KNMI

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How to represent subgrid atmospheric processes in
Climate Models
A. Pier Siebesma siebesma_at_knmi.nl
Faculty for Applied Sciences
Climate Research
Multiscale Physics
Regional Climate Division
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The Climate System A Multiscale Challenge
Earth 107 m
Courtesy Harm Jonker, TU Delft
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No single model can encompass all relevant
processes
10 m
100 m
1 km
10 km
100 km
1000 km
10000 km
mm
Cloud microphysics
turbulence
?
Cumulus clouds
Cumulonimbus clouds
Mesoscale Convective systems
Extratropical Cyclones
Planetary waves
DNS
Large Eddy Simulation (LES) Model
Subgrid
Cloud System Resolving Model (CSRM)
Numerical Weather Prediction (NWP) Model
Global Climate Model
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Architecture of a Global Climate Model
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Unresolved (subgrid) Processes in Climate Models
Source ECMWF Model documentation
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Climate Model Sensistivity estimates of GCMs
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,
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Relative Contributions to the uncertainty in
climate feedbacks
Cloud feedback
Surface albedo feedback
Water vapor feedback
Radiative effects only
Source Dufresne Bony, Journal of Climate 2008
Uncertainty in climate sensitivity mainly due to
(low) cloud feedbacks
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Governing Equations for incompressible flows in
the atmosphere
Continuity Equation (incompressible)
with
NS Equations
gravity term
coriolis term
Heat equation
Moisture equation
Condensed water eq.
Gas law
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Filtered Equations for the Thermodynamic Variables
subgrid
Radiative heating
resolved
Precipitation
Net Condensation Rate
Large scale advection
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Schematic View of how scales are connected in
traditional GCMs
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?
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1. Inherent lack of understanding of certain
physical processes
100,600mm
lt 100 mm
gt800mm

• 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.
Source Andrew Heymsfield
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2. Non-linear character of many cloud related
processes
Example 1 Autoconversion of cloud water to
precipitation in warm clouds
Kessler Autoconversion Rate (Kessler 1969)
With ql cloud liquid water ql critical
threshold H Heaviside function A
Autoconversion rate
Autoconversion rate is a convex function
Larson et al. JAS 2001
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Example 2 Cloud fraction and Cloud liquid water
(Thijs Heus TU Delft/KNMI) LES
Cloud fraction
Cloud liquid water
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Example 3 Cloud Albedo Bias
Neglecting Cloud inhomogeneity causes a positive
bias in the cloud albedo.
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• These biased errors slowly go away when
  increasing model resolution

• Typically allowed if ?x lt 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).

For Example
So if only.. we would know the pdf .
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3. Interactions between the various subgrid
processes

• Subgrid processes strongly interact with each
  other while in (most) GCMs they only interact
  indirectly through the mean state leading to
  inconsistencies and biases.

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4. Statistical versus Stochastic Convection

• 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.

500km
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4. Statistical versus Stochastic Convection
Stochastic Convection That takes into account
fluctuations so that the ensemble mean is not
satisfied each timestep but more in a canonical
sense
Statistical ensemble mean Deterministic
convection parameterization
Microcanonical limit
Convection Explicitly resolved
100m
1km
1000km
100km
resolution
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New Pathways
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Pathway 1 Global Cloud Resolving Modelling
(Brute Force)
NICAM simulation MJO DEC2006 Experiment
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

MTSAT-1R
NICAM 3.5km
Miura et al. (2007, Science)
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Pathway 2 Superparameterization
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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
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Remarks
Pathway 3 Consistent pdf based parameterizations
turbulence
Resolved Scales
convection
Resolved Scales
clouds
radiation
Large scales
100 km
Unresolved scales
Increase consistency between the
parameterizations! How? Lets have a closer look
at the subgrid variability and the way this is
treated in tradiational parameterizations
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Statistical Cloud Schemes (1)

• Estimate ac and ql using the subgrid variability

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Statistical Cloud Schemes (2)
Convenient to introduce The distance to the
saturation curve
Normalise s by its variance
So that ac and ql can be written in a single
variable PDF
What to choose for G(t) ???
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Statistical Cloud Schemes (3)
Gaussian Case
Cloud cover and liquid water function of only one
variable!!!!
Sommeria and Deardorf (JAS,1976)
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Verification (with LES)
Cloud cover
Bechtold and Cuijpers JAS 1995 Bechtold and
Siebesma JAS 1999
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Verification (with Observations)
Wood and Field (unpublished)
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Remarks
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Convective transport in Shallow Cumulus
Characteristics
Courtesy Bjorn Stevens
LES Heus TU Delft
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Typical Mean Profiles
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(No Transcript)
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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)
wc
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How to estimate updraft fields and mass flux?
Betts 1974 JAS ArakawaSchubert 1974
JAS Tiedtke 1988 MWR Gregory Rowntree 1990
MWR Kain Fritsch 1990 JAS And many more..
The old working horse
Entraining plume model
Plus boundary conditions at cloud base.
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Standard transport parameterization approach
This unwanted situation can lead to

• Double counting of processes
• Inconsistencies
• Problems with transitions between different
  regimes
• dry pbl ? shallow cu
• scu ? shallow cu
• shallow cu ?deep cu

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Remarks
Intermezzo (2)
turbulence
Resolved Scales
convection
Resolved Scales
clouds
radiation
Large scales
100 km
Unresolved scales
Increase consistency between the
parameterizations! How?
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Eddy-Diffusivity/Mass Flux approach a way out?

• 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

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• LeMone Pennell (1976, MWR)

Cumulus clouds are the condensed, visible parts
of updrafts that are deeply rooted in the
subcloud mixed layer (ML)
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The (simplest) Mathematical Framework
zinv
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Cumulus Topped Boundary Layer
Neggers, Kohler Beljaars accepted for JAS
2009 alternatives Lappen and Randall JAS
2001 Rio and Hourdin JAS
2008
Figure courtesy of Martin Koehler
Moist updraft
Dry updraft
K diffusion
Flexible moist area fraction
Top 10 of updrafts that is explicitly modelled
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• Assume a Gaussian joint PDF(ql,qt,w) shape for
  the cloudy updraft.
• Mean and width determined by the multiple
  updrafts
• Determine everything consistently from this joint
  PDF

An reconstruct the flux

• Remarks
• No closure at cloud base
• No detrainment parameterization
• Pdf can be used for cloud scheme and radiation

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Convection and turbulence parameterization give
estimate of ss
radiation scheme
Cloud scheme

• 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.

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But Many open problems remain
Conceptually on process basis

• 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)

Parameterization

• Vertical velocity in convective clouds
• Convection on the 1km10km scale. (stochastic
  convection)
• Microphysicis (precip)
• Transition regimes.

Climate
Determine and understand the processes that are
responsable for the uncertainty in cloud-climate
feedback.
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A slow, but rewarding Working Strategy
See http//www.gewex.org/gcss.html
Large Eddy Simulation (LES) Models Cloud
Resolving Models (CRM)
Single Column Model Versions of Climate Models
3d-Climate Models NWPs
Global observational Data sets
Observations from Field Campaigns
Development
Testing
Evaluation
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Tested for a large number of GCSS Cases..
?l
qsat
qt
Cloud fraction
Condensate
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A slow, but rewarding Working Strategy
See http//www.gewex.org/gcss.html
Large Eddy Simulation (LES) Models Cloud
Resolving Models (CRM)
Single Column Model Versions of Climate Models
3d-Climate Models NWPs
Global observational Data sets
Observations from Field Campaigns
Development
Testing
Evaluation