Regional Frequency Analysis of Annual Peak Flows in Pakistan Using Linear Combination of Order Statistics

Abstract

For this paper we conducted a regional analysis (RA) of annual peak flows using linear combination of order statistics, i.e., linear-moments (LM) and trimmed linear moments (TLM). Design flood estimates are calculated and compared at different return periods, which are useful for water resources management, including hydrological structures and basin management. The main objective of our study was to compare regional design flood estimates for untrimmed and trimmed samples. LM is the special case of TLM, when we have no trimming from either side. First, regional flood frequency analysis is performed for LM and then for TLM. After initial screening of the annual peak flow series, a discordancy measure was used to diagnose the discordant sites. No site was found to be discordant. For homogeneity of the region, the homogeneity measure "H" was employed using simulation study based on Kappa distribution, and found that the nine sites on the Indus Basin included in the study constitute a single homogeneous region. In this study we used TLM with trimming values (γ, 0), where γ = 1, 2, 3, 4. In order to determine the most appropriate probability distribution for regional quantile estimates, different probability distributions are used, namely: generalized extreme value (GEV), generalized pareto (GPA), generalized logistic (GLO), Pearson type three (PE3), and generalized normal (GNO). L-moments ratio diagram and Z-test as goodness of fit are engaged to identify the most suitable probability distribution. A comparison revealed that GNO is the best distribution for first three cases as (0, 0), (1, 0), and (2, 0), while for the last two cases of (3, 0) and (4, 0) the most appropriate choice is GEV. A simulation study was also carried out to evaluate the performance and robustness of the best fit probability distribution using relative bias (RB) and relative root mean square error (RRMSE).

Regional Flood Frequency Analysis of the Pannonian Basin

“…For all six distributions, the Z statistics for flood volumes showed that the distributions satisfied the test criteria |Z| < 1.96, N (1.54), LN (0.12), G (1.23), GP (0.33), PIII (0.58) and LPIII (1.52). In this case, when all distributions satisfy the goodness-of-fit test, the distribution closest to zero will be considered as the best fit [41]. As presented, the LN distribution has the value closest to zero, so it can be selected as the appropriate distribution for the flood volumes.…”

State-of-the-Art Statistical Approaches for Estimating Flood Events

“…As described by [ 4 ], extensive literature for FFA is available, not only for the detailed description of PDFs, but also for parameter estimation. The commonly used PDFs for modeling of the APFDs include: generalized extreme value (GEV), generalized logistic (GLO), generalized Pareto (GPA), Pearson type 3 (P3), log Pearson type 3 (LP3), Weibull (WEI), extreme value type 1, extreme value type 2, normal, log normal, gamma, and exponential [ 4 , 5 , 6 , 7 , 8 , 9 ].…”

“…Wang found that LH-moments produce consistent quantile estimates for large return periods, since LH-moments provide greater weight to the larger values in the APFD series and hence better fits to the upper tail of PDFs. This characteristic is even more relevant when sample sizes are small, which is a common reality of streamflow monitoring in developing countries, including Pakistan [ 8 , 9 , 12 , 13 , 14 ]. Various studies have been conducted on LH-moments in different regions of the world [ 11 , 15 , 16 , 17 , 18 , 19 , 20 , 21 , 22 , 23 ].…”

Modeling of flood extremes using regional frequency analysis of sites of Khyber Pakhtunkhwa, Pakistan

“…RFA has also been applied in a few of the published studies in Pakistan. These include: for rainfall (Ahmad et al, 2013; Ahmad et al, 2016a; Ahmad et al, 2017a; Hussain et al, 2017; Khan et al, 2017; Shahzadi et al, 2013), for floods (Ahmad et al, 2016b; Ahmad et al, 2017b; Batool, 2017; Hussain, 2011; Hussain, 2017; Hussain & Pasha, 2009), for wind (Fawad et al, 2018; Fawad et al, 2019). Highlights of some published literature concerning flood frequency analysis in Pakistan are provided in the following section:…”