Copula‐Based Bivariate Return Period Analysis and Its Implication to Hydrological Design Event

Extreme climate events frequently have more severe effects on terrestrial vegetation activity than long-term changes in climate averages. However, changes in extreme climate events as well as their potential risk on vegetation activity are still poorly understood. By using the Middle and Lower Reaches of the Yangtze River (MLR-YR) in China as an example, this paper aims to understand the vegetation response to changes in extreme precipitation events from 1982 to 2012 using the maximum normalized difference vegetation index (NDVI) as an indicator. By applying extreme value theory (EVT), the potential risks of extreme precipitation events on vegetation activity were analyzed by conducting return period analysis. Results indicated that vegetation activity could be affected by extreme precipitation events, especially the combined effects of the frequency and intensity of precipitation extremes. For instance, vegetation activity could be enhanced in the regions with weakened intensity but increased occurrence of extreme precipitation events. In addition, we found potential risk of extreme precipitation events on vegetation activity from the results of precipitation extreme trend and return period analysis. These phenomena can be associated with the local occurrence of extreme precipitation events, different land cover types, and soil moisture cumulative effect on vegetation growth. This study stresses the importance of considering both current changes in and the potential risk of extreme precipitation events to understand their effects on vegetation activity.

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A bivariate return period based on copulas for hydrologic dam design: accounting for reservoir routing in risk estimation

Hydrology and Earth System Sciences ◽

10.5194/hess-17-3023-2013 ◽

2013 ◽

Vol 17 (8) ◽

pp. 3023-3038 ◽

Cited By ~ 89

Author(s):

A. I. Requena ◽

L. Mediero ◽

L. Garrote

Keyword(s):

Return Period ◽

Risk Estimation ◽

Design Flood ◽

Flood Peak ◽

Probability Of Occurrence ◽

Reservoir Routing ◽

Maximum Water ◽

Dam Overtopping ◽

Bivariate Return Period ◽

Water Elevation

Abstract. A multivariate analysis on flood variables is needed to design some hydraulic structures like dams, as the complexity of the routing process in a reservoir requires a representation of the full hydrograph. In this work, a bivariate copula model was used to obtain the bivariate joint distribution of flood peak and volume, in order to know the probability of occurrence of a given inflow hydrograph. However, the risk of dam overtopping is given by the maximum water elevation reached during the routing process, which depends on the hydrograph variables, the reservoir volume and the spillway crest length. Consequently, an additional bivariate return period, the so-called routed return period, was defined in terms of risk of dam overtopping based on this maximum water elevation obtained after routing the inflow hydrographs. The theoretical return periods, which give the probability of occurrence of a hydrograph prior to accounting for the reservoir routing, were compared with the routed return period, as in both cases hydrographs with the same probability will draw a curve in the peak-volume space. The procedure was applied to the case study of the Santillana reservoir in Spain. Different reservoir volumes and spillway lengths were considered to investigate the influence of the dam and reservoir characteristics on the results. The methodology improves the estimation of the Design Flood Hydrograph and can be applied to assess the risk of dam overtopping.

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Swell wave progression in the English Channel: implications for coastal monitoring

Anthropocene Coasts ◽

10.1139/anc-2021-0008 ◽

2021 ◽

Vol 4 (1) ◽

pp. 281-305

Author(s):

Thomas Dhoop ◽

Charlie Thompson

Keyword(s):

Water Level ◽

Return Period ◽

High Water ◽

English Channel ◽

Coastal Monitoring ◽

Period Analysis ◽

Significant Wave ◽

Joint Return ◽

Joint Return Period ◽

Joint Consideration

Energetic swell waves, particularly when they coincide with high water levels, can present significant coastal hazards. To better understand and predict these risks, analysis of the sea levels and waves that generate these events and the resulting coastal impacts is essential. Two energetic swell events, neither of which were predicted by modelled flood forecasts, occurred in quick succession in the English Channel. The first event, on 30 January 2021, produced moderate significant wave heights at or just below the 0.25 year return period along the southwest English coast, but combined with significant swell caused overtopping at East Beach in West Bay and at Chesil Beach. The second event, on 1 February 2021, generated the highest wave energy periods measured at many locations along the southern English coastline and, at high water, caused waves to run up over the promenades at Poole Bay and Christchurch Bay and caused overtopping at Hayling Island. Both events are described in detail, and their spatial footprints are mapped through a joint return period analysis using a copula function. It is found that typical joint return period analysis of water level and significant wave height underestimates potential impacts, while a joint consideration of water level and wave power (P) describes the 31 January event better and a joint consideration of water level and energy period (Te) best describes the 1 February event. Therefore, it is recommended that Te and P are adopted for coastal monitoring purposes, and that future studies further explore the use of both parameters for swell monitoring.

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Bivariate return period based on copulas for hydrologic dam design: comparison of theoretical and empirical approach

Hydrology and Earth System Sciences Discussions ◽

10.5194/hessd-10-557-2013 ◽

2013 ◽

Vol 10 (1) ◽

pp. 557-596 ◽

Cited By ~ 7

Author(s):

A. I. Requena ◽

L. Mediero ◽

L. Garrote

Keyword(s):

Return Period ◽

Design Flood ◽

Flood Peak ◽

Probability Of Occurrence ◽

Maximum Water ◽

Bivariate Copula ◽

Dam Overtopping ◽

Bivariate Return Period ◽

Water Elevation

Abstract. Hydrologic frequency analyses are usually focused on flood peaks. Multivariate analyses on flood variables have not been so exhaustively studied despite the fact that they are required to represent the full hydrograph, which is essential for designing some structures like dams. In this work, a bivariate copula model was used to obtain the bivariate joint distribution of flood peak and volume. An empirical bivariate return period was defined in terms of acceptable risk to the dam through the maximum water elevation reached during the routing process, in order to perform a risk assessment of dam overtopping. A Monte Carlo procedure was developed to compare the probability of occurrence of a flood with the return period linked to the risk of dam overtopping. The procedure is applied to the case study of the Santillana reservoir in Spain. A set of synthetic peak-volume pairs was generated by the fitted copula and synthetic hydrographs were routed through the reservoir. Different reservoir volumes and spillway lengths were considered. Hydrographs with the same risk were represented by a curve in the peak-volume space. These curves were compared to those linked to the probability of occurrence of a flood event, in order to improve the estimation of the Design Flood Hydrograph.

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