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Climate change is widely recognized as one of the most challenging, urgent and complex problem facing humanity. There are rising interests in understanding and quantifying climate changing. We analyze the climate trend in Canada using Canadian monthly surface air temperature, which is longitudinal data in nature with long time span. Analysis of such data is challenging due to the complexity of modeling and associated computation burdens. In this paper, we divide this type of longitudinal data into time blocks, conduct multivariate regression and utilize a vine copula model to account for the dependence among the multivariate error terms. This vine copula model allows separate specification of within-block and between-block dependence structure and has great flexibility of modeling complex association structures. To release the computational burden and concentrate on the structure of interest, we construct composite likelihood functions, which leave the connecting structure between time blocks unspecified. We discuss different estimation procedures and issues regarding model selection and prediction. We explore the prediction performance of our vine copula model by extensive simulation studies. An analysis of the Canada climate dataset is provided. [ABSTRACT FROM AUTHOR]

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Multiple flood-generating mechanisms can affect the communities and infrastructure systems across coastal areas. Reliable design flood estimation and risk assessment in these regions demand characterization of the interrelationships between different drivers as well as the corresponding compounding effects. In this study, we assess the compound flood risks across Canada's coasts considering eight bivariate flooding scenarios acquired from four major drivers including precipitation, streamflow, skew surge, and total water level. For each scenario, an initial dependency test based on Kendall's Tau is conducted. The individual variability of each driver, at different locations, is characterized through parametric extreme value distributions followed by developing the bivariate joint distributions using copula functions. Parameters of the copula functions and the marginal distributions are inferred based on the Bayesian approach. Further, compound flood risks and failure probabilities are analyzed considering the OR, AND, Kendall, and conditional hazard scenarios. Results suggest that most locations can be affected by compound flooding associated with at least two bivariate events. Among the studied scenarios, the concurrent occurrence of extreme precipitation and sea level is the most common across ~ 80% of the coastal locations. In addition, critical sites that can be affected by the majority of the bivariate events (six out of eight combinations) are identified at the Pacific, south of Lake Huron, Lake Erie, and Lake Ontario. Besides, the estimated failure probabilities show higher hydrologic risks associated with the bivariate analysis of flood drivers compared to the univariate estimates. [ABSTRACT FROM AUTHOR]

Although potentially useful for financially hedging systemic weather-related risks, weather contracts/derivatives (also referred to as parametric insurance) have not seen wide adoption in agriculture outside of applications in developing countries, frequently supported by governments and non-governmental organizations (NGOs). A significant impediment is the lack of financial firms willing to stand ready to sell weather derivatives to individual agricultural producers in the over-the-counter market who, due to the localized nature of weather, face idiosyncratic weather-related risks. In particular, the administrative and reinsurance costs of supplying relatively small contracts with specific terms to many different producers are often prohibitive. The current study considers the potential use of weather derivatives in hedging the aggregate yield/revenues of viticulture producers represented by an industry association located in the province of Ontario, Canada. We examine the sensitivity of aggregate industry yields to several relevant weather-related risks employing copula function analysis. We then consider the potential of a weather derivative in hedging the financial risk associated with cold winter temperatures, which pose the greatest risk to aggregate vinifera yields. The issue of attributing costs and payouts to individual association members remains unresolved, and several alternatives are suggested. [ABSTRACT FROM AUTHOR]

This paper features an application of Regular Vine (R-vine) copulas, a recently developed statistical tool to assess composite risk. Copula-based dependence modelling is a popular tool in conditional risk assessment, but is usually applied to pairs of variables. By contrast, Vine copulas provide greater flexibility and permit the modelling of complex dependency patterns using a wide variety of bivariate copulas which may be arranged and analysed in a tree structure to explore multiple dependencies. This study emphasises the use of R-vine copulas in an analysis of the co-dependencies of five reservoirs in the cascade of the Saint-John River basin in Eastern Canada. The developed R-vine copulas lead to the joint and conditional return periods of maximum volumes, for hydrologic design and cascade reservoir management in the basin. The main attraction of this approach to risk modelling is the flexibility in the choice of distributions used to model heavy-tailed marginals and co-dependencies. [ABSTRACT FROM AUTHOR]

Severe flooding in coastal areas can result from the joint probability of oceanographic, hydrological, and meteorological factors, resulting in compound flooding (CF) events. Recently, copula functions have been used to enable a much more flexible environment in joint modelling. Incorporating a higher dimensional copula framework via symmetric 3-D Archimedean or elliptical copulas has statistical limits, and the preservation of all lower-level dependencies would be impossible. The heterogeneous dependency in CF events can be effectively modelled via a fully nested Archimedean (FNA) copula. Incorporating FNA under parametric settings is insufficiently flexible since it is restricted by the prior distributional assumption of the function type for both marginal density and copulas in parametric fittings. If the marginal density is of a specific parametric distribution, it could be problematic if underlying assumptions are violated. This study introduces a 3-D FNA copula simulation in a semiparametric setting by introducing nonparametric marginal distributions conjoined with parametric copula density. The derived semiparametric FNA copula is applied in the trivariate model in compounding the joint impact of rainfall, storm surge, and river discharge based on 46 years of observations on the west coast of Canada. The performance of the derived model has also been compared with the FNA copula constructed with parametric marginal density. It is concluded that the performance of FNA with nonparametric marginals outperforms the FNA copula built under parametric settings. The derived model is employed in multivariate analysis of flood risks in trivariate primary joint and conditional joint return periods. The trivariate hydrologic risk is analyzed using failure probability (FP) statistics. The investigation reveals that trivariate events produce a higher FP than bivariate (or univariate) events; thus, neglecting trivariate joint analysis results in FP being underestimated. Moreover, it indicates that trivariate hydrologic risk values increase with an increase in the service time of hydraulic facilities. [ABSTRACT FROM AUTHOR]

Low-lying coastal communities are often threatened by compound flooding (CF), which can be determined through the joint occurrence of storm surges, rainfall and river discharge, either successively or in close succession. The trivariate distribution can demonstrate the risk of the compound phenomenon more realistically, rather than considering each contributing factor independently or in pairwise dependency relations. Recently, the vine copula has been recognized as a highly flexible approach to constructing a higher-dimensional joint density framework. In these, the parametric class copula with parametric univariate marginals is often involved. Its incorporation can lead to a lack of flexibility due to parametric functions that have prior distribution assumptions about their univariate marginal and/or copula joint density. This study introduces the vine copula approach in a nonparametric setting by introducing Bernstein and Beta kernel copula density in establishing trivariate flood dependence. The proposed model was applied to 46 years of flood characteristics collected on the west coast of Canada. The univariate flood marginal distribution was modelled using nonparametric kernel density estimation (KDE). The 2D Bernstein estimator and beta kernel copula estimator were tested independently in capturing pairwise dependencies to establish D-vine structure in a stage-wise nesting approach in three alternative ways, each by permutating the location of the conditioning variable. The best-fitted vine structure was selected using goodness-of-fit (GOF) test statistics. The performance of the nonparametric vine approach was also compared with those of vines constructed with a parametric and semiparametric fitting procedure. Investigation revealed that the D-vine copula constructed using a Bernstein copula with normal KDE marginals performed well nonparametrically in capturing the dependence of the compound events. Finally, the derived nonparametric model was used in the estimation of trivariate joint return periods, and further employed in estimating failure probability statistics. [ABSTRACT FROM AUTHOR]

The interaction between oceanographic, meteorological, and hydrological factors can result in an extreme flooding scenario in the low-lying coastal area, called compound flooding (CF) events. For instance, rainfall and storm surge (or high river discharge) can be driven by the same meteorological forcing mechanisms, tropical or extra-tropical cyclones, resulting in a CF phenomenon. The trivariate distributional framework can significantly explain compound events' statistical behaviour reducing the associated high-impact flood risk. Resolving heterogenous dependency of the multidimensional CF events by incorporating traditional 3D symmetric or fully nested Archimedean copula is quite complex. The main challenge is to preserve all lower-level dependencies. An approach based on decomposing the full multivariate density into simple local building blocks via conditional independence called vine or pair-copulas is a much more comprehensive way of approximating the trivariate flood dependence structure. In this study, a parametric vine copula of a drawable (D-vine) structure is introduced in the trivariate modelling of flooding events with 46 years of observations of the west coast of Canada. This trivariate framework searches dependency by combining the joint impact of annual maximum 24-h rainfall and the highest storm surge and river discharge observed within the time ±1 day of the highest rainfall event. The D-vine structures are constructed in three alternative ways by permutation of the conditioning variables. The most appropriate D-vine structure is selected using the fitness test statistics and estimating trivariate joint and conditional joint return periods. The investigation confirms that the D-vine copula can effectively define the compound phenomenon's dependency. The failure probability (FP) method is also adopted in assessing the trivariate hydrologic risk. It is observed that hydrologic events defined in the trivariate case produce higher FP than in the bivariate (or univariate) case. It is also concluded that hydrologic risk increases (i) with an increase in the service design life of the hydraulic facilities and (ii) with a decrease in return periods. [ABSTRACT FROM AUTHOR]

Changes in the regional characteristics of temperature and precipitation can intensify the occurrence and severity of extreme events such as rain-on-snow-induced flooding, droughts and wildfires. Analyzing these climate variables in isolation without considering their interdependencies might result in severe underestimation of their combined effects. In addition, the assumption of linearity between temperature and precipitation does not represent the real physical processes that govern these climate variables. In this study, copula functions are used to describe the joint behaviour of temperature and precipitation across 15 ecozones of Canada at multiple temporal scales. The Clausius-Clapeyron (CC) relation is investigated using daily records to quantify changes in extreme precipitation with temperature increases. In addition, using historical records, dating back to 1910s, temporal changes in the dependence structure across southern Canada are analyzed using a non-stationary framework. Results show clear signs of accelerated warming and wetting over northern Canada while strong evidence of hot and dry conditions is found in the Prairie provinces. Analyses over seasonal and monthly scales indicate increases in warm-wet and hot-dry conditions in winter and summer, respectively. Non-stationary analyses reveal shifts towards warm and wet climate conditions for the majority of southern Canada. Considerable deviations from the theoretical CC scaling rate of 6.8% is observed for extreme precipitation over parts of Canada with super-CC scaling rates observed in northern Canada and sub-CC scaling rates in the majority of southern Canada. [ABSTRACT FROM AUTHOR]

This study proposes a copula-based chance-constrained waste management planning (CCWMP) method. The method can effectively reflect the interactions between random parameters of the waste management planning systems, and thus can help analyze the influences of their interactions on the entire systems. In particular, a joint distribution function is established using preestimated marginal distributions of random variables and an optimal copula selected from widely used Gaussian, Student’st, Clayton, Frank, Gumbel, and Ali-Mikhail-Haq copulas. Then a set of joint probabilistic constraints in the chance-constrained programming problems is converted into individual probabilistic constraints using the joint distribution function. Further, this method is applied to residential solid waste management in the city of Regina in Canada for demonstrating its applicability. Nine scenarios based on different joint and marginal probability levels are considered within a multiperiod and multizone context to effectively reflect dynamic, uncertain, and interactive characteristics of the solid waste management systems in the city. The results provide many decision alternatives under these scenarios, including cost-effective and environmentally friendly decision schemes. Moreover, the results indicate that even though the effect of the joint probability levels on the system costs is more significant than that of the marginal probability levels, the effect of marginal probability levels is notable, and there exists a trade-off between the total system cost and the constraint-violation risk. Therefore, the results obtained from the present study would be useful to support the city’s long-term solid waste management planning and formulate local policies and regulation concerning the city’s waste generation and management.Implications: The CCWMP method not only can solve chance-constrained problems with unknown probability distributions of random variables in the right-hand sides of constraints, but also can effectively reflect the interactions between the random parameters and thus help analyze the influences of their interactions on the entire systems. The results obtained through applying this method to the city of Regina in Canada can provide many decision alternatives under different joint probability levels and marginal probability levels, and would be useful to support the city’s long-term solid waste management planning. [ABSTRACT FROM PUBLISHER]

In the present work, climate change impacts on three spring (March-June) flood characteristics, i.e. peak, volume and duration, for 21 northeast Canadian basins are evaluated, based on Canadian regional climate model (CRCM) simulations. Conventional univariate frequency analysis for each flood characteristic and copula based bivariate frequency analysis for mutually correlated pairs of flood characteristics (i.e. peak-volume, peak-duration and volume-duration) are carried out. While univariate analysis is focused on return levels of selected return periods (5-, 20- and 50-year), the bivariate analysis is focused on the joint occurrence probabilities P1 and P2 of the three pairs of flood characteristics, where P1 is the probability of any one characteristic in a pair exceeding its threshold and P2 is the probability of both characteristics in a pair exceeding their respective thresholds at the same time. The performance of CRCM is assessed by comparing ERA40 (the European Centre for Medium-Range Weather Forecasts 40-year reanalysis) driven CRCM simulated flood statistics and univariate and bivariate frequency analysis results for the current 1970-1999 period with those observed at selected 16 gauging stations for the same time period. The Generalized Extreme Value distribution is selected as the marginal distribution for flood characteristics and the Clayton copula for developing bivariate distribution functions. The CRCM performs well in simulating mean, standard deviation, and 5-, 20- and 50-year return levels of flood characteristics. The joint occurrence probabilities are also simulated well by the CRCM. A five-member ensemble of the CRCM simulated streamflow for the current (1970-1999) and future (2041-2070) periods, driven by five different members of a Canadian Global Climate Model ensemble, are used in the assessment of projected changes, where future simulations correspond to A2 scenario. The results of projected changes, in general, indicate increases in the marginal values, i.e. return levels of flood characteristics, and the joint occurrence probabilities P1 and P2. It is found that the future marginal values of flood characteristics and P1 and P2 values corresponding to longer return periods will be affected more by anthropogenic climate change than those corresponding to shorter return periods but the former ones are subjected to higher uncertainties. [ABSTRACT FROM AUTHOR]

Using the copula method, bivariate distributions of flood peak and volume, and flood volume and duration were derived. A major advantage of this method is that marginal distributions of individual variables (i.e., flood peak, volume, and duration) can be of any form and the variables can be correlated. The copula method was applied to obtain the conditional return periods that are needed for hydrologic design. The derived distributions were tested using flood data from Amite River at Denham Springs, La., and the Ashuapmushuan River at Saguenay, Quebec, Canada. The derived distributions were also compared with the Gumbel mixed and the bivariate Box–Cox transformed normal distributions. The copula-based distributions were found to be in better agreement with plotting position-based frequency estimates than were other distributions. [ABSTRACT FROM AUTHOR]