A distributional multivariate approach for assessing performance of climate-hydrology models

Vezzoli, Renata; Salvadori, Gianfausto; Michele, Carlo De

doi:10.1038/s41598-017-12343-1

Cited by 20 publications

(25 citation statements)

References 38 publications

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“…The time-varying moment model that expresses the distribution parameters or moments as functions of time or some other explanatory variable or variables have been widely employed to capture the nonstationarities of univariate flood series (Strupczewski et al, 2001;Villarini et al, 2009). In this study, the nonstationary marginal distributions of the multivariate flood series…”

Section: Nonstationary Marginal Distributions Based On the Time-varyimentioning

confidence: 99%

“…Due to climate change as well as certain anthropogenic driving forces (Milly et al, 2008), the nonstationarities of both univariate and multivariate flood series have been widely reported (Xiong and Guo, 2004;Villarini et al, 2009;Vogel et al, 2011;López and Francés, 2013;Bender et al, 2014;Xiong et al, 2015;Blöschl et al, 2017;Kundzewicz et al, 2018). The multivariate flood distribution exhibits more complex nonstationarity behaviours than the univariate distribution, including nonstationarities of individual margins and the dependence structure between the margins (Quessy et al, 2013;Bender et al, 2014;Xiong et al, 2015;Kwon et al, 2016;Sarhadi et al, 2016;Qi and Liu, 2017;Vezzoli et al, 2017;Bracken et al, 2018;Salvadori et al, 2018).…”

Section: Introductionmentioning

confidence: 99%

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Multivariate hydrologic design methods under nonstationary conditions and application to engineering practice

Jiang

Xiong

Yan

et al. 2019

Hydrol. Earth Syst. Sci.

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Abstract. Multivariate hydrologic design under stationary conditions is traditionally performed through the use of the design criterion of the return period, which is theoretically equal to the average inter-arrival time of flood events divided by the exceedance probability of the design flood event. Under nonstationary conditions, the exceedance probability of a given multivariate flood event varies over time. This suggests that the traditional return-period concept cannot apply to engineering practice under nonstationary conditions, since by such a definition, a given multivariate flood event would correspond to a time-varying return period. In this paper, average annual reliability (AAR) was employed as the criterion for multivariate design rather than the return period to ensure that a given multivariate flood event corresponded to a unique design level under nonstationary conditions. The multivariate hydrologic design conditioned on the given AAR was estimated from the nonstationary multivariate flood distribution constructed by a dynamic C-vine copula, allowing for time-varying marginal distributions and a time-varying dependence structure. Both the most-likely design event and confidence interval for the multivariate hydrologic design conditioned on the given AAR were identified to provide supporting information for designers. The multivariate flood series from the Xijiang River, China, were chosen as a case study. The results indicated that both the marginal distributions and dependence structure of the multivariate flood series were nonstationary due to the driving forces of urbanization and reservoir regulation. The nonstationarities of both the marginal distributions and dependence structure were found to affect the outcome of the multivariate hydrologic design.

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Section: Nonstationary Marginal Distributions Based On the Time-varyimentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Multivariate hydrologic design methods under nonstationary conditions and application to engineering practice

Jiang

Xiong

Yan

et al. 2019

Hydrol. Earth Syst. Sci.

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“…But the optimum time-varying copulas perform better than stationary ones for Z-Q and Z-S in terms of AICc. Frank is found to be the more appropriate bivariate copula for both Z-Q and Z-S, and parameters θ t ZQ , θ t ZS expressed in Equations (12) and (13), respectively, as below: Figure 3b shows the QQ plot of the two bivariate copulas above. It displays a good agreement between empirical distribution and theoretical distribution.…”

Section: Nonstationary Dependence Of Bivariate Flood Variablesmentioning

confidence: 99%

“…Yet, the designs of hydraulic structures (e.g., dam spillways, dikes, and river channels), cross drainage structures (e.g., culverts and bridges) and urban drainage systems require not only peak discharge (Q) value but also peak water stage (Z) and suspended sediment load (S). In fact, the multivariate frequency analysis can provide more comprehensive understanding of the flood event than simple univariate analysis [9][10][11][12][13].…”

Section: Introductionmentioning

confidence: 99%

Nonstationary Analysis for Bivariate Distribution of Flood Variables in the Ganjiang River Using Time-Varying Copula

Wen

Jiang

2019

Water

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Nonstationarity of univariate flood series has been widely studied, while nonstationarity of some multivariate flood series, such as discharge, water stage, and suspended sediment concentrations, has been studied rarely. This paper presents a procedure for using the time-varying copula model to describe the nonstationary dependence structures of two correlated flood variables from the same flood event. In this study, we focus on multivariate flood event consisting of peak discharge (Q), peak water stage (Z) and suspended sediment load (S) during the period of 1964–2013 observed at the Waizhou station in the Ganjiang River, China. The time-varying copula model is employed to analyze bivariate distributions of two flood pairs of (Z-Q) and (Z-S). The main channel elevation (MCE) and the forest coverage rate (FCR) of the basin are introduced as the candidate explanatory variables for modelling the nonstationarities of both marginal distributions and dependence structure of copula. It is found that the marginal distributions for both Z and S are nonstationary, whereas the marginal distribution for Q is stationary. In particular, the mean of Z is related to MCE, and the mean and variance of S are related to FCR. Then, time-varying Frank copula with MCE as the covariate has the best performance in fitting the dependence structures of both Z-Q and Z-S. It is indicated that the dependence relationships are strengthen over time associated with the riverbed down-cutting. Finally, the joint and conditional probabilities of both Z-Q and Z-S obtained from the best fitted bivariate copula indicate that there are obvious nonstationarity of their bivariate distributions. This work is helpful to understand how human activities affect the bivariate flood distribution, and therefore provides supporting information for hydraulic structure designs under the changing environments.

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“…In recent years, it has been widely applied to various aspects of hydrological studies [13]. The main applications of the Copula Function include the analysis of: precipitation characteristics [12], the correlation between flood peak and flood volume [14,15], the frequency and recurrence interval of floods [16][17][18], characteristics of storms [19,20], the frequency and recurrence intervals of droughts [21], drought assessment [22], risk assessment [23], and an assessment of environmental hydrological model performance [24]. Due to the specialty of the water table, the establishment of the Copula Function for this purpose is relatively difficult; therefore, no research that uses the Copula Function to analyze the water table has been reported.…”

Section: Introductionmentioning

confidence: 99%

Probability Analysis of the Water Table and Driving Factors Using a Multidimensional Copula Function

You

Liu

2018

Water

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Abstract:The relationship between the water table and driving factors is a reliable theoretical reference for the reasonable planning of surface water resources and the water table. Previous research has neglected the distribution and probabilities of the water table. However, this paper analyzes the relationship between the water table and driving factors from a statistical perspective by correcting the variables and introducing the Kernel Distribution Estimation and the Copula Function. The average data of the buried depth of the phreatic water, annual irrigation volume of the surface water, and precipitation in the Jinghui Irrigation District in China from 1977 to 2013 were adopted. We precisely obtained the two-dimensional (2D) and three-dimensional (3D) Joint Distribution Function of each driving factor and the marginal distribution of the water table, calculate the conditional probability in different ranges, and exactly predict the design value of surface water irrigation giving set conditions. Eventually, we emphasize the importance of probability analysis and prediction in groundwater planning.

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A distributional multivariate approach for assessing performance of climate-hydrology models

Cited by 20 publications

References 38 publications

Multivariate hydrologic design methods under nonstationary conditions and application to engineering practice

Multivariate hydrologic design methods under nonstationary conditions and application to engineering practice

Nonstationary Analysis for Bivariate Distribution of Flood Variables in the Ganjiang River Using Time-Varying Copula

Probability Analysis of the Water Table and Driving Factors Using a Multidimensional Copula Function

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