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

Abstract

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)...