Projection methods for error suppression in the meteorological fields before calculation of derivatives

Abstract

In finite-difference approximation of derivatives on a grid with step of h, the error decreases with decreasing h. However, if the original function is given on a grid with an error of order of e, then the approximate differentiation error grows like C e/h k , where k is the derivative order and C is a constant depending on a chosen finite-difference approximation. Projection methods are discussed that are designed to decrease the errors of this kind. On the latitude-longitude grids, the step near the poles along the latitude circles is very small. Methods are proposed for projecting scalar and vector meteorological fields on the subspaces of smooth fields. The projected fields obtained take into account asymptotics of the smooth fields in the vicinity of the pole in the spherical coordinates, separately for each Fourier harmonic in longitude. Results are presented of such smoothing in the polar regions on the fields of objective analysis by Hydrometeorological Center of Russia and on the first-guess fields at standard isobaric heights. Fig. 1. Averaged corrections to (a) first-guess and (b) objective analysis fields of height. Hereafter, in figures, at the horizontal axes, latitude numbers are indicated.

Peregee-Syzygy Tides in Atmosphere

“…These anomalies are computed according to Bagrov's technique (Bagrov, Loktionova, 1994). The daily mean temperature anomalies for each station were determined by applying a piecewise parabolic approximation (Gordin, 1994), that used the monthly means. Data from MIDL for several stations in European Russia were used in the present study.…”