thoughts on statistical cloud schemes denver 2004 a.tompkins 1 some thoughts on statistical cloud...

Thoughts on statistical cloud schemes Denver 2004 A.Tompkins1

Some thoughts on statistical cloud

schemes

Some thoughts on statistical cloud

schemes

Adrian Tompkins, ECMWFAdrian Tompkins, ECMWF

With Contributions from:

Rob Pincus (NOAA-CIRES Climate Diagnostics Center)

Georg Bauml (Max Plank Institut fur Meteorologie, Hamburg)

…and my cloud “mentor” Steve Klein

Plus material stolen from Jean-Christoph Golaz and Vince Larson…

ADRIAN

a recipe for seafood laksa soup

a recipe for seafood laksa soup


So just what will I speak about?So just what will I speak about?

Some background things (preparing the ingredients)

Statistical cloud schemes (the laksa paste)

My scheme (so hands off !) (the soup)

Level of complexity required? (noodles)

Linking with other model components (combining the ingredients)

Conclusions and future developments? (presentation)


Some Background

things

Some Background

things

Preparing the ingredients…

Clean fish, slice garlic and chilli finely, grate ginger and palm sugar, toast and grind cumin and coriander

seeds

Preparing the ingredients…

Clean fish, slice garlic and chilli finely, grate ginger and palm sugar, toast and grind cumin and coriander

seeds


~50

0m

~100km

Issues of ParameterizationIssues of Parameterization

HORIZONTAL COVERAGE, CMost of this talk will concentrate on this issue


~50

0m

~100km


VERTICAL COVERAGEMost models assume that this is 1

This can be a poor assumption with coarse vertical grids.


~50

0m

~100km


Vertical overlap of cloudImportant for Radiation and Microphysics Interaction


Issues of ParameterizationIssues of Parameterization~

500m

~100km

cloud inhomogeneity


~50

0m

~100km


Just these issues can become very complex!!!


Horizontal Cloud Cover: The ProblemHorizontal Cloud Cover: The Problem

Local criterion for existence of cloud:

qtotal > qsat (T,p)

This assumes that no supersaturation can exist

(poor assumption for ice clouds)

Partial coverage of a grid-box with clouds is only possible if there is a inhomogeneous distribution of temperature and/or

humidity

Homogeneous distribution of water vapour and temperature:

Cloud cover zero or one

2,sq

q

x

q

1,sq

One Grid-cell


Horizontal Cloud Cover: The ProblemHorizontal Cloud Cover: The Problem

Heterogeneous distribution

of T and q…

q

x

q

sq

…clouds exist before the grid-mean relative humidity reaches 100%


Diagnostic Relative Humidity SchemesDiagnostic Relative Humidity Schemes

Many schemes, from the mid 1970s onwards, based cloud cover on the relative humidity (RH):

E.g. Sundqvist et al. MWR 1989

0111 RH

RHCC

RH0 = critical relative humidity at which cloud assumed to form,

(function of height, typical value above BL is 60%)

CC(cloud fraction)

1

Relative humidity

RH0 100



Since these schemes form cloud when RH<100%, they implicitly assume subgrid-scale variability for total water, qt, (and/or temperature, T) existsHowever, the actual PDF (the shape)

for these quantities and their variance (width) are often not known“Given a RH of X% in nature, the

mean distribution of qt is such that, on average, we expect a cloud cover of Y%”



Advantages:Better than homogeneous assumption,

since clouds can form before grids reach saturation

Disadvantages:Cloud cover not well coupled to other

processesIn reality, different cloud types with

different coverage can exist with same relative humidity. This can not be represented


Aside:Aside:


Statistical Cloud Schemes

Laksa Paste

Squish garlic, chilli, coriander and cumin, shrimp paste, coconut

crème, tumeric, lemongrass, palm sugar

in food processor

Statistical Cloud Schemes

Laksa Paste

Squish garlic, chilli, coriander and cumin, shrimp paste, coconut

crème, tumeric, lemongrass, palm sugar

in food processor


Total Water qt=vapour + liquid + iceqsat

G(qt)Cloudy Region

qv ql+qi

1. The PDF form G(qt) 2. The moments of the distribution3. The mean saturation mixing ratio qsat

Cloud cover can be derived

Horizontal GCM grid pointsStatistical Schemes for Cloud

ParameterizationStatistical Schemes for Cloud

Parameterization


Statistical schemesStatistical schemes

Based on Mellor JAS 77 and Sommeria and Deardorff JAS 77, and much development by Bougeault, 81, 82…

Two tasks: Specification of the:

(1) PDF

(2) PDF momentsPDF of what?


Statistical SchemesStatistical Schemes

Some schemes just take variability of total water into account, and assume temperature is homogeneous

sq

tt dqqGC )(

Examples: Le Treut and Li, Clim Dyn 91, Bony and Emanuel, JAS 01, Tompkins JAS 02

qt

G(q

t)

qs

x

y

C

PROBABLY REASONABLE ABOVETHE PBL, especially in the tropics where

gravity waves remove temperature perturbations efficiently


Statistical SchemesStatistical Schemes

Others form variable ‘s’ that also takes temperature variability into account, which affects qs

)( LtL Tqas

LsL T

T

q

1

1

L

pL C

La

LCL

L qTTp

LIQUID WATER TEMPERATUREconserved during changes of state

ss

dssGC )(

S is simply the ‘distance’ from the linearized saturation vapour pressure curve

qs

T

qt

LT

S

INCREASES COMPLEXITYOF IMPLEMENTATION

Cloud mass if Tvariation is neglected


Role of temperature variabilityRole of temperature variability

Previous slide implicitly neglected temperature

variability

Reasonable but not robust assumption as this ARM SGP site

data shows

Tompkins 2003, QJRMS


TASK 1: Specification of the PDFTASK 1: Specification of the PDFLack of observations to determine PDF

Aircraft data Limited coverage e.g. Ek and Mahrt (91), Wood and Field JAS (00), Larson et al.

JAS (01)Tethered balloon

Boundary layer e.g. Price QJ (01)

Satellite Difficulties resolving in vertical e.g. Barker et al. JAS (96)

Cloud Resolving models have also been used Realism of microphysical parameterisation? e.g. Bougeault JAS(82), Lewellen and Yoh JAS (93), Xu and

Randall JAS (96), Tompkins JAS (02)


CRM dataCRM data

qt

G(qt)

Tompkins JAS 02CRM data

90x90x21km 3D domain350m horizontal resolution

Instantaneous scene

Fairly UnimodalSmooth

PBL negative skewness Detrainment from

downdraughtsAbove PBL positive

skewness - Detrainment from updraughts

qsat


Balloon and Satellite PDFsBalloon and Satellite PDFs

Price QJRMS 2001Example Balloon data

PBL humidity

Barker et al. JAS 1996PDF of Liquid Water Path (LWP)

28km horizontal resolution - Large Cloud Cover scenes:

SmoothUnimodal

Greater sampling possibilities


Aircraft Observed PDFsAircraft Observed PDFs

Wood and field JAS 2000Aircraft observations low clouds < 2km

qt

G(qt)

Hei

ght

qt ql T

Hemysfield and McFarlane JAS 98Aircraft IWC obs during CEPEX


They used aircraft data to test many different PDF forms:

One of the most

comprehensive

investigations of suitable

PDFs

JAS 2001

One of the most

comprehensive

investigations of suitable

PDFs

JAS 2001


Problems with using assumed PDFProblems with using assumed PDF

1. Cloud water 2. humidity 3. total water varianceTake 3 piecesof information

Throw oneaway

1. total water mean 2. total water variance

Use this info tofit assumed PDF

Extract humidityand cloud water

q-satCloud cover

1. Cloud water 2. humidityDifferentValues!!!


Found multi parameter

multimodal PDF gave smallest error

The (many) defining parameters have to

be specified in a scheme

Found multi parameter

multimodal PDF gave smallest error

The (many) defining parameters have to

be specified in a scheme


They used aircraft and LES data to test 5 different PDF

forms:

They went further to examine joint PDFs:

J. Atmos. Sci. 2002

They went further to examine joint PDFs:

J. Atmos. Sci. 2002


Examined examples of joint PDFsExamined examples of joint PDFs


Tested errors for each form

Tested errors for each form

Lewellen and Yoh best but

requires iteration

Lewellen and Yoh best but

requires iteration

Note: these figures are

not absolute but depend on

closure assumptions

Note: these figures are

not absolute but depend on

closure assumptions


TASK 1: Specification of PDFTASK 1: Specification of PDF

Many function forms have been used

Symmetrical distributions:

Triangular:Smith QJRMS (90)

s or qt

s or qt

Gaussian:Mellor JAS (77)

s or qt

G(s

or

q t)

Uniform:Letreut and Li (91)

s or qt

s4 polynomial:Lohmann et al. J. Clim (90)


TASK 1: Specification of PDFTASK 1: Specification of PDF

skewed distributions:

s or qt

G(s

or

q t)

Exponential:Sommeria and Deardorff JAS (77)

Lognormal:

Bony & Emanuel JAS (01)

s or qt s or qt

Gamma:Barker et al. JAS (96)

s or qt

Beta:Tompkins JAS (02)

s or qt

Double Normal:Lewellen and Yoh JAS (93)

Golaz bimodal Gaussian


TASK 2: Specification of PDF momentsTASK 2: Specification of PDF moments

Need also to determine the moments of the distribution:Variance (Symmetrical PDFs)Skewness (Higher order PDFs)

s or qt

G(s

or

q t)

e.g. HOW WIDE?

saturation

cloud forms?


C

sq

1-C


Some schemes fix the moments (e.g. Smith 1990) based on critical RH at which clouds assumed to form

If moments (variance, skewness) are fixed, then statistical schemes can be reduced to a RH formulation

esv qCCqq )1(

tq

(1-RH0)qs

qt

G(q

t)eq

20 )1)(1(1 CRH

q

qRH

s

v

0111 RH

RHC Sundqvist formulation!!!

))1)(1(1( 0 CRHqq se where

Solution for Smith scheme more complex



Some schemes use the turbulence parameterisation to determine T’L and q’t , their correlation and thus also s’.

T’L , q’tExample: Ricard and Royer, Ann Geophy,

(93), Lohmann et al. J. Clim (99)

Disadvantage:Can give good estimate in boundary layer, but

above, other processes will determine variability

Lohmann et al. (who used this turbulence approach to set the PDF variance) found it necessary to impose a

minimum variance above the planetary boundary layer


Golaz scheme chooses double Gaussian 115 defining parameters, reduced to 10 through closures

E.g. skewness of T is zero, skewness of qtot fixed ratio of w

10 prognostic equations for moments E.g. w,q,T, q’T’, T’T’ etc…

Advection by large-scale flowSubgrid turbulence

Creation of variance by subgrid motions

Dissipation


Clouds in GCMs - Processes that can affect distribution moments

Clouds in GCMs - Processes that can affect distribution moments

convection

turbulence

dynamics

microphysics


Golaz et al. were able to neglect some terms

Golaz et al. were able to neglect some terms

2

222

2tqmicrot

ttt q

z

qw

z

qqw

Dt

qD

Production of variance by unresolved motions in the presence of a vertical gradientThis includes both convective and turbulent motions

Dissipation term

Includes advection by theresolved flow

Transport of variance byunresolved motions

Change due to microphysical processes


Production of varianceProduction of variance

For convective motions? )( tutct qqMqw

Depends on definition of variance, above relevant if variance of whole grid box is considered

If it is the environmental variance then only affected by detrainment al la Tiedtke.

Steve Klein outlines how to tackle this with a mass flux convection scheme in a GCSS preprint from 2003


Production of varianceProduction of variance

Courtesy of Steve Klein:

Change due to difference in variance

Change due to difference in means

Transport

Also equivalent terms due to entrainment


Variance of updraughtsVariance of updraughts

Requires closure of variance of updraft air (implicitly zero in the Tiedtke approach)

Simply carry variance as a passive tracer in mass flux

scheme


Steve Klein diagnosed these terms from a 2D CRM model

Steve Klein diagnosed these terms from a 2D CRM model

Equal?

Skewness terms can be derived in similar way


MicrophysicsMicrophysics

Change in variance

However, the tractability depends on the PDF form for the subgrid fluctuations of q, given by G:

Where P is the precipitation generation rate, e.g:

tqP nlKqP

)1()( qlcrit

ql

eKqP l

tt

q

qq

t dqqGqPt

satt

)(max_

Can get p

retty nasty!!!

Depending on form

for P

and G


Autoconversion loss from one level is straightforward, provided G(qt) and P

are simple

Autoconversion loss from one level is straightforward, provided G(qt) and P

are simple

tt

q

qq

t dqqGqPt

satt

)(max_

0.0 0.2 0.4 0.6 0.8 1.0Normalis$d tim$st$p

0

2*10-7

4*10-7

6*10-7

8*10-7

1*10-6

ql v

aria

nc$

Explicit integration of microphysicsVs integration of simple variance term


But quickly can get untractableBut quickly can get untractable

E.g: Semi-Langrangian ice sedimentionSource of

variance in bottom layer is trickyIn reality of

course wish also to retain the sub-flux variability too


My Scheme

The soup

Fry laksa paste for 3 minutes,

then add coconut milk and stock, simmer for 15

minutes

My Scheme

The soup

Fry laksa paste for 3 minutes,

then add coconut milk and stock, simmer for 15

minutes


Prognostic Statistical SchemePrognostic Statistical Scheme

Tompkins JAS (02) introduced a scheme for GCM (ECHAM5)

Prognostic equations are introduced for the variance and skewness of the total water PDF

These, specify both the shape and width of the PDF, allowing the cloud cover to be diagnosed.

A full treatment of the variance equation is included, with the third order skewness treated in an simplified way

AND IF YOU BELIEVE THAT, YOU WILL BELIEVE ANYTHING!!!

In fact, a short cut was taken to circumnavigate the microphysics and convective detrainment terms

(And ok, you got me, I admit it, the skewness budget was ‘botched’)


• POSITIVE / NEGATIVE SKEWNESS POSSIBLE, also SYMMETRIC• LIMITED FUNCTION• UNIMODAL

Prognostic Statistical SchemePrognostic Statistical Scheme

• Scheme uses the Beta distribution for qt variability• Justified from use of CRM data (observations agree-ish)• Temperature variations are ignored.

101

11

10

)(

)()(

),(

1)(

qp

tt

qtt

ptt

t qq

qqqq

qpBqG

qtqt0 qt1

G(q

t)

Stupid assumption No1 – Fix p=constant


Which prognostic equations?Which prognostic equations?

Take a 2 parameter distribution & Partially cloudy conditions

qsat

Cloud cover

qsat Cloud coverCan specify distribution with(a) Mean(b) Varianceof total water

Can specify distribution with(a) Water vapour(b) Cloud watermass mixing ratio

qv ql+i


Which prognostic equations?Which prognostic equations?qsat(a) Water vapour

(b) Cloud watermass mixing ratio

qv ql+i

qsat

qv qv+ql+i

• Cloud water budget conserved• Avoids Detrainment term• Avoids Microphysics terms (almost)

But problems arise in

Clear sky conditions

(turbulence)

Overcast conditions

(…convection +microphysics)(al la Tiedtke)


Which prognostic equations?Which prognostic equations?

Take a 2 parameter distribution & Partially cloudy conditions

qsat

(a) Mean(b) Varianceof total water

• “Cleaner solution”• But conservation of liquid water compromised due to PDF• Need to parametrize those tricky microphysics terms!


Governing equations must be chosen with care…

Governing equations must be chosen with care…

Combine the advantages of the above two by using a flexible PDF that involves one extra degree of freedom in partially cloudy conditions.

:o) Cloud budget ensured :o) Consistent treatment of Variance Equation:o) Allows BIMODALITY for example in partially

cloudy conditions:o( PDF more complex:o( Requires parameterization of those tricky

variance termsPDF form devised (double Beta distribution) on beach

in Gianova Lido, near Pescara, in summer 2002 under a yellow and red striped umbrelloni

But…Tested with ARM aircraft data Failure… since cloud/vapour is a variance type – PDF

was not flexible enough to find a solution. (failure rate>90%)


The scheme has five governing prognostic equations

The scheme has five governing prognostic equations

Prognostic equations for:

1. * Cloud liquid water

2. * Cloud ice

3. * Water vapour

4. Variance of qtot

5. * “Skewness” of qtot * = truly prognostic and

used to fit PDF in partially cloudy conditions, otherwise variance is used

Processes represented:

1. Deep convective detrainment

2. Microphysics

3. Turbulence

4. Advection

5. Dissipation


Partially cloudyPartially cloudy

* ql

* qv

* q’t3

q’t2

* ql

* qv

* q’t3

q’t2

Time=i Time=i+1

Slaving of varianceSubset process (turbulence)

* = used to define PDF giving cloud cover


Clear sky or OvercastClear sky or Overcast

ql

qv

* q’t3

* q’t2

ql

qv

* q’t3

* q’t2

Time=i Time=i+1

Subset process (turbulence)

* = used to define PDF giving cloud cover

* *


Variance equation of Tompkins(2002)Variance equation of Tompkins(2002)

2

222

2tqmicrot

ttt q

z

qw

z

qqw

Dt

qD

Production of variance by unresolved motions in the presence of a vertical gradientThis includes turbulent motions only

Dissipation term

Includes advection by theresolved flow

Transport of variance byunresolved motions

Change due to microphysical processes

EFFECT OF VARIANCE CHANGES ADDED TO CLOUD AND VAPOUR BUDGETS


Production of variance Production of variance

z

qqw tt 2 Vertical gradient of qt is known

For turbulent motions the flux termis already calculated in the turbulencescheme

tqw


Transport of VarianceTransport of Variancez

qw t

2

For convective motions, simple advective term: z

qgM

z

qw tc

t

22

For turbulent motions we parameterize the transport in terms of e (TKE) as in a typical 1.5 order closure z

qe

z

qw tt

22

Eddy length scale


Dissipation of VarianceDissipation of Variance

)( 1122

2

hvtt

qq

qt

Dissipation defined as Newtonian relaxation, with the timescale

resulting from two processes:

Process 1: 3D Turbulence

ev

After Garrat, Atmospheric Boundary Layer,

1992, who suggests =7.44

Implicit in this is the assumption that the eddy length scale also describes the length-scale of the total water perturbations. This is not a good assumption above the PBL, where qt perturbations will occur on much larger scales

MESOSCALE FLUCTUATIONS

Thus, only applied in PBL - Results in a short time-scale (~10 minutes), and this is solved implicitly to avoid numerical instabilities


Aside: Mesoscale fluctuations Aside: Mesoscale fluctuations

Fluctuations occur on length scales comparible to grid length.Upscale cascade from

turbulenceGravity wavesSubgrid instabilities (cloud

top instabilities)……It is clear that modals are

deficient in representing these

E.g: Lohmann shows inadequacy of ECMWF model, and how enhancement of turbulence activity can produce improved spectra

From haag and Kaerchner

ECMWF resolved motions only

aircraft


Dissipation of VarianceDissipation of Variance

Process 2: Horizontal Mixing

GCM grid cell

x

Large-scale wind shear

Horizontal wind shear will cause mixing (destruction of qt variance) even if stable temperature stratification suppresses vertical turbulence

xtq /2

Use simple order 1 closureAssume the scale of the moisture variability occurs on gridscale - The internal horizontal moisture flux which destroys variance is proportion to the moisture gradient which is approximated by , where x is the grid length.

222

y

v

x

uch

x

t

ihq

q

xt

212

Subgrid-scale qt flux


But this variance change then needs to be translated into equivalent changes in

cloud and vapour variables, (also discussed by Larson 2004)

But this variance change then needs to be translated into equivalent changes in

cloud and vapour variables, (also discussed by Larson 2004)

Implied Source/Sink of ice/liquid cloud water taken into account

Fro

m L

arso

n


The generation of cloud by cooling or warming also has to be consistent with

the PDF

The generation of cloud by cooling or warming also has to be consistent with

the PDF

qv ql+i

qsat

qv ql+i

qsat


Skewness Budget: ConvectionSkewness Budget: Convection

convection Convective updraught detrainment increases the skewness of total water by introducing air with

high water contents

Change of skewness linearly related to detrained cloud mass flux

at the moment

3D CRM Results

Long Distribution Tail from convective detrainment


It gets worse: Skewness budgetIt gets worse: Skewness budget

Skewness less important than variance since it is a higher order moment (less effect on cloud cover).

3

33

tl qmicrotcu

qt qKD

Dt

qD

Microphysics term treated simply inboth variance and skewness equations

Dissipation time-scales identical to variance equation

Tunable constant

Detrainment term from cumulus parameterization scheme

Embarrassing!!! I should have read some of David Randall’s workAND, instead of skewness I simply used the shape parameters


Actually do you know what the most embarrassing thing in that paper was?

THIS!!!

Actually do you know what the most embarrassing thing in that paper was?

THIS!!!


Schematic: How the scheme worksSchematic: How the scheme works

TIM

E

Convection detrains cloud condensate at a certain level, BUT, also increases the distribution skewness and width

Turbulent processes reduce width, as do microphysical processes

Return to clear sky conditions

Start with clear sky

From the distribution the cloud fraction can be

diagnosed


Scheme in action… Deep Convective Regime

Scheme in action… Deep Convective Regime

Deep convection: causes distribution to widen considerably and skewness increases(skewness also advected from neighbouring regions)

minmaxqsat

qt


Scheme in actionScheme in action

MinimumMaximumqsat

Turbulence breaks up cloud Turbulence creates cloud


Column model results for deep convective case

Column model results for deep convective case


Shoddy things about my schemeShoddy things about my scheme

Skewness budgetVariance budget “implicit” Microphysics still needed to be

tackled for overcast conditionsConvection detrainment implicit

Working on ECMWF scheme to tackle these (the other nightmare)


Complexity required?

Boil noodles

Complexity required?

Boil noodles


How much complexity?How much

complexity?

To start in ECMWF

model have built the simplest

statistical scheme possible

To start in ECMWF

model have built the simplest

statistical scheme possible

qt

G(q

t)

qs

Cloud waterVapour

Simply use mean vapour and cloud

water to fit a symmetrical PDF

(Beta distribution) and then diagnose

cloud cover

Simply use mean vapour and cloud

water to fit a symmetrical PDF

(Beta distribution) and then diagnose

cloud cover


How much complexity?How much

complexity?

Default Tiedtke Clouds

0 45 90 135 180 225 270 315 360longitude

-90

-45

0

45

90la

titud

e

2040

4040

60

60

60

6060

60 60

%0 20 40 60 80 100

Statistical Cloud Scheme

0 45 90 135 180 225 270 315 360longitude

-90

-45

0

45

90

latit

ude

20

40

40

40

40

60 60

60

60

6060

%0 20 40 60 80 100

difference

0 45 90 135 180 225 270 315 360longitude

-90

-45

0

45

90

latit

ude

-15

-5

-5

-5-5

-5-5

-5

-5-5

-5

5

5

5

5

55

%-25 -15 -5 5 15 25

RMS

0 45 90 135 180 225 270 315 360longitude

-90

-45

0

45

90

latit

ude

10

10

20

20

3030

30

3030

30

30

30 30

5050

%0 10 20 30 40 50 60

Default Tiedtke Clouds

0 45 90 135 180 225 270 315 360longitude

-90

-45

0

45

90la

titud

e

2040

4040

60

60

60

6060

60 60

%0 20 40 60 80 100


0 45 90 135 180 225 270 315 360longitude

-90

-45

0

45

90

latit

ude

20

40

40

40

40

60 60

60

60

6060

%0 20 40 60 80 100

difference

0 45 90 135 180 225 270 315 360longitude

-90

-45

0

45

90

latit

ude

-15

-5

-5

-5-5

-5-5

-5

-5-5

-5

5

5

5

5

55

%-25 -15 -5 5 15 25

RMS

0 45 90 135 180 225 270 315 360longitude

-90

-45

0

45

90

latit

ude

10

10

20

20

3030

30

3030

30

30

30 30

5050

%0 10 20 30 40 50 60

Results of a 4 month

total cloud cover

climatology at T95

resolution

Results of a 4 month

total cloud cover

climatology at T95

resolution

…simplicity aids data

assimilation dilemma…

…simplicity aids data

assimilation dilemma…


Links with other model

components

add fish to soup, simmer 5

minutes, add noodles

Links with other model

components

add fish to soup, simmer 5

minutes, add noodles


You might be tempted to say…You might be tempted to say…

Hurrah! We now have cloud variability in our models, where

before there was none!

WRONG! Nearly all components of GCMs contain implicit/explicit assumptions concerning subgrid fluctuations

e.g: RH-based cloud cover, thresholds for precipitation evaporation, convective triggering, plane parallel bias corrections for radiative transfer… etc.


Variability in CloudsVariability in Clouds

Is this desirable to have so many independent tunable parameters?

‘M’ tuningparameters

‘N’ Metricse.g. Z500 scores, TOA radiation fluxes

With large M, task of reducing error in N metricsBecomes easier, but not necessarily for the right reasons

Solution: Increase N, or reduce M


Advantage of Statistical SchemeAdvantage of Statistical Scheme


Radiation

Microphysics Convection Scheme

Thus ‘complexity’ is not synonymous with ‘M’: the tunable parameter space

Can use information inOther schemes


Use in other Schemes (II) IPA Biases

Use in other Schemes (II) IPA Biases

Knowing the PDF allows the IPA bias to be tacked

Knowing the PDF allows the IPA bias to be tacked

Split PDF and perform N radiation calculations Total

Waterqsat

G(qt)

Thick Cloud etc.

Use Moments to find best-fit Gamma Distribution PDF and apply Gamma weighted TSA Barker (1996)

TotalWaterqsat

G(qt)Gamma Function

TotalWaterqsat

G(qt)

Use variance to calculate Effective thickness ApproximationEffective Liquid = K x LiquidCahalan et al 1994

ETA adjustment


Variability in other Schemes: RadiationVariability in other Schemes: Radiation

Beta Weighted Two Stream Approximation

Effective Thickness Approximation = 0.7

(Cahalan et al. 1994)

Seasonal Average Albedo differences

Geo

rg B

aum

l 200

3, P

hD T

hesi

s


Rob Pincus McICARob Pincus McICA


McICA in the ECMWF

model

McICA in the ECMWF

model


Result is not equal in the two cases since microphysical processes are non-linear

Example on right: Autoconversion nonlinear function. Grid mean cloud less than threshold and gives zero precipitation formation. Threshold often

“tuned” to counter the neglect of variability.

Cloud inhomogeneity and microphysics biases

Cloud inhomogeneity and microphysics biases

qLqL0

cloud range

mea

n precipgeneration

Most current microphysical schemes use the grid-mean cloud mass (i.e: neglect variability)

cloud

Reality Model


Cloud Variability and MicrophysicsWork with Rob Pincus

Cloud Variability and MicrophysicsWork with Rob Pincus

Used the ECWMF model modified so cloud cover is parameterized using the simple statistical scheme

With the column model, conducted two experiments Exp1: Default microphysicsExp 2: Divide cloud into 100 sub-

columns and calculate microphysics taking subgrid fluctuations into account (using Rob’s cloud generator)

1 2 43 5…


Mean = 0.117250

0 1 2 3 4 5 6time (days)

0.0

0.1

0.2

0.3

0.4

Liq

uid

Wa

ter

Pa

th (

kg

/m^

2)

Mean = 0.117250

0 1 2 3 4 5 6time (days)

0.0

0.1

0.2

0.3

0.4

Liq

uid

Wa

ter

Pa

th (

kg

/m^

2)

Mean = 0.326782

0 1 2 3 4 5 6time (days)

0.0

0.2

0.4

0.6

0.8

Liq

uid

Wa

ter

Pa

th (

kg

/m^

2)

Mean = 0.326782

0 1 2 3 4 5 6time (days)

0.0

0.2

0.4

0.6

0.8

Liq

uid

Wa

ter

Pa

th (

kg

/m^

2)

Mean = 0.0169738

0 1 2 3 4 5 6time (days)

0.00

0.05

0.10

0.15

Ice

Wa

ter

Pa

th (

kg

/m^

2)

Mean = 0.0169738

0 1 2 3 4 5 6time (days)

0.00

0.05

0.10

0.15

Ice

Wa

ter

Pa

th (

kg

/m^

2)

Mean = 0.0695898

0 1 2 3 4 5 6time (days)

0.00

0.05

0.10

0.15

0.20

0.25

Ice

Wa

ter

Pa

th (

kg

/m^

2)

Mean = 0.0695898

0 1 2 3 4 5 6time (days)

0.00

0.05

0.10

0.15

0.20

0.25

Ice

Wa

ter

Pa

th (

kg

/m^

2)

Liq

uid

Ice

Default 100 columns

0.05

0.4

0.1

0.1

Time Time

Deep convection case


Clouds also

become

longer lived

Clouds also

become

longer lived

Cloud Fraction - 1C

0 1 2 3 4 5 6time (days)

60

50

40

30

20

Mo

de

l L

ev

el

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.40

0.45

0.50

0.55

0.60

0.65

0.70

0.75

0.80

0.85

0.90

0.95

Cloud Fraction - 1C

0 1 2 3 4 5 6time (days)

60

50

40

30

20

Mo

de

l L

ev

el

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.40

0.45

0.50

0.55

0.60

0.65

0.70

0.75

0.80

0.85

0.90

0.95

Cloud Fraction - 100C

0 1 2 3 4 5 6time (days)

60

50

40

30

20

Mo

de

l L

ev

el

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.40

0.45

0.50

0.55

0.60

0.65

0.70

0.75

0.80

0.85

0.90

0.95

Cloud Fraction - 100C

0 1 2 3 4 5 6time (days)

60

50

40

30

20

Mo

de

l L

ev

el

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.40

0.45

0.50

0.55

0.60

0.65

0.70

0.75

0.80

0.85

0.90

0.95

Default

100 columns


What is going on?What is going on?

PRESS= 96 (hPa)

0.0 0.2 0.4 0.6 0.8 1.0cloud water mixing ratio (g kg-1)

0.0

0.2

0.4

0.6

0.8

V(i

ce

) (m

/s)

PRESS= 96 (hPa)

0.0 0.2 0.4 0.6 0.8 1.0cloud water mixing ratio (g kg-1)

0.0

0.2

0.4

0.6

0.8

V(i

ce

) (m

/s)

0.0 0.2 0.4 0.6 0.8 1.0cloud water mixing ratio (g kg -1)

0.00

0.05

0.10

0.15

0.20

1000*r

ate

of

ch

an

ge o

f clo

ud

wate

r

critical cloud watercritical cloud water

0.0 0.2 0.4 0.6 0.8 1.0cloud water mixing ratio (g kg -1)

0.00

0.05

0.10

0.15

0.20

1000*r

ate

of

ch

an

ge o

f clo

ud

wate

r

critical cloud watercritical cloud water

Sundqvist Scheme is not strongly nonlinear when above critical threshold

Creation of snow ‘side-effect’ of ice sedimentation. (Ice

falling into clear sky is treated as snow)

A~q0.16

Non-diagonal Jacobians -Ice processes dominate in deep convective situations

through accretion processesREALISM?


Conclusions and future

directions?

Garnish with fresh coriander

leaves and serve

Conclusions and future

directions?

Garnish with fresh coriander

leaves and serve


ConclusionsConclusions

Move towards statistical schemes is a move towards greater coherency and self-consistency in models.

Information concerning microphysics, especially in ice phase crucial for further improvement, both in terms of means and spatial and temporal fluctuations.


FutureFuture

Intention at ECMWF is to move towards a statistical scheme framework to replace the existing prognostic cloud fraction

This will be accomplished in stages and will be combined with a simple treatment of the cloud ice variable that will allow super saturation with respect to ice

Statistical information to provide greater link to convection (sources!), boundary scheme, radiation

As always there is the issue of data assimilation


And finally…And finally…

In terms of clouds…

We have come a long way…

But we can still improve

thoughts on statistical cloud schemes denver 2004 a.tompkins 1 some thoughts on statistical cloud...

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