Paradigm Shift in distribution preferences for Flood Frequency Analysis and the ‘LMoFit’ R-Package

2021 ◽  
Author(s):  
Mohanad Ashraf Zaghloul ◽  
Simon Michael Papalexiou ◽  
Amin Elshorbagy
Keyword(s):  
Frequency Analysis ◽  
R Package ◽  
Flood Frequency ◽  
Flood Frequency Analysis ◽  
Future Application ◽  
Shape Parameters ◽  
Gev Distribution ◽  
Economical Design ◽  
Upper Limits ◽  
Alternative Power

<p>Safe and economical design of dams, highways, bridges, and other infrastructures require accurate estimates of the magnitude and frequency of peak floods obtained by flood frequency analysis (FFA). The Generalized Extreme Value (GEV) distribution is the traditional preference for FFA along with other distributions having location, scale, and shape parameters. In this poster, two alternative power-type distributions comprising one location and two shape parameters are explored, these are Burr type III (BrIII) and Burr type XII (BrXII) distributions. The performances of BrIII and BrXII are compared against that of GEV in describing annual maximum streamflow records at 1088 sites across Canada. A generic L-moment algorithm is developed to fit these distributions regardless of the unavailability of some of their analytical L-moment expressions. This algorithm is devised in the R package “LMoFit” on CRAN. The latter comparison shows that: (1) the three distributions perform equally-well in describing the observed peaks; (2) the BrIII and the BrXII distributions predict larger streamflow peaks increasing the heaviness of their right tails compared to that of the GEV distribution; (3) the predictions of the GEV distribution reach the upper limits of the distribution in 39% of the sites, while the corresponding predictions of BrIII and BrXII are not limited and exceed the reached limits of GEV; (4) the GEV distribution might be underestimating the risk of extreme events, especially for large return periods. Accordingly, there are potential limitations in using the GEV distribution for FFA and the findings suggest BrIII and BrXII distributions as consistent alternatives for future FFA practices. The “LMoFit” R package is devised to facilitate the future application of the suggested distributions.</p>

scholarly journals A grey-based method for evaluating the effects of rating curve uncertainty on frequency analysis of annual maxima

2012 ◽  
Vol 15 (1) ◽  
pp. 194-210 ◽  
Author(s):  
S. Alvisi ◽  
M. Franchini
Keyword(s):  
Frequency Analysis ◽  
Measurement Errors ◽  
Flood Frequency ◽  
Flood Frequency Analysis ◽  
Annual Maximum ◽  
Rating Curve ◽  
Upper Limits ◽  
Using Data ◽  
River Po ◽  
Discharge Measurements

A grey-based technique for characterizing the rating curve uncertainty due to discharge measurement errors and its effect on flood frequency analysis is here presented. On the basis of river stage and discharge measurements, the grey parameters of the rating curve are estimated by using a grey non-linear regression. Commencing with this grey rating curve and a set of annual maximum stages, we show how the probability distribution (here assumed of EV1 type) of the grey annual maximum discharges can be estimated. The grey EV1 distribution can be estimated through two approaches, the first of which directly exploits the grey discharges corresponding to the annual maximum stages, whereas with the second approach two different sets of extreme (crisp) discharges, and therefore two EV1 distributions of extreme (crisp) values which delimit the grey discharges of a given return period, are obtained by considering the lower and upper limits of the grey parameters of the rating curve. The methodology is illustrated using data pertaining to a gauged section of the River Po (Italy). The results show that the first approach yields a wider grey EV1 distribution with respect to that resulting from the second approach: physical justification of this is given.

scholarly journals A data-based comparison of flood frequency analysis methods used in France

2014 ◽  
Vol 14 (2) ◽  
pp. 295-308 ◽  
Author(s):  
K. Kochanek ◽  
B. Renard ◽  
P. Arnaud ◽  
Y. Aubert ◽  
M. Lang ◽  
...  
Keyword(s):  
Frequency Analysis ◽  
Gumbel Distribution ◽  
Flood Frequency ◽  
Flood Frequency Analysis ◽  
Local Version ◽  
Simulation Approach ◽  
Ungauged Catchments ◽  
Gev Distribution ◽  
Continuous Simulation ◽  
Regional Estimation

Abstract. Flood frequency analysis (FFA) aims at estimating quantiles with large return periods for an extreme discharge variable. Many FFA implementations are used in operational practice in France. These implementations range from the estimation of a pre-specified distribution to continuous simulation approaches using a rainfall simulator coupled with a rainfall–runoff model. This diversity of approaches raises questions regarding the limits of each implementation and calls for a nation-wide comparison of their predictive performances. This paper presents the results of a national comparison of the main FFA implementations used in France. More accurately, eight implementations are considered, corresponding to the local, regional and local-regional estimation of Gumbel and Generalized Extreme Value (GEV) distributions, as well as the local and regional versions of a continuous simulation approach. A data-based comparison framework is applied to these eight competitors to evaluate their predictive performances in terms of reliability and stability, using daily flow data from more than 1000 gauging stations in France. Results from this comparative exercise suggest that two implementations dominate their competitors in terms of predictive performances, namely the local version of the continuous simulation approach and the local-regional estimation of a GEV distribution. More specific conclusions include the following: (i) the Gumbel distribution is not suitable for Mediterranean catchments, since this distribution demonstrably leads to an underestimation of flood quantiles; (ii) the local estimation of a GEV distribution is not recommended, because the difficulty in estimating the shape parameter results in frequent predictive failures; (iii) all the purely regional implementations evaluated in this study displayed a quite poor reliability, suggesting that prediction in completely ungauged catchments remains a challenge.

Application of Higher Probability Weighted Moments in Flood Frequency Analysis

2012 ◽  
Vol 518-523 ◽  
pp. 4139-4143
Author(s):  
Yang Li ◽  
Song Bai Song
Keyword(s):  
Frequency Analysis ◽  
Maximum Flow ◽  
Flood Frequency ◽  
Flood Frequency Analysis ◽  
Annual Maximum ◽  
Gev Distribution ◽  
Probability Weighted Moments ◽  
Northern Shaanxi ◽  
Flood Analysis ◽  
Better Than

This paper aims to study the use of higher probability moments (PWMs) for flood frequency analysis. By estimating the parameters of GEV distribution and matching higher PWMs to annual maximum flow series in northern Shaanxi. The results show that higher PWMs describe the data reasonably better than lower PWMs in flood analysis. This method involves no more complication than lower PWMs that be commonly used, and is suitable for flood frequency analysis.

scholarly journals A data-based comparison of flood frequency analysis methods used in France

2013 ◽  
Vol 1 (5) ◽  
pp. 4445-4479 ◽  
Author(s):  
K. Kochanek ◽  
B. Renard ◽  
P. Arnaud ◽  
Y. Aubert ◽  
M. Lang ◽  
...  
Keyword(s):  
Frequency Analysis ◽  
Gumbel Distribution ◽  
Flood Frequency ◽  
Flood Frequency Analysis ◽  
Local Version ◽  
Simulation Approach ◽  
Ungauged Catchments ◽  
Gev Distribution ◽  
Continuous Simulation ◽  
Regional Estimation

Abstract. Many flood frequency analysis (FFA) implementations are used in operational practice in France. These implementations range from the estimation of a pre-specified distribution to continuous simulation approaches using a rainfall simulator coupled with a rainfall-runoff model. This diversity of approaches raises questions regarding the optimal ambits of each implementation and calls for a nation-wide comparison of their predictive performances. This paper presents the results of a national comparison of the main FFA implementations used in France. More accurately, eight implementations are considered, corresponding to the local, regional and local-regional estimation of Gumbel and Generalized Extreme Value (GEV) distributions, as well as the local and regional estimation of a continuous simulation approach eventually resulted in a local and a regional version. A data-based comparison framework is applied to these eight competitors to evaluate their predictive performances in terms of reliability and stability, using daily flow data data from more than one thousand gauging stations in France. Results from this comparative exercise suggest that two implementations dominate their competitors in terms of predictive performances, namely the local version of the continuous simulation approach and the local-regional estimation of a GEV distribution. More specific conclusions include the following: (i) the Gumbel distribution is not suitable for Mediterranean catchments, since this distribution demonstrably leads to an underestimation of flood quantiles; (ii) the local estimation of a GEV distribution is not recommended, because the difficulty in estimating the shape parameter results in frequent predictive failures; (iii) all the purely regional implementations evaluated in this study displayed a quite poor reliability, suggesting that prediction in completely ungauged catchments remains a challenge.

Calculation Higher Probability Weighted Moments for Generalized Extreme Value in Hydrology

2012 ◽  
Vol 518-523 ◽  
pp. 4015-4021 ◽  
Author(s):  
Song Bai Song ◽  
Yang Li ◽  
Yan Kang
Keyword(s):  
Frequency Analysis ◽  
Extreme Value ◽  
Flood Frequency ◽  
Flood Frequency Analysis ◽  
Frequency Curve ◽  
Generalized Extreme Value ◽  
Gev Distribution ◽  
Probability Weighted Moments

In flood frequency analysis, the observed data of the smaller censored flows have no influence on fitting frequency curve, and the final fitting still depends very mainly on the larger flows. It also exhibits two or more distinct segments. The higher probability weighted moments(HPWMS) showed its potential merit for these estimating flood samples. In this paper, a detail approximating calculation of the parameter for common generalized extreme value (GEV) distribution by HPWMS method is given. This method has no more complication procedures than traditional lower orders of probability weighted moments.

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