Modelling of Extreme Rainfall in Punjab: Pakistan Using Bayesian and Frequentist Approach

Abstract

In this study we compared the efficiency of frequentist approach with Bayesian approach by carrying out extreme value analysis of Annual Maximum Daily Rainfall (AMDR). For frequentist frequency analysis of AMDR, we used the data of one station i.e. Lahore in Punjab province, Pakistan while for Bayesian analysis we used the data of three other neighboring stations as prior information. During frequentist approach, Generalized Extreme Value (GEV) was found to be a best-fit distribution on the data. In frequentist method, the parameters of GEV distribution were estimated using Maximum Likelihood Estimation (MLE), while in the Bayesian framework the Markov Chain Monte Carlo (MCMC) simulation technique along with Metropolis-Hasting algorithm and Gibbs sampler were implemented. Findings of this study indicate that despite the asymptotic requirements of the MLE, its performance can be enhanced by adopting the Bayesian MCMC paradigm. In order to acquire the posterior densities of GEV parameters, non-informative and informative priors based on the historical data of surrounding weather stations were employed. The result of Bayesian MCMC might be affected by the choice of priors. In addition, the performance of the parameters estimation methods was verified by employing several robustness measures. Robustness measures results proved that the Bayesian MCMC method performed better than MLE in estimating GEV parameters and future return levels. Therefore, the findings of these analyses could be helpful in adopting proper flood protection measures and designing infrastructures of culverts, buildings, bridges and dams in the region.

A comprehensive study on the Bayesian modelling of extreme rainfall: A case study from Pakistan

“…The following marginal independent NIPs in different studies (Coles and Tawn, 2005; Fawcett and Walshaw, 2008; Eli et al ., 2012; Diriba et al ., 2017; Ahmad et al ., 2019; Diriba and Debusho, 2020) were used. …”

“…The RLs for the GEV model corresponding to the return period T =1=p, denoted by w p where F w p = 1 −p À Á and 0<p<1, is attained by using quantile function by the inverse of (2) given by (Coles, 2001) and also discussed by Ahmad et al (2019) &Debusho (2020).…”

“…with w p 1 <w p 2 <w p 3 discussed by Diriba et al (2017), Ahmad et al (2019), and Diriba and Debusho (2020).…”

“…Procedures to analyse extreme values comprise the frequency of happening of extreme events with the practice of probabilistic models for both similar or dissimilar processes for one or more climate variables (Noto and La Loggia, 2009; Lenderink and Fowler, 2017). Several research studies exist in literature in favour of selection and evaluation of different extreme value probabilistic models for extreme data, but due to the accessibility of the small length of observed data as compared to return periods of interest, continuously this work has been challenging and provocative (Fadhilah et al ., 2007; El Adlouni and Ouarda, 2010; Olofintoye et al ., 2009; Suhaila et al ., 2011; Rahman et al ., 2013; Khudri and Sadia, 2013; Marani and Ignaccolo, 2015; Ahmad et al ., 2016; Ahmad et al ., 2019).…”

“…They establish the best fit distribution among five extreme value distributions by classical modelling. On the other side, Coles and Dixon (1999), Coles (2001), and Ahmad et al (2019) used likelihood-based inference methods for modelling extreme value models. Researchers are more interested in Bayesian modelling than a classical setup to obtain more valuable results about uncertainty extreme environmental events.…”