Fix Streamfunction Direction in Plotting Code

[QianyeSu]

PR Description

Background

In the current plotting code, the direction of the streamfunction does not align with the definition in the reference [Oort and Yienger, 1996]. Specifically:

• Negative values correspond to clockwise rotation, while positive values correspond to counterclockwise rotation.
• According to the reference, positive values should correspond to clockwise rotation, and negative values should correspond to counterclockwise rotation.

Changes

1. Adjusted the streamfunction calculation to match the reference definition:
   • Updated formula: $\psi\left(\phi,\ p\right)=\frac{2\pi R \cos\phi}{g}\int_{0}^{Ps}\bar{v\left(\phi,\ p\right)}dp$
   • Added a negative sign in the code: (sf * -const) / 1e10
2. Updated the plotting code to ensure the correct streamfunction direction:
   • Positive values correspond to clockwise rotation.
   • Negative values correspond to counterclockwise rotation.

Impact

• The corrected streamfunction direction aligns with the reference, facilitating comparison with other research results.
• Improves the scientific accuracy of the code.

Testing

• Local tests have been conducted, and the plotting results meet expectations.
• The streamfunction direction matches the reference [Oort and Yienger, 1996].

References

Oort A H, Yienger J J. American Meteorological Society, 1996. Observed Interannual Variability in the Hadley Circulation and Its Connection to ENSO[J]. Journal of Climate, 1996, 9(11): 2751–2767.

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Code Changes

# Before （Hadley）
m4 = ax4.contourf(lat, level, (sf), levels=21, cmap='RdBu_r')

# After（Hadley）
m4 = ax4.contourf(lat, level, (sf * -const) / 1e10, levels=21, cmap='RdBu_r')

Code Changes

# Before （Walker）
m4 = ax4.contourf(lon, level, (sf), levels=21, cmap='RdBu_r')

# After（Walker）
m4 = ax4.contourf(lat, level, (sf * const) / 1e10, levels=21, cmap='RdBu_r')

[miniufo]

Thank you very much. Rescaling here is important for atmospheric applications, which is missing previously.

You have changed the size of the figure, which may render the docs here a bit larger. But that's not a big problem. I will first include your contribution and then make some changes to fit the docs.