Modelling bivariate rainfall distribution and generating bivariate correlated rainfall data in neighbouring meteorological subdivisions using copula

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.     

The effect of land cover change on duration and severity of high and low flows

Land cover has been increasingly recognized as an important factor affecting hydrologic processes at the basin and regional level. Therefore, improved understanding of how land cover change affects hydrologic systems is needed for better management of water resources. The objective of this study is to investigate the effects of land cover change on the duration and severity of high and low flows by using the Soil Water Assessment Tool model, Bayesian model averaging and copulas. Two basins dominated by different land cover in the Ohio River basin are used as study area in this study. Two historic land covers from the 1950s and 1990s are considered as input to the Soil Water Assessment Tool model, thereby investigating the hydrologic high and low flow response of different land cover conditions of these two basins. The relationships between the duration and severity of both low and high flow are defined by applying the copula method; changes in the frequency of the duration and severity are investigated. The results show that land cover changes affect both the duration and severity of both high and low flows. An increase in forest area leads to a decrease in the duration and severity during both high and low flows, but its impact is highest during extreme flows. The results also show that the land cover changes have had significant influences on changes in the joint return periods of duration and severity of low and high flows. While this study sheds light on the role of land cover change on severity and duration of high and low flow conditions, more studies using various land cover conditions and climate types are required in order to draw more reliable conclusions in the future. Copyright © 2016 John Wiley & Sons, Ltd.     

Time-variant fragility analysis of the bridge system considering time-varying dependence among typical component seismic demands

This paper presents a copula technique to develop time-variant seismic fragility curves for corroded bridges at the system level and considers the realistic time-varying dependence among component seismic demands. Based on material deterioration mechanisms and incremental dynamic analysis, the time-evolving seismic demands of components were obtained in the form of marginal probability distributions. The time-varying dependences among bridge components were then captured with the best fitting copula function, which was selected from the commonly used copula classes by the empirical distribution based analysis method. The system time-variant fragility curves at different damage states were developed and the effects of time-varying dependences among components on the bridge system fragility were investigated. The results indicate the time-varying dependence among components significantly affects the time-variant fragility of the bridge system. The copula technique captures the nonlinear dependence among component seismic demands accurately and easily by separating the marginal distributions and the dependence among them.     

Improved estimators of correlation and R2 for skewed hydrologic data

ABSTRACT

The coefficient of determination R² and Pearson correlation coefficient ρ = R are standard metrics in hydrology for the evaluation of the goodness of fit between model simulations and observations, and as measures of the degree of dependence of one variable upon another. We show that the standard product moment estimator of ρ, termed r, while well-behaved for bivariate normal data, is upward biased and highly variable for bivariate non-normal data. We introduce three alternative estimators of ρ which are nearly unbiased and exhibit much less variability than r for non-normal data. We also document remarkable upward bias and tremendous increases in variability associated with r using both synthetic data and daily streamflow simulations from 905 calibrated rainfall–runoff models. We show that estimators of ρ = R accounting for skewness are needed for daily streamflow series because they exhibit high variability and skewness compared to, for example, monthly/annual series, where r should perform well.     

Bivariate flood frequency analysis using the copula function: a case study of the Litija station on the Sava River

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.     

INTERNATIONAL HYDROLOGICAL DECADE / WORKING GROUP ON “THE INFLUENCE OF MAN ON THE HYDROLOGICAL CYCLE”

Abstract

Floods, as extreme hydrological phenomena, can be described by more than one correlated characteristic, such as peak, volume and duration. These characteristics should be jointly considered since they are generally not independent. For an ungauged site, univariate regional flood frequency analysis (FA) provides a limited assessment of flood events. A recent study proposed a procedure for regional FA in a multivariate framework. This procedure represents a multivariate version of the index-flood model and is based on copulas and multivariate quantiles. The performance of the proposed procedure was evaluated by simulation. However, the model was not tested on a real-world case study data. In the present paper, practical aspects are investigated jointly for flood peak (Q) and volume (V) of a dataset from the Côte-Nord region in the province of Quebec, Canada. The application of the proposed procedure requires the identification of the appropriate marginal distribution, the estimation of the index flood and the selection of an appropriate copula. The results of the case study show that the regional bivariate FA procedure performed well. This performance depends strongly on the performance of the two univariate models and, more specifically, the univariate model of Q. The results show also the impact of the homogeneity of the region on the performance of the univariate and bivariate models.

Editor D. Koutsoyiannis     

Probabilistic rainfall thresholds for flood forecasting: evaluating different methodologies for modelling rainfall spatial correlation (or dependence)

Rainfall threshold (RT) method is one of the evolving flood forecasting approaches. When the cumulative rainfall depth for a given initial soil moisture condition intersects the threshold rainfall curve, the peak discharge is expected to be equal or greater than the threshold discharge for flooding at the target site. Besides the total rainfall depth, spatial and temporal distribution of rainfall impacts the flood peak discharge and the time to peak. To revisit a previous study conducted by the authors, in which spatially independent rainfall pattern was assumed, the spatial distribution of rainfall was simulated following a Monte Carlo approach. The structure of the spatial dependence among sub‐watersheds' rainfalls was taken into account under three different scenarios, namely independent, bivariate copula (2copula) and multivariate Gaussian copula (MGC). For each set of generated random dimensionless rainfalls, the probabilistic RT curves were derived for dry moisture condition. Results were evaluated with both historical and simulated events. For the simulated events, threshold curves were assessed by means of categorical statistics, such as hit rate, false rate and critical success index (CSI). Results revealed that the best performance based on the CSI criterion corresponded to 50% curve in 2copula and MGC scenarios as well as 90% curve in the independent scenario. The recognition of 50% curve in 2copula and MGC scenarios is in agreement with our expectations that the mean probable curve should have the best performance. Moreover, the proposed inclusion of spatially dependent rainfall scenario improved the performance of RT curves by about 25% in comparison with the presumed spatially uniform rainfall scenario. Copyright © 2011 John Wiley & Sons, Ltd.     

南水北调中线降水丰枯遭遇风险分析

受降水丰枯变化不确定性和差异性的影响,南水北调中线工程水源区与受水区降水的丰枯遭遇状态各不相同,给南水北调工程水资源调度运行带来风险。联合copula函数和贝叶斯网络理论,建立了南水北调中线工程水源区和受水区降水丰枯遭遇风险分析模型,对南水北调中线工程调水最不利的丰枯遭遇风险概率进行了研究。利用copula函数建立了水源区和受水区年降水量联合分布函数,计算条件概率,结合贝叶斯网络进行丰枯遭遇风险分析。结果表明南水北调中线4个受水区调水风险的概率均在25%以下,并对不同情景的调水风险进行了仿真分析。     

Improving extreme wind speed prediction for North Sea offshore oil and gas fields

The paper adresses accuracy improving of statistical prediction, extracted from a shorter stochastic process, using the information provided by another synchronous highly correlated stochastic process that has been measured for a longer time. As an example, the specific issue of improving extreme wind speed prediction has been addressed. For this purpose, an efficient transfer of information is necessary between two synchronous, highly correlated stochastic processes. To illustrate the efficiency of the proposed technique, two time series of measured wind speed data from North sea oil and gas fields were used.