On the Theoretical Predictability of Extrapolation Methods

Abstract

By use of a statistical theory developed previously, five extrapolation formulas are generalized to take into account uncertainties of initial states, due to lack of information between observing stations. This furnishes expressions for theoretical standard deviations of extrapolated displacements as functions of the mean distance between stations. These standard deviations and the normal distribution provide limiting probabilities of forecast displacements. Examples are presented for each of the five extrapolation methods. Variances of forecasts are analyzed into component valances of initial and past locations of extrapolated features. It is shown that these components usually make unequal contributions to the total variance, in a given prediction.