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1.
Regional bivariate modeling of droughts using L-comoments and copulas   总被引：1，自引：0，他引：1  
The regional bivariate modeling of drought characteristics using the copulas provides valuable information for water resources management and drought risk assessment. The regional frequency analysis (RFA) can specify the similar sites within a region using L-comoments approach. One of the important steps in the RFA is estimating regional parameters of the copula function. In the present study, an optimization-based method along with the adjusted charged system search are introduced and applied to estimate the regional parameters of the copula models. The capability of the proposed methodology is illustrated by copula functions on drought events. Three commonly used copulas containing Clayton, Frank and Gumbel are employed to derive the joint distribution of drought severity and duration. The result of the new method are compared to the method of moments and after applying several goodness-of-fit tests, the results indicate that the new method provides higher accuracy than the classic one. Furthermore, the results of the upper tail dependence coefficient indicate that the Gumbel copula is the best-fitted copula among the other ones for modeling drought characteristics.  相似文献   

2.
This study presents copula‐based multivariate probabilistic approach to model severity–duration–frequency (S‐D‐F) relationship of drought events in western Rajasthan, India. Drought occurrences are analysed using standardized precipitation index computed on monthly mean areal precipitation, aggregated at a time scale of 6 months. After testing with a series of probability density functions, the drought variable severity is found to be better represented with log‐normal distribution, whereas duration is well fitted with exponential distribution. Four different classes of bivariate copulas – Archimedean, extreme value, Plackett, and elliptical families are evaluated for modelling joint distribution of drought characteristics. It is observed that the extreme value copula – Gumbel–Hougaard copula – performed better as compared with other classes of copulas, based on results of various statistical tests and upper tail dependence coefficient. The joint distribution obtained from best performing copula is then employed to determine conditional return period and to derive drought severity‐duration‐frequency (S‐D‐F) curves for the study region. The results of the study suggests that the copula method can be used effectively to derive the drought S‐D‐F curves, which can be helpful in planning and adopting suitable drought mitigation strategies in drought‐prone areas. Copyright © 2011 John Wiley & Sons, Ltd.  相似文献   

3.
In recent years, the bivariate frequency analysis of drought duration and severity using independent drought events and copula functions has been under extensive application. Meanwhile, emphasis on the procedure of independent drought data collection leads to the omission of the actual potential of short-term extreme droughts within a long-term independent drought. However, a long-term individual continuous drought as an Unconnected Drought Runs can be considered as a combination of short-term Connected Drought Runs. Thus, an advanced and new procedure of data collection in the bivariate drought characteristics analysis has been developed in this study. The results indicated a high relative advantage of the new proposed procedure in analysing bivariate drought characteristics (i.e., drought duration and severity frequency analysis). This advantage has been reflected in the more appropriate determination of the best copula and significant reduction in the uncertainty of bivariate drought frequency analysis.  相似文献   

4.
Droughts are one of the normal and recurrent climatic phenomena on Earth. However, recurring prolonged droughts have caused far‐reaching and diverse impacts because of water deficits. This study aims to investigate the hydrological droughts of the Yellow River in northern China. Since drought duration and drought severity exhibit significant correlation, a bivariate distribution is used to model the drought duration and severity jointly. However, drought duration and drought severity are often modelled by different distributions; the commonly used bivariate distributions cannot be applied. In this study, a copula is employed to construct the bivariate drought distribution. The copula is a function that links the univariate marginal distributions to form the bivariate distribution. The bivariate return periods are also established to explore the drought characteristics of the historically noticeable droughts. The results show that the return period of the drought that occurred in late 1920s to early 1930s is 105 years. The significant 1997 dry‐up phenomenon that occurred in the downstream Yellow River (resulting from the 1997–1998 drought) only has a return period of 4·4 years and is probably induced by two successive droughts and deteriorated by other factors, such as human activities. Copyright © 2007 John Wiley & Sons, Ltd.  相似文献   

5.
This study aims to model the joint probability distribution of drought duration, severity and inter-arrival time using a trivariate Plackett copula. The drought duration and inter-arrival time each follow the Weibull distribution and the drought severity follows the gamma distribution. Parameters of these univariate distributions are estimated using the method of moments (MOM), maximum likelihood method (MLM), probability weighted moments (PWM), and a genetic algorithm (GA); whereas parameters of the bivariate and trivariate Plackett copulas are estimated using the log-pseudolikelihood function method (LPLF) and GA. Streamflow data from three gaging stations, Zhuangtou, Taian and Tianyang, located in the Wei River basin, China, are employed to test the trivariate Plackett copula. The results show that the Plackett copula is capable of yielding bivariate and trivariate probability distributions of correlated drought variables.  相似文献   

6.
A new method of parameter estimation in data scarce regions is valuable for bivariate hydrological extreme frequency analysis. This paper proposes a new method of parameter estimation (maximum entropy estimation, MEE) for both Gumbel and Gumbel–Hougaard copula in situations when insufficient data are available. MEE requires only the lower and upper bounds of two hydrological variables. To test our new method, two experiments to model the joint distribution of the maximum daily precipitation at two pairs of stations on the tributaries of Heihe and Jinghe River, respectively, were performed and compared with the method of moments, correlation index estimation, and maximum likelihood estimation, which require a large amount of data. Both experiments show that for the Ye Niugou and Qilian stations, the performance of MEE is nearly identical to those of the conventional methods. For the Xifeng and Huanxian stations, MEE can capture information indicating that the maximum daily precipitation at the Xifeng and Huanxian stations has an upper tail dependence, whereas the results generated by correlation index estimation and maximum likelihood estimation are unreasonable. Moreover, MEE is proved to be generally reliable and robust by many simulations under three different situations. The Gumbel–Hougaard copula with MEE can also be applied to the bivariate frequency analysis of other extreme events in data‐scarce regions.  相似文献   

7.
This study presents spatio-temporal analysis of droughts in one of the most drought prone region in India–western Rajasthan and develops drought intensity-area-frequency curves for the region. The meteorological drought conditions are analyzed using 6-month standardized precipitation index (SPI-6) estimated at spatial resolution of 0.5° × 0.5°. Spatio-temporal analysis of SPI-6 indicates increase in frequency of droughts at the central part of the region. The non-parametric Mann–Kendall test for seasonal trend analysis showed increase in number of grids under drought during the study period. Further, bivariate frequency analysis of drought characteristics—intensity and areal extent is carried out using copula methods. For modeling joint dependence between drought variables, three copula families namely Gumbel-Hougaard, Frank and Plackett copulas are evaluated. Based on goodness-of-fit as well as upper tail dependence tests, it is found that the Gumbel-Hougaard copula best represents the drought properties. The copula-based joint distribution is used to compute conditional return periods and drought intensity–area–frequency (I–A–F) curves. The I–A–F curves could be helpful in risk evaluation of droughts in the region.  相似文献   

8.
Multivariate modeling of droughts using copulas and meta-heuristic methods   总被引：3，自引：3，他引：0  
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.  相似文献   

9.
Although water resources management practices recently use bivariate distribution functions to assess drought severity and its frequency, the lack of systematic measurements is the major hindrance in achieving quantitative results. This study aims to suggest a statistical scheme for the bivariate drought frequency analysis to provide comprehensive and consistent drought severities using observed rainfalls and their uncertainty using synthesized rainfalls. First, this study developed a multi-variate regression model to generate synthetic monthly rainfalls using climate variables as causative variables. The causative variables were generated to preserve their correlations using copula functions. This study then focused on constructing bivariate drought frequency curves using bivariate kernel functions and estimating their confidence intervals from 1,000 likely replica sets of drought frequency curves. The confidence intervals achieved in this study may be useful for making a comprehensive drought management plan through providing feasible ranges of drought severity.  相似文献   

10.
Asymmetric copula in multivariate flood frequency analysis   总被引：2，自引：0，他引：2  
The univariate flood frequency analysis is widely used in hydrological studies. Often only flood peak or flood volume is statistically analyzed. For a more complete analysis the three main characteristics of a flood event i.e. peak, volume and duration are required. To fully understand these variables and their relationships, a multivariate statistical approach is necessary. The main aim of this paper is to define the trivariate probability density and cumulative distribution functions. When the joint distribution is known, it is possible to define the bivariate distribution of volume and duration conditioned on the peak discharge. Consequently volume–duration pairs, statistically linked to peak values, become available. The authors build trivariate joint distribution of flood event variables using the fully nested or asymmetric Archimedean copula functions. They describe properties of this copula class and perform extensive simulations to highlight differences with the well-known symmetric Archimedean copulas. They apply asymmetric distributions to observed flood data and compare the results those obtained using distributions built with symmetric copula and the standard Gumbel Logistic model.  相似文献   

11.
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.  相似文献   

12.
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13.
As an alternative to the commonly used univariate flood frequency analysis, copula frequency analysis can be used. In this study, 58 flood events at the Litija gauging station on the Sava River in Slovenia were analysed, selected based on annual maximum discharge values. Corresponding hydrograph volumes and durations were considered. Different bivariate copulas from three families were applied and compared using different statistical, graphical and upper tail dependence tests. The parameters of the copulas were estimated using the method of moments with the inversion of Kendall's tau. The Gumbel–Hougaard copula was selected as the most appropriate for the pair of peak discharge and hydrograph volume (Q‐V). The same copula was also selected for the pair hydrograph volume and duration (V‐D), and the Student‐t copula was selected for the pair of peak discharge and hydrograph duration (Q‐D). The differences among most of the applied copulas were not significant. Different primary, secondary and conditional return periods were calculated and compared, and some relationships among them were obtained. Copyright © 2014 John Wiley & Sons, Ltd.  相似文献   

14.
Uncertainty and variability in bivariate modeling of hydrological droughts   总被引：2，自引：1，他引：1  
There are two kinds of uncertainty factors in modeling the bivariate distribution of hydrological droughts: the alteration of predefined critical ratios for pooling droughts and excluding minor droughts and the temporal variability of univariate and/or bivariate characteristics of droughts due to the impact of human activities. Daily flow data covering a period of 56 hydrological years from two gauging stations from a humid region in South China are used. The influences of alterations of threshold values of flow and critical ratios of pooling droughts and excluding minor droughts on drought properties are analyzed. Six conventional univariate models and three Archimedean copulas are employed to fit the marginal and joint distributions of drought properties, the Kolmogorov–Smirnov and Anderson–Darling methods are used for testing the goodness-of-fit of the univariate model, and the Cramer-von Mises method based on Rosenblatt’s transform is applied for the test of the bivariate model. The change point analysis of the copula parameter of bivariate distribution of droughts is first made. Results demonstrate that both the statistical characteristics of each drought property and their bivariate joint distributions are sensitive to the critical ratio of excluding minor droughts. A model can be selected to fit the marginal distribution for drought deficit volume or maximum deficit, but it is not determined for drought duration with the lower ratios of the pooling and excluding droughts. The statistical uncertainty of drought duration makes the modeling of bivariate joint distribution of drought duration and deficit volume or of drought duration and maximum deficit undermined. Change points significantly occurred in the period from the late 1970s to the middle 1980s for a single drought property and the copula parameter of their joint distribution due to the impact of human activities. The difference between two subseries separated by the change point is remarkable in the magnitudes of drought properties and the joint return periods. A copula function can be selected to optimally fit the bivariate distribution, provided that the critical ratios of pooling and excluding droughts are great enough such as the optimal value of 0.4 in the case study. It is valuable that the modeling and designing of the bivariate joint correlation and distribution of drought properties can be performed on the subseries separated by the change point of the copula parameter.  相似文献   

15.
The paper aims to develop researches on the spatial variability of heavy rainfall events estimation using spatial copula analysis. To demonstrate the methodology, short time resolution rainfall time series from Stuttgart region are analyzed. They are constituted by rainfall observations on continuous 30 min time scale recorded over a network composed by 17 raingages for the period July 1989–July 2004. The analysis is performed aggregating the observations from 30 min up to 24 h. Two parametric bivariate extreme copula models, the Husler–Reiss model and the Gumbel model are investigated. Both involve a single parameter to be estimated. Thus, model fitting is operated for every pair of stations for a giving time resolution. A rainfall threshold value representing a fixed rainfall quantile is adopted for model inference. Generalized maximum pseudo-likelihood estimation is adopted with censoring by analogy with methods of univariate estimation combining historical and paleoflood information with systematic data. Only pairs of observations greater than the threshold are assumed as systematic data. Using the estimated copula parameter, a synthetic copula field is randomly generated and helps evaluating model adequacy which is achieved using Kolmogorov Smirnov distance test. In order to assess dependence or independence in the upper tail, the extremal coefficient which characterises the tail of the joint bivariate distribution is adopted. Hence, the extremal coefficient is reported as a function of the interdistance between stations. If it is less than 1.7, stations are interpreted as dependent in the extremes. The analysis of the fitted extremal coefficients with respect to stations inter distance highlights two regimes with different dependence structures: a short spatial extent regime linked to short duration intervals (from 30 min to 6 h) with an extent of about 8 km and a large spatial extent regime related to longer rainfall intervals (from 12 h to 24 h) with an extent of 34 to 38 km.  相似文献   

16.
A bivariate pareto model for drought   总被引：2，自引：2，他引：0  
Univariate Pareto distributions have been so widely used in hydrology. It seems however that bivariate or multivariate Pareto distributions have not yet found applications in hydrology, especially with respect to drought. In this note, a drought application is described by assuming a bivariate Pareto model for the joint distribution drought durations and drought severity in the State of Nebraska. Based on this model, exact distributions are derived for the inter arrival time, magnitude and the proportion of droughts. Estimates of 2, 5, 10, 20, 50 and 100 year return periods are derived for the three variables, drought duration, drought severity and the pairwise combinations: (drought duration, drought severity), (inter arrival time of drought, proportion of drought) and (drought duration, drought magnitude). These return period estimates could have an important role in hydrology, for example, with respect to measures of vegetation water stress for plants in water-controlled ecosystems.  相似文献   

17.
This study aims to model the joint probability distribution of periodic hydrologic data using meta-elliptical copulas. Monthly precipitation data from a gauging station (410120) in Texas, US, was used to illustrate parameter estimation and goodness-of-fit for univariate drought distributions using chi-square test, Kolmogorov–Smirnov test, Cramer-von Mises statistic, Anderson-Darling statistic, modified weighted Watson statistic, and Liao and Shimokawa statistic. Pearson’s classical correlation coefficient r n , Spearman’s ρ n, Kendall’s τ, Chi-Plots, and K-Plots were employed to assess the dependence of drought variables. Several meta-elliptical copulas and Gumbel-Hougaard, Ali-Mikhail-Haq, Frank and Clayton copulas were tested to determine the best-fit copula. Based on the root mean square error and the Akaike information criterion, meta-Gaussian and t copulas gave a better fit. A bootstrap version based on Rosenblatt’s transformation was employed to test the goodness-of-fit for meta-Gaussian and t copulas. It was found that none of meta-Gaussian and t copulas considered could be rejected at the given significance level. The meta-Gaussian copula was employed to model the dependence, and these results were found satisfactory.  相似文献   

18.
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19.
Subimal Ghosh 《水文研究》2010,24(24):3558-3567
The rainfall patterns of neighbouring meteorological subdivisions of India are similar because of similar climatological and geographical characteristics. Analysing the rainfall pattern separately for these meteorological subdivisions may not always capture the correlation and tail dependence. Furthermore, generating the multivariate rainfall data separately may not preserve the correlation. In this study, copula method is used to derive the bivariate distribution of monsoon rainfall in neighbouring meteorological subdivisions. Different Archimedean copulas are used for this purpose and the best copula is selected based on nonparametric test and tail dependence coefficient. The fitted copula is then applied to derive the bivariate distribution, joint return period and conditional distribution. Bivariate rainfall data is generated with the fitted copula and it is observed with the increase of sample size, the generated data is able to capture the correlation as well as tail dependence. The methodology is demonstrated with the case study of two neighbouring meteorological subdivisions of North‐East India: Assam and Meghalaya meteorological subdivision and Nagaland, Manipur, Mizoram and Tripura meteorological subdivision. Copyright © 2010 John Wiley & Sons, Ltd.  相似文献   

20.
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.  相似文献   

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