28.2.9 restorst

Ocean tracers are driven directly by surface tracer fluxes. In some cases, specification of surface tracer flux may lead to surface tracers drifting far away from observed data. This may be due to errors in the data or in paramaterizations not capturing the proper physics. When this happens, it is desirable to restrict how closely sea surface tracers remain to prescribed data by use of a restoring term. The prescribed data typically comes from options simple_sbc,  time_mean_sbc_data, or  time_varying_sbc_data as described above. Enabeling option restorst provides the restoring by means of Newtonian damping.

The damping is actually converted to a sea surface tracer flux and enters the tracer equation as a top boundary condition for vertical diffusion. The amount of damping is defined by a time scale dampts in days which is input through namelist ( Refer to Section 14.4). Note that the damping time scale may by set differently for each tracer.

A Newtonian damping term applied to the first vertical level may be converted into a surface tracer flux by vertically summing as in

$$\sum_{k=1}^{km}(\kappa t_z)_z \Delta z = -\sum_{k=1}^{km}\del... ...,k}\cdot\frac{1}{dampts_n \cdot 86400.0}(t - t^\star) \Delta z$$ (28.22)

where t is temperature and $\delta^{1,k}$ is the Kronecker delta ( $\delta^{1,1}=1$ and $\delta^{1,k>1}=0$). The left hand side of Equation (28.22) equates to stf - bmf where stf is the surface tracer flux and bmf is the bottom tracer flux (which is taken as zero). Applying the indexing terminology of MOM, the equation becomes

$$stf_{i,j,n} = -\frac{dzt_{k=1}}{dampts_n \cdot 86400.0}(t_{i,1,j,n,\tau-1} - t^\star_{i,j,n,time})$$ (28.23)

where $t^\star_{i,j,n,time}$ represents prescribed surface data for tracer n and dampts_n is the damping time scale (Note that ``stf'' entered the tracer equation as a newtonian damping term in MOM 1 so the factor dzt<sub>k=1</sub> was not there.). The effective damping coefficient is $\rho_\circ c_p \cdot dzt_{k=1}/(dampts_n\cdot 86400.0)$and is printed out when the model executes. The damping coefficient is printed in units of ``Watts/m²/deg C'' for n=1 and ``Kg/m<sup>2</sup>/sec/model salinity unit'' for n=2. Recall that a ``model salinity unit'' is (ppt-35)/1000 where ``ppt'' is ``parts per thousand'' or ``grams of salt per kilogram of water''. The ``ppt'' unit of salinity has been largely replaced by ``practical salinity units'' or ``psu'' in the literature which is based on conductivity measurements instead of measuring ``grams of salt per kilogram of water''. For n>2, the ``model salinity unit'' is replaced by ``tracer unit''. It should be apparent that two models with differing dzt_k=1 require differing values of dampts_n to insure both models are getting the same tracer flux across the top layer.