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

[Martin Losch]

Mark and others,

I have just included a check (obcs_check.F) in the code that makes  
the model stop with an appropriate error message if someone tries to  
use OBCS together with the CD-scheme.

Martin

On Sep 27, 2006, at 10:03 AM, Martin Losch wrote:

> 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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