Includes bibliography. / The objective of this thesis is to review existing methods for estimating missing values in rainfall records and to propose a number of new procedures. Two classes of methods are considered. The first is based on the theory of variable selection in regression. Here the emphasis is on finding efficient methods to identify the set of control stations which are likely to yield the best regression estimates of the missing values in the target station. The second class of methods is based on the EM algorithm, proposed by Dempster, Laird and Rubin (1977). The emphasis here is to estimate the missing values directly without first making a detailed selection of control stations. All "relevant" stations are included. This method has not previously been applied in the context of estimating missing rainfall values.

Simulations based on a month of radar data from Florida, and a summer of radar data from Nelspruit, South Africa, were used to quantify the errors in the measurement of mean areal rainfall which arise simply as a result of the extreme variability of convective rainfall, even with perfect remote sensing instruments. The raingauge network measurement errors were established for random and regular network configurations using daily and monthly radar-rainfall accumulations over large areas. A relationship to predict the measurement error for mean areal rainfall using sparse networks as a function of raining area, number of gauges, and the variability of the rainfield was developed and tested. The manner in which the rainfield probability distribution is transformed under increasing spatial and temporal averaging was investigated from two perspectives. Firstly, an empirical relationship was developed to transform the probability distribution based on some measurement scale, into a distribution based on a standard measurement length. Secondly, a conceptual model based on multiplicative cascades was used to derive a scale independent probability distribution.

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