1. Numerical Mixing in the COSIMA Models
Ryan Holmes
Jan Zika, Matthew England, Steve Griffies, Kial Stewart, Andy Hogg and others

2. Diathermal Heat Transport in MOM5
Wm-2
MOM5 Eulerian heat budget diagnostics (each x,y,z,t):
Integrate the heat budget
over temperature layers
Walin 1982
Watts

3. Example: MOM025-SIS
1.6PW
Surface forcing Increases temperature contrasts
Downgradient heat transfer from Mixing

4. Example: MOM025-SIS Seasonality:
Numerical mixing is quantified by the heat flux that it drives between different temperature classes
Provides an estimate resolved in temperature and time
Does not require targeted simulations, or sorting
Can be extended to a horizontally- resolved (x,y,T,t) estimate of numerical mixing using lateral volume transports
What follows: Comparisons across COSIMA model suite
- 1º, ¼º and 1/10º,
- GFDL50/KDS50/75/135
- GM/Redi on/off
- background vertical diffusivity
Seasonality:

5. Horizontal Resolution
Surface Forcing
Note not clean comparison:
MOM025/MOM01 – CORE-NYF
ACCESS-OM2 – JRA55 RYF8585
MOM01 = KDS75. Others = GFDL50
Tendency
Redi Mixing
1/4º models have largest numerical mixing
Numerical mixing reduced in MOM01
Significantly reduced in 1-degree model
Vertical Mixing
Numerical Mixing

6. Vertical Resolution Surface Forcing Tendency Redi Mixing
ACCESS-OM2 1-degree RYF9091
Tendency
Both vertical and numerical reduce with vertical resolution.
Changes focused at warmer temperatures
Changes reflected in reduced total transport
Redi Mixing
Vertical Mixing
Numerical Mixing

7. Neutral Physics Surface Forcing Tendency Redi Mixing Vertical Mixing
ACCESS-OM2 1/4-degree RYF8485
Tendency
Numerical Mixing reduces at cooler temperatures when Redi turned on
However, it is not reduced to zero
Turning GM on further reduces the explicit Redi mixing and numerical mixing
Redi mixing not insignificant at high temperatures, however GM effect is.
Redi Mixing
Vertical Mixing
Numerical Mixing

8. Background Diffusion Surface Forcing Tendency Vertical Mixing
MOM025-SIS
Tendency
Vertical Mixing
Numerical mixing reduces with increased background diffusion
Changes focused at warm temperatures
Compensation is not complete -> Surface ocean structure impacted
In particular, tropical SSTs cool with more background mixing, driving a stronger air-sea heat flux
Numerical Mixing

9. Spatial Structure
Increasing Background Diffusion
No Background Diffusivity
Background Diffusivity 10-5 / 10-6 Equator
Reduced numerical mixing traced to tropics, in particular the Eastern Pacific
Large numerical heat fluxes in eddying WBC regions
Background Diffusivity 10-5 (1 year only)

10. Background Diffusion – Equatorial Temperature Biases
10-5 everywhere
MOM01 No Backgrounnd
No Background Diffusivity
In MOM025, 10-6 m2s-1 equatorial background diffusivity works best
In MOM01, reduced numerical mixing without added diffusion results in large biases

11. Summary
Diathermal framework -> nice way to quantify numerical mixing in realistic runs
MOM5 is numerically diffusive (can exceed explicit mixing)
Numerical mixing sensitive to:
Horizontal resolution
Vertical resolution (warm temperatures, tropics)
Neutral physics (cold temperatures)
Background diffusion (warm temperatures, tropics, links to TC biases)
Some questions to consider:
What are the implications of mixing numerically vs. physically?
As resolution increases, numerical mixing decreases. When do we turn on explicit mixing?
How do we balance these choices across latitude?

12. Summary

13. Spatial Structure Method
Construct budget for volume of fluid warmer than a given T within each fluid column.
1) Lateral volume fluxes, 2) diathermal water-mass transformations (diagnosed online), and 3) tendency (diagnosed from T-snapshots).
Issues:
WMTs at T-centres while lateral fluxes at T-edges.
Tendency and lateral fluxes are noisy (requires multiple years).

14. Spatial Structure at 10C

15. Spatial Structure at 10C

16. Spatial Structure at 10C

17. Suite Vertical Mixing Seasonality

18. Suite Numerical Mixing Seasonality

19. Extras: Observational Diathermal Surface Forcing
Calculation performed by Sjoerd Groeskamp using WOA13 climatological SSTs, CORE surface heat fluxes (which have a global ~4Wm-2 imbalance) and a solar penetration scheme due to Marel and Antoine (1994)

20. Extras