Mathematical Science

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Browsing Mathematical Science by Author "Zvarevashe, Willard"

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    A data adaptive approach to the analysis of South African climate variability and its agricultural impacts
    (University of Zululand, 2020) Zvarevashe, Willard
    Climate variability, which is mostly physically identified through extreme rainfall and temperature, has a significant impact on the daily livelihoods of people and other species. The temperature has been increasing at an average of 0.65ºC per decade since 1900, and this may be attributed to natural and human factors. Climate variability has more adverse effects on Africa due to lack of resources, failure to adapt, and high dependence on the rain for agricultural purposes. Although Africa is the most affected continent, there are few studies on the climate variability impact on the continent. Therefore, there is a need to carry out more studies using historical data to model the climate variability impact. The climate has become more variable recently, as can be observed by the increase in the occurrence of floods and droughts. Due to this high volatility, linear statistical methods are inconclusive. Some of the non-linear methods, such as Fourier and wavelet transform-based methods make several assumptions. In this study, a data-adaptive method, ensemble empirical mode decomposition (EEMD), is used to decompose the climate data into multiple time series called intrinsic mode functions (IMF). IMFs represents the variability of the time series at different time scales. EEMD is a noise assisted method and there is a challenge on the amplitude of noise to be added. Therefore, in this study, a method to find the optimal amplitude of the noise is proposed. To determine the physical meaning of the IMFs synchronisation is employed. Synchronisation is a method that can be used to find the correlations between oscillating systems. Rainfall is synchronised with temperature, El iii Niño-Southern Oscillation (ENSO) and Quasi-Biennial Oscillation (QBO) to investigate their variability impact on rainfall at different time scales. It has been shown that models, coupled with decomposition, perform better than single models; hence, for the first time, the decomposed data (IMFs) are modelled using generalised extreme value distribution (GEVD). GEVD was found in previous studies to be the best suitable for many hydrological and meteorological problems. However, many studies assume stationarity of the data. In this study, the diagnostic plots (quantile-quantile plot, probability-probability plot and probability density plot) reveals that the IMFs GEVD model provided a better fit. The goodness-of-fit test using Kolmogorov-Smirnov (K-S) and Anderson-Darling (A-D) test shows that IMFs GEVD models are more robust, compared to the original rainfall time series GEVD model. EEMD is used to investigate the climate variability impact on agriculture using grapevines and sugarcane as case studies. The IMFs from the Normalised DifferenceVegetativeIndex(NDVI)aresynchronisedtorainfallandtemperature. NDVI is used because it was found in previous studies to be positively correlated to the yield in many crops and has been used to gauge the expected yield for crops. The results show that an increase of temperature for the period under studydoesnothavenoticeableimpactongrapevines’NDVI.However, thisisnot the case with sugarcane where it is shown that temperature variability has an impactontheNDVIatseasonal,and26months(approximately2years)periods. ThisstudyisthefirsttousethedecompositionofNDVItoinvestigatetheclimate variability impact on plants. Furthermore, few statistical studies do not look at thegrowthphaseofcropsandplantationsbutuseyieldasabasisfortheanalysis of climate variability impact. The proposed model may be used for short and medium term planning to predict the future NDVI and expected yields.
University of Zululand