[MITgcm-support] OBC problem: spurious boundary jets with C-D coupling

[Martin Losch]

Hi Mark,

the CD scheme does not work with OBCS. I am sorry that you had to  
find this out the hard way. I don't even think that this is  
documented anywhere, except for some email in the support-archives.  
Prescribing values for the D-grid velocities along open boundaries is  
simply not implemented although it should not be so difficult: in  
obcs_apply_uv.F one could easily set the uVelD and vVelD to  
appropriate values, that may already be enough. One would have to  
sort out how to average/extrapolate consistently.

For some reason, the CD-scheme is not seem to be very popular any  
more (although it does effectively reduce grid scale noise and I use  
it myself). One of the reasons may be that the couple constant tauCD  
is a tunable parameter whose value is not pre-determined. If   
tauCD=deltaT(mom), then the CD-scheme does not have any effect (then  
rCD = 1-deltaTmom/tauCD = 0 and uVelD=uVel, see pkg/cd_code/ 
cd_code_scheme.F and model/src/ini_parms.F). tauCD should be  
something larger than deltaT(mom), the large tauCD, the stronger the  
coupling between C and D grid velocities and the smoother and less  
energetic are the results.

What can you do to reduce the grid scale noise: viscosity, in  
particular bi-harmonic viscosity, and use StaggerTimeStep=.true.  
(that was suggested to me once, but I haven't really seen it to have  
too much effect). Maybe Jean-Michel has a better suggestion?

For the linear free surface the boundary values for eta are always  
zero. If you want to change that, you'll have to use the nonlinear  
free surface (turn on by enabling the flag in CPP_OPTIONS.h and  
setting some parameters in data, see e.g., global_ocean.cs32x15), but  
that means also prescribing the free surface along the boundaries.

Martin
PS. Maybe I'll have a look at CD-scheme+OBCS in the future, as it  
bugs me, too. Unless there is a principle problem that I have  
overlooked, it shouldn't be too difficult. (but feel free to try it  
out yourself and contribute your code  (o:)

On Sep 27, 2006, at 6:28 AM, Mark Hadfield wrote:

> I am attempting to apply MITgcm to limited-area ocean simulations  
> around New Zealand. (I am also collaborating with Jill Schwarz in  
> her Ross Sea work.) My first attempt, loosely based on the lab_sea  
> case, was spectacularly unsuccessful. Within a few hours of  
> starting from rest, narrow jets developed along the open  
> boundaries. Within a day the velocities had developed to several m/ 
> s, at which point the model crashed with large Eta values where the  
> jets impinged on topography.
>
> To cut a long story short, I have reproduced this problem in a  
> minimal test case (below) and established that it occurs when the  
> CD scheme is enabled (useCDscheme=.true.) AND the CD scheme  
> coupling time scale, tauCD, is set to a value other than its  
> default (which is equal to the momentum time step, deltaTMom). My  
> first NZ region simulation is now chugging along with the CD scheme  
> disabled and giving sensible results. (Unfortunately, it is  
> developing some grid-scale noise in the velocity field; I am  
> controlling that with viscosity.)
>
> By the way, does leaving tauCD at its default actually have the  
> effect of disabling the CD coupling? The results I have seen  
> suggest this is the case, but mitgcm.org won't let me look at the  
> documentation today to confirm.
>
> For now, it seems that the CD scheme and OBCs are incompatible and  
> the simplest workaround is to disable the CD scheme. I don't know  
> how much of a limitation that will be for me. As others have  
> noticed on this list, the model leaves the outermost Eta values at  
> zero. I presume the CD scheme is accessing those zero values,  
> whereas the ordinary C-grid scheme is not. Might this be solved  
> simply with a zero-gradient boundary condition on Eta?
>
> In case anyone's interested, the files for the test case are in
> ftp://ftp.niwa.co.nz/incoming/hadfieldm/dmf/work/channel/mitgcm/run01/
> The domain is a 600 km x 600 km wide and 2000 m deep, with open  
> boundaries on all 4 sides. Coriolis parameter f is set to -1.0E-4  
> (this is the southern hemisphere) and beta is zero. Model grid  
> dimensions are 40 x 40 x 1. At t = 0, the interior is at rest and a  
> zonal jet is imposed at the western and eastern boundaries. The jet  
> is in geostrophic balance with a tanh-shaped step in sea surface  
> height, eta:
> eta = Z tanh(y/D)
> where y is N-S position relative to the centre of the channel, D is  
> the transition zone half-width (60 km) and Z is 0.2 m. So the jet  
> velocity is
> ubar = -(g Z)/(f D cosh(y/D)^2)
> where g is gravitational acceleration and f is Coriolis parameter.  
> Peak velocity is about 0.32 m/s. (Note that eta is given here for  
> completeness but eta data are not supplied to the model.)
>
> To simplify things, we solve for the velocity field only, without  
> advection or diffusion:
> saltStepping = .FALSE.
> tempStepping = .FALSE.
> momStepping = .TRUE.
> momAdvection = .FALSE.
> momViscosity = .FALSE.
> In the first run...
> ftp://ftp.niwa.co.nz/incoming/hadfieldm/dmf/work/channel/mitgcm/ 
> run01/runa/
> the CD scheme is enabled and tauCD is left at its default. The  
> velocity field adjusts in less than one day to a steady state: the  
> jet spreads more or less radially from its source at the western  
> boundary, occupies the whole width of the channel in the centre,  
> and converges (is confluent?) to its sink on the eastern boundary.  
> The expected symmetry is maintained/ The difference in Eta across  
> the jet is what you would expect from geostrophy, except that Eta  
> at the exterior points stays zero.
>
> In the second run...
> ftp://ftp.niwa.co.nz/incoming/hadfieldm/dmf/work/channel/mitgcm/ 
> run01/runb/
> the tauCD is set to twice deltaTmom. Here westward jets develop  
> next to the northern and southern boundaries. These jets continue  
> to develop over the duration of the simulation (10 d) and by the  
> end the velocity field is dominated by a pair of gyres, with  
> westward velocities of ~ 2 m/s at the boundaries and an eastward  
> return flow of ~ 1 m/s in the centre.
>
>
> -- Mark Hadfield "Kei puwaha te tai nei, Hoea tahi tatou"  
> m.hadfield at niwa.co.nz National Institute for Water and Atmospheric  
> Research (NIWA)
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