Accession Number : AD0286807

Title :   THE PROPAGATION OF ERROR IN NUMERICAL INTEGRATION OF THE DISCRETE VORTICITY EQUATION

Corporate Author : CALIFORNIA UNIV LOS ANGELES

Personal Author(s) : GATES,W. LAWRENCE

Report Date : 15 MAY 1962

Pagination or Media Count : 1

Abstract : By use of a discrete analogue of the finite Fourier transform, an implicit form of the linear difference barotropic vorticity equation is solved for arbitrary discrete initial data. This solution is applied to the problem of the spread of an initially isolated discrete error, representing either a round-off, observational, or other local numerical error. Of the complete spectrum of discrete error components present, the shorter wave components move outward in a dispersive fashion with an error wave of approximately 4 delta x length moving most rapidly, while the longer error components of length greater than 9 delta x move upstream, where delta x is the space mesh size. Such ropagating error fields appear to be characteristic of a discrete system in response to a broad initial error spectrum, as with an abrupt jump or isolated erroneous value. As time progresses the error distribution appears whiter, although the root-mean-square error remains at approximately 5% of the original isolated error in the case N equals L/delta equals 36. After 240 (1 hr) time steps, only an occasional local error reaches 40% of the original value. (Author)

Descriptors :   *EQUATIONS, *ERRORS, *NUMERICAL INTEGRATION, *NUMERICAL ANALYSIS, *VORTICES, *WEATHER FORECASTING, DIFFERENTIAL EQUATIONS, INTEGRAL TRANSFORMS, MATHEMATICAL PREDICTION, SERIES(MATHEMATICS), STATISTICAL DISTRIBUTIONS, STATISTICAL FUNCTIONS

Distribution Statement : APPROVED FOR PUBLIC RELEASE