Adaptation of P.D. Thompson's Scheme to the Constraint of Potential vorticity Conservation

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Abstract
The dynamical adjustment scheme of P.D. Thompson (1969) has been adapted to the two-parameter baroclinic model which has potential vorticity as the constraint. In contrast to Thompson's approach, which used a differential-difference form of the constraint in space-time, the governing equations are discretized. Analyses simulated from analytic functions and analyses derived at the National Meteorological Center (NMC) are used to test the adjustment procedure. The reduction in error variance is related to the characteristics of the analysis error and the consequences of discretization, i.e., truncation error in the constraint and associated Euler–Lagrange equations. The principal results are as follows: 1) Significant reduction in mean square error of vorticity can be accomplished with systematic or random error sources when r = |V| Δt/Δs < 1, where |V| is the geostrophic advection speed, Δt is one-half the time interval between maps, and Δs is the spatial resolution along the steering contours. 2) The limit of error reduction is reached as r→0, and the limiting values obtained from experiment compare favorably with the theoretical results of Thompson. 3) Height fields that are post-processed from adjusted vorticities also exhibit reduced error variance. 4) Results from the two-parameter model indicate that the strategy of adjustment will be useful in assimilating a sequence of mean temperature (thickness) fields derived from the VISSR Atmospheric Sounder (VAS) which is to be carded on all GOES satellites during this decade.

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