Initial tests 10 for the GCR (balanced variable)

• This is a controlled test whereby the PV on the RHS of the equation has originated from a given streamfunction (hence we know that the solution exists, and we know what the solution is). Take the raw streamfunction and filter it with 1 vertical mode, compute the PV from this. This is the RHS PV.
• The first guess is zero.
• No preconditioning.
• 50 iterations (restart 5).
• Euclidean inner product for GCR coefficients (mass weighting crashed in this case).
• Data location /export/custard/disk-01/ross/PV_Results/GCR_Test/PV/RevisedTest/AnsKnown_2

• For each variable, horizontal (long/lat) and vertical (lat/eta) plots are shown.
• For PV variables the extra modes are shown in addition.
• For the horizonal plots, the level is L30 (eta=0.445).
• For the vertical plots, the longitude slice is Greenwich meridian.
• Each field (except for the PV modes) is decomposed into large horiz/small vert (left) and small horiz/large vert (right) scales.
• The plots show the max, min, and mean (calculated by the plotter).
• Plots of balanced pressure have been shown without density scaling in the linear balance equation (to allow us to see the vertical structure). This is for diagnostic purposes only - the actual density scaled pressures are used in the calculations.

1. The raw pressure perturbation (ref: p)

2. The raw theta perturbation - hydrostatic balance with 1 (ref: Theta_p)

3. The raw vorticity perturbation (ref: Vort)

4. The raw streamfunction perturbation (ref: psi)

5. The pressure in balance with 4. (ref: Gp)

6. The theta in hydrostatic balance with 5. (ref: Theta_Gp)

7. The PV calculated from 4. and 5. (ref: PV)

8. The filtered streamfunction perturbation (ref: psi_filt)

9. The pressure in balance with 8. (ref: filtered_Gp)

10. The theta in hydrostatic balance with 9. (ref: filtered_Theta)

11. The PV calculated from 8. and 9. (ref: filtered_PV)

12. The PV calculated from raw data (ref: PV_RHS)

13. The 'solution' streamfunction perturbation (ref: Solution)

14. The pressure in balance with 13. (ref: final_Gp)

15. The pressure in balance with 14. (ref: final_Theta)

16. The PV calculated from 13. and 14. (ref: final_PV)

The convergence (Error norm vs total iteration)