss days as demonstrated by traditional goodness-of-fit measures (i.e., pseudo-R

Reliable estimates of future changes in extreme weather phenomena, such as tropical cyclone maximum wind speeds, are critical for climate change impact assessments and the development of appropriate adaptation strategies. However, global and regional climate model outputs are often too coarse for direct use in these applications, with variables such as wind speed having truncated probability distributions compared to those of observations. This poses two problems: How can model-simulated variables best be adjusted to make them more realistic? And how can such adjustments be used to make more reliable predictions of future changes in their distribution?This study investigates North Atlantic tropical cyclone maximum wind speeds from observations (1950–2010) and regional climate model simulations (1995–2005 and 2045–55 at 12- and 36-km spatial resolutions). The wind speed distributions in these datasets are well represented by the Weibull distribution, albeit with different scale and shape parameters.A power-law transfer function is used to recalibrate the Weibull variables and obtain future projections of wind speeds. Two different strategies, bias correction and change factor, are tested by using 36-km model data to predict future 12-km model data (pseudo-observations). The strategies are also applied to the observations to obtain likely predictions of the future distributions of wind speeds. The strategies yield similar predictions of likely changes in the fraction of events within Saffir–Simpson categories—for example, an increase from 21% (1995–2005) to 27%–37% (2045–55) for category 3 or above events and an increase from 1.6% (1995–2005) to 2.8%–9.8% (2045–55) for category 5 events.

Summary Background With more than a million spectators expected to travel among 12 different cities in Brazil during the football World Cup, June 12–July 13, 2014, the risk of the mosquito-transmitted disease dengue fever is a concern. We addressed the potential for a dengue epidemic during the tournament, using a probabilistic forecast of dengue risk for the 553 microregions of Brazil, with risk level warnings for the 12 cities where matches will be played. Methods We obtained real-time seasonal climate forecasts from several international sources (European Centre for Medium-Range Weather Forecasts [ECMWF], Met Office, Meteo-France and Centro de Previsao de Tempo e Estudos Climaticos [CPTEC]) and the observed dengue epidemiological situation in Brazil at the forecast issue date as provided by the Ministry of Health. Using this information we devised a spatiotemporal hierarchical Bayesian modelling framework that enabled dengue warnings to be made 3 months ahead. By assessing the past performance of the forecasting system using observed dengue incidence rates for June, 2000–2013, we identified optimum trigger alert thresholds for scenarios of medium-risk and high-risk of dengue. Findings Our forecasts for June, 2014, showed that dengue risk was likely to be low in the host cities Brasilia, Cuiaba, Curitiba, Porto Alegre, and Sao Paulo. The risk was medium in Rio de Janeiro, Belo Horizonte, Salvador, and Manaus. High-risk alerts were triggered for the northeastern cities of Recife (p high =19%), Fortaleza (p high =46%), and Natal (p high =48%). For these high-risk areas, particularly Natal, the forecasting system did well for previous years (in June, 2000–13). Interpretation This timely dengue early warning permits the Ministry of Health and local authorities to implement appropriate, city-specific mitigation and control actions ahead of the World Cup. Funding European Commission's Seventh Framework Research Programme projects DENFREE, EUPORIAS, and SPECS; Conselho Nacional de Desenvolvimento Cientifico e Tecnologico and Fundacao de Amparo a Pesquisa do Estado do Rio de Janeiro.

Earth system models (ESMs) provide high resolution simulations of variables such as sea surface temperature (SST) that are often used in off-line biological impact models. Coral reef modellers have used such model outputs extensively to project both regional and global changes to coral growth and bleaching frequency. We assess model skill at capturing sub-regional climatologies and patterns of historical warming. This study uses an established wavelet-based spatial comparison technique to assess the skill of the coupled model intercomparison project phase 5 models to capture spatial SST patterns in coral regions. We show that models typically have medium to high skill at capturing climatological spatial patterns of SSTs within key coral regions, with model skill typically improving at larger spatial scales (≥4°). However models have much lower skill at modelling historical warming patters and are shown to often perform no better than chance at regional scales (e.g. Southeast Asian) and worse than chance at finer scales (

Future climate change projections are often derived from ensembles of simulations from multiple global circulation models using heuristic weighting schemes. This study provides a more rigorous justification for this by introducing a nested family of three simple analysis of variance frameworks. Statistical frameworks are essential in order to quantify the uncertainty associated with the estimate of the mean climate change response. The most general framework yields the “one model, one vote” weighting scheme often used in climate projection. However, a simpler additive framework is found to be preferable when the climate change response is not strongly model dependent. In such situations, the weighted multimodel mean may be interpreted as an estimate of the actual climate response, even in the presence of shared model biases. Statistical significance tests are derived to choose the most appropriate framework for specific multimodel ensemble data. The framework assumptions are explicit and can be checked using simple tests and graphical techniques. The frameworks can be used to test for evidence of nonzero climate response and to construct confidence intervals for the size of the response. The methodology is illustrated by application to North Atlantic storm track data from the Coupled Model Intercomparison Project phase 5 (CMIP5) multimodel ensemble. Despite large variations in the historical storm tracks, the cyclone frequency climate change response is not found to be model dependent over most of the region. This gives high confidence in the response estimates. Statistically significant decreases in cyclone frequency are found on the flanks of the North Atlantic storm track and in the Mediterranean basin.

Sahelian drought is investigated by analysing de-trended observations between 1900 and 2010, which show that substantial Northern Hemisphere volcanic eruptions preceded three of the four driest summers. Modelling both episodic volcanic eruptions and geoengineering by continuous deliberate stratospheric injection shows that large asymmetric aerosol loadings in the Northern Hemisphere are a precursor of Sahelian drought, whereas if the aerosol loadings are concentrated in the Southern Hemisphere greening of the Sahel is induced.