Changing AKT_BAK values has no effect on model results

[tasha]

I changed AKT_BAK in ocean.in to try (one at a time) all three of the following:

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     AKT_BAK == 1.0d-6 1.0d-6                   ! m2/s
     AKT_BAK == 5.0d-6 5.0d-6                   ! m2/s
     AKT_BAK == 0.5d-6 0.5d-6                   ! m2/s

The model results for the three different runs appear to be exactly the same. In ocean_his.nc, the variable AKT_BAK correctly reflects the altered value.

Is there a reason that changes in AKT_BAK aren't reflected in the model results? Do only certain mixing schemes use these coefficients? I looked through the code and searched the ROMS website, but wasn't able to find an answer to my questions.

Thanks, Tasha

[mathieu]

AKT_BAK is the background vertical tracer advection mixing coefficient for tracers. It is thanks to it that temperature/salinity got slowly uniformized vertically.
The mixing coefficient is described by the turbulence parameterization and this is of course a difficult problem with no ideal solution. The AKT_BAK is simply given as a parameter with which one can work and a priori the default values 1.0d-6 are good.
If you think that the vertical mixing is important for tracer you can output the value with Hout(idVvis) = T. You will then see that Akt is larger than its background value and very often almost equal to it.
If you are in a mood for experience you can also try larger value like 1.0d0. No blowup should occur, at worst a vertical uniformization of tracer concentration for the wet cells having such large values. It is not surprising that such small change have small/zero influence.

[nganju]

Malcolm Scully at ODU has nicely illustrated that the "Galperin correction" in the turbulence scheme effectively sets a minimum TKE value that overrides the change in Akt_bak. Hopefully he will see this and give the detailed explanation, but I think the solution is to change TKE_min in the input file for the GLS closure.

[nganju]

I think it's "GLS_Kmin", and in gls_corstep.h the tke is set to MAX(Tke,gls_kmin)...
You can try dropping this value to 1e-9 and see if changing AKt_bak now gives different results...

[arango]

Yes, Malcolm Scully mentioned that to me too. He mentioned that Umlauf and Burchard used a value of 1.0E-9 in their original GLS model. It is in my long to-do list to check this value.

[scully_ROMS]

In the gls implementation in ROMS, the Galperin correction is used to limit the turbulent length scale so it does not exceed the Ozmidov scale. This effectively limits the dissipation rate.

In the gls implementation this is done in the following statement:

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            gls(i,j,k,nnew)=MAX(gls(i,j,k,nnew),gls_fac5*             &
     &                            tke(i,j,k,nnew)**(tke_exp4)*          &
     &                            (SQRT(MAX(0.0_r8,                     &
     &                                  buoy2(i,j,k)))+eps)**           &
     &                            (-gls_n(ng)))

[/color]

So, when the Galperin correction is imposed, gls ~ 0.228*tke*N (for k-epsilon, where the variable gls = dissipation rate). The limit on the dissipation rate is the same for k-omega and kkl (just with different coefficients above).

By definition, the eddy coefficients are AKv = cmue*tke^2*epsilon^-1 and AKt = cmue'*tke^2*epsilon^-1 (using k-epsilon notation, where cmue and cmue' are the stability parameters).

So, under the Galperin correction AKv and AKt asymptote to AKv = cmue*tke*0.0288^-1*N^-1 and AKt = cmue'*tke*0.0288^-1*N^-1, respectively.

Further, under the quasi-equilibrium Kantha and Clayson stability functions, both cmue and cmue' asymptote to constant values under the Galperin correction because alphaN becomes constant (where alphaN = N^2*tke^2*dissipation^-2). For Canuto, the stability functions are still a function of the gradient richardson number under the Galperin correction, but the result is effectively the same).

As a result, when the Galperin correction is imposed (which is most of the time in a stratified flow from my experience) the eddy coefficients become:

AKv ~ AKt ~ 0.05*tke*N^-1.

So for a given stratification (N), the minimum values of AKv and AKt are set by the minimum value of tke. In ROMS the recommended minimum tke is 7.6e-6, which will prevent the values of AKv and AKt from ever reaching the background values when they are set low (< 10^-5 depending on your stratification). For example if N~.05, then the lowest value of AKv will be ~ 7.6e-6. Under stronger stratification, the minimum viscosity/diffusivity will increase. This also causes the effective background viscosity/diffusivity to vary with stratification, which does not seem like a good thing to me.

So, in order for the model to reach low values of background viscosity/diffusivity, you must reduce tke_min below the recommended value for gls in ROMS. For instance, GOTM uses tke_min = 10^-10. When I use this value in ROMS, the model runs fine and achieves the specified background viscosity.

It should also be noted that in ROMS the recommended minimum value of tke is different for k-epsilon and gls-mellor-yamada (kkl). The recommended value for kkl is slightly lower than the k-epsilon and k-omega value. This can lead to the different closures performing differently even though it is really just the result of different effective background viscosity/diffusivity. This can actually make a significant difference when you are looking at biologically important fluxes of materials (like oxygen) across the pycnocline.

[jcwarner]

I think it is great that Malcolm and others are using this closure scheme and conducting sensitivity tests on all these "user defined parameters." When i coded this back in 2003-2004 ish ?, i provided sets of coefficients that seemed to represent values in the literature at that time. However, time moves on, people use GOTM and other models, and these values become adjusted. Recently i tried some of these lower settings for my Hudson work and there was not any appreciable difference in our results because that estuary is more energetic than the Chesp Bay.

The GLS approach is a formalism that allows users to easily test coefficients for different closure schemes in a common numerical setting. As far as i can tell, the original Umlauf_Burchard GLS paper did not specify min values. GOTM may provide a suggested set of coefficients for its use as a 1D vertical model. When i coded this in, we conducted numerous 1D vertical tests and achieved identical results as GOTM at that time. However the application of the GLS method for a full 3D model application may yield different results. If you determine a set of coefficients that seem more applicable for your particular application, then please share them out. They may work for others.

[arango]

I am planning to move some of those parameters to standard input so it is much easier to play with their values.

[jcwarner]

as far as i know, all the parameters that a user can modify are already in standard input (ie the ocean.in file).