Growth of random errors in temperature forecasts by numerical method using centred time-differences

Abstract

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.