Flood Frequency Analysis Research Articles

Are historical stage records useful to decrease the uncertainty of flood frequency analysis ? A 200-year long case study

Flood frequency analysis (FFA), a widely used method to estimate flood hazard, is affected by several sources of uncertainty. Extending flood samples by reanalyzing historical systematic stage records has the potential to reduce sampling uncertainty, but the historical flood discharges derived from this reanalysis are generally affected by large uncertainties. This paper explores whether historical stage records improve design flood estimates through a chain of uncertainty estimation methods for FFA. Uncertainties are estimated and propagated from stage and rating curves to design flood estimates using Monte Carlo procedures. The role of both streamflow and sampling uncertainties in design flood estimation is examined. This procedure is applied to the 205-year long stage series of the Rhône River at Beaucaire, France (95 590 km2). The estimated streamflow 95% uncertainty varies from 30% (XIXth Century) to 5% (1967–2020). The total uncertainty of design flood is significantly reduced when the length of the series increases from 20 to 100 years due to sampling uncertainty reduction. However, the total uncertainty remains stable beyond this sample size: this is because large uncertainties affecting the XIXth Century flood discharges compensate for the reduction in sampling uncertainty. Enlarging the sample size to two centuries leads to including the two largest known floods in 1840 and 1856. In turn, this induces a 15% increase of the 1000-year flood estimates.

Improved historical reconstruction of daily flows and annual maxima in gauged and ungauged basins

This study presents a method to improve the reconstruction of historical flows on gauged and ungauged basins. To do so, a multi-model weighted averaging of hydrological model simulations for a large spatial domain in the province of Quebec, Canada, is used. The distributed hydrological model HYDROTEL was implemented over the region and covered 95 gauged basins. An optimal interpolation (OI) assimilation method was first implemented as a baseline to improve the HYDROTEL flow simulations over the 95 basins. Then, a series of multi-model averaging techniques were applied to an ensemble of 144 HYDROTEL simulations that were generated by modifying parameter sets, driving weather datasets and evapotranspiration modules. The averaging methods were applied in a leave-one-out cross-validation scheme, where all 94 gauged basins were pooled together to compute the weights, and those weights were applied to the 95th basin. All basins were evaluated in such a manner and compared to the OI method. Implementing a year-by-year (or shorter period) weighting scheme instead of computing weights over all available data significantly improved the results. This allowed the weights to better reflect each year’s hydrological characteristics rather than compromising to improve the overall average. The Kling-Gupta Efficiency (KGE) and peak flow metrics showed that the Granger-Ramanathan variant “A” (GRA) was similar in performance to the OI method but did not have the drawbacks that OI can typically introduce. The multi-model application can also be further improved by adding more simulations from other hydrological models, whereas the OI method cannot make use of such additional information, thus hitting a performance plateau. This study shows that it is possible to improve regional hydrological model simulations, both for overall flows and peak flows, and on the historical period for both gauged and ungauged basins. This can then be used to better estimate risk in flood frequency analysis and other statistical analyses.

Assessment of dredging impact on hydrodynamics of Surma River using hydrodynamic model: HEC-RAS approach

Abstract Surma River is the main source of fresh water in the South-Eastern region of Bangladesh. Every year, huge amounts of sediment loads are coming from upstream, which are settling down on the Surma River bed, hindering the safe passage of flow that contributes to the change in the hydrodynamic of the river. Recently, dredging has been done in the Sunamganj area to increase the navigability of the river. In this study, the hydrodynamics of the Surma River has been investigated to check the impact of dredging with the help of HEC-RAS. Flood frequency analyses have been done for 5, 10, 25, 50, and 100 years return periods, and a comparison of water level, velocity, and discharge has been done before and after dredging. Before dredging the water level, the flow path was very high, and velocity was low, but after dredging the water level, the flow path decreases and velocity increased. Discharge also decreases after dredging in the six stations, which are located in the dredged area, and the values are 1,375.41, 1,374.31, 1,373.73, 1,369.7, 1,373.11, and 1,372.08 m3/s. Before dredging, the values are 1,669.62, 1,665.53, 1,664.69, 1,658.12, 1,624.23, and 1,383.98 m3/s.

Predicting Flood Frequency with the LH-Moments Method: A Case Study of Prigor River, Romania

The higher-order linear moments (LH-moments) method is one of the most commonly used methods for estimating the parameters of probability distributions in flood frequency analysis without sample censoring. This article presents the relationships necessary to estimate the parameters for eight probability distributions used in flood frequency analysis. Eight probability distributions of three parameters using first- and second-order LH-moments are presented, namely the Pearson V distribution, the CHI distribution, the inverse CHI distribution, the Wilson–Hilferty distribution, the Pseudo-Weibull distribution, the Log-normal distribution, the generalized Pareto Type I distribution and the Fréchet distribution. The exact and approximate relations for parameter estimation are presented, as are the exact and approximate relations for estimating the frequency factor specific to each method. In addition, the exact and approximate relationships of variation in the LH-skewness–LH-kurtosis are presented, as is the variation diagram of these statistical indicators. To numerically represent the analyzed distributions, a flood frequency analysis case study using the annual maximum series was carried out for the Prigor River. The analysis is presented compared to the linear moments (L-moments) method, which is the method that is intended to be used in the development of a new norm in Romania for determining the maximum flows. For the Prigor River, the most fit distributions are the Pseudo-Weibull and the generalized Pareto Type I for the linear moments method and the CHI and the Wilson–Hilferty distributions for the first higher-order linear moments method. The performance was evaluated using linear and higher-order linear moment values and diagrams.

Regional flood frequency analysis using data-driven models (M5, random forest, and ANFIS) and a multivariate regression method in ungauged catchments

Flooding is recognized worldwide joined of the most expensive natural hazards. To adopt proper structural and nonstructural measurements for controlling and mitigating the rising flood risk, the availability of streamflow values along a river is essential. This raises concerns in the hydrological assessment of poorly gauged or ungauged catchments. In this regard, several flood frequency analysis approaches have been conducted in the literature including index flow method (IFM), square grids method (SGM), hybrid method (HM), as well as the conventional multivariate regression method (MRM). While these approaches are often based on assumptions that simplify the complex nature of the hydrological system, they might not be able to address uncertainties associated with the complexity of the system. One of the powerful tools to deal with this issue is data-driven model that can be easily adopted in complex systems. The objective of this research is to utilize three different data-driven models: random forest (RF), adaptive neuro-fuzzy inference system (ANFIS), and M5 decision tree algorithm to predict peak flow associated with various return periods in ungauged catchments. Results from each data-driven model were assessed and compared with the conventional multivariate regression method. Results revealed all the three data-driven models performed better than the multivariate regression method. Among them, the RF model not only demonstrated the superior performance of peak flow prediction compared to the other algorithms but also provided insight into the complexity of the system through delivering a mathematical formulation.

Generation of type-specific synthetic design flood hydrographs

ABSTRACT Design flood hydrographs are essential for hydraulic engineering and flood risk assessment. Typically, they are derived from quantiles estimated from flood frequency analyses of flood peaks. This usually does not take into account that one and the same flood peak can occur with different volumes and various hydrograph shapes due to different meteorological and catchment-specific processes. In view of this issue, we generate design flood scenarios, i.e. type-specific design hydrographs are created for a flood quantile of a certain return period based on type-specific flood volumes and hydrograph shapes. Additionally, the probability of each flood type is derived. Different probability density functions are used as templates for generating different hydrograph shapes by varying their parameters. An ensemble of synthetic design flood hydrographs is obtained, which allows the consideration of best- and worst-case scenarios. A case study for 162 catchments in Germany demonstrates the applicability of the approach.

Regional flood frequency analysis based on peaks-over-threshold approach: A case study for South-Eastern Australia

Study regionSoutheast Australia Study focusRegional flood frequency analysis (RFFA) is a widely adopted statistical method to estimate design floods in ungauged catchments. Annual maximum flood (AMF) model is the most popular method in developing RFFA techniques. However, the AMF-based approaches are criticised for its limitations in the range of very frequent to frequent flood estimation. As an alternative, the peaks-over-threshold (POT) based approach has shown theoretical advantages in this flood range. POT based RFFA is currently underemployed internationally due to its complexity in modelling. This study develops POT-based RFFA techniques for south-eastern Australia using data from 151 catchments. A comparison is made between ordinary least squares (OLS) and weighted least squares (WLS) methods in developing POT-based RFFA techniques. New hydrological insights for the regionThe OLS based method is found to perform better than the WLS. The median relative error values of the developed prediction equations range 31–38%. The new POT-based RFFA technique overcomes the limitations of the current Australian Rainfall and Runoff, which does not have any RFFA technique for very frequent floods. It is expected that these new POT-based RFFA technique will be used in practice in south-east Australia.

Bivariate copula for flood frequency analysis in Johor river basin

Flooding is a multi-attribute event that is described by many factors such as peak flow and flood volume. It is extremely vital to consider both the flood volume and the flood peak while studying the flood frequency analysis as the univariate analysis cannot accurately portray the flood issue and suffers from an underestimation and an overestimation problem. Traditional univariate and multivariate modeling techniques have several mathematical shortcomings including the inability to distinguish between the marginal and joint behavior of the variables under study. Therefore, the copula function was introduced to tackle the above restriction. Six copula models will be applied in this study to find the best bivariate distribution between the flood variables in Johor River Basin, Malaysia, including Gaussian, Student-t, Clayton, Gumbel, Frank, and Joe. Before that, several marginal distributions were fitted to select the most appropriate distribution for flood variables. It was found that the Pearson Type-III fits both the flood peak flow and the flood volume best. The evaluation of the best univariate marginal distribution and the copula model will be based on Akaike Information Criterion (AIC). Our findings suggested that Frank Copula is more suited to represent the relationship between peak flow and flood volume as it portrays the lowest AIC values of -69.41 and highest log-likelihood values of 35.7, where both values outperform the other proposed copula models. However, future research which considers all three flood variables which are peak flow, volume, and duration should be conducted to attain a more reliable result.

Flood Frequency Analysis under Nonstationary Modeling in the Gorganrood River Basin, Iran

The nonstationary hydrologic processes due to climate variability and intensification of human activities are challenging and questionable for researchers. This study investigates nonstationary partial duration series (PDS) records for the period 1971–2017 at 14 hydrological stations across the Gorganrood River Basin, Iran. The Gorganrood Basin is very diverse in terms of climate such as humid, semihumid, Mediterranean, semiarid, and arid climates. Change points are analyzed using the Pettitt technique. Trends of PDS are detected using the Mann–Kendall method. The nonstationarity of the PDS series is examined by generalized additive models for location, scale, and shape (GAMLSS). Results indicate that abrupt changes are significant for the PDS series in the Gorganrood River Basin. Change points have a considerable effect on trend detection, and these may be attributed to the fact that an abrupt increase or decrease in mean values affects trend changes. In addition, the GAMLSS results showed that the most suitable performance distribution was LNO distribution and then RGE distribution in the Gorganrood River Basin. On other hand, the GAMLSS model and the Pettitt test have good capability in detecting stationary and nonstationary PDS series.

Investigation of Infiltration Loss in North Central Texas by Retrieving Initial Abstraction and Constant Loss from Observed Rainfall and Runoff Events

Accurate modeling of infiltration losses is vital for runoff estimation and thus the development of flood design/protection criteria and water management schemes, etc. In design flood practices, the initial abstraction and constant loss (IACL) method has been widely applied due to its simplicity. However, due to a lack of physical equivalent properties, the IACL method is often subject to issues in parametrization and has large dependency on calibration efforts for storm events. Despite the wide range/variability of IACL values, a single set of IA and CL values is normally adopted for specific flood frequency, which may introduce uncertainty and bias in resulting peak streamflow. In this study, we identified a total of 2,036 rainfall-runoff events for 18 watersheds in North Central Texas to estimate the total losses with their IA and CL components based on time-series of mean areal precipitation (MAP) and streamflow data. Threshold behavior is found for all studied subbasins between the summation of gross rainfall and antecedent soil moisture versus runoff depth: below the threshold, runoff depth is minimal; whereas above it, runoff is largely linearly correlated with the summation of rainfall and antecedent soil moisture. This finding provides a convenient way to estimate/predict total loss or runoff depth given MAP and antecedent soil moisture. In addition, this study shows that the IA and CL values can be approximated by the gamma and Weibull distributions, respectively. The fitted distributions of IA and CL values can be applied in a Monte Carlo simulation framework to stochastically simulate numerous rainfall-runoff events for a flood frequency analysis.

Dynamic flood frequency analysis for west flowing rivers of Kerala, India

Conventional Flood Frequency Analysis (FFA) may underestimate flood quantiles and increase hydraulic infrastructure vulnerability in changing climates. This study uses annual maximum streamflow data from 17 hydrologic stations along west-flowing rivers in Kerala, India, for Non-Stationary (NS) FFA. The Generalized Extreme Value model with a linear temporal location parameter worked effectively for five stations. Kidangoor and Pattazhy stations must account for non-stationarity for longer return periods (RPs) (>50 years), whereas Neeleeswaram and Perumannu stations must for shorter RPs (<50 years). An extensive study was conducted for Neeleswaram station (Periyar basin) by simulating NS models incorporating four large-scale climate oscillations as covariates. The stationary assumption underestimated flood return levels of 2-year RP by about 61% which increases the flood risk leading to failure of hydraulic infrastructures. It was observed that the best fitted climate-based NS model achieves stationary return level of 150-years RP at 25-years RP itself. The study proved that the climate-based NS models captured the 2018 August Floods in Periyar basin better than stationary and time-based models. The regional variability in FF curve behaviour concludes that NSFFA for Kerala cannot be generalised and must be done at a local-scale.

Regional Flood Frequency Analysis: A Bibliometric Overview

In water resources management, environmental and ecological studies, estimation of design streamflow is often needed. For gauged catchments, at-site flood frequency analysis is used for this purpose; however, for ungauged catchments, regional flood frequency analysis (RFFA) is the preferred method. RFFA attempts to transfer flood characteristics from gauged to ungauged catchments based on the assumption of regional homogeneity. A bibliometric analysis on RFFA is presented here using Web of Science (WoS) and Scopus databases. A total of 626 articles were selected from these databases. From the bibliometric analysis, it has been found that Journal of Hydrology and Water Resources Research are the two leading journals reporting RFFA research. In RFFA research, leading countries include Canada, USA, UK, Italy and Australia. In terms of citations, the top performing researchers are Ouarda T, Burn D, Rahman A, Haddad K and Chebana F. Future research should be directed towards the identification of homogeneous regions, application of efficient artificial intelligence (AI)-based RFFA models, incorporation of climate change impacts and uncertainty analysis.

Trivariate Flood Frequency Analysis (Q,V,D) through Copula Functions

El análisis de frecuencias de crecientes trivariado, del gasto máximo (Q), el volumen escurrido (V) y la duración total (D), permite estimar con mayor exactitud el Hidrograma de la Creciente de Diseño. Para procesar registros anuales conjuntos de Q y V disponibles, se propuso estimar D como la duración del hidrograma Gamma hasta el 0.1% del Q. Después a cada registro de Q, V y D se le busca su distribución de probabilidades idónea para obtener las funciones marginales. En seguida, se adopta la Función Cópula (FC) que mejor representa a las variables conjuntas Q–V, Q–D y V–D. Para estas búsquedas y las trivariadas subsecuentes, se trabajó con las FC de Clayton, Frank, Gumbel–Hougaard y Joe. En ambos casos, la selección de la mejor FC se basa en los errores de ajuste entre las probabilidades empíricas y teóricas. A las ternas de datos Q, V y D se les buscó las FC de mejor ajuste simétricas y asimétricas de las cuatro familias citadas. A continuación, se calculan los periodos de retorno conjuntos de tipo OR, AND y de Kendall. Estos últimos, permiten la estimación de los eventos de diseño de Q, V y D. Se describe el análisis de frecuencias trivariado, para las 55 crecientes anuales de la estación hidrométrica La Cuña de la Región Hidrológica No. 12–3 (Río Santiago), México. Por último, se formulan las conclusiones, las cuales destacan la sencillez de los análisis de frecuencias trivariados, cuando se realizan con FC.

Evaluation of Various Generalized Pareto Probability Distributions for Flood Frequency Analysis

This article analyzes six probability distributions from the Generalized Pareto family, with three, four and five parameters, with the main purpose of identifying other distributions from this family with applicability in flood frequency analysis compared to the distribution already used in the literature from this family such as Generalized Pareto Type II and Wakeby. This analysis is part of a larger and more complex research carried out in the Faculty of Hydrotechnics regarding the elaboration of a norm for flood frequency analysis using the linear moments method. In Romania, the standard method of parameter estimation is the method of ordinary moments, thus the transition from this method to the method of linear moments is desired. All the necessary elements for the distribution use are presented, such as the probability density functions, the complementary cumulative distribution functions, the quantile functions, and the exact and approximate relations for estimating parameters, for both methods of parameter estimation. All these elements are necessary for a proper transition between the two methods, especially since the use of the method of ordinary moments is done by choosing the skewness of the observed data depending on the origin of the maximum flows. A flood frequency analysis case study, using annual maximum and annual exceedance series, was carried out for the Prigor River to numerically present the analyzed distributions. The performance of this distribution is evaluated using a linear moments diagram.

Hydrological characteristics of extreme floods in the Klaserie River, a headwater stream in southern Africa

Climate change models for southern Africa predict less frequent, but more intense, rainfall events, and an increased frequency of tropical cyclones. With their steep topography and small catchments, headwater streams generate large floods following intense rainfall events. Large flooding events in headwater streams are under studied in southern Africa. In this paper, we explore flooding in the upper Klaserie River, Limpopo River System, South Africa to determine the flow distribution and flood frequency for the catchment. In addition, we determine the return level for a large, economically damaging, flood generated following the landfall of a sub-tropical depression in January 2012 and, attempt to identify rainfall patterns that resulted in similar floods. An annual hydrological cycle with summer maxima and winter minima for both rainfall and flow was identified. The flood frequency analysis demonstrated that the January 2012 flood had an estimated return level of 225 years. This flood had a peak flowrate exceeding 1200 m3s-1 in a system with an average daily flowrate of 1 m3s-1. Regression tree analysis showed that a two-day rainfall in excess of 240 was a predictor for four of the five largest floods. A two-day rainfall in excess of 400 mm distinguished the January 2012 flood from other floods. Non-stationarity analyses for the flow and rainfall data and a SWAT hydrological model are recommend for the upper Klaserie River to evaluate climate and land cover changes, and their relationship to the magnitude of the 2012 flood. Our study demonstrates that South African river monitoring data can be used to detect and characterize major floods, despite deficiencies in these data. Continuation of these monitoring programs is vital for river health monitoring and the detection of trends in floods resulting from human activities and climate change.

Flood Frequency Analysis of Jiadhal River Basin, India using Log Pearson Type III Distribution Method

Flood is considered as the most widespread and disastrous natural calamity in the world which adversely affects the socio-economic condition and lives of the people living within the floodplain areas of the world. The Jiadhal River basin of Dhemaji district, Assam experiences a high magnitude of flood almost every year, leaving the people of that area in jeopardy. In this regard, flood frequency analysis is considered an important step for proper planning and managing the region in terms of floods. Flood frequency analysis (FFA) is one of the utmost important and necessary measures taken to develop any floodplain region. In this present study, a FFA of the Jiadhal River Basin is carried out using the Log Pearson Type III (LP3) probability distribution method which is used to predict future flood events based on historical records. The data used in the study was for a period of 46 years. The method was used to predict the flood discharge estimations at 2, 10, 25, 50 and 100 years recurrence period. The result says that after 10 years the return period will surpass the water-carrying capacity of the Jiadhal River.

Revisiting Turcotte’s approach: flood frequency analysis

Flood frequency estimation forms the basis for engineering design of hydraulic structures, including bridges and culverts, local and regional development planning, and flood insurance. In the United States, the Water Resources Council recommends using the Log-Pearson Type III (LP3) distribution as a standard for use with the annual peak flow data. However, researchers have argued for the use of more than one streamflow value in a year thus increasing the sample size and decreasing the sampling error in the estimates of the flood quantiles. In this study, conducted over Iowa, the authors revisit the method proposed by Donald Turcotte and others to use power-law distribution applied to streamflow peak values for events separated by a time window. In contrast to those earlier studies, the authors applied formal statistical approach based on the maximum likelihood method and Kolmogorov-Smirnov statistic for parameter estimation. They also propose a novel simulation framework for the estimation of the sampling uncertainty of the power-law distribution. They apply the methodology to streamflow data from 62 USGS stream gauges in Iowa. The key finding of the study is that low-probability quantile estimates using Turcotte’s method result in conservative estimates when compared with LP3 distribution confirming the earlier outcomes.

Frequency Analysis of Extreme Events Using the Univariate Beta Family Probability Distributions

This manuscript presents three families of distributions, namely the Beta, Beta Prime and Beta Exponential families of distributions. From all the distributions of these families, 14 statistical distributions of three, four and five parameters are presented that have applicability in the analysis of extreme phenomena in hydrology. These families of distributions were analyzed regarding the improvement of the existing legislation for the determination of extreme events, specifically the elaboration of a norm regarding frequency analysis in hydrology. To estimate the parameters of the analyzed distributions, the method of ordinary moments and the method of linear moments were used; the latter conforms to the current trend for estimating the parameters of statistical distributions. The main purpose of the manuscript was to identify other distributions from these three families with applicability in flood frequency analysis compared to the distributions already used in the literature from these families, such as the Log–logistic distribution, the Dagum distribution and the Kumaraswamy distribution. The manuscript does not exclude the applicability of other distributions from other families in the frequency analysis of extreme values, especially since these families were also analyzed within the research carried out in the Faculty of Hydrotechnics and presented in other materials. All the necessary elements for their use are presented, including the probability density functions, the complementary cumulative distribution functions, the quantile functions and the exact and approximate relations for estimating parameters. A flood frequency analysis case study was carried out for the Prigor RiverRiver, to numerically present the proposed distributions. The performance of this distributions were evaluated using the relative mean error, the relative absolute error and the L-skewness–L-kurtosis diagram. The best fit distributions are the Kumaraswamy, the Generalized Beta Exponential and the Generalized Beta distributions, which presented a stability related to both the length of the data and the presence of outliers.

Flood Frequency Analysis Using the Gamma Family Probability Distributions

This article presents six probability distributions from the gamma family with three parameters for the flood frequency analysis in hydrology. The choice of the gamma family of statistical distributions was driven by its frequent use in hydrology. In the Faculty of Hydrotechnics, the improvement of the estimation of maximum flows, including the methodological bases for the realization of a regionalization study with the linear moments method with the corrected parameters, was researched and is an element of novelty. The linear moments method performs better than the method of ordinary moments because it avoids the choice of skewness depending on the origin of the flows, and is the method practiced in Romania. The L-moments method conforms to the current trend for estimating the parameters of statistical distributions. Observed data from hydrometric stations are of relatively short length, so the statistical parameters that characterize them are of a sample that requires correction. The correction of the statistical parameters is proposed using the method of least squares based on the inverse functions of the statistical distributions expressed with the frequency factor for L-moments. All the necessary elements for their use are presented, such as quantile functions, the exact and approximate relations for estimating parameters, and frequency factors. A flood frequency analysis case study was carried out for the Ialomita river to verify the proposed methodology. The performance of this distributions is evaluated using Kling–Gupta and Nash–Sutcliff coefficients.

Using climate information as covariates to improve nonstationary flood frequency analysis in Brazil

ABSTRACT Climatic drivers of floods have been widely used to improve nonstationary flood frequency analysis (FFA). However, the forecast ability of nonstationary FFA with out-of-sample prediction has not been comprehensively evaluated. We use 379 flood records from Brazil to assess the ability of process-informed nonstationary models for out-of-sample FFA using the generalized extreme value (GEV) distribution. Five drivers of floods are used as covariates: annual temperature, El Nino Southern Oscillation, annual rainfall, annual maximum rainfall, and annual maximum soil moisture content. Our results reveal that a nonstationary model is preferable when there is a significant correlation between flood and climate covariates in both the training period and full record. The rainfall-based covariates lead to better out-of-sample nonstationary FFA models. These findings highlight that using climate information as covariates in nonstationary FFA is a promising approach for estimating future floods and, hence, better infrastructure design, risk assessment and disaster preparedness.