Effects of Planetary Wave Propagation and Finite Depth on the Predictability of Atmospheres
Abstract Theoretical predictability of the atmosphere is limited in part by the rate at which small-scale observational errors in the initiation of a forecast grow both in amplitude and in length scale with increasing time. Processes of error growth are examined for the case of equivalent barotropic motion on a β-plane. From direct numerical simulations and from statistical closure theory, it is seen that larger β implies slower rate of error growth. Thus planetary wave propagation enhances predictability. Inclusion of a finite equivalent depth also enhances predictability. For values of β and of the equivalent depth representative of Earth's atmosphere, a theoretical predictability time scale is increased fourfold over earlier calculations based on uniformly rotating, “rigid lid” models.