1. Representing Diverse Scales in OLAM Advantages and Challenges of Locally-Refined Unstructured Grids Robert L. Walko Rosenstiel School of Meteorology and Physical Oceanography University of Miami, Miami, FL Presented at IPAM, UCLA, April 16, 2010 Acknowledgments: 1) Roni Avissar – Dean of Rosenstiel School 2) Pratt School of Engineering, Duke University 3) NSF, NASA, DOE 4) William R. Cotton, Roger A. Pielke, Sr.

2. Outline: 1.Background and motivation for OLAM (the Ocean-Land-Atmosphere Model) 2.Summary of OLAM dynamic core – local mesh refinement – some physics 3.Numerical experiments to examine how convection responds to variable resolution 4.What the experiments tell us – some suggestions for future research 5.Summary

3. OLAM background  OLAM is based partly on RAMS, a limited area model specializing in mesoscale and cloud scale simulations.  The original motivation for OLAM was to provide a unified global-regional modeling framework in order to avoid the disadvantages of limited area models. External GCM domain Traditional RCM domain Information flow Numerical noise at lateral boundary OLAM global lower resolution domain OLAM local high resolution region Well behaved transition region Information flow

4.  OLAM went through several versions, including overlapping polar- stereographic projections, but eventually we settled on the geodesic mesh because of its facility in local mesh refinement.

5.  OLAM works with either triangles or hexagons as the primary mesh. With hexagons, a few pentagons and heptagons are required for local mesh refinement.

6.  Physical parameterizations were adapted from RAMS, with others added later.  OLAM’s dynamic core was a new formulation, not from RAMS.

7. Mass & Momentum conserving FV dynamic core Momentum conservation (component i) Total mass conservation conservation Scalar conservation (e.g. ) Equation of State Momentum definition = potential temperature = ice-liquid potential temperature Total density

8. ,. Discretized equations: Integrate over finite volumes and apply Gauss Divergence Theorem:

9. Terrain-following coordinates OLAM uses cut (“shaved”) grid cells

11. Anomalous vertical dispersion Wind Terrain-following coordinate levels Terrain

15.  Investigate behavior of parameterized and/or resolved convection across grid scales.  We look only at accumulated surface precipitation at end of 6 hours.  Choose very simple horizontally-homogeneous forcing of environment (no topography, no land/water, no large-scale flow or disturbances).  Begin with horizontally-homogeneous, conditionally unstable atmosphere at rest.  Impose constant surface sensible heat flux (~300 W m -2 ). Numerical experiments

16. Grid number Grid cell size 1 200 km 2 100 3 50 4 25 5 12 6 6 7 3

18. Cumulus parameterization only – no microphysics

22. Average parameterized convective precipitation over each refinement zone

25. We need to ask ourselves: Do we want convective parameterization to give uniform precipitation at all scales where it is applied? Or not? Is convective parameterization performing as intended, i.e., according to its design? In particular, is it responding correctly to the host model’s ability (and tendency) to generate stronger W on finer grids? If we choose to take the “route 1” approach described by A. Arakawa, can we adjust the fractional updraft area in a way to achieve the desired result? We find that area-averaged parameterized precipitation is insensitive to grid spacing for cells larger than about 30 km, but increases (by about 50%) as cells reduce to 3 km.

26. Microphysics only – no cumulus parameterization

31. Average resolved convective precipitation over each refinement zone

33. Should the model even be allowed to produce convective-type vertical motion on 6 km, 12 km, or larger cells? Such convection is unrealistically wide, and is not well represented on the grid. Perhaps a convective parameterization should be retained at these resolutions to remove convective instability (the “route 1” approach)

34. Cumulus parameterization and microphysics together

40. Horizontally averaged combined precipitation

41. Horizontally-averaged parameterized convective precipitation

42. Obviously, in locations where convection is resolvable, we want resolved convection to prevail and parameterized convection to become inactive. This will not not happen unless parameterized convection is switched off or is somehow supressed. Can this transition be made smoothly?

43. Many more complicating factors need to be considered:  Ambient wind  Large-scale disturbances  Orographic lifting  High-CAPE convection (not generally permitted by parameterized convection) Can blending methods be made to work well for all situations?

44. Possible configuration for embedded “superparameterization” grid:  Inner cells fine enough to resolve primary updraft and rain-cooled downdraft  Overall cluster of cells wide enough to encompass mesoscale subsidence  Achieves both goals with fewer cells than uniform embedded grid

46. Motion of convection grid

48. Summary: Local mesh refinement within a single model framework enables numerical experiments that examine how a model represents parameterized and resolved convection: 1)at different scales 2)where grid scale changes OLAM has the appropriate tools for this investigation, including extensions for topographic, land/sea, and realistic large-scale forcing Both “route 1” and “route 2” approaches are being investigated.