Convective Parameterization

1. Convective Parameterization Jack Kain and Mike Baldwin OAR/NSSL/CIMMS

2. What is Convective Parameterization? • A technique used in NWP to predict the collective effects of (many) convective clouds that may exist within a single grid element…As a function of larger-scale processes and/or conditions

3. Eta Grid Points

4. Why do NWP models need to worry about it? • Direct concern • To predict convective precipitation • Feedback to larger scales • Deep convection “overturns” the atmosphere, strongly affecting mesoscale and larger scale dynamics • Changes vertical stability • Redistributes and generates heat • Redistributes and removes moisture • Makes clouds, strongly affecting surface heating and atmospheric radiation

5. How Does the Feedback Occur in a Model? • At every grid point, predictive variables change at each time step as a function of a number of processes, including convection…

6. …when activated, a convective parameterization computes the changes in temperature and moisture (and possibly cloud water, momentum, etc.) that would occur at each vertical level if convection developed in the given grid-point environment • for example • where tc is a convective timescale, typically 30min to 1hr

7. How to Parameterize... • Relate unresolved effects (convection) to grid-scale properties using statistical or empirical techniques • What properties of convection do we need to predict? • convective triggering (yes/no) • convective intensity (how much rain?) • vertical distribution of heating • vertical distribution of drying

8. When, where, and how much... • Triggering (always requires positive area on a thermodynamic [e.g., Skew-T Log-P] diagram) - Different approaches 1.) mass or moisture convergence exceeding a certain threshold at a grid point, or 2.) positive destabilization rate, or 3.) perturbed parcels can reach their level of free convection, or 4.) sufficient cloud layer moisture

9. When, where, and how much... • Convective intensity (net heating) • proportional to mass or moisture convergence • sufficient to offset large-scale destabilization rate • sufficient to eliminate CAPE (constrained by available moisture)

10. When, where, and how much... • Vertical distribution of heating and drying • determined by nudging to empirical reference profiles • estimated using a simple 1-D cloud model to satisfy the constraints on intensity

11. Quasi-equilibrium schemes • Arakawa-Schubert for example • Large-scale destabilization rate ~ convective stabilization rate • Convective stabilization is achieved by an ensemble of cloud types

12. Convergence schemes • Kuo-type schemes • If: • atmosphere is conditionally unstable • horizontal moisture (or maybe mass) convergence is positive • Then: • converged moisture is assumed to go up in deep convective clouds (rather than broadscale ascent) • convective heating is distributed vertically according to the distribution of T’-T where T’ is the moist adiabatic profile of most unstable air • moisture is all condensed out (or a specified fraction is condensed out)

13. Current EMC models use different approaches • RUC II: Grell scheme • Eta: Betts-Miller-Janjic (Kain-Fritsch used experimentally) • MRF/AVN: Grell-Pan scheme • Grell, Grell-Pan, and Kain-Fritsch schemes are Mass-Fluxschemes*, meaning they use simple cloud models to simulate rearrangements of mass in a vertical column • Betts-Miller-Janjic adjusts to “mean post-convective profiles” based on observational studies

15. Grell and Grell-Pan Schemes • Initiation (on/off) 1.) Find highest qe air in column below ~400mb level…does CAPE exist? 2.) Evaluate CAP strength: Does lifted parcel reach LFC (level of free convection) within 150 mb of its source level? 3.) Is large-scale destabilization rate > 0? (i.e. is d(CAPE)/dt > 0?) • If yes to all 3, initiate convection...

16. Grell and Grell-Pan Schemes • Characteristics of convection • use simple models of an updraft and downdraft to simulate mass rearrangements by convection • make updraft and downdraft mass fluxes strong enough that their stabilizing effect approximately balances rate of large-scale destabilization:

17. Grell and Grell-Pan Schemes • Feeding back the effects of convection • Introduce tendency terms in the prognostic equations for temperature and moisture: • where a represents T or qv

18. Kain-Fritsch Scheme • Basic operating procedures are similar to Grell-type schemes except… • Convective inhibition evaluated in terms of negative area, not pressure depth • Large-scale destabilization not required, only CAPE • Updraft and downdraft formulations more sophisticated • Convective intensity based on instantaneous CAPE value rather than d(CAPE)/dt

19. Betts-Miller-Janjic Scheme • Checks for CAPE, cloud depth, using highest qe air in lowest 130mb above surface • makes a “first-guess” at a reference temperature profile based on a moist adiabat • makes a corresponding first guess reference profile for moisture based on an imposed sub-saturation (~relative humidity) • imposes enthalpy conservation

22. Enthalpy conservation • This usually requires an adjustment to the “first-guess” profiles (“sliding over” on a skew-T) of both T and q • Implications of this adjustment: • BMJ convection will be weak (or non-existent) when cloud column RH is low even if CAPE exists, increase with intensity as column moistens • Nudges grid-scale T, q to convectively adjusted profiles over a ~1h time scale

23. Kain-Fritsch convective initiation check • Beginning at the surface, mix in model layers overhead until a mixture 50-100mb deep is found. This compromises a potential updraft source layer. Find mean q, qv of this layer. • Lift a parcel with these characteristics to its LCL. At the LCL, compute a temperature perturbation, DTp based on grid point vertical velocity: • DTp = (wg - wc)1/3 + DTp(RH) • where wg is the grid point vertical velocity (cm/s), • wc is a correction factor wc=2*Z(LCL)/2km

24. Kain-Fritsch convective initiation check • For example: • wg - wc=1 cm/s -> DTp=1.0 K • wg - wc=10 cm/s -> DTp=2.5 K • In the Eta Model, an additional perturbation, DTp (RH) (magnitude ~0.5K) is given to account for low RH • So…In a typical convective environment with some larger-scale forcing, • DTp ~ 1 - 2 K

25. Kain-Fritsch convective initiation check • Is (DTp(LCL) + DTp) > Tg???? • If no, move up one model level and repeat process above • If yes, compute a vertical velocity perturbation, Wp, based on magnitude of DTp. • For DTp=1.5K, Wp ~ 4-5 m/s

26. Kain-Fritsch convective initiation check • Release a parcel at the LCL with T given by Tp(LCL) and vertical velocity Wp, begin solving “parcel buoyancy equation” at model levels overhead • Determine cloud top as highest model level where Wp > 0

27. Kain-Fritsch convective initiation check • Is Z(top) - Z(LCL) > 3km? • If yes, initiate deep convection from this source layer • If no, remember this layer as a possible source for shallow convection, move up to next potential source layer and repeat all above steps • If no potential source layer in the lowest 300mb can generate a convective cloud, move on to next grid point

28. Stabilizing mechanisms of Kain-Fritsch • Convective Updraft • removes high qe air from lower troposphere, transports it aloft • generates condensation

29. Stabilizing mechanisms of Kain-Fritsch • Convective Downdraft • draws mass from layer beginning at cloud base and extending up 150-200mb • deposits low qe air in sub-cloud layers • assumed to be saturated above cloud base, RH decreasing at ~10%/km below • continues until it either 1) reaches the surfaces or 2) becomes warmer than the environment • mass flux = updraft mass flux at cloud base

30. Stabilizing mechanisms of Kain-Fritsch • Return flow, i.e., “compensating subsidence” • compensates for any mass surplus or deficit created by updraft and downdraft • typically the updraft creates a mass surplus aloft and deficit below so that return flow is downward

31. Kain-Fritsch precipitation amounts • It depends… • Updraft generates condensation • Updraft dumps condensate into environment • Downdraft evaporates condensate at a rate that depends on • RH of downdraft source air • depth of downdraft • Any leftover condensate accumulates at the ground as precipitation

32. Consider some typical convective environments

33. Negative Precipitation

34. Shallow convection allowed

35. BMJ Heating/Drying profiles • heating K/hr • drying %RH/hr

36. Increase cloud layer RH by 20%

37. Deep convection allowed

38. Heating/Drying profiles

39. Kain-Fritsch Trigger • Increase source layer Td by 1 K • some parcels break cap, initiate deep convection updraft path updraft source layer downdraft path

40. Kain-Fritsch adjusted profile

41. Heating/Drying profiles

42. BMJ 1st guess profiles

43. After enthalply adjustment • Deep convection allowed • Strong cooling from 850-600mb • rainfall = 0.032 cm/h

44. Heating/drying profiles

45. Increase cloud-layer RH by 5% • Rainfall = 0.211 cm/h

46. Increase cloud-layer RH by 10% • Rainfall = 0.388 cm/h

47. RH increased 10%

48. Convective Rainfall vs. Change in cloud-layer RH Precip Amount Change in cloud-layer RH

49. BMJ Oklahoma Tornadoes • Too dry for deep convection • can see shallow convection grow with time

50. BMJ Oklahoma Tornadoes • Still too dry • 24h fcst valid 5 Oct 98