Flood frequency analysis for an urban watershed: comparison between several statistical methodologies simulating synthetic rainfall events

<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>

Keith Beven was amongst the first to propose and demonstrate a combination of conceptual rainfall–runoff modelling and stochastically generated rainfall data in what is known as the ‘continuous simulation’ approach for flood frequency analysis. The motivations included the potential to establish better links with physical processes and to avoid restrictive assumptions inherent in existing methods applied in design flood studies. Subsequently, attempts have been made to establish continuous simulation as a routine method for flood frequency analysis, particularly in the UK. The approach has not been adopted universally, but numerous studies have benefitted from applications of continuous simulation methods. This paper asks whether industry has yet realized the vision of the pioneering research by Beven and others. It reviews the generic methodology and illustrates applications of the original vision for a more physically realistic approach to flood frequency analysis through a set of practical case studies, highlighting why continuous simulation was useful and appropriate in each case. The case studies illustrate how continuous simulation has helped to offer users of flood frequency analysis more confidence about model results by avoiding (or exposing) bad assumptions relating to catchment heterogeneity, inappropriateness of assumptions made in (UK) industry‐standard design event flood estimation methods, and the representation of engineered or natural dynamic controls on flood flows. By implementing the vision for physically realistic analysis of flood frequency through continuous simulation, each of these examples illustrates how more relevant and improved information was provided for flood risk decision‐making than would have been possible using standard methods. They further demonstrate that integrating engineered infrastructure into flood frequency analysis and assessment of environmental change are also significant motivations for adopting the continuous simulation approach in practice. Copyright © 2016 John Wiley & Sons, Ltd.

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 is crucial for understanding flood risks in specific regions. This study applied the Gumbel Distribution Method to analyze flood frequency using river discharge data from the Kadamaian and Wariu Rivers in Kota Belud, Sabah, Malaysia. The analysis involved data collection, parameter estimation, goodness-of-fit testing, and determination of annual recurrence intervals (ARIs). The study found that the ARIs for the Kadamaian and Wariu Rivers are 50 years and 30 years, respectively, highlighting the need for targeted flood mitigation strategies in these areas. These findings emphasize the higher flood risk in the Kadamaian River basin, necessitating more robust flood control measures compared to the Wariu River basin. The Gumbel distribution provided accurate flood frequency estimations validated by the Kolmogorov-Smirnov test and correlation coefficient (R2). The calculated ARIs offer valuable insights for flood hazard assessment and contingency planning. These findings underscore the importance of accurate flood frequency analysis in enhancing flood mitigation strategies and disaster preparedness. It is recommended that local authorities incorporate these results into flood management and urban planning initiatives.

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

Influence of dike breaches on flood frequency estimation

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.

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

Rainfall records with time steps less than 15 min, which are required for designing storm water sewerage in urban areas, are rarely available throughout the Moroccan territory. The study was conducted with the objective to tackle this problem through the use of design storm structures with time steps that vary from 5 to 15 min. For this purpose, we used two structural families of design storms: (i) design storms derived from Intensity-Duration-Frequency (IDF) curves of Chicago, Composite, Desbordes, Watt, Weibull, Uniform, and Triangular design storm types; (ii) design storms from the Soil Conservation Service (SCS) synthetic rainfall. The selected design storm structures are those adapted to the rainfall distribution of Tangiers experimental basin and their resulted peak flows are comparable to the flow generated using the synthetic rainfall events. We also did sensitivity analysis for the Storm Water Management Model (SWMM) to changes of different design storm structural parameters, which includes storm duration, time steps, and intensity peak position. We evaluated how changes on these parameters affect peak flows and runoff volumes. In addition, Principal Component Analysis (PCA) method was used to validate the sensitivity analysis by identifying key storm parameters that significantly affect peak flows and Runoff volumes. SWMM model calibration results showed that the Desbordres and Chicago structures best fitted observed flow. Moreover, comparison of different SCS synthetic rainfall forms to observed rainfall events retains that of type 1. Furthermore, the Weibull and watt storms have both a shape parameter that has been calibrated by using the observed events. Overall, simulation results confirmed that peak flow was greatly affected by design storm structures, but was not closely correlated with rainfall intensity.

This article explores the relationship between commodity price cycles and the US business cycle. Commodity price cycles are known to foster capricious macroeconomic activity, and understanding their behaviour offers valuable economic insight. The US business cycle is a key indicator of the broader economic conditions, reflecting changes in economic activity, consumer spending, and overall market conditions. By examining the dynamics and interplay between these two cycles, this study provides insights into the potential synchronisation, lag, or lead between commodity price cycles and the US business cycle. The study employs a Fourier analysis of commodity price cycles and the US business cycle. In addition, the same empirical method will be used to analyse historical rainfall patterns in the US as a means of furthering the role of historical rainfall patterns in shaping agricultural productivity and subsequent price movements. Results show dominant cycles of 14.2 years throughout the commodity price dataset, 3.8 years within the US business cycle, and 14.2 years in US historical rainfall patterns. The study also identifies several factors that influence the relationship between these two cycles, including global demand, trade policies, and financial market fluctuations.

The reassessment of flood risk at York, UK, is pertinent in light of major flooding in November 2000, and heightened concerns of a perceived increase in flooding nationally. Systematic flood level readings from 1877 and a wealth of documentary records dating back as far as 1263 AD give the City of York a long and rich history of flood records. This extended flood record provides an opportunity to reassess estimates of flood frequency over a time scale not normally possible within flood frequency analysis. This paper re-evaluates flood frequency at York, considering the strengths and weaknesses in estimates resulting from four contrasting methods of analysis and their corresponding data: (a) single-site analysis of gauged annual maxima; (b) pooled analysis of multi-site gauged annual maxima; (c) combined analysis of systematic annual maxima augmented with historical peaks, and (d) analysis of only the very largest peaks using a Generalized Pareto Distribution. Use of the historical information was found to yield risk estimates which were lower and considered to be more credible than those achieved using gauged records alone. Citation Macdonald, N. & Black, A. R. (2010) Reassessment of flood frequency using historical information for the River Ouse at York, UK (1200–2000). Hydrol. Sci. J. 55(7), 1152–1162.

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

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.