Uncertainty of Initial State as a Factor in the Predictability of Large Scale Atmospheric Flow Patterns

Abstract

This article deals with the predictability of the atmosphere or, more exactly, with the gradual growth of “inherent” errors of prediction, due to errors in an initial state that is reconstructed from measurements at a finite number of points. By investigating the initial time-derivatives of the error arising from random analysis error, it is found that the increase of the RMS (root-meansquare) wind error in predictions over periods of a few days depends on:

1) the period of the forecast

2) the initial RMS vector wind error

3) the difference between the characteristic scale of the initial error field and the scale of fluctuations in the true initial flow pattern

4) the area average of the vertical wind shear between 250 and 750 mb

5) the RMS vector deviation of the wind at about 500 mb from its area average and

6) the average static stability of the atmosphere. The joint effect of these various factors is given explicitly by a single equation, relating the increase of inherent error to the statistical properties of the initial error field and true initial flow pattern.

In many winter situations, and for initial error fields whose scale is typical of the present observational network, the inherent RMS vector wind error may double its initial value after two days, and rise to the error of sheer guessing in about a week. Doubling the overall density of regular reporting stations would virtually eliminate the increase of inherent error in forecasts over a few days. It is also found that zonally-averaged wind fields are inherently more predictable than unaveraged wind fields, at least in cases of predominantly barotropic flow.

The results outlined above are interpreted in the terms of a variety of practical and administrative problems, in each of which a dominant factor is the predictability of the atmosphere. Examples are the problems of estimating limits of confidence in forecasts, deciding on the most economical density and distribution of regular reporting stations, fixing the maximum range beyond which detailed “forecasts” have lost essentially all predictive and economic value and, finally, that of establishing the point of rapidly diminishing returns in the development of more complicated and costly methods of prediction.