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

parameterisation developmentparameterisation development

Adrian Tompkins, tompkins@ecmwf.intAdrian Tompkins, tompkins@ecmwf.int

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?

• In the early 1960s there were three sources of information concerning cumulus clouds– Direct observations

• Why were cloud resolving models conceived?

E.G: Warner (1952)

Limited coverage of a few variables

• In the early 1960s there were three sources of information concerning cumulus clouds– Direct observations– Laboratory Studies

• Why were cloud resolving models conceived?

Realism of laboratory studies?

Difficulty to incorporate latent heating effects

Turner (1963)

• In the early 1960s there were three sources of information concerning cumulus clouds– Direct observations– Laboratory Studies– Theoretical Studies

• Why were cloud resolving models conceived?

• Linear perturbation theories• Quickly becomes difficult to obtain analytical

solutions when attempting to increase realism of the model

• 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?

Outline

• Why were cloud resolving models conceived?

• What do they consist of ?

What is a CRM?The concept

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

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!

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?

What is a CRM?The Issues1. RESOLUTION: Dependence on turbulence formulation

1

2. DOMAIN SIZE: Purpose of simulation3. LARGE-SCALE FLOW? Reproduction of observations? Open BCs?4. DIMENSIONALITY: 3 dimensional dynamics?

2

34

5. TIME: Length of integration

5

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

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

•What do they consist of ?

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 ?

Your notes contain more details on the following:

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 parameterization flux of prognostic quantities due to unresolved eddies

Most models use 1 or 1.5 order schemes

ALSO UNCERTAIN!!!

Basic Equations

• Continuity:

0)()()(

wvu zyx

•This is known as the analastic 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

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

1

Buoyancy)608.01( LV 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 liquid water

• 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

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.

SUBGRID-SCALETURBULENCE

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

• Make analogy between molecular diffusion:

jxj Ku

• and likewise for other variables: u,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

• 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!

MICROPHYSICS

• The condensation of water vapour into small cloud droplets and their re-evaporation can be accurately related to the thermodynamics 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 well understood• Operate on scales smaller than the model grid• Therefore parameterisation is difficult but important

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

Numerics of 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; begin of timestep value of qgraup are used to calculate the RHS of the equation. If sinks result in a negative mmr, simply reset to zero (I.e. no conservation is imposed)

qsnow-crit = 10-3 kg kg-1

S =0 below this threshold

T0 =0oC

Outline

• Why were cloud resolving models conceived?

• What do they consist of?

• How have they developed?

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

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)

Ogura 1963

LiquidCloud

7 Minutes 14 Minutes

Cloud reaches domain

top by 14 Minutes

Cloud occupies

significant proportionof model domain

History:1960s - 1970s 1980s 1990s-present

Equation set Basic dynamicsTurbulence

+ Warm rainmicrophysics

+ ice phasemicrophysics

+ radiation (?)

+ 1.5 orderturbulence closure+improvedadvection schemes

Integrationlength

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/PeriodicBCs

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

Aim Simulate singleCloud development

-Single clouds,-Several cloudlifecycles

-Comparisonswithobservations

Many varyingapplications!

3D animation example

Outline

• Why were cloud resolving models conceived?

• What do they consist of?

• How have they developed?

• To which purposes have they been applied?

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 parameterisation

schemes• Developing aspects of parameterisations• Long term simulation of observed systems

• All of the above play a role in the use of CRMs to develop parameterization schemes

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

Sui et al. JAS 1994Analysis of the hydrological cycle:

Note dependence on Microphysics

Tompkins JAS 2001, convective-water vapour

feedback

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 PARAMETERIZATION SCHEMES

Example: Animation of coldpool triggering

Uses: Testing Cumulus Parameterisation schemes• Parameterisations 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 parameterisations (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 parameterization schemes

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.

Uses: Developing Aspects of parameterizations schemes

• The information can be used to derive statistics for use in parameterisation 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

Uses: Developing Parameterization Schemes

PARAMETERISATION

GCMS - SCMS

CRMs OBSERVATIONSValidation

Validation (and development)

Validation (and development)

Provide extra quantities not available from data

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

Simulation of Observed Systems• Still controversy about the way to apply “Large-

scale forcing”• Relies on argument of scale separation (as do

most convective parameterisation schemes)

CRM domain

W

With periodic BCs must have zero mean vertical velocity. Normal to

apply terms:

dzdr

dzd vww ,

Note inconsistency between subsidence in model and observations. Require open BCs to allow consistent treatment

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

Simulation of Observed Systems

• Thus part of the atmospheric cooling (destabilisation) due to the observed “large-scale” ascent will in fact be a result of the observed convection• This could lead to convection in the simulation.

Good? Not really!

Why not?

• Because we are not testing the ability of our model to simulate convection! Perhaps a key process essential for the presence of the convection (e.g. orography or triggering due to cold pool outflow) is missing or misrepresented in our model. And yet the presence of convection in the observations leads us to simulate convection

Uses: Simulation of Observed Systems

(see Emanuel, Atmospheric Convection, 1994, Emanuel, Mapes 1997 NATO ASI)

• However, examination of other unconstrained quantities is possible, for a more objective analysis

• A good example is the water vapour transport of convection, which is unconstrained, and difficult to represent (microphysics), and therefore comparing the moisture evolution is a more stringent test of CRM simulations (or indeed convective parameterisation schemes.)

How can we proceed?

(1) We require a large enough domain such that all subsidence is contained within it, thus only the “large-scale” component is

measured - THIS RELIES ON THE EXISTENCE OF SCALE SEPARATION(2) We only describe our best guess at the initial conditions, do not

apply any forcing but USE A MODEL WITH OPEN BCs so that the mean vertical velocity is able to evolve with time. But neglects time-varying

LARGE-SCALE flow, which may be important (e.g. MJO). Approach adopted by GCSS

(3) NEW APPROACH OF MODIFYING “LARGE-SCALE” FORCING IN RESPONSE TO LATENT HEATING SIMULATED IN CRM

Bergman, John W., Sardeshmukh, Prashant D. 2004: Dynamic Stabilization of Atmospheric Single Column Models. J. of Climate: 17, pp. 1004-1021

M~

cM

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

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

Observations - Radar Open BCs

Open BCsOpen BCs

Periodic BCs

Simulations (total hydrometeor content)

Conclude that only 3D models with ice and open

BCs reproduce structure well

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

CRM

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)

Summary

• CRMs have been proven as much useful tools for simulating individual systems and in particular for investigating certain process interactions

• They can also be used to test and develop parameterisation 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 parameterisation schemes 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

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?

Future 1

• 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?

Future 2

• Global cloud resolving model simulations?– Earth Simulator (2km Global resolution aim)

• Cloud resolving convective parameterisation(CRCP)?– 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 are: • explicit cloud radiation interactions• no trigger or closure requirement

– Disadvantages?

Cost!

CRCP

CAM CRCP OBS

Claim improves tropical variability

Further improvements?