Subgrid-Scale Transport in Cloud-Resolving Models

1. Subgrid-Scale Transport in Cloud-Resolving Models Chin-Hoh Moeng NCAR Earth System Lab & CMMAP IPAM workshop (May 2010) NCAR & CMMAP are sponsored by the National Science Foundation

2. OUTLINE 1. SGS processes in climate models 2. Database (Giga-LES) and approach 3. A priori test of a two-part SGS scheme

3. governed by different equations • applied to different scales • used by different groups of researchers

4. SGS in conventional GCMs GCM scales (resolvable) shallow st/cu deep convection PBL turbulence microphysics; radiation; land-processes SGS processes---represented separately cld-scale interactions missing in most GCMs.

5. However, cloud-scale interactions are many and crucial: cloud/precip. PBL turbulence cloud/precip. land process cloud dynamics microphysics cloud dynamics mass transport cloud amount radiation ….

6. As computer power grows, global models are using finer grid: Fine-grid NWP  Global Cloud Resolving Model (GCRM)to explicitly calculate large cloud systems.

7. Fine-grid NWP or GCRM Unified GCM-CRM dynamics

8. Conventional GCM grid ~ O(100 km) CRM grid ~ several kms SGS in CRMs

9. SGS processes in CRMs:  small and thin clouds (PBL stratocumulus and fair-weather cu) transport by small conv. & turbulence cloud microphysics radiative transfer land processes …

10. Within a deep cloud system, there are: turbulent motions small, shallow clouds They transport heat, moisture,… & are crucial to cloud system development.

11. Objective: To improve representation of SGS transport in CRMs.

12. OUTLINE 1.SGS processes in climate models 2. Database (Giga-LES) and approach 3. A priori test of a two-part SGS scheme

13. Benchmark simulation: Giga-LES • Grid points: 2048 x 2048 x 256 • Domain: 204.8 km x 204.8 km x 27 km • Grid size: dx = dy = 100 m; dz = 50 m ~ 150 m • Performed by Marat Khairoutdinov • Code: SAM (Marat’s LES/CRM code) • Computer: Brookhaven’s BlueGene • Idealized GATE sounding & steady LS forcing • Time integration: 24 hrs (including spin-up) • Total 4D data ~ 5.5 TB (available to public)

14. Numerical database: Giga-LES Use a unified CRM-LES code.

15. Cloud Resolving Model (CRM) Large Eddy Simulation (LES) 100 km 10 km 1 km 100 m 10 m deep convection system PBL turb./shallow cloud anelastic dynamics (typically) Boussinesq ice microphysics warm rain SGS includes all turb. SGS just small turb eddies Unified dynamics for both scales (e.g., SAM)  Giga-LES

16. Computer-generated cloud field: A typical LES domain N  205 km (~ a GCM grid cell) from Marat Khairoutdinov

17. On the other hand…. ~ Giga-LES domain size

18. The benchmark simulation: resolves convection system, large & small convection and turbulence… To learn how small conv. & turbulence respond to deep (large) convection. … to express SGS fluxes in terms of CRM-resolved flow field.

19. typical CRM grid Spectra and co-spectrum of w and q w-spectra 1. no spectral gap near CRM grid z ~5 km z ~1 km 2. energy peak near CRM grid q-spectra z ~5 km z ~1 km wq-cospectra 3. lots of q-flux by motions below CRM grid z ~5 km z ~1 km

20. Separate scales of Giga-LES into large conv. & small conv./turbulence 10 km 1 km 100 m 100 km These are scales resolved in giga-LES. Split the Giga-LES field into: CRM-resolvable &CRM-SGS using a smooth low-pass filter.

21. FS: CRM resolvable SFS: CRM-SGS SFS(w-var) Apply a Gaussian filter with a filter width of 4 km FS SFS(q-var) FS 1. most of w-variance in SFS 2. about half of q-flx in SFS SFS (wq-cov) FS

22. Horizontal distributions of q-fluxes before & after filtering benchmark q-flux  -5000~15000 W/m2 CRM resolvable flux SFS flux -700~1500 W/m2 at z=200m

23. The SFS fluxes (Leonard term) further decompose: (Cross term) The L term represents the largest SFS eddies. (Reynolds term) Germano 1986; Leonard 1974

24. SFS-wq components retrieved from Giga-LES at z~ 5 km total SFS q-flx L-term -100 ~ 4000 W/m2 -300 ~ 20000 W/m2 C-term R-term -1000 ~ 5000 W/m2 -200 ~ 16000 W/m2 filter width=4 km

25. use Taylor series: Approximation for the L term following Leonard (1974) and Clark et al (1979)

26. It is a good approximation withno closure assumption. Correlation coefficient between the benchmark L term and the approximation, for filter widths of 4 & 10 km.

27. The two-part scheme for SGS fluxes in CRMs The Giga-LES suggests that C ~ L. are CRM resolvable variables. where

28. First part is the commonly used Smag.-Deardorff SGS model needed for energy dissipation. Second part is the L+C term, for scale interaction; it is easy to implement in CRMs.

29. OUTLINE 1.SGS processes in climate models 2. Database (Giga-LES) and approach 3. A priori test of the two-part SGS scheme

30. A prioritest of the SGS scheme: Horizontal distributions of vertical q-flux at z ~ 1.5 km from the 2-part scheme from old K-scheme from LES (“truth”) y(km) x (km) spatial correlation

31. A priori test for SFS wq deep cld layer Spatial correlation coefficients with the LES-retrieved SFS-wq Contributions to the horizontally averaged SFS-wq solid curves: filter width = 4 km dotted curves: filter width = 10 km

32. A priori test for SFS uq Spatial correlation coefficients with the LES-retrieved SFS-uq Contributions to the horizontally averaged SFS-uq

33. A priori test for SFS uw Spatial correlation coefficients with the LES-retrieved SFS-uw Contributions to the horizontally averaged SFS-uw solid curves: 4 km dotted curves: 10 km

34. SUMMARY Giga-LES is useful benchmark to study SGS for CRMs. No spectral gap exists between CRM-resolvable & SGS. Most energy & transport occur near typical CRM grid, thus largest SGS eddies are important. A prior test of the two-part SGS transport scheme shows promising results. Full test next… NCAR is sponsored by the National Science Foundation