Probabilistic Flood Height Estimation of the Limpopo River at the Beitbridge using r-Largest Order Statistics

Authors

Robert Kajambeu, Department of Statistics, University of Venda, Private Bag X5050, Thohoyandou, 0950, South AfricaFollow
Caston Sigauke, Department of Statistics, University of Venda, Private Bag X5050, Thohoyandou, 0950, South AfricaFollow
Alphonce Bere, Department of Statistics, University of Venda, Private Bag X5050, Thohoyandou, 0950, South AfricaFollow
Delson Chikobvu, Department of Mathematical Statistics and Actuarial Science, University of the Free State, P. O. Box 339, Bloemfontein 9300, South AfricaFollow
Daniel Maposa, Department of Statistics and Operations Research, University of Limpopo, Private Bag X1106, Sovenga, 0727, South AfricaFollow
Murendeni Maurel Nemukula, School of Mathematics, Statistics and Computer Science, University of KwaZulu-Natal, Private Bag X54001, Durban, 4000, South AfricaFollow

Author Country (or Countries)

South Africa

Abstract

The paper presents modelling of uncertainty in extreme return levels of the flood heights of the Limpopo river at the Beitbridge in which the delta and profile likelihood approaches are used in the estimation of the confidence intervals. The modelling approach discussed in this study is a hybrid modelling framework blending a variety of statistical models, techniques and approaches. Monthly flood height data for the years 1992 to 2014 are used. The method is based on a joint generalised extreme value distribution of the r-largest order statistics. The method is more efficient in its use of data than the traditional single maximum observation per block. Estimation of parameters is done using the maximum likelihood method. Using the r-largest order statistics approach, the paper shows that the flood height data can suitably be modelled by the Gumbel class distribution. The 100-year return level is estimated to be 4.981 metres with a confidence interval estimate of (4.886,5.083) using the profile likelihood method. This study is important as it enables accurate estimation of return levels and periods of extreme flood heights. Such analysis helps in risk mitigation, for example, the design of bridges by civil engineers.

Digital Object Identifier (DOI)

http://dx.doi.org/10.18576/amis/140203

Recommended Citation

Kajambeu, Robert; Sigauke, Caston; Bere, Alphonce; Chikobvu, Delson; Maposa, Daniel; and Maurel Nemukula, Murendeni (2020) "Probabilistic Flood Height Estimation of the Limpopo River at the Beitbridge using r-Largest Order Statistics," Applied Mathematics & Information Sciences: Vol. 14: Iss. 2, Article 3.
DOI: http://dx.doi.org/10.18576/amis/140203
Available at: https://digitalcommons.aaru.edu.jo/amis/vol14/iss2/3