On a method for parametric representation of the state of the atmosphere

Abstract

In a discussion of possible parametric repreeentations of the state of the atmosphere it is shown that the common use in numerical prediction models of parameters directly given by the height of certain pressure levels is inefficient. An alternative method is suggested where atmospheric variables are expanded in empirical orthogonal functions. The expansion takes for height data the form Z (x, y, t, p) = F0 (p) + ∑1K zk (x, y, t) Fk (p), where F0 (p) represents an area average and the functions Fk (p) and the coefficients zk (x, y, t) are determined using a least square residual condition and a condition of finality. Expansions of this type have been made on height and wind data for eight days. Results from these expansions are given. The convergence is found to be surprisingly rapid and two or at most three modes are sufficient for an accurate description of the large scale structure of the troposphere and the lower stratosphere. The form of the pressure functions in the lowest modes is found to be approximately conservative. Finally, maps of the coefficient fields are presented and a brief discussion given of a case of pronounced baroclinic development.