A note on the effect of grid-point numerical errors on the large scale flow characteristics of a four-level model of the atmosphere

Abstract

The four-level model described by Searle & Davies (1975) in an accompanying paper was integrated for a 100 days period using (a) the (Chilton, U.K.) Atlas Computer, (b) the I.B.M. 360/195 at Harwell, U.K., with firstly single precision and secondly double precision; identical finite difference schemes and computer programmes were applied and also identical initial data employed in each of the three cases. The computed eddy kinetic energy function in (a) diverged quickly from those in (b) after about 400 time steps of ½ hour duration. After about 1 500 time steps of the same duration the single and double precision results in (b) also diverged quite sharply and the energy functions were out of phase after a further 1 000 time steps. The implication is that the effect of truncation and other errors at the grid points of numerical models on the exact timing of large scale dynamics is very serious, and presents a formidable mathematieal-physical-computing probem. This must be solved before accurate long period weather predictions may be achieved.