AbstractA general formulation of the problem of objective analysis by computer consists of a simple equation in which the value of a meteorological variable at a given grid point is expressed in terms of three components which together include all potential ingredients. Several specialized analysis equations associated with existing schemes are obtained from the general equation, and the relevant methods of specifying weights are outlined. These methods were evaluated by performing a 500 mb height analysis using ‘perfect’ data and the same trial field with each. The best relative results were obtained when weights were determined by solving a system of linear equations involving weight parameters based on the autocovariances of observed minus trial values (residuals). A consideration of conditioning problems suggests that the choice of weight parameter should be appropriate to the manner in which the trial value at the grid point is synthesized. The implications of the investigation are that an optimum method of analysis should take into account data type, quality, distribution, predictability, prediction reliability and a statistical or empirical evaluation of the structure of the meteorological field about every grid po