CALCULATION OF CLIMATE LOADS DESIGN VALUES ACCORDING TO THE PROBABILITY MODEL OF ANNUAL MAXIMUM SERIES

The aim of this work is to improve a method for determining the characteristic values of climatic loads according to a probabilistic model of the annual maxima sequence, by choosing a rational type of generalized extreme value distribution law. An analysis is provided regarding the suitability of using four types of distributions for describing a data collection of maximum values of climatic loads. Using example data from the meteorological stations of Ukraine, it is found that for coefficients of variation smaller than 0.85–1.0, it is advisable to use the double exponential Gumbel distribution (generalized extreme value distribution type-I), and at higher values of the coefficient of variation, it is advisable to use the Weibull distribution (generalized extreme value distribution type-III). Recommendations are provided for considering the accuracy in the estimations of the characteristic values of loads according to the probabilistic model for the annual maximum value series.

Modeling the wind speed in North Morocco

The change of the wind speed is strictly related to several natural factors such as local topographical and the ground cover variations, then any adjustment has to take into account the statistical variation for each specific region under study. Unlike the Weibull distribution, which is most used in wind speed modeling, we investigate two alternative distribution functions for wind speed by using the extreme value theory. The generalized Champernowne distribution function and the mixture Log-normal-Pareto distribution function are considered. We demonstrate that the proper generalized extreme value distribution gives a good fit for wind speed in the North Moroccan. In order to validate the models, a comparison of the produced aggregate wind energy in the aeolian wind turbine was being established. The empirical study shows that the generalized extreme value distribution reflects better the intensity of the wind power energy.

Estimation of value at risk for stock prices in mobile phone industry

Risk management and market losses prediction played a vital role in the financial sector. Value-at-Risk (VaR) is one of the effective measures for financial risk management. This research studies three mobile phone companies which are Apple Inc, Google Inc and Microsoft Corporation. The stocks of these companies are listed under the National Association of Securities Dealers Automated Quotations stock exchange (NASDAQ). The Value-at-Risk is evaluated by using two non-parametric methods and four parametric methods. Two non-parametric methods used are the basic historical method and age-weighted historical method, while the four parametric methods are normal distribution, student’s t-distribution, generalized extreme value distribution, and variance gamma distribution. Shapiro-Wilk normality test indicates that the return series of the selected companies are not normally distributed. This study found that, at 95% confidence level, the risks of the selected stocks are different for each method, and the stock of Microsoft Corporation is the least risky stock as it gives the lowest VaR. Through the conditional coverage test, this study founds that the age-weighted historical method overestimated the VaR. In addition, this study also concludes that the basic historical method, generalized extreme value distribution and variance gamma distribution are superior to other methods in the backtesting procedure.

Bias Correction for Precipitation Simulated by RegCM4 over the Upper Reaches of the Yangtze River Based on the Mixed Distribution Quantile Mapping Method

Traditional multi-parameter single distribution quantile mapping (QM) methods excel in some respects in correcting climate model precipitation, but are limited in others. Multi-parameter mixed distribution quantile mapping can potentially exploit the strengths of single distribution methods and avoid their weaknesses. The correction performance of mixed distribution QM methods varies with the geographical location they are applied to and the combination of distributions that are included. This study compares multiple sets of single distribution and multi-parameter mixed distribution QM methods in order to correct the precipitation bias in the upper reaches of the Yangtze River basin (UYRB) in RegCM4 simulated precipitation. The results show that, among the selected distributions, the gamma distribution has the highest performance in the basin; explaining more than 50% of the precipitation events based on the weighting coefficients. The Gumbel distribution had the worst performance, only explaining about 10% of the precipitation events. The performance parameters, such as the root mean square error (RMSE) and the correlation coefficient (R) of the corrected precipitation, that were derived by using mixed distribution were better than those derived by using single distribution. The QM method that is based on the gamma-generalized extreme value distribution best corrected the precipitation, could reproduce the annual cycle and geographical pattern of observed precipitation, and could significantly reduce the wet bias from the RegCM4 model in the UYRB. In addition to enhancing precipitation climatology, the correction method also improved the simulation performance of the RegCM4 model for extreme precipitation events.

Hydrological regionalization of streamflows for the Tocantins River Basin in Brazilian Cerrado biome

The Brazilian Cerrado biome is the largest and richest tropical savanna in the world and is among the 25 biodiversity hotspots identified worldwide. However, the lack of adequate hydrological monitoring in this region has led to problems in the management of water resources. In order to provide tools for the adequate management of water resources in the Brazilian Cerrado biome region, this paper develops the regionalization of maximum, mean and minimum streamflows in the Tocantins River Basin (287,405.5 km2), fully located in the Brazilian Cerrado biome. The streamflow records of 32 gauging stations in the Tocantins River Basin are examined using the Mann-Kendall test and the hydrological homogeneity non-parametric index-flood method. One homogeneous region was identified for the estimate of the streamflows Qltm (long-term mean streamflow), Q90% (streamflow with 90% of exceeding time), Q95% (streamflow with 95% of exceeding time) and Q7,10 (minimum annual streamflow over 7 days and return period of 10 years). Two homogeneous regions were identified for maximum annual streamflow estimation and the Generalized Extreme Value distribution is found to describe the distribution of maximus events appropriately within the both regions. Regional models were developed for each streamflow of each region and evaluated by cross-validation. These models can be used for the estimation of maximum, mean and minimum streamflows in ungauged basins within the Tocantins River Basin within the area boundaries identified. Therefore, the results provided in this paper are valuable tools for practicing water-resource managers in the Brazilian Cerrado biome. Keywords: l-moments, statistical hydrology, water use rights concessions.

Seasonal and continual wind speed modelling for the coastal urban city, Karachi

ABSTRACT. Variation in wind speed not only indicates the strengthening or weakening of pressure systems but its role in wind farm in the vicinity of coastal area is also crucial. Probability distributions through time series of wind speed data serves foremost basic need for the said parameters. Exploratory data analysis revealed that for coastal city Karachi, maximum wind speed (~23 m/s) occurred during monsoon with its peak during postmonsoon with maximum deviation (~3.5 m/s). Mean / trimmed mean during spring and postmonsoon (~11.5 m/s) as well as in premonsoon and monsoon (~18.5 m/s) remain almost identical while minimum wind blowing during winter and postmonsoon are also identical (~6 m/s). Autumn and winter exhibits least standard deviations. Critical and statistical values have been compared for distribution modelling, while parametric values of different seasonal and continual distributions are also estimated. The study is supported by cumulative distribution functions and probability-probability plots. It is not uncommon to use Weibull distribution for wind speed modelling. By using daily data time series of wind speed for the coastal station Karachi, it has been explored that widely accepted Weibull distribution provides comparatively poor distribution results when compared to other more complicated models (i.e., Wakeby and generalized extreme value distributions]. It is found that annual and seasonal wind comes after the Wakeby distribution except premonsoon summer which follows the generalized extreme value distribution (GEV) for the city. No continual and / or seasonal wind speed follows the Weibull distribution, ultimately and / or more appropriately. The study may give some new insights for aviation and wind engineering purposes.

Estimation of dry events duration in Northern Tunisia – Analysis of extremes trends

Modeling of extremes dry spells in Northern Tunisia, in order to detect the severity of the phenomenon, is carried out. Dry events are considered as a sequence of dry days (below a threshold) separated by rainfall events from each other. The maximum dry event duration follows the Generalized Extreme Value distribution. The data series adherence to the probability distribution was verified by the Anderson-Darling test. The positive trend and non-stationarity of dry spells was verified respectively by the Mann–Kendall test and Dickey–Fuller and augmented Dickey–Fuller tests. The irregular distribution of rainfall in the growing season for Sidi Abdelbasset station has increased the number of dry spells. The increase of rainy days in Ghézala dam and Sidi Salem gauge stations resulted in a decrease of dry spells in this area. Regarding the return period of one year (wet season), dry events occurred from 14 to 27 d in this region constitute an agricultural potential risk. The Southern region was the most vulnerable.

An Analysis of Precipitation Extreme Events Based on the SPI and EDI Values in the Free State Province, South Africa

Recognizing that, over the last several years, extreme rainfall has led to hazardous stress in humans, animals, plants, and even infrastructure, in the present study, we aimed to investigate the characteristics of droughts over the Free State (FS) Province of South Africa in order to determine the future likelihood of reoccurrences of precipitation extremes using the generalized extreme value distribution (GEV) and extreme frequency analysis (EFA). In this regard, daily rainfall datasets from nine South African weather service homogenous climatic districts, spanning from 1980 to 2019, were used to compute: (a) the total annual rainfall, (b) the Effective Drought Index (EDI), and (c) the Standard Precipitation Index (SPI). The SPI was calculated for 3, 6, and 12 month accumulation periods (hereafter SPI-3, SPI-6, and SPI-12, respectively). The trend analysis results of the EDI and SPI-3, -6, and -12 showed that the Free State Province is generally negative, illustrating persistent drought. An analysis of the GEV parameters across the EDI and SPI-3, -6, and -12 values illustrated that the location, scale, and shape parameters exhibited a noticeable spatial variability across the Free State Province with the location parameter largely negative, the scale parameter largely positive, while the shape parameter pointed to an inherent Type III (Weibull) GEV distribution. In addition, the return levels for the drought/wet duration and severity of the EDI and SPI-3, -6, and -12 values generally showed increasing patterns across the corresponding return periods; the spatial contrasts were only noticeable in the return levels derived from the wet/drought duration and severity derived from SPI-3, -6, and -12 values (and not in the EDI). Further, the EFA results pointed to a noticeable spatial contrast in the return periods derived from the EDI and SPI-3, -6, and -12 values for each of the extreme precipitation categories: moderately wet, severely wet, extremely wet to moderately dry, and severely dry. Over four decades, the FS Province has generally experienced a suite of extreme precipitation categories ranging from moderately wet, severely wet, extremely wet to moderately dry, severely dry, and extremely dry conditions. Overall, the present study contributes towards implementation of effective drought early warning systems and can be used to enhance drought related policy and decision making in support of water resource management and planning in the FS Province.