Corrigendum for NHN22 and NH18: fix in nonlinear zonal advective flux calculation

[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.

Please refer to Issue #83 for a preliminary comparison between originally published figures and updated figures.

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This discussion was created from the release Corrigendum for NHN22 and NH18: fix in nonlinear zonal advective flux calculation.