On the Use of Copulas in Hydrology: Theory and Practice

Salvadori, Gianfausto; Michele, Carlo De

doi:10.1061/(asce)1084-0699(2007)12:4(369)

Cited by 281 publications

(125 citation statements)

References 61 publications

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“…where θ 1 is a dependence parameter estimated over the set of observations (Salvadori and De Michele, 2007). Figure 5 illustrates the selected flood events associated with different return periods, Tr.…”

Section: Development Of Flood Scenarios and Model Simulationsmentioning

confidence: 99%

Probabilistic flood hazard mapping: effects of uncertain boundary conditions

Domeneghetti

Vorogushyn

Castellarin

et al. 2013

Hydrol. Earth Syst. Sci.

109

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Abstract.Comprehensive flood risk assessment studies should quantify the global uncertainty in flood hazard estimation, for instance by mapping inundation extents together with their confidence intervals. This appears of particular importance in the case of flood hazard assessments along dike-protected reaches, where the possibility of occurrence of dike failures may considerably enhance the uncertainty. We present a methodology to derive probabilistic flood maps in dike-protected flood prone areas, where several sources of uncertainty are taken into account. In particular, this paper focuses on a 50 km reach of River Po (Italy) and three major sources of uncertainty in hydraulic modelling and flood mapping: uncertainties in the (i) upstream and (ii) downstream boundary conditions, and (iii) uncertainties in dike failures. Uncertainties in the definition of upstream boundary conditions (i.e. design-hydrographs) are assessed through a copula-based bivariate analysis of flood peaks and volumes. Uncertainties in the definition of downstream boundary conditions are characterised by uncertainty in the rating curve with confidence intervals which reflect discharge measurement and interpolation errors. The effects of uncertainties in boundary conditions and randomness of dike failures are assessed by means of the Inundation Hazard Assessment Model (IHAM), a recently proposed hybrid probabilistic-deterministic model that considers three different dike failure mechanisms: overtopping, piping and microinstability due to seepage. The results of the study show that the IHAM-based analysis enables probabilistic flood hazard mapping and provides decision-makers with a fundamental piece of information for devising and implementing flood risk mitigation strategies in the presence of various sources of uncertainty.

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Section: Development Of Flood Scenarios and Model Simulationsmentioning

confidence: 99%

Probabilistic flood hazard mapping: effects of uncertain boundary conditions

Domeneghetti

Vorogushyn

Castellarin

et al. 2013

Hydrol. Earth Syst. Sci.

109

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“…The kernel distribution estimation method can be applied to obtain the marginal distribution of the random variables X and Y, and then the copula fit function can be called to estimate the unknown parameters. After the copula parameters are estimated, the copula statistic function is called to obtain the Spearman rank correlation coefficient [83].…”

Section: Natural Driving Forces Analysis With Copula Modelmentioning

confidence: 99%

A System Analysis on Steppe Sustainability and Its Driving Forces—A Case Study in China

et al. 2018

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Abstract:Steppe is an indispensable component for terrestrial ecosystems and it is of great significance to systematically analyze steppe sustainability and its driving forces. In this study, we propose a steppe dynamics ranking method based on Pauta criterion and a steppe sustainability assessment method with an effect matrix. The natural driving forces on steppe sustainability were systematically analyzed using the copula model, and the anthropogenic driving factors, including land use, were analyzed by using spatial overlay and statistical analysis methods. The results showed the following: (1) in general, steppe sustainability showed a trend of improvement from 2001 to 2010 in China. However, there were still some degraded areas scattered within the study area; (2) the consistent effect of steppe dynamics on steppe sustainability was significant on the whole, although there was a diverse effect on it; (3) among the natural factors, precipitation was the strongest positive driving force, followed by temperature average, while sunshine duration had strong negative driving force. The impact caused by land use factors was controlled during that decade, and the steppe land that evolved from urban and built-up land, cropland, and forest was vulnerable and resulted in steppe sustainability degradation.

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“…To illustrate this, a simple example in the context of this paper is presented. For more mathematical details, the reader is referred to Nelsen (2006), Genest and Favre (2007) and Salvadori and De Michele (2007).…”

Section: Copulasmentioning

confidence: 99%

Copula-based downscaling of spatial rainfall: a proof of concept

Berg

Vandenberghe

Baets

et al. 2011

Hydrol. Earth Syst. Sci.

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Abstract. Fine-scale rainfall data is important for many hydrological applications. However, often the only data available is at a coarse scale. To bridge this gap in resolution, stochastic disaggregation methods can be used. Such methods generally assume that the distribution of the field is stationary, i.e. the distribution for the entire (fine-scale) field is the same as the distribution of a smaller region within the field. This assumption is generally incorrect and we provide a proof of concept of a method to estimate the distribution of a smaller region. In this method, a copula is used to construct a bivariate distribution describing the relation between the scales. This distribution is then used to estimate the distribution of the fine-scale rainfall within a single coarse-scale pixel, by conditioning on the coarse-scale rainfall depth.

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On the Use of Copulas in Hydrology: Theory and Practice

Cited by 281 publications

References 61 publications

Probabilistic flood hazard mapping: effects of uncertain boundary conditions

Probabilistic flood hazard mapping: effects of uncertain boundary conditions

A System Analysis on Steppe Sustainability and Its Driving Forces—A Case Study in China

Copula-based downscaling of spatial rainfall: a proof of concept

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