Towards a systematic approach to comparing distributions used in flood frequency analysis

<p>The Glomma river is the largest in Norway and repeated destructive floods continue to represent a major climate hazard. Area planning and dam safety assessment in Norway, including the large catchment that feeds Glomma, are based on estimates of design flood sizes from 200 to 1000 years return periods despite the fact that most streamflow time series are ≤50 years. Consequently, design flood estimates are subject to sample uncertainty. Other data than streamflow measurements such as historical data and lake sediment cores can be employed not only to increase knowledge about floods, but also to reduce uncertainty in design flood estimates. By merging different data sources, it is possible to reduce the uncertainty associated with flood frequency analysis. The primary objective of this study is to combine systematic- historical and paleo-information in a methodological effort to improve flood frequency analysis.</p><p>We approach this ambition by (i) compiling historical flood data from the existing literature, (ii) presenting  high resolution XRF, MS and CT scanning data from a sediment core covering the last 10 000 years, and (iii) combining flood data from systematic streamflow measurements, historical sources and lacustrine sediment cores for estimating design floods and assessing non-stationarities in flood frequency.</p><p>Based on the lake sediments from Lake Flyginsjøen, which faithfully records flood events in Glomma, we can estimate flood frequency in a moving window of 50 years. Whenever the discharge is sufficient the floodwater crosses a local threshold and suspended sediments are deposited in the lake, providing information about how flood frequency has changed over the last 10 00 years. </p><p>The lake sediment data shows that past flood frequency is non-stationarity on different time scales. Periods with increased flood activity corresponds broadly to similar timeseries from eastern Norway and also in the Alps on centennial time scales. The flood frequency shows significant non-stationarities within periods with increased flood activity as was the case for the 18th century. The lake data indicates that the major historical flood in 1789 is the largest on record for the last 10 000 years at this site.</p><p>The results show that estimation of flood quantiles can benefit from the inclusion of historical and paleodata. The paleodata were in particular useful for evaluating how the flood information in historical data represent flood frequency on longer time scales. Using the frequency of floods obtained from the paleo-flood record resulted in minor changes in design flood estimates.   <br><br>This study has shown that the potential advantage of including paleoflood data and we suggest that paleodata has a high potential for detecting links between climate and flood frequency. The data presented here can be used alone, or in combination with paleoflood data from other locations in Norway and Europe, to assess and better understand the potential links between changes in climate and the corresponding changes in flood frequency.</p>

With the release of the 2016 edition of Australian Rainfall and Runoff (ARR), this paper asks the question, from here to where? It focuses on the core business of ARR, which is the estimation of flood quantiles, and assesses the accuracy of the two main approaches: flood frequency (FF) and joint probability (JP), of which the design storm (DS) approach is the simplest. The sources of uncertainty affecting FF and JP quantile estimation are dissected, and it is argued that the prevailing wisdom of the DS approach being more accurate than FF is questionable. A comparative error analysis of quantile estimates derived using gauged and regional application of FF and DS methods is presented using data from twenty-six well-gauged catchments. While FF tended to have better skill than DS methods, the skill levels were low. In the worst case, the regional DS method produced 90% probability limits for the 1 in 100 AEP quantile of 35% to 290%! These findings bring little comfort and highlight the fact there is much “unfinished business”. Two strategies are offered as a way forward: the first to reduce quantile uncertainty and the second to communicate and manage the large uncertainty inherent in quantile estimation.

Flood frequency analysis is used by water resources professionals to estimate the probability of exceedence associated with a flood of a given magnitude. The estimation of flood frequencies is important because they are used in the planning and design of hydraulic structures, in flood-plain management, and in reservoir operation. The index flood method is commonly used to develop a flood frequency curve that relates flood magnitude to flood rarity. This method involves scaling a dimensionless flood frequency curve by the index flood. The index flood is a middle-sized flood for which the mean or median of the flood data series is typically used. When the catchment of interest is ungauged, statistical models, such as multiple regression, are often used to relate the index flood to catchment descriptors. In this study six different parameter estimation techniques and three regionalization techniques are compared in terms of ability to predict the index flood for an ungauged catchment. A case study employing a split-sample experiment with data from catchments in Ontario, Canada, was used to evaluate the approaches. The models were assessed using three performance indices to evaluate the capability to predict the index flood for 20 stations. The dimensionless nonlinear model outperformed all of the other parameter estimation techniques for each of the three indices selected. The performance was improved through the use of geostatistical residual mapping, however, the improvement was small. The residual mapping was found to greatly improve the estimates obtained using ordinary least-squares regression.Key words: index flood, flood frequency analysis, regression, residual mapping, geostatistics.

A basin -wide flood frequency analysis using Index flood and L-moment s approach offers an attractive solution to provide flood quant ile estimations at hundreds of ungauged sites within the Red River Basin of the North . L-moments diagrams and hierarchical clustering techniques were used initially to delineate hydrologic regions within the basin . Although the northern plain is relatively flat and almost monotonous, the analyses have show n that four homogeneous regions could be established for the basin . The whole basin as a region is also established for the purpose of flood estimations along the main stem . Appropriate probability distrib utions are fitted to t he pooled regional flood peak s in each region . Monte Carlo simulations are performed to decide the best distribution for each region , and the dominant distributions found are the Log -Pearson Type III and the generalized Pareto distrib utions . The regression of index flood with the physical factors of drainage area and basin slopes for two of the five regions are not very satisfactory . However, t he flood quantile estimates are sufficient for preliminary planning purposes. Basis for Reg ional Flood Frequency Analysis and L -moments The Red River of the North Basin has 91 gauged sites but that number was not sufficient for economic planning purposes as flood quantile estimations at hundreds of ungauged sites within the basin were required . Regional flood frequency analysis is a good alternative approach to flood quantile estimation using a single station approach. It is well accepted that using a regional approach in flood frequency analysis is effective in extending the flood information at a site to sites within a homogeneous region. Recent papers by Burn and Goel (2000), Cunderlik and Burn (2002), Pfister et al. (2002), and Lim and Lye (2003) are examples of such undertakings. The extension enables flood quantile estimates for any site i n a region to be expressed or inferred in terms of flood data recorded at all gauging sites in that region. Design flood estimations using a regional approach can often be carried out using methods such as the index -flood method and the direct regression o n quantiles method.

<p>Flood frequency analysis (FFA) has long been the standard procedure for obtaining design floods for all kinds of purposes. Ideally, the data at the basis of the statistical operations have a high temporal resolution, in order to facilitate a full account of the observed flood peaks and hence a precise model fitting and flood quantile estimation.</p><p>Unfortunately, high-resolution flows are rarely disposable. Often, average daily flows pose the only available/sufficiently long base for flood frequency analysis. This averaging naturally causes a significant smoothing of the flood wave, such that the “instantaneous” peak can no longer be observed. As a possible consequence, design floods derived from these data may be severely underrated.</p><p>How strongly the original peaks are flattened and how this influences the design flood estimation depends on a variety of factors and varies from gauge to gauge. In this study we are looking at a range of errors arising from the use of daily instead of instantaneous flow data. These include differences in the observed individual flood peaks and mean annual maximum floods, as well as the estimated distribution parameters and flood quantiles. The aim is to identify catchment specific factors that influence the magnitude of these errors, and ultimately to provide a means for error assessment on the mere basis of local hydrological conditions, specifically where no high-resolution data is available.</p><p>The analyses are carried out on an all-German dataset of discharge gauges, for which high-resolution data is available for at least 30 years. The classical FFA approach of fitting distributions to annual maximum series is utilized for error assessment. For identification of influencing factors, both the discharge series themselves and a catalogue of climatic and physiographic catchment descriptors are screened.</p>

In flood frequency analysis, expanding the additional information with hydrological reasoning beyond local at‐site flood samples can be very useful for improving the accuracy of flood frequency distribution (FFD) estimation as well as reflecting a better understanding of flood characteristics. In this study, a river network‐based hierarchical model is developed to estimate the FFDs in the Upper Yangtze basin by making full use of the hydrological reasoning information of both the flood dependence within the river network and reservoir regulation. Under this hierarchical model, a covariate analysis based on the generalized additive model for location, scale and shape is performed to obtain the conditional distribution of the interested flood variable given both its upstream flood variables and the reservoir index quantifying reservoir regulation; and then, the FFD of the interested flood variable is derived by combining its conditional distribution with the probability distribution of the upstream flood variables. The application to the Upper Yangtze basin indicates that the proposed hierarchical model suggests a satisfactory performance in FFD estimation. It is also found that the reservoir regulation, especially that of the Three Gorges Reservoir, is of great significance in reducing the flood magnitude in the basin. Compared to the conventional FFD estimation method that directly fits the assumed theoretical probability distributions to the at‐site flood samples, the hierarchical model incorporating the flood dependence within the river network exhibits an advantage in capturing the effect of reservoir regulation on the floods as well as in reducing the uncertainty in flood quantile estimation.

Influence of dike breaches on flood frequency estimation

Historical and paleoflood information can substantially improve flood frequency estimates if appropriate statistical procedures are properly applied. However, the Federal guidelines for flood frequency analysis, set forth in Bulletin 17B, rely on an inefficient “weighting” procedure that fails to take advantage of historical and paleoflood information. This has led researchers to propose several more efficient alternatives including the Expected Moments Algorithm (EMA), which is attractive because it retains Bulletin 17B's statistical structure (method of moments with the Log Pearson Type 3 distribution) and thus can be easily integrated into flood analyses employing the rest of the Bulletin 17B approach. The practical utility of EMA, however, has been limited because no closed‐form method has been available for quantifying the uncertainty of EMA‐based flood quantile estimates. This paper addresses that concern by providing analytical expressions for the asymptotic variance of EMA flood‐quantile estimators and confidence intervals for flood quantile estimates. Monte Carlo simulations demonstrate the properties of such confidence intervals for sites where a 25‐ to 100‐year streamgage record is augmented by 50 to 150 years of historical information. The experiments show that the confidence intervals, though not exact, should be acceptable for most purposes.

Flood frequency analysis (FFA) provides information about the probable size of flood flows. Empirical methods are more commonly employed in engineering design and planning, and among empirical methods the at-site frequency analysis is by far the most commonly used method. When applying the methods of at-site flood frequency analysis, it is clear that the role of hydrology seems minor at best and the role of statistics seems to be the lead one, whereas it should be the other way round. FFA entails the estimation of the upper quantiles of an assumed form of a probability density function of the annual or partial duration maximum flows, as the true function is not known. In the paper, the five two-parameter models and their three-parameter counterparts have been assumed successively for describing the annual peak flows for Nowy Targ gauging station on the Dunajec River. The 1 % quantile has been estimated by four optimization criteria. To find the best fitting model, three discrimination procedures have been applied. The best fitting model and, thus, hydrological design value depends on the optimization criterion and the procedure of discrimination. It is characteristic for hydrological size of samples. At the same time, the designers of the hydraulic structures want to have a unique value, not accepting the uncertainty. It seems essential that we should go back and start examining the way in which we have been doing the hydrological frequency analysis.

Bayesian estimation of extreme flood quantiles using a rainfall-runoff model and a stochastic daily rainfall generator

The log-Gumbel distribution is one of the extreme value distributions which has been widely used in flood frequency analysis. This distribution has been examined in this paper regarding quantile estimation and confidence intervals of quantiles. Specific estimation algorithms based on the methods of moments (MOM), probability weighted moments (PWM) and maximum likelihood (ML) are presented. The applicability of the estimation procedures and comparison among the methods have been illustrated based on an application example considering the flood data of the St. Mary's River.

Regional flood frequency analysis by combining self-organizing feature map and fuzzy clustering

The paper illustrates the results of regional flood frequency analysis of eleven sites of the four major rivers of Punjab, Pakistan. The discordancy measure (D i ) shows that none of the site, in the cluster of eleven sites, is discordant. Timing of the flood occurrences has been used, initially, for the formation of homogeneous region, but the heterogeneity measure (H) has shown a small amount of heterogeneity. To reduce the amount of heterogeneity, a subjective adjustment has been made considering the fact that a couple of site is located at the confluence of rivers. As a result, two homogeneous regions have been identified, i.e., Region 1 having nine sites and Region 2 containing couple of site located at the confluence of the rivers. In order to find out suitable candidate(s) for regional distribution L-moment ration diagram, average weighted distance and Z DIST statistics have been used. To obtain the flood quantiles at ungauged sites, multiple linear regression relationship has been developed, between mean of annual maximum peak flows (AMPF) at gauged sites (l 1) and best subset of site characteristics, i.e., average rainfall during monsoon and catchment area of the rivers to which the sites belong. A cross-validation with the observed AMPF from 2010 to 2014 and historical data (the highest of the AMPF attained so far at various sites of Region 1) showed that the estimates based on this model/procedure are accurate and useful, especially for the longer return periods.

Flood frequency analysis estimates reliable design flood, which is critical for the safety of any hydraulic, hydrologic construction and management. The overall objective of this study is to perform flood frequency analysis for Seonath and Hasdeo river basins of Chhattisgarh state, India. In this study, homogeneous regions are delineated by Ward cluster analysis. Cluster variables are L-moment ratios of annual maximum events and catchment characters. Index flood is performed for parametric quantile estimation of flood events. L-moments are employed in regionalization, frequency distribution selection, and distribution parameter estimation. Locally weighted polynomial model (Locfit) is performed for at-site frequency analysis. Flood quantiles are estimated for regions and at sites. In regional flood frequency analysis, regionalisation based on annual maximum flood series shows better flood quantiles than regionalisation based on site characteristics. It reveals that geophysical homogeneity does not mean hydrologic homogeneity. Regional formulae for annual mean discharge are formulated based on catchment character for estimation of flood quantiles for ungauged catchments.KeywordsFlood frequency analysisCluster analysisL-momentsIndex floodLocfit

We examine some performance indices (PIs) that are used to compare regional and at‐site flood quantile estimation methods. These include the relative bias, the regional average root‐mean‐square‐error (RMSE), the regional average relative root‐mean‐square‐error (RRMSE), and the average RMSE and RRMSE ratios of quantile estimators. We study the dependence of these PIs on the relative variability (coefficient of variation) of the data. This is done by examining the effect of a location shift in the data on these PIs. The aim is to bring awareness to the fact that when comparing hydrological quantile estimators, some PIs are more greatly affected than others by data shifts in location. Among the PIs considered, we identify those that are invariant to a location shift in the data and those that are not. This is done under both assumptions of homogeneous and heterogeneous hydrological region. The generalized extreme value distribution is used to demonstrate some of the results, but the conclusions are applicable to other distributions with a location parameter. It is argued that because of the lack of invariance to location shift of certain quantile estimation methods and PIs, additional precautions need to be taken when comparing these methods. Although we focus discussion around flood frequency analysis, the points raised should be viewed within the broader context of hydrological frequency analysis.