NOTE ON THE ACCUMULATED ERROR IN THE NUMERICAL INTEGRATION OF A SIMPLE FORECAST MODEL

A linearized, two-level forecast model with known analytic solution is numerically integrated to examine the behavior of the accumulated error (truncation and machine word “round-off” error). The results indicate that for linear models numerically integrated with centered differences: 1) the ratio of space increment to disturbance wavelength that yields sufficient accuracy in a reasonable amount of computation real time is on the order of 10−1 to 10−2; 2) the largest time increment consistent with the stability criterion should be used for computation expediency. Computations performed on computers having different word lengths did not yield significant differences in the results for this model integrated out to 7 days.