Cloud Resolving Models:Cloud Resolving Models:Their development and their use in Their development and their use in

parametrization developmentparametrization development

Richard Forbes, Richard Forbes, forbes@ecmwf.int Adrian TompkinsAdrian Tompkins

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OutlineOutline

1.1. Why were cloud resolving models (CRMs) Why were cloud resolving models (CRMs) conceived?conceived?

2.2. What do they consist of?What do they consist of?

3.3. How have they developed?How have they developed?

4.4. To which purposes have they been To which purposes have they been applied? applied?

5.5. What is their future?What is their future?

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• 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

Why were cloud resolving models conceived?

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• 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)

Why were cloud resolving models conceived?

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• 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

Why were cloud resolving models conceived?

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• 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

Why were cloud resolving models conceived?

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OutlineOutline

1.1. Why were cloud resolving models Why were cloud resolving models conceived? conceived?

2.2. What do they consist of ?What do they consist of ?

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What is a CRM?The concept

GCM grid too coarse to resolve convection - Convective motions must be parametrized

GCM Grid cell ~100km

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!

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What is a CRM?The physics

dynamics

radiation

turbulence

microphysics

SWIR 1. Momentum equations

surfacefluxes

2. Turbulence Scheme

5. Surface Fluxes

3. Microphysics

4. Radiation?

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What is a CRM?The Issues

1. RESOLUTION: Dependence on turbulence formulation.

1

2. DOMAIN SIZE: Purpose of simulation.3. LARGE-SCALE FLOW? Reproduction of observations? Lateral BCs.4. DIMENSIONALITY: 2 or 3 dimensional dynamics?

2

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5. TIME: Length of integration.

5

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Lateral Boundary Conditions

W

Early models used impenetrable Lateral Boundary Conditions

Cloud development near boundaries affected by their presence

No longer in use

Periodic Boundary Conditions

Easy to implement

Model boundaries are ‘invisible’

No mean ascent is allowable (W=0)

Open Boundary Conditions

Mean vertical motion is unconstrained

Very difficult to avoid all wave reflection at boundaries

Difficult to implement, also need to specific BCs

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Spatial and Temporal Scales?

1. O(1km)

1. Deep convective updraughts

2. O(100m)

2. Turbulent Eddies3. O(10km)

3. Anvil cloud associated with one event

4. O(1000km)

4. Mesoscale convective systems, Squall lines, organised convection

~30 minutes

days-weeks

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DYNAMICAL CORE

MICROPHYSICS(ice and liquid phases)

SUBGRID-SCALETURBULENCE

BOUNDARYCONDITIONS

RADIATION(sometimes - Expensive!)

Open or periodic Lateral BCsLower boundary surface fluxes

Upper boundary Newtonian damping (to prevent wave reflection)

What do they consist of ?

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DYNAMICAL CORE

Prognostic equations for u,v,w,,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-SCALETURBULENCE

Attempt to parameterize flux of prognostic quantities due to unresolved eddies

Most models use 1 or 1.5 order schemes

ALSO UNCERTAIN!!!

What do they consist of ?

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Basic Equations

• Continuity:

0)()()(

wvu zyx

• 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

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Basic Equations

• Momentum:

xxp

DtDu Ffv

1

yyp

DtDv Ffu

1

zyxtDtD wvu

Where:

Diabatic terms(e.g. turbulence)

CoriolisPressureGradient

Overbar = mean state

zzp

DtDw Fg

v

vv

1

Buoyancy)608.01( LVv rr

DYNAMICAL CORE

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

Mixing ratio of vapour and condensate variables

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• Moisture:

Basic Equations

• Thermodynamic:– Diabatic processes:

• Radiation• Diffusion• Microphysics (Latent heating)

)( ecLFQDtD

RTp ...)( ecF

v

v

rDtDr

• Equation of State:

...)( ecFL

L

rDtDr

Condensation Evaporation

Microphysics terms

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SUBGRID-SCALETURBULENCE

• 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: uuu

)(1

jxt uj

• Doing this, eddy correlation terms are obtained: e.g.

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SUBGRID-SCALETURBULENCE

• Many models used “First order closure” (Smagorinsky, MWR 1963)

• Make analogy between molecular diffusion:

jxj Ku

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.

i

j

j

i

x

u

xulcK

2

Dimensionless Constant = 0.02 -0.1

Reference Cotton and Anthes, 1989

Storm and Cloud Dynamics

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• 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

SUBGRID-SCALETURBULENCE

jjuu 21

Reference: Stull(1988), An Introduction to Boundary Layer Meteorology

See Boundary Layer Course for more details!

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• 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

Microphysics

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Microphysics

• Most schemes use a bulk approach to microphysical parameterization

• Just one equation is used to model each category

qtotal qrainWarm - Bulk

qvap qrain qliq qsnow qgraup qice Ice - Bulk

Ice - Bin resolving

Different drop size bins

From Dare 2004, microphysical scheme at BMRC

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Microphysics

graupgraupgraup qV

dz

dS

Dt

Dq

1

For example:

Sources and sinksFall speed of graupel

For Example, (Lin et al. 1983) snow to graupel conversion

)(10 )(09.03 0critsnowsnow

TTgraupelsnow qqeS

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).

qsnow-crit = 10-3 kg kg-1

S =0 below this threshold

T0 =0oC

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OutlineOutline

1.1. Why were cloud resolving models Why were cloud resolving models conceived?conceived?

2.2. What do they consist of?What do they consist of?

3.3. How have they developed?How have they developed?

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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 airbubble3k

m

100m

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Possible 2D domain configurations

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

Axi-symmetric

z

r

Slab Symmetric

z

x

For reference see Soong and Ogura JAS (1973)

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Ogura 1963

LiquidCloud

7 Minutes 14 Minutes

Cloud reaches domain

top by 14 Minutes

Cloud occupies

significant proportionof model domain

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History:

1960s - 1970s

1980s 1990s-present

Equation set Basic dynamics Turbulence

+ Warm rain microphysics

+ ice phase microphysics

+ radiation (?) + 1.5 order turbulence closure +improved advection schemes

Integration length

10 minutes hours Many hours Days - weeks

Domain size

2D: O(10km) 2D: O(100km) 3D: O(202 km) Open BCs

2D: O(200km) 3D: O(302 km) Open/Periodic BCs

2D: O(103 – 104km) 3D:O(2002 km) Open/Periodic BCs

Aim Simulate single Cloud development

-Single clouds, -Several cloud lifecycles

-Comparisons with observations

Many varying applications!

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OutlineOutline

1.1. Why were cloud resolving models Why were cloud resolving models conceived?conceived?

2.2. What do they consist of?What do they consist of?

3.3. How have they developed?How have they developed?

4.4. To which purposes have they To which purposes have they been applied?been applied?

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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

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Uses: Radiative-Convective equilibrium experiments

• 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)

• Long term integrations until fields reach equilibrium

Radn cooling =

surface rain = moisture fluxes

= convective heating

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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

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Example: 350m resolution 3D CRM simulation used in a variety of parametrization ways

90 km

Used to understand

coldpool triggering

Used as a cloud-field proxy to develop

parametrization to correct radiative

geometrical biases

Used to set closure parameters for a simplified cloud model

Tompkins JAS 2001

Di Giuseppe & Tompkins JGR 2003, JAS2005

Tompkins & di Giuseppe 2006

Di Giuseppe & Tompkins JAS 2003

Used to justify PDF decision in cloud scheme of ECHAM5Tompkins JAS 2002

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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.

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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.

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Uses: Developing aspects of parametrization schemes

• 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

),( lrRHFCC

CC

CC

cloud cover

relative humidity cloud mixing ratio lr

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Uses: Developing Parametrization Schemes

PARAMETRIZATION

GCMs - SCMs

CRMs OBSERVATIONSValidation

(and development)

Validation (and development)

Validation (and development)

Provide extra quantities not available from data

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Simulation Observations

Simulation

All types of convection developed in response to applied forcing - Could be considered a successful validation exercise?

For example, Grabowski (1998) JAS performed week-long simulations of convection during GATE, in 3D with a 400 by 400 km 3D domain.

CR

Ms

OB

SE

RV

AT

ION

SV

alid

atio

n

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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:

dzdr

dzd vww ,

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Simulation of Observed Systems

M~

Radiosonde stationsmeasure

cMMM ~

• 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

cM

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GCSS - GEWEX Cloud System Study (Moncrieff et al. Bull. AMS 97)

Use observations to evaluate parameterizations of subgrid-scale processes in a CRMStep 1

Evaluate CRM results against observational datasetsStep 2

Use CRM to simulate precipitating cloud systems forced by large-scale observationsStep 3

Evaluate and improve SCMs by comparing to observations and CRM diagnostics

Step 4

PARAMETERISATION

GCMS - SCMS

CRMs OBSERVATIONS

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GCSS: Validation of CRMsRedelsperger et al QJRMS 2000SQUALL LINE SIMULATIONS

Observations - Radar Open BCs

Open BCsOpen BCs

Periodic BCs

Simulations from different models(total hydrometeor content)

Conclude that only 3D models with ice and open

BCs reproduce structure well

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GCSS: Comparison of many SCMs with a CRMBechtold et al QJRMS 2000 SQUALL LINE SIMULATIONS

CRM

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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)

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OutlineOutline

1.1. Why were cloud resolving models Why were cloud resolving models conceived?conceived?

2.2. What do they consist of?What do they consist of?

3.3. How have they developed?How have they developed?

4.4. To which purposes have they been To which purposes have they been applied? applied?

5.5. What is their future?What is their future?

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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?

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– Grabowski and Smolarkiewicz, Physica D 1999. 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 m

ultimodelling

framew

ork developed at CS

U

Cloud Resolving Convective Parametrization 2D CRMs in a global model

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CAM

CRCP

OBS

Improves diurnal cycle and tropical variability?

Cloud Resolving Convective Parametrization 2D CRMs in a global model

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

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Convective-scale Limited Area NWPExample of 1km UK Met Office Unified Model (MetUM) Simulation of Thunderstorms on 25th Aug 2005, 13 UTC

Model simulated OLR and surface rain rate

Meteosat low resolution infra-red and radar-derived surface rain rate

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MODIS 13:10 UTC

Convective-scale Limited Area NWPExample of 1km UK Met Office Unified Model (MetUM) Simulation of Thunderstorms on 25th Aug 2005, 13 UTC

Model simulated OLR and surface rain rate

MODIS high resolution visible image

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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

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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!

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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.