From practical and theoretical viewpoints, performance analysis of communications with correlated fading channels is important. In this study, the authors exploit a novel approach based on Copula ...function concept to investigate the impact of correlation of Rayleigh fading channels on communication performances. One of the most convenient ways to describe the dependence between several variables is using Copula functions. For this purpose, by applying the Farlie–Gumbel–Morgenstern Copula function, they derive closed-form expressions for outage probability as well as coverage region in a wireless multiple access channel. It is shown that the fading correlation improves the outage probability and coverage region for negative dependence structure. Specifically, whenever the dependence structure tends to negative values, the outage and coverage region performance improvement is increased. Finally, the efficiency of the analytical results is illustrated numerically.
Time series clustering with a dissimilarity matrix based on tail dependence coefficients estimated by copula functions has been proposed in 2011 by De Luca and Zuccolotto, who used a two-step ...procedure allowing to resort to the k-means algorithm. The possibility to carry out hierarchical clustering directly on the dissimilarity matrix is still an open issue and the main concerns are relative to the meaning of the most common linkage methods in the context of tail dependence. In this paper, in a multivariate copula approach, we propose a linkage method based on the tail dependence coefficients between the clusters that are agglomerated at each iteration of the hierarchical clustering algorithms.
•Agricultural drought risk and its dynamic evolution characteristics are fully explored.•The 4-month is the most timescale for SPI in monitoring agricultural drought in the PRB.•Risk factors method ...is more suitable than return period way in assessing agricultural drought risk.•The agricultural drought risk of the PRB generally showed an increasing trend except for the PRD.
Assessment of agricultural drought risk is significant for risk division and management. Nevertheless, the drought risk dynamic evolution characteristics have not been revealed. To this end, the agricultural drought conditions are characterized by the standardized precipitation index (SPI), and the time scale of SPI is determined based on agricultural damage data. The joint return periods of various drought severities and durations under different agricultural drought scenarios are calculated by using copula functions. Moreover, drought risk factors (resilience, vulnerability, and exposure) are also used to characterize drought risk. Subsequently, based on the moving window, the joint return period and risk factors in each window are calculated, and agricultural drought dynamics are explored. The Pearl River Basin (PRB) is selected as a case study. Results indicated that: (1) the 4-month most appropriate timescale for the SPI in characterizing agricultural drought based on agricultural damage data in the PRB; (2) risk factors method is more suitable than joint return period in assessing agricultural drought risk; (3) most of the PRB exhibit a significant increasing agricultural drought risk, while the drought risk of the Pearl River Delta has a decreased trend within the past 50 years. Generally, this study show new insights into agricultural drought risk assessment, thus promoting local agricultural drought preparedness and mitigation.
•A new fully quantitative assessment framework for multi-hazard risk assessment.•Joint probability of contributing hazards including statistical inter-dependencies.•Fully hydrodynamic modelling of ...interactive compound flooding processes.
Multi-hazard risk assessment may provide comprehensive analysis of the impact of multiple hazards but still needs to resolve major challenges in three aspects: (1) proper consideration of hazard inter-dependency, (2) physically based modelling of hazard interactions, and (3) fully quantitative risk assessment to show the probability of loss. Compound flooding is a typical multi-hazard problem that involves the concurrence of multiple hazard drivers, e.g. heavy rainfall, extreme river flow, and storm surge. These hazard drivers may result from the same weather system and are thus statistically inter-dependent, physically overlayed and interacted in the same region. This paper aims to address the mentioned challenges and develop an integrated assessment framework to quantify compound flood risk. The framework is constructed based on the three typical components in disaster risk assessment, i.e. hazard, vulnerability and exposure analysis. In hazard analysis, joint probability and return period distributions of the three hazard drivers of compound flooding are estimated using Copula functions with hazard dependency analysis, which are then used to generate random multi-hazard events to drive a 2D high-performance hydrodynamic model to produce probabilistic inundation maps and frequency-inundation curves. Vulnerability and exposure analysis provides damage functions of the elements at risk, which are used to quantify multi-hazard risk with the frequency-inundation curves. The framework is applied in the Greater London and its downstream Thames estuary to demonstrate its capability to analyse hazard interactions and inter-dependencies to produce fully quantitative risk assessment results such as risk curves quantifying the probability of loss and risk maps illustrating the annual expected loss of residential buildings.
•Simulate the interaction of temporal occurrence of rainfall-runoff-storm surge.•Using joint probability and Copula functions to reduce errors of coupled modeling.•Enhance the underlying simulation ...of integrated inland and coastal flooding.
The formation of urban coastal flooding is mainly ruled by the interaction between rainfall-runoff and storm surge. This study aims to advance the understanding of coastal urban flood mechanism by developing an integrated modeling and multivariate analysis framework, which involves a hydrologic model (Storm Water Management Model (SWMM)), as the core model, coupled with a coastal hydrodynamic model (Delft3D). The uncertainty associated with the flood depth prediction by integrated models is analyzed using the multivariate Gaussian Copula. The performance of the integrated modeling framework is evaluated for the Chittagong City of Bangladesh, which has experienced extreme and frequent coastal urban floods. Results from modeling indicate that changes in the tidal phase of coastal urban flooding alter the flood’s duration and depth. The intensity of compound flooding is higher for the co-occurrence of rainfall and surge peaks than the occurrence of both events in succession. The average flood duration and depth can be increased by about 2.5 h and 0.24 m, respectively, during compound events. When the storm surge occurs during the transition phase, between high/low tides (2–4 h before peak low/high tide), the duration of flood extends due to longer surge duration (4–4.5 h). Finally, the multivariate Gaussian Copula model adjusts the integrated modeling outputs and enhances the skill to predict the inundation depth by 4.6–24.3%. The findings of this study are critical for a better understanding of coastal urban flood processes and enhancing the informed decision-making for emergency management and planning in low-lying coastal regions.
•Trends in and dependence between sea level and precipitation increase the probability of compound flooding along US coastlines, most notably along the Southeast coast.•A Bayesian copula-based ...framework captures the uncertainty in the quantification of compound flood frequency.•Precipitation trends play a major role in increasing the uncertainty in compound flood frequency.•To account for non-stationarity, a long historical record is required.
When elevated coastal water levels and heavy precipitation occur simultaneously or in succession, their joint impact may be exacerbated compared to their individual occurrence. Sea-level rise, shifts in precipitation patterns, and the presence of correlation between flooding drivers can increase the frequency of these compound events. In this study, a copula-based Bayesian framework that incorporates the impact of dependence between flooding drivers (i.e., sea level and precipitation) and accounts for the nonstationarity in these hydrologic variables is developed. The framework is used to assess how the individual and combined effects of dependence and nonstationarity influence the frequency and magnitude of compound coastal-pluvial flooding. Furthermore, the Bayesian framework allows for the incorporation of uncertainty, which may arise from shortage of data, model selection, and parameter estimation, into flood frequency analysis. The proposed framework is applied to 32 station pairs across the US coastlines to identify locations that experience the highest risk of compound flooding and to assess the major contributors to uncertainty in the bivariate return period. The results show that the Southeast Atlantic coast experiences the highest increase in the risk of compound flooding, followed by the Gulf and Northeast Atlantic coasts. Sea-level rise and dependence between flooding drivers have a larger influence on bivariate return periods than changes in precipitation patterns. Under a nonstationary framework, precipitation is the major contributor to uncertainty compared to sea level and dependence. In addition, results demonstrate that uncertainty is highly dependent on the length of joint data. This study highlights the importance of incorporating hydrological dependence and trends and associated uncertainty into the quantification of return periods to permit reliable estimation of flood hazards.
Flood control schemes and the scale of drainage facilities are closely related to the occurrence of rainstorms and the tide level of an outer river, so it is necessary to study the probability of the ...occurrence of rainstorms and the tide levels. Based on the daily rainfall and tide level data of Jiangyin station from 1956 to 2018 in the Wuchengxiyu region of Taihu Lake basin, copula functions were used to establish the joint distribution function of annual 1-day, 3-day, 7-day, and 15-day maximum rainfall and the highest tide level of the Yangtze River for different return periods. Based on this information, a risk probability model was constructed to evaluate the flood and tidal risks.
It was found that when the design criteria of rainfall and tide level were similar, the probability of the simultaneous occurrence of rainfall and tide level greater than their respective magnitudes was significantly less than their respective design frequencies. The encounter combination analysis method proposed in this study has a wide application prospect for flood control and drainage design.
Drought is an extremely widespread and common natural disaster that significantly impacts both the socio-economic activities of a community and the natural environment. A comprehensive and accurate ...understanding of hydrological drought is important for the drought prediction and risk management. In this study, a discussion of the characteristics of the historical and future hydrological drought in the Tarim River Basin (TRB) is presented. The research was conducted by modeling the relationship between the ecological water supply and the irrigation water supply using the Community Land Model-Distributed Time Variant Gain Model (CLM-DTVGM) and a copula function. The conclusions are as follows: (1) the Pearson-III probability distribution is the optimal marginal probability distribution for calculating the historical and future runoff from the mountainous region and the Alaer hydrological station; (2) the AMH is the optimal copula function for calculating the joint probability for joint between the ecological and irrigation flows, while the Arch 12, from Bayesian theory, is the optimal copula function under future scenarios (i.e., RCP 2.6, RCP 4.5, and RCP 8.5); and (3) the probability and recurrence period are 0.25 and 4 years, respectively, for the historical hydrological drought, when a multi-year runoff average is used as the threshold. In comparison, the probabilities for the future hydrological drought under the RCP 2.6, RCP 4.5, and RCP 8.5 scenarios are 0.23, 0.15, and 0.18, respectively, which are related to the recurrence periods of 4.3, 7, and 5.6 years, respectively. These results can be used to significantly improve water saving awareness and drought prediction ability in the TRB.
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•The risk of hydrological drought is still very serious in the Tarim River Basin.•Increased agricultural water will increase the risk of hydrological drought in the TRB.•The larger probability of drought, the longer recurrence period of drought in the TRB•Different hydrological sequence couplings need to consider different copula functions.
Drought is projected to intensify under warming climate and will continuously threaten global food security. Assessing the risk of yield loss due to drought is key to developing effective agronomic ...options for farmers and policymakers. However, little has been known about determining the likelihood of reduced crop yield under different drought conditions and defining thresholds that trigger yield loss at the regional scale in Australia. Here, we estimated the dependence of yield variation on drought conditions and identified drought thresholds for 12 Australia’s key wheat producing regions with historical yield data by developing bivariate models based on copula functions. These identified drought thresholds were used to investigate drought statistics under climate change with an ensemble of 36 climate models from Coupled Model Intercomparison Project Phase 6 (CMIP6). We found that drought-induced yield loss was region-specific. The drought thresholds leading to the same magnitude of wheat yield reduction were smaller in regions of southern Queensland and larger in Western Australia mainly due to different climate and soil conditions. Drought will be more frequent and affect larger areas under future warming climates. Based on our results, we advocate for more effective crop management options, particularly in regions where wheat yield is vulnerable to drought in Australia. This will mitigate potential drought impacts on crop production and safeguard global food security.
•A probabilistic analysis method is developed to quantify the probability of yield loss due to drought•The impact of drought on yield loss varies depending on the region•Yield loss is more sensitive to drought in Western Australia than other regions•Drought will be more frequent and affect larger areas under climate change
Water scarcity tends to be aggravated by increase in water demand with the trend of socio-economic development. Thus, non-stationary characteristics of water demand should be identified in water ...resources allocation (WRA) to alleviate the potential influences from water shortages. In this study, a Copula-based interval linear programming model was established for regional WRA. Through combining correlation analysis and an interval linear programming model, this model can: 1) identify interactions between water demand and socio-economic development levels based on Copula functions, 2) explore variations in water shortage with consideration of multiple risk tolerance levels of decision-makers based on Copula sampling, and 3) obtain desired strategies for WRA through an interval linear programming model. Also, Dalian City in China was selected as a case study area to verify the effectiveness of the model for WRA to five water users (i.e., agricultural sector, industrial sector, public service sector, domestic residents, and ecological environment). Considering multiple tolerance levels of decision-makers to water shortage risk, three scenarios (i.e., S1 to S3), indicating 20%, 40%, and 60% of their low, medium, and high tolerance levels, were proposed. The results showed that the correlation between the amount of water demand and indicators of socio-economic development can be described by Clayton and Gaussian Copula functions. The total water supply of Dalian in 2030 would increase by 2.06%–2.65%, compared with the one in 2025. The allocation of water resources across districts was influenced by varied water demand, energy consumption, and risk tolerance levels. Compared with the amount of water allocation in 2025, the contribution of transferred water sources would increase by 6.71% and 7.04% under S1 and S2 in 2030, respectively, and decrease by 14.31% under S3. With the increase of risk tolerance levels of decision-makers, the amount of water supply in Dalian City would gradually decrease.
•A Copula-based programming model is developed for water allocation management.•Decision-makers' tolerance to water shortage risk is incorporated.•Variations of water demand along with socio-economic development are identified.
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