Enforce consistency of LES_driven_SCM

[ilopezgp]

The current definition of the LES_driven_SCM,

• [x] 1. ~~Initializes the SCM profiles as the average over the last 6 hours in LES. [Cases.jl]~~ Initializes the SCM profiles as the 1-hour LES mean around t_end - 6 hours.
• [x] 2. Applies the same horizontal and vertical eddy advection tendency as LES, since these are constant in time in LES as well. [Cases.jl]
• [x] 3. Applies a relaxation to the GCM momentum profile, consistent with the LES simulations (which also relaxes to the GCM profiles). This means that this is ~~the only~~ a time-dependent tendency ~~that we have~~. [Cases.jl]
• [x] 4. ~~Instead of using a relaxation term for temperature and q_t, we instead apply the last 6-hour average relaxation tendency from LES. This is no longer a relaxation term, because it induces a tendency based on the mean difference between the GCM and the LES, none of which are the SCM. [Cases.jl; Turbulence_PrognosticTKE.jl]~~ Applies a relaxation term for thetali and q_t to the GCM profiles, consistent with the LES simulations. This is a time-dependent term. In steady-state, it is the term that balances the vertical gradient of vertical SGS momentum flux. It is important that we relax to the GCM values so that this balance can be the same in LES and in the SCM.
• [ ] 5. Applies the average radiative heating rates over the last 6 hours of LES to the SCM. [Radiation.jl]. We'll eventually want to at least have the option to use interactive radiation from RRTMG.
• [ ] 6. Applies the average surface conditions over the last 6 hours of LES to the SCM. [Cases.jl], but we'll eventually want to at least have the option to have fixed SST with interactive fluxes.
• [ ] 7. The simulations are then run for 6 hours. This is fine only for statistical steady-state solutions such as the ones from Shen et al (2022). If the boundary layer is growing, for example, then we cannot really compare the simulations. In addition, the 6 hour timescale is adequate for cases where radiative and surface fluxes are constant. If we make 5. or 6. interactive, we may have to extend the integration time to allow the SCM to equilibrate.

~~I think most of these points are OK. However, I think 3. and 4. are inconsistent, and I think we should correct 4. to be similar to 3., using the relaxation timescale in equation (9) of Shen et al.~~ For calibration, point 7 is very important. We can only do this for simulations that are in statistical steady-state.

[yairchn]

I think you are right about point 4. we should fix this. About 7 - I think they are all more or less run to steady state - no?

[ilopezgp]

I think the forcing is steady-state, but that need not imply that the state is. For example, if we have any simulation without clouds, surface heating cannot be compensated by cloud-top radiative cooling and the boundary layer would grow (similar to Soares, Nieuwstadt). If you compare different times between LES and SCM, you will get different results and bias your calibration process!

[szy21]

Agreed we should fix 4.

For 7, yes right now all the GCM driven LES cases are run to the steady state. I think it depends on what we want to use for calibration at the end. I assume we would want to be able to calibrate all kinds of cases, so it would be good to not assume a steady state.

[ilopezgp]

I agree with @szy21 in that assuming steady-state can be detrimental in the future. A small fix that could go a long way is the following,

• Initialize the SCM profiles with the LES profiles at t_end - 6h (maybe we can average from t_end - 6.15 h to t_end - 5.45 h to smooth the profiles). -> Update: We are doing this now, from t_end - 6.5 h to t_end - 5.5 h.
• Run the simulations only for 6 hours in order to calibrate using the last ~3 hours from both SCM and LES. Three hours of spin up should be more than enough for an SCM in my opinion, @costachris can confirm for these particular cases.

This setup is not perfect, but since we start from the same place and we are inputting the same energy (we input the average surface and radiative fluxes from LES), we should have very close statistics over 3 hours from LES and SCM. And of course, fix 4. This should work relatively well for non-stationary systems if there aren't very strong nonlinear interactions going on with the radiation. Even if there are, using the time-dependent radiative fluxes would not be better since those are coming from the LES cloud. I would say TBD for when we have RRTMG in TC.jl.

We can also test nudging and forcing with LES time-dependent data instead of the 6h mean and see what works best. This would affect the surface fluxes, radiative fluxes, and the profiles that we nudge to (which would be a function of time).

[costachris]

So it sounds like the immediate priorities are to a) Use an average 30 mins around t_end - 6 to initialize the SCM + run for 6 hours and b) fix 4.

And I agree 3 hours should be enough for spin-up based on what I've seen .

[ilopezgp]

After our meeting with Tapio: The plan forward is approved, pending revisiting the surface fluxes in the future (which Tapio would prefer to be fixed SST with interactive fluxes), and using RRTMG interactively.

[yairchn]

After our meeting with Tapio: The plan forward is approved, pending revisiting the surface fluxes in the future (which Tapio would prefer to be fixed SST with interactive fluxes), and using RRTMG interactively.

we could use the current coded 'SurfaceMoninObukhov' function (currently unused as GABLS is using its dry version) and have it ready before we use SurfaceFluxes.jl. I am happy to do that we myself

[costachris]

The SCM now uses a relaxation to LES profiles for theta and qt in the same manner as Zhaoyi's paper. Initial conditions for the SCM are the 1-hour LES mean around t_end - 6 hours, and the SCM simulation is run for 6 hours. Addressing points 1 & 4. #511

[costachris]

#1298 nudges thetali, qt, U, and V to the GCM profile (initial LES profile).

Edit (Ignacio): Before, we were nudging to LES profiles. This change is important because the steady-state horizontal momentum equation requires a balance between the vertical gradient of SGS flux and the nudging tendency. Since the nudging tendency in LES is non-zero (i.e., the GCM and LES profiles of horizontal velocity do not match in the lower part of the boundary layer), we need the same non-zero term to attain the same balance as the LES (if our model were to be perfect).