The Extension of P.D. Thompson' Scheme to Multiple Times

Abstract

P.D. Thompson devised a scheme to correct imperfect analyses of a conservative quantity at two observation times. His scheme has been extended to include a sequence of observation times. When the times are equally spaced, the governing adjustment equations simplify to an equation in one variable, a weighted average of the conservative property at the various times. The weights are found from Pascal' rule. The primary advantage of adding more observation times is to reduce the mean square error in the analyses. The limiting value of mean square error reduction is ½,??,?,(k/k for 2,3,4,?k times, respectively. The applicability of this method to adjustment of a sequence of mean temperature (thickness) fields from the VISSR Atmospheric Sounder (VAS) is discussed.