[MITgcm-support] KPP scheme and background viscosities

Mon Apr 19 19:19:32 EDT 2010

Hi Abbas,

On Apr 19, 2010, at  15:38 PM, Abbas Dorostkar wrote:

> Sorry, my email must be a bit confusing!
>
> I set the explicit horizontal diffusivity to a very small value of  
> 10^-7 m^2 s^{-1} as the 3-DST advection scheme is unconditionally  
> stable and introduces numerical diffusivity where needed to  
> eliminate grid-scale noise.
>
Sorry, I have a viscosity/diffusivity dyslexia: I wondered why you  
have the horizontal viscosity set to 1 m^2/s. That seems very high for  
the resolutions you are using and will lead to a lot of unintended  
diapycnal viscosity.

> I mentioned that the model is not sensitive to the background  
> vertical viscosity in the range of 10^-7 to10^-4 m^2 s^{-1} while  
> the background vertical diffusivity is 10^-7 m^2 s^{-1}. However,  
> increasing the background vertical viscosity to 10^-3 m^2 s^{-1}  
> gives me a better agreement. From literature, researchers usually  
> use the constant value of 10^-3 m^2 s^{-1} for vertical viscosity  
> when the KPP is not used. I am not sure if there is any relation here.
>
There is certainly nothing magical or "correct" about 10^-3 m^2/s.  
There are some situations and geometries where it can be expected to  
work well, and others where it won't.  I think the choice of  
viscosities and diffusivities depends on what you think those numbers  
are supposed to represent.  In the open ocean the turbulent viscosity  
and diffusivities are approximately equal at 10^-5 m^2/s. This  
represents turbulence due to breaking of the ambient broadband  
internal wavefield, and would not typically be resolved in a numerical  
model (though your high resolution might mean you *do* resolve all the  
internal waves)  I'd be very surprised if a lake had a higher  
"background" viscosity.  Anything much above that is usually due to  
large breaking waves, boundary layer effects or shear instabilities.  
If these are explicitly represented in your model, great!  If not, you  
need to include higher turbulence where you think they will exist.

Again, with your high resolution, KPP might be appropriate for these  
turbulent regions, since it puts high viscosity where the velocity  
shears are high, and you may resolve all the important shears in your  
flow.  However, KPP is also meant for models that do not explicitly  
resolve unstable water columns, and may asymptote to unreasonable  
turbulence values if you have convection, a breaking wave, or a  
resolved K-H billow.

So, in short, I'd have a background diffusivity and viscosity that is  
as low as possible, yet still represents any unresolved turbulent  
structures you think you may have. 10^-3 m^2/s seems very high by that  
criteria. I would add on top of this a scheme that did a good job of  
getting the turbulence correct where there are resolved turbulent  
structures.

For you to see no change until you make the background 10^-3 m^2/s,  
indicates to me that KPP is never turning on higher than 10^-3.  Have  
you output the viscosities and diffusivities used by the model?

> On the other hand, increasing the background vertical diffusivity  
> from 10^-7 to 10^-4 m^2 s^{-1} while the background vertical  
> viscosity is 10^-3 m^2 s^{-1} gives me a poorer not better agreement.
>
It might be helpful to know what you are trying to get to "agree"? I'm  
having some trouble getting my head around you knowing the initial and  
boundary conditions on a lake well enough to get "agreement" with an  
observed internal wavefield so well that the mixing scheme is the most  
important factor.

Cheers,  Jody

> Please let me know what you think
>
> Thanks
>
> Abbas
>
>
>
>
>
>
> On Mon, Apr 19, 2010 at 4:38 PM, Jody Klymak <jklymak at uvic.ca> wrote:
> Hi Abbas,
>
> I'm surprised that increasing the background diffusivity would give  
> you a better agreement.  It means either a) that this is simply  
> fortuitous, or b) that KPP is not ramping up the turbulence enough.
>
> On Apr 19, 2010, at  8:34 AM, Abbas Dorostkar wrote:
>
>> I have simulated basin-scale internal waves in a lake using the  
>> hydrostatic version of MITgcm on a 400x400 horizontal grid spacing.  
>> The smallest vertical grid spacing is 0.5 m. A staggered baroclinic  
>> time-stepping is used for the tracer equation. The tracer advection  
>> scheme is a 3-DST so I set the horizontal eddy diffusivity to 1E-7.  
>> The horizontal eddy viscosity is constant with the value of 1. The  
>> vertical eddy viscosities and diffusivities are computed by the KPP  
>> scheme.
>>
>
> Why is your horizontal diffusivity so high?  For a high-resolution  
> run like this you should be able to have much smaller horizontal  
> mixing, i.e. 10^-3 or 10^-4 m^2 s^{-1}. I'm assuming you have  
> solitary waves and the like, and a large horizontal viscosity acting  
> on those is going to have a very high diapycnal viscosity.
>
>> The model is not sensitive to the background vertical viscosity in  
>> the range of 1E-7 to 1E-4. However, the background viscosity of  
>> 1E-3 reduces the root-mean-square error between the model and field  
>> data by 20% over the simulation which uses a value of 1E-5.  Also,  
>> the model also does not show sensitivity to the background vertical  
>> diffusivity ranging 1E-7 to 1E-5.  However, using higher values  
>> such as 1E-4 gives very poor error statistics.  Does anybody have  
>> in any inputs?
>>
>
> So higher diffusivity or lower viscosity give poor results?  That's  
> confusing.
>
>> The model gets unstable if I use background vertical viscosity  
>> larger than 1E-3 unless I use smaller time step. I was wondering if  
>> MITgcm has a viscous limitation controlled by the vertical eddy  
>> viscosity (ViscAz) such that (deltaT)*(ViscAz)/(deltaZ)**2 < 1.
>>
>
> Its pretty hard to understand why you would need such a high  
> background turbulent viscosity.  I don't think there is a viscous  
> limitation in the model anywhere.
>
> I admit to being somewhat ignorant about exactly what KPP does; Have  
> you tried running this with KPP turned off?
>
> You may want to check out a paper we recently published in ocean  
> modelling doi:10.1016/j.ocemod.2010.02.005 where we use the Thorpe  
> scale to set the vertical viscosity and diffusivity in a convective  
> overturn.  This assumes you resolve turbulent overturns, which at  
> 0.5 m, I suspect you might.  Not sure if it is useful to your  
> situation in particular.
>
> Cheers,  Jody
>
>
>
>
>>
>> Thanks in advance for your ideas
>>
>> Abbas
>>
>> _______________________________________________
>> MITgcm-support mailing list
>> MITgcm-support at mitgcm.org
>> http://mitgcm.org/mailman/listinfo/mitgcm-support
>
> --
> Jody Klymak
> http://web.uvic.ca/~jklymak/
>
>
>
>
>
> _______________________________________________
> MITgcm-support mailing list
> MITgcm-support at mitgcm.org
> http://mitgcm.org/mailman/listinfo/mitgcm-support
>
>
>
>
> -- 
> Abbas Dorostkar, M.Sc (Eng.)
> PhD Student
> Room 444, Ellis Hall
> Dept. of Civil Engineering
> Queen's University
> Kingston, ON, CANADA K7L 3N6
> _______________________________________________
> MITgcm-support mailing list
> MITgcm-support at mitgcm.org
> http://mitgcm.org/mailman/listinfo/mitgcm-support

--
Jody Klymak
http://web.uvic.ca/~jklymak/

-------------- next part --------------
An HTML attachment was scrubbed...
URL: <http://mitgcm.org/pipermail/mitgcm-support/attachments/20100419/e1aa15ae/attachment.htm>