How to output horizontal diffusion terms of Held Suarez case in CESM simpler models?

[Nuanliang]

Code version: release-cesm2.1.5-0-g7a6c5b0.
No change in the source tree.

Hi everyone,

I'm exploring some research question using CESM simpler model, specifically with dry Held Suarez configuration (Held Suarez | Community Earth System Model). Recently, I have found that the horizontal numerical diffusions of either u/v momentum or temperature might play some important role (if their equations are the only ones involving numerical diffusion in the model). I've been trying to save the horizontal diffusions of u&v momentum and temperature to the model output.

Checking the CAM history fields list (CAM History Fields), there seems to be 3 variables that are relevant to horizontal diffusions: DUH (U horizontal diffusive heating), DVH (V horizontal diffusive heating), and DTH. As I checked and plotted them out separately, the DUH is completely zero, while DVH and DTH look exactly the same. Is this DVH or DTH the horizontal diffusion of temperature?

On the other hand, what would be the right terms for horizontal diffusions in u&v momentum equations? I couldn’t find them on the list. If they are not given directly, can we save them by modifying the source code?

Since there seems to be no similar question on the forum, I suppose it's appropriate to post this question. It would be great to get some feedbacks, thanks!

 

[islas]

I think for Held-Suarez, the only diffusive tendencies that come in from physics are those due to the surface drag tendencies. I think there's not currently code in there to output these tendencies but it could be added with some source code modifications. Those would be the ptend%u and ptend%v that are output from held_suarez_1994. But are you also referring to the diffusion that would be present in the dycore e.g., at the model top? Can you advise which dycore you're using?

 

[Nuanliang]

I think for Held-Suarez, the only diffusive tendencies that come in from physics are those due to the surface drag tendencies. I think there's not currently code in there to output these tendencies but it could be added with some source code modifications. Those would be the ptend%u and ptend%v that are output from held_suarez_1994. But are you also referring to the diffusion that would be present in the dycore e.g., at the model top?

Hi Isla,

Thanks for the reply. I'm actually talking about the numerical diffusion terms, not the ones from physics. The diffusion terms that are controlled by eul_hdif_order and eul_hdif_coef these 2 parameters. My understanding is that the numerical diffusion is included at each model level, not just the model top?

Can you advise which dycore you're using?

The dycore that I'm using is the default one, the Eulerian spectral-tranform dycore.

 

[islas]

I see. Yes, the Eulerian spectral-transform dycore has del4 diffusion on each level. I think it's not trival to output this tendency. The calculation is being done in the grcalc.F90 and from the looks of things there are vorticity and divergence tendencies in spectral space from this routine. Will ask around to see if anyone knows this dycore well enough to explain how best to output these tendencies. But a simple solution to doing that does not currently exist.

 

[Nuanliang]

Got it. Thanks for the clarification. Looking forward to hearing back soon!

 

[Nuanliang]

Hi everyone,

Maybe another question related to this, I wonder if this numerical diffusivity is being applied to both horizontal momentum equations and temperature? Are there any other controlling equations that are using numerical diffusion?

 

[islas]

I received the following advice from Dave Williamson about your original question. I'm afraid it'll involve some digging in the code to relate the equations he describes from the users guide to what you're seeing in the code and then finding the right place to output the tendencies. Diffusion is being applied to vorticity, divergence, and temperature. I think you can find more details in the technical note that Dave refers to below.

Equation numbers below refer to: Collins et. al. Description of … CAM3.0, NCAR Technical Note NCAR/TN-469+STR. All the NCAR Technical Notes are available online from the NCAR library.

The δ/ζ horizontal diffusion terms are calculated in spectral space and then transformed to grid space to give equivalent u/v horizontal diffusion. There they are used to calculate the frictional heating. At that point they can be written to the history buffer (I believe that is not currently done, but I think that is all you need to do to get the tendencies.)

If you want to follow the equations, (3.23, 3.24) give the continuous equations, with (3.76, 3.77) and (3.82, 3.83) defining the diffusion terms in spectral space. The general time split approximations are in (3.88). The specific δ/ζ implicit time split equation is (3.16) with solutions (3.171, 3.173). From this, the spectral coefficients for the diffusion tendencies can be backed out (3.189, 3.190). These tendencies are transformed to grid space as is done for U and V from δ/ζ in (3.18, 3.187). These grid terms, FuH, FvH are then used to get the frictional heating, FFH, in (3.191). At that point they could be put in the history buffer. The momentum equations in grid space look like the temperature equation (3.193), i.e. ukn+1 = uk* + 2Δt FuH(uk*)