Objective analysis using Hough vectors evaluated at irregularly spaced locations

• Published in: Monthly weather review 1984-01, Vol.112 (9), p.1804-1817
• Main Authors: HALBERSTAM, I, SHU-LIN TUNG
• Format: Article
• Language: English
• Subjects: Earth, ocean, space; Exact sciences and technology; External geophysics; Meteorology; Weather analysis and prediction
• ISSN: 0027-0644; 1520-0493
• DOI: 10.1175/1520-0493(1984)112<1804:oauhve>2.0.co;2

Objective analysis can be performed on irregularly spaced observation points by fitting selected functions to the observations. A simple least squares fit is found to be both impractical and ill conditioned, the latter because of gaps in the data exceeding the smallest wavelengths of the fitting functions. Alternative fits can be made practical either by breaking down the least squares fit into a stepwise fitting of several subsets or by imposing a finality condition that yields errors greater than least squares, but are, nevertheless, bounded by a number related to the distribution of the data points. The method of finality involves sequential subtraction of each vector's successive contribution. Ordering of the vectors efficiently then becomes rather crucial. The ill-conditioned behavior of these fits can be suppressed by adding first-guess information in areas that lack data. Tests of the methods using Hough functions evaluated at observation sites as the basis vectors and data from FGGE IIa and IIIa, as well as from a forecast field from the Air Force Geophysics Laboratory global spectral model, show that the finality method is a viable alternative analysis procedure worth exploring. The stepwise least squares method is also a practical method if sufficient realistic data are distributed throughout the domain. Use of residuals (forecast minus observation values) proves to be a more accurate procedure than use of observed and forecast values themselves.