posedness

Using a mathematical perturbation of smooth, large-scale atmospheric flow in the presence of vertical shear (jet stream), Browning and Kreiss (1984) showed that the hydrostatic equations can lead to unbounded exponential growth (ill posedness) and the non-hydrostatic equations can lead to rapid exponential growth on the time scale of a few hours when the wave length resolved by a numerical model approaches 10 km.

Exponential Growth in Physical Systems « Climate Audit 2007

Will you provide additional information relative to the basis of the ill-posedness of hydrostatic models?

Exponential Growth in Physical Systems « Climate Audit 2007

If there is overturning caused by numerics, physics, or ill posedness in the hydrostatic system, the model must be stabilized either by large dissipation or an ad hoc adjustment to reinstate the hydrostatic balance and usually both.

Exponential Growth in Physical Systems « Climate Audit 2007

And at finer resolutions the hydrostatic model blows up even sooner as expected from the ill-posedness.

Exponential Growth in Physical Systems « Climate Audit 2007

The ill posedness of the IBVP for the hydrostatic system was shown mathematically in 1976.

Exponential Growth in Physical Systems « Climate Audit 2007

You seem to have numerical accuracy, numerical stability, ill posedness and fast exponential growth confused.

Exponential Growth in Physical Systems « Climate Audit 2007

Once we have these facts, we can discuss analytically the posedness and accuracy of the process.

Anthony Watts at UCAR « Climate Audit 2007

This modification was made in order to overcome the ill posedness of the hydrostatic system for open boundary problems IBVP in the midlatitudes so that the approximate system could be used to supply accurate, well posed boundary conditions for fine mesh limited area models.

Possible ITCZ Influence « Climate Audit 2007

Auxiliary differential equation models can also affect the well- or ill-posedness of the overall equation system.

This "Fix" in the GISS Code « Climate Audit 2007

The latter, although in some agreement with the nonhydrostatic model at the lower resolution up to 12 hr all runs start with the same balanced large-scale initial conditions, in the higher resolution run blows up because of the ill-posedness of the hydrostatic system as expected from the mathematical theory in the reference cited above.

Exponential Growth in Physical Systems « Climate Audit 2007