A Copula-based Approach for Assessing Flood Protection Overtopping Associated with a Seasonal Flood Forecast in Niamey, West Africa (original) (raw)

Copula-Based Bivariate Flood Risk Assessment on Tarbela Dam, Pakistan

Hydrology

Flooding from the Indus river and its tributaries has regularly influenced the region of Pakistan. Therefore, in order to limit the misfortune brought about by these inevitable happenings, it requires taking measures to estimate the occurrence and effects of these events. The current study uses flood frequency analysis for the forecast of floods along the Indus river of Pakistan (Tarbela). The peak and volume are the characteristics of a flood that commonly depend on one another. For progressively proficient hazard investigation, a bivariate copula method is used to measure the peak and volume. A univariate analysis of flood data fails to capture the multivariate nature of these data. Copula is the most common technique used for a multivariate analysis of flood data. In this paper, four Archimedean copulas have been tried using the available information, and in light of graphical and measurable tests, the Gumbel Hougaard copula was found to be most appropriate for the data used in t...

Flood susceptibility assessment in Kelantan river basin using copula

Bivariate frequency analysis of flood variables of different station locations of Kelantan river basin was conducted using copula for the assessment of the geographical distribution of flood risk. Seven univariate distribution functions of flood variables were fitted with flood variables such as peak flow, flood volume, and flood duration to find the best-fitted distributions. The joint dependent structures of flood variables were modeled using Gumbel copula. The results of the study revealed that different variables fit with different distributions. The correlation analysis among variables showed a strong association. Joint distribution functions of peak-flow and volume, peak-flow and duration, and volume and duration revealed that the joint return periods were much higher than univariate return periods of same flood variables. The flood risk analysis based on joint return period of flood variables revealed the highest risk of devastating flood in the downstream. The locations identified as highly susceptible to flood risk by joint distributing of flood variables had experienced most severe floods in recent history, which indicates the effectiveness of the method for the analysis of flood risk. It is expected that this procedure can be helpful for better assessment of flood impacts.

Joint modelling of flood peaks and volumes: A copula application for the Danube River

Journal of Hydrology and Hydromechanics

Flood frequency analysis is usually performed as a univariate analysis of flood peaks using a suitable theoretical probability distribution of the annual maximum flood peaks or peak over threshold values. However, other flood attributes, such as flood volume and duration, are necessary for the design of hydrotechnical projects, too. In this study, the suitability of various copula families for a bivariate analysis of peak discharges and flood volumes has been tested. Streamflow data from selected gauging stations along the whole Danube River have been used. Kendall’s rank correlation coefficient (tau) quantifies the dependence between flood peak discharge and flood volume settings. The methodology is applied to two different data samples: 1) annual maximum flood (AMF) peaks combined with annual maximum flow volumes of fixed durations at 5, 10, 15, 20, 25, 30 and 60 days, respectively (which can be regarded as a regime analysis of the dependence between the extremes of both variables...

Deriving Design Flood Hydrographs Based on Copula Function: A Case Study in Pakistan

Deriving Design Flood Hydrographs Based on Copula Function: A Case Study in Pakistan, 2019

Flood events are characterized by flood peaks and volumes that can be mutually constructed using a copula function. The Indus basin system of Pakistan is periodically threatened by floods during monsoon seasons and thus causes huge losses to infrastructure as well as the community and economy. The design flood hydrograph (DFH) of suitable magnitude and degree is imperative for sheltering dams against the flood risk. The hydrological pair of flood peak and volume is required to be defined using a multivariate analysis method. In this paper, the joint probability function of the hydrological pair is employed to derive the DFH in the Indus basin system of Pakistan. Firstly, we compared the fitting performance of different probability distributions (PDs) as a marginal distribution. Next, we compared the Archimedean family of copulas to construct the bivariate joint distribution of flood peak and volume. Later, the equal frequency combination (EFC) method and most likely combination (MLC) method using "OR" joint return period (JRP or), was involved to derive the design flood quantiles. Finally, we derived the DFH using the two combination methods based on Gumbel-Hougaard copula for different return periods. We presented the combination methods for updating the shape of the DFH in Pakistan. Our study will contribute towards the improvement of design standards of dams and environmental recovery in Pakistan.

Probabilistic assessment of flood risks using trivariate copulas

Theoretical and Applied Climatology, 2013

In this paper, a copula-based methodology is presented for probabilistic assessment of flood risks and investigated the performance of trivariate copulas in modeling dependence structure of flood properties. The flood is a multi-attribute natural hazard and is characterized by mutually correlated flood properties peak flow, volume, and duration of flood hydrograph. For assessing flood risk, many studies have used bivariate analysis, but a more effective assessment can be possible considering all three mutually correlated flood properties simultaneously. This study adopts trivariate copulas for multivariate analysis of flood risks, and applied to a case study of flood flows of Delaware River basin at Port Jervis, NY, USA. On evaluation of various probability distributions for representation of flood variables, it is found that the flood peak flow and volumes can be best represented by Fréchet distribution, whereas flood duration by log-normal distribution. The joint distribution is modeled using four trivariate copulas, namely, three fully nested form of Archimedean copulas: Clayton, Gumbel-Hougaard, Frank copulas; and one elliptical copula: Student's t copula. Based on distance-based performance measures, graphical tests, and tail-dependence measures, it is found that the Student's t copula best representing the trivariate dependence structure of flood properties as compared to the other copulas. Similar results are found for bivariate copula modeling of flood variables pairs, where Student's t copula performed better than the other copulas. The obtained copula-based joint distributions are used for multivariate analysis of flood risks, in terms of primary and secondary return periods. The resultant trivariate return periods are compared with univariate and bivariate return periods, and addressed the necessity of multivariate flood risk analysis. The study concludes that the trivariate copulabased methodology is a viable choice for effective risk assessment of floods.

A process-based analysis of the suitability of copula types for peak-volume flood relationships

Proceedings of the International Association of Hydrological Sciences, 2015

The work aims at analyzing the bivariate relationship between flood peaks and flood volumes, with a particular focus on the type and seasonality of flood generation processes. Instead of the usual approach that deals with an analysis of the annual maxima of flood events, the current analysis includes all independent flood events in a catchment. Flood events are considered independent when they originate from distinguishably different synoptic/meteorological situations. The target region is located in the northern part of Austria, and consists of 72 small and mid-sized catchments. On the basis of the discharge measurements with a time resolution of 1 h from the period 1976-2007, independent flood events were identified and were assigned to one of the three following flood generation type categories: synoptic floods, flash floods and snowmelt floods. These were subsequently divided into two seasons, thereby separating predominantly rainfall-fed and snowmelt-fed floods. Nine frequently-used copula types were locally fitted to the samples of the flood type and seasonal data. Their goodness-of-fit was examined locally as well as analyzed in a regional scope. It was concluded that (i) treating flood processes separately is beneficial for the statistical analysis; (ii) suitability patterns of acceptable copula types are distinguishably different for the seasons/flood types considered, (iii) the Clayton and Joe copulas shows an unacceptable performance for all the seasons/flood types in the region; (iv) the rejection rate of the other copula types depends on the season/flood type and also on the sample size; (v) given that usually more than one statistically suitable dependence model exists, an uncertainty analysis of the design values in the engineering studies resulting from the choice of model seems unavoidable; (vi) reducing uncertainty in the choice of model could be attempted by a deeper hydrological analysis of the dependence structure between flood peaks and volumes in order to give hydrological support to the decision on model's suitability in specific regions and for typical flood generation mechanisms.

Bivariate Flood Frequency Analysis of Upper Godavari River Flows Using Archimedean Copulas

Water Resources Management, 2012

In this paper, a copula based methodology is presented for flood frequency analysis of Upper Godavari River flows in India. By using the specific advantages of copula method in modeling the joint dependence structure of uncertain variables, this study applies Archimedean copulas for frequency analysis of flood characteristics annual peak flow, flood volume and flood duration. To determine the best fit marginal distributions for flood variables, few parametric and nonparametric probability distributions are examined and the best fit model is adopted for copula modeling. Four Archimedean family of copulas, namely Ali-Mikhail-Haq, Clayton, Gumbel-Hougaard and Frank copulas are evaluated for modeling the joint dependence of annual peak flow-volume, and flood volume-duration pairs. The performance of two parameter estimation methods, namely method-of-momentslike estimator based on inversion of Kendall's tau and maximum pseudo-likelihood estimator for copulas are investigated. On performing Monte Carlo simulation to assess the performance of copula distributions in modeling the joint dependence structure of flood variables, it is found that the developed copula models are well representing the observed flood characteristics. From standard statistical tests, Frank copula has been identified as the best fitted copula for both bivariate models. The Frank copula function is used for obtaining joint and conditional return periods of flood characteristics, which can be useful for risk based design of water resources projects.

Copula-Based Modeling of Flood Control Reservoirs

Water Resources Research, 2017

Copulas are shown in this paper to provide an effective strategy to describe the statistical dependence between peak flow discharge and flood volume featuring hydrographs forcing a flood control reservoir. A 52 year time series of flow discharges observed in the Panaro River (Northern Italian Apennines) is used to fit an event-based bivariate distribution and to support time-continuous modeling of a flood control reservoir, located online along the river system. With regard to reservoir performances, a method aimed at estimating the bivariate return period is analytically developed, by exploiting the derived distribution theory and a simplified routing scheme. In this approach, the return period is that of the peak flow discharge released downstream from the reservoir. Therefore, in order to verify the reliability of the proposed method, a nonparametric version of its frequency distribution is assessed by means of continuous simulation statistics. Copula derived and nonparametric distributions of the downstream peak flow discharge are found to be in satisfactory agreement. Finally, a comparison of bivariate return period estimates carried out by using alternative approaches is illustrated.

BIVARIATE FREQUENCY ANALYSIS OF FLOOD VARIABLES USING COPULA IN KELANTAN RIVER BASIN

A copula based methodology is presented in this study for bivariate flood frequency analysis of Kelantan river basin located in Northeast Malaysia. The joint dependence structures of three flood characteristics, namely, peak flow (Q), flood volume (V) and flood duration (D) were modelled using t-Copula. Various univariate distribution functions of flood variables were fitted with observed flood variables to find the best distributions. Cumulative joint distribution functions (CDF) of peak flow and volume (Q-F), peak flow and duration (Q-D) and volume and duration (V-D) revealed that return period of joint return periods are much higher compared to univariate return period. The joint probabilities of occurrence of 0.8, 0.6, 0.4, 0.2 and 0 can be expected when flood duration greater than 65 h, 54 h, 46 h, and 32 h, and the flood volume higher than 0.62 km3, 0.33 km3, 0.25 km3, and 0.22 km3 respectively.