This can most easily be seen by considering that the slowly evolving large scale flow satisfies elliptic equations for all variables except the vertical
component of the vorticity.
For forecast models these errors can be overcome by continually inserting new vertical
component of vorticity observational data every 6 hours, thus reducing the error that has spread upward from the erroneous boundary layer.
For weather forecasts, the vertical
component of vorticity is available from obs and using the above theory, the slowly evolving component can be determined in the troposphere.
It has also been proved mathematically that if one uses only the vertical
component of vorticity (a simple interpolation in time and space can be used), then the rest of the slowly evolving in time solution, i.e. the horizontal divergence, the vertical velocity, the potential temperature, and the pressure) can be determined using solutions of a simple set of elliptic equations (Browning and Kreiss 2002 and Page et al. 2005).
A mathematical analysis of the process (reference available on request) has shown that the wind data, i.e. the vertical
component of vorticity, is the only information that is necessary to drive this process.
If numerical methods can not accurately compute the solution of the basic dynamical system (so called dynamical cores) either because of ill posedness, fast exponential growth, or inadequate resolution to properly resolve the rapid nonlinear cascade of the vertical
component of vorticity (requires unphysically large dissipation to overcome), then adding necessarily unphysical parameterizations to overcome these deficiencies can not lead to a correct physical solution as the resolution is reduced.
Not exact matches
Consistent with an enhanced cyclonic
component, the arctic anticyclone was weakened and
vorticity of winds became positive.