A Dynamical Method of Analyzing Meteorological Data

This paper deals with the problem of reconstructing meteorological conditions in “holes”-i.e., large regions from which no data are received, but which are surrounded by regions in which the frequency and density of observations are fairly high. The method proposed here is a combination of numerical procedures of analysis and prediction, by which one can generate a series of increasingly exact analyses in a hole. It is shown that the error of this method approaches a definite lower limit which depends on:

1. The size and shape of a hole
2. The average time required for individual particles to travel across the hole.
3. The average absolute rate of flow across the boundary of the hole, and
4. A statistical measure of the inaccuracies inherent in the prediction system.

Numerical estimates of the accuracy attainable by this method indicate that dynamical methods are significantly better than conventional methods based on pure interpolation and smoothing. Finally, some aspects of the problem of network design are reviewed in the light of our present results.