Entrainment…..but what about detrainment?

1. Entrainment…..but what about detrainment? Some new views on lateral mixing in shallow cumulus convection A. Pier Siebesma, Wim de Rooy, Roel Neggers and Stephan de Roode siebesma@knmi.nl • Importance detrainment vs entrainment • A turbulent mixing view on entrainment and detrainment • Thermodynamic constraints on cloud mixing • How to put things at work Faculty for Applied Sciences Climate Research Regional Climate Division Multiscale Physics

2. Strong Dependency of convective activity on tropospheric humidity Derbyshire et al, QJRMS 2004 Mass Flux Not reproduced by any convection parameterization!!

3. …….Also for shallow convection Stephan de Roode

4. Led to many interesting studies…………….. • Grabowski et al. (2006): Need entrainment rate to decrease with time of day • Kuang and Bretherton (2006): Weaker entrainment rates for deep than for shallow convection - increasing parcel size as cold pools form? • Khairoutdinov and Randall (2006): Demonstration of downdraft/cold pool role in transition from shallow to deep convection • Bechtold et al. (2008): Explicit parameterization of entrainment rate as f(1-RH) Mainly concentrating on the role of entrainment M M M But …., what about detrainment?

5. Entrainment and Detrainment Detrainment varies much more than Entrainment De Rooy and Siebesma MWR 2007

6. Ac Ly Lb Lx A closer “turbulent” look at entrainment/detrainment Average Budget Equation over (cloudy core) area Ac: Apply Gauss Theorem:

7. divergence convergence Organized versus Turbulent entrainment/detrainment • Traditionally entrainment/detrainment is treated rather advective (as opposed to a turbulent mixing process). • The very old notion that there is a distinction between dynamical and turbulent entrainment (i.e. Houghton and Cramer 1951) has gone. Can we restore this?

8. Asai Kasahari (1967) Revisited Apply Reynolds decomposition on the cloud core interface: divergence Diffusivity approach for the turbulent term at the interface: convergence Upwind approximation at the interface:

9. Gives finally: Entrainment Detrainment

10. Shallow Convection: mostly divergence Organized detrainment (Tiedtke 1989) Turbulent entrainment/detrainment The variation in organized detrainment from case to case explains the larger spread in detrainment So what determines the shape of the mass flux (or the organized detrainment)?

11. P C E Thermodynamic arguments: Kain-Fritch (1990) The Kain-Fritsch Scheme • The periphery of a cloud consists of air parcels that have distinct fractions environmental air and cloudy air 1- • is the mixed fraction at which the mixed parcel is neutrally buoyant. • Positive (negative) buoyant mixtures are entrained (detrained). • A greater yields a greater entrainment and smaller detrainment ! Courtesy: Stephan de Roode

12. 0.5 Thermodynamic arguments: Kain-Fritch (1990) KAIN FRITSCH • The mixed parcels have distinct probabilities of occurrence. • Ascribe a PDF to the mixed parcels in order to determine the expectation values of the mass of the entrained and detrained air. • Specify an inflow rate in order to set the upper bounds of entrainment and detrainment. • dictates the vertical gradient of the updraft mass flux use:

13. Is the decrease of mass flux well correlated with cc ? Normalized mass flux in the middle of the cloud layer De Rooy and Siebesma MWR 2007

14. And how about relative humidity only……..?

15. How to put these ideas to work? Neggers JAS 2009 • Assume a Gaussian joint PDF(ql,qt,w) shape for the cloudy updraft. • Mean and width determined by the multiple updrafts • Determine everything consistently from this joint PDF

16. Reconstruction of the cloud core fraction Assume that the 2 parcels lie on a mixing line Buoyancy along the mixing line at a specified height

17. Example: Reconstruction of the cloud core fraction • Determine cc • Calculate the core fraction ac • Determine mass flux directly: M=ac wc c No explicit detrainment parameterization required anymore Buoyancy along the mixing line at a specified height

18. Conclusions • In shallow cumulus it is detrainment rather than entrainment that regulates the shape of the mass flux and hence the moistening of the cloud layer. • This shape is regulated the zero buoyancy point on the mixing line cc : strong decrease of the mass flux is promoted by low CAPE but also through low RH. • The physical relationship is made explicit in the Dual Eddy Diffusivity Mass Flux framework in which the cloud core fraction can be directly related to cc • This allows a direct determination of the mass flux which makes an explicit detrainment parameterization obsolete.

19. Assume a Gaussian joint PDF(ql,qt,w) shape for the cloudy updraft. • Mean and width determined by the multiple updrafts • Determine everything consistently from this joint PDF An reconstruct the flux: • Remarks: • No closure at cloud base required. • No convection triggering required. • No detrainment parameterization required! • Pdf used for cloud scheme and possible for radiation.

20. Further new concepts: a bimodal statistical cloud scheme Extension of EDMF into the representation of sub-grid clouds updraft mode passive mode The observed turbulent PDF in shallow cumulus has a clear bimodal structure; 1 updraft mode, 1 passive (diffusive) mode This decomposition conceptually matches that defining EDMF -> favours an integrated treatment of transport and clouds within the PBL

21. Adopted in cloud parameterizations: • Lateral • mixing Horizontal or vertical mixing? Cloud-top mixing Observations (e.g. Jensen 1985) However: cloud top mixing needs substantial adiabatic cores within the clouds.

22. adiabat (SCMS Florida 1995) No substantial adiabatic cores (>100m) found during SCMS except near cloud base. (Gerber) Does not completely justify the entraining plume model but……… It does disqualify a substantial number of other cloud mixing models.

23. The (simplest) Mathematical Framework : zinv

24. The flexible updraft area partitioning allows the representation of gradual transitions between different convective regimes:

25. Overview dry PBL Mass flux contribution acts like a more intelligent counter-gradient contribution inversion a1 M1 + K-diff. w1 PBL Shallow Cumulus 10% inversion cloud a2 w2 M2 stratocumulus cloud base a1 w1 subcloud + K-diff. M1 10% inversion + K-diff. cloud base a2 w2 M2 + K-diff. subcloud M2: humidity supply for StCu clouds (coupling to surface) 10%

26. Cloudtop Cloudtop entrainment • Entrance level Lateral entrainment Inflow from subcloud Measurement level Cloudbase Cloudtop Backtracing particles in LES: where does the air in the cloud come from? Courtesy Thijs Heus

27. Height vs. Source level Virtually all cloudy air comes from below the observational level!!

28. Conclusions: • Kain Fritsch looks “reasonable” at first sight. • Thermodynamic considerations alone is not enough to parameterize lateral mixing and the mass flux • Kinematic ingredients need to be included e0 = F (wcore,z)

29. 2. Non-linear character of many cloud related processes Example 1: Autoconversion of cloud water to precipitation in warm clouds : Kessler Autoconversion Rate (Kessler 1969) With: ql : cloud liquid water ql : critical threshold H : Heaviside function A : Autoconversion rate Autoconversion rate is a convex function: Larson et al. JAS 2001

30. Further new concepts: a bimodal statistical cloud scheme Extension of EDMF into the representation of sub-grid clouds updraft mode passive mode The observed turbulent PDF in shallow cumulus has a clear bimodal structure; 1 updraft mode, 1 passive (diffusive) mode This decomposition conceptually matches that defining EDMF -> favours an integrated treatment of transport and clouds within the PBL

31. Single column model & IFS results

32. SCM LES Tested for a large number of GCSS Cases……………….. l qsat qt Cloud fraction Condensate

33. SCM LES EDMF bimodal clouds: a closer look BOMEX ATEX The advective PDF captures convective (updraft) clouds, while the diffusive PDF picks up the more passive clouds

34. Transient & steady state shallow cumulus • Continental: ARM SGP • Marine: RICO

35. Moist convective inhibition effects PBL equilibration: response to a +1 g/kg perturbation in ML humidity • RICO

36. A slow, but rewarding Working Strategy See http://www.gewex.org/gcss.html Large Eddy Simulation (LES) Models Cloud Resolving Models (CRM) Single Column Model Versions of Climate Models 3d-Climate Models NWP’s Global observational Data sets Observations from Field Campaigns Development Testing Evaluation

37. Conclusions and Outlook • EDMF framework is explained, that presently extend its range of applicability to conditionally • unstable cloud layers (shallow cumulus) • Just enough complexity is added to enable gradual transitions to and from shallow cumulus convection • Attaching a bimodal statistical cloud scheme to the EDMF framework makes the treatment of transport and cloud consistent throughout the PBL scheme • The double PDF allows representation of complex cloud structures, such as cumulus rising into stratocumulus • Scheme is calibrated against independent datasets (LES), and tested for a broad range of different PBL scenarios (GCSS!!) Status: • Partly operational in ECMWF (fully later this year) • Implemented in ECHAM, RACMO, AROME (but coupled with a TKE scheme) Further research on: • Coupling with TKE-schemes • Initialisation from other layers than the surface layer • Microphysics • Extension to deep convection. • Momentum transport

39. Early Plume models (1) L Continuity Equation R Assume circular geometry: z Scaling Ansatz :

40. Early Plume models (2) Plume models have proven extremely succesful for plumes but…… • Can not straightforwardly be translated to clouds because: • Plume-environment mixing is essentially a dilution process, hence plume width grows with z. With clouds phase transition come into play that calls for detrainment process as well. • Plume entrainment rate gives estimates an order of magnitude smaller than for entrainment in clouds. • In parameterization there is a need for an entrainment rate for cloud ensembles rather than for individual clouds (bulk model vs spectral model

41. Also for shallow convection (ARM case)

42. Also for shallow convection (ARM case) De Rooy and Siebesma MWR 2007

43. Asai Kasahari Revisited Intermezzo: Steady state model with no gradient in fraction and with mass flux appr for conserved variables: Dynamical entrainment Turbulent entrainment

44. Classic “Mechanistic” view on entrainment and detrainment • Convective Mass Flux : M = r ac wc • Crucial parameter in parameterizing convective transport in large scale models • Shape and Magnitude determined by the inflow (entrainment) and the outflow (detrainment) • Entrainment determined (by conditional sampling) using simplified budget equations: • Detrainment as a residual of the continuity equation: M M M

46. Clouds: use a bulk approach: Cloud ensemble: approximated by 1 effective cloud:

47. wc a a a and apply the mass flux approximation on ……

48. Simple Bulk Mass flux parameterization e d M Requires only a parameterization for fc and M : • Tiedtke 1989, Betts 1974: • = d = 0.2/R ~ 2 10-4 m-1 Based on entraining plume models Where e : fractional entrainment rate d : fractional detrainment rate Plus boundary conditions at cloud base are required (I.e. mass flux closure )

49. Diagnose through conditional sampling: Entrainment factor Measure of lateral mixing Typical Tradewind Cumulus Case (BOMEX) Data from LES: Pseudo Observations Total moisture (qt =qv +ql)

50. Trade wind cumulus: BOMEX LES Order of magnitude larger than in operational models!! Observations (Neggers et al (2003) Q.J.M.S.) Cumulus over Florida: SCMS