Extreme Value Analysis Of Rainfall Research Articles

Intercomparison of Rainfall Estimates of Three Distributions for Computation of PFD using Rational Formula and SUH Approach

Peak flood discharge (PFD) for a given return period is considered as one of the most important parameters for planning and design of hydraulic structures, river protection works, and development of integrated water resources management projects. This can be achieved by adopting various methods such as flood frequency analysis, rational formula, envelope curves and Synthetic Unit Hydrograph (SUH) approach. Out of which, rational formula is applied for estimation of PFD for ungauged catchments with catchment area less than 25 km2 while SUH approach is adopted for ungauged catchments with catchment area more than 25 km2. This paper aims to investigate the study on intercomparison of probability distributions for estimation of extreme (i.e., 1-day maximum) rainfall for computation of PFD by adopting rational formula and SUH approach for the Vadhavan Port Project (VPP). The annual 1-day maximum rainfall series is extracted from the daily rainfall data observed at Dahanu site during the period 1969 to 2019 and also used for estimation of rainfall. The probability distributions viz., Extreme Value Type-1, 2-parameter Log Normal and Log Pearson Type-3 (LP3) adopted in extreme value analysis of rainfall is evaluated through diagnostic test using root mean square error and accordingly LP3 is adjudged as the best fit for estimation of rainfall. The 1-day maximum rainfall obtained from LP3 is considered to compute the rainfall intensity by applying one-third rule of IMD (India Meteorological Department) and also used for computation of PFD through rational formula. In SUH approach, the areal rainfall, physiographic and SUH parameters of the ungauged catchments are considered for computation of PFD. The study suggests the 25-year, 50-year and 100-year return period PFDs at six locations within the study area using rational formula and SUH approach could be considered for design purposes while designing any civil and hydraulic structures in the VPP.

Exploring extreme value analysis of rainfall for some nuclear power plant sites in India

Extreme rainfall is an important consideration for safety of nuclear installations. Literature reported estimation of the same for Indian nuclear power plant sites using Gumbel and Frechet distributions, fitted by least square (graphical) method (LSM). In these reports, the goodness-of-fit was examined graphically by plots on probability papers. In this study, the data for six nuclear sites collected from literature were analysed. For this purpose, in addition to Gumbel and Frechet, other distributions were included and the parameters of the distributions were evaluated using Lieblein technique and maximum likelihood estimation, as well as LSM. The goodness-of-fit was evaluated using the quantitative tool: Anderson-Darling test; and qualitative tools: probability plot and quantile plot – which are suitable for evaluating goodness-of-fit of extreme value distributions. Maximum daily rainfall for return periods of 50, 100 and 1000 years were reported from the fitted distributions. Comparison with the respective values (50 and 100 year return period) from literature demonstrated that the extreme rainfall reported for these sites were quite accurate with maximum variation within ten per cent.

NORA3. Part II: Precipitation and Temperature Statistics in Complex Terrain Modeled with a Nonhydrostatic Model

Abstract The 3-km Norwegian Reanalysis (NORA3) is a convection-permitting, nonhydrostatic hindcast for the North Sea, the Norwegian Sea, and the Barents Sea as well as the Scandinavian Peninsula. It has a horizontal resolution of 3 km and provides a full three-dimensional atmospheric state for the period 1995–2020 with a surface analysis and boundary conditions from ERA5, a global reanalysis. In complex terrain it is found to outperform both the host reanalysis ERA5 and also the earlier hydrostatic 10-km Norwegian Hindcast Archive (NORA10), in terms of 2-m temperature and daily precipitation. Of particular interest is the representation of extreme rainfall. It is found that the upper percentiles are much better represented than in ERA5, with very little bias up to 99.9%, suggesting that the new hindcast archive is well suited for hydrological mapping and extreme-value analysis of rainfall in complex terrain. Significance Statement High-resolution hindcasts that permit realistic convection allow very detailed modeling of the surface temperature, precipitation, and wind field in complex terrain. There is a need for detailed mapping of rainfall and temperature extremes (upper percentiles) to assess the impact of rapid climate change. We present an assessment of the performance of the model from Part I for near-surface temperature and precipitation, which are found to be much improved in comparison with ERA5 and with earlier NORA10. The focus is on the Norwegian mainland and the Svalbard Archipelago, because the complex terrain found in these regions is challenging to represent in weather prediction models. The improvement in precipitation statistics is particularly pronounced, with nearly unbiased results up to the 99.9th percentile.

Intercomparison of estimators of extreme value family of distributions for rainfall frequency analysis

Estimation of rainfall for a given return period is of utmost importance for planning and design of minor and major hydraulic structures. This can be achieved through Extreme Value Analysis (EVA) of rainfall by fitting Extreme Value family of Distributions (EVD) such as Generalized Extreme Value, Extreme Value Type-1, Extreme Value Type-2 and Generalized Pareto to the series of observed Annual 1-Day Maximum Rainfall (AMR) data. Based on the intended applications and the variate under consideration, Method of Moments (MoM), Maximum Likelihood Method (MLM) and L-Moments (LMO) are used for determination of parameters of probability distributions. The adequacy of fitting EVD to the AMR series was evaluated by quantitative assessment using Goodness-of-Fit (viz., Chi-square and Kolmogorov-Smirnov) and diagnostic test (viz., D-index) tests and qualitative assessment by the fitted curves of the estimated rainfall. The paper presents a study on intercomparison of EVD (using MoM, MLM and LMO) adopted in EVA of rainfall with illustrative example and the results obtained thereof.

Bivariate Extreme Value Analysis of Rainfall and Temperature in Nigeria

Bivariate Extreme Value Analysis of Rainfall and Temperature in Nigeria

Smoothing of 70-Year Daily Rainfall Data Based on Moving Average and Weighted average Technique

An extreme value analysis of rainfall for Thanjavur town in Tamil Nadu was carried out using 70 years of daily rainfall data. Moving average method is a simple method to understand rainfall trend of the selected station. The analysis has been carried out for monthly, seasonal and annual rainfalls. No other graphical methods such as Ordinate graph, Bar diagram, Chronological chart will describe about the trend or cyclic pattern. By smoothening out the extreme variations and indicating the trend or cyclic pattern is known as moving average curve. Through this moving average curve, it is possible to understand the trend which can be used in the future years. From the results of annual wise rainfall analysis, based on 3-year, 5-year, 10-year moving average, it is found that there is no persistent regular cycle is visible and where as in 30-year, 40-year, 50-year moving average a horizontal linear trend has been observed. In Winter season, Summer season, North-East monsoon, South- West monsoon wise rainfall analysis, for 3-year, 5-year, 10-year moving average denote no apparent trend or cyclicity where as in 30-year, 40-year, 50- year moving average a horizontal linear cycle has been noticed. It is clear from the study that there is no large variation of rainfall that had been occurred in the Thanjavur city based on selected years of analysis.

Comparison of probability distributions in extreme value analysis of rainfall and temperature data

Estimation of rainfall and temperature for a desired return period is a prerequisite for planning, design and operation of various hydraulic structures and for evaluation of technical and engineering appraisal of large infrastructure projects. This can be computed through Extreme Value Analysis (EVA) by fitting probability distributions to the annual series of 1-day maximum rainfall, maximum and minimum temperature. This paper details the study on adoption of Extreme Value Type-1, Extreme Value Type-2, 2-parameter Log Normal and Log Pearson Type-3 (LP3) probability distributions in EVA of rainfall and temperature for Hissar. Based on the applicability, standard parameter estimation procedures such as method of moments, maximum likelihood method (MLM) and order statistics approach are used for determination of parameters of distributions. The adequacy on fitting of probability distributions used in EVA of rainfall and temperature is evaluated by goodness-of-fit (GoF) tests, viz. Anderson–Darling and Kolmogorov–Smirnov and diagnostic test using D-index. The GoF and diagnostic tests results suggest the LP3 (MLM) is better suited amongst four probability distributions adopted in EVA of rainfall and temperature for Hissar.

Intercomparison of Probability Distributions using Goodness-of-Fit and Diagnostic Tests for Extreme Value Analysis of Rainfall

Intercomparison of Probability Distributions using Goodness-of-Fit and Diagnostic Tests for Extreme Value Analysis of Rainfall

Intercomparison of Probability Distributions for Extreme Value Analysis of Rainfall under Missing Data Scenario

Intercomparison of Probability Distributions for Extreme Value Analysis of Rainfall under Missing Data Scenario

Comparison of L-moments of Probability Distributions for Extreme Value Analysis of Rainfall for Estimation of Peak Flood Discharge for Ungauged Catchments

Comparison of L-moments of Probability Distributions for Extreme Value Analysis of Rainfall for Estimation of Peak Flood Discharge for Ungauged Catchments

Quantitative Assessment on Fitting of Gumbel and Frechet Distributions for Extreme Value Analysis of Rainfall

Rainfall frequency analysis plays an important role in hydrologic and economic evaluation of water resources projects. It helps to estimate the return periods and their corresponding event magnitudes thereby creating reasonable design criteria. Depending on the size, life time and design criteria of the structure, different return periods are generally stipulated for adopting Extreme Value Analysis (EVA) results. This paper illustrates the use of quantitative assessment on fitting of Gumbel (EV1) and Frechet (EV2) probability distributions to the series of annual 1-day maximum rainfall (AMR) data using Goodness-of-Fit (GoF) and diagnostic tests. Order Statistics Approach (OSA) is used for determination of parameters of the distributions. Based on GoF (using AndersonDarling and Kolmogorov-Smirnov) and diagnostic (using D-index) test results, the study identifies the EV1 distribution is better suited for EVA of rainfall for Fatehabad and Hissar.