#### Reading: Interdependence between the Water Levels of Kotte Canal and Kelani River using Copulas

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# Interdependence between the Water Levels of Kotte Canal and Kelani River using Copulas

#### K. Perera,

Department of Engineering Mathematics, Faculty of Engineering

#### P. N. Wikramanayake

##### The Open University of Sri Lanka, Nawala, LK
Department of Civil Engineering,

## Abstract

The interdependence of water levels of the Colombo canal system and the Kelani River is important for flood management in the city of Colombo. This study aims at deriving the interdependence between the water levels of the Kotte canal and the Kelani River using the Copula method. The advantage of the Copula method is that it is not necessary to assume that the water levels are independent or normally distributed or have the same of marginal distribution. Since there was a dependency between the two water levels (Kendall’s rank correlation (τ) p-value < 0.05) the Copula method was used to derive the joint distribution. By considering the minimum values of the Akaike Information Criterion (AIC) and the Bayesian Information Criterion (BIC), the lognormal distribution was identified as the best marginal distribution for both water levels and the Clayton copula was identified as the best Copula. By combining the identified marginal distributions using the Clayton copula, the joint distribution was derived for the two water levels and the joint return periods were calculated. The joint distribution has a peak at (0.32, 0.34) implying that these are the most frequently occurring pair of water levels. Also the return periods for the river to be high when the canal water level is high were quite long which shows that drainage to the river is feasible. Moreover the return periods were lower when the river water level is high and canal water level is low which can be used to design the gates and the flood bund to prevent flooding in the city.

Sri Lankan Journal of Applied Statistics 2015;16(2): 135-146

##### DOI: http://doi.org/10.4038/sljastats.v16i2.7828
How to Cite: Perera, K., Sumathipala, P.L.N.S. & Wikramanayake, P.N., (2015). Interdependence between the Water Levels of Kotte Canal and Kelani River using Copulas. Sri Lankan Journal of Applied Statistics. 16(2), pp.135–146. DOI: http://doi.org/10.4038/sljastats.v16i2.7828
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