Gumbel Method Research Articles

A Basic Wind Speed Map for Oman

The aim of this research was to develop the first basic wind speed map for Oman. Hourly mean wind speed records from 40 metrological stations were used in the calculation. The period of continuous records ranged from 4–37 years. The maximum monthly hourly mean and the maxima annual hourly mean wind speed data were analysed using the Gumbel and Gringorten methods. Both methods gave close results in determining basic wind speeds, with the Gumbel method giving slightly higher values. Due to a lack of long-term records in some regions of Oman, basic wind speeds were extrapolated for some stations with only short-term records, which were defined as those with only 4– 8 years of continuous records; in these cases, monthly maxima were used to predict the long-term basic wind speeds. Accordingly, a basic wind speed map was developed for a 50-year return period. This map was based on basic wind speeds calculated from actual annual maxima records of 29 stations with at least 9 continuous years of records as well as predicted annual maxima wind speeds for 11 short-term record stations. The basic wind speed values ranged from 16 meters/second (m/s) to 31 m/s. The basic wind speed map developed in this research is recommended for use as a guide for structural design in Oman.

Applied statistics for extreme wind estimate

AbstractThe assessment of extreme wind speeds is a crucial issue for securing structural safety of wind turbines and inquiring largest loads to which turbines must be prepared to undergo.International standards suggest applying the Gumbel method of fitting the annual maxima to their theoretic probability distribution. Yet, often, wind databases are too short to apply such methods with statistical significance, and other procedures are commonly adopted [such as peaks over threshold (POT) and independent storms], which involve dependency on arbitrary thresholds for filtering data and issues of sub‐asymptocity, i.e. how well the selected dataset fits to density functions describing the distribution of peaks or extreme values.The present paper aims at contributing to such currently ongoing debate, providing a statistical analysis of the application of POT and independent storms methods on wind time series of various lengths from different geographical areas.The CERN data analysis framework ROOT has been employed for guaranteeing excellent standards of computational precision and wealth of statistical information. Analysis of uncertainties in the wind speeds estimates and tests of the goodness of fit of the datasets to the proper distributions have been carried on. An algorithm for choosing the optimum thresholds was developed, which encapsules and compromises the statistical complexity of the methods. A declustering procedure has been carried on for discriminating proper peaks in the POT method: it has been tested that such declustering provides a dramatic improvement of the statistical quality of the method. Copyright © 2014 John Wiley & Sons, Ltd.

A comparison of methods to estimate peak wind loads on buildings

The most appropriate statistical technique to estimate a peak pressure coefficient from wind tunnel data is not a settled issue. The lack of a standard acceptable method can lead to inconsistent definitions and interpretations of peak pressure coefficients, particularly since time constraints associated with wind tunnel tests necessitate relatively short test durations. A Gumbel model is commonly used to represent the peak distribution, where parameters are determined using observed peaks. Recent papers have proposed several variations of a peak estimation procedure using the entire time history and a translation from a Gaussian peak distribution model to non-Gaussian. It is shown that, in the case of mildly non-Gaussian data, translation methods achieve accuracy comparable to the Gumbel method. It is also shown that translation methods lose accuracy when the record deviates significantly from Gaussian, while the Gumbel model maintains stable accuracy and precision. This paper presents two new translation-based peak pressure coefficient estimation schemes that offer accurate and stable performance for strongly non-Gaussian data. Very long duration wind tunnel data provide empirical peak distributions with which to compare the relative performance of the Gumbel, existing translation and proposed new translation methods. One of the new methods slightly outperforms the Gumbel method.

Measurement-Based Vehicle Load Model for Urban Expressway Bridges

Significant changes in vehicle loads have occurred in China due to the development of the automobile industry and transportation within the past two decades, particularly the rapid increase in traffic flow and the large-scale emergence of heavy trucks. However, research into vehicle loadings on urban bridges is not well developed. In this study, based on traffic flow data collected using a weigh-in-motion system installed on an expressway in an urban logistics zone, we analyzed the traffic flow, vehicle types, and gross vehicle weight (GVW) features and developed models for the vehicle load and fatigue load. According to the axle space, axle types, and axle number, the trucks in the traffic flow were classified into 10 representative vehicle types. The probability distribution of the GVW was fitted to a three-class mixed log-normal distribution. Using the improved Gumbel method, we determined the extreme value distribution of the vehicle loadings in the purpose reference period and assessed the vehicle loadings of urban bridges. In addition, using the equivalent damage theory, six equivalent vehicle models were established according to the measurements of the axle weight and axle space, thereby obtaining a simplified model of fatigue vehicle loadings on urban expressway bridges.

Estudo das precipitações para diferentes períodos de retorno no municipio de São João do Jaguaribe/CE

The knowledge of the probable maximum rainfall is of great importance in the development of hydraulic engineering projects and agricultural. The objective of this workwas to determine the city of São João do Jaguaribe-CE the maximum precipitation for return periods of 2 , 5 , 10 , 20 , 50 and 100 years through the Gumbel distribution . To estimate the parameters of Gumbel used the method of moments, which is a technique of resolutions of complex integral equations by reducing these to a simple system of linear equations . The results obtained for the maximum rainfall return periods of 2, 5 , 10 , 20 , 50 and 100 years were 41,71 ; 112,17 ; 158,82 ; 203,57 ; 261,50 and 304,91mm . The Gumbel method was suitable in the estimation of maximum rainfall , which represents an alternative in determining the maximum rains project . The results are meaningful and useful work for soil conservation, proper sizing of roads, spillways of dams, urban drainage and choice of crops to be planted.

Hydrological assessment for mini hydropower potential at Sungai Pahang @ Temerloh

Sg Pahang at Temerloh was considered for assessment of hydropower potential using hydrological analysis method and hydrological model. The available data related to topography, soil, land use, weather and discharge pertaining to the study catchment were used to characterize the catchment. The characterization was required for water resources hence hydropower assessment. The hydrology of the study catchment was simulated through the model. This hydrological study is required due to the proposed mini hydroelectric power plant at Pulau Temerloh. It is essential to evaluate the existing river flow characteristic and to model the environmental flow assessment of the river. Two rainfalll stations, JPS Temerloh and Pintu Kawalan Paya Kertam Station are selected to develop the Rainfall Intensity Duration frequency (RIDF) Curve to determine the rainfall intensity of the area. Daily river flow were recorded at Sg Pahang at Temerloh and Sg Pahang at Lubok Paku were used to develop the Flow Duration Curve (FDC) to study the characteristic of Sungai Pahang flow. The 7 days low flow with 10 years return period (7Q10 low flow) was obtained using both Gumbel Method and Log Pearson Type III Method. The results from FDC shows that 50% percentage of time the Sg Pahang @ Temerloh is exceeded over a historical period is 400 m3/s and 50% percentage of time the Sg Pahang @ Lubok Paku is exceeded over a historical period is 650 m3/s. The required environmental flow are set to be 7Q10 low flow which is 64.215 m3/s for Sg Pahang at Temerloh and 79.24 m3/s for Sg Pahang at Lubok Paku. The results show the water resources are abundant and hence boost the mini hydropower potentiality at Sg Pahang.

A study on the use of Gumbel approximation with the Bernoulli spatial scan statistic

The Bernoulli version of the spatial scan statistic is a well established method of detecting localised spatial clusters in binary labelled point data, a typical application being the epidemiological case-control study. A recent study suggests the inferential accuracy of several versions of the spatial scan statistic (principally the Poisson version) can be improved, at little computational cost, by using the Gumbel distribution, a method now available in SaTScan(TM) (www.satscan.org). We study in detail the effect of this technique when applied to the Bernoulli version and demonstrate that it is highly effective, albeit with some increase in false alarm rates at certain significance thresholds. We explain how this increase is due to the discrete nature of the Bernoulli spatial scan statistic and demonstrate that it can affect even small p-values. Despite this, we argue that the Gumbel method is actually preferable for very small p-values. Furthermore, we extend previous research by running benchmark trials on 12 000 synthetic datasets, thus demonstrating that the overall detection capability of the Bernoulli version (i.e. ratio of power to false alarm rate) is not noticeably affected by the use of the Gumbel method. We also provide an example application of the Gumbel method using data on hospital admissions for chronic obstructive pulmonary disease.

Inland water bodies in Chile can locally increase rainfall intensity

Summary Analysis of precipitation observations from Chile indicated that man-made water reservoirs might be affecting the intensity of extreme precipitation events. Fifty rain gauges were used to evaluate rainfall intensities under different climates, using the Gumbel method ( T = 5 and 100 years) and average maximum recorded rainfall intensities to construct IDF curves for each station. A spatial analysis of the stations was undertaken to establish graphical relationships on documented maximum annual rainfall intensities for 1 h and those obtained by the Gumbel method as a function of latitude, longitude, elevation, and the distance from water bodies. The Mann–Whitney U test was applied with an error of 5%. Values obtained from stations located close to water bodies were compared to those located away from them. The results show significant changes in dryer climates.

Predicting violations of national ambient air quality standards using extreme value theory for Delhi city

Type I asymptotic distribution of extreme values was used for making predictions of the expected number of violations of the National Ambient Air Quality Standards (NAAQS) for 24–hour average sulfur dioxide (SO2), nitrogen dioxide (NO2) and suspended particulate matter (SPM), monitored at the four National Ambient Air Quality Monitoring (NAAQM) stations run by the Central Pollution Control Board (CPCB) for Delhi city. The parameters of the distribution were estimated using Gumbel's method. A comparison of the predicted violations of NAAQS and the exceedance of the maximum pollution concentration with that of the observed data indicates that Type I asymptotic distribution adequately fits to the observed extreme value data. The application of extreme value theory as a tool for managing urban air quality was highlighted.

Impact of the shale mine on the River Purtse hydrological regime in north-east Estonia

The present paper studies long-term (1923–2005) changes in the hydrological regime of the medium (100–1,000 km2) river of the Ordovician oil shale field of north-east Estonia. The changing regime in the heavily mined catchments is contrasted with a morphologically similar reference catchment (River Keila) where there has been no mining activity. The Gumbel Method and Rodionov Regime Shifts Algorithm (STARS) were used to study high- and low-water changes of the mining area. The study shows that mine water has no significant impact on the River Purtse annual run-off; however, it has influence on the low water period and minimum flow values, increasing the amount of run-off. Mine water discharge can affect the course of the run-off during the high water period and high water season peaks. Therefore, in terms of the river maximum flows return period, there are no major differences between the mining and natural catchments.

Risk-based inspection for large-scale crude oil tanks

Periodic Internal Inspection Method often results in under-inspection or over-inspection for large-scale crude oil tank. Therefore, how to determine reasonable internal inspection interval (INTII) has great significance on balancing the safe operation requirement and inspection cost for crude oil tanks. Here, RBI (risk-based inspection) technology is used to quantitatively assess the risk of crude oil tanks in an oil depot in China. The risk comparison between tank shell and bottom shows that the risk of tank depends on the risk of tank bottom. The prediction procedure of INTII for crude oil tanks is also presented. The INTII predicted by RBI method is gradually extended with the increasing of the acceptable risk level. The method to determine the acceptable risk of crude oil tanks is proposed, by which 3.54E+04 are taken as the acceptable risk of the oil depot. The safety factor of 0.8 is proposed to determine the final INTIIs for 18 crude oil tanks. The INTII requirement in China code SY/T 5921, 5–7 years, is very conservative and lower than predicted service life of tanks. The INTIIs predicted by Gumbel method are smaller than by RBI method for tanks with short INTII. Therefore, this paper recommends RBI method to predict the INTII for crude oil tanks.

Developing an empirical formulae to estimate rainfall intensity in Riyadh region

The purpose of this paper is to develop an empirical formula to estimate design rainfall intensity based on intensity–duration–frequency (IDF) curves. These curves have been generated from a 32-year recorded rainfall data for Riyadh region. Rainfall intensity–duration–frequency curves describe rainfall intensity as a function of duration for a given return period which are important for the design of storm water drainage systems and hydraulic structures. The formula is derived using the analysis of results of three different frequency methods, namely: Gumbel, Log Pearson III, and Log normal. These methods are used to obtain the IDF curves for six different durations (10, 20, 30 min, and 1, 2, 24 h) and six frequency periods (2, 5, 10, 25, 50, 100 years) where the best method of IDF estimation is recommended for future analysis. The equation can predict rainfall intensity in Riyadh region for any return period with a given storm duration and calibrated parameters obtained from IDF curves. Good match was achieved between its results and other analytical methods results such as Gumbel method. Moreover, it allows incorporating data from non-recording stations, thus remedying the problem of establishing IDF curves in places with a sparse network of rain-recording stations.

<strong>ANALISIS PERIODE ULANG HUJAN MAKSIMUM DENGAN BERBAGAI METODE</strong><br>(RETURN PERIOD ANALYZE MAXIMUM RAINFALL WITH THREE METHOD)

Lush rainfall intensity in Indonesia mostly often affecting to flood disaster. Managing in flood problem must be supporting by good infrastructure of flood management such as dam, irrigation system, drainages,etc. In designing a water building, we needs maximum rainfall information with certain return period. The amount of maximum rainfall for design are different according to lifetime and reservoir capacity such as for a big dam that needs maximum rainfall information with long return period approximately 50,100 years, and for irrigation system needs shorter maximum rainfall information about 2,5,10 years. We use three methods in this analysis: E.J. Gumbel Method, Log Pearson III Method and Iway Kadoya Method. Result of analysis from above methods show that Log Pearson III method and Iway Kadoya method as identically as E.J Gumbell method.

Estimation of return periods for extreme sea levels: a simplified empirical correction of the joint probabilities method with examples from the French Atlantic coast and three ports in the southwest of the UK

The joint probability method (JPM) to estimate the probability of extreme sea levels (Pugh and Vassie, Extreme sea-levels from tide and surge probability. Proc. 16th Coastal Engineering Conference, 1978, Hamburg, American Society of Civil Engineers, New York, pp 911–930, 1979) has been applied to the hourly records of 13 tide-gauge stations of the tidally dominated Atlantic coast of France (including Brest, since 1860) and to three stations in the southwest of the UK (including Newlyn, since 1916). The cumulative total length of the available records (more than 426 years) is variable from 1 to 130 years when individual stations are considered. It appears that heights estimated with the JPM are almost systematically greater than the extreme heights recorded. Statistical analysis shows that this could be due: (1) to surge–tide interaction (that may tend to damp surge values that occur at the time of the highest tide levels), and (2) to the fact that major surges often occur in seasonal periods that may not correspond to those of extreme astronomical tides. We have determined at each station empirical ad hoc correction coefficients that take into account the above two factors separately, or together, and estimated return periods for extreme water levels also at stations where only short records are available. For seven long records, for which estimations with other computing methods (e.g. generalized extreme value [GEV] distribution and Gumbel) can be attempted, average estimations of extreme values appear slightly overestimated in relation to the actual maximum records by the uncorrected JPM (+16.7 ± 7.2 cm), and by the Gumbel method alone (+10.3 ± 6.3 cm), but appear closer to the reality with the GEV distribution (−2.0 ± 5.3 cm) and with the best-fitting correction to the JPM (+2.9 ± 4.4 cm). Because the GEV analysis can hardly be extended to short records, it is proposed to apply at each station, especially for short records, the JPM and the site-dependent ad hoc technique of correction that is able to give the closest estimation to the maximum height actually recorded. Extreme levels with estimated return times of 10, 50 and 100 years, respectively, are finally proposed at all stations. Because astronomical tide and surges have been computed (or corrected) in relation to the yearly mean sea level, possible changes in the relative sea level of the past, or foreseeable in the future, can be considered separately and easily added to (or deduced from) the extremes obtained. Changes in climate, on the other hand, may modify surge and tide distribution and hence return times of extreme sea levels, and should be considered separately.

REDUCTION EFFECT OF PEAK FLOW IN THE ANNULAR NO. 7 LINE UNDERGROUND RESERVOIR AND EVALUTION OF SAFETY FACTOR ON RAINFALL CHARACTERISTICS

Recently, in Tokyo, a local torrential rain more than 100 mm for one hour has been happened by heat island effect. In this study, reduction effect of peak flow with increased storage capacityon the annular No. 7 line underground reservoir was analyzed by simulation based on data. As regards to characteristics of rainfalldistribution, it was quantitativelyevaluated using runoff rate and reduction rate. As a result, difference of reduction rate was clarified by rainfall characteristics. Therefore, those influences, which characteristics of rainfall gave to reduction effect of peak flow was examined by rainfall analysis by Gumbel method. As a result, the case that heavy rain persistently from two hours for four hours has low reduction rate was led.

Extreme avalanche runout: a comparison of empirical models

The prediction of snow avalanche runout distances and the probability of exceeding the predicted positions is the first and most important step required before making decisions about placement of facilities or control structures in snow avalanche prone terrain. There are two main prediction methods for calculating runout distances: (1) procedures linked to the selection of friction coefficients in avalanche dynamic models, and (2) empirical, statistical prediction based on terrain parameters for a set of extreme runout distances for the mountain range in question. Within the second method there are presently two competing empirical approaches to prediction: (i) ordinary least squares regression analysis related to angles measured for the path profile in question, and (ii) extreme value prediction of runout based on a Gumbel distribution of a dimensionless terrain parameter. In this paper a comparison of the two empirical methods with emphasis on the slope steepness in the runout zone is provided. The comparison is important, since the choice of method does affect the probability of the runout position being exceeded, particularly far into the runout zone where facilities are most likely to be located. The analysis shows that comparison of the models hinges on slope steepness in the runout zone and differences in calculating exceedance probabilities from the distributions used in the analysis (Gumbel distribution and Gaussian). The method based on the dimensionless Gumbel parameter provides more conservative predictions for flat terrain in the runout zone, and the regression - least squares method is more conservative for steep terrain in the runout zone. In addition, the Gumbel method is shown to be compatible with the characteristics of runout zone slope steepness shown by field data: there is very little dependence of runout distance on runout zone slope steepness.Key words: snow avalanche, runout, empirical methods, statistical methods.

The accuracy of design values predicted from extreme value analysis

This paper reports a study of predicted values of the 1:50yr windspeed produced by four different methods of extreme value analysis. The methods used were the obsolete Classical Gumbel method; Gumbel–Lieblein BLUE; the Modified Gumbel method and the Method of Independent Storms. For each method, synthetic wind records were generated consisting of 100 storm maxima for each year and for a duration of 10(10)50 years. The parent distribution was chosen so that q=V2 had an exponential probability distribution. For each method tested, 10000 data sets were analysed and the slope and intercept parameters were used to predict a value of q50 for each set. The 10000 realisations of q50 were then examined for bias and statistical variation about the (known) theoretical value. The tests indicate that where sufficiently continuous data is available, the Method of Independent Storms should be used. Otherwise if only annual maxima are available, Gumbel–Lieblein BLUE gives the best results for small data sets, but Modified Gumbel is an acceptable alternative, particularly for samples N>25.

Application of extreme value theory for predicting violations of air quality standards for an urban road intersection

Extreme value theory (EVT) has been used for making predictions of the expected number of violations of the National Ambient Air Quality Standards (NAAQS) as prescribed by the Central Pollution Control Board (CPCB), India, for hourly- and eight-hourly average carbon monoxide(CO) concentration for an Air Quality Control Region (AQCR) comprising of an urban road intersection. Almost 100% contribution to the CO pollution in the region is due to vehicular traffic. The parameters of the extreme value distribution (EVD) have been estimated by four methods viz. method of moments, maximum likelihood, least square fit and Gumbel's fitting method. Least square fit and Gumbel's method gave the best fit and predictions. A comparison of the predicted violations of NAAQS and the exceedence of the maximum pollution concentration with that of the observed data suggests that the theory performs satisfactorily for the extreme air pollution events.

Improving the Gumbel analysis by using M-th highest extremes

Improvements to the Gumbel method of extreme value analysis of wind data made over the last two decades are reviewed and illustrated using sample data for Jersey. A new procedure for extending the Gumbel method to include M-th highest annual extremes is shown to be less effective than the standard method, but leads to a method for calibrating peak-over-threshold methods against the standard Gumbel approach. Peak-over-threshold methods that include at least the 3rd highest annual extremes, specifically the modified Jensen and Franck method and the Method of independent storms are shown to give the best estimates of extremes from observations.

Comparison of earthquake recurrence-rate estimates using the Gumbel and Gutenberg-Richter formulae

AbstractOne thousand earthquakes distributed according to Gutenberg and Richter's formula, log N = 6 − M, were assumed to occur during a 50-yr period. Various fractions were assumed to be overlooked, and randomly distributed errors were added to their magnitudes. These data were used to calculate the expected recurrence rates of large earthquakes using methods developed by Gumbel and by Gutenberg and Richter. Although the method of Gutenberg and Richter leads to a more accurate estimation of recurrence rates with ideal data, when the data are incomplete and reported magnitudes contain errors, Gumbel's method sometimes leads to a more accurate estimate.