The salinity equation

INTERFACE:

   subroutine salinity(nlev,dt,cnpar,nus,gams)

DESCRIPTION:

This subroutine computes the balance of salinity in the form

$$\dot{S} = {\cal D}_S - \frac{1}{\tau^S_R}(S-S_{obs}) \; , \quad$$ (30)

where $\dot{S}$ denotes the material derivative of the salinity $S$, and ${\cal D}_S$ is the sum of the turbulent and viscous transport terms modelled according to

$${\cal D}_S = \dfrac{\partial}{\partial {z}} \left( \left( \nu^S_t... ...S \right) \dfrac{\partial {S}}{\partial {z}} - \tilde{\Gamma}_S \right) \quad .$$ (31)

In this equation, $\nu^S_t$ and $\nu^S$ are the turbulent and molecular diffusivities of salinity, respectively, and $\tilde{\Gamma}_S$ denotes the non-local flux of salinity, see section 4. In the current version of GOTM, we set $\nu^S_t = \nu^\Theta_t$ for simplicity.

Horizontal advection is optionally included (see obs.nml) by means of prescribed horizontal gradients $\partial_xS$ and $\partial_yS$ and calculated horizontal mean velocities $U$ and $V$. Relaxation with the time scale $\tau^S_R$ towards a precribed (changing in time) profile $S_{obs}$ is possible.

Inner sources or sinks are not considered. The surface freshwater flux is given by means of the precipitation - evaporation data read in as $P-E$ through the airsea.nml namelist:

$${\cal D}_S = S (P-E), z=\zeta,$$ (32)

with $P-E$ given as a velocity (note that ${\cal D}_S$ is the flux in the direction of $z$, and thus positive for a loss of salinity) . Diffusion is numerically treated implicitly, see equations (7)-(9). The tri-diagonal matrix is solved then by a simplified Gauss elimination. Vertical advection is included, and it must be non-conservative, which is ensured by setting the local variable adv_mode=0, see section 8.5 on page .

USES:

   use meanflow,     only: avmols
   use meanflow,     only: h,u,v,w,S,avh
   use observations, only: dsdx,dsdy,s_adv
   use observations, only: w_adv_discr,w_adv_method
   use observations, only: sprof,SRelaxTau
   use airsea,       only: precip,evap
   use util,         only: Dirichlet,Neumann
   use util,         only: oneSided,zeroDivergence
 
   IMPLICIT NONE

INPUT PARAMETERS:

 
   number of vertical layers
   integer, intent(in)                 :: nlev
 
    time step (s)
   REALTYPE, intent(in)                :: dt
 
   numerical "implicitness" parameter
   REALTYPE, intent(in)                :: cnpar
 
   diffusivity of salinity (m^2/s)
   REALTYPE, intent(in)                :: nus(0:nlev)
 
   non-local salinity flux (psu m/s)
   REALTYPE, intent(in)                :: gams(0:nlev)

REVISION HISTORY:

   Original author(s): Hans Burchard & Karsten Bolding
   $Log: salinity.F90,v $
   Revision 1.12  2007-12-07 10:12:20  kb
   replaced p_e with precip and included evap
   Revision 1.11  2007-01-06 11:49:15  kbk
   namelist file extension changed .inp --> .nml
   Revision 1.10  2006-11-06 13:36:45  hb
   Option for conservative vertical advection added to adv_center
   Revision 1.9  2005-11-17 09:58:20  hb
   explicit argument for positive definite variables in diff_center()
   Revision 1.8  2005/06/27 13:44:07  kbk
   modified + removed traling blanks
   Revision 1.7  2004/08/18 11:43:10  lars
   updated documentation
   Revision 1.6  2004/01/07 12:17:47  lars
   Removed latex bug
   Revision 1.5  2003/06/13 09:27:15  hb
   Implemented freshwater fluxes
   Revision 1.4  2003/03/28 09:20:35  kbk
   added new copyright to files
   Revision 1.3  2003/03/28 08:56:56  kbk
   removed tabs
   Revision 1.2  2003/03/10 08:50:07  gotm
   Improved documentation and cleaned up code
   Revision 1.1.1.1  2001/02/12 15:55:57  gotm
   initial import into CVS