Making pseudosalt more like actual salt (real salt? more salt-like? more salty?)

[mnlevy1981]

I've been working on a fix for #1545 and testing via the MOM_CFC_cap.F90 and pseudo_salt_tracer.F90 modules. I'm in the process of bringing the February changes to main onto my branch, and making sure my branch can pass dimensional scaling tests. In doing so, I noticed a small discrepancy in how units are set when salt and pseudosalt are registered. Here is the register_tracer() call for salt:

      call register_tracer(CS%tv%S, CS%tracer_Reg, param_file, HI, GV, &
                           tr_desc=vd_S, registry_diags=.true., flux_nameroot='S', &
                           flux_units=S_flux_units, flux_longname='Salt', &
                           flux_scale=conv2salt, convergence_units='kg m-2 s-1', &
                           convergence_scale=0.001*GV%H_to_kg_m2, CMOR_tendprefix="osalt", diag_form=2)

vs the same call for pseudosalt:

  call register_tracer(tr_ptr, tr_Reg, param_file, HI, GV, name="pseudo_salt", &
                       longname="Pseudo salt passive tracer", units="psu", &
                       registry_diags=.true., restart_CS=restart_CS, &
                       mandatory=.not.CS%pseudo_salt_may_reinit)

The code mods below bring flux_scale, convergence_units, and convergence_scale into agreement between the two (but I am now noticing that I should also set flux_units):

diff --git a/src/tracer/pseudo_salt_tracer.F90 b/src/tracer/pseudo_salt_tracer.F90
index 579751952..cf3874697 100644
--- a/src/tracer/pseudo_salt_tracer.F90
+++ b/src/tracer/pseudo_salt_tracer.F90
@@ -74,6 +74,7 @@ function register_pseudo_salt_tracer(HI, GV, param_file, CS, tr_Reg, restart_CS)
   real, pointer :: tr_ptr(:,:,:) => NULL()
   logical :: register_pseudo_salt_tracer
   integer :: isd, ied, jsd, jed, nz
+  real :: conv2salt            ! A conversion factor for salt fluxes [m H-1 ~> 1] or [kg m-2 H-1 ~> 1]
   isd = HI%isd ; ied = HI%ied ; jsd = HI%jsd ; jed = HI%jed ; nz = GV%ke

   if (associated(CS)) then
@@ -95,9 +96,16 @@ function register_pseudo_salt_tracer(HI, GV, param_file, CS, tr_Reg, restart_CS)
   tr_ptr => CS%ps(:,:,:)
   call query_vardesc(CS%tr_desc, name=var_name, caller="register_pseudo_salt_tracer")
   ! Register the tracer for horizontal advection, diffusion, and restarts.
+  if (GV%Boussinesq) then
+    conv2salt = GV%H_to_m ! Could change to GV%H_to_kg_m2 * 0.001?
+  else
+    conv2salt = GV%H_to_kg_m2
+  endif
   call register_tracer(tr_ptr, tr_Reg, param_file, HI, GV, name="pseudo_salt", &
                        longname="Pseudo salt passive tracer", units="psu", &
                        registry_diags=.true., restart_CS=restart_CS, &
+                       flux_scale=conv2salt, convergence_units='kg m-2 s-1', &
+                       convergence_scale=0.001*GV%H_to_kg_m2, &
                        mandatory=.not.CS%pseudo_salt_may_reinit, Tr_out=CS%tr_ptr)

   CS%tr_Reg => tr_Reg

I'm happy to include the above diffs (and the additional flux_units argument) in my branch or in a separate PR (either here or to dev/ncar) if this is indeed a bug rather than a feature. If there are edge-cases not accounted for in my fix, I can address those as well.

[Hallberg-NOAA]

The proposed changes look to me like a good idea. There is one minor simplification, though, that could be made, if we note that the variable GV%H_to_mks takes the two expressions in the proposed new variable conv2salt, which would let us avoid the need to have Boussinesq or non-Boussenesq options in this part of the code.