Richard Forbes (with thanks to Adrian Tompkins) forbes@ecmwft

1. Numerical Weather Prediction Parametrization of Diabatic ProcessesClouds (3)The ECMWF Cloud Scheme Richard Forbes (with thanks to Adrian Tompkins) forbes@ecmwf.int

2. The ECMWF Cloud Scheme Outline • Basic approach • Sources and Sinks • Convective detrainment • Stratiform cloud formation and evaporation • Precipitation generation, melting and evaporation • Ice sedimentation numerics • Ice supersaturation • Summary

3. WATER VAPOUR Evaporation Condensation CLOUD FRACTION CLOUD Liquid/Ice Evaporation Autoconversion PRECIP Rain/Snow The ECMWF Cloud Scheme • Based on Tiedtke (1993) • Prognostic moisture variables: • Water vapour • Condensate (Liquid and Ice) • Cloud fraction • “Single moment” bulk microphysics • Grid-box mean specific humidities • Diagnostic precipitation

4. 1 All liquid All ice Mixed phase Liquid fraction 0 -23°C 0°C Temperature The ECMWF Cloud SchemeBasic assumptions • Clouds fill the whole model layer in the vertical (fraction=cover). • Clouds have the same thermal state as the environmental air (homogeneous T). • Rain water/snow is diagnosed each timestep (equilibrium assumption) but is subject to evaporation / sublimation and melting in the column. • Cloud ice and water are distinguished only as a function of temperature - only one equation for condensate is necessary.

5. y Cloud Cloud free x The ECMWF Cloud SchemeRepresenting sub-grid heterogeneity ECMWF cloud parametrization In the real world y Cloud Cloud free x Humidity variations in cloud-free air but, No in-cloud variability

6. C G(qt) 1-C qt qs qs The ECMWF Cloud SchemeRepresenting sub-grid heterogeneity ECMWF cloud parametrization In the real world Cloud cover is integral under supersaturated part of PDF G(qt) qt A mixed ‘uniform-delta’ total water distribution is assumed

7. 3 1 2 4 5 1.Convective Detrainment (deep and shallow) 2. (A)diabatic warming/cooling (radiation/dynamics) 3. Subgrid turbulent mixing (cloud top, horiz eddies) 4. Precipitation generation 5. Precipitation evaporation/melting The ECMWF Cloud SchemeSchematic of sources and sinks Cloud condensate Cloud fraction Some (not all) of these are derived from a pdf approach 6. Advection/sedimentation

8. The ECMWF Cloud SchemeSources and sinks Cloud liquid water/ice ql Cloud fraction C A: Transport of Cloud (Advection + Sedimentation) SCV : Detrainment from Convection SBL: Source/Sink Boundary Layer Processes c: Source due to Condensation e: Sink due to Evaporation Gp: Precipitation Sink

9. Convective Source Term

10. Convective source termLinking clouds and convection Basic idea: Use detrained condensate as a source for cloud water/ice Examples: Ose (1993), Tiedtke(1993), Del Genioet al. (1996), Fowler et al. (1996) Source terms for cloud condensate and fraction can be derived using the mass-flux approach to convection parametrization.

11. (-Muql)k-1/2 (-Muql)k+1/2 Convective source termSource of water/ice condensate Detrainment of mass from cumulus updraughts Updraught mass flux (Muqlu)k-1/2 k-1/2 Standard equation for mass flux convection scheme ECHAM, ECMWF and many others... Duqlu k k+1/2 (Muqlu)k+1/2

12. (MuC)k-1/2 (MuC)k+1/2 Convective source termSource of cloud fraction Similar equation for the cloud fraction k-1/2 Du k k+1/2

13. Condensation and Evaporation Microphysics - ECMWF Seminar on Parametrization 1-4 Sep 2008 13

14. Convection Cloud formation dealt with separately Turbulent Mixing Cloud formation dealt with separately Stratiform cloud formationChanges in water vapour, q Local criterion for cloud formation: q > qs(T,p) • Two ways to achieve this in an unsaturated parcel: • Increase q • Decrease qs Processes that can increase q in a gridbox Advection

15. but……… there are numerical problems in models u t Stratiform cloud formationNumerical advection Advection does not mix air !!! It merely moves it around conserving its properties, including clouds. qt qs t+Dt q2 q1 T T1 T2 Because of the non-linearity of qs(T), q2 > qs(T2) so cloud forms This is a numerical problem and should not be used as cloud producing process! Would be preferable to advect moist conserved quantities instead of T and q

16. = w Stratiform cloud formationChanges in saturation, qs Postulate: The main (but not only) cloud production mechanisms for stratiform clouds are due to changes in qs. Hence we will link stratiform cloud formation to dqs/dt (i.e. changes in p, T).

17. C G(qt) 1-C qt Stratiform cloud formation: The cloud generation term is split into two components: Existing clouds “New” clouds and assumes a mixed ‘uniform-delta’ total water distribution

18. Stratiform cloud formation: Increase of existing clouds,c1 C G(qt) qt Already existing clouds are assumed to be at saturation at the grid-mean temperature. Any change in qs will directly lead to condensation. Note that this term would apply to a variety of PDFs for the cloudy air (e.g. uniform distribution)

19. G(qt) qt Stratiform cloud formation: Formation of new clouds, c2 Due to lack of knowledge concerning the variance of water vapour in the clear sky regions we have to resort to the use of a critical relative humidity, RHcrit G(qt) qt RHcrit = 0.8 is used throughout most of the troposphere

20. Stratiform cloud formation: Formation of new clouds, c2 For the case of RH>RHcrit We know qe from C G(qt) 1-C qt similarly

21. Stratiform cloud formation: Formation of new clouds, c2 For the case of RH<RHcrit C G(qt) 1-C Term inactive if RH<RHcrit qt Perhaps for large cooling this is inaccurate? • As stated in the statistical scheme lecture: • With prognostic cloud water and here cover we can write source and sinks consistently with an underlying distribution function • But in overcast or clear sky conditions we have a loss of information. Hence the use of Rhcrit in clear sky conditions for cloud formation

22. Evaporation of clouds No effect on cloud cover Processes: e=e1+e2 • Large-scale descent and cumulus-induced subsidence C G(qt) • Diabatic heating qt • Turbulent mixing (e2) Diffusion process proportional to the saturation deficit of the environmental air GCM grid cell Dx where K = 5.10-6s-1

23. Problem: Reversible Scheme? Cooling: Increases cloud cover C G(qt) 1-C qt Subsequent warming of same magnitude: No effect on cloud cover C G(qt) 1-C qt Process not reversible

24. Precipitation Generation + Melting and Evaporation

25. Gp ql qlcrit Precipitation generationMixed phase and water clouds Representing autoconversion and accretion in the warm phase, aggregation and the Bergeron process in the mixed phase. (T > -23°C) Sundqvist(1978, 1989) Accretion/aggregation Bergeron Process c0=10-4s-1 c2=0.5 c1=100 qlcrit=0.3 g kg-1 P = precipitation rate T= temperature (K)

26. Gp ql qlcrit Precipitation generationIce clouds Representing aggregation in the ice phase (T < -23°C). Rate decreases as the temperature decreases. c0=10-3 e0.025(T - 273.15) s-1 qicrit=3.10-5 kg kg-1

27. Precipitation melting • The part of the grid box that contains precipitation is • assumed to cool to Tmelt over a timescale tau • Occurs whenever wet bulb temperature Tw > 0°C • Is limited such that cooling does not lead to T<0°C

28. Precipitation evaporation Evaporation (Kessler 1969, Monogram)

29. Precipitation Evaporation Mimics radiation schemes by using a ‘2-column’ approach of recording both cloud and clear precipitation fluxes This allows a more accurate assessment of precipitation evaporation NUMERICS: Solved implicitly to avoid numerical problems Jakob and Klein (QJRMS, 2000)

30. Clear sky region Grid slowly saturates Precipitation Evaporation • Numerical “Limiters” have to be applied to prevent grid scale saturation Clear sky region Grid can not saturate

31. Ice Particle Sedimentation And Numerical Issues

32. McFarquhar and Heymsfield (1997) Ice Sedimentation (before 30r2 in 2006)Numerical problems Illustration of sedimentation numerical issues with ice sedimentation fromoldIFS Cycle 25r3 to Cycle 30r1 Pure ice clouds (T<250 K) Two size classes of ice, boundary at 100 μm Explicitly calculate ice settling flux: For IWC<100vi= 0.15m/s For IWC>100 Heymsfield and Donner (1990) Ice falling in cloud below is source for ice in that layer, ice falling into clear sky is converted into snow

33. Real advection Perfect advection w Ice Sedimentation (before 30r2 in 2006)Numerical problems Problem: we neglect vertical subgrid-scales

34. Solution (not very satisfactory): Only allow sedimentation of cloud mass into existing cloudy regions, otherwise convert to snow – Results in higher effective sedimentation rates AND vertical resolution sensitivity Ice flux Snow flux Ice Sedimentation (before 30r2 in 2006)Further numerical problems Since we only allow ice to fall one layer in a timestep, and since the cloud fills the layer in the vertical, the cloud lower boundary is advected at the CFL rate of Dz / Dt

35. Ice Sedimentation (before 30r2 in 2006)Further numerical problems 100 vs 50 layer resolution k k+1 Ice flux Snow flux Sink at level k depends on dz This is numerically correct, but if then converted to snow and “lost” will introduce a resolution sensitivity

36. Modified Ice Representation (from 31r1)To tackle ice settling deficiency Pure ice clouds (T<250 K) Only one size class of ice Calculate ice settling flux with constant fall speed vi= 0.15m/s modified by a function of temperature and pressure (Heymsfield and Iaquinta, 2000) As seen earlier, an autoconversion term converts some of the prognostic ice mass to the diagnostic "snow" flux, which is then treated diagnostically.

37. Modified Numerics (from 31r1)To tackle ice settling deficiency Advected quantity (e.g. ice) fall speed Options: (1) Semi-Lagrangian (2) Time splitting (3) Implicit numerics Constant Explicit Source/Sink Implicit Source/Sink (not required for short timesteps) Implicit: Upstream forward in time, k=vertical level n=time level f = cloud water (qX) what is short? Solution

38. 100 vs 50 layer resolution Improved Numerics in SCM Cirrus Case 29r1 Scheme cloud ice cloud fraction time 30r2 Scheme cloud ice cloud fraction time evolution of cloud cover and ice

39. Cirrus Clouds and Ice Supersaturation Microphysics - ECMWF Seminar on Parametrization 1-4 Sep 2008 39

40. Air that is supersaturated with respect to ice is common(Pictures courtesy of Klaus Gierens and Peter Spichtinger, DLR) Aircraft flight data 3000 km ice supersaturated segment observed ahead of front Microwave limb sounders

41. GCM gridbox C Clear sky Cloudy region Cirrus CloudsHomogeneous nucleation • Want to represent super-saturation and homogeneous nucleation • Include simple diagnostic parameterization in existing ECMWF cloud scheme • Desires: • Supersaturated clear-sky states with respect to ice • Existence of ice crystals in locally subsaturated state • Only possible with extra prognostic equation ?

42. Unlike “parcel” models, or high resolution LES models, we have to deal with subgrid variability GCM gridbox qvenv=? qvcld =? Clear Cloud (qicld) C 1-C Three items of information: qv, qi, C (grid-box mean vapour, cloud ice and cover) • We know qi occurs in the cloudy part of the gridbox • We know the mean in-cloud cloud ice (qicld=qi/C) • What about the water vapour? In the days of no ice supersaturation: • Clouds: qvcld=qs • Clear sky: qvenv=(qv-Cqs)/(1-C)

43. In the bad old days No supersaturation 1. (qv-Cqs)/(1-C) qs Lohmann and Karcher: Humidity uniform across gridcell 2. qv qv Klaus Gierens: Humidity in clear sky part equal to the mean total water 3. qv+qi qv-qi(1-C)/C Current assumption including supersaturation: Hang on… Looks familiar??? 4. (qv-Cqs)/(1-C) qs Different approaches to represent clear sky and cloudy humidity GCM gridbox C qvenv qvcld

44. From Mesoscale Model Lohmann and Karcher: Humidity uniform across gridcell 2. qv qv qvenv qvcld GCM gridbox Critical Scrit reached uplifted box 1 timestep Ice is formed, qi increases, qvcld reduces 1 timestep qvenv=qvcld Artificial flux of vapour from clear sky to cloudy regions!!! Assumption ignores fact that difference processes are occurring on the subgrid-scale

45. From GCM perspective Current assumption: Hang on… Looks familiar??? 4. (qv-Cqs)/(1-C) qs qvenv qvcld GCM gridbox Critical Scrit reached Difference to standard scheme is that environmental humidity must exceed Scrit to form new cloud uplifted box qvcld reduces to qs qvenv unchanged qi increases microphysics qidecreases qvenvunchanged No artificial flux of vapour from clear sky from/to cloudy regions Assumption seems reasonable: BUT! Does not allow nucleation or sublimation timescales to be represented, due to hard adjustment

46. B C A RH wrt ice PDFat 250hPaone month average Aircraft observations A: Numerics and interpolation for default model B: The RH=1 microphysics mode C: Drop due to GCM assumption of subgrid fluctuations in total water

47. Summary of ECMWF Scheme • Scheme introduces two prognostic equations for cloud water/ice and cloud mass. • Sources and sinks for each physical process • Some derived using assumptions concerning subgrid-scale PDF for vapour and clouds. J More simple to implement than a prognostic statistical scheme since “short cuts” are possible for some terms. Also nicer for assimilation since prognostic quantities directly observable. L Loss of information (no memory) in clear sky (a=0) or overcast conditions (a=1) (critical relative humidities necessary etc). • Nothing to stop solution diverging for cloud cover and cloud water. (eg. ql>0, a=0). Unphysical “safety switches” necessary. • Diagnostic ice / water split and no ice supersaturation 0<T<-23°C • Artificial split between prognostic ice and diagnostic snow variables • Many microphysical assumptions are empirically based

48. And in the future……..

49. ECMWF IFS Cloud Scheme Developments WATER VAPOUR Evaporation Condensation CLOUD FRACTION CLOUD Liquid/Ice Evaporation CLOUD FRACTION Autoconversion PRECIP Rain/Snow Current Cloud Scheme New Cloud Scheme • Prognostic condensate & cloud fraction • Diagnostic liquid/ice split as a function of temperature between 0°C and -23°C • Diagnostic representation of precipitation • Prognostic liquid & ice & cloud fraction • Prognostic snow and rain (sediments/advects) • New additional sources and sinks • Existing sources and sink formulation retained (cond/evap/autoconv)

50. New prognostic cloud microphysicsRepresentation of mixed phase • The most significant change in the new scheme is the improved physical representation of the mixed phase. • Current scheme: diagnostic fn(T) split between ice and liquid cloud(a crude approximation of the wide range of values observed in reality). • New scheme: wide range of supercooled liquid water for a given T. PDF of liquid water fraction of cloud for the diagnostic mixed phase scheme (dashed line) and the prognostic ice/liquid scheme (shading)