Maximum Daily Rainfall Data Research Articles

Statistical analysis of annual maximum rainfall in North-East India: an application of LH-moments

An attempt has been made to determine the best fitting distribution to describe the annual series of maximum daily rainfall data for the period 1966 to 2007 of nine distantly located stations in North East India. The LH-moments of order zero (L) to order four (L4) are used to estimate the parameters of three extreme value distributions viz. generalized extreme value distribution (GEV), generalized logistic distribution (GLD), and generalized Pareto distribution (GPD). The performances of the distributions are assessed by evaluating the relative bias (RBIAS) and relative root mean square error (RRMSE) of quantile estimates through Monte Carlo simulations. Then, the boxplot is used to show the location of the median and the associated dispersion of the data. Finally, it can be revealed from the results of boxplots that zero level of LH-moments of the generalized Pareto distribution would be appropriate to the majority of the stations for describing the annual maximum rainfall series in North East India.

Hydrologic behavior and flood probability for selected arid basins in Makkah area, western Saudi Arabia

In arid regions, flash floods often occur as a consequence of excessive rainfall. Occasionally causing major loss of property and life, floods are large events of relatively short duration. Makkah area in western Saudi Arabia is characterized by high rainfall intensity that leads to flash floods. This study quantifies the hydrological characteristics and flood probability of some major wadis in western Saudi Arabia, including Na’man, Fatimah, and Usfan. Flood responses in these wadis vary due to the nature and rainfall distribution within these wadis. Rainfall frequency analysis was performed using selected annual maximums of 24-h rainfall from eight stations located in the area. Two of the most applied methods of statistical distribution, Gumbel’s extreme value distribution and log Pearson type III distribution, were applied to maximum daily rainfall data over 26 to 40 years. The Gumbel’s model was found to be the best fitting model for identifying and predicting future rainfall occurrence. Rainfall estimations from different return periods were identified. Probable maximum floods of the major wadis studied were also estimated for different return periods, which were extrapolated from the probable maximum precipitation.

Comparative Study of ANNs versus Parametric Methods in Rainfall Frequency Analysis

Quantile estimation in rainfall/flood frequency analysis is very important in engineering design of water infrastructure. Many existing methods are based on parametric modeling with the assumption that the underlying probability distribution is known a priori. The estimation performance hence relies largely on the assumed distribution of the observations in addition to the historical measurements. If the distribution is not appropriate to describe the observations, the estimated parameters are prone to large errors. In this paper, artificial neural network and fuzzy logic based methods are used to obtain quantile estimates which avoid the difficult problem of distribution determination while increasing the accuracy of the estimated quantiles. A complete comparison with the conventional parametric methods is given through realistic annual maximum daily rainfall data and Monte Carlo simulations for various sample sizes. The results demonstrate that the artificial neural network techniques yield higher accur...

Stochastic Analysis of Rainfall Events in Ilorin, Nigeria

This paper reports on a stochastic analysis of rainfall events in Ilorin, Nigeria. Rainfall, the most common form of precipitation in most parts of the world, is a principal component of the hydrologic cycle. Rainfed agricultural practices dominate agricultural activities in Ilorin, which could be enhanced by accurate predictions of rainfall attributes. Since rainfall exhibits natural variability, its analysis in a stochastic framework provides a more realistic premise. Five probability distribution namely the normal, lognormal, logPearson typeIII exponential and extreme value type I distributions – were used in this study because of their desirable properties. The analysis was based on 41 years of daily and monthly rainfall data (1955-1995) for Ilorin, with peak values computed for each year.Weibull plotting positions and the number of rainy days were also determined. September had the highest number of rainy days, followed by June. Rains are least expected in Ilorin in January and December. The maximum daily rainfall has a mean depth of 85mm and a standard deviation of 28mm while the corresponding values for the maximum monthly rainfall are 275mm and 56mm. The logPearson type III distribution best suited the maximum daily rainfall data while the normal distribution best described the maximum monthly rainfall for Ilorin. JARD Vol. 1 2001: pp. 39-50

DETECTION OF MEAN AND VARIANCE JUMP AND NORMALIZATION OF OUTLIER IN HYDROLOGICAL TIME SERIES

A non-stationary time series is composed of the trend and some jumps by the change of a mean value and a variance. There is no study example which hasdealt with the power of test fora jump of variance in a hydrological time series.In this paper, the Monte Carlo simulations are applied to compare the power of the statistical tests: Student's t test, F test, Mann-Whitney test and bootstrap test to assess the significance of jumps to affect the mean value and the variance of a time series with Normal, Logarithm Normal and General Extreme Value distributions. And also, the outliers in the annual maximum daily rainfall (MDR) and annual maximum non-rainfall days (NRD) data of each 22 meteorological observatories in Hokkaido are detected at Tomakomai and Hiroo for MDR data, and at Esashi for NRD data, respectively. Then the normalized conditionsto change these three outliers into normal values are introduced by using a numerical simulation.

Frequency analysis of extreme rainfall using L‐moment

AbstractThis research seeks to derive the design rainfalls through the L‐moment with the test of homogeneity, independence and outlier of data on annual maximum daily rainfall in 38 Korean rainfall stations. To select the appropriate distribution of annual maximum daily rainfall data according to rainfall station, generalized extreme value (GEV), generalized logistic (GLO) and generalized pareto (GPA) probability distributions were applied and their aptness was judged using an L‐moment ratio diagram and the Kolmogorov–Smirnov (K–S) test. The GEV and GLO distributions were selected as the appropriate distributions. Their parameters were estimated from the observed and simulated annual maximum daily rainfall using Monte Carlo techniques. Design rainfalls were then derived using the L‐moment. Appropriate design rainfalls were suggested by doing a comparative analysis of design rainfall from the GEV and GLO distributions according to rainfall stations. Copyright © 2003 John Wiley & Sons, Ltd.

Prediction of maximum daily rainfall at Ootacamund

The maximum daily rainfall data for 30 years (1967-1996) of Ootacamund, Nilgiris, recorded by India Meteorological Department were collected from the Directorate of Statistics, Chennai. Two programs were developed in BASIC for Lognormal and Gumbel distributions. The theroetical values so obtained were in close agreement with the observed data except at the highest rainfall for both the distributions.

STATISTICAL CONSIDERATIONS ON THE RANDOMNESS OF ANNUAL MAXIMUM DAILY RAINFALL1

ABSTRACT: Annual maximum daily rainfall data from nine stations throughout the southern slopes of the Eastern Italian Alps with record length of 67–68 years have been analyzed with the aim of verifying if their internal structure justifies the assumption of independence and identical distribution, or the “White noise hypothesis.” The approach is to consider the hypothesis H0 of white noise as the intersection of several sub‐hypotheses, each concerning one of the characteristics of a white noise process. To this end the nine series were subjected to various statistical tests regarding randomness, independence, change‐points, and predictability. The results are examined first individually and then globally. They indicate that in eight of the nine considered time series the “white noise hypothesis” was rejected.

A COMPARISON OF STATISTICAL TESTS ON THE EXTREME‐VALUE TYPE‐1 DISTRIBUTION1

ABSTRACT: The effects of the selections of plotting position formulae and class division schemes on goodness of fit tests are investigated for the extreme‐value type‐1 distribution using annual flood and annual maximum daily rainfall data. It was found that the plotting position formulae have a minor influence on the tests which involve their use, while the class division schemes may have a pronounced effect on the X2‐test. The study also recommended the maximum likelihood method for fitting purposes and a new test which is independent of the afore‐mentioned selections for judging the goodness of fit.