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In low‐lying coastal regions, the joint occurrence of high river flow and high water levels can cause coastal flooding with substantial economic and social implications. Recent studies over Canada's coasts have shown that neglecting the interdependency between flood drivers can underestimate the risk of flooding by up to 50%. However, to date, such interdependency has not been investigated for the coasts of the St. Lawrence River, Estuary and Gulf system (StL), where Sea Level Rise (SLR), along with intensified river peaks, are already threatening these communities. In this study, a copula‐based bivariate frequency analysis was applied to quantify the likelihood of occurrence of flooding events under dependent and independent assumptions, for 26 sites along the StL. Furthermore, to quantify the impact of anthropogenic climate change, the joint return period in historical period was compared with that of projected SLR associated with RCP 8.5 for the year 2100. Results show that (a) the independence assumption can underestimate the likelihood of occurrence of flooding event in the Fluvial Section of the StL by up to 30 times and (b) the SLR can increase the likelihood of occurrence of flooding event by up to 50 times in the Estuary and the Gulf and by up to 5 times in the Fluvial Section of the StL. This study highlights the need for explicit consideration of the dependence between flood drivers and of SLR in the delineation of flood maps along the coast of the St. Lawrence. Plain Language Summary: Coastal communities are at risk of flooding from both high river streamflow and high coastal water levels at the same time. However, to date, this kind of compound event has not been investigated for the coasts of the StL. As such, in this study, extreme return levels were computed at 26 sites along the St. Lawrence River, Estuary and Gulf system by taking the probability of occurrence of both high peak flow and high coastal water levels, as well as the probability of their joint occurrence. Furthermore, the impact of climate change was estimated by incorporating an increase in sea level as projected by high emission scenarios. Results show that joint occurrence of high river flow and water levels is likely to happen in the Fluvial Section of the St. Lawrence River, but less so elsewhere, and that sea level rise will have a severe impact on likelihood of occurrence of flooding events in the Estuary and the Gulf, but limited impact along the Fluvial Section. This study highlights the need to take both flood drivers, their interaction with each other, as well as the impacts of sea level rise into consideration in the delineation of flood maps located along the coast of StL. Key Points: Bivariate Frequency Analysis of extreme water level and river flows of 26 river outlets along the coast of the St. Lawrence River under independent and dependent assumption between flood driversThe assumption of independence can underestimate the likelihood of occurrence by up to 30 times in the Fluvial SectionSea level rise increases the likelihood flooding up to 5 and 50 times in the Fluvial and Estuary/Gulf of St. Lawrence River [ABSTRACT FROM AUTHOR]

Abstract In low‐lying coastal regions, the joint occurrence of high river flow and high water levels can cause coastal flooding with substantial economic and social implications. Recent studies over Canada's coasts have shown that neglecting the interdependency between flood drivers can underestimate the risk of flooding by up to 50%. However, to date, such interdependency has not been investigated for the coasts of the St. Lawrence River, Estuary and Gulf system (StL), where Sea Level Rise (SLR), along with intensified river peaks, are already threatening these communities. In this study, a copula‐based bivariate frequency analysis was applied to quantify the likelihood of occurrence of flooding events under dependent and independent assumptions, for 26 sites along the StL. Furthermore, to quantify the impact of anthropogenic climate change, the joint return period in historical period was compared with that of projected SLR associated with RCP 8.5 for the year 2100. Results show that (a) the independence assumption can underestimate the likelihood of occurrence of flooding event in the Fluvial Section of the StL by up to 30 times and (b) the SLR can increase the likelihood of occurrence of flooding event by up to 50 times in the Estuary and the Gulf and by up to 5 times in the Fluvial Section of the StL. This study highlights the need for explicit consideration of the dependence between flood drivers and of SLR in the delineation of flood maps along the coast of the St. Lawrence.

Two or more spatio-temporally co-located meteorological/climatological extremes (co-occurring extremes) place far greater stress on human and ecological systems than any single extreme could. This was observed during the California drought of 2011–2015 where multiple years of negative precipitation anomalies occurred simultaneously with positive temperature anomalies resulting in California’s worst drought on observational record. The large-scale drivers which modulate the occurrence of extremes in two or more variables remains largely unexplored. Using California wintertime (November–April) temperature and precipitation as a case study, we apply a novel, nonparametric conditional probability distribution method that allows for evaluation of complex, multivariate, and nonlinear relationships that exist among temperature, precipitation, and various indicators of large-scale climate variability and change. We find that multivariate variability and statistics of temperature and precipitation exhibit strong spatial variation across scales that are often treated as being homogeneous. Further, we demonstrate that the multivariate statistics of temperature and precipitation are highly non-stationary and therefore require more robust and sophisticated statistical techniques for accurate characterization. Of all the indicators of the large-scale climate conditions we studied, the dipole index explains the greatest fraction of multivariate variability in the co-occurrence of California wintertime extremes in temperature and precipitation.

This paper devises a regression-type model for the situation where both the response and covariates are extreme. The proposed approach is designed for the setting where the response and covariates are modeled as multivariate extreme values, and thus contrarily to standard regression methods it takes into account the key fact that the limiting distribution of suitably standardized componentwise maxima is an extreme value copula. An important target in the proposed framework is the regression manifold, which consists of a family of regression lines obeying the latter asymptotic result. To learn about the proposed model from data, we employ a Bernstein polynomial prior on the space of angular densities which leads to an induced prior on the space of regression manifolds. Numerical studies suggest a good performance of the proposed methods, and a finance real-data illustration reveals interesting aspects on the conditional risk of extreme losses in two leading international stock markets. [ABSTRACT FROM AUTHOR]

Southern South America (SSA) is an extended region where temperature and precipitation daily extreme events have several impacts on the different socio-economic activities. In this work, their individual and compound occurrence over SSA and their association with atmospheric circulation were studied during 1979–2015, using meteorological stations and the CPC gridded dataset. Results were generally in good agreement between both datasets. The occurrence of a warm night (minimum temperature exceeding the 90th percentile) or a cold day (maximum temperature below the 10th percentile) significantly increases the probability of heavy precipitation (daily precipitation exceeding the 75th percentile) in southern Chile and southeastern South America. These compound events were regionally conditioned by specific circulation types. In addition, both individual and compound extremes showed trends in the different sub-regions. On one hand, heavy precipitation exhibited a significant increase over central-eastern Argentina and Uruguay, northeastern Argentina and southern Brazil during the warm season, and a significant decrease in central and southern Chile during the cold season. On the other hand, warm (cold) extremes generally presented significant upward (downward) trends. Compound events showed significant positive trends for selected regions, in some cases coincident with trends in individual extremes. Changes in the frequency of circulation patterns were found to partly influence some of these trends, like the increases in heavy precipitation and warm extremes during the warm season.

Two or more spatio-temporally co-located meteorological/climatological extremes (co-occurring extremes) place far greater stress on human and ecological systems than any single extreme could. This was observed during the California drought of 2011–2015 where multiple years of negative precipitation anomalies occurred simultaneously with positive temperature anomalies resulting in California's worst drought on observational record. The large-scale drivers which modulate the occurrence of extremes in two or more variables remains largely unexplored. Using California wintertime (November–April) temperature and precipitation as a case study, we apply a novel, nonparametric conditional probability distribution method that allows for evaluation of complex, multivariate, and nonlinear relationships that exist among temperature, precipitation, and various indicators of large-scale climate variability and change. We find that multivariate variability and statistics of temperature and precipitation exhibit strong spatial variation across scales that are often treated as being homogeneous. Further, we demonstrate that the multivariate statistics of temperature and precipitation are highly non-stationary and therefore require more robust and sophisticated statistical techniques for accurate characterization. Of all the indicators of the large-scale climate conditions we studied, the dipole index explains the greatest fraction of multivariate variability in the co-occurrence of California wintertime extremes in temperature and precipitation. [ABSTRACT FROM AUTHOR]

This paper presents a method for estimating environmental contours in an arbitrary number of dimensions. The method, referred to as Direct-IFORM, does not require a model for the joint distribution of the variables. It can therefore be applied in higher dimensions without degradation in performance. The method involves multiple univariate analyses under rotations of the axes to estimate return values in various directions, which are used to form a contour. The method accounts for serial correlation in the observations, which removes the positive bias that occurs when this is neglected. An efficient open-source code is provided for estimating Direct-IFORM contours. A four-dimensional example is presented for contours of wind speed, wave height, wave period and wind-wave misalignment direction. The application of the method to the design of offshore wind turbines is discussed. • Method presented for estimating contours without need to fit joint distribution. • Method applicable in higher dimensions without degradation in performance. • Method accounts for serial correlation in observations, reducing positive bias. • Open source code in MATLAB and Python provided for estimating Direct-IFORM contours. • Example presented for 4-dimensional contours of wind and wave parameters. [ABSTRACT FROM AUTHOR]

Abstract: Understanding extreme ocean environments and their interaction with fixed and floating structures is critical for the design of offshore and coastal facilities. The joint effect of various ocean variables on extreme responses of offshore structures is fundamental in determining the design loads. For example, it is known that mean values of wave periods tend to increase with increasing storm intensity, and a floating system responds in a complex way to both variables. Specification of joint extremes in design criteria has often been somewhat ad hoc, being based on fairly arbitrary combinations of extremes of variables estimated independently. Such approaches are even outlined in design guidelines. Mathematically more consistent estimates of the joint occurrence of extreme environmental variables fall into two camps in the offshore industry — response-based and response-independent. Both are outlined here, with emphasis on response-independent methods, particularly those based on the conditional extremes model recently introduced by (Heffernan and Tawn, 2004), which has a solid theoretical motivation. We illustrate an application of the conditional extremes model to joint estimation of extreme storm peak significant wave height and peak period at a northern North Sea location, incorporating storm direction as a model covariate. We also discuss joint estimation of extreme current profiles with depth off the North West Shelf of Australia. Methods such as the conditional extremes model provide valuable additions to the metocean engineer's toolkit. [Copyright &y& Elsevier]

Abstract: Characterising the joint distribution of extremes of ocean environmental variables such as significant wave height (H S ) and spectral peak period (T P ) is important for understanding extreme ocean environments and in the design and assessment of marine and coastal structures. Many applications of multivariate extreme value analysis adopt models that assume a particular form of extremal dependence between variables without justification. Models are also typically restricted to joint regions in which all variables are extreme, but regions where only a subset of variables is extreme can be equally important for design. The conditional extremes model of Heffernan and Tawn (2004) provides one approach to overcoming these difficulties. Here, we extend the conditional extremes model to incorporate covariate effects in all of threshold selection, marginal and dependence modelling. Quantile regression is used to select appropriate covariate-dependent extreme value thresholds. Marginal and dependence modelling of extremes is performed within a penalised likelihood framework, using a Fourier parameterisation of marginal and dependence model parameters, with cross-validation to estimate suitable model parameter roughness, and bootstrapping to estimate parameter uncertainty with respect to covariate. We illustrate the approach in application to joint modelling of storm peak H S and T P at a Northern North Sea location with storm direction as covariate. We evaluate the impact of incorporating directional effects on estimates for return values, including those of a structure variable, similar to the structural response of a floating structure. We believe the approach offers the ocean engineer a straightforward procedure, based on sound statistics, to incorporate covariate effects in estimation of joint extreme environmental conditions. [Copyright &y& Elsevier]

ABSTRACT This study assesses recent and future changes in joint temperature and precipitation regimes at 28 sites in Bavaria, based on statistical downscaling of the ECHAM4 B2 Scenario (WETTREG). Monthly meteorological data of three future decades (2021-2030, 2031-2040 and 2041-2050) were compared with modelled data for the reference period 1971-2000. The bivariate data were classified into four weather types or modes (cooler/drier, cooler/wetter, warmer/wetter and warmer/drier relative to the 1971-2000 reference period). For the three future decades, a systematic change at all locations throughout the year was revealed. Both the cooler modes are predicted to occur less frequently in future decades; changes in warmer modes differ seasonally: In winter months, they are predicted to occur in the warmer/wetter mode, whereas in spring and summer months in the warmer/drier mode. Climatological extremes were defined as monthly weather events outside the 90% confidence ellipse of a Gaussian model of events in the reference period. An increase of extremes in the decade 2041-2050 was striking for June, which is predicted to be warmer and drier for half of the years. The same decade is predicted to experience the most extreme warm and wet modes, one in three Februarys and one in two winters are likely to be in this mode. The magnitude of these future changes in climate was related to the present mean annual temperature of the stations by rank regression. Stations with currently cooler climates are more likely to retain the normal conditions of the baseline period in contrast to currently warmer stations where the increase of extreme warm and wet conditions in summer and winter is expected to be larger. Copyright © 2012 Royal Meteorological Society [ABSTRACT FROM AUTHOR]

Abstract: Characterising the dependence between extremes of wave spectral parameters such as significant wave height (H S ) and spectral peak period (T P ) is important in understanding extreme ocean environments and in the design and assessment of marine structures. For example, it is known that mean values of wave periods tend to increase with increasing storm intensity. Here we seek to characterise joint dependence in a straightforward manner, accessible to the ocean engineering community, using a statistically sound approach. Many methods of multivariate extreme value analyses are based on models which assume implicitly that in some joint tail region each parameter is either independent of or asymptotically dependent on other parameters; yet in reality the dependence structure in general is neither of these. The underpinning assumption of multivariate regular variation restricts these methods to estimation of joint regions in which all parameters are extreme; but regions where only a subset of parameters are extreme can be equally important for design. The conditional approach of , similar in spirit to that of but with better theoretical foundation, overcomes these difficulties. We use the conditional approach to characterise the dependence structure of H S and T P . The key elements of the procedure are: (1) marginal modelling for all parameters, (2) transformation of data to a common standard Gumbel marginal form, (3) modelling dependence between data for extremes of pairs of parameters using a form of regression, (4) simulation of long return periods to estimate joint extremes. We demonstrate the approach in application to measured and hindcast data from the Northern North Sea, the Gulf of Mexico and the North West Shelf of Australia. We also illustrate the use of data re-sampling techniques such as bootstrapping to estimate the uncertainty in marginal and dependence models and accommodate this uncertainty in extreme quantile estimation. We discuss the current approach in the context of other approaches to multivariate extreme value estimation popular in the ocean engineering community. [Copyright &y& Elsevier]

This paper explores the joint extreme-value behavior of discontinuous random variables. It is shown that as in the continuous case, the latter ischaracterized by the weak limit of the normalized componentwise maxima and the convergence of any compatible copula. Illustrations are provided and an extension to the case of triangular arrays is considered which sheds new light on recent work of Coles and Pauli (Stat Probab Lett 54:373-379, 2001) and Mitov and Nadarajah (Extremes 8:357-370, 2005). This leads to considerations on the meaning of the bivariate upper tail dependence coefficient of Joe (Comput Stat Data Anal 16:279-297, 1993) in the discontinuous case. [ABSTRACT FROM AUTHOR]

The joint extremal spatial dependence of wind speed and significant wave height in the North East Atlantic is quantified using Metop satellite scatterometer and hindcast observations for the period 2007–2018, and a multivariate spatial conditional extremes (MSCE) model, ultimately motivated by the work of Heffernan and Tawn (2004). The analysis involves (a) registering individual satellite swaths and corresponding hindcast data onto a template transect (running approximately north-east to south-west, between the British Isles and Iceland), (b) non-stationary directional-seasonal marginal extreme value analysis at a set of registration locations on the transect, (c) transformation from physical to standard Laplace scale using the fitted marginal model, (d) estimation of the MSCE model on the set of registration locations, and assessment of quality of model fit. A joint model is estimated for three spatial quantities: Metop wind speed, hindcast wind speed and hindcast significant wave height. Results suggest that, when conditioning on extreme Metop wind speed, extremal spatial dependence for all three quantities decays over approximately 600–800 km. • Characterise joint extremal spatial dependence between multiple metocean variables. • Methodology motivated by model of Heffernan and Tawn (2004). • Satellite scatterometer (Metop) and hindcast data (Reistad et al., 2011) incorporated. • Marginal directional and seasonal covariate effects accommodated. • Extremal spatial dependence decays over 600–800 km for conditioning on an extreme occurrence of wind speed. [ABSTRACT FROM AUTHOR]