On the extended-range predictability of large-scale quasi-stationary patterns in the atmosphere

Abstract

A principal objective of this article is to establish theoretically the result that, contrary to some previously held beliefs, internal nonlinear processes (wave-wave and wave-mean interactions) among the large scales not likely to be the dominant mechanisms that lead to unpredictability of the low-frequency portion of the large-scale waves in the extra-tropical atmosphere. It is further argued that theoretically quasi-stationary long waves can probably be predicted at extended ranges if boundary forcings and tropical influence can be treated as known during the range of prediction.

The problem of long-range predictability of quasi-stationary long waves is studied here using a three-dimensional quasi-geostrophic channel model of the atmosphere, with lateral and lower boundary forcings prescribed. The low-frequency component of the flow is isolated by taking the running-time mean with an averaging period taken to be longer than the typical lifecycle of synoptic-scale baroclinic waves. When this period is chosen to be 10 days or longer, it is found that the evolution of the large-scale flow is not governed by a regular initial-value problem and detailed information of the initial condition is not “remembered’ by the quasi-stationary waves beyond the predictability limit for the atmosphere as a whole. Instead, it is found that the extended-range evolution of the stationary waves responds to the corresponding evolution of the zonal index, which measures the total zonal geostrophic angular momentum in the channel. Some issues of theoretical predictability, such as the effect of small errors in the initial condition and of small uncertainties in our knowledge of the transient eddy fluxes, are addressed. It is argued that, since the evolution of the zonal index is found to be governed by a remarkably simple first order nonlinear differential equation of a single scalar function of time, whose solution has predictable properties, the quasi-stationary long waves, whose evolution is determined by the prognostic information contained in the zonal index, are perhaps also predictable beyond the “predictability limit”