Stochastic simulation of precipitation-consistent daily reference evapotranspiration using vine copulas

Pham, Minh Tu; Vernieuwe, Hilde; Baets, Bernard De; Willems, Patrick; Verhoest, Niko

doi:10.1007/s00477-015-1181-7

Cited by 38 publications

(32 citation statements)

References 58 publications

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“…11), where only daily observed precipitation and 348 temperature data are available, 50 stochastically-generated evapotranspiration time series are 349 generated using the three-dimensional C-vine copula V T P E . The results shown in Section 2.3.2 350 and the work of Pham et al (2016) reflect that the C-vine copula V T P E performs well and its …”

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confidence: 83%

“…Therefore, one may consider to rely 68 on another approach based on stochastically-generated time series. More importantly, in order to 69 obtain a correct evaluation of the water balance of a catchment and its discharge, these stochastic 70 evapotranspiration data need to be consistent with the accompanying precipitation time series 71 data (Pham et al, 2016). In this case, we can make use of the copula-based approach introduced 72 in the work of Pham et al (2016) in which the statistical dependence between evapotranspiration, 73 precipitation and temperature is described by three-and four-dimensional vine copulas.…”

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confidence: 99%

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A coupled stochastic rainfall-evapotranspiration model for hydrological impact analysis

Pham¹,

Vernieuwe²,

Baets³

et al. 2017

Preprint

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9A hydrological impact analysis concerns the study of the consequences of certain scenarios 10 on one or more variables or fluxes in the hydrological cycle. In such exercise, discharge is often 11 considered, as especially extreme high discharges often cause damage due to the coinciding 12 floods. Investigating extreme discharges generally requires long time series of precipitation and 13 evapotranspiration that are used to force a rainfall-runoff model. However, such kind of data 14 may not be available and one should resort to stochastically-generated time series, even though 15 the impact of using such data on the overall discharge, and especially on the extreme discharge 16 events is not well studied. In this paper, stochastically-generated rainfall and coinciding

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confidence: 83%

mentioning

confidence: 99%

A coupled stochastic rainfall-evapotranspiration model for hydrological impact analysis

Pham¹,

Vernieuwe²,

Baets³

et al. 2017

Preprint

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“…The Archimedean copula (2-dimensional) is symmetric and easy to construct through the generating function as where φ is the generating function which is non-increasing. Based on the choice of Archimedean copulas, different copulas within the family may cover different ranges of dependence (Nelsen 2006). For example, the Gumbel-Hougaard copula may only model the positive dependence, while…”

Section: Copula Families and Parameter Estimationmentioning

confidence: 99%

“…The vine copula has also been applied in high-dimensional hydrological frequency analysis (e.g., Pham et al 2016;Arya and Zhang 2017;Verneiuwe et al 2015) The parameters of the parametric copula functions constructed above may be estimated with one of the following three approaches:…”

Section: Copula Families and Parameter Estimationmentioning

confidence: 99%

Copula–entropy theory for multivariate stochastic modeling in water engineering

Singh

Zhang

2018

Geosci. Lett.

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The copula-entropy theory combines the entropy theory and the copula theory. The entropy theory has been extensively applied to derive the most probable univariate distribution subject to specified constraints by applying the principle of maximum entropy. With the flexibility to model nonlinear dependence structure, parametric copulas (e.g., Archimedean, extreme value, meta-elliptical, etc.) have been applied to multivariate modeling in water engineering. This study evaluates the copula-entropy theory using a sample dataset with known population information and a flood dataset from the experimental watershed at the Walnut Gulch, Arizona. The study finds the following: (1) both univariate and joint distributions can be derived using the entropy theory. (2) The parametric copula fits the true copula better using empirical marginals than using fitted parametric/entropy-based marginals. This suggests that marginals and copula may be identified separately in which the copula is investigated with empirical marginals. (3) For a given set of constraints, the most entropic canonical copula (MECC) is unique and independent of the marginals. This allows the universal solution for the proposed analysis. (4) The MECC successfully models the joint distribution of bivariate random variables. (5) Using the "AND" case return period analysis as an example, the derived MECC captures the change of return period resulting from different marginals.

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“…On the contrary, for the practitioners, this also means that the set of models considered here (and preferred due their relative simplicity in many copula studies) may not be adequate for the variety of flood shape types and other copula models may be needed to be considered. Alternative copula models include, e.g., vine copulas, which allow for constructing a multivariate copula based on the mixing of bivariate copulas (e.g., Gräler et al, 2013;Pham et. al., 2015;Vernieuwe et al, 2015) or entropy copulas, which integrate the concept of copulas with the principle of maximum entropy (i.e., the entropy variables are mutually independent from each other; AghaKouchak, 2014).…”

Section: A Comparison Of Similarity Of Empirical Copulas For Each Flomentioning

confidence: 99%

A regional comparative analysis of empirical and theoretical flood peak-volume relationships

Szolgay

Gaál

Bacigál

et al. 2016

Journal of Hydrology and Hydromechanics

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This paper analyses the bivariate relationship between flood peaks and corresponding flood event volumes modelled by empirical and theoretical copulas in a regional context, with a focus on flood generation processes in general, the regional differentiation of these and the effect of the sample size on reliable discrimination among models. A total of 72 catchments in North-West of Austria are analysed for the period . From the hourly runoff data set, 25 697 flood events were isolated and assigned to one of three flood process types: synoptic floods (including long-and short-rain floods), flash floods or snowmelt floods (both rain-on-snow and snowmelt floods). The first step of the analysis examines whether the empirical peak-volume copulas of different flood process types are regionally statistically distinguishable, separately for each catchment and the role of the sample size on the strength of the statements. The results indicate that the empirical copulas of flash floods tend to be different from those of the synoptic and snowmelt floods. The second step examines how similar are the empirical flood peak-volume copulas between catchments for a given flood type across the region. Empirical copulas of synoptic floods are the least similar between the catchments, however with the decrease of the sample size the difference between the performances of the process types becomes small. The third step examines the goodness-of-fit of different commonly used copula types to the data samples that represent the annual maxima of flood peaks and the respective volumes both regardless of flood generating processes (the traditional engineering approach) and also considering the three process-based classes. Extreme value copulas (Galambos, Gumbel and Hüsler-Reiss) show the best performance both for synoptic and flash floods, while the Frank copula shows the best performance for snowmelt floods. It is concluded that there is merit in treating flood types separately when analysing and estimating flood peak-volume dependence copulas; however, even the enlarged dataset gained by the process-based analysis in this study does not give sufficient information for a reliable model choice for multivariate statistical analysis of flood peaks and volumes.

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Stochastic simulation of precipitation-consistent daily reference evapotranspiration using vine copulas

Cited by 38 publications

References 58 publications

A coupled stochastic rainfall-evapotranspiration model for hydrological impact analysis

A coupled stochastic rainfall-evapotranspiration model for hydrological impact analysis

Copula–entropy theory for multivariate stochastic modeling in water engineering

A regional comparative analysis of empirical and theoretical flood peak-volume relationships

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