Transcript Numerical Weather Prediction Parametrization of diabatic

Cloud Resolving Models:
Their development and their use in
parameterisation development
Adrian Tompkins, [email protected]
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?
• 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
• 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 to incorporate
latent heating effects
Turner (1963)
• 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
• 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
Outline
• Why were cloud resolving models
conceived?
• What do they consist of ?
What is a CRM?
The concept
GCM Grid cell ~100km
• GCM grid too coarse to
resolve convection Convective motions must
be parameterised
• 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
radiation
SW
IR
1. Momentum equations
2. Turbulence Scheme
3. Microphysics
dynamics
4. Radiation?
microphysics 5. Surface Fluxes
surface
fluxes
turbulence
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? Open BCs?
4. DIMENSIONALITY: 3 dimensional dynamics?
5. TIME: Length of integration
1
5
3
2
4
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
W
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
Spatial and Temporal Scales?
1. Deep convective
updraughts
~30 minutes
3. O(10km)
2. Turbulent Eddies
2. O(100m)
1. O(1km)
4. O(1000km)
days-weeks
3. Anvil cloud
associated with one
event
4. Mesoscale
convective
systems, Squall
lines, organised
convection
•What do they consist of ?
MICROPHYSICS
(ice and liquid phases)
SUBGRID-SCALE
TURBULENCE
RADIATION
(sometimes - Expensive!)
DYNAMICAL CORE
BOUNDARY
CONDITIONS
Open or periodic Lateral BCs
Lower 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
MICROPHYSICS
(ice and liquid phases)
Prognostic equations for u,v,w,q,rv,(p)
affected by, advection, turbulence, microphysics,
radiation, surface fluxes...
Prognostic equations for bulk water categories:
rain, liquid cloud, ice, snow, graupel…
sometimes also their number concentration.
HIGHLY UNCERTAIN!!!
SUBGRID-SCALE
TURBULENCE
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:

x
( u) 

y
( v) 

z
( w)  0
•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:
Du
Dt
Dv
Dt
Dw
Dt
Pressure
Gradient
Coriolis
1 p
 x
1 p
 y
 fv  Fx
 fu  Fy



DYNAMICAL CORE
1 p
 z
g
q  q 
q
Diabatic terms
(e.g. turbulence)
 Fz
Mixing ratio of vapour and liquid water
Where: qD  q (1  0.608rV  rL )
Dt
 t  u x  v y  w z
Buoyancy
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
Basic Equations
• Thermodynamic: Dq
Dt
– Diabatic processes:
 Qq  Fq  L(c  e)
• Radiation
• Diffusion
• Microphysics (Latent heating)
p  RT
 Frv  (c  e)
 FrL  (c  e)
• Equation of State:
• Moisture:
Drv
Dt
DrL
Dt
Condensation
Evaporation
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 “largescale” resolved variables
• Progress is made by considering flow, u, to consist of a
resolved component, plus a local unresolved perturbation:
u  u  u
• Doing this, eddy correlation terms are obtained: e.g.
q
t

1 
 x j
(  ujq )
SUBGRID-SCALE
TURBULENCE
• Many models used “First order closure” (Smagorinsky, MWR 1963)
• Make analogy between molecular diffusion:
u jq    Kq
q
x j
• 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 lengthscale l and the wind shear.
Reference Cotton and Anthes, 1989
Storm and Cloud Dynamics
Dimensionless Constant = 0.02 -0.1
2 ui
q
x j
Kq  c l

u j
xi
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 12 uj uj (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!
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
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
Warm - Bulk
qtotal
qrain
Ice - Bulk
qvap
qrain
Ice - Bin
resolving
Different drop size bins
qliq
qsnow
qgraup
qice
Numerics of Microphysics
For example:
Dqgraup
Dt
S
1 d
Vgraup qgraup 
 dz
Fall speed of graupel
Sources and sinks
For Example, (Lin et al. 1983) snow to graupel conversion
Ssnow graupel  103 e0.09(T T0 ) (qsnow  qsnow crit )
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;
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)
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:
3km
– Diffusion - Radiation - Coriolis Force
– 3km by 3km
– 100m resolution
– 6 second timestep
3km
• Reversible ascent (no rain production)
• Axisymmetric model domain
Warm air
bubble
100m
Possible 2D domain configurations
Axi-symmetric
Slab Symmetric
r
z
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)
Ogura 1963
7 Minutes
14 Minutes
Cloud reaches
domain
top by 14
Minutes
Liquid
Cloud
Cloud
occupies
significant
proportion
of model
domain
History:
1960s -
1970s
1980s
1990s-present
Equation set
Basic dynamics
Turbulence
+ Warm rain
microphysics
+ ice phase
microphysics
Integration
length
10 minutes
hours
Many hours
+ radiation (?)
+ 1.5 order
turbulence closure
+improved
advection schemes
Days - weeks
Domain size
2D: O(10km)
2D: O(100km)
3D: O(202 km)
Open BCs
2D: O(200km) 2D: O(103 – 104km)
3D: O(302 km) 3D:O(2002 km)
Open/Periodic Open/Periodic BCs
BCs
Aim
Simulate single
-Single clouds,
Cloud development -Several cloud
lifecycles
-Comparisons
with
observations
3D animation example
Many varying
applications!
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
• 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)
Tompkins JAS 2001,
convective-water vapour feedback
Sui et al. JAS 1994
Analysis of the hydrological cycle:
Note dependence on Microphysics
Uses: Investigating specific
process interactions
• Large scale
organisation:
– Gravity Waves: Oouchi,
J. Met. Soc. Jap (1999)
– Water Vapour: Tompkins,
JAS, (2001)
USE CRM TO INVESTIGATE A
CERTAIN PROCESS THAT IS
PERHAPS DIFFICULT TO EXAMINE IN
OBSERVATIONS
• Cloud-radiative
interactions:
– Tao et al. JAS (1996)
• Convective triggering in
Squall lines:
– Fovell and Tan MWR
(1998)
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
CC
CC  F ( RH , rl )
cloud cover
relative humidity
CC
cloud mixing ratio
rl
Uses: Developing
Parameterization Schemes
PARAMETERISATION
GCMS - SCMS
Validation (and
development)
Validation (and
development)
CRMs
Provide extra quantities
not available from data
Validation
OBSERVATIONS
Simulation
Observations
Validation
OBSERVATIONS
For example, Grabowski (1998) JAS performed
week-long simulations of convection during GATE, in
3D with a 400 by 400 km 3D domain.
CRMs
Simulation
All types of convection developed in response to applied forcing Could be considered a successful validation exercise?
Simulation of Observed Systems
• Still controversy about the way to apply “Largescale forcing”
• Relies on argument of scale separation (as do
most convective parameterisation schemes)
With periodic BCs must have zero
mean vertical velocity. Normal to
apply terms:
W
CRM domain
 w ,w
dq
dz
drv
dz
Note inconsistency between subsidence
in model and observations. Require open
BCs to allow consistent treatment
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
Mc
~
M
Radiosonde stations
measure
~
M  M  Mc
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
• 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.)
(see Emanuel, Atmospheric Convection, 1994, Emanuel, Mapes 1997 NATO ASI)
How can we proceed?
Mc
~
M
(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
GCSS - GEWEX Cloud
System Study
(Moncrieff et al. Bull. AMS 97)
PARAMETERISATION
GCMS - SCMS
CRMs
OBSERVATIONS
Step 1
Use observations to evaluate parameterizations of
subgrid-scale processes in a CRM
Step 2
Evaluate CRM results against observational datasets
Step 3
Use CRM to simulate precipitating cloud systems forced by
large-scale observations
Step 4
Evaluate and improve SCMs by comparing to
observations and CRM diagnostics
GCSS: Validation of CRMs
Redelsperger et al QJRMS 2000
SQUALL LINE SIMULATIONS
Observations - Radar
Simulations (total hydrometeor content)
Open BCs
Open BCs
Conclude that only 3D
models with ice and open
BCs reproduce structure well
Periodic BCs
Open BCs
GCSS: Comparison of many SCMs with a
CRM
Bechtold 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 gridpoints
– Advantages are:
• explicit cloud radiation interactions
• no trigger or closure requirement
– Disadvantages?
Cost!
CRCP
CAM
CRCP
OBS
Claim improves tropical variability
Further improvements?