Analysis and Modelling of Extreme Rainfall: A Case Study for Dodoma, Tanzania

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Emmanuel Iyamuremye
Samson W. Wanyonyi
Drinold A. Mbete

Abstract

The analysis of climate change, climate variability and their extremes has become more important as they clearly affect the human society and ecology. The impact of climate change is reflected by the change of frequency, duration and intensity of climate extreme events in the environment and on the economic activities. Climate extreme events, such as extreme rainfall threaten to environment, agricultural production and loss of people’s lives. Dodoma daily rainfall data exported from R-Instat software were used after being provided by Tanzania Meteorological Agency. The data were recorded from 1935 to 2011. In this essay, we used climate indices of rainfall to analyse changes in extreme rainfall. We only used 6 rainfall indices related to extremes to describe the change in rainfall extremes. Extreme rainfall indices did not show statistical evidence of a linear trend in Dodoma rainfall extremes for 77 years. Apart from the extreme rainfall indices, this essay utilized two techniques in extreme value theory namely the block maxima approach and peak over threshold approach. The two extreme value approaches were used for univariate sequences of independent identically distributed (iid) random variables. Using Dodomadaily rainfall data, this essay illustrated the power of the extreme value distributions in modelling of extreme rainfall. Annual maxima of Dodoma daily rainfall from 1935 to 2011 were fitted to the Generalized Extreme Value (GEV) model. Gumbel was found to be the best fit of the data after likelihood ratio test of GEV and Gumbel models. The Gumbel model parameters were considered to be stationary and non-stationary in two different models. The stationary Gumbel model was found to be good fit of Dodoma maximum rainfall. Later, the levels at which maximum Dodoma rainfall is expected to exceed once, on average, in a given period of time T = 2, 5, 10, 20, 30, 50 and 100 years, were obtained using stationary Gumbel model. Lastly, the data of exceedances were fitted to     the Generalized Pareto (GP) model under stationary climate assumption.

Keywords:
Climate extreme indices, extreme value theory, generalized extreme value distribution, generalized Pareto distribution, block maxima, peak over threshold and tail distribution, return level.

Article Details

How to Cite
Iyamuremye, E., Wanyonyi, S. W., & Mbete, D. A. (2019). Analysis and Modelling of Extreme Rainfall: A Case Study for Dodoma, Tanzania. Asian Journal of Probability and Statistics, 3(2), 1-29. https://doi.org/10.9734/ajpas/2019/v3i230086
Section
Original Research Article