Flood frequency analysis integrated with unprecedented flood samples and mixed probability distribution

The fundamental assumption of flood frequency analysis is that flood samples are generated by the same flood generation mechanism (FGM). However, flood events are usually triggered by the interaction of meteorological factors and watershed properties, which results in different FMGs. To solve this problem, researchers have put forward traditional two-component mixture distributions (TCMD-T) without clearly linking each component distribution to an explicit FGM. In order to improve the physical meaning of mixture distributions in seasonal snow-covered areas, the ratio of rainfall to flood volume (referred to as rainfall–flood ratio, RF) method was used to classify distinct FGMs. Thus, the weighting coefficient of each component distribution was determined in advance in the rainfall–flood ratio based TCMD (TCMD-RF). TCMD-RF model was applied to 34 basins in Norway. The results showed that flood types can be clearly divided into rain-on-snow-induced flood, snowmelt-induced flood and rainfall-induced flood. Moreover, the design flood and associated uncertainties were also estimated. It is found that TCMD-RF model can reduce the uncertainties of design flood by 20% compared with TCMD-T. The superiority of TCMD-RF is attributed to its clear classification of FGMs, thus determining the weighting coefficients without optimization and simplifying the parameter estimation procedure of mixture distributions.

Quality discharge measurements and frequency analysis are two major prerequisites for defining a design flood. Flood frequency analysis (FFA) utilizes a comprehensive understanding of the probabilistic behavior of extreme events but has certain limitations regarding the sampling method and choice of distribution models. Entropy as a modern-day tool has found several applications in FFA, mainly in the derivation of probability distributions and their parameter estimation as per the principle of maximum entropy (POME) theory. The present study explores a new dimension to this area of research, where POME theory is applied in the partial duration series (PDS) modeling of FFA to locate the optimum threshold and the respective distribution models. The proposed methodology is applied to the Waimakariri River at the Old Highway Bridge site in New Zealand, as it has one of the best quality discharge data. The catchment also has a history of significant flood events in the last few decades. The degree of fitness of models to the exceedances is compared with the standardized statistical approach followed in literature. Also, the threshold estimated from this study is matched with some previous findings. Various return period quantiles are calculated, and their predictive ability is tested by bootstrap sampling. An overall analysis of results shows that entropy can be also be used as an effective tool for threshold identification in PDS modeling of flood frequency studies.

The River Chenab is one of the main western rivers of the Indus River system in Pakistan, which undergoes intensive inundation almost every year during the late monsoon period. The present study performs flood frequency analyses for the river basin as well as simulates different levels of water flow in the system to speculate all kinds of inundation under different scenarios, i.e., to predict flood hazard and flood extended areas. Flood frequency analyses were performed at MARALA Headworks to Khanki Headworks. Data were collected from the Punjab Irrigation Department, Pakistan and from USGS and ASTER GDEM. The peak discharge of MARALA Headworks had been analyzed for 25 years. The preprocessing was performed in HEC Geo-RAS after preprocessing model run in HEC-RAS. After analysis the data were exported in HEC-RAS to ARCMAP to generate a floodplain and inundation map. Our analysis generated the result that different areas would be under water in different return periods. Flood hazards maps for different return periods 10, 20, 50 and 100 years were conducted using annual peaks flow of 35 years from 1980 to 2016. The maximum discharges at up and down stream for different periods were obtained using Gumbel distribution model results which showed that different areas were predicted under water in different return periods and affected areas after five years' return period.

Flooding is one of Africa’s most impactful natural disasters, significantly affecting human lives, infrastructure, and economies. This study examines the spatial and temporal distribution of historical flood events across the continent from 1927 to 2020, with a focus on fatalities, affected populations, and economic damage. Data from the Emergency Events Database (EM-DAT), the fifth generation of bias-corrected European Centre for Medium-Range Weather Forecasts Reanalysis (ERA5), and the Climate Hazards Group InfraRed Precipitation with Stations (CHIRPS) observational datasets were used to calculate extreme precipitation indices—Consecutive Wet Days (CWD), annual precipitation on very wet days (R95PTOT), and Annual Maximum Precipitation (AMP). Spatial analysis tools and the Mann–Kendall test were used to assess trends in flood occurrences, while Pearson correlation analysis identified key meteorological drivers across 16 African capital cities for 1981–2019. A flood frequency analysis was conducted using Weibull, Gamma, Lognormal, Gumbel, and Logistic probability distribution models to compute flood return periods for up to 100 years. Results reveal a significant upward trend with a slope above 0.50 floods per year in flood frequency and impact over the period, particularly in regions such as West Africa (Nigeria, Ghana), East Africa (Ethiopia, Kenya, Tanzania), North Africa (Algeria, Morocco), Central Africa (Angola, Democratic Republic of Congo), and Southern Africa (Mozambique, Malawi, South Africa). Positive trends (at 99% significance level with slopes ranging between 0.50 and 0.60 floods per year) were observed in flood-related fatalities, affected populations, and economic damage across Regional Economic Communities (RECs), individual countries, and cities of Africa. The CWD, R95PTOT, and AMP indices emerged as reliable predictors of flood events, while non-stationary return periods exhibited low uncertainties for events within 20 years. These findings underscore the urgency of implementing robust flood disaster management strategies, enhancing flood forecasting systems, and designing resilient infrastructure to mitigate growing flood risks in Africa’s rapidly changing climate.

Advances in space–time tools and techniques offer new possibilities to improve methods for exploratory data analysis and parameter estimation in regional flood frequency analysis (FFA). A general framework and methodological approach are proposed which integrate concepts and techniques of regional FFA, geostatistical theory and analytical geographical information systems (GIS) using data on climate, vegetation, geography and flood timing and magnitude statistics. Non-parametric methods are used to screen data and to delineate homogeneous regions. Simulations are used to identify discordant sites, diagnose each region using the signal-to-noise ratio and test regions for homogeneity based on L-moment ratios. Geostatistical measures of spatial autocorrelation are used to diagnose hierarchical spatial models for each L-moment ratio and to obtain map estimates of parameters using spatially explicit kriging techniques (analogous to regression). In addition to storing and displaying the spatio-temporal information accurately, the GIS is used to quantify spatial associations between dependent and independent variables and to diagnose homogeneous regions for further refinement using a simple spatial contrast measure. Analysis of data from central and eastern Canada (except the eastern parts of Newfoundland), encompassing a large area with significant random and systematic variability, demonstrates that: (i) map sets of L-mean and L-CV (coefficient of variation) for flood timing and magnitude can serve as indicators of climatic influences on the flood-generating mechanisms; (ii) models of spatial autocorrelation can be used to map point variables and their geostatistical spatial variance, which indicates whether maps are significant; and (iii) associations between L-CV and snow or vegetation could support improved mapping using co-kriging or geostatistical simulations. The map-based method provides parameter values at ungauged sites and maps of spatial variance that could support decisions to add or remove gauges from a hydrometric network. Copyright © 2000 John Wiley & Sons, Ltd.

This study applied Log-Pearson Type III probability distribution to model time series annual peak flow records of River Niger recorded at Lokoja gauging station. This was necessitated by the need to provide reliable data for safe and economic hydrologic design for security of lives and property at downstream of river Niger basin. Though several methods have been adopted in the study area for flood mitigation, however, it has become apparent that these measures are inadequate and no attempt has been made to apply statistical approach for provision of sustainable solution. Though flood cannot be prevented but the impact can be reduced by applying adequate counter measures. Therefore, this study shows the result of flood frequency analysis based on annual peak flow measurement covering a period of 18 years (1995-2012) carried by National Inland Water Ways (NIWA) at Lokoja gauge station. The probability distribution function was applied to return periods (T) of 2, 5, 10, 25, 50, 100 and 200 years. The predicted discharges corresponding to these return periods are 18886.065, 22425.127, 24889.683, 28145.456, 30670.104, 33281.363 and 35997.757 m3/s, respectively. This study also revealed that the return period of 2012 flood is over 50 years. The predictive model which relates the expected discharge to return period is given by X = 3679.7 In(R) + 16381 where X is the expected discharge and R is the return period. Key words: Flood, return periods, discharge, prediction, hydrologic design.

As flood frequency analysis (FFA) is an exact and vigorous zone of analysis in statistical hydrology, so, in this regard, numerous probability models, parameters estimation procedures, regionalization problems, and other associated issues are being scrutinized in statistical hydrology. For this reason, research on FFA has been conducted with fluctuating passion over the past couple of decades. Therefore, there is a need to introduce flexible probability models and their parametric estimation techniques in statistical hydrology. However, for accurate probability modeling of upcoming flood events researchers try their best to study the heavy tailed distributions. In light of this, we intend to put forth a flexible probability model that not only addresses the problems with regional flood statistics but also illustrates the reasonable return periods for flood events brought on by melting glaciers and rising temperatures. We have described and examined some mathematical and statistical aspects of the suggested approach in light of the aforementioned scenario, and we have used it on actual flood data sets. To ensure realistic predictions using the proposed model, we have also analyzed it in terms of Mellin transformation.

A common problem in flood frequency analysis is estimation, from a short gauged record, of the flood corresponding to a return period of 50–1000 years. One would expect that an estimate of the historical maximum event; i.e., the maximum flood in a period of perhaps 100–200 years, would, if properly included in the estimation procedure, improve the resulting estimate of the flood magnitude at the given return period. We attempt to assess the value of historical information using computer simulation. An annual flood sequence and a historical maximum event are generated from ah extreme‐value distribution (of type I or II) and quantitiles of the distribution are estimated by maximum likelihood, both including the excluding the historical event. After many such simulations have been performed the accuracy of the quantile estimates is assessed. We also consider the effect of errors in the magnitude of historical discharge estimates and the use of historical data in regional flood frequency analysis.

Flood frequency analysis should consider small and frequent floods. Despite the complexities in partial duration series implementation, it can give a better flood estimation in a way that it does not exclude any significant high flow events, even if it is not the highest event of the year. This study employs the streamflow data recorded at Kajang station, Sungai Langat, Malaysia over a 36-year period spanning from 1978 to 2013. The paper attempts to conduct flood frequency analysis using two approaches, annual maximum and partial duration series. The optimal threshold value is selected to be 48.7 m3/s, where the dispersion index stabilizes at around 1, DI = 1 . The results have shown that generalized extreme value (GEV) distribution describes the annual maximum data while the lognormal (LN3) and generalized Pareto (GPA) distribution is chosen as the best fit distribution at Kajang station for a partial duration series. There is a slight difference between estimated streamflow magnitude when using GPA and LN3 for selected return periods, while a considerable difference was observed when using annual maximum at a higher return period. As a conclusion, PDS gives more relevant magnitude estimation rather than AMS. Flood frequency plays an important role in understanding the nature and magnitude of high flow, which in turn can assist relevant agencies in the design of hydrological structures and reduce flood impacts.

Joseph G. Zötl Karsthydrogeology 1974 Springer Vienna x + 291 D.M. 138.00

A realistic estimation of flood magnitude for a given return period is essential for successful operation and economical design of pivotal hydraulic structures such as dams, reservoirs and spillways, bridges, small culverts, urban drainage systems, flood plain zoning, economic evaluation of flood protection projects, etc. The flood frequency analysis is generally used for flood estimation, entirely based on the assumption that the floods are random and the floods in future are supposed to bear similar statistical properties that have occurred in the past. If adequate data are available at-site flood frequency analysis is used, otherwise regional flood frequency analysis (RFFA) is preferred for flood estimation. The RFFA for various small and medium catchments of India with different approaches have been carried out and reported in the literature. The focus of the present study is to carry out the RFFA using different approaches i.e. conventional method and L-moment and comparing the results for the Krishna and Penner subzone 3(h) of India. It was found that the values of growth factors obtained by the conventional method are higher than those of L-moment methods, thus leading to conservative estimate of the peak floods.

Impacts of climate and land-use change on flood events with different return periods in a mountainous watershed of North China

Statistical distributions play a crucial role in water resources management and civil engineering, particularly for analyzing data variability and predicting rare events with extremely long return periods (e.g., T = 1000 years, T = 10,000 years). Among these, the Pearson III (PE3) distribution is widely used in hydrology and flood frequency analysis (FFA). This study aims to provide a comprehensive guide to the practical application of the PE3 distribution in FFA. It explores five parameter estimation methods, presenting both exact and newly developed approximate relationships for calculating distribution parameters and frequency factors. The analysis relies on data from four rivers with varying morphometric characteristics and record lengths. The results highlight that the Pearson III distribution, when used with the L-moments method, offers the most reliable quantile estimates, characterized by the smallest biases compared to other methods (e.g., 31% for the Nicolina River and, respectively, 5% for the Siret and Ialomita Rivers) and the highest confidence in predicting rare events. Based on these findings, the L-moments approach is recommended for flood frequency analysis to improve the accuracy of extreme flow forecasts.

Reconstructions of the most severe historic flood events contribute to improved quantification of design discharges corresponding to large return periods. Reducing the uncertainty of design discharges has a great significance in constructing proper flood defences to protect the hinterland from future flooding. However, reconstructions of the peak discharges of such historic flood events are generally associated with large uncertainties, which arise from the accuracy of the historic topography, hydraulic roughness of the river channels and floodplains, and the historic hydrograph shape. This study sets up a one dimensional-two dimensional (1D-2D) coupled hydraulic model, stretching from the upstream of Bonn at Remagen to downstream of Düsseldorf, Germany, with the length of 113 km to reconstruct the maximum discharge of the 1374 flood event (Qmax,1374), which is considered to be the largest flood of the last millennium in the Lower Rhine catchment. An uncertainty analysis was performed by adopting different river bed levels and roughness values in order to estimate the influence of these uncertainties on the reconstructed peak discharge. The upstream discharge wave was varied corresponding to a wide range of peak discharges from 12,000 to 24,000 m3/s. The resulting Qmax,1374 was determined of between 14,400 and 18,500 m3/s, were then used in a flood frequency analysis to determine the design discharges corresponding to different return periods. Compared to the design discharge computed with previous estimations of the 1374 peak discharge, we found a significant reduction of 2,000 m3/s in the design discharge corresponding to a 100,000 year return period, which is the maximum safety standard adopted in the Dutch water policy for some downstream dike sections.

In 2008, the Environment Agency and the Meteorological Office launched a pilot Extreme Rainfall Alert (ERA) service as a first step towards providing a warning for surface water flooding. An ERA is based on rainfall intensity thresholds of an average of 1‐in‐30 year storms, to represent rainfall thought likely to cause severe surface water flooding in urban areas. This research investigates whether this return period is appropriate for warning of surface water flooding by examining the intensity and return period of rainfall associated with observed surface water flood (SWF) events. Data from rainfall gauges and flood events were analysed which showed that most of the SWF events were associated with rainfall intensities of less than 1‐in‐10 year return period. Improvements in data recording could provide flood magnitudes and durations, which would facilitate better understanding of the relationship between flood magnitude and rainfall intensity and allow more informed debate about SWF warning thresholds.