On representative observations

Abstract

The traditional concept of a “representative observation” is examined and the need for a rigorous and objective definition is discussed in the light of the advancing technology of numerical weather analysis and prediction. Recent advances in the theory of sampling and filtering of multi-dimensional stochastic processes now make meaningful the following definition: a representative observation is a datum pertaining to a particular point and time, which is the result of an optimum filtering operation on the continuous raw data field, under the criterion of minimum average mean square error of reconstruction from the subsequent sampled values on a given space/time lattice.
 In many cases of interest, the applicable filter weighting functions can be determined without complete knowledge of the wave-number spectra of the “signal” and “noise” processes. While the required operations can only be approximated in the case of conventional surface and upper air observations, in two important areas—radar and satellite instrumentation—simple and elegant mechanization may be feasible. In addition, the development yields usable insight into such questions as the density and arrangement of observation networks, numerical smoothing of discrete data, and approximations to derivatives used in numerical analysis and prediction.