Search Results

You are looking at 1 - 6 of 6 items for :

  • Author or Editor: Philip D. Thompson x
  • Monthly Weather Review x
  • Refine by Access: All Content x
Clear All Modify Search
Philip D. Thompson

Abstract

We propose here a method of “stochastic-dynamic” prediction that is computationally more efficient than integration of the full set of “second-moment” equations. This gain is achieved by omitting covariances between modes in different interacting triads, and by expressing intratriad covariances in terms of error variances, via the conditions for invariance of products of invariants. The resulting evolution equations for the error variances of all modal amplitudes constitute a closed system involving only those error variances.

To test the accuracy of this method, we have compared the predicted error variances with those calculated directly from an ensemble of 100 individual predictions, starting from an ensemble of 100 initial states containing random errors. These agree very well up to about the doubling time of total rms error, but later diverge as the effects of indirect interactions accumulate.

Full access
Philip D. Thompson

Abstract

No abstract available.

Full access
Philip D. Thompson

Abstract

This note deals with a new class of solutions of the nondivergent barotropic vorticity equation. In general, these solutions require a complete representation in spherical harmonics and are therefore good comparison solutions for testing the accuracy of spectral methods of numerical integration.

Full access
Philip D. Thompson

Abstract

No abstract available.

Full access
Philip D. Thompson

Abstract

Starting with the vorticity equation for barotropic flow, we derive a system of stochastic differential equations that determines the time-evolution of the local variance of vorticity error originating in a large ensemble of initial states containing random and statistically isotropic initial errors. Those equations show that the local growth or decay of error variance depends primarily on the detailed structure of the true vorticity field; in general, the most rapid growth of error can be expected in concentrated regions of strong vorticity gradient.

Those stochastic differential equations provide the basis for a simple method of stochastic-dynamic prediction. It requires only a modest increase over the total volume of computation for deterministic prediction.

Full access
Owen E. Thompson, Philip A. Arkin, and William D. Bonner

Abstract

A comprehensive summary of diurnal wind variations in the midwestern region of the United States is presented. Analyses are based on seven summers of four per day soundings at Fort Worth, Tex., Topeka, Kan., and International Falls, Minn. It is found that the diurnal oscillations are most prominent at Fort Worth, of significant amplitude at Topeka, and, although of lesser amplitude, still detectable at International Falls. An analysis is made of the forcing required to account for that part of the wind oscillation which cannot be attributed to Coriolis effects. This analysis indicates that the forcing is comparatively small at Fort Worth when the wind oscillations are largest owing to a resonance there with natural inertial oscillations. Significant forcing is present at higher latitude stations even though the manifestation of the forcing in the wind field is somewhat smaller in amplitude. The data suggest that forcing mechanisms at low and high attitudes may propagate to cause wind oscillations in the middle levels.

Full access