[MITgcm-support] Momentum Budget

Emily Shroyer eshroyer at whoi.edu
Fri Dec 10 08:30:20 EST 2010


Thanks for the help. I assume that the following should add up to the 
total momentum tendency:

TOTUTEND/86400=Um_Diss+Um_Advec+Um_Cori+Um_dPHdx+Um_Ext+UDIAG1

with a similar balance for the v-momentum equation. Note that UDIAG1 
accounts for the sea-surface gradient. I have also appended data, 
data.pkg, data.kpp. The only thing that should look unfamiliar is a 
package named rlx. This is based off the rbcs package but it relaxes the 
momentum to a certain state in a masked region. I have been careful to 
only look at the budget well upstream, outside of this region.

I am fairly certain that I am missing a term related to the vertical 
viscosity. This may have something to do with my set-up of KPP, but I 
did try turning it off and I was still having problems. The imbalance is 
only significant in the equation when I turn on the winds. In the 
surface cell the correction is in the opposite direction of those below. 
I think this is because I am adding in the term for momentum input from 
the wind (Um_Ext), but not the total loss to viscosity. Beneath the 
surface the correction is of the opposite sign, i.e., I am only not 
accounting for viscosity correctly. The imbalance decreases with depth, 
and is negligible at a certain point. The correction seems to be of the 
same shape and magnitude as the approximate term for the vertical 
viscosity nu_{kpp}*d2u/dz2. Its also of (roughly) the same shape as 
VISrE_Um. Any advice would be appreciated. Emily

Jean-Michel Campin wrote:
> Hi Emily,
>
> I am not sure that all the diagnostics needed to close the momentum
> budget are there (although I though we put them), and it also depend
> on the level of details you are interested in.
> There are 2 things that could be useful:
> 1) write the list of terms (translated in diagnostics output name)
>  that you expect to sum to zero in the momentum budget.
> 2) attached the main parameter files (data, data.pkg, + may be
>  few other like data.kpp if you are using kpp).
>
> Thanks,
> Jean-Michel
>
> On Thu, Dec 09, 2010 at 01:02:55PM -0500, Emily Shroyer wrote:
>   
>> Thanks Matt,
>> For some reason things still are not adding up quite right. The balance  
>> is almost perfect, until I turn on wind forcing then the sum of terms  
>> differs significantly from the total tendency.  I attached a figure of  
>> the zonal balance at one grid cell as a function of time. Winds turn on  
>> around day 12, the black line and the red dashed line would line up if I  
>> was including everything correctly. This is one reason I thought that  
>> the vertical viscosity term might be missing, i.e., maybe I am not  
>> accounting for the flux of momentum from the surface properly. The other  
>> is that if I evaluate this term (nu*d^2u/dz^2) on my own, the difference  
>> is roughly correct. I tried manipulating the VISrE_Um and VISrI_Um terms  
>> but I am not sure exactly how these are scaled, the units appear to be  
>> in m^4/s^2, so surface area alone is not going to work. I will likely  
>> just return to estimating a momentum budget from the normal output  
>> fields, a little messy and it won't balance perfectly, but at least I  
>> know what it does. Thanks again, Emily
>>
>>
>> Matthew Mazloff wrote:
>>     
>>> Hi Emily,
>>>
>>> I believe there are a few tricks to this
>>>
>>> Disclaimer -- this info may be out of date or not apply to your  
>>> specific setup....
>>>
>>>
>>> I think the tendency term is in units per day, not per second, so try 
>>> rescaling from m/s/d to m/s^2 by dividing by 86400
>>>
>>> For vector invariant momentum formulation (not sure about flux form) 
>>> Um_Advec includes coriolis
>>>
>>> I believe Um_dPHdx does not include pressure forcing from SSH  
>>> gradient, you need to add that in
>>>
>>> Note that UBotDrag and USidDrag should be in Um_Diss
>>>
>>> If you want to look at the implicit vertical viscous flux (VISrE_Um)  
>>> then I believe this has units m^3/s^2 and so needs to be rescaled by  
>>> surface area ( divide by RAW and RAS for zonal, meridionaly momentum  
>>> balance respectively) 
>>>
>>>
>>> Hope this helps -- or at least gives you some ideas...
>>>
>>> -Matt
>>>
>>>
>>>
>>> Request to developers...maybe the momentum diagnostics could be  
>>> cleaned up?
>>>
>>>
>>>
>>>
>>> On Dec 7, 2010, at 1:46 PM, Emily Shroyer wrote:
>>>
>>>       
>>>> I would like to output terms of the momentum budget using the diagnostic
>>>> package. My data.diagnostic file is set as:
>>>>
>>>> &diagnostics_list
>>>>  diag_mnc     = .TRUE.,
>>>>  frequency(1) = -43200.,
>>>>  filename(1) = 'UmomDiag',
>>>>  fields(1,1) = 'TOTUTEND','UBotDrag ','USidDrag
>>>> ','Um_Diss','Um_Advec','Um_Cori',
>>>>                'Um_dPHdx','Um_Ext','Um_AdvZ3','UDIAG1  ',
>>>>
>>>>  frequency(2) = -43200.,
>>>>  filename(2) = 'VmomDiag',
>>>>  fields(1,2) = 'TOTVTEND','VBotDrag ','VSidDrag
>>>> ','Vm_Diss','Vm_Advec','Vm_Cori',
>>>>                'Vm_dPHdy','Vm_Ext','Vm_AdvZ3','UDIAG2  ',
>>>>
>>>> &
>>>>
>>>> The terms Udiag1/2 were added to account for gradients in the sea
>>>> surface height. Unfortunately, the total tendency is not quite equal to
>>>> the sum of the other terms. I think that difference may be associated
>>>> with the implicit diffusivity term? I am using a KPP mixing scheme,
>>>> although I have also tried a MY scheme. I spent  a bit of time trying to
>>>> decide where best to output this term with a user defined diagnostic
>>>> without any result. My questions are 1) Is it likely that this is indeed
>>>> the term I am missing in the momentum budget or have a missed something
>>>> else? 3) If so, does anyone have a suggestion as to where best to output
>>>> this term with the user diagnostic?
>>>>
>>>> Thanks for any advice, Emily
>>>>
>>>> -- 
>>>> Emily Shroyer, Postdoctoral Scholar
>>>>
>>>> Woods Hole Oceanographic Institution
>>>> Clark 316A, MS #21
>>>> Woods Hole, MA 02543
>>>>
>>>> phone: 508 289 2525
>>>>
>>>>
>>>> _______________________________________________
>>>> MITgcm-support mailing list
>>>> MITgcm-support at mitgcm.org <mailto:MITgcm-support at mitgcm.org>
>>>> http://mitgcm.org/mailman/listinfo/mitgcm-support
>>>>         
>>> ------------------------------------------------------------------------
>>>
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>>>   
>>>       
>> -- 
>> Emily Shroyer, Postdoctoral Scholar
>>
>> Woods Hole Oceanographic Institution
>> Clark 316A, MS #21
>> Woods Hole, MA 02543
>>
>> phone: 508 289 2525
>>
>>     
>
>
>   
>> _______________________________________________
>> MITgcm-support mailing list
>> MITgcm-support at mitgcm.org
>> http://mitgcm.org/mailman/listinfo/mitgcm-support
>>     
>
>
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>   


-- 
Emily Shroyer, Postdoctoral Scholar

Woods Hole Oceanographic Institution
Clark 316A, MS #21
Woods Hole, MA 02543

phone: 508 289 2525

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