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Droughts are catastrophic and have become frequent in the last decade. The Upper Kangsabati River Basin (UKRB) in West Bengal state of India is affected by droughts. This research comprehensively evaluates meteorological drought and its spatial variability within the basin. Drought severity levels vary spatially with time, making it difficult for policymakers to prioritize preventive measures for different parts of the UKRB. Droughts were characterized using Standardized Precipitation Index (SPI) for 16 precipitation grid points. SPI-12 showed that the basin experienced two severe and three extreme drought years within the study period. Run theory was applied on SPI-3 to extract drought events, which varied from 34 to 41, spatially in the basin, with the maximum severity being 18.08. After fitting the appropriate marginal distributions to the extracted drought duration and severity, their bivariate relationship was established using copula. Generalized Pareto distribution and Frank copula fitted best for the marginal and bivariate distributions, respectively. Finally, the conditional OR return period of the historical droughts was determined from that relationship. It showed that parts of the basin experienced extreme drought of 50-year return period. The most likely event scenario was determined from the OR return period contours and applied to create the spatially distributed drought hazard maps, which is the uniqueness of the study. The present study suggested that the western and central regions of UKRB would experience more severe droughts when return period increases. Additionally, the modified Mann–Kendall (MMK) test applied to detect drought trends indicated no significant trend for monsoon months. [ABSTRACT FROM AUTHOR]

In this study, a regional rainfall frequency analysis has been conducted for the Lower Brahmaputra Basin in India, and regional rainfall intensity-duration-frequency curves are generated. Two sets of data have been used in this study—annual maximum series (AMS) and partial duration series (PDS). The discordancy measure (Di) was used to assess each of these 12 data sets from the Lower Brahmaputra Basin. For both data sets, it was verified that all the 12 sites form a homogeneous zone using the heterogeneity measure (H), which was based on the L-moments technique. The generalised extreme value, generalised logistic, generalised Pareto, lognormal, and Pearson Type III frequency distributions were considered as candidate distributions in this study. The generalised extreme value distribution has been recognised as the best-fit distribution for the region based on AMS, whereas the generalised Pareto distribution has been identified as the best-fit distribution for the region based on PDS, using the L-moment goodness of fit test measure. Then using the regional frequency relationship for the best fit distribution for the region, the IDF curves for this region have been constructed. Finally, rainfall IDF relationships were found out for the region based on three general IDF relationships—the original Kothyari and Garde IDF equation for India, the updated Kothyari and Garde IDF equation and the Sherman IDF equation. [ABSTRACT FROM AUTHOR]

Recently, the Central Public Health and Environmental Engineering Organization (CPHEEO), India, emphasized extreme rainfall analysis based on the probabilistic approach. The extreme rainfall analysis was performed using hourly rainfall data for Ahmedabad city, India. The analysis was carried out to obtain (a) clock hour correction factor (CHCF) for annual maximum rainfall series (AMS) and partial duration maximum rainfall series (PDS); (b) empirical factors for converting PDS to AMS for different return period extreme rainfall; and (c) conversion factors for various return period 24-h maximum rainfall. The AMS and PDS were fitted with generalized extreme value and generalized Pareto distribution, respectively, for fixed window (FW) and sliding window (SW). The CHCF for daily maximum rainfall for AMS and PDS were 1.134 and 1.139, respectively, against 1.15 suggested by IS 5542: 2003. The empirical factor for converting PDS to AMS for a 2-year return period of 24-h extreme rainfall (FW) was found to be 0.86. The conversion factor for 24-hextreme rainfall PDS (FW) from a 50-year return period to a 5-year return period was found to be 0.54. The empirical and conversion factors derived in the present study for Ahmedabad city are site-specific. [ABSTRACT FROM AUTHOR]

Monsoon-related extreme flood events are experienced regularly across India, bringing costly damage, disruption and death to local communities. This study provides a route towards estimating the likely magnitude of extreme floods (e.g., the 1-in-100-year flood) at locations without gauged data, helping engineers to design resilient structures. Gridded rainfall and evapotranspiration estimates were used with a continuous simulation hydrological model to estimate annual maximum flow rates at nine locations corresponding with river flow gauging stations in the Wainganga river basin, a data-sparse region of India. Hosking–Wallis distribution tests were performed to identify the most appropriate distribution to model the annual maxima series, selecting the Generalized Pareto and Pearson Type III distributions. The L-moments and flood frequency curves of the modeled annual maxima were compared to gauged values. The Probability Distributed Model (PDM), properly calibrated to capture the dynamics of peak flows, was shown to be effective in approximating the Generalized Pareto distribution for annual maxima, and may be useful in modeling peak flows in areas with sparse data. Confidence in the model structure, parameterization, input data and catchment representation build confidence in the modeled flood estimates; this is particularly relevant if the method is applied in a location where no gauged flows exist for verification. [ABSTRACT FROM AUTHOR]

City size plays an important role in the context of growing urbanization in developing countries, such as India. In the backdrop of this fact certain questions are pertinent: whether economic activities are concentrated in a few large cities; which economic factors determine the size of large cities; whether it is possible to trace different groups among the large cities, and whether the relationship pertaining to city size, migration, and poverty is discernible are some of the research issues which are analyzed in this paper by considering 47 million-plus cities in India. The estimated Pareto distribution suggests that within the group of large million-plus cities, production is not so diversified, though the extreme form of concentration such as primacy or rank size rule does not hold either. In fact, three broad groups are evident, as brought out by the results of the cluster analysis. Both OLS and Tobit regression results indicate that the wage rate, amount of municipal solid waste generation, and the number of salaried employed persons are positively associated with city population while the number of registered motor vehicles has a negative effect on it. However, the infrastructure index calculated through factor analysis does not show any significant effect on the city size. Based on the results of factor analysis, increased migration and reduced poverty are seen to be associated with city size. Finally, we bring out the important policy suggestions for sustainable urban development. [ABSTRACT FROM AUTHOR]

The COVID-19 pandemic has become major problem for financial markets and world economy. In this paper we investigated the extreme tail behavior of NIFTY 50 index during the COVID-19 pandemic. The extreme behavior of the stock market is examined through GPD model by suing high frequency data (5-min interval) of log returns ranging from 11th March 2020 to 30th Sept 2020 which provide more precise description of NIFTY 50 tail distribution in the pandemic period. The result indicates GPD give a real picture of uncertainties associated with COVID-19. The finding of study will assist in decision making to monitor COVID-19 impact on financial markets. [ABSTRACT FROM AUTHOR]

Northeast India is seismically most active region in India, and it falls under Zone V which represents the highest seismic risk in the country. This region has been experienced two great earthquakes like the 1897 Shillong (Mw 8.1) and the 1950 Assam earthquake (Mw 8.4) and several large earthquake (Mw ≥ 7) during last 122 years. Probabilistic approach and number statistical tools have been used by various researchers for finding the future earthquake recurrence rates. Using the earthquake catalogue, Gutenberg–Richter parameter has been estimated to evaluate seismic risk for six different regions: Eastern Himalayan, Indo-Burma region, Bengal Basin, Shillong Plateau, Mishmi Thrust, and Naga Thrust. Assuming that the earthquake occurrence is Poisson model, based on the obtained Gutenberg–Richter (G–R) relations, the probability of occurrence of earthquake of specified magnitude in given time is estimated for six seismotectonic regions. Further in this study, we made an attempt to estimate the probability of earthquake using four known statistical models, namely Exponential, Rayleigh, Weibull, and Pareto. The whole region is divided into six tectonic blocks to estimate the probability of an earthquake (Mw ≥ 5.5) through the maximization of conditional probability of earthquake occurrence. Time intervals for the occurrence of the next large earthquake in the six regions have been estimated by the maximization of conditional probability of earthquake occurrence. Pareto distribution shows the highest conditional probability compared to other distribution although it shows the lowest recurrence time compared to others. Rayleigh shows the lowest conditional probability, and Exponential shows intermediate probabilities in between Weibull and Pareto distributions. Specified four typical probability density models have been validated with the predicted event in Eastern Himalayan and Naga Thrust for earthquake Mw ≥ 5.5 recorded event. [ABSTRACT FROM AUTHOR]

For this investigation, we employ maximum significant wave heights associated spectral wave energy periods off Aguçadoura (41.46°N, −8.85°W), off Portugal in the North Atlantic Ocean, which were generated over a period of 34 years (1979–2012) by the wave model (SWAN). Conditional Mean Functions of generalised Pareto, Erlang , and three-parameter Weibull distributions are taken into account to determine the distribution of wave energy period. The values computed from the SWAN model data are reasonably coherent with the mean, mean maximum, and most frequent maximum energy periods, as well as the average of the one-third and one-tenth of the highest energy periods projected from the models. The generalised Pareto distribution is used to develop a parametric relation (based on order statistics) that can be used to accurately predict the average of one-third of the highest wave periods. Substantial linear functional relationships exist between computed besides estimated energy period versus peak period statistics. The average of one-third of the highest energy periods to mean energy periods accurately depicts the empirical ratio of significant wave period to mean wave period of 1.2. Daily maximum significant wave heights and associated spectral wave energy periods and peak periods by WAMAN (Wave monitoring along nearshore) wave rider buoy off Kozhicode (11.2698°N, 75.6722°E), southwest coast of India in the Arabian Sea during the winter season (January 2018 to April 2018) are also subjected to Conditional Mean Function Analysis. The sample values are consistent with the population estimates of the mean and the average of the one-third of the highest wave periods. An attempt is made to approximate the range of peak periods associated with extreme significant wave heights by taking into account the steepness constraints of a wave profile and dispersion relations for spectral peak periods. • Explored the distribution function of spectral wave energy periods by conditional mean functions. • Estimated certain spectral wave energy period and peak period statistics with required precision. • Parametric relation derived from generalised Pareto distribution to estimate average of one-third the highest wave period. • The ratio of mean of one-third the highest wave energy periods to mean wave period is 1.2. • The range of peak periods of extreme significant wave heights are attained from dispersion relation and wave steepnes. [ABSTRACT FROM AUTHOR]

We apply five distributions–lognormal, double-Pareto lognormal, lognormal-upper tail Pareto, Pareto tails-lognormal, and Pareto tails-lognormal with differentiability restrictions–to estimate the size distribution of all Indian cities. Since India contains numerous small cities, it is important to explicitly model the lower-tail behavior for studying the distribution of all Indian cities. Our results rigorously confirm, using both graphical and formal statistical tests, that among these five distributions, Pareto tails-lognormal is a better suited parametrization of the Indian city size data, verifying that the Indian city size distribution exhibits a strong reverse Pareto in the lower tail, lognormal in the mid-range body, and Pareto in the upper tail. [ABSTRACT FROM AUTHOR]

The climate change induced by global warming has raised concerns over safety of coastal and offshore infrastructure. At several places in the world therefore studies are being made to know the effect of such change on design and operational ocean parameters. This paper is oriented in this direction and its aim is to specify future changes in the design significant wave height (Hs) over a series of locations along the Indian coastline. Thirty-nine sites were selected along the 7000-km-long Indian coast and design Hs with a return period of 100 years were calculated on the basis of past as well as future wave data of duration 27 years each. The simulation of waves was done by running a numerical wave model forced by wind derived from a modeling experiment called CORDEX. Fitting of data to Generalized Pareto Distribution gave the 100-year Hs at all 39 locations. The results indicate that the design Hs calculated on the basis of projected data was much higher than the one based on historical data. Such increase was as small as 5 % and as high as 58 % as per the location. The west coast sites showed a higher rise in the Hs value than the east ones. [ABSTRACT FROM AUTHOR]

Abstract: This work presents a comprehensive study of the evolution of the expenditure distribution in India. The consumption process is theoretically modeled based on certain physical assumptions. The proposed statistical model for the expenditure distribution may follow either a double Pareto distribution or a mixture of log-normal and Pareto distribution. The goodness-of-fit tests with the Indian data, collected from the National Sample Survey Organisation Reports for the years of 1983–2007, validate the proposal of a mixture of log-normal and Pareto distribution. The relative weight of the Pareto tail has a remarkable magnitude of approximately 10%–20% of the population. Moreover, though the Pareto tail is widening over time for the rural sector only, there is no significant change in the overall inequality measurement across the entire period of study. [ABSTRACT FROM AUTHOR]

• Influence of threshold selection in modeling POT based extreme rainfall is studied. • Threshold uncertainty increases under the non-stationary condition. • Threshold uncertainty is more for low-probability (high return period) events. Recent studies report that the extreme rainfall characteristics in most parts of the globe exhibit temporal non-stationarity. Therefore, modeling the nonstationary behavior of extreme rainfall for different water resources applications is vital. When modeling non-stationarity in extreme rainfall series, previous studies consider a single threshold value in the peaks over threshold (POT) approach to extract extreme rainfall series. However, extreme rainfall series extracted with different threshold values may have a different degree of non-stationarity. Consequently, it is essential to understand the effect of threshold selection in modeling peaks over threshold based nonstationary extreme rainfall series. This study aims at quantifying the threshold uncertainty (i.e., uncertainty in extreme rainfall return levels due to the choice of the threshold) in modeling peaks over threshold based nonstationary extreme rainfall series using the Generalized Pareto Distribution (GPD). To study the threshold uncertainty, extreme rainfall series over India from the India Meteorological Department's high-resolution gridded (0.25° Longitude × 0.25° Latitude) daily rainfall dataset is used. For modeling non-stationarity in extreme rainfall series, different indices representing four physical processes, namely, global warming, El Niño–Southern Oscillation (ENSO), Indian Ocean Dipole (IOD) and local temperature anomaly are linked with the scale parameter of the GPD. Uncertainties in extreme rainfall return levels calculated over India indicate that the uncertainty created due to the choice of threshold is 54% higher under the nonstationary condition when compared to the stationary condition. [ABSTRACT FROM AUTHOR]