1. Convective Parameterization Jack Kainand 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  c 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- Flux schemes*, 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  e 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  represents T or q v

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  e 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 v of this layer. Lift a parcel with these characteristics to its LCL. At the LCL, compute a temperature perturbation, DT p based on grid point vertical velocity:  T p = (w g - w c ) 1/3 +  T p (RH) –where w g is the grid point vertical velocity (cm/s), –w c is a correction factor w c =2*Z(LCL)/2km

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

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

26. Kain-Fritsch convective initiation check Release a parcel at the LCL with T given by T p (LCL) and vertical velocity W p, begin solving “parcel buoyancy equation” at model levels overhead Determine cloud top as highest model level where W p > 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  e 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  e 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 T d by 1 K some parcels break cap, initiate deep convection updraft path downdraft path updraft source layer

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 Change in cloud-layer RH Precip Amount

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

51. BMJ Oklahoma Tornadoes Shallow convection cloud top now up to ~650mb

52. Shallow convection profile Transports moisture upward