The growth of initial random errors in temperature forecasts by numerical method using centred time-differenced is investigated. Horizontal advection in one dimension is considered. Assuming that there is no correlation between the initial random errors as the different grid points and neglecting any correlation that may develop in the col1rse of computation, the random errors grow much more rapidly in this method than in forward time differencing. In both methods, correlations develop between the random errors at different grid points in the course of computation. When these are taken in to account, the growth of random errors is further enhanced in the forward differences. In the centred time-differences method, these correlations keep the random error almost at the initial level.

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A curvilinear regression study of weather factors with the wheat yield et Dharwar is made by the successive approximation technique developed by Ezekiel and Fox (1950). Various weather factors are tried and the following tentative conclusions are drawn. An optimum of about 160C minimum temperature 29.30C maximum temperature and 220 to 230C mean temperature with 60 to 65 hours of bright sunshine per week and 50 to 60 percent humidity appear to be the most favourable condition for wheat in Dharwar. An optimum total water requirement may be assessed as equivalent of 40 to 50 cm of rainfall during the period July to end of the Vegetative phase.

A mathematical method is developed to calcalate the value of any parameter at a grid-point from its average values over three squares symmetric around the point. The weighting functions are derived from the dimensions of the scanning squares. This procedure takes into account all differentials below the sixth order in a Taylor expansion. Truncation error due to neglect of higher order differentials is assessed. Certain refinements to the weighting functions due to using finite number of observations in scanning squares are introduced. Modification and suppression of small waves are discussed in relation to scan-length, average distance between  observatories and their random distribution. The method was tried on long and short waves by a numerical experiment.

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