Initial tests 8 for the GCR (balanced variable)
This page is repeated in both frames to allow comparison between figures.
This test uses a revised system with some bugs corrected. Characteristics of this test:
- Try to invert a given PV distribution (itself calculated from data) to give the balanced streamfunction.
- The first guess of the balanced streamfunction is the streamfunction calculated from data, but filtered with 3 normal modes in the vertical.
- No preconditioning is used.
- The GCR is not taken to convergence, but after 50 iterations with k=5 restart (250 iterations in total).
- The GCR calculates coefficients and error norms with a mass weighted inner product.
Notes about the plots on this page:
- 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)
Horizontal plots at L30
Vertical plots at Greenwich meridian
2. The raw theta perturbation - hydrostatic balance with 1 (ref: Theta_p)
Horizontal plots at L30
Vertical plots at Greenwich meridian
3. The raw vorticity perturbation (ref: Vort)
Horizontal plots at L30
Vertical plots at Greenwich meridian
4. The raw streamfunction perturbation (ref: psi)
Horizontal plots at L30
Vertical plots at Greenwich meridian
5. The pressure in balance with 4. (ref: Gp)
Horizontal plots at L30
Vertical plots at Greenwich meridian
6. The theta in hydrostatic balance with 5. (ref: Theta_Gp)
Horizontal plots at L30
Vertical plots at Greenwich meridian
7. The PV calculated from 4. and 5. (ref: PV)
Horizontal plots at L30
Vertical plots at Greenwich meridian
PV modes
8. The filtered streamfunction perturbation (ref: psi_filt)
Horizontal plots at L30
Vertical plots at Greenwich meridian
9. The pressure in balance with 8. (ref: filtered_Gp)
Horizontal plots at L30
Vertical plots at Greenwich meridian
10. The theta in hydrostatic balance with 9. (ref: filtered_Theta)
Horizontal plots at L30
Vertical plots at Greenwich meridian
11. The PV calculated from 8. and 9. (ref: filtered_PV)
Horizontal plots at L30
Vertical plots at Greenwich meridian
PV modes
12. The PV calculated from raw data (ref: PV_RHS)
Horizontal plots at L30
Vertical plots at Greenwich meridian
PV modes
13. The 'solution' streamfunction perturbation (ref: Solution)
Horizontal plots at L30
Vertical plots at Greenwich meridian
14. The pressure in balance with 13. (ref: final_Gp)
Horizontal plots at L30
Vertical plots at Greenwich meridian
15. The pressure in balance with 14. (ref: final_Theta)
Horizontal plots at L30
Vertical plots at Greenwich meridian
16. The PV calculated from 13. and 14. (ref: final_PV)
Horizontal plots at L30
Vertical plots at Greenwich meridian
PV modes
The convergence (Error norm vs total iteration)
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