Have applications of continuous rainfall–runoff simulation realized the vision for process‐based flood frequency analysis?

Nonstationary flood and low flow frequency analysis in the upper reaches of Huaihe River Basin, China, using climatic variables and reservoir index as covariates

Abstract. Estimates for rare to very rare floods are limited by the relatively short streamflow records available. Often, pragmatic conversion factors are used to quantify such events based on extrapolated observations, or simplifying assumptions are made about extreme precipitation and resulting flood peaks. Continuous simulation (CS) is an alternative approach that better links flood estimation with physical processes and avoids assumptions about antecedent conditions. However, long-term CS has hardly been implemented to estimate rare floods (i.e. return periods considerably larger than 100 years) at multiple sites in a large river basin to date. Here we explore the feasibility and reliability of the CS approach for 19 sites in the Aare River basin in Switzerland (area: 17 700 km2) with exceedingly long simulations in a hydrometeorological model chain. The chain starts with a multi-site stochastic weather generator used to generate 30 realizations of hourly precipitation and temperature scenarios of 10 000 years each. These realizations were then run through a bucket-type hydrological model for 80 sub-catchments and finally routed downstream with a simplified representation of main river channels, major lakes and relevant floodplains in a hydrologic routing system. Comprehensive evaluation over different temporal and spatial scales showed that the main features of the meteorological and hydrological observations are well represented and that meaningful information on low-probability floods can be inferred. Although uncertainties are still considerable, the explicit consideration of important processes of flood generation and routing (snow accumulation, snowmelt, soil moisture storage, bank overflow, lake and floodplain retention) is a substantial advantage. The approach allows for comprehensively exploring possible but unobserved spatial and temporal patterns of hydrometeorological behaviour. This is of particular value in a large river basin where the complex interaction of flows from individual tributaries and lake regulations are typically not well represented in the streamflow observations. The framework is also suitable for estimating more frequent floods, as often required in engineering and hazard mapping.

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.

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.

<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>

To obtain the flooding frequency distribution for an urban watershed, different methods based on simulations of synthetic rainfall events were compared with an empirical analysis of the flooding data and with the results of long‐term simulations. A copula‐based multivariate statistical analysis of the main hydrological variables was proposed to generate synthetic hyetographs. Two different approaches were adopted to assess a temporal pattern to the synthetic rainfall: one analyses all available historical rainfall patterns, and another adopts the cluster analysis in three different variants to reduce the computational effort of the analysis.To test the methodology reliability, the analysis was carried out for a real urban watershed. To carry out the flooding frequency analysis, all generated synthetic hyetographs were used as input of a dual drainage mathematical model of the analysed drainage system. Results showed that the method based on the analysis of all historical rainfall patterns was efficient in the estimation of flooding frequency, especially for higher return periods and approximately halved the computational costs of ordinary long‐term analysis. Regarding clustering approaches, although attractive for their computational efficiency, their adoption must be carefully evaluated because it could neglect relevant information and result in a less accurate flood frequency analysis.

Karmakar and Simonovic (2008)describe the methodology of assigning appropriate marginal distributions for three flood characteristics. It is found that the gamma distribution is best fitted for peak flow (P), and a nonparametric distribution from the orthonormal series method best fits to volume (V) and duration (D), based on the root mean square error, Akaike information criterion and Bayesian information criteria. In addition, the chi‐square test is performed to check the significance of fitness. In this paper, a methodology is developed to derive bivariate joint distributions of the flood characteristics using the concept of copulas, considering a set of parametric and nonparametric marginal distributions forP, VandDto mathematically model the correlated structure among them. In the conventional method of flood frequency analysis, the marginal distribution functions of peak flow, volume and duration are assumed to follow some specific parametric distribution function. The concept of copulas relaxes the restriction of traditional flood frequency analysis by selecting marginals from different families of probability distribution functions for flood characteristics. The present study performs a better selection of marginal distribution functions for flood characteristics by parametric and nonparametric estimation procedures, and demonstrates how the concept of copulas may be used for establishing a joint distribution function with mixed marginal distributions. The results obtained are useful for hydrologic design and planning purposes. The methodology is demonstrated with 70 years of stream flow data of Red River at Grand Forks of North Dakota, USA.

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.

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.

Similarity and differences between linear flood routing modelling (LFRM) and flood frequency analysis (FFA) techniques are presented. The moment matching used in LFRM to approximate the impulse response function (IRF) was applied in FFA to derive the asymptotic bias caused by the false distribution assumption. Proceeding in this way, other estimation methods were used as approximation methods in FFA to derive the asymptotic bias. Using simulation experiments, the above investigation was extended to evaluate the sampling bias. As a feedback, the maximum likelihood method (MLM) can be used for approximating linear channel response (LCR) by the IRFs of conceptual models.Impulse responses of the convective diffusion and kinematic diffusion models were applied and developed as FFA models. Based on kinematic diffusion LFRM, the equivalence of estimation problems of discrete‐continuous distribution and single‐censored sample are shown both for the method of moments (MOM) and the MLM. Hence, the applicability of MOM is extended for the case of censored samples.Owing to the complexity and non‐linearity of hydrological systems and resulting processes, the use of simple models is often questionable. The rationale of simple models is discussed. The problems of model choice and overparameterization are common in mathematical modelling and FF modelling. Some results for the use of simple models in the stationary FFA are presented. The problems of model discrimination are then discussed.Finally, a conjunction of linear stochastic processes and LFRM is presented. The influence of river courses on stochastic properties of the runoff process is shown by combining Gaussian input with the LCR of the simplified Saint Venant model. It is shown that, from the classification of the ways of their development, both LFRM and FFA can benefit. Copyright © 2006 John Wiley & Sons, Ltd.

Influence of dike breaches on flood frequency estimation

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.

Analyses of the magnitude and frequency of a 400-year flood record in the Fish River Basin, Namibia

Flood frequency analysis and discussion of non-stationarity of the Lower Rhine flooding regime (AD 1350–2011): Using discharge data, water level measurements, and historical records

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.