Dynamics of Daily Rainfall and Temperature in Makurdi

Having a detailed knowledge of rainfall and temperature dynamics is important for an adequate management of our meteorological and hydrological resources. Chaos theory being the basis for studying nonlinear dynamic systems has opened a lot of doors towards understanding complex systems in nature such as the weather. In this study the dynamics of daily rainfall and temperature in Makurdi from January 1st 1977 December 31st 2010 is investigated using chaos theory. A variety of nonlinear techniques such as power spectrum, phase space reconstruction, Lyapunov exponents and correlation dimension are applied. The optimal delay times were calculated for rainfall and temperature using the average mutual information technique while optimal embedding dimensions were also obtained using the method of false nearest neighbors. Phase space reconstruction was carried out with these optimal values using the method of delays. The phase portraits showed geometry of distinct shapes interwoven to form spongy like structures indicating the presence of randomness and chaos in the data with that of rainfall concentrated at the origin due to the numerous zeros in the rainfall values. The correlation dimensions were estimated using the Grassberger-Procaccia algorithm and found to be 1.02 and 5.82 for the rainfall and temperature respectively while the Lyapunov exponents were calculated using Rosensteins approach and obtained as 0.00832/day and 0.00574/day for daily rainfall and temperature respectively. The small values (less than20) of the correlation dimensions obtained suggest the presence of chaotic behavior of low dimensions, inferring that the rainfall dynamics is dominantly governed by a minimum (maximum) of 2 (18) variables while the temperature dynamics is governed by a minimum (maximum) of 6 (17) variables. The positive values of the largest Lyapunov exponents confirm the presence of chaotic dynamics in rainfall and temperature records over Makurdi and suggest predictability of within 112 days and 174 days for rainfall and temperature respectively.