Vapour pressure (interchangeably referred to as atmospheric humidity) and solar radiation data are, for different reasons, difficult data to obtain in South Africa. Relative humidity measuring instruments (from which vapour pressure values can be obtained) require constant maintenance , while solar radiation can only be measured electronically. Data from both of these variables are, however, required as inputs to the Penman-Monteith equation, which has become the internationally accepted reference for the estimation of potential evaporation. It is necessary, therefore, to produce estimates of vapour pressure and solar radiation over South Africa from more common surrogates, e.g. rainfall and temperature data. Several methods of estimating vapour pressure and solar radiation from the literature are reviewed in this dissertation. Considerably greater attention is focused on models of vapour pressure than solar radiation , as less literature exists on this subject. In general, the methods involved in estimating vapour pressure tend to be relatively rudimentary. The FAO 56 documentation advises using saturated vapour pressure at minimum air temperature as an estimate of vapour pressure, yet the implicit assumptions of using this approach can fail in many circumstances, particularly in the more arid regions . It was found that monthly vapour pressure at any given location in South Africa could be estimated from geographical (invariate) data alone. It was also found that the most influential factor affecting daily vapour pressure at a given location within a given time frame (less than one month) was "air masses". Air masses proved too complicated to model from surrogate data of temperature and rainfall , however, and were thus omitted from the final model. Daily values of vapour pressure and vapour pressure deficit were estimated by holding vapour pressure for a given month constant, but varying temperature on a daily basis It was found that this method produced acceptable results for both elements throughout South Africa. The need for estimating solar radiation has existed for considerably longer than for vapour pressure. Professions other than agriculture, principally architecture and civil engineering, have long required solar radiation data/values. For this reason the art of estimating solar radiation values is better established and more models were available in the literature. Several suitable and recently developed solar radiation models, which use surrogate data (temperature and rainfall) , were identified from the literature survey. These models were then applied in situ and the results were compared with observed values. It was found that the majority of models produced similar output to one another. However, the Liu and Scott (2001) model, which is an enhancement of the Bristow and Campbell (1984) model, was found to be the best available model of those tested, particularly in the more humid locations of South Africa . Verification analyses revealed that the Liu and Scott (2001) model could be used to interpolate solar radiation where a sparse network of solar radiation measuring stations exists, e.g. in the arid locations of South Africa . The structure of the Liu and Scott (2001) model , however, prevented it from being employed in a subsequent exercise on mapping solar radiation over South Africa . For this purpose, the Hunt et al . (1998) model was employed. The estimation of two elements , vapour pressure and solar radiation , was improved upon, and the Penman-Monteith equation can thus now be more confidently applied throughout South Africa. Of these two elements, it is vapour pressure , which, because of a paucity of research to date on the subject, lends itself to expansive research in the future . / Thesis (M.Sc.)-University of KwaZulu-Natal, Pietermaritzburg, 2004.