Flood Peak Volume Research Articles

Evaluating the comprehensive flood impact assessment on the head reach of the Chiniot dam project

The major sources of surface water available to Pakistan are perennial flows of the River Indus and its tributaries i.e. Jhelum and Chenab Rivers. The creation of a reservoir of 0.9 MAF Capacity will cause the water level to rise and reduction in flow velocity on the Chenab River upstream of Chiniot Bridge. Consequently, it will cause sediment deposition which would further increase the water level due to the raised river bed level by deposited sediments. To study this storage, the reservoir has been modelled in HEC-RAS software to assess pre-dam and post-dam scenarios to simulate different conditions of river flow for water surface profile and sediment delta modelling of the reservoir reach, using historical daily water and sediment flows (1985–2022). The results of flood routing showed that the reservoir has attenuated the peak flood volume with safe releases at downstream side with proper operation of spillway gates. The average sediment inflow in the reservoir is worked out to be 38.4 metric tons. The results of sediment modelling and reservoir flood management indicated that after every 05 years of normal reservoir operation, reservoir flushing is recommended. Without sediment flushing, the river bed would be further raised beyond 189.0 m due to incoming sediment, resulting in further rise of water level up to 192.8 m which is the existing crest level of upstream training works of Talibwala Motorway Bridge.

Variation characteristics of hydrological response to water conservancy construction in the Qinhe River Basin of the Loess Plateau, China

AbstractInvestigating the response characteristics of various hydrological factors to water conservancy projects area in basin and evaluating their impact on the ecological environment are crucial for ecological protection and restoration on the Loess Plateau, China, with a complex environment. In this study, we employed a geomorphology‐based hydrological model to simulate the hydrological elements of the Qinhe River Basin on the Loess Plateau. We explored the response characteristics of the water cycle and hydrological processes to the construction of reservoirs in the basin. Additionally, we also examined multiyear changes in peak flood volume and sediment discharge during flood seasons influenced by reservoirs. The sub‐basins hosting reservoirs initialled an increase in evaporation, followed by a decrease. During the change periods, both runoff and soil water decreased, but remained higher than the mean values for the basin during the same period. The Normalized Difference Vegetation Index of sub‐basins associated with five reservoirs was obviously higher than the mean value for the basin during the same period. The peak flood volume and sediment discharge in the basin were characterized by decreasing trends, with the latter showing weak sustainability. The value of each index for a sub‐basin associated with a reservoir was higher than the average value for the basin. The construction and operation of reservoirs had a positive impact on the ecology of the basin. Water and soil conservation measures, including sediment regulation and storage using reservoirs, effectively decreased water hazard and soil erosion in the basin. This study provides a scientific basis for the construction of water conservancy projects and ecological governance in the basin.

도시유역 물순환 분석체계 개선연구

Recently, disasters such as floods, localized heavy rains, and typhoons have occurred every year due to climate change. In the past, studies focused on flood control, where damage frequently occurred, but recently, as interest in urban water circulation has increased, awareness of water circulation management has increased. The most important thing to manage the water cycle is to set quantitative water management goals and the exact water cycle application point. Therefore, in this study, to improve the limitations of the water cycle analysis using only the land cover map in the existing urban watershed, an overlapping map analysis was conducted, and an integrated analysis of the building area and building information was conducted for the points where the land cover map was not analyzed. To review the effectiveness of LID facilities, the model was used to analyze Hyoja-dong, Seoul. It was analyzed that peak flood volume was reduced by 28% and 30%, the Return period 5 years, 10 years Rain duration 10min runoff volume was reduced by 18% and 14%, and the flooded area was reduced by 92% and 93%.

LID 적용가능 위치 판단을 위한 중첩지도 분석

Due to climate change and rapid urbanization, most urban areas are paved, and there is insufficient space to infiltrate or store rainwater, and flood damage increases due to heavy rainfall. Research on LID techniques is being conducted to reduce the damage caused by water disasters. A systematic procedure for LID installation, quantitative scale, and facility installation in urban watersheds is required. Therefore, in this study, overlapping maps were analyzed to improve the limitations of water cycle analysis using only land cover maps in urban watersheds. Based on the overlapping map analysis, the procedure for determining the LID facility installation was presented. The peak flood volume and runoff volume were analyzed in Gimhae, Gyeongsangnam-do, using the model (XP-SWMM). As a result of the study, it was confirmed that the exact capacity of the facility can be distributed according to the target amount of water circulation by reflecting the characteristics of the basin or building information.

Bivariate hydrologic risk analysis for the Xiangxi River in Three Gorges Reservoir Area, China

BackgroundHydrological extremes such as floods generally have multidimensional attributes with complex dependence structures. This leads to the urgent demand of hydrological risk analysis within a multivariate context. In this study, the bivariate hydrologic risk framework is proposed based on the bivariate copula method. In the proposed risk analysis framework, bivariate flood frequency would be analyzed for different flood variable pairs (i.e., flood peak-volume, flood peak-duration, flood volume-duration), and the bivariate hydrologic risk is then derived based on the joint return period of a flood variable pair. The distribution of one flood variable conditional on another flood variable can also be obtained through the copula method.ResultsThe proposed method is applied to the risk analysis for the Xiangxi River in the Three Gorges Reservoir area, China, based on 50 years streamflow measurements. The results indicate that the bivariate risk for flood peak flow-duration would keep constant for some time and then decrease as the increase of the flood duration. The bivariate risk for flood peak-volume holds a similar trend with the bivariate risk of flood peak-duration. The probability density functions (PDFs) of the flood volume and duration conditional on flood peak can also be generated through the best fitted copula function.ConclusionThe results indicate that the distributions of flood volume would be highly influenced by the flood peak flows, in which the flood volume would be expected to increase as the increase of flood return period. Conversely, the distribution of the flood duration would not change significantly with the variation in the flood peak return period. The obtained conclusions from the bivariate hydrologic analysis can provide decision support for flood control and mitigation.

Bivariate Nonstationary Extreme Flood Risk Estimation Using Mixture Distribution and Copula Function for the Longmen Reservoir, North China

Recently, the homogenous flood generating mechanism assumption has become questionable due to changes in the underlying surface. In addition, flood is a multifaced natural phenomenon and should be characterized by both peak discharge and flood volume, especially for flood protection structures. Hence, in this study, data relating to the 55-year reservoir inflow, annual maximum flood peak (AMFP), and annual maximum flood volume (AMFV) for the Longmen Reservoir in North China have been utilized. The 1-day AMFV exhibits a significant correlation with AMFP. The extreme flood peak-volume pairs are then used to detect the heterogeneity and to perform nonstationary flood risk assessment using mixture distribution as the univariate marginal distribution. Moreover, a copula-based bivariate nonstationary flood frequency analysis is developed to investigate environmental effects on the dependence of flood peak and volume. The results indicate that the univariate nonstationary return period is between the joint OR and the AND return periods. The conditional probabilities of 1-day AMFV, when AMFP exceeds a certain threshold, are likely to be high, and the design flood values estimated by joint distribution are larger than the ones in the univariate nonstationary context. This study can provide useful information for engineers and decision-makers to improve reservoir flood control operations.

Comparison between bivariate and trivariate flood frequency analysis using the Archimedean copula functions, a case study of the Karun River in Iran

Historically, severe floods have caused great human and financial losses. Therefore, the flood frequency analysis based on the flood multiple variables including flood peak, volume and duration poses more motivation for hydrologists to study. The main goal of this paper is conducting a tri-variate flood frequency analysis through simultaneously processing the three main variables of any flood event. In addition to this analysis, three bi-variate flood frequency analyses are also performed considering the variables pairwise. Meanwhile, the Archimedean copula functions are employed to conduct such analyses, and finally compared based on their performance in estimating the accurate and reliable flood frequencies. Bivariate and trivariate flood frequency analysis and modeling using Archimedean copula functions is focused. For this purpose, the annual flood data over a 55-year historical period recorded at the Dez Dam hydrometric station were used. According to the goodness-of-fit criteria along with the analytical tail dependence results based on the extreme value theory, the Frank function built upon the couple of the flood peak-volume and the couple of the flood peak-duration as well as the Clayton function built upon the flood volume-duration were identified to be the best copula families to be adopted. The trivariate analysis was conducted and the Clayton family was chosen as the best copula function. Thereafter, the common and conditional cumulative probability distribution functions were built and analyzed to determine the periodic "and", "or" and "conditional" bivariate and trivariate flood return periods. The results suggest that the bivariate conditional return period obtained for short-term periods is more reliable than the trivariate conditional return period. Additionally, the trivariate conditional return period calculated for long-term periods is more reliable than the bivariate conditional return period.

Peak flood volume and its suspended sediment at various rainfall in Kedungbulus catchment in Gombong, Central Java, Indonesia

Flood is a natural disaster that frequently happens and causes many material and immaterial losses. During flooding, the suspended sediment is carried along by the streamflow. The amount of sediment transported varies and depends on natural and anthropogenic factors. Limited studies have been conducted regarding the relationship between peak flood volume and its sediment content. Therefore, a study with the purpose to understand the relationship of rainfall characteristics, peak flood volume, and suspended sediment was undertaken in Kedungbulus Catchment in Gombong, Central Java, Indonesia. The size of Kedungbulus catchment is 37.8 km2. To collect the required data, an automatic stream water level recorder was installed in the outlet of the catchment. In addition, an automatic and two conventional rain gauges were set up inside the catchment. Hydrograph and statistical analysis were conducted on 2016-2017 data. The results showed that during the study period, the highest peak flood volume occurred on October 8, 2016. The flood duration was 490 minutes, with the time to peak was 135 minutes. At the highest peak flood volume, the stream water was 5,091,221 m3, and the suspended sediment was around 2,394 tons. Rainfall depth significantly affects the peak flood volume and its suspended sediment. The rainfall intensity and Antecedent Soil Moisture Content (ASMC) weakly correlate with peak flood volume and its suspended sediment content.

Risk variation of reservoir regulation during flood season based on bivariate statistical approach under climate change: a case study in the Chengbihe reservoir, China

The risk analysis of reservoir regulation in the flood season is crucial and provides the valuable information for reservoir flood control, safety operation, and decision making, especially under climate change. The purpose of this study is to propose a framework for reasonably estimating the variation of reservoir regulation risk including the dam extreme risk and the overtopping risk during the flood season under climate change. The framework consists of an integrated diagnostic system for detecting the climate abrupt change time, a copula function-based bivariate statistical approach for modeling the dependence between the flood peak and flood volume, a Monte Carlo simulation for generating numerous random flood peak–volume pairs, and a risk calculation model for routing the design flood hydrographs to obtain the frequency curve of the maximum water level reached in front of dam and evaluating the reservoir regulation risk. The methodology was implemented in the Chengbihe reservoir in south China by using the 55-year (1963–2017) hydrometeorological data, including temperature, evaporation, precipitation, and streamflow, in the flood season. Results show that the hydrometeorological series during the flood season changed abruptly in 1992 and the entire data can be divided into two periods (1963–1992 and 1993–2017). The dam extreme risk and overtopping risk during the two periods are assessed, respectively, and a comparison analysis is made based on different flood limit water-level schemes (185.00–188.50 m). It demonstrates that both the dam extreme risk and the dam overtopping risk increase under the influence of climate change. The dam extreme risk increases by 22.91–95.03%, while the climate change-induced increase in the dam overtopping risk is between 38.62 and 123.59%, which indicates that the dam overtopping risk is more sensitive to climate change than the dam extreme risk. The risk evaluations in the study are of great significance in the safety operation and risk management of reservoirs under future climate change.

A synthetic equation for storage function model parameter estimation based on kinematic wave approximation

ABSTRACT The storage function model (SFM) is a rainfall–runoff model widely used in Korea for flood forecasting and warning systems. The traditional equations for parameter estimation are based on observed data under limited conditions, and so it is difficult to sensitively consider the factors affecting actual runoff. The aim of this study is to develop synthetic equations for SFM parameter estimation that are useful for ungauged watersheds, through 35 000 applications of the distributed kinematic wave model (KWM) for virtual watersheds. The parameter estimation equation developed in this study was applied to 101 observed events of 16 basins in Korea. We obtained satisfactory results from the application of a synthetic equation to actual basins. That is to say, the peak flood volume simulated by the equation was comparable with the observed volume. The relative error (RE), mean absolute percent error (MAPE), and percent bias (PBIAS) were used as criteria to evaluate the performance of the equation. For the results, RE and MAPE were within 10%, and PBIAS was within 15%.

The capacity of grey infrastructure in urban flood management: A comprehensive analysis of grey infrastructure and the green-grey approach

Urban inundation management should take various forms to deal with different flood situations, rapid population growth, and climate change. Research on the advantages and disadvantages of grey infrastructure, such as deep tunnels and pipe networks, is necessary to apply hybrid green-grey infrastructure scientifically and efficiently. A novel urban flood model was applied in a highly urbanized region to evaluate the grey infrastructure. Green-grey approaches were also compared. The results showed that deep tunnels decreased the peak flood volume and shortened the time of peak flow. Pipe network improvements decreased the peak flood volume but did not affect the time of peak flow. However, the deep tunnels could not mitigate local inundations caused by insufficient sewer pipe capacity, whereas pipe network improvements could not mitigate inundations caused by backwater flooding. Moreover, pipe network improvements tended to generate new downstream inundation hot-spots. Green-grey infrastructures performed better than grey infrastructures for urban flood reduction. A hybrid green-grey approach was recommended. Suitable combinations of green-grey infrastructures improve the stability and effectiveness of urban flood management.

Parameter Uncertainty and Sensitivity Evaluation of Copula-Based Multivariate Hydroclimatic Risk Assessment

Extensive uncertainties exist in hydroclimatic risk analysis. Especially in multivariate hydrologic risk inferences, uncertainties in individual hydroclimatic extremes such as floods and their dependence structure may lead to bias and uncertainty in future hydrologic risk predictions. In this study, a parameter uncertainty and sensitivity evaluation (PUSE) framework is proposed to quantify parameter uncertainties and then reveal their contributions to the multivariate hydroclimatic risk predictions. The predictive risks are finally generated by “integrating” the values over the posterior distributions of the parameters. The proposed approach was applied for bivariate risk analysis of compound floods at the Xiangxi River to characterize the concurrence probabilities of flood peaks and volumes. The results demonstrate that the proposed approach can quantify uncertainties in a copula-based multivariate risk analysis and characterize effects and contributions of parameters in marginal and dependence structures on the multivariate hydroclimatic risk predictions. In terms of the bivariate risk for flood peak and volume at the Xiangxi River, uncertainties in model parameters would lead to noticeable uncertainties even for moderate floods. The performances of the copula model for flood peak-volume at Xiangxi River are mainly affected by the uncertainties in location parameters of the two individual flood variables. Also, parameter uncertainty in the dependence structure (i.e., copula) would also poses explicit impacts on performance of the copula-based risk analyses model. These uncertainties would result into higher bivariate predictive risks than the values obtained by “optimal/deterministic” predictions. This indicates that uncertain- ties are required to be considered to provide reliable multivariate hydroclimatic risk predictions.

Bivariate Hydrologic Risk Assessment of Flood Episodes using the Notation of Failure Probability

Floods are becoming the most severe and challenging hydrologic issue at the Kelantan River basin in Malaysia. Flood episodes are usually thoroughly characterized by flood peak discharge flow, volume and duration series. This study incorporated the copula-based methodology in deriving the joint distribution analysis of the annual flood characteristics and the failure probability for assessing the bivariate hydrologic risk. Both the Archimedean and Gaussian copula family were introduced and tested as possible candidate functions. The copula dependence parameters are estimated using the method-of-moment estimation procedure. The Gaussian copula was recognized as the best-fitted distribution for capturing the dependence structure of the flood peak-volume and peak-duration pairs based on goodness-of-fit test statistics and was further employed to derive the joint return periods. The bivariate hydrologic risks of flood peak flow and volume pair, and flood peak flow and duration pair in different return periods (i.e., 5, 10, 20, 50 and 100 years) were estimated and revealed that the risk statistics incrementally increase in the service lifetime and, at the same instant, incrementally decrease in return periods. In addition, we found that ignoring the mutual dependency can underestimate the failure probabilities where the univariate events produced a lower failure probability than the bivariate events. Similarly, the variations in bivariate hydrologic risk with the changes of flood peak in the different synthetic flood volume and duration series (i.e., 5, 10, 20, 50 and 100 years return periods) under different service lifetimes are demonstrated. Investigation revealed that the value of bivariate hydrologic risk statistics incrementally increases over the project lifetime (i.e., 30, 50, and 100 years) service time, and at the same time, it incrementally decreases in the return period of flood volume and duration. Overall, this study could provide a basis for making an appropriate flood defence plan and long-lasting infrastructure designs. Doi: 10.28991/cej-2020-03091599 Full Text: PDF

Bivariate flood distribution analysis under parametric copula framework: a case study for Kelantan River basin in Malaysia

Flood is becoming an intensive hydro-climatic issue at the Kelantan River basin in Malaysia. Univariate frequency analysis would be unreliable due to multidimensional behaviour of flood, which often demands multivariate flow exceedance probabilities. The joint distribution analysis of multiple interacting flood characteristics, i.e. flood peak, volume and duration, is very useful for understanding critical hydrologic behaviour at a river basin scale. In this paper, a copula-based methodology is incorporated for multivariate flood frequency analysis for the 50-year annual basis flood characteristics of Kelantan River basin at Guillemard bridge station in Malaysia. Investigation reveals that the Lognormal (2P), Johnson SB-4P and Gamma-3P are selected as marginal distributions for the flood peak flow, volume and duration series. Several bivariate families such as mono-parametric, bi-parametric (i.e. mixed version) and rotated version of Archimedean copulas and also the elliptical copula are introduced to cover a large dependence pattern of flood characteristics. The dependence parameter of bivariate copulas is estimated by the method of moments (MOM) based on the inversion of Kendall’s tau and maximum pseudo-likelihood estimator. To analytically validate and recognize most parsimonious copulas, GOF test and Cramer–von Mises distance statistics (Sn) with the parametric bootstrap method are employed. The Gaussian copula is identified as the most justifiable model for joint modelling of the flood peak–volume and peak–duration combination for MOM-based parameter estimation procedure. Similarly, the Frank copula is selected as the best-fitted structure for modelling peak–duration combination based on MPL estimators, but the MOM estimator recognized Gaussian copula as most suitable for peak–volume pair. Furthermore, the best-fitted copulas are used for obtaining the joint and conditional return periods of the flood characteristics.

A nonparametric copula distribution framework for bivariate joint distribution analysis of flood characteristics for the Kelantan River basin in Malaysia

The joint distribution analysis of multidimensional flood characteristics i.e., flood peak flow, volume and duration, often facilitates a comprehensive understanding in the hydrologic risk assessments. Copula-based methodology are frequently incorporated via parametric approach to model dependence structure of parametric based univariate marginal distributions. But, if the targeted copulas and univariate marginal distributions belongs to some specific parametric families, it might be problematic, if the underlying assumption are violated. Also, no universal rules and literatures are imposed to model any hydrologic vectors and their joint dependence structure through any fixed or pre-defined distributions. In this literature, a nonparametric copula simulation are incorporated and applied as a case study for 50 years annual maximum flood samples of the Kelantan River basin at the Gulliemard bridge station in Malaysia. In this study, a combination of both parametric and nonparametric marginal distribution separately conjoined by a nonparametric copulas framework, which is based on the Beta kernel function. The Beta kernel copula function are incorporated to estimate bivariate copula density which further used to derived joint cumulative density of flood peak-volume, volume-duration and peak-duration pairs and their associated joint as well as conditional return periods.

Hydrological risk analysis of dam overtopping using bivariate statistical approach: a case study from Geheyan Reservoir, China

Hydrological risk analysis is essential and provides useful information for dam safety management and decision-making. This study presents the application of bivariate flood frequency analysis to risk analysis of dam overtopping for Geheyan Reservoir in China. The dependence between the flood peak and volume is modelled with the copula function. A Monte Carlo procedure is conducted to generate 100,000 random flood peak-volume pairs, which are subsequently transformed to corresponding design flood hydrographs (DFHs) by amplifying the selected annual maximum flood hydrographs (AMFHs). These synthetic DFHs are routed through the reservoir to obtain the frequency curve of maximum water level and assess the risk of dam overtopping. Sensitive analysis is performed to investigate the influence of different AMFH shapes and correlation coefficients of flood peak and volume on estimated overtopping risks. The results show that synthetic DFH with AMFH shape characterized by a delayed time to peak results in higher risk, and therefore highlight the importance of including a range of possible AMFH shapes in the dam risk analysis. It is also demonstrated that the overtopping risk is increased as the correlation coefficient of flood peak and volume increases and underestimated in the independence case (i.e. traditional univariate approach), while overestimated in the full dependence case. The bivariate statistical approach based on copulas can effectively capture the actual dependence between flood peak and volume, which should be preferred in the dam risk analysis practice.

Process-based selection of copula types for flood peak-volume relationships in Northwest Austria: a case study

Abstract The case study aims at selecting optimal bivariate copula models of the relationships between flood peaks and flood volumes from a regional perspective with a particular focus on flood generation processes. Besides the traditional approach that deals with the annual maxima of flood events, the current analysis also includes all independent flood events. The target region is located in the northwest of Austria; it consists of 69 small and mid-sized catchments. On the basis of the hourly runoff data from the period 1976- 2007, independent flood events were identified and assigned to one of the following three types of flood categories: synoptic floods, flash floods and snowmelt floods. Flood events in the given catchment are considered independent when they originate from different synoptic situations. Nine commonly-used copula types were fitted to the flood peak - flood volume pairs at each site. In this step, two databases were used: i) a process-based selection of all the independent flood events (three data samples at each catchment) and ii) the annual maxima of the flood peaks and the respective flood volumes regardless of the flood processes (one data sample per catchment). The goodness-of-fit of the nine copula types was examined on a regional basis throughout all the catchments. It was concluded that (1) the copula models for the flood processes are discernible locally; (2) the Clayton copula provides an unacceptable performance for all three processes as well as in the case of the annual maxima; (3) the rejection of the other copula types depends on the flood type and the sample size; (4) there are differences in the copulas with the best fits: for synoptic and flash floods, the best performance is associated with the extreme value copulas; for snowmelt floods, the Frank copula fits the best; while in the case of the annual maxima, no firm conclusion could be made due to the number of copulas with similarly acceptable overall performances. The general conclusion from this case study is that treating flood processes separately is beneficial; however, the usually available sample size in such real life studies is not sufficient to give generally valid recommendations for engineering design tasks.

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

AbstractThis 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 1976–2007. 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.

Similarity of empirical copulas of flood peak-volume relationships: a regional case study of North-West Austria

Abstract This paper analyses the bivariate relationship between flood peaks and corresponding flood event volumes modelled by empirical copulas in a regional context in the North-West of Austria. Flood data of a total of 69 catchments in the region are analysed for the period 1976–2007. In order to increase the sample size and the homogeneity of the samples for the statistical analysis, 24872 hydrologically independent flood events were isolated and assigned to one of three flood process types: synoptic floods, flash floods or snowmelt floods in contrary to the more traditional engineering approach of selecting annual maxima of flood peaks and corresponding flood volumes. The first major part of the paper examines whether the empirical peak-volume copulas of different flood process types are statistically distinguishable, separately for each catchment. The results indicate that the empirical copulas of flash floods tend to be different from those of the synoptic and snowmelt floods in the target region. The second part examines how similar are the empirical flood peak-volume copulas between catchments for a given flood type. For the majority of catchment pairs, the empirical copulas of all flood types are indeed statistically similar. The flash floods show the largest degree of spatial heterogeneity. It is concluded that there is merit in treating flood types separately and in pooling events of the same type in a region when analysing and estimating flood peak-volume dependence copulas; however, the sample size of the analysed events is a limiting factor in spite of the introduced event selection procedure.

Hydrologic risk analysis in the Yangtze River basin through coupling Gaussian mixtures into copulas

In this study, a bivariate hydrologic risk framework is proposed through coupling Gaussian mixtures into copulas, leading to a coupled GMM-copula method. In the coupled GMM-Copula method, the marginal distributions of flood peak, volume and duration are quantified through Gaussian mixture models and the joint probability distributions of flood peak-volume, peak-duration and volume-duration are established through copulas. The bivariate hydrologic risk is then derived based on the joint return period of flood variable pairs. The proposed method is applied to the risk analysis for the Yichang station on the main stream of the Yangtze River, China. The results indicate that (i) the bivariate risk for flood peak-volume would keep constant for the flood volume less than 1.0 × 105 m3/s day, but present a significant decreasing trend for the flood volume larger than 1.7 × 105 m3/s day; and (ii) the bivariate risk for flood peak-duration would not change significantly for the flood duration less than 8 days, and then decrease significantly as duration value become larger. The probability density functions (pdfs) of the flood volume and duration conditional on flood peak can also be generated through the fitted copulas. The results indicate that the conditional pdfs of flood volume and duration follow bimodal distributions, with the occurrence frequency of the first vertex decreasing and the latter one increasing as the increase of flood peak. The obtained conclusions from the bivariate hydrologic analysis can provide decision support for flood control and mitigation.