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Boxplots of error estimates for the two approaches with Gumbel distribution used for design flood level estimation at cross-sections (A,B). The red lines represent the median (50th percentile), the lower and upper ends of the blue box represent the 25th and 75th percentile, respectively. Outliers are represented by red dots.

Boxplots of error estimates for the two approaches with Gumbel distribution used for design flood level estimation at cross-sections (A,B). The red lines represent the median (50th percentile), the lower and upper ends of the blue box represent the 25th and 75th percentile, respectively. Outliers are represented by red dots.

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Article
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The design of flood defence structures requires the estimation of flood water levels corresponding to a given probability of exceedance, or return period. In river flood management, this estimation is often done by statistically analysing the frequency of flood discharge peaks. This typically requires three main steps. First, direct measurements of...

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Context 1
... application of the simulation framework described in Section 2 and depicted in Figure 1, to a 98-km reach of the Po River (Section 3), allows us to compare the accuracy and precision of the two approaches for the estimation of design flood levels. Figure 3 shows boxplots of errors when the estimation of design flood levels is based on the two methods that are considered in this study. Water 2019, 11, x ...
Context 2
... application of the simulation framework described in Section 2 and depicted in Figure 1, to a 98-km reach of the Po River (Section 3), allows us to compare the accuracy and precision of the two approaches for the estimation of design flood levels. Figure 3 shows boxplots of errors when the estimation of design flood levels is based on the two methods that are considered in this study. Figure 3. Boxplots of error estimates for the two approaches with Gumbel distribution used for design flood level estimation at cross-sections A and B. The red lines represent the median (50th percentile), the lower and upper ends of the blue box represent the 25th and 75th percentile, respectively. ...
Context 3
... 3 shows boxplots of errors when the estimation of design flood levels is based on the two methods that are considered in this study. Figure 3. Boxplots of error estimates for the two approaches with Gumbel distribution used for design flood level estimation at cross-sections A and B. The red lines represent the median (50th percentile), the lower and upper ends of the blue box represent the 25th and 75th percentile, respectively. ...
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... left panel of Figure 3 refers to the common approach (when the estimation is based on annual maximum flows), and it shows a substantial underestimation, which is larger in section A, where the rating curve has larger errors (Figure 2). Moreover, and there is no substantial improvement in accuracy and precision after increasing the sample size from 30 to 100 years. ...
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... right panel of Figure 3 refers to the alternative approach (when the estimation is based on annual maximum levels), and it shows an underestimation of the design flood by 0.8 m with a more The left panel of Figure 3 refers to the common approach (when the estimation is based on annual maximum flows), and it shows a substantial underestimation, which is larger in section A, where the rating curve has larger errors (Figure 2). Moreover, and there is no substantial improvement in accuracy and precision after increasing the sample size from 30 to 100 years. ...
Context 6
... right panel of Figure 3 refers to the alternative approach (when the estimation is based on annual maximum levels), and it shows an underestimation of the design flood by 0.8 m with a more The left panel of Figure 3 refers to the common approach (when the estimation is based on annual maximum flows), and it shows a substantial underestimation, which is larger in section A, where the rating curve has larger errors (Figure 2). Moreover, and there is no substantial improvement in accuracy and precision after increasing the sample size from 30 to 100 years. ...
Context 7
... right panel of Figure 3 refers to the alternative approach (when the estimation is based on annual maximum levels), and it shows an underestimation of the design flood by 0.8 m with a more significant reduction of uncertainty after increasing the sample size from 30 to 100 years. These differences are substantial when the estimation of design flood levels is used for flood defence design or risk assessment. ...
Context 8
... example application demonstrates that the alternative approach can work better than the common approach in terms of both accuracy and precision (Figure 3). These results were unavoidable as they were associated with the specific test site, as well as the arbitrary assumptions about the parent distribution and the hydraulic model. ...

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Citations

... Therefore, the probabilistic methods based on hydrological observation data statistic analysis have been more popular in studying and predicting diverse design hydrological characteristics. In particular, it is in the case of forecasting maxima water discharges relating to riverine floods [1][2][3]. ...
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... For example, the design annual exceedance probabilities in terms of prediction of maximum water levels and possible inundation zones because of floods may be established at 0.005, year -1 (or 0.5%, year -1 ), 1%, 2%, 5%, and 10%, or something else; the corresponding return periods of the design floods -200, 100, 50, 20, and 10 years, etc. In hydrological investigations relating to river floods, these estimations are usually done by statistically analysing the frequency of flood peak discharges [29][30][31][32][33]. Practically, it is done in such a way. ...
... In hydrological investigations relating to river floods, these estimations are usually done by statistically analysing the frequency of flood peak discharges [29][30][31][32][33]. Practically, it is done in such a way. Direct annual maximum water levels' h (m) measurements at a near-located gauging (hydrological) station are converted into maxima annual discharges Q (m 3 /s) by using a rating curve ) (h f Q = [7,33]. As a result of longterm (not less than 30-40 years) uninterrupted hydrological measurements, time series of annual maximum water discharges of floods are formed. ...
... Gathered data are statistically analysed, and, in the frame of the stationary hypothesis, a relevant maxima annual discharges' probability distribution is chosen, which has to fit the observed data [29,34,35]. This probability distribution is used to derive a predicted peak discharge corresponding to a chosen design return period p r T , or a chosen design annual probability of exceedance P [33]. In the next step, the established peak discharge of a chosen design annual probability of exceedance may be used as the input value for the hydraulic modelling to derive the corresponding design flood level [33,36], taking into account the current conditions with hydromorphological characteristics of the river channel and floodplain [37]. ...
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... Since the natural disaster as extreme floods is the basis for planning and design of various hydraulic structures, hydrological forecasting, flood risk reflection characteristics such as trends of extreme floods and its changes, and its formation conditions, the probable maximal flood and its characteristics have a great practical importance. The determining of the probable maximal flood is the practical importance, especially for the planning, design, and operation of hydrotechnical structures (Apel et al., 2004;Blöschl et al., 2013;Okoli et al., 2019). ...
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... The first hydro-meteorological approach employs historical rainfall-runoff data to estimate design rainfall converted to design rainfall-excess for its convolution using unit hydrograph to estimate design runoff/flood (Subramanya 2013). The second statistical flood frequency analysis employs measurements of annual maximum water levels at a river cross-section for the derivation of annual maximum flows for fitting to a suitable probability distribution to derive the design peak flow corresponding to a particular return period (Okoli et al. 2019). However, the unavailability of discharge data limits their application to ungauged catchments. ...
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Wide field application of curve number (CN) methodology in design flood estimation and forecasting studies is a well-accepted reality. The parameter CN is often regarded as a constant, but it is in fact a random variable, for it relies on a number of factors governing the process of rainfall-runoff. This paper suggests an alternative procedure to estimate design runoff (Q) using design storm (P) and design curve number (CN) values. To this end, design CN values for different durations and return periods have been derived from 25 years of daily annual maximum P-Q data of 10 Indian catchments. When compared, the computed design Q from design CN values was either very close to or slightly greater than the observed Q. The performance is also evaluated using coefficient of determination (R2), percentage of bias (PBIAS), and normalized Nash-Sutcliffe efficiency (NNSE). The magnitude of design CN is found to decrease for longer durations and smaller return periods, and vice versa, and such a behavior invoked the development of an empirical relation for estimation of design CN from given return period and duration for gauged as well as ungauged watersheds. The statistical analysis revealed the general extreme value (GEV) to fit best the P-CN series, whereas multiple probability distributions, viz., GEV, Gumbel max, log Pearson 3, and Gen Pareto fitted best the Q series. The 50-year, 100-year, and 200-year runoff estimated from the P-CN series exceeded only marginally those derived from the conventional Q series approach.
... et. al, 1999); Rainfall-runoff Model (Lamb, 2005); Weibull formula (Selaman et. al, 2007); Log-Pearson Type III distribution (Sathe, et. al. 2012); Probability plotting method (Connell and Mohssen, 2017); California Method (Ganamala, and Kumar, 2017); Hazens Method (Ganamala, and Kumar, 2017); Gumbel's method (Bhagat, 2017) and Probability Models (Okoli et. al., 2019). From this above all methods, Gumbel's Method is most commonly used. So, this study were focus, used the peak discharge data and selected the method of Gumbel's distribution which is widely used for predicting extreme hydrological events such as floods (Zelenhasic, 1970;Haan, 1977;Shaw, 1983). ...
Article
Quantification of peak flood (extreme-hydrological event) discharge of a channel or river saying for a desired return period is a pre-requisite for design, planning and management of hydraulic configurations like, dam, bridges, spillways, barrages, etc. this paper figure out the result of a study carried out at estimation the frequency of Lower Godavari River division’s flood by using the methods of Gumbel distribution which is one of the probability distribution methods used to model stream flows. The method was used to model the annual maximum river discharge for a period of 25 years (1991-92 to 2015-16). The analysis of the regression equation (R2) gives a value, which shows that this distributional method (Gumbel) is suitable for prophesying the expected flow in the future on this river.