A simple question about the t3dmix2_s

[seashellingolds]

Hi All

I happened to look at the code in the t3dmix2_s.h and met something I couldnt understand.

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cff=0.25_r8*(diff3d_r(i,j,k)+diff3d_r(i-1,j,k))*pmon_u(i,j)
FX(i,j)=cff*(Hz(i,j,k)+Hz(i-1,j,k))*(t(i,j,k,nrhs,itrc)-t(i-1,j,k,nrhs,itrc))

similar for FE

cff=dt(ng)*pm(i,j)*pn(i,j)
cff1=cff*FX(i+1,j)-FX(i,j))
cff2=cff*FE(i,j+1)-FE(i,j))
cff3=cff1+cff2
t(i,j,k,nnew,itrc)=t(i,j,k,nnew,itrc)+cff3

What I wanted to ask is why cff3 in the last line doesnt need to be divided by Hz? (FX and FE have been multiplied by Hz). Do I miss anything here?

Thanks a lot

[shchepet]

Because at this moment t(i,j,k,nnew,itrc) has the meaning of tracer concentration
multiplied by Hz(i,j,k). Since Hz changes because of free surface evolution, tracers
are multiplied by Hz at time step "n" before the barotropic time stepping begins for
the current 3D time step, then all fluxes are added in to the product, and finally the
outcome is divided by Hz, which happens implicitly during the tri-diagonal solver
associated with vertical diffusion.

This algorithm allows to avoid extra storage associated with Hz because only one
time frame is needed for it.

[wilkin]

Immediately above the code segment you quote there is the comment:

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!
! Time-step harmonic, S-surfaces diffusion term (m Tunits).
!

At this place in the code the tracer array is in flux units of layer thickness (Hz, in m) times Tracer units (Tunits). The return to simple tracer units occurs later.

See also https://www.myroms.org/wiki/index.php/Horizontal_Mixing