1. Clouds and Large Model Grid Boxes
Damian Wilson
Atmospheric Processes and Parametrization
Met Office
With help from: Andrew Bushell, Jeremy Price, Keith Williams, Rob Wood, Paul Field, Olaf Stiller

2. Contents What is a cloud…?
Why do we need to represent clouds in a model?
What do we need to know about them?
How can we estimate these quantities?
How effective are current methods?
How can we do better?
What have we learnt?

3. Contents What is a cloud…?
Why do we need to represent clouds in a model?
What do we need to know about them?
How can we estimate these quantities?
How effective are current methods?
How can we do better?
What have we learnt?

4. Contents What is a cloud…?
Why do we need to represent clouds in a model?
What do we need to know about them?
How can we estimate these quantities?
How effective are current methods?
How can we do better?
What have we learnt?

5. Clouds in the atmosphere
Clouds have several effects in the atmosphere:
Radiative transfer
Latent heat
Chemistry
Moisture transport
Visibility
To fully calculate the effect of each we would need to know the full three dimensional distribution of liquid and ice contents.

6. Radiative importance of clouds
12Z 10/1/03
2152Z
-6 to to to 0
18Z
18Z

7. Contents What is a cloud…?
Why do we need to represent clouds in a model?
What do we need to know about them?
How can we estimate these quantities?
How effective are current methods?
How can we do better?
What have we learnt?

8. A basic cloud representation
On the very small scale, we can represent clouds by growing particles (e.g. Köhler theory).
On the slightly larger scale we might assume that condensational growth or evaporation is fast enough to maintain the surroundings at saturation.
This assumption isn’t good enough for ice, so we must use a distribution of particles and integrate the depositional growth equation.
And...

9. Clouds are subgrid-scale
Structure exists in the horizontal and vertical. We may need to know cloud fractions as well as condensates.

10. Is subgrid-scale cloud information important?
Some simple theory
Some simulations

11. Subgrid-scale cloud
Subgrid-scale cloud information is important for radiation.
It is also important for precipitation.        
Precipitation falling through dry air will evaporate.
C = 0.5,  =2 gives transmission of 0.64
Precipitation falling through cloud will grow.
C = 1, =1 gives transmission of 0.37

12. Feedbacks of cloud fraction
Half cloud fraction
Control

13. What do we need to know about clouds?
Cloud fraction
Cloud thickness - how much condensate is present
Cloud morphology
Particle phase and size distributions

14. Contents What is a cloud…?
Why do we need to represent clouds in a model?
What do we need to know about them?
How can we estimate these quantities?
How effective are current methods?
How can we do better?
What have we learnt?

15. Instantaneous condensationqT
qT=qsat(T)
qT>qsat Cloudy 
condensate
qT<qsat Clear T
Consider as a 1D distribution of qT - qsat

16. Diagnostic cloud schemes
Then we can diagnose the cloud fraction and water content
If we know about the shape of the distribution of moisture about its mean
Cloudy
(qT-qsat)’
-<qT-qsat>
We often assume that changes in the mean state will not change the shape of the distribution
And the mean state of the gridbox

17. The Smith Scheme What shape of PDF should we use? Probability
(1-RHcritical) qsat
Clear l
Cloudy
-<qT-qsat>
(qT-qsat)’

18. Contents What is a cloud…?
Why do we need to represent clouds in a model?
What do we need to know about them?
How can we estimate these quantities?
How effective are current methods?
How can we do better?
What have we learnt?

19. Moisture Distributions from Balloons
A simple symmetric fluctuation around the mean can be a good way of representing variability in a gridbox.

20. Moisture Distributions from Balloons
Some distributions, e.g. convective, are not symmetrical even after detrending.

21. Aircraft results
These results cannot be reproduced by a single PDF.

22. Do these inaccuracies matter?
Forecasts
Climate predictions

23. Forecast problems 12Z 22/7/02 0821Z 22/7/02 1435Z 22/7/02
The extent of stratocumulus is often underestimated

24. Link between liquid water content and cloud fraction
The relationship between C and l depends on the width of the distribution.
Large liquid water contents are produced for cloud fractions near 1.
Probability
Clear l
Cloudy
<qT - qsat>
qT-qsat
<l> at C=1

25. ISCCP data ISCCP satellite data
Stable
Unstable
ISCCP satellite data
Down
High thick: Vertical velocity controlled.
Low thick: Stability controlled. Up
HadSM3 model
Thick cloud overestimated.

26. Contents What is a cloud…?
Why do we need to represent clouds in a model?
What do we need to know about them?
How can we estimate these quantities?
How effective are current methods?
How can we do better?
What have we learnt?

27. Building a prognostic scheme
We choose specify the sources and sinks of
Liquid condensate
Ice condensate
Liquid cloud fraction
Ice cloud fraction
Total cloud fraction
For all processes which occur in the model
We can use Cloud resolving models, observations and conceptual models to help.

28. Conceptual models
Adiabatic cooling by lifting is assumed not to alter the PDF
Cloudy
-<qT-qsat>
(qT-qsat)’
Precipitation is assumed not to change the cloud fraction   

29. Does a prognostic scheme do any better?
Forecast results
Microphysical comparison

30. Forecast problems 0821Z 12Z 22/7/02 1435Z
The extent of the stratocumulus is increased

31. Microphysical evaluation
Smith
Wood and Field
The link between liquid water content and cloud fraction has been broken.

32. Contents What is a cloud…?
Why do we need to represent clouds in a model?
What do we need to know about them?
How can we estimate these quantities?
How effective are current methods?
How can we do better?
What have we learnt?

33. Summary
Clouds have a large effect on radiative transfer, hence surface temperatures and circulation.
Clouds are usually below the size of model grid-boxes.
Symmetric probability density function parametrizations are good in many cases (for liquid cloud) but have problems.
Prognostic cloud schemes allow a more direct link between processes and clouds.
Modelled climate feedbacks and weather forecasts depend strongly on how sub-grid clouds are represented.

35. Are prognostic and diagnostic schemes are different?qT q
Distribution assumptions (e.g. triangular).
Width l
Skewness C qT q
Distribution assumptions (e.g. triangular).
Width l
Skewness C
Change assumptions

36. Vertical Velocities
Control - black line
No cloudy LW radiation - reduces <w2>
Half cloud fraction - reduces <w2>
No convection - increases <w2>
The longwave cooling is driving convective or large-scale instability and hence the structure. Halving the cloud fraction reduces the longwave cooling.

37. Climate cloud feedback
A simple change in the clouds can have an impact on the cloud feedback
T = 3.1C
T = 3.4C

38. Theoretical evolution of cloud
Smith
Warm and precipitate
Theory
Xu and Randall
Cool and precipitate
Tiedtke

39. Ice cloud Nucleation Ice super-saturation Liquid saturation
Fall of ice
Sublimation
The assumption of instantaneous condensation for ice cloud is not good. It excludes the possibility of supercooled liquid cloud.

40. Clouds 
A cloud droplet will grow and shrink by diffusion of water vapour molecules to and from the surface until a dynamic equilibrium is reached with the surroundings.   

41. Radiative importance of clouds
Clouds reflect a large amount of solar radiation.

42. Moisture Distributions from Balloons
Distributions may be skewed by a large-scale change across a gridbox

43. A prognositic scheme?
Anvils detrained from convective cores can exist long after the convection has died down.

44. CRM under uniform forcing
Width of PDF
Spread reduces with time
Shape changes with time
PDF Amplitude