Scheduled Downtime
On Friday 21 April 2023 @ 5pm MT, this website will be down for maintenance and expected to return online the morning of 24 April 2023 at the latest

Typo found in primitive equations WRF Technical notes V3

This post was from a previous version of the WRF&MPAS-A Support Forum. New replies have been disabled and if you have follow up questions related to this post, then please start a new thread from the forum home page.


New member
Dear WRF support team,

I am looking to the equations listed in the WRF-ARW technical note ( and I was wondering if some typos are present in the primitive equations appearing in this document. For example, equations 2.38 and 2.39 have the same right-hand terms (Fu) and theys should be different for U and V. Also, the terms that go with (mx/my) are exactly the same in 2.38 and 2.39 and they should be different.

In equations 2.23-2.24 appear a (mx/my) term in 2.23 and a (my/mx) term in 2.24. Is it possible that these two terms should be the same?

Could you notice me if there is a new document with typos corrected?

Thanks in advanced,

Best Regards,
There are errors in equation 2.39 in the online WRFV3 technical note. As you have noted, the right-hand-side forcing term should be F_V instead of F_U. Additionally, the map-scale factor ratio preceding the horizontal pressure gradient terms should be (m_y/m_x) instead of (m_x/m_y). The map-scale factor terms and the right-hand-side terms are correct in the full-variables version of the horizontal momentum equations, 2.23 and 2.24.

The apparent asymmetry of the map-scale factor coefficients in the comparison of the horizontal momentum equations for U and V arise from the decision to include the factor (1/m_y) in the definition of the covariant velocity Omega (defined immediately following equation 2.22). This is a somewhat arbitrary decision that was made when the latitude-longitude grid was incorporated into WRF over a decade ago. The equations, with the corrections given above, are correct (and they are correct in the model code).

The geopotential equation 2.42 is correct as written. Substituting in the perturbation plus reference geopotential for the full geopotential in 2.42 does not lead to any simplification of the equation. Note that the reference state geopotential will vary in the horizontal (see the first paragraph in Section 2.5 of the technical note) thus horizontal derivatives of the geopotential along coordinate surfaces are non-zero and no simplification is possible.

Thanks for pointing out the errors. We are in the process of finalizing a WRF Version 4 technical note that will contain these corrections. We will be announcing the availability of the new technical note when it is released.