cloud resolving models: their development and their use in parameterisation development adrian...
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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?
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