Analysis of Annual Maximum Rainfall for Frequency Distribution to Determine the Best-fitted Probability Distribution for Different Sites in Pakistan.

Abstract

In the project of irrigation and addition structure of hydraulic, it is important to assess the specific probability of extreme rainfall. The novelty of this study is the use of KS, Chi-square, root mean square error (RMSE), and peak weight root means square error (PWRMSE) to evaluate the fit theoretical and Empirical distributions. Thirty-seven years of meteorological data from 1980 to 2017, the frequency analysis of the annual maximum rainfall in 10 regions of Pakistan was conducted. Used eight formulas to predict the annual return period of the maximum hourly precipitation every year. Five different probability distribution functions (PDF) are used to predict the probability distribution of the annual maximum hourly rainfall. Use the chi-square test and Kolmogorov- Smirnov to assess the goodness of fit. It shows that the log-logistics distribution is the overall best-fitting PDF of the annual maximum hourly rainfall in most areas of Pakistan. Besides, the peak weight relative mean square error and root mean square error goodness of fit test indicators both indicate that most suitable distribution of the probability function of all stations analysis is similar. The value of root means square error (RMSE) is almost always smaller than peak weight root means square error (PWRMSE). This is due to the higher weighting of value above the average value in the PWRMSE goodness of fit index, while for the RMSE goodness of fit index individual value has an equal weight.

Determination of Suitable Probability Distribution of Rainfall in Pakistan Considering Multiplicity

“…In addition, to assess the fitness visually, various techniques were employed, including a quantile-quantile (Q-Q) plot, L-moment ratio plot, a PP plot and extreme value plots. The advantage of the above graphical test and fit test have been applied to maximum rainfall data (Yuan et al, 2018;Kunz et al, 2010;Lawan et al, 2015;Khan et al, 2021). In the context of climate change, goodness of fit is consistently used to select the best fit distribution for modelling.…”

“…A reference (Beskow et al, 2015) suggested that for maximum rainfall series, the number of adjusted series for GLO distribution of EV1 is the least, which is considered to be the most suitable PDF for only one sequence. Although the presentation in the Rio Grande was not satisfactory, some authors informed permissible GLO distribution indicators in regional studies (Beskow et al, 2015;Khan et al, 2021), because GEV has made appropriate adjustments to more than 96 % of the series. In this study, compared with other PDFs, GEV offers better modifications for shorter sequences and better modification for longer average sequences.…”

Revisiting the use of the Gumbel distribution: A Frequency Analysis Perspective

“…This aspect is mainly due to the simple parameter estimation expressions, as well as the simple and accessible expression of the quantile function (inverse function). In hydrology, the applicability of the Gumbel distribution is diverse, being mainly used for frequency analysis of maximum flows , maximum precipitation and the construction of IDF curves [43][44][45][46][47][48][49][50][51][52][53][54][55][56][57][58], minimum flows [59][60][61][62][63][64], etc.. The main and only advantage of the Gumbel distribution is the simplicity and accessibility of expressions and relationships.…”

Revisiting the use of the Gumbel distribution: A Frequency Analysis Perspective

“…This aspect is mainly due to the simple parameter estimation expressions, as well as the simple and accessible expression of the quantile function (inverse function). In hydrology, the applicability of the Gumbel distribution is diverse, being mainly used for frequency analysis of maximum flows , maximum precipitation and the construction of IDF curves [43][44][45][46][47][48][49][50][51][52][53][54][55][56][57][58], minimum flows [59][60][61][62][63][64], etc.. The main and only advantage of the Gumbel distribution is the simplicity and accessibility of expressions and relationships.…”