On the concept and implementation of sequential analysis for linear random fields
Daniel P. Petersen · Tellus A Dynamic Meteorology and Oceanography · 1968
Formulas are derived for the optimum (least-mean-square) linear mixing of prognostic information and synoptic observations in objective analyses. Exploitation of these results makes possible a continuing synoptic analysis, updated as new measurements are reported, without the necessity of globally simultaneous observations. For the special case of an unbounded, spatially periodic observation lattice in a homogeneous field, solutions in the wave-number domain are obtained. A one-dimensional wave equation and a thermal diffusion problem are treated as examples.This research has been supported in part by the Techniques Development Laboratory, Weather Bureau, Environmental Science Services Administration, United States Department of Commerce.