Heavy rainfall frequency analysis in the Benin section of the Niger and Volta Rivers basins: is the Gumbel's distribution a one-size-fits-all model?

West African populations are increasingly exposed to heavy rainfall events which cause devastating floods. For the design of rainwater drainage facilities (to protect populations), practitioners systematically use the Gumbel distribution regardless of rainfall statistical behaviour. The objective of this study is twofold. The first is to update existing knowledge on heavy rainfall frequency analysis in West Africa to check whether the systematic preference for Gumbel's distribution is not misleading, and subsequently to quantify biases induced by the use of the Gumbel distribution on stations fitting other distributions. Annual maximum daily rainfall of 12 stations located in the Benin sections of the Niger and Volta Rivers' basins covering a period of 96 years (1921–2016) were used. Five statistical distributions (Gumbel, GEV, Lognormal, Pearson type III, and Log-Pearson type III) were used for the frequency analysis and the most appropriate distribution was selected based on the Akaike (AIC) and Bayesian (BIC) criteria. The study shows that the Gumbel's distribution best represents the data of 2/3 of the stations studied, while the remaining 1/3 of the stations fit better GEV, Lognormal, and Pearson type III distributions. The systematic application of Gumbel's distribution for the frequency analysis of extreme rainfall is therefore misleading. For stations whose data best fit the other distributions, annual daily rainfall maxima were estimated both using these distributions and the Gumbel's distribution for different return periods. Depending on the return period, results demonstrate that the use of the Gumbel distribution instead of these distributions leads to an overestimation (of up to +6.1 %) and an underestimation (of up to −45.9 %) of the annual daily rainfall maxima and therefore to an uncertain design of flood protection facilities. For better validity, the findings presented here should be tested on larger datasets.

Application of Gumbel’s Distribution Method for Flood Frequency Analysis of Lower Ganga Basin (Farakka Barrage Station), West Bengal, India

The analysis of flood frequency will depend on the historical peak discharge data for at least 10 years. This study has taken into account peak annual maximum discharge data for 72 years (1949 to 2020). The discharge data was collected from the Farakka Barrage Gauging station (24°48'15.10" N and 87°55'52.70" E) situated in the upper part of lower Ganga basin. The flood frequency analysis of the lower Ganga basin’s upper portions has been carried out using Gumbel’s frequency distribution method. Gumbel’s method (XT) is a prediction analysing statistical approach. The discharge data was tabulated in descending order and rank has been assigned based on the discharge volume. The return period was calculated based on Weibull’s formula (P) for this analysis. The flood frequency data was plotted on a graph where X-axis shows the return period and the Yaxis is the discharge value. The R2 value of this graph is 0.9998 which describe Gumbel’s distribution method is best for the flood frequency analysis. The flood frequency analysis is an essential step to assess the flood hazard.

Determinação de equações de chuvas intensas para a encosta superior do nordeste do Rio Grande do Sul

The relationship intensity, duration and frequency is very important for the hydraulic project’s development, mainly in regions where there is no study updated data. This paper objective was to determine the intensity-duration-frequency curves at Rio Grande do Sul hillside, in order to provide tools for hydraulic structures design and hydrological studies in the region. For the return periods 2, 5, 10, 20, 25, 50 and 100 - year precipitation determination was used Gumbel’s and log-normal statistical distributions, using the Rain Relationship Duration Method for 20 rainfall stations. For Gumbel’s distribution data adherence verification, was used the Kolmogorov-Smirnov adhesion tests and Chi-Square adhesion, with, 5% significance level. The general IDF equation coefficients a, b, c and d were obtained through non-linear regression and the adjustment quality was measured by both determination coefficient and standard error. Different intense rainfall curves were obtained with the methodology applied, for the region, each one shows a good parameters adjustment, important tool for extreme precipitations estimating.

An approximate method for 1-D simulation of pollution transport in streams with dead zones

Analytical solutions describing the 1D substance transport in streams have many limitations and factors, which determine their accuracy. One of the very important factors is the presence of the transient storage (dead zones), that deform the concentration distribution of the transported substance. For better adaptation to such real conditions, a simple 1D approximation method is presented in this paper. The proposed approximate method is based on the asymmetric probability distribution (Gumbel’s distribution) and was verified on three streams in southern Slovakia. Tracer experiments on these streams confirmed the presence of dead zones to various extents, depending mainly on the vegetation extent in each stream. Statistical evaluation confirms that the proposed method approximates the measured concentrations significantly better than methods based upon the Gaussian distribution. The results achieved by this novel method are also comparable with the solution of the 1D advection-diffusion equation (ADE), whereas the proposed method is faster and easier to apply and thus suitable for iterative (inverse) tasks.

Study on energy distributions of strong seismic events in the USCB

The paper presents the statistical analysis of energy distribution of strong seismic shocks (energy E ≥ 105 J) occurred in the Upper Silesian Coal Basin which is one of the most seismically active mining areas in the world. In the USCB tremor epicenters do not occur uniformly throughout the whole basin but group in several regions belonging to different structural units and are separated by regions where strong shocks are not observed. The aim of the studies was to determine the modality of the energy distributions and to compare the modal types in regions of the USCB where the shocks epicenters cluster. An analysis was made for shocks with energies equal to or greater than 105 J recorded by Upper Silesian Regional Seismological Network operated by Central Mining Institute (CMI), which took place between 1987 – 2012. The analysis has proven the bimodality of seismic energy distribution in the three of five studied areas of the Upper Silesian Coal Basin. The Gumbel’s distribution II type best fit the experimental energy distribution for almost all studied tectonic units except the main syncline area, where the Gumbel’s distribution I type matched better the low-energy mode. This is due to too short time window, causing a shortage of the strongest shocks in seismic catalogue.

Occurrence probability of maximum sea levels in Polish ports of Baltic Sea coast

Occurrence probability of maximum sea levels in Polish ports of Baltic Sea coast In this work long-term probability of occurrence of maximum sea levels in some points of Polish Baltic Sea coast, was determined. Use was made of multi-year series of measurement data on maximum yearly sea levels, and their probability distributions were determined. To the analysis Gumbel's distribution and Pearson distribution of 3rd type as well as quantile methods and the highest credibility method, were applied. Kolmogorov test was used to examine conformity of the theoretical distributions with real random variable distribution. As results from the analysis, the highest sea levels of 1000- year return period can be expected in Polish ports of the west part of the coast, i.e. Kolobrzeg (750, 2 cm, i.e. 2,5 m above the average sea level) and Swinoujscie (723,6 cm). Lower sea levels of the same return period can be expected in Ustka (720,2 cm), Wladyslawowo (709,7 cm) and Gdansk (716, 7 cm), respectively.

Analysis of Hydrologic Data Using Pearson Type III Distribution

Computation of reliable and precise long term estimates from the available short term hydrologic records is often a challenging task for the design engineers/hydrologists. Peak flow magnitudes relating to ‘sixteen’ streams were utilised for deriving long term estimates using Maximum likelihood method (Gumbel 1941 and Panchang et al. 1962). The results revealed that most of peak flows were underestimated and their departures from the respective prototype magnitudes were of the order of 10 to 40 per cent. These peak flow magnitudes were graduated by the Pearson type III distribution with the result that a perfect calibration (departure within 1 per cent only) was achieved for three streams. For remaining streams the departures were reduced and were within 20 per cent. The precision of the estimates, deduced from the use of the Pearson type III distribution, was ascertained by evaluating the confidence intervals for these estimates. For three cases the confidence intervals (deduced from the latter distribution) were smaller than their counterparts deduced from the Gumbel's distribution. For the remaining streams' data, the confidence intervals were nearly double those obtained with the Gumbel's distribution. Thus to achieve conformity between prototype and model (using the Pearson type III distribution), one has to be content with even slightly less precise estimates, but which are, otherwise, realistic.