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The streamflow process is an crucial information resource for the joint optimal operation of reservoirs. As the length and representativeness of historical streamflow samples are insufficient for practice projects, streamflow stochastic generation approaches are usually used to expand the streamflow series. For the joint operation and management of the multi-reservoir system, the multisite streamflow stochastic generation (MSSG) with high-dimensional temporal-spatial correlation poses a challenge. This paper develops the generative adversarial network as a novel MSSG model. In contrast to the existing literature on MSSG, which solely focuses on a specific case study and provides a comparatively one-sided assessment, this paper evaluates multiple characteristics of streamflow at various time scales from three MSSG models in two instances. Specifically, three MSSG models, namely the seasonal autoregression (SAR) model coupled with the master station method, the Copula model coupled with the master station method, and the deep convolutions generative adversarial network (DCGAN) model, are employed to generate monthly, ten-daily, and daily streamflow series of the two-reservoir and eight-reservoir systems. This study aims to examine the performance of three models and provide recommendations for implementing MSSG approaches in practice. Results show that: (1) the priority should be given to the maximum iterations on the DCGAN model at a large time scale, while at a smaller time scale, the training of the model is directly linked to the setting of batch size; (2) the Copula model is capable for better retaining statistical characteristics of streamflow series for similarity; (3) the SAR model excels in simulating the extremes of streamflow; and (4) the DCGAN model possesses a significant advantage in capturing the temporal-spatial higher-order correlation, especially in systems comprising more than two reservoirs and with small time scales (e.g., daily streamflow). Furthermore, this study presents comprehensive and multi-scale recommendations for selecting MSSG approaches, thereby providing a theoretical foundation and practical value for MSSG in diverse scenarios. [ABSTRACT FROM AUTHOR]

This study proposes an alternative risk assessment approach for evaluating extreme air pollution events through vine copula modeling. Three characteristics of unhealthy air pollution events (i.e., severity, intensity, and duration) in Klang, Malaysia, are examined. The vine copula is fitted using sequential maximum likelihood estimation and joint maximum likelihood estimation, with a subsequent comparison based on criteria such as log-likelihood, Akaike's information criterion, and Bayesian's information criterion. Model fitting and comparison studies demonstrate that the most well-fitted vine copula model, achieved through joint maximum likelihood estimation, comprises the Joe, Rotated Tawn type 2 (180 degrees), and Rotated BB8 (90 degrees) copulas. The positive Kendall's τ correlation coefficient (0.26) for the obtained vine copula indicates that higher values of one characteristic are likely to be associated with higher values of the other characteristics, and vice versa. Furthermore, with the upper tail dependence coefficient (0.31) surpassing the lower tail dependence coefficient (0.18), indicating stronger dependence in the upper tail of their distribution, this underscores the significance of conducting risk assessments for extreme air pollution events characterized by extreme levels of severity, intensity, and duration. A vine copula-based simulation study is conducted to delve deeper into the risk assessment, revealing that extreme air pollution events are not linked to the highest values of joint and conditional probabilities. These findings suggest that extreme values in those distinct characteristics do not consistently occur simultaneously. The return period measures also indicate that extreme air pollution events have long waiting periods. Despite the current status of extreme air pollution events in Klang being controllable, achieving effective control necessitates ongoing efforts, encompassing regulatory actions, industrial controls, robust public transportation programs, and a dedicated transition to cleaner energy sources. This task is crucial for ensuring continuous clean air quality, sustaining our environment, and avoiding negative impacts on the economy and public well-being. [ABSTRACT FROM AUTHOR]

Mankind is currently facing a crucial challenge in terms of climate change which may result in severe drought in many areas across the world. The present study analysed the joint return periods of meteorological drought events for historical and future projections across the Vidarbha region of India. To describe the drought occurrences in the area, the study used the standardized precipitation evapotranspiration index. The properties of each drought event, viz., duration, severity, and peak, were identified to model the multivariate drought risks. Several copula families were evaluated using statistical tests for joint dependency modelling of drought properties. The obtained joint distribution and selected univariate marginals are further used for estimating trivariate return periods for the historical and future climate change scenarios. The drought properties exhibited good interdependency justifying the use of a trivariate framework. The observed historical data of rainfall, maximum and minimum temperature were collected from the India Meteorological Department. The latest future projections of climate variables from coupled model intercomparison project phase 6 (CMIP6) datasets were acquired from NASA Earth Exchange Global Daily Downscaled Projections (NEX-GDDP-CMIP6) for six general circulation models. The copula-based trivariate frequency analysis was performed to compare the return periods associated with 'moderate' and 'above moderate drought' (i.e., combination of severe and extreme drought) events for the reference period (1981–2020) and future periods (2021–2100) under two SSP scenarios, SSP2-4.5 and SSP5-8.5. The 'AND' condition return period showed high drought risk during historical period covering a larger area. The findings of the study suggested that for 'AND' condition the trivariate frequency of above moderate droughts would increase in the future across Vidarbha region. The analysis showed that during near future more area will be under the risk of above moderate drought conditions compared to the far future, and the high-risk zones will be more under SSP5-8.5 than SSP2-4.5 scenario. The frequency of moderate drought episodes will be higher than the above moderate drought events, but the percentage area in the high-risk zone will be lower. The 'OR' condition return period projected alleviation of drought risk in the future, while the far future projected more area under drought risk compared to near future for the SSP scenarios. [ABSTRACT FROM AUTHOR]

The association of daily precipitation extremes (PEX) with maximum daily temperature (T), dew point temperature (DPT) and precipitable water (PW) are investigated throughout India during 1979–2016 using station-based data and gridded products from India Meteorological Department and climate reanalyses (ERA5). The dependence structure of PEX with physical covariates are modelled through copula for selected cities with different climatic types. The largest scaling coefficients, both negative (upto − 25%/°C with T) and positive (28%/°C with DPT, four times Clausius-Clapeyron rates) are observed in Mumbai. For all the cities, the median value of rainfall extremes increases with decrease in the conditioning variables T and DPT; but increases with increase in PW. Future scaling analyses using ensemble mean of 13 General Circulation Models (GCMs) from CMIP6 show strongly negative to slight positive scaling with T over a large part of India, although there are fluctuations over the three epochs (2015–2040, 2041–2070 and 2071–2100). [ABSTRACT FROM AUTHOR]

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]

Warming temperatures and severe droughts have contributed to increasing fire activity in California. Decadal average summer temperature in California has increased by 0.8 °C during 1984–2014, while the decadal total size of large fires has expanded by a factor of 2.5. This study proposes a multivariate probabilistic approach for quantifying changes to fire risk given different climatic conditions. Our results indicate that the risk of large fires in California increases substantially in response to unit degree changes in summer temperature. The probability of annual mean fire size exceeding its long-term average increases by 30% when summer temperature anomaly increases by 1 °C (from −0.5 °C to + 0.5 °C). Furthermore, the probability of annual average fire size exceeding its long-term average doubles when the annual precipitation decreases from the 75th (wet) to the 25th (dry) percentile. The proposed model can help manage fire-prone regions where fire activity is expected to intensify under projected global warming. [ABSTRACT FROM AUTHOR]

Rainfall and storm tides are both flood drivers in coastal zones. The complex interplay between them can lead to or exacerbate the impacts of flooding. While the dependence between rainfall and storm tides has been extensively studied, the compound effects of them on coastal flood risk have not been well researched. With Haikou city as the case study, this study investigates the bivariate return period of compounding rainfall and storm tide events based on copula functions and the failure probability is used to assess the variation of bivariate flood risk during the entire project lifetime. The results show that (1) there is a significant correlation between rainfall and storm tides. Therefore, bivariate RP analysis can provide more adequate and comprehensive information about risks than univariate RP analysis. Kendall RP can describe the bivariate RP more accurately since the dangerous region of Kendall RP is divided by the joint probability value. (2) Neglecting the compounding impacts and the dependence of rainfall and storm tides causes significant underestimation of the joint RP and failure probability. (3) The bivariate hydrologic risk value will decrease quickly when the design rainfall is higher than 100 mm and it becomes small and decrease slowly when the design rainfall exceeds 450 mm. Furthermore, the bivariate hydrologic risk value would not decrease until the storm tide is higher than 2 m and the values would become quite small as the storm tide exceeds 4.5 m. Such bivariate hydrologic risk analysis can provide decision support for hydraulic facility design as well as actual flood control and mitigation. [ABSTRACT FROM AUTHOR]

Copulas and other multivariate models can give joint exceedance probabilities for multivariate events in the natural environment. However, the choice of the most appropriate multivariate model may not always be evident in the absence of knowledge of dependence structures. A simple nonparametric alternative is to approximate multivariate dependencies using "line mesh distributions", introduced here as a data-based finite mixture of univariate distributions defined on a mesh of L = C(m, 2) lines extending through Euclidean n-space. That is, m data points in n-space define a total of L lines, where C() denotes the binomial coefficient. The utilitarian simplicity of the method has attraction for joint exceedance probabilities because just the data and a single bandwidth parameter within the 0, 1 interval are needed to define a line mesh distribution. All bivariate planes in these distributions have the same Pearson correlation coefficients as the corresponding data. Marginal means and variances are similarly preserved. Using an example from the literature, a 5-parameter bivariate Gumbel model is replaced with a 1-parameter line mesh distribution. A second illustration for three dimensions applies line mesh distributions to data simulated from a trivariate copula. [ABSTRACT FROM AUTHOR]

Vegetation is known to influence the hydrological state variables, suction ψ and volumetric water content (θw) of soil. In addition, vegetation induces heterogeneity in the soil porous structure and consequently the relative permeability (kr) of water under unsaturated conditions. The indirect method of utilising the soil water characteristic curve (SWCC) is commonly adopted for the determination of kr. In such cases, it is essential to address the stochastic behaviour of SWCC, in order to conduct a robust analysis on the kr of vegetative cover. The main aim of this study is to address the uncertainties associated with kr, using probabilistic analysis, for vegetative covers (i.e., grass and tree species) with bare cover as control treatment. We propose two approaches to accomplish the aforesaid objective. The univariate suction approach predicts the probability distribution functions of kr, on the basis of identified best probability distribution of suction. The bivariate suction and water content approach deals with the bivariate modelling of the water content and suction (SWCC), in order to capture the randomness in the permeability curves, due to presence of vegetation. For this purpose, the dependence structure of ψ and θw is established via copula theory, and the kr curves are predicted with respect to varying levels of ψ-θw correlation. The results showed that the kr of vegetative covers is substantially lower than that in bare covers. The reduction in kr with drying is more in tree cover than grassed cover, since tree roots induce higher levels of suction. Moreover, the air entry value of the soil depends on the magnitude of ψ-θw correlation, which in turn, is influenced by the type of vegetation in the soil. kr is found to be highly uncertain in the desaturation zone of the relative permeability curve. The stochastic behaviour of kr is found to be most significant in tree covers. Finally, a simplified case study is also presented in order to demonstrate the impact of the uncertainty in kr, on the stability of vegetates slopes. With an increment in the parameter α, factor of safety (FS) is found to decrease. The trend of FS is reverse of this with parameter n. Overall FS is found to vary around 4-5%, for both bare and vegetative slopes. [ABSTRACT FROM AUTHOR]

In order to improve the reliable monitoring and prediction of drought behavior, it is crucial to comprehensively consider composite indices. Initially, four univariate drought indices were evaluated: the Standardized Precipitation Index, the Standardized Soil Moisture Index of the top two layers (SSI1 and SSI2), and the Standardized Precipitation Evapotranspiration Index. Subsequently, this paper introduces five composite drought indices: the Multivariate Standardized Drought Index, the modified Aggregate Drought Index, the Joint Drought Deficit Index, the Machine Learning (ML-based) Drought Index (SVMs), and the Artificial Intelligence (AI-based) Drought Index (ANF-PSOs) models based on precipitation (P), soil moisture at two layers (SM1 and SM2), and reference evapotranspiration as input variables. These drought indices are formulated using P-ETref inputs, P-SM1 inputs, and P-SM2 inputs. The study covers 30 main basins classified into six climate zones, including coastal wet, mountain, semi mountain, semi desert, desert, and coastal desert across Iran from 1979 to 2021. The performance of the studied models was evaluated using the correlation coefficient and root mean square error in comparison with SPI at the same time scales as the target model. Drought characteristics, including the number of drought events, duration, frequency, and intensity, were determined for each model at monthly, seasonal, and yearly time scales. The results revealed that the recommended P-SM1 inputs for SVMs and ANF-PSOs models significantly outperformed the MSDIs, modified ADIs, and JDIs models. The results indicated that the introduced composite models effectively captured the comprehensive SM situation without being heavily influenced by individual parameters. The behavioral patterns of these indices remained consistent, except for the specific performance of ETref, which caused some inconsistencies. Moreover, a comparison among different climates revealed that ETref played a prominent role in the discrepancies observed in the output of the composite models, resulting in a strong relationship between P and ETref. Consequently, when constructing composite indices, the information conveyed by ETref was more readily disregarded by JDI and ADI but retained in ANF-PSO. This research sheds light on the mechanisms of these ML-based and AI-based composite approaches in integrating different drought features. It offers valuable insights into the performance of composite drought models and provides benchmarks, particularly in dry climates, to enhance drought monitoring methods. [ABSTRACT FROM AUTHOR]

This study used gridded daily maximum temperature data (1° × 1°) for 1951-2014 period to analyze the trend in monthly extreme warm days (ExWD) and changes in its probability distribution in each grid. It also analyzed the trend in spatial spread of annual ExWD over the study period at four exceedance levels and further related the number of ExWDs with cereal crop productivity of India. Extreme warm days have increased throughout India but were statistically significant in 42% grids. The increase was consistent over all the months in north-eastern region, southern plateau and both the coastal plains. It also increased significantly over north-western and central India during April to June summer period. The probability distribution of ExWD also changed significantly in many grids, especially in southern plateau and both the coastal plains. The changes indicated increased frequency in the existing levels of extremes and new occurrences of higher frequency of extremes. The analysis of land area affected by different levels of extremes indicated significant increase, with the rate being highest for higher extremes. In terms of extreme warm day temperatures, the study identified southern plateau, east and west coast plains, and north-eastern India as highly vulnerable. Using copula probability model, study showed that increase in ExWD from 20 to 60% may increase the probability of 5% or more yield loss from 17 to 53% for Kharif cereals, 11 to 43% for Rabi cereals and 19 to 63% for wheat crop. The results may be used for devising zone specific adaptation strategies. [ABSTRACT FROM AUTHOR]

Heat stress, a major threat to rice (Oryza sativa) production across China, would tend to increase in frequency and intensity under warming climate. Unlike probabilistic analysis via a univariate character, heat stress events, characterized by three variables (i.e., duration, peak and accumulated detrimental intensity), were identified in the past years. Nine distribution functions (i.e., Beta, Cauchy, Logistic, Normal, Exponential, Gamma, Lognormal, Weibull and Generalized Extreme Value) were firstly introduced and compared to select the best-fit marginal distribution of univariable by using Kolmogorov-Smirnov test, and seven copula functions (i.e., Normal and t, Gumbel-Hougaard, Clayton, Frank, Joe, Ali-Mikhail-Haq) were applied in the distributions of multivariables by Akaike Information Criterion statistics. It was obvious that higher magnitude was in the eastern parts in the context of heat stress frequency and characteristic variables. Critical values of heat stress variables corresponding to the certain return periods (i.e. 5, 10, 20 and 50 years) successively expanded in intensity and spatial scope. Inter-correlations of heat stress variables were significant, enlightening the importance of copula in connecting heat stress variables. The combined and co-occurrence bivariate and trivariate return period at certain univariate value corresponding to the given return periods, were consistent at the spatial scale. Accordingly, it was highlighted that eastern parts, especially Zhejiang, central-northern Fujian and eastern Jiangxi, were prone to heat stress, as a consequence of not only univariate but also multivariate probabilistic analysis. These results can be helpful in quantitatively assessing the vulnerability of rice to heat stress and provide us desired information of prevention strategies for heat stress. [ABSTRACT FROM AUTHOR]

Floods have changed in a complex manner, triggered by the changing environment (i.e., intensified human activities and global warming). Hence, for better flood control and mitigation in the future, bivariate frequency analysis of flood and extreme precipitation events is of great necessity to be performed within the context of changing environment. Given this, in this paper, the Pettitt test and wavelet coherence transform analysis are used in combination to identify the period with transformed flood-generating mechanism. Subsequently, the primary and secondary return periods of annual maximum flood (AMF) discharge and extreme precipitation (Pr) during the identified period are derived based on the copula. Meanwhile, the conditional probability of occurring different flood discharge magnitudes under various extreme precipitation scenarios are estimated using the joint dependence structure between AMF and Pr. Moreover, Monte Carlo-based algorithm is performed to evaluate the uncertainties of the above copula-based analyses robustly. Two catchments located on the Loess plateau are selected as study regions, which are Weihe River Basin (WRB) and Jinghe River Basin (JRB). Results indicate that: (1) the 1994-2014 and 1981-2014 are identified as periods with transformed flood-generating mechanism in the WRB and JRB, respectively; (2) the primary and secondary return periods for AMF and Pr are examined. Furthermore, chance of occurring different AMF under varying Pr scenarios also be elucidated according to the joint distribution of AMF and Pr. Despite these, one thing to notice is that the associate uncertainties are considerable, thus greatly challenges measures of future flood mitigation. Results of this study offer technical reference for copula-based frequency analysis under changing environment at regional and global scales. [ABSTRACT FROM AUTHOR]

We present a novel methodology to compute conditional risk measures when the conditioning event depends on a number of random variables. Specifically, given a random vector $$(\mathbf {X},Y)$$ , we consider risk measures that express the risk of Y given that $$\mathbf {X}$$ assumes values in an extreme multidimensional region. In particular, the considered risky regions are related to the AND, OR, Kendall and Survival Kendall hazard scenarios that are commonly used in environmental literature. Several closed formulas are considered (especially in the AND and OR scenarios). An application to spatial risk analysis involving real data is discussed. [ABSTRACT FROM AUTHOR]

Many recent works show that copulas turn out to be useful in a variety of different applications, especially in environmental sciences. Here the variables of interest are usually continuous, being times, lengths, weights, and so on. Unfortunately, the corresponding observations may suffer from (instrumental) adjustments and truncations, and eventually may show several repeated values (i.e., ties). In turn, on the one hand, a tricky issue of identifiability of the model arises, and, on the other hand, the assessment of the risk may be adversely affected. A possible remedy is to adopt suitable randomization procedures: here three different strategies are outlined. The goal of the work is to carry out a simulation study in order to evaluate the effects of the randomization of multivariate observations when ties are present. In particular, it is investigated whether, how, and to what extent, the randomization may change the estimation of the structural risk: for this purpose, a coastal engineering example will be used, as archetypical of a broad class of models and problems in engineering applications. Practical advices and warnings about the use of randomization techniques are hence given. [ABSTRACT FROM AUTHOR]

In this study, bivariate hydrologic risk analysis was conducted based on the daily streamflow discharge at the Xianyang station on the Wei River. This bivariate hydrologic risk analysis was conducted based on copula methods, in which the bivariate hydrologic frequency was firstly quantified through copulas, and the bivariate hydrologic risk analysis was then characterized based on the joint return period of flood pairs. The maximum likelihood estimation (MLE) and the method-of-moments-like (MOM) estimator were compared in estimating the unknown parameters in copula. The results showed that the Gumbel-Hougaard copula was most appropriate for modelling the dependence for all three flood pairs, in which the parameter of the copula for flood peak-volume was estimated by MLE and the parameters of the copulas for flood peak-duration and volume-duration were needed to be obtained by MOM. The bivariate hydrologic risk values are then obtained based on the AND-joint return period. The results show that the bivariate hydrologic values will not decrease until the corresponding volume for a flood is larger than 1.0 × 10 m/s. For the bivariate hydrologic risk for flood peak-duration, the value will decrease quickly when the duration is longer than 5 days. Such bivariate hydrologic risk analysis can provide decision support for hydraulic facility design as well as actual flood control and mitigation. [ABSTRACT FROM AUTHOR]

Reservoir storage plays an important role in water supply during the dry season when precipitation is insufficient. In a watershed where the streams are controlled by reservoirs, drought occurrences depend on not only precipitation variations but also reservoir regulation. In this study, the joint dependence structure of the reservoir storage and its relevant variables of precipitation and/or upstream outflow were analyzed for two cascade reservoirs in a headwater basin of the Huaihe River, China. Correlation analysis indicates that the reservoir storage in October (the end of the wet season) depends highly on the regional precipitation at time scales of several months, e.g., 7 months for the upstream and 9 months for the downstream. Additionally, the downstream storage is correlated with outflow from the upstream reservoir at the 5-month timescale significantly. For estimation of the joint probability of pairs of the storage and its relevant variables, univariate marginal distributions and bivariate copula were appropriately selected in terms of statistical tests. The bivariate return period of $$T(X < x,Y < y)$$ and $$T(X \le x,Y \ge y)$$ and the conditional probability of $$P(Y \ge y|X \le x)$$ were estimated by using the selected Clayton copula. The results from contour lines of the bivariate return period demonstrate that the probability of drought occurrences affected by both reservoir storage and precipitation/outflow is smaller than that by either of the variables. Meanwhile, the concurrent drought probability between precipitation and reservoir storage in the upstream is higher than that in the downstream. The estimated conditional probability offers useful information on how much the regular storage could be remained under some specified drought levels of precipitation/upstream outflow. Therefore, the results are helpful for improving the operation strategies of the cascade reservoirs for the adaptive management of drought under different climate variations. [ABSTRACT FROM AUTHOR]

Uncertainty analysis of radar rainfall enables stakeholders and users have a clear knowledge of the possible uncertainty associated with the rainfall products. Long-term empirical modeling of the relationship between radar and gauge measurements is an efficient and practical method to describe the radar rainfall uncertainty. However, complicated variation of synoptic conditions makes the radar-rainfall uncertainty model based on historical data hard to extend in the future state. A promising solution is to integrate synoptic regimes with the empirical model and explore the impact of individual synoptic regimes on radar rainfall uncertainty. This study is an attempt to introduce season, one of the most important synoptic factor, into the radar rainfall uncertainty model and proposes a seasonal ensemble generator for radar rainfall using copula and autoregressive model. We firstly analyze the histograms of rainfall-weighted temperature, the radar-gauge relationships, and Box and Whisker plots in different seasons and conclude that the radar rainfall uncertainty has strong seasonal dependence. Then a seasonal ensemble generator is designed and implemented in a UK catchment under a temperate maritime climate, which can fully model marginal distribution, spatial dependence, temporal dependence and seasonal dependence of radar rainfall uncertainty. To test its performance, 12 typical rainfall events (4 for each season) are chosen to generate ensemble rainfall values. In each time step, 500 ensemble members are produced and the values of 5th to 95th percentiles are used to derive the uncertainty bands. Except several outliers, the uncertainty bands encompass the observed gauge rainfall quite well. The parameters of the ensemble generator vary considerably for each season, indicating the seasonal ensemble generator reflects the impact of seasons on radar rainfall uncertainty. This study is an attempt to simultaneously consider four key features of radar rainfall uncertainty and future study will investigate their impacts on the outputs of hydrological models with radar rainfall as input or initial conditions. [ABSTRACT FROM AUTHOR]

In environmental applications, the estimation of the structural risk is fundamental. Beside the knowledge of the physical response of the structure to the loads of interest, a statistical model for the behavior of the input variables is generally required, possibly accounting for the fact that these variables are usually non-independent. For this purpose, a multivariate approach based on copulas is adopted in this paper. In particular, the following classes of dependence structures are often used in practice: the Extreme Value copulas, and the Archimedean copulas. However, how to properly select a suitable Extreme Value or Archimedean copula is a problem open to many solutions. As a viable one, this work shows how two semi-parametric approximations to, respectively, Extreme Value and Archimedean copulas, can be used in order to circumvent the troublesome selection issue in the estimation of the structural risk. Suitable simulation studies are performed, in order to check and evaluate the performance of the approximating techniques introduced in this work. [ABSTRACT FROM AUTHOR]

Risk assessment plays an important role in disaster risk management. Existing multi-hazard risk assessment models are often qualitative or semi-quantitative in nature and used for comparative study of regional risk levels. They cannot estimate directly probability of disaster losses from the joint impact of several hazards. In this paper, a quantitative approach of multi-hazard risk assessment based on vulnerability surface and joint return period of hazards is put forward to assess the risk of crop losses in the Yangtze River Delta region of China. The impact of strong wind and flood, the two most prominent agricultural hazards in the area, is analyzed. The multi-hazard risk assessment process consists of three steps. First, a vulnerability surface, which denotes the functional relationship between the intensity of the hazards and disaster losses, was built using the crop losses data for losses caused by strong wind and flood in the recent 30 years. Second, the joint probability distribution of strong wind and flood was established using the copula functions. Finally, risk curves that show the probability of crop losses in this multi-hazard context at four case study sites were calculated according to the joint return period of hazards and the vulnerability surface. The risk assessment result of crop losses provides a useful reference for governments and insurance companies to formulate agricultural development plans and analyze the market of agricultural insurance. The multi-hazard risk assessment method developed in this paper can also be used to quantitatively assess multi-hazard risk in other regions. [ABSTRACT FROM AUTHOR]

Complex phenomena in environmental sciences can be conveniently represented by several inter-dependent random variables. In order to describe such situations, copula-based models have been studied during the last year. In this paper, we consider a novel family of bivariate copulas, called exchangeable Marshall copulas. Such copulas describe both positive and (upper) tail association between random variables. Specifically, inference procedures for the family of exchangeable Marshall copulas are introduced, based on the estimation of their (univariate) generator. Moreover, the performance of the proposed methodologies is shown in a simulation study. Finally, an illustration describes how the proposed procedures can be useful in a hydrological application. [ABSTRACT FROM AUTHOR]

The hourly rainfall stochastic model SHYPRE is based on the simulation of descriptive variables. It generates long series of hourly rainfall and enables an at-site empirical estimation of distribution quantiles over France. The present study focuses on the improvement of the rainfall generator by modelling storm characteristics dependence by the copula approach. An evaluation framework is proposed to evaluate the goodness-of-fit of a given method over a territory with a particular care for the extreme part of the distribution. It is used to illustrate the impact of the copula choice on the estimation of rainfall quantiles. Contrary to Clayton copula, both the Gumbel's and Frank's permit to improve significantly the performance of the model in the sub-daily rainfall generation. According to our criteria, the final version of SHYPRE proposes a better estimation of rainfall quantiles than the classical extreme value distributions. [ABSTRACT FROM AUTHOR]

This study investigated the utility of two meta-heuristic algorithms to estimate parameters of copula models and for derivation of drought severity-duration-frequency (S-D-F) curves. Drought is a natural event, which has huge impact on both the society and the natural environment. Drought events are mainly characterized by their severity, duration and intensity. The study adopts standardized precipitation index for drought characterization, and copula method for multivariate risk analysis of droughts. For accurate estimation of copula model parameters, two meta-heuristic methods namely genetic algorithm and particle swarm optimization are applied. The proposed methodology is applied to a case study in Trans Pecos, an arid region in Texas, USA. First, drought severity and duration are separately modeled by various probability distribution functions and then the best fitted models are selected for copula modeling. For modeling the joint dependence of drought variables, different classes of copulas, namely, extreme value copulas, Plackett and Student's t copulas are employed and their performance is evaluated using standard performance measures. It is found that for the study region, the Gumbel-Hougaard copula is the best fitted copula model as compared to the others and is used for the development of drought S-D-F curves. Results of the study suggest that the meta-heuristic methods have greater utility in copula-based multivariate risk assessment of droughts. [ABSTRACT FROM AUTHOR]

The present paper reports on the use of copula functions to describe the distribution of discrete spatial data, e.g. count data from environmental mapping or areal data analysis. In particular, we consider approaches to parameter point estimation and propose a fast method to perform approximate spatial prediction in copula-based spatial models with discrete marginal distributions. We assess the goodness of the resulting parameter estimates and predictors under different spatial settings and guide the analyst on which approach to apply for the data at hand. Finally, we illustrate the methodology by analyzing the well-known Lansing Woods data set. Software that implements the methods proposed in this paper is freely available in Matlab language on the author's website. [ABSTRACT FROM AUTHOR]

Probabilistic characteristics of hydrological droughts in a basin are closely related to the variability and availability of water resources of the basin. The East River basin in China is the main source for water supply for mega cities in the Pearl River Delta and cities in the vicinity of the Delta, such as Hong Kong. The water supply is subject to the vagaries of weather and water resources in the basin exhibit probabilistic characteristics. Using daily streamflow data for a period of 1975-2009 from 4 hydrological stations in the East River basin, this study attempts to determine probabilistic characteristics of hydrological droughts using copula functions. The bivariate quantile curves of the secondary return periods for hydrological drought of all the hydrological stations have been built and the results a higher risk of hydrological droughts in the upper East River basin. Furthermore, water resources should be managed by considering the entire East River basin in order to sustain the regional socio-economic development, and the extreme value copula has been used to describe the extreme drought events in the East River basin. [ABSTRACT FROM AUTHOR]

The study of environmental problems usually requires the description of variables with different nature and the assessment of relations between them. In this work, an algorithm for flexible estimation of the joint density for a circular-linear variable is proposed. The method is applied for exploring the relation between wind direction and SO concentration in a monitoring station close to a power plant located in Galicia (NW-Spain), in order to compare the effectiveness of precautionary measures for pollutants reduction in two different years. [ABSTRACT FROM AUTHOR]

The spatialCopula toolbox contains a set of Matlab functions that provides utilities for copula-based analysis of spatially referenced data, a topic which has re cently attracted much attention in spatial statistics. These tools have been developed to support the work flow in parameter estimation, spatial interpolation and visualization. They offer flexible and user-friendly software for dealing with non-Gaussian and extreme value data that possibly contain a spatial trend or geometric anisotropy. The objective of this paper is to give an introduction to the concept behind the software and to outline the functionality of the toolbox. We illustrate its usefulness by analyzing a data set here referred to as the Gomel data set, which includes moderately skewed radioactivity measurements in the region of Gomel, Belarus. The source codes are freely available in Matlab language on the author's website (). [ABSTRACT FROM AUTHOR]

With the increase of both magnitude and frequency of hydrological extreme events such as drought and flooding, the significance of adequately modeling hydrological extreme events is fully recognized. Estimation of extreme rainfall/flood for various return periods is of prime importance for hydrological design or risk assessment. However, due to knowledge and data limitation, uncertainty involved in extrapolating beyond available data is huge. In this paper, different sources of uncertainty in statistical modeling of extreme hydrological events are studied in a systematic way. This is done by focusing on several key uncertainty sources using three different case studies. The chosen case studies highlight a number of projects where there have been questions regarding the uncertainty in extreme rainfall/flood estimation. The results show that the uncertainty originated from the methodology is the largest and could be >40% for a return period of 200 years, while the uncertainty caused by ignoring the dependence among multiple hydrological variables seems the smallest. In the end, it is highly recommended that uncertainty in modeling extreme hydrological events be fully recognized and incorporated into a formal hydrological extreme analysis. [ABSTRACT FROM AUTHOR]