Double count of runoffs in the variable volume (vvl) case

[Robin_Waldman]

Context

I am diagnosing the 3D salinity trend in NEMO v3.6 with variable volume (z star coordinate), time splitting, with a runoff depth specification (ln_rnf_depth_ini = .true. and rn_dep_max = 10.).

Analysis

In the case of a river runoff with no salt content, the runoff causes a negative salinity trend through the divergence of the vertical velocity which causes a dilution of salt. This dilution effect is applied over the depth controlled by rn_dep_max in the routine dom_vvl_sf_nxt which is called in the routine div_cur updating the divergence hdivn. However, the runoff dilution effect is accounted for a second time in the update of the vertical scale factor fse3t_a performed in the routine dom_vvl_sf_nxt. Indeed, the fse3t_a update is proportional to the sea surface height variation, itself accounting for the net volume flux at the surface (runoff plus emp). In the end, the vertical velocity update of routine wzv counts emp once through the fse3t_a update, but it counts the runoff twice through both the hdivn and fse3t_a updates.

Recommendation

Unless I am missing something, there seems to be a double count of the dilution effect induced by runoff in the variable volume case. If this is the case, my recommendation is to remove the runoff effect from the sea surface height variation in the update of vertical velocities (e.g. computing a temporary after vertical scale factor that removes the effect of runoff on sea surface height variations).

If I have missed something, I would be very happy to have a clearer explanation than section 7.9 of the NEMO user book which I found confusing. Thanks a lot!

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