Tracer timestep selection criteria

[minghangli-uni]

Hi all,

As highlighted in Lecture: MOM6 time stepping, the tracer advection timestep does not necessarily need to be shortened to match the horizontal grid resolution. Instead, it can capture the natural timescale of tracers, such as the diurnal cycle (~hourly resolution), regardless of the grid size. In both GFDL OM4 and the more recent GFDL OM5, the tracer timestep was set to 7200s (2 hours). Inspired by this, we did similar tests using the ACCESS-OM3 (MOM6-CICE6) 0.25deg RYF configuration, starting from initial conditions and running the model for 5 years. The results are summarised below,

Experiment details

1. Control (run0): (red line in line plots)
   • baroclinic timestep = coupling timestep = tracer timestep = 1350s
   • DIABATIC_FIRST=True
   • configuration available at: here
2. Perturbation (run1): (green line in line plots)
   • baroclinic timestep = coupling timestep = tracer timestep = 1350s
   • DIABATIC_FIRST=False
3. Perturbation (run2): (blue line in line plots)
   • baroclinic timestep = coupling timestep = 1350s
   • tracer timestep = 10800s (3 hours)
   • DIABATIC_FIRST=False

1. line plots

1.1 Global mean ocean potential temperature (thetaoga)

The DIABATIC_FIRST parameter did not significantly impact this diagnostic. However, run2 with the 3-hour tracer timestep shows a slower increase in global mean temperature compared to the control and run1.

• difference compared to the control run (red)

1.2 Global mean ocean salinity (soga)

The salinity values are consistent across all three runs, with minimal differences between them.

• difference compared to the control run (red)

2. 2D snapshots comparisons

We compared snapshots of various fields for the first month (1900-02-01) and after 5 years (1905-01-01). Note:

• The differences represent the perturbation runs subtracted from the control run, highlighting impacts of the perturbations.
• The top-left figure in each set shows the control run difference with itself, which is blank intentionally.

After 5 years, the differences between runs increase, suggesting that the tracer timestep significantly affects field evolution. While the DIABATIC_FIRST parameter had minimal impact, increasing the tracer timestep led to slower changes in global temperature and larger discrepancies in field distributions over time. We’re now curious to understand the criteria GFDL uses to evaluate if a tracer timestep is optimal.

2.1 Vertically Integrated Advective Zonal Flux of Heat T_adx_2d

• 1900-02-01
• 1905-01-01

2.2 Sea Surface Temperature (tos)

• 1900-02-01
• 1905-01-01

2.3 Potential Temperature (thetao) Depth vs Latitude (Averaged over all longitudes)

• 1900-02-01
• 1905-01-01

[minghangli-uni]

We also tested tracer timesteps shorter than 3 hours, restarting from a 15-year run instead of starting from initial conditions. The differences observed were similar to those in run2.

[minghangli-uni]

Update on snapshot and mean statistiscs for some integrated diagnotics

This update provides the snapshot and mean statistics of some integrated diagnostics, including,

• Transports (3.1 - 3.8),
• Global Ocean Meridional Heat Transport (MHT) (4.1 - 4.2),

For each diagnostic, data are collected as both end-of-month snapshots and monthly means. The snapshots capture variability at specific points in time, while the mean statistics smooth out high-frequency fluctuations, offering a more stable representation. As shown in the plots, the monthly means provide improved accuracy and clarity compared to the individual snapshots.

Additionally, we are interested in learning more about the criteria used by GFDL to determine the optimal tracer timestep. Could anyone provide insights on this?

3.1 Drake Passage Transport (snapshots at the end of each month)

3.2 Drake Passage Transport (monthly mean)

3.3 Ombai Transport (snapshots at the end of each month)

3.4 Ombai Transport (1-month mean)

3.5 Timor Transport (snapshots at the end of each month)

3.6 Timor Transport (1-month mean)

3.7 Lombok Transport (snapshots at the end of each month)

3.8 Lombok Transport (1-month mean)

4.1 Global Ocean Meridional Heat Transport (mean of all end-of-month snapshots)

4.2 Global Ocean Meridional Heat Transport (mean of all monthly means)

[theresa-morrison]

Hi Minghang, I think this is a good question and appreciate the results you’ve shared. We think about the things you laid out in your first post when choosing DT_THERM such as: resolving the diurnal cycle, the tracer advective CFL, and of course the increased computational cost of a shorter time step. It is worth keeping in mind that DT_THERM is also the frequency of regridding and remapping the vertical coordinates, so if the layers have significantly changed in a period of DT_THERM there can also be issues. We have seen some similar results to what you show here with more modest changes in DT_THERM and are looking into the impact of DT_THERM on the solution.

I have been working on and testing separating the tracer advection and DT_THERM timesteps. This is more of an issue with our higher resolution regional models, where the limiting factor may be the tracer advective CFL.

[awallcraft]

I am concerned that DT=1350 may be too long. MOM6 will optionally truncate velocities that exceed CFL, but that is a very bad thing to do routinely. You should check your output for reports of "Truncations", if this never happens then you are OK. I'm sure DT=900 is below CFL for 0.25 degree, but 1350 may be too high.

At 1/12 degree I use DT_THERM=1200, 1/3 of my coupling time, because 1800 would be exceeding the advective CFL in a few places. There is no advective CFL limit on tracer advection, because of MOM6's time scheme, but that does not mean you should exceed the usual CFL unless there is a good reason to. At 1/4 degree maximum velocities will be lower so DT_THERM = 3600 will certainly be less than CFL everywhere and 7200 might be mostly "safe" but 10800 is surely above CFL at many times and places.

[minghangli-uni]

Thanks very much @theresa-morrison and @awallcraft for your helpful responses, suggestions, and for sharing your test experiences. I’ll keep you updated on our progress, and I would appreciate it if you could also share any updates from your side.