how to represent subgrid atmospheric processes in climate |models multiscale physics regional...

How to represent subgrid atmospheric processes in Climate |Models

Multiscale PhysicsRegional Climate Division

A. Pier Siebesmasiebesma@knmi.nl

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.

18

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

21

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

32

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