39.7.2.3 Vertical diffusion

The contribution from vertical diffusion is given by

$$(\rho_{\theta})_{i,k,j} \, (diffvert_{\theta})_{i,k,j} + (\rho_{s})_{i,k,j} \, (diffvert_{s})_{i,k,j},$$ diffvert_i,k,j = (39.99)

where the contribution from each tracer takes the form

$$(diffvert_{\theta})_{i,k,j} dz\_tr_{i,k,j} \, \biggl( diff\_fb_{i,k-1,j} - diff\_fb_{i,k,j} \biggr),$$ = (39.100)

with

$$diff\_fb_{i,k,j} diff\_cbt_{i,k,j} \biggl( t_{i,k,j,1} - t_{i,k+1,j,1} \biggr) \, dz\_wtr_{i,k,j}.$$ = (39.101)

Note that if the double-diffusive aspect of KPP vertical mixing (Section 32.2.3) is enabled, then the vertical diffusion coefficient $diff\_cbt_{i,k,j}$ is generally different for temperature and salinity. As inside of tracer.F, the surface and bottom tracer fluxes are incorporated into the vertical tracer flux at the top and bottom model levels, respectively. In the integration of the tracer equation in tracer.F, vertical diffusion is usually computed implicitly in time. For the purposes of this diagnostic, however, it will be evaluated explicitly.