Mathematical and numerical analysis of the discrete fragmentation coagulation equation with growth, decay and sedimentation.

Abstract

The importance and need for solar energy man and living organisms cannot be overemphasised. It is therefore necessary to estimate the amount of solar radiation incident on South African surfaces and how it can be harnessed for solar energy application. The amount of solar radiation received by a surface depends on solar elevation, weather patterns, geographical location, cloud cover, aerosols, time of the day as well as surface reflectivity. Some of these factors influencing the amount of solar radiation are studied in this thesis. We made use of measurements from the South African Universities Radiometric Network (SAURAN), Ozone Monitoring Instrument (OMI), Clouds and the Earth’s Radiant Energy System (CERES) and the Modern Era Retrospective Analysis for Research and Application (MERRA) over different South African surfaces by extension, Africa. Measurements from the SAURAN network were used to study the seasonal variation in global horizontal irradiance (GHI), direct normal irradiance (DNI) and diffuse horizontal irradiance (DHI) over South African cities and Namibian city from 2013 to 2017. The selected South African cites are Alexander Bay, Durban, Bloemfontein, Pretoria and Port Elizabeth while Windhoek was selected in Namibia. Over a longer period, we examined the trend in shortwave flux and total cloud fraction over the same surfaces using MERRA data. The results reveal summer maximum and winter minimum for GHI, DNI and DHI. We observed that measurements of GHI, DNI and DHI from Durban and Port Elizabeth were much higher than other locations. For shortwave flux over the surfaces, the result showed that the North-western region received the highest amount of solar radiation while the South-eastern region received the least. This decrease down east was linked with low cloud fraction in the Northwest while the cloud fraction in the Southeast was very high. However, the amount of solar energy received in the South-eastern part of South Africa is still higher than the amount received in the United States and several European countries who are maximizing solar energy potential. The result revealed that South Africa received good amount of solar radiation throughout the year and this must be harnessed more. We obtained a statistically significant trend in shortwave flux of 2.65 Wm-2 per decade over Alexander Bay between 2009 and 2017 while a significant trend of 2.34 Wm-2 per decade was obtained in Port Elizabeth between 2000 and 2009. We then investigated the seasonal variation in temperature, ultraviolet aerosol index (UVAI) and total column ozone over different geographic zones of South Africa using datasets from OMI from 2004 to 2016. Cape Town was selected for the southern region, Springbok in the west, Durban for east while Irene and Johannesburg were selected for the Northern region. The results indicated the influence of warm Agulhas current on Durban temperature and cold Benguela current on Cape Town temperature. The result of seasonal variation in UVAI showed a spring time maximum attributed to biomass burning. High UVAI in Durban was linked to significant emissions from local sugar cane burning while that of Cape Town was attributed to marine aerosols. Ozone seasonality shows the well-established spring timemaximum and autumn minimum for southern mid-latitudes. We then used second order Fourier decomposition to determine the increasing and decreasing trend in UVAI and total ozone. This study was then extended over Africa as we estimated the interannual and seasonal variation in shortwave flux, ozone and aerosol index over Africa. The results reveal that Eastern, Central and Southern Africa received more solar radiation compared to Northern and Western Africa. However, all regions received good amount of radiation which makes Africa a potential place for solar energy exploration. In the eastern part of Africa, high ozone was observed in Malindi which was attributed to its unique location while a systematic increase in total ozone was observed in Ethiopia. For western regions of Gambia and Senegal, ozone trends were similar and its precursors were suggested to be from natural sources with little anthropogenic contributions. High ozone in Mozambique was attributed to the atmosphere being rich in carbon dioxide, carbon monoxide, methane, organic and inorganic particles as well as biomass burning. Total ozone in Algeria was low compared to other North African regions. This was attributed to the injection of cold and dry air from higher latitudes to southern Spain and Algeria which creates vortex on the Algerian coast and the formation of cyclone. However, in Morocco, ozone was very high and it was linked to the presence of high-level volatile organic compounds from forests made up of Eucalyptus and Pine trees. The result of the Aerosol Index (AI) showed very high absorption properties in Namibia being one of the three places on earth with persistent low-level cloud and the only location with steady supply of tiny aerosol particles from inland fires. High aerosols index observed in Algeria linked to high desert fires resulting in pollutions while high aerosol index in Congo was attributed to high mineral dust concentration from the Sahara and high nitric acid concentrations from biomass burning in the Congo basin. We also assessed the effect of aerosols and clouds on surface energy budget over eight South African regions using MERRA and CERES datasets. Both datasets showed similar pattern in climatology and interannual variability of both shortwave and longwave radiation. We determined aerosol forcing on both shortwave and longwave flux and showed that it had more effects on shortwave compared to longwave which results in dimming. We obtained the Bowen ratio and it showed a strong negative correlation with aerosol effect anomaly in winter and spring which indicates that as aerosol effect increases, less radiation reaches the earth.