1. Richard Forbes, forbes@ecmwf.int
Cloud Resolving Models: Their development and their use in parametrization development
Richard Forbes,
Adrian Tompkins

2. Outline Why were cloud resolving models (CRMs) conceived?
What do they consist of?
How have they developed?
To which purposes have they been applied?
What is their future?
Cloud Resolving Models

3. Why were cloud resolving models conceived?
In the early 1960s there were three sources of information concerning cumulus clouds
Direct observations
E.G: Warner (1952)
Limited coverage of a few variables

4. Why were cloud resolving models conceived?
In the early 1960s there were three sources of information concerning cumulus clouds
Direct observations
Laboratory Studies
Realism of laboratory studies?
Difficulty of incorporating latent heating effects
Turner (1963)

5. Why were cloud resolving models conceived?
In the early 1960s there were three sources of information concerning cumulus clouds
Direct observations
Laboratory Studies
Theoretical Studies
Linear perturbation theories
Quickly becomes difficult to obtain analytical solutions when attempting to increase realism of the model

6. Why were cloud resolving models conceived?
In the early 1960s there were three sources of information concerning cumulus clouds
Laboratory Studies
Theoretical Studies
Analytical Studies
Obvious complementary role for Numerical simulation of convective clouds
Numerical integration of complete equation set
Allowing more complete view of ‘simulated’ convection

7. Outline Why were cloud resolving models conceived?
What do they consist of ?
Cloud Resolving Models

8. What is a CRM? The concept
GCM Grid cell ~100km
GCM grid too coarse to resolve convection - Convective motions must be parametrized
In a cloud resolving model, the momentum equations are solved on a finer mesh, so that the dynamic motions of convection are explicitly represented. But, with current computers this can only be accomplished on limited area domains, not globally!

9. What is a CRM? The physics
radiation SW IR
1. Momentum equations
2. Turbulence Scheme
dynamics
3. Microphysics
4. Radiation?
microphysics
turbulence
5. Surface Fluxes
surface
fluxes
Cloud Resolving Models

10. What is a CRM? The Issues
1. RESOLUTION: Dependence on turbulence formulation.
2. DOMAIN SIZE: Purpose of simulation.
3. LARGE-SCALE FLOW? Reproduction of observations? Lateral BCs.
4. DIMENSIONALITY: 2 or 3 dimensional dynamics?
5. TIME: Length of integration. 4 3 1 5 2
Cloud Resolving Models

11. Lateral Boundary Conditions
Early models used impenetrable Lateral Boundary Conditions
L Cloud development near boundaries affected by their presence
No longer in use
Periodic Boundary Conditions
J Easy to implement
J Model boundaries are ‘invisible’
L No mean ascent is allowable (W=0)
Open Boundary Conditions
J Mean vertical motion is unconstrained
L Very difficult to avoid all wave reflection at boundaries
L Difficult to implement, also need to specific BCs W

12. Spatial and Temporal Scales?
1. O(1km)
1. Deep convective updraughts
~30 minutes
3. O(10km)
3. Anvil cloud associated with one event
2. O(100m)
2. Turbulent Eddies
4. O(1000km)
4. Mesoscale convective systems, Squall lines, organised convection
days-weeks
Cloud Resolving Models

13. What do they consist of ? MICROPHYSICS SUBGRID-SCALE TURBULENCE
(ice and liquid phases)
SUBGRID-SCALE
TURBULENCE
RADIATION
(sometimes - Expensive!)
DYNAMICAL CORE
Open or periodic Lateral BCs
Lower boundary surface fluxes
Upper boundary Newtonian damping (to prevent wave reflection)
BOUNDARY
CONDITIONS

14. (ice and liquid phases)
What do they consist of ?
DYNAMICAL CORE
Prognostic equations for u,v,w,q,rv,(p)
affected by, advection, turbulence, microphysics, radiation, surface fluxes...
MICROPHYSICS
(ice and liquid phases)
Prognostic equations for bulk water categories: rain, liquid cloud, ice, snow, graupel… sometimes also their number concentration.
HIGHLY UNCERTAIN!!!
SUBGRID-SCALE
TURBULENCE
Attempt to parameterize flux of prognostic quantities due to unresolved eddies
Most models use 1 or 1.5 order schemes
ALSO UNCERTAIN!!!

15. Reference: Emanuel (1994), Atmospheric Convection
Basic Equations
Continuity:
This is known as the anelastic approximation, where horizontal and temporal density variations are neglected in the equation of continuity. Horizontal pressure adjustments are considered to be instantaneous. This equation thus becomes a diagnostic relationship.
This excludes sound waves from the equation solution, which are not relevant for atmospheric motions, and would require small timesteps for numerical stability. Based on Batchelor QJRMS (1953) and Ogura and Phillips JAS (1962)
Note: Although the analastic approximation is common, some CRMs use a fully elastic equation set, with a full or simplified prognostic continuity equation. See for example, Klemp and Wilhelmson JAS (1978), Held et al. JAS (1993).
Reference: Emanuel (1994), Atmospheric Convection
Cloud Resolving Models

16. Basic Equations Momentum: DYNAMICAL CORE Pressure Gradient Coriolis
Diabatic terms
(e.g. turbulence)
Mixing ratio of vapour and condensate variables
Buoyancy
Where:
Overbar = mean state
Since cloud models are usually applied to domains that are small compared to the radius of the earth it is usual to work in a Cartesian co-ordinate system The Coriolis parameter if applied, is held constant, since its variation across the domain is limited
Cloud Resolving Models

17. Basic Equations Thermodynamic: Equation of State: Moisture:
Diabatic processes:
Radiation
Diffusion
Microphysics (Latent heating)
Equation of State:
Moisture:
Microphysics terms
Condensation Evaporation
Cloud Resolving Models

18. All scales of motion present in turbulent flow
SUBGRID-SCALE
TURBULENCE
All scales of motion present in turbulent flow
Smallest scales can not be represented by model grid - must be parameterised.
Assume that smallest eddies obey statistical laws such that their effects can be described in terms of the “large-scale” resolved variables
Progress is made by considering flow, u, to consist of a resolved component, plus a local unresolved perturbation:
Doing this, eddy correlation terms are obtained: e.g.
Cloud Resolving Models

19. Dimensionless Constant = 0.02 -0.1
SUBGRID-SCALE
TURBULENCE
Many models used “First order closure” (Smagorinsky, MWR 1963)
Make analogy between molecular diffusion:
and likewise for other variables: v,r, etc…
K are the coefficients of eddy diffusivity
K set to a constant in early models
Improvements can be made by relating K to an eddy length-scale l and the wind shear.
Reference Cotton and Anthes, 1989
Storm and Cloud Dynamics
Dimensionless Constant =
Cloud Resolving Models

20. Reference: Stull(1988), An Introduction to Boundary Layer Meteorology
SUBGRID-SCALE
TURBULENCE
Length scale of turbulence related to grid-length
Further refinement is to multiply by a stability function based on the Richardson number: Ri. In this way, turbulence is enhanced if the air is locally unstable to lifting, and suppressed by stable temperature stratification
First order schemes still in use (e.g. U.K. Met Office LEM) although many current CRMs use a “One and a half Order Closure” - In these, a prognostic equation is introduced for the turbulence kinetic energy (TKE), which can then be used to diagnose the turbulent fluxes of other quantities.
Note: Krueger,JAS 1988, uses a more complex third order scheme
Reference: Stull(1988), An Introduction to Boundary Layer Meteorology
See Boundary Layer Course for more details!
Cloud Resolving Models

21. Microphysics
The condensation of water vapour into small cloud droplets and their re-evaporation can be accurately related to the thermodynamical state of the air.
However, the processes of precipitation formation, its fall and re-evaporation, and also all processes involving the ice phase (e.g. ice cloud, snow, hail) are:
Not completely understood
Operate on scales smaller than the model grid
Therefore parameterisation is difficult but important
Cloud Resolving Models

22. From Dare 2004, microphysical scheme at BMRC
Microphysics
Most schemes use a bulk approach to microphysical parameterization
Just one equation is used to model each category
qtotal
qrain
Warm - Bulk
qvap
qrain
qliq
qsnow
qgraup
qice
Ice - Bulk
Ice - Bin resolving
Different drop size bins

23. Microphysics For example: Fall speed of graupel Sources and sinks
For Example, (Lin et al. 1983) snow to graupel conversion
qsnow-crit = 10-3 kg kg-1
S =0 below this threshold
T0 =0oC
Not many papers mention numerics. Often processes are considered to be resolved by the O(10s) timesteps used in CRMs, and therefore a simple explicit solution is used; beginning of timestep value of qgraup used to calculate the RHS of the equation. If sinks result in a negative mass, some models reset to zero (i.e. not conserving).

24. Outline Why were cloud resolving models conceived?
What do they consist of?
How have they developed?
Cloud Resolving Models

25. HISTORY:1960s
One of the first attempts to numerically model moist convection made by Ogura JAS (1963)
Same basic equation set, neglecting:
Diffusion - Radiation - Coriolis Force
Reversible ascent (no rain production)
Axisymmetric model domain
3km by 3km
100m resolution
6 second timestep
3km
Warm air
bubble
100m

26. Possible 2D domain configurations
Axi-symmetric z r
Slab Symmetric z x
Motions function of r and z
+ Pseudo-”3D” motions (subsidence)
- No wind shear possible
- Difficult to represent cloud ensembles
Use continued mainly in hurricane modelling
Motions functions of x and z
+ can represent ensembles
- Lack of third dimension in motions
- Artificially changes separation scale
Still much used to date
For reference see Soong and Ogura JAS (1973)

27. significant proportion
Ogura 1963
7 Minutes
14 Minutes
Cloud reaches domain
top by 14 Minutes
Cloud occupies
significant proportion
of model domain
Liquid
Cloud

28. History:

29. Outline Why were cloud resolving models conceived?
What do they consist of?
How have they developed?
To which purposes have they been applied?
Cloud Resolving Models

30. 1990s really saw an expansion in the way in which CRMs have been used
Use of CRMs
1990s really saw an expansion in the way in which CRMs have been used
Long term statistical equilibrium runs -
Investigating specific process interactions
Testing assumptions of cumulus parametrization schemes
Developing aspects of parametrizations
Long term simulation of observed systems
All of the above play a role in the use of CRMs to develop parametrization schemes
Cloud Resolving Models

31. Uses: Radiative-Convective equilibrium experiments
Long term integrations until fields reach equilibrium
Radn cooling =
= convective heating
surface rain = moisture fluxes
Sample convective statistics of equilibrium, and their sensitivity to external boundary conditions
e.g Sea surface Temperature
Also allows one to examine process interactions in simplified framework
Computationally expensive since equilibrium requires many weeks of simulation to achieve equilibrium
2D: Asai J. Met. Soc. Japan (1988), Held et al. JAS (1993), Sui et al. JAS (1994), Grabowski et al. QJRMS (1996), 3D: Tompkins QJRMS (1998), J. Clim. (1999)

32. Uses: Investigating specific process interactions
Large scale organisation:
Gravity Waves: Oouchi, J. Met. Soc. Jap (1999)
Water Vapour: Tompkins, JAS, (2001)
Cloud-radiative interactions:
Tao et al. JAS (1996)
Convective triggering in Squall lines:
Fovell and Tan MWR (1998)
USE CRM TO INVESTIGATE A CERTAIN PROCESS THAT IS PERHAPS DIFFICULT TO EXAMINE IN OBSERVATIONS
UNDERSTANDING THIS PROCESS ALLOWS AN ATTEMPT TO INCLUDE OR REPRESENT IT IN PARAMETRIZATION SCHEMES

33. Example: 350m resolution 3D CRM simulation used in a variety of parametrization ways
Used to understand coldpool triggering
Used to set closure parameters for a simplified cloud model
Tompkins JAS 2001
Di Giuseppe & Tompkins JAS 2003
Used as a cloud-field proxy to develop parametrization to correct radiative geometrical biases
Used to justify PDF decision in cloud scheme of ECHAM5
Tompkins JAS 2002
90 km
Di Giuseppe & Tompkins JGR 2003, JAS2005
Tompkins & di Giuseppe 2006

34. Uses: Testing Cumulus Parametrization schemes
Parametrizations contain representations of many terms difficult to measure in observations
e.g. Vertical distribution of convective mass fluxes for mass-flux schemes
Assume that despite uncertain parametrizations (e.g. microphysics, turbulence), CRMs can give a reasonable estimate of these terms.
Gregory and Miller QJRMS (1989) is a classic example of this, where a 2D CRM is used to derive all the individual components of the heat and moisture budgets, and to assess approximations made in convective parametrization schemes.

35. Gregory and Miller QJRMS 1989
Updraught,
Downdraught,
non-convective
and net
cloud mass fluxes
They compared these profiles to the profiles assumed in mass flux parameterization schemes - concluded that the downdraught entraining plume model was a good one for example – but note resolution issues.

36. Uses: Developing aspects of parametrization schemesCC
cloud cover
relative humidity
cloud mixing ratio
The information can be used to derive statistics for use in parametrization schemes
E.g. Xu and Randall, JAS (1996) used CRM to derive a diagnostic cloud cover parameterisation where

37. Uses: Developing Parametrization Schemes
GCMs - SCMs
CRMs
OBSERVATIONS
Validation (and development)
Validation
(and development)
Validation
(and development)
Provide extra quantities not available from data

38. CRMs
OBSERVATIONS
Validation
For example, Grabowski (1998) JAS performed week-long simulations of convection during GATE, in 3D with a 400 by 400 km 3D domain.
Simulation
Observations
Simulation
All types of convection developed in response to applied forcing - Could be considered a successful validation exercise?

39. Simulation of Observed Systems
Still controversy about the way to apply “Large-scale forcing”
Relies on argument of scale separation (as do most convective parametrization schemes)
CRM domain W
With periodic BCs must have zero mean vertical velocity. Normal to apply terms:

40. Simulation of Observed Systems
An observational array measures the mean mass flux.
If an observational array contains a convective event, but is not large enough to contain the subsidence associated with this event, then the measured “large scale” mean ascent will also contain a component due to the net cumulus mass flux Mc
Radiosonde stations
measure

41. GCSS - GEWEX Cloud System Study (Moncrieff et al. Bull. AMS 97)
PARAMETERISATION
GCMS - SCMS
GCSS - GEWEX Cloud System Study (Moncrieff et al. Bull. AMS 97)
CRMs
OBSERVATIONS
Use observations to evaluate parameterizations of subgrid-scale processes in a CRM
Step 1
Evaluate CRM results against observational datasets
Step 2
Use CRM to simulate precipitating cloud systems forced by large-scale observations
Step 3
Evaluate and improve SCMs by comparing to observations and CRM diagnostics
Step 4

42. Simulations from different models (total hydrometeor content)
GCSS: Validation of CRMs Redelsperger et al QJRMS 2000 SQUALL LINE SIMULATIONS
Simulations from different models
(total hydrometeor content)
Observations - Radar
Open BCs
Periodic BCs
Open BCs
Open BCs
Conclude that only 3D models with ice and open BCs reproduce structure well

43. GCSS: Comparison of many SCMs with a CRM Bechtold et al QJRMS 2000 SQUALL LINE SIMULATIONS

44. Issues of this approach
Confidence is gained in the ability of the SCMs and CRMs to simulate the observed systems
Sensitivity tests can show which physics is central for a reasonable simulation of the system… But…
Is the observational dataset representative?
What constitutes a good or bad simulation? Which variables are important and what is an acceptable error?
Given the model differences, how can we turn this knowledge into improvements in the parameterization of convection?
Is an agreement between the models a sign of a good simulation, or simply that they use similar assumptions? (Good Example: Microphysics)

45. Outline Why were cloud resolving models conceived?
What do they consist of?
How have they developed?
To which purposes have they been applied?
What is their future?
Cloud Resolving Models

46. Future - Issues Fundamental issues remain unresolved: Resolution?
At 1 or 2 km horizontal resolution much of the turbulent mixing is not resolved, but represented by the turbulence scheme.
Indications are that CRM ‘solutions’ have not converged with increasing horizontal resolution at 100m.
Dimensionality
2D slab symmetric models are still widely used, despite contentions to their ‘numerical cheapness’
Representation of microphysics?
Representing interaction with large scale dynamics?
Re-emergence of open BCs?

47. Cloud Resolving Convective Parametrization 2D CRMs in a global model
Grabowski and Smolarkiewicz, Physica D Places a small 2D CRM (roughly 200km, simple microphysics, no turbulence) in every grid-point of the global model
Still based on scale separation and non-communication between grid-points
Advantages and Disadvantages?
From Khairoutdinov, illustrating multimodelling framework developed at CSU

48. Cloud Resolving Convective Parametrization 2D CRMs in a global model
CAM
CRCP
OBS
Improves diurnal cycle
and tropical variability?

49. Convective-scale Limited Area NWP Example of 1km UK Met Office Unified Model (MetUM) Simulation of Thunderstorms on 25th Aug 2005

50. Convective-scale Limited Area NWP Example of 1km UK Met Office Unified Model (MetUM) Simulation of Thunderstorms on 25th Aug 2005, UTC
Model simulated OLR and surface rain rate
Meteosat low resolution infra-red and radar-derived surface rain rate

51. Convective-scale Limited Area NWP Example of 1km UK Met Office Unified Model (MetUM) Simulation of Thunderstorms on 25th Aug 2005, UTC
MODIS 13:10 UTC
Model simulated OLR and surface rain rate
MODIS high resolution visible image

52. Global “CRMs”
Global cloud resolving model simulations? Or at least cloud-permitting model simulations
3.5 km resolution 7 day forecast of the NICAM global model on the Earth Simulator (FRCGC, JAMSTEC)
Miura et al., (2007), Geophys. Res. Lett., vol. 34.
Courtesy of M. Satoh

53. Summary
CRMs have been proven as very useful tools for simulating individual systems and in particular for investigating certain process interactions.
They can also be used to test and develop parametrization schemes since they can provide supplementary information such as mass fluxes not available from observational data.
However, if they are to be used to develop parametrization schemes, it is necessary to keep their limitations in mind (turbulence, microphysics)
not a substitute for observations, but complementary
Care should be taken in the experimental design!
Large scale forcing
The distinctions between traditional CRMs, limited area NWP and even GCMs is beginning to blur!

54. Summary - Feedback Welcome! forbes@ecmwf.int
LECTURE 1: Discussed microphysical processes. Examined the basic issues that must be considered when considering cloud parameterisation.
LECTURE 2: We focussed on cloud cover, and in particular on statistical schemes which diagnose cloud cover from knowledge of the subgrid- scale variability of T and qt .
LECTURE 3: Overview of the ECMWF cloud scheme.
LECTURE 4: We considered some different methods of cloud validation with their respective strengths and weaknesses.
LECTURE 5: Discussed what Cloud Resolving Models are and how they have been used for parametrization development.
Cloud Resolving Models