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How to represent subgrid atmospheric processes in Climate |Models
Multiscale PhysicsRegional Climate Division
A. Pier [email protected]
Faculty for Applied SciencesClimate Research
The Climate System: A Multiscale Challenge:
Landsat 65km
LES 10km
~mm ~1m~1m-100m
Earth 107 m
Courtesy: Harm Jonker, TU Delft
3
10 m 100 m 1 km 10 km 100 km 1000 km 10000 km
turbulence Cumulus
clouds
Cumulonimbus
clouds
Mesoscale
Convective systems
Extratropical
Cyclones
Planetary
waves
Large Eddy Simulation (LES) Model
Cloud System Resolving Model (CSRM)
Numerical Weather Prediction (NWP) Model
Global Climate Model
No single model can encompass all relevant processes
DNS
mm
Cloud microphysics
Architecture of a Global Climate Model
Unresolved (subgrid) Processes in Climate Models
Source: ECMWF Model documentation
Climate Model Sensistivity estimates of GCM’s participating in IPCC AR4
Source: IPCC Chapter 8 2007
• Spread in climate sensitivity:
concern for many aspects of climate change research, assesment of climate extremes, design of mitigation scenarios.
What is the origin of this spread?
Radiative Forcing, Climate feedbacks,
Relative Contributions to the uncertainty in climate feedbacks
Source: Dufresne & Bony, Journal of Climate 2008
Radiative effects only
Water vapor feedback
Surface albedo feedback
Cloud feedback
Uncertainty in climate sensitivity mainly due to (low) cloud feedbacks
8
Governing Equations for incompressible flows in the atmosphere
2
2
j
i
iu
j
ij
i
x
u
x
pF
x
uu
t
ui
2
2
jjj
xF
xu
t
2
2
jqq
jj
x
qF
x
qu
t
q
0
i
i
x
u
vdTRp
Continuity Equation
(incompressible)
NS Equations
Heat equation
Moisture equation
Gas law
jcijiu ufFi 33 with
gravity
term
coriolis
term
Condensed water eq.2
2
j
lqq
j
lj
l
x
qF
x
qu
t
qll
9
rll
ll
vv
vv
radp
Pecqwzz
qwq
t
q
ecqwzz
qwq
t
q
Qecc
Lwzz
wt
v
v
v
Large scale Large scale
advectionadvection
Large scale Large scale
subsidencesubsidence
Vertical Vertical turbulent/ turbulent/ convective convective transporttransport
Net Net Condensation Condensation RateRate
Filtered Equations for the Thermodynamic Variables
Radiative heating
Precipitation
resolved
subgrid
Resolved
Scales
turbulence
~ 250 km
convection
clouds
radiation
Small scales Large scales
Schematic View of how scales are connected in traditional GCM’s
Depiction of the interaction between resolved and parameterized unresolved cloud-related processes (convection, turbulence, clouds and radiation) in present-day climate models. (from Siebesma et al, Perturbed Clouds in our climate system MIT)
Which are the problems, errors and uncertainties that we have to face with this approach?
1. Inherent lack of understanding of certain physical processes
< 100 m [100,600m] >800m
Source : Andrew Heymsfield
Uncertainties in ice and mixed phase microphysics:
•Supersaturation
•Liquid vs ice
•Habits
•Size distribution
•Sedimentation
•Interaction with radiation
No fundamental equations available describing these properties and processes.
2. Non-linear character of many cloud related processes
crlcrl qqHqqKA
With:
ql : cloud liquid water
ql : critical threshold
H : Heaviside function
A : Autoconversion rate
: Kessler Autoconversion Rate (Kessler 1969)
Example 1: Autoconversion of cloud water to precipitation in warm clouds
Autoconversion rate is a convex function:
_______
ll qAqA
Larson et al. JAS 2001
Example 2: Cloud fraction and Cloud liquid water
ststc qqHqqHa ______________
(Thijs Heus TU Delft/KNMI) LES
qsat
qt
T
qsat(T)
qt .(T,qt)
Cloud fraction:
ststststl qqHqqqqHqqq _________________________
Cloud liquid water:
Plane parallel cloud
Scu
Clo
ud a
lbedo
Liquid water path (LWP)
x
x
a
a(LWP) < a(LWP)
Neglecting Cloud inhomogeneity causes a positive bias in the cloud albedo.
Example 3: Cloud Albedo Bias
•These biased errors slowly go away when increasing model resolution:
LWPLWP x 0
•Typically allowed if x < 100m , i,e, at the LES model scale
•So for all models operating at a coarser resolution additional information about the underlying Probability Density Function (pdf) is required of temperature, humidity (and vertical velocity).
),,( wqTP t
dTdqTqqHTqPqqHa tsttstc )(),(______________
For Example:
So if only….. we would know the pdf .
Resolved
Scales
turbulence
~ 250 km
convection
clouds
radiation
Small scales Large scales
3. Interactions between the various subgrid processes
•Subgrid processes strongly interact with each other while in (most) GCM’s they only interact indirectly through the mean state leading to inconsistencies and biases.
17
4. Statistical versus Stochastic Convection 4. Statistical versus Stochastic Convection
~500km
•Traditionally (convection) parameterizations are deterministic:
•Instantaneous grid-scale flow and mean state is taken as input and convective response is deterministic
•One to one correspondency between sub-grid state and resolved state assumed.
•Conceptually assumes that spatial average is a good proxy for the ensemble mean.
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4. Statistical versus Stochastic Convection4. Statistical versus Stochastic Convection
resolution
100m 1km 1000km100km
Convection
Explicitly
resolved
Statistical ensemble mean
Deterministic convection
parameterization
Stochastic Convection
That takes into account fluctuations so that the ensemble mean is not satisfied each timestep but more in a canonical sense Microcanonical limit
19
New Pathways
20
Resolved
Scales
3.5 km
turbulence
convection
clouds
radiation
Pathway 1: Global Cloud Resolving Modelling (Brute Force)
NICAM simulation: MJO DEC2006 NICAM simulation: MJO DEC2006 ExperimentExperiment
MTSAT-1R NICAM 3.5km
Miura et al. (2007, Science)
3.5km run: 7 days from 25 Dec 2006
•Short timeslices
•Testbed for interactions:
deep convection and the large scale•Boundary clouds, turbulence, radiation still unresolved
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Pathway 2: Superparameterization
2D
CRM
turbulence
(b)
convection
clouds
radiation
5 km 250 km
Resolved
Scales
22
Pathway 2: Superparameterization
What do we get? •Explicit deep convection
•Explicit fractional cloudiness
•Explicit cloud overlap and possible 3d cloud effects
•Convectively generated gravity waves
But…..
A GCM using a super-parameterization is three orders of magnitude more expensive than a GCM that uses conventional parameterizations.
On the other hand super-parameterizations provide a way to utilize more processors for a given GCM resolution
Boundary Layer Clouds, Microphysics and Turbulence still needs to be parameterized
23
Remarks:
Resolved
Scales
turbulence
convection
clouds
radiation
~100 km Large scalesUnresolved scales
Resolved
Scales
vuqv ,,,
Pathway 3: Consistent pdf based parameterizations
Increase consistency between the parameterizations!
How?
Let’s have a closer look at the subgrid variability and the way this is treated in tradiational parameterizations
24T
qsat(T)
qt .(T,qt)
Statistical Cloud Schemes (1):
•Estimate ac and ql using the subgrid variability:
25
Statistical Cloud Schemes (2):
Convenient to introduce:
“The distance to the saturation curve”
),( Tpqqs st
Normalise s by its variance:
sst
So that ac and ql can be written in a single variable PDF:
0 0
)(,)( dtttGqdttGa slc
What to choose for G(t) ???
26
Statistical Cloud Schemes (3):
Gaussian Case: dttdttG )2exp(2
1)( 2
)2exp(2
1
))2/(1(21
2ttaq
terfa
csl
c
Cloud cover and liquid water function of only one variable!!!!
s
st qqtQ
Sommeria and Deardorf (JAS,1976)
27
Verification (with LES)
s
st qqtQ
Cloud cover
Bechtold and Cuijpers JAS 1995
Bechtold and Siebesma JAS 1999
28
Verification (with Observations)
Wood and Field (unpublished)
29
Remarks:
• Correct limit: if and the scheme converges to the all-or-nothing limit
• Parameterization problem reduced to finding the subgrid variability, i.e. finding .
00 sthendx
s
30
Convective transport in Shallow Cumulus: Characteristics
Courtesy Bjorn Stevens
LESHeus
TU Delft
31
Typical Mean ProfilesHorizontal Variability
Upward transport by moist buoyant cumulus cores
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less distinct updrafts in subcloud layer
)()( cc
ceawwawaw 1 )()( cc
ceawwawaw 1
a
wc
aa
)( cM )( cM
Strong bimodal character of joint pdf has inspired the design of mass flux parameterizations of turbulent flux in Large scale models
(Betts 1973, Arakawa& Schubert 1974, Tiedtke 1988)
34
vvcc
tcc
gBaBwb
z
w
z
M
M
qz
0
22
l
,2
1
1
,for)(
vvcc
tcc
gBaBwb
z
w
z
M
M
qz
0
22
l
,2
1
1
,for)(
M
The old working horse:
Entraining plume model:
Plus boundary conditions
at cloud base.
How to estimate updraft fields and mass
flux? Betts 1974 JAS
Arakawa&Schubert 1974 JAS
Tiedtke 1988 MWR
Gregory & Rowntree 1990 MWR
Kain & Fritsch 1990 JAS
And many more……..
35
•Double counting of processes
•Inconsistencies
•Problems with transitions between different regimes:
dry pbl shallow cu
scu shallow cu
shallow cu deep cu
This unwanted situation can lead to:
Swzt
zKw )( uMw
Standard transport parameterization approach:
36
Remarks:
Resolved
Scales
turbulence
convection
clouds
radiation
~100 km Large scalesUnresolved scales
Resolved
Scales
vuqv ,,,
Intermezzo (2)
Increase consistency between the parameterizations!
How?
37
zinv
•Nonlocal (Skewed) transport through strong updrafts in clear and cloudy boundary layer by advective Mass Flux (MF) approach.
•Remaining (Gaussian) transport done by an Eddy Diffusivity (ED) approach.
Advantages :
•One updraft model for : dry convective BL, subcloud layer, cloud layer.
•No trigger function for moist convection needed
•No switching required between moist and dry convection needed
Eddy-Diffusivity/Mass Flux approach : a way out?
38
Cumulus clouds are the condensed, visible parts of updrafts that are deeply rooted in the subcloud mixed layer (ML)
LeMone & Pennell (1976, MWR)
39
zinv
The (simplest) Mathematical Framework :
)(
)()1(
u
euuu
e
u
u
u
Mz
K
wawawaw
40
Figure courtesy of Martin Koehler
Cumulus Topped Boundary Layer
Neggers, Kohler & Beljaars accepted for JAS 2009
alternatives: Lappen and Randall JAS 2001
Rio and Hourdin JAS 2008
Dry updraft
Moist updraft
K diffusion
Top 10 % of updrafts that is explicitly modelled
Flexible moist area fraction
N
iiiPBL M
zKw
1
)(''
18 April 2023
•Assume a Gaussian joint PDF(l,qt,w) shape for the cloudy updraft.
•Mean and width determined by the multiple updrafts
•Determine everything consistently from this joint PDF
utulu qwa ,, ,,,
Remarks:
•No closure at cloud base
•No detrainment parameterization
•Pdf can be used for cloud scheme and radiation
An reconstruct the flux:
uuuwaw________
42
Convection and turbulence parameterization give estimate of s
)(
)(
s
stl
s
stc
qqgq
qqfa
Cloud scheme : radiation scheme :
),( stqR
•Subgrid variability (at least the 2nd moment) for the thermodynamic variables needs to be taken into acount in any GCM for parameterizations of convection, clouds and radiation in a consistent way.
•At present this has not be accomplished in any GCM.
43
But… Many open problems remain
•Convective Momentum Transport
•Influence of Aerosols/Precipitation on the (thermo)dynamics of Scu and Cu
•Mesoscale structures in Scu and Shallow Cu
•Transition from shallow to deep convection (deep convective diurnal cycle in tropics)
Conceptually on process basis
Parameterization
•Vertical velocity in convective clouds
•Convection on the 1km~10km scale. (stochastic convection)
•Microphysicis (precip)
•Transition regimes.
Climate
Determine and understand the processes that are responsable for the uncertainty in cloud-climate feedback.
44
A slow, but rewarding Working Strategy
Large Eddy Simulation (LES) Models
Cloud Resolving Models (CRM)
Single Column Model
Versions of Climate Models
3d-Climate Models
NWP’s
Observations from
Field Campaigns
Global observational
Data sets
Development Testing Evaluation
See http://www.gewex.org/gcss.html
18 April 2023
l
qt
qsat
Cloudfraction
Condensate
SCMLES
Tested for a large number of GCSS Cases………………..
46
A slow, but rewarding Working Strategy
Large Eddy Simulation (LES) Models
Cloud Resolving Models (CRM)
Single Column Model
Versions of Climate Models
3d-Climate Models
NWP’s
Observations from
Field Campaigns
Global observational
Data sets
Development Testing Evaluation
See http://www.gewex.org/gcss.html
