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Flood analysis using generalized logistic models in partial duration series

Bhunya, Pradeep; Singh, P.K.; Ojha, C.S.P. and Berndtsson, Ronny LU (2012) In Journal of Hydrology 420. p.59-71
Abstract (Swedish)
Abstract in Undetermined

As a generalization of the commonly assumed Poisson distribution (PD) used to estimate the annual number of peaks over threshold in partial duration series (PDS) model, the negative binomial (NB) distribution is proposed in this study. Instead of generalized pareto distribution (GPD) and exponential distribution (ED) models popularly applied to predict the probability of the exceedances of peak over threshold, the performance of the general logistic distribution (GLD) models is analyzed. Two different models for analyzing extreme hydrologic events are compared, based on, PDS and annual maximum series (AMS), respectively. The performance of the two models in terms of uncertainty of T-year event... (More)
Abstract in Undetermined

As a generalization of the commonly assumed Poisson distribution (PD) used to estimate the annual number of peaks over threshold in partial duration series (PDS) model, the negative binomial (NB) distribution is proposed in this study. Instead of generalized pareto distribution (GPD) and exponential distribution (ED) models popularly applied to predict the probability of the exceedances of peak over threshold, the performance of the general logistic distribution (GLD) models is analyzed. Two different models for analyzing extreme hydrologic events are compared, based on, PDS and annual maximum series (AMS), respectively. The performance of the two models in terms of uncertainty of T-year event estimator [q(T)] is evaluated in the cases of estimation with the method of moments (MOMs), maximum likelihood (ML), and probability weighted moments (PWMs). The annual maximum distribution corresponding to a PDS model with Poisson distributed count of peaks above threshold and GLD for flood exceedances was found to be an extreme value type I (EV1) distribution. The comparison between PDS and AMS is made using ratio of variance of the T-year event estimates, which is derived analytically after checking the reliability of the expressions with Monte Carlo simulations. The results reveal that the AMS/NB-GLD and PDS/GLD models using PWM estimation method give least variance of flood estimates with the PDS model giving marginally better results. From the overall results, it was observed that the Poisson distribution performs better, where the difference between mean (mu) and variance of counts of threshold exceedances is small otherwise the NB distribution is found to be efficient when used in combination with generalized logistic distribution in the PDS model, and this is more prominent for it mu < 1.4. Hence, in such cases when the PDS data have a mean less than this, the AMS/NB-GLD and PDS/GLD should be a better model for q(T) estimation as compared to PDS/ED. (Less)
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author
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
Negative binomial distribution, Generalized pareto distribution, Exponential distribution, Probability weighted moments, Monte Carlo simulations, General logistic distribution
in
Journal of Hydrology
volume
420
pages
59 - 71
publisher
Elsevier
external identifiers
  • wos:000301082000006
  • scopus:84856208778
ISSN
0022-1694
DOI
10.1016/j.jhydrol.2011.11.037
language
English
LU publication?
yes
id
e9811b03-f796-4c59-9e2f-8c714681a017 (old id 2199549)
date added to LUP
2011-10-31 12:19:22
date last changed
2017-08-20 03:56:53
@article{e9811b03-f796-4c59-9e2f-8c714681a017,
  abstract     = {<b>Abstract in Undetermined</b><br/><br>
As a generalization of the commonly assumed Poisson distribution (PD) used to estimate the annual number of peaks over threshold in partial duration series (PDS) model, the negative binomial (NB) distribution is proposed in this study. Instead of generalized pareto distribution (GPD) and exponential distribution (ED) models popularly applied to predict the probability of the exceedances of peak over threshold, the performance of the general logistic distribution (GLD) models is analyzed. Two different models for analyzing extreme hydrologic events are compared, based on, PDS and annual maximum series (AMS), respectively. The performance of the two models in terms of uncertainty of T-year event estimator [q(T)] is evaluated in the cases of estimation with the method of moments (MOMs), maximum likelihood (ML), and probability weighted moments (PWMs). The annual maximum distribution corresponding to a PDS model with Poisson distributed count of peaks above threshold and GLD for flood exceedances was found to be an extreme value type I (EV1) distribution. The comparison between PDS and AMS is made using ratio of variance of the T-year event estimates, which is derived analytically after checking the reliability of the expressions with Monte Carlo simulations. The results reveal that the AMS/NB-GLD and PDS/GLD models using PWM estimation method give least variance of flood estimates with the PDS model giving marginally better results. From the overall results, it was observed that the Poisson distribution performs better, where the difference between mean (mu) and variance of counts of threshold exceedances is small otherwise the NB distribution is found to be efficient when used in combination with generalized logistic distribution in the PDS model, and this is more prominent for it mu &lt; 1.4. Hence, in such cases when the PDS data have a mean less than this, the AMS/NB-GLD and PDS/GLD should be a better model for q(T) estimation as compared to PDS/ED.},
  author       = {Bhunya, Pradeep and Singh, P.K. and Ojha, C.S.P. and Berndtsson, Ronny},
  issn         = {0022-1694},
  keyword      = {Negative binomial distribution,Generalized pareto distribution,Exponential distribution,Probability weighted moments,Monte Carlo simulations,General logistic distribution},
  language     = {eng},
  pages        = {59--71},
  publisher    = {Elsevier},
  series       = {Journal of Hydrology},
  title        = {Flood analysis using generalized logistic models in partial duration series},
  url          = {http://dx.doi.org/10.1016/j.jhydrol.2011.11.037},
  volume       = {420},
  year         = {2012},
}