1. Numerical Weather Prediction Parametrization of Diabatic Processes Clouds (1) Cloud Microphysics
Richard Forbes
and Adrian Tompkins
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3. Outline LECTURE 1: Cloud Microphysics LECTURE 2: Cloud Cover in GCMs
Overview of GCM cloud parametrization issues
Microphysical processes
2.1 Warm phase
2.2 Cold phase
Summary
LECTURE 2: Cloud Cover in GCMs
LECTURE 3: The ECMWF Cloud Scheme
LECTURE 4: Validation of Cloud Schemes
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4. 1. Overview of GCM Cloud Parametrization Issues

5. 1. Water Cycle 2. Radiative Impacts 3. Dynamical Impacts
The Importance of Clouds
1. Water Cycle
2. Radiative Impacts
3. Dynamical Impacts
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6. Clouds in GCMs - What are the problems ?
radiation
convection
microphysics
turbulence
dynamics
Clouds are the result of complex interactions between a large number of processes
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7. Clouds in GCMs - What are the problems ?
Many of these processes are only poorly understood - For example, the interaction with radiation
Cloud top and base height
Cloud fraction and overlap
Amount of condensate
Cloud-radiation interaction
In-cloud conden-sate distribution
Cloud environment
Phase of condensate
Cloud particle shape
Cloud particle size
Cloud macrophysics
Cloud microphysics
“External” influence
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8. Cloud Parametrization Issues:
Microphysical processes
Macro-physical
subgrid heterogeneity
Numerical issues
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9. Cloud Parametrization Issues: Which quantities to represent ?
Cloud water droplets
Rain drops
Pristine ice crystals
Aggregate snow flakes
Graupel pellets
Hailstones
Note for ice phase particles: Additional latent heat. Terminal fall speed of ice hydrometeors significantly less (lower density). Optical properties are different (important for radiation).

10. Cloud Parametrization Issues: Complexity ?
Small ice
Medium ice
Large ice
Ice Mass
Liquid Mass
Ice mass
Ice number
Cloud
Mass
“Single Moment”
Schemes
“Double Moment”
Schemes
“Spectral/Bin”
Microphysics
Most GCMs only have simple single-moment schemes

11. Cloud Parametrization Issues: Diagnostic or prognostic variables ?
Cloud condensate mass (cloud water and/or ice), ql.
Diagnostic approach
Prognostic approach
Sources
Sinks
Advection + sedimentation
CAN HAVE MIXTURE OF APPROACHES
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12. Simple Bulk Microphysics
VAPOUR (prognostic)
Evaporation
Condensation
CLOUD (prognostic)
Evaporation
Autoconversion
RAIN (diagnostic)
Why ?
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13. Microphysics - a “complex” GCM scheme
Fowler et al., JCL, 1996
Similar complexity to many schemes in use in CRMs
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14. 2. Microphysical Processes
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15. Cloud microphysical processes
We would like to include into our models:
Formation of clouds
Release of precipitation
Evaporation of both clouds and precipitation
Therefore we need to describe
Nucleation of water droplets and ice crystals from water vapour
Diffusional growth of cloud droplets (condensation) and ice crystals (deposition)
Collection processes for cloud drops (collision-coalescence), ice crystals (aggregation) and ice and liquid (riming) leading precipitation sized particles
The advection and sedimentation (falling) of particles
the evaporation/sublimation/melting of cloud and precipitation size particles
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16. Microphysics: A complex system!
Overview of
Warm Phase Microphysics T > 273K
Mixed Phase Microphysics ~250K < T < 273K
Pure ice Microphysics T < ~250K

17. 2. Microphysical Processes 2.1 Warm Phase
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18. Droplet Classification

19. Nucleation of cloud droplets: Important effects for particle activation
Planar surface: Equilibrium when e=es and number of molecules impinging on surface equals rate of evaporation
Surface molecule has fewer neighbours
Curved surface: saturation vapour pressure increases with smaller drop size since surface molecules have fewer binding neighbours.

20. Nucleation of cloud droplets: Homogeneous Nucleation
Drop of pure water forms from vapour
Small drops require much higher super saturations
Kelvin’s formula for critical radius for initial droplet to “survive”
Strongly dependent on supersaturation
Would require several hundred percent supersaturation (not observed in the atmosphere).
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21. Nucleation of cloud droplets: Heterogeneous Nucleation
Collection of water molecules on a foreign substance, RH > ~80% (Haze particles)
These (hydrophilic) soluble particles are called Cloud Condensation Nuclei (CCN)
CCN always present in sufficient numbers in lower and middle troposphere
Nucleation of droplets (i.e. from stable haze particle to unstable regime of diffusive growth) at very small supersaturations.

22. Nucleation of cloud droplets: Important effects for particle activation
Planar surface: Equilibrium when e=es and number of molecules impinging on surface equals rate of evaporation
Surface molecule has fewer neighbours
Curved surface: saturation vapour pressure increases with smaller drop size since surface molecules have fewer binding neighbours.
Effect proportional to 1/r (curvature effect)
Dissolved substance reduces vapour pressure
Presence of dissolved substance: saturation vapour pressure reduces with smaller drop size due to solute molecules replacing solvent on drop surface (assuming esollute<ev)
Effect proportional to 1/r3 (solution effect)

23. Nucleation of cloud droplets: Heterogeneous Nucleation
Haze particle in equilibrium
“Curvature term”
Small drop – high radius of curvature easier for molecule to escape
equilibrium
e/es
“Solution term”
Reduction in vapour pressure due to dissolved substance

24. Diffusional growth of cloud water droplets
Once droplet is activated, water vapour diffuses towards it = condensation
Reverse process = evaporation
Droplets that are formed by diffusion growth attain a typical size of 0.1 to 10 mm
Rain drops are much larger
drizzle: 50 to 100 mm
rain: >100 mm
Other processes must also act in precipitating clouds
For r > 1 mm and neglecting diffusion of heat
D=Diffusion coefficient, S=Supersaturation
Note inverse radius dependency
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25. Collection Collision-coalescence of water drops
Rain drop shape Chuang and Beard (1990)
Drops of different size move with different fall speeds - collision and coalescence
Large drops grow at the expense of small droplets
Collection efficiency low for small drops
Process depends on width of droplet spectrum and is more efficient for broader spectra – paradox
Large drops can only be produced in clouds of large vertical extent – Aided by turbulence (differential evaporation), giant CCNs ?
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26. Parameterizing nucleation and droplet growth
Nucleation: Since “Activation” occurs at supersaturations less than 1%, most schemes assumes all supersaturation is immediately removed as liquid water
Note that this assumption means that models can just use one “prognostic” equation for the total water mass, the sum of vapour and liquid
Usually, the growth equation is not explicitly solved, and in single-moment schemes simple (diagnostic) assumptions are made concerning the droplet number concentration when needed (e.g. radiation). These often assume more CCN in polluted air over land.

27. Microphysical Parametrization “Autoconversion” of cloud drops to raindropsql
qlcrit Gp
Linear function of ql (Kessler, 1969)
Function of ql with additional term to avoid singular threshold and non-local precipitation term (Sundqvist 1978)
Or, for example, for a more complex double-moment parametrization (Seifert and Beheng,2001), derived directly from the stochastic collection equation.
Kessler
Sundqvist ql
qlcrit Gp
Microphysics - ECMWF Seminar on Parametrization 1-4 Sep
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28. Schematic of Warm Rain Processes
Coalescence
~10 microns
RH>100.6%
“Activation”
Diffusional
Growth
Heterogeneous Nucleation
RH>78% (Haze)
CCN
Different fall speeds

29. 2. Microphysical Processes 2.2 Cold Phase
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30. Kepler (1611) “On the Six-Cornered Snowflake”

31. “The Six-Cornered Snowflake”
Ken Libbricht

32. Ice Microphysical Processes
Ice nucleation
Depositional Growth (and sublimation)
Collection (aggregation/riming)
Splintering
Melting

33. Ice Nucleation Droplets do not freeze at 0oC !
Ice nucleation processes can also be split into Homogeneous and Heterogeneous processes, but complex and not well understood.
Homogeneous freezing of water droplets occurs below about -38oC,
Homogeneous nucleation of ice crystals dependent on a critical relative humidity (fn of T, Koop et al. 2000).
Frequent observation of ice between 0oC and colder temperatures indicates heterogeneous processes active.
Number of activated ice nuclei increases with decreasing temperature.
Observations:
< -20oC Ice free clouds are rare
> -5oC ice is unlikely (unless ice falling from above!)
ice supersaturation ( > 10% ) observations are common
Fletcher 1962

34. Ice Nucleation: Heterogeneous nucleation
I will not discuss heterogeneous ice nucleation in great detail in this course due to lack of time and the fact that these processes are only starting to be tackled in Large-scale models. See recent work of Ulrike Lohmann for more details
aerosol
Supercooled drop

35. Pure ice Phase: Homogeneous Ice Nucleation
At cold temperature (e.g. upper troposphere) difference between liquid and ice saturation vapour pressures is large.
If air mass is lifted, and does not contain significant liquid particles or ice nuclei, high supersaturations with respect to ice can occur, reaching 160 to 170%.
Long lasting contrails are a signature of supersaturation
Institute of Geography, University of Copenhagen

36. Diffusional growth of ice crystals Deposition
Equation for the rate of change of mass for an ice particle of diameter D due to deposition (diffusional growth), or evaporation
Deposition rate depends primarily on
the supersaturation, s
the particle shape (habit), C
the ventilation factor, F
The particular mode of growth (edge growth vs corner growth) is sensitive to the temperature and supersaturation

37. Diffusional growth of ice crystals Ice Habits
Ice habits can be complex, depend on temperature: influences fall speeds and radiative properties

38. Diffusional growth of ice crystals Animation

39. Homogeneous Freezing Temperature
Diffusional growth of ice crystals Mixed Phase Clouds: Bergeron Process (I)
Ice Saturation
Homogeneous Freezing Temperature
Water Saturation
The saturation water vapour pressure with respect to ice is smaller than with respect to water
A cloud, which is saturated with respect to water is supersaturated with respect to ice !
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40. Ice particles grow at the expense of water droplets
Diffusional growth of ice crystals Mixed phase cloud Bergeron process (II)
Ice particles grow at the expense of water droplets
Ice particle enters water cloud
Cloud is supersaturated with respect to ice
Diffusion of water vapour onto ice particle
Cloud will become sub-saturated with respect to water
Water droplets evaporate to increase water vapour
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41. Collection processes: Ice Crystal Aggregation
Ice crystals can aggregate together to form “snow”
“Sticking” efficiency increases as temperature exceeds –5C
Irregular crystals are most commonly observed in the atmosphere (e.g. Korolev et al. 1999, Heymsfield 2003)
CPI
Model
500 mm
Westbrook et al. (2008)
Field & Heymsfield ‘03
T=-46oC
Lawson, JAS’99

42. Parametrization of ice crystal diffusion growth and aggregation
Some schemes represent ice processes very simply, removing ice super-saturation (as for warm rain process).
Others, have a slightly more complex representation allowing ice supersaturation (e.g. current ECMWF scheme).
Increasingly common are schemes which represent ice, supersaturation and the diffusional growth equation, and aggregation represented as an autoconversion to snow or parametrization of an evolving particle size distribution (e.g. Wilson and Ballard, 1999). See Lohmann and Karcher JGR 2002(a,b) for another example of including ice microphysics in a GCM. 42
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43. Collection processes: Riming – capture of water drops by ice
Graupel formed by collecting liquid water drops in mixed phased clouds (“riming”), particulaly when at water saturation in strong updraughts (convection). Round ice crystals with higher densities and fall speeds than snow dendrites
Hail forms if particle temperature close to 273K, since the liquid water “spreads out” before freezing. Generally referred to as “Hail” – The higher fall speed (up to 40 m/s) imply hail only forms in convection with strong updraughts able to support the particle long enough for growth

44. Rimed Ice Crystals

45. Rimed Ice Crystal
emu.arsusda.gov

46. Heavily Rimed Ice Crystal
emu.arsusda.gov

47. Parametrization of rimed ice particles
Most GCMs with parametrized convection don’t explicitly represent graupel or hail (too small scale)
In cloud resolving models, traditional split between ice, snow and graupel and hail but this split is rather artificial.
Degree of riming can be light or heavy.
Alternative approach:
Morrison and Grabowski (2008) have three ice prognostics, ice number concentration, mixing ratio from deposition, mixing ratio from riming.
Avoids artificial thresholds between different categories. 47
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48. Other microphysical processes Splintering, Shedding Evaporation, Melting
Other processes include evaporation (reverse of condensation), ice sublimation (reverse of deposition) and melting.
Shedding: Large rain drops break up – shedding to form smaller drops, places a limit on rain drop size.
Splintering of ice crystals, Hallet-Mossop splintering through riming around -5°C. Leads to increased numbers of smaller crystals.

49. Particle Size Distributions
Mass Distribution
Densities
Terminal fall speeds
From Fleishauer et al (2002, JAS)
Field (2000), Field and Heymsfield (2003)
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50. Falling Precipitation
Need to know size distribution
For ice also affected by ice habit
Poses problem for numerics
Courtesy: R Hogan, U. Reading
From R Hogan

51. Microphysics at the Cloud Scale
Typical time-height cross section of a front from the vertically pointing 94GHz radar at Chilbolton, UK
Ice Nucleation and diffusion growth
Aggregation
Warm phase
Melting
Interaction with the dynamics
Fall streaks, small scale dynamics drives microphysics
Image from Robin Hogan. Data from RCRU RAL.
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52. Cloud ParametrizationClouds 1

54. 3. Summary
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55. Summary: Warm Cloud E.g: Stratocumulus Evaporation Condensation
(Rain formation - Fall Speeds - Evaporation of rain)

56. Summary: Deep Convective Cloud
Heteorogeneous Nucleation of ice
Splintering/Bergeron Process
Melting of Snow and Graupel
Precipitation Falls Speeds
Evaporation in Sub-Cloud Layer

57. Summary: Cirrus cloud Homogeneous Nucleation
(representation of supersaturation)
Heterogeneous Nucleation
(representation of nuclei type and concentration)
Diffusional growth, Aggregation
Sedimentation of ice crystals

58. Simple Bulk Microphysics
VAPOUR (prognostic)
Evaporation
Condensation
CLOUD (prognostic)
Evaporation
Autoconversion
RAIN (diagnostic)
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59. Microphysics - a “complex” GCM scheme
Fowler et al., JCL, 1996
Similar complexity to many schemes in use in CRMs
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60. Summary 1: A complex system!
Molecular Scale
Nucleation/activation, Diffusion/condensation/evaporation
Particle Scale
Collection/collision-coalescence/aggegation, Shedding/splintering
Parcel Scale
Particle Size Distributions
Cloud Scale
Heterogeneity
Interaction with the dynamics (latent heating)

61. Summary 2: Simplifying assumptions
Parametrization of cloud and precipitation microphysical processes:
Need to simplify a complex system
Accuracy vs. complexity vs. computational efficiency trade off
Appropriate for the application and no more complexity than can be constrained and understood
Dynamical interactions (latent heating), radiative interactions
Still many uncertainties (particularly ice phase)
Particular active area of research is aerosol-microphysics interactions.
Microphysics often driven by small scale dynamics…..
Next lecture: Cloud Cover
Sub-grid scale heterogeneity
Linking the micro-scale to the macro-scale

62. References Reference books for cloud and precipitation microphysics:
Pruppacher. H. R. and J. D. Klett (1998). Microphysics of Clouds and Precipitation (2nd Ed). Kluwer Academic Publishers.
Rogers, R. R. and M. K. Yau, (1989). A Short Course in Cloud Physics (3rd Ed.) Butterworth-Heinemann Publications.
Mason, B. J., (1971). The Physics of Clouds. Oxford University Press.
Hobbs, P. V., (1993). Aerosol-Cloud-Climate Interactions. Academic Press.
Houze, Jr., R. A., (1994). Cloud Dynamics. Academic Press.
Straka, J., (2009). Cloud and Precipitation Microphysics: Principles and Parameterizations. Cambridge University Press. Not yet released!