GCR try 1 (balanced variable)
The following pictures are from a test with the balanced transform.
Given a PV field (bulk + extra modes), the GCR asks what is the balanced streamfunction that leads to that PV.
This test uses no preconditioning, an initial guess for the streamfunction of zero and a GCR 'restart' every 3 iterations. The results are plotted after 250 outer iterations (250*3 iterations in total) and compared to the result that it should converge to.
Level 11 in bulk
Left panel (above): PV specified, right panel: PV implied after 250 outer iterations.
Left panel (below): target streamfunction (from which the specified PV is derived), right panel: streamfunction implied after 250 outer iterations.
Extra mode 1 (no single level streamfunction is associated with this)
Left panel: PV specified, right panel: PV implied after 250 outer iterations (all latitudes shown).
Extra mode 1 (no single level streamfunction is associated with this)
Left panel: PV specified, right panel: PV implied after 250 outer iterations (all latitudes shown, except poles).
Extra mode 2 (no single level streamfunction is associated with this)
Left panel: PV specified, right panel: PV implied after 250 outer iterations (all latitudes shown - unlike mode 1, no extra structure can be seen for mode 2 if the poles are removed).
Vorticity field used to contruct the target streamfunction and PV (level 11 in bulk)
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Residual
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