[MITgcm-support] KPP scheme and background viscosities

Tue Apr 20 15:13:01 EDT 2010

Hi Jody,

Thanks for your reply!

I have done extensive sensitivity runs to see how the results change with
various mixing schemes.  I have used both temperature contours and
statistical metrics to assess the MITgcm skill through modeled and observed
temperature comparisons.  I have an unpublished paper that I could send if
you are interested.

Interestingly, changing the horizontal viscosity from 10^-5 to 1 m^2/s has
no effect on the results. \

BTW, I am just able to resolve basin-scale internal waves but not solitary
waves with 400x400 m grid spacing. I did the simulations in hydrostatic
mode. To resolve solitary waves I need to have 40x40 m grid spacing.  I am
outputting viscosities and diffusivities to be able to find an answer!

Cheers,

Abbas

On Mon, Apr 19, 2010 at 7:19 PM, Jody Klymak <jklymak at uvic.ca> wrote:

> 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<http://dx.doi.org/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
>> _______________________________________________
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>>
>>
>>  --
>> Jody Klymak
>> http://web.uvic.ca/~jklymak/ <http://web.uvic.ca/%7Ejklymak/>
>>
>>
>>
>>
>>
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>>
>>
>
>
> --
> Abbas Dorostkar, M.Sc (Eng.)
> PhD Student
> Room 444, Ellis Hall
> Dept. of Civil Engineering
> Queen's University
> Kingston, ON, CANADA K7L 3N6
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>
>  --
> Jody Klymak
> http://web.uvic.ca/~jklymak/ <http://web.uvic.ca/%7Ejklymak/>
>
>
>
>
>
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>

-- 
Abbas Dorostkar, M.Sc (Eng.)
PhD Student
Room 444, Ellis Hall
Dept. of Civil Engineering
Queen's University
Kingston, ON, CANADA K7L 3N6
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