The primary focus of this thesis is to describe the prevailing atmospheric conditions when heavy rainfall occurs over the Gauteng Province in South Africa. This thesis first describes the characteristics of daily heavy rainfall over Gauteng by defining different heavy rainfall classes and considering the seasonal distribution of these events. Late summer (January, February and March) has considerably more heavy rainfall days than early summer. The change of the character of the atmosphere as the summer season progresses is highlighted by the investigation into the monthly average synoptic circulation patterns when heavy rainfall occurs. The weather systems change from extra-tropical in the first few months of the summer rainfall season to tropical in February months. It is also shown how cyclonic vorticity advection occurs in the upper troposphere whenever heavy rainfall occurs, irrespective of the time of the season. A deep layer of horizontal wind convergence is also present when heavy rainfall occurs and this is replaced by horizontal wind divergence above that. A monthly climatology of sounding-derived parameters associated with heavy rainfall is constructed and it is again apparent how the atmosphere changes from one where conditional instability dominates the production of heavy rainfall in early summer to one where convective instability plays a dominant role in late summer. Twelve sounding-derived variables are identified to describe the thermodynamical profile of the atmosphere when heavy rainfall occurs over Gauteng. They include variables not previously used such as the Elevated K-Index and the meridionial wind component near the surface. Self-organizing maps are used to create a climatology of the vertical profile of the atmosphere during heavy rainfall and this methods captures the changes to the atmospheric state during the progression of the summer season. Favourable sounding-derived parameters and circulation criteria are combined in a self-organizing map to predict daily rainfall frequencies. This method produces encouraging results and methods should be explored to create probabilistic daily rainfall forecast for Gauteng in an operational environment.