IMPORTANT bugfix release 0.7.2 + corrigendum

[csyhuang]

Two weeks ago, we discovered that there is a mistake in the derivation of expression of nonlinear zonal advective flux term:
$$\frac{1}{a\cos\phi} \frac{\partial}{\partial \lambda} \int^{\Delta\phi}_0 u_e q_e \cos(\phi+\phi^\prime) d\phi^\prime$$

The correct definition of $u_e$ in the integral should be:

$$u_e(\lambda, \phi, \phi^\prime, z, t) \equiv \omega_e a \cos\phi = \frac{u(\lambda, \phi + \phi^\prime, z, t)\cos\phi}{\cos(\phi+\phi^\prime)} - u_{\text{REF}}(\phi, z, t)$$

where $\omega = \frac{u}{a\cos\phi}$ is the angular velocity (and $\phi^\prime \in [0, \Delta\phi]$).

The fix has been done in the following commit and will be published in release 0.7.2:

1995e1d#diff-7e797030d6c037af018d523e2e6a20f0d9f01c3dd8f41a2d7f044b4800684455

This error led to an underestimation of nonlinear component of advective flux ("ua2" in the code). Fixing this error indeed makes traffic jam mechanism (i.e. how waves are slowed down by the nonlinear effect that grows with wave amplitude) more robust.

We will submit corrigendums for Neal et al. (2022, GRL) and Nakamura and Huang (2018, Science) to update the numerical results. The correct derivation of the flux expression can be found in the corrected supplementary materials of NH18. There is no change in conclusions in any of the articles.

Below are previews of updated figures (scale not adjusted yet) in Neal et al. (2022, GRL) and Nakamura nad Huang (2018, Science) due to this fix:

[csyhuang]

Updated figures in Neal et al (2022, GRL)

Below are (preliminary) figures generated with scripts/nhn_grl2022/sample_run_script.py without changing the scale of the axes before and after the fix to assess the error. The corrigendum will have the image color axes adjusted.

Figure	Version published in the paper	After the fixes (release v0.6.4+v0.7.2)
3(c)
3(d)
4(b)
4(c)
4(d)
5

[csyhuang]

#Updated figures in Nakamura and Huang (2018, Science)

Original Fig. 4:

Updated Fig. 4:

Original Fig. 5:

Updated Fig. 5:

[csyhuang]

This is closed by release v0.7.2.