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Namelist option: eddy viscosity for diffusion

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Hi everyone,

I found a ppt "Preliminary results from variable-resolution mesh tests", which discuss about the problem of existence of high-wavenumber modes for variable resolution mesh. If I got it correctly, in core_atmosphere, the default filtering technique is using "config_horiz_mixing = 2d_smagorinsky", in which the diffusion term explicitly added to the equations of motion using the 2nd-order diffusion(Kh). The 4th-order hyperdiffusion(K4) can be adjusted by "config_visc4_2dsmag".

However, if I want to adjust manually by choosing "config_horiz_mixing = 2d_fixed", in what way should I adjust the two options, namely, "config_h_mom_eddy_visc2" and "config_h_mom_eddy_visc4"? It will be great if anyone can tell me more about these two values, such as how they make impact on the simulations, their order of magnitude.

I also discovered that "2d_smagorinsky" option is available for core_atmosphere but not the others, for instance, the core for shallow water wave(core_sw).

Any comments will be appreciated, thanks~
With the “2d_fixed” option, the horizontal and vertical eddy viscosities are set from the namelist.atmosphere parameters config_h_mom_eddy_visc2, config_v_mom_eddy_visc2, config_h_theta_eddy_visc2, and config_v_theta_eddy_visc2. These eddy viscosities are in units meters^2/second, “mom” in the name corresponds to the eddy viscosities used in u and w momentum equations, and ‘theta” referes to that used in the theta_m equation, all in the dynamics. The “_h” and “_v” referes to horizontal eddy mixing and vertical eddy mixing, respectively. There are also a similar set of parameters for 4th-order horizontal mixing using hyperviscosities with a similar naming convection. The hyperviscosity has units meters^4/second. We do not have 4th-order vertical mixing implemented in MPAS atmosphere.

In contrast. 2d_Smagorinsky formulation sets the 2nd-order eddy viscosities such that they are proportional to the horizontal deformation. See equation (17) and the associated discussion in

Skamarock, W. C, J. B. Klemp, M. G. Duda, L. Fowler, S.-H. Park, and T. D. Ringler, 2012: A Multi-scale Nonhydrostatic Atmospheric Model Using Centroidal Voronoi Tesselations and C-Grid Staggering. Mon. Wea. Rev., 140, 30903105. doi:10.1175/MWR-D-11-00215.1

The length scale used in the Smagorinsky 2nd-order mixing eddy viscosity formulation is taken from the namelist.atmosphere parameter “config_len_disp” and should be chosen equal to the nominal cell-center separation distance (i.e. the nominal dx) in meters. The 4th-order hyperviscosity is also applied when the Smagorinsky scheme is chosen and it uses a hypervisocity set by namelist.atmosphere parameters: hyperviscosity = config_visc4_2dsmag*config_len_disp^3. As before, the units of the hyperviscosity are meters^4/second. “config_visc4_2dsmag” gives hyperviscosities that are smaller than typically used in climate models (by a factor of 5 to 10 or more). In addition, there is also a namelist.atmosphere parameter “config_del4u_div_factor” that multiplies the hyperviscosity when applied to the horizontal momentum equation. The default value is 10, and results in values closer to what is typically used in other climate and weather models. Note that the namelist parameter “config_del4u_div_factor” does not appear in the default namelist - you will have to add it if you want to change the value from the default.

We use the Smagorinsky formulation in real-data applications in MPAS-atmosphere because we do not want a constant 2nd-order mixing active everywhere. 2nd-order mixing is not very scale selective, and the Smagorinsky formulation only turns it on where horizontal deformations are large, i.e. where one might expect scale collapse to be occuring and hence where some filtering is needed. It is not a perfect turbulence model (and it has no real theoretical support at the scales we use it at), hence we augment it with the 4th-order hyper-diffusion (which is much more scale-selective).

If one wants to manually choose the eddy viscosities and hyperviscosities by choosing to use the “2d_fixed” configuration, then one will have a constant 2nd-order mixing over the entire domain. I cannot recommend this because the 2nd-order mixing is not sufficiently scale selective. Eddy viscosity values needed to keep noise levels at acceptable levels tend to damp the resolved modes too much in my view. Also note that that vertical 2nd-order mixing is part of the PBL scheme, so the vertical eddy viscosities should be zero if this option is used in a real-data application using a PBL scheme.

Finally, the cores in MPAS are developed independently, and options in one core are not necessarily implemented in another. The decision to implement and support an option for a particular core is up the the primary developers of that core. The shallow-water solver has not seen any significant active development since the early days of the MPAS project, and many of the options in the atmospheric solver do not appear in the shallow water core.