Increase of random errors in temperature forecasts by numerical method and limiting period of reliable forecasts

Abstract

It is shown that random errors of temperature observations increase in the course of forecasting temperature field by numerical method. The forecast equation under test is the advection equation for temperature with 'forward, differencing in time and 'centred' differencing in space, under an assumption that errors in temperature and wind at neighbouring grid-points are statistically uncorrelated :with one another. An analytical expression has been derived for its growth as a function of wind speed, time step, grid distance, temperature gradient and random errors in wind and temperature. The analytical result has also been verified by numerical experiment. With a grid of 200 n. miles and time step of 20 min., in a wind regime of 20 kt, the standard deviation of initial random error doubles itself in about 12 days.