Double moment microphysics schemes for Numerical Weather Prediction models: why and how? F. Chosson M.K. Yau

Double moment microphysics schemes for Numerical Weather

Prediction models: why and how?

F. ChossonM.K. Yau

“For microphysics, the main question for forecast models is whether to go to double-moment schemes

that predict number concentrations[…] This would make sense in forecast systems […],

which are likely to be developed more in the future.”

Third International Workshop on Next-Generation NWP Model, 2010.

Hong, S. Y. and J. Dudhia, 2012: Next-Generation Numerical Weather Prediction: BridgingParameterization, Explicit Clouds, and Large Eddies. Bull. Amer. Meteor. Soc.

A bulk scheme: use of a probability distribution function (PDF)of cloud particles

N(D)

D

Mn= ∫ Dn N(D) dD

Prognostic equations of the moments Mn of the PDF of each hydrometeor species

number concentration

Diameter

Clouds in NWP models: a bulk approach

• M0 → total concentration• M1 → characteristic size• M2 → sedimentation

fall speed, extinction

• M3 → mass mixing ratio• M3/M2 → effective diameter• M5 → precipitation flux• M6 → radar reflectivity

Available in single, double or triple moment mode for various number of hydrometeor species

à Simple Moment à Double Moment à Triple Moment

Qx Qx +Nx

Qx

+Nx

+Zx

Simple Moment Double Moment Triple Moment

M3

M3

+M0

M3

+M0

+M6

Bulk microphysics schemes

Qtot

Qc QiQsQr

QgQh

Hydrometeor classes

Complexity, number of equations, advected fields and numerical cost

LAM-2.5km LAM-REG

GLOBAL

GCM100m 500m 1km 4km 10km 30km 100km2.5km

15km

CRMLES

Challenge: Which microphysical scheme?

SimpleDoubleTriple

Simple

CRM

CLIMAT

Clouds in NWP models: a scale dependence

Defining the microphysics scheme of the future.

Consistence with small scales:a lesson from Cloud Resolving Models

microphysical processes representation implied withinconvective phenomena, squall line and intenseprecipitation periods impose a sufficient number ofhydrometeors classes (categories):liquid phase: cloud water Qc

rain Qrsolid phase: “ice” category Qi

“snow” category Qsgraupel and/or hail Qg / Qh

Nb Classes ≥5

Double Moment

Double moment schemes better than single momentconceptually and by comparison with the observations.(e.g. Lim and Hong, 2009; Morrison et al., 2009; Milbrandt et al., 2009?)

Consistence with the radiative transfer:

Qx

Reff

τ

ω

g

Microphysicalparameters

Opticalparameters

RadiativeTransfer

Qx

Nx

Shape

Double Moment

Nb Classes ice phase≥2


LUT

Consistance with the observations:A-train, E-train, GPM, ground radar

and lidar, precipitation gauges...

Grenier et al., 2009Retrieval of Qx and Reff (Nx)

To be able to compare/to validate and to correct at more and more

compatibles scales…

Retrieval of the hydrometeor class (cloud masks)Retrieval of the precipitation profiles

Double (Triple) Moment

Nb Classes ≥5


Consistence with the observations:simulating remotely observables parameters and retrieval schemes

simul. Obs.

Retrieval

physicalparameter

physicalparameter

physicalParameter

Model

Hyp

othe

sisH

ypot

hesi

s

Hyp

othe

sis

Hyp

othe

sis

Radiances Radiances

Double (Triple) Moment

Nb Classes suffisant


Retrieval

Consistency with prediction of weather-related threats.Making it more feasible?Icing severity

size of graupel / hail particles?

Double Moment


hail, droplets, rain drops, drizzle

Consistence with present and futurdeveloppements:

Implementation of aerosol modules within air quality models, and why not NWP models themselves

Taking into account in-cloud heterogeneous chemistry

Climate mode: possibility to test some hypothesisabout aerosol indirect effects.(e.g. dehydratation-greenhouse feedback in Arctic, Blanchet and Girard, 1994)

Double Moment

Classes neige pluie


GCM

CRM

LAM-2.5km LAM-REG

GLOBAL

CLIMAT

100m 500m 1km 4km 10km 30km 100km2.5km

15km

Double Moment

Challenge: Which microphysical scheme?

LES CRM

THE microphysics scheme of the future.

LAM-2.5km LAM-REG

GLOBAL


15km

CRMLES

Double

CRM

Toward bigger scales


GLOBAL


15km

CRMLES

CRM

LAM-2.5km LAM-REG

Double Toward bigger scales

Toward smaller scales


LAM-2.5km LAM-REG

GLOBAL


15km

CRMLES

CRM

PROBLEM NUMBER 1: Spatial resolutionPROBLEM NUMBER 2: Temporal resolution

to be solved!

LAM-2.5km LAM-REG




tqdqPDFa

s

PROBLEM NUMBER 1: Spatial resolution

motto:

keep it simple!

Subgrid Cloud fraction schemeTompkins,

2005

tq

Simple PDF of total water content LeTreut and Li (1991)

q21

tq qq t

q2

qq t sq

cldtqclr

tq

q

qqqa st

2

a

qqqqqqq cstcld

ccldtot

cldv

2

2stclr

vclrt

qqqqq

“cloud”fraction

in-cloud water vapor

clear-skywater vapor

001 Uqq s PDF width

ALLOWS DIAGNOSTIC OF:


Subgrid Cloud fraction scheme

fromJ. Quaas

JGR,2012

001 Uqq s PDF width

Varia

bilit

y ∆

q t

the PDF width is adapted to the spatial resolution!

Spatial scale (m)

1 km

resolution:1.8°

resol:25 km



a

subgrid cloudfraction In-cloud

microphysical process

xxproc

x q,NFt

q

.

a.a

q,

a

NF

t

q xx

proc

x

.

CLOUDY CLASSES: Pristine IceSnowCloud droplets x

x

N

q

xx

xx

NaN

qaq



Precipitation Fraction

fraction concernedby precipitation?

cldpkclr

pk

pk aaa

• Maximum-random overlap

• Precipitationcomes from clouds above

subgrid cloud fraction

clear-sky precipitationfraction

in-cloudprecipitation

fraction


motto:

keep it simple!


fraction concernedby precipitation?

• Precipitation production within a fraction of the cloud fraction

• Special tunable parameter!

subgrid cloud fraction

clear-sky precipitationfraction

in-cloudprecipitation

fraction


Special for you

increase your

precip for free!

Precipitationmicrophysical process

xxproc

x q,NFt

q

.

ppx

p

x

proc

x a.a

q,

a

NF

t

q

.

PRECIP. CLASSES: RainGraupelHail x

x

N

q

xp

x

xp

x

NaN

qaq

pa

subgrid precip.fraction

Precipitation FractionPROBLEM NUMBER 1: Spatial resolution

pacloud-precip interactionmicrophysical process

rcproc

c qqFt

q,

.

pcldp

rc

proc

c aa

q

a

qF

t

q.,

.

OVERLAP OF PRECIPITATIONAND CLOUD FRACTIONS

pclda

a

Precipitation and cloud fraction overlapsPROBLEM NUMBER 1: Spatial resolution

Intercomparison

f(T)

Milbrandt and Yau(2005) original

Milbrandt and Yau(2005) + SCPF

Sundqvist et al.(1989)

•1 moment•1 hydrometeor class•diagnostic precipitation

•2 moments•6 hydrometeor classes•prognostic precipitation

+ Subgrid Cloud and Precipitation Fraction Scheme


North American RegionalReanalysis(∆x = 30km ouput 3h)

GEMRHcrit

U00

winter cold front representative profile

Test with a 1D kinematic model

experimental

1D kinem

atic model


1D kinematic intercomparisonMilbrandt & Yau original M&Y with SCPF Sundqvist

+ +


Milbrandt and Yau(2005)

3D GEM-LAM model intercomparison

f(T)

Milbrandt and Yau(2005)

Sundqvist et al.(1989)

GEM-LAMregional

∆x = 15 km∆t = 450 sec

20 Dec. 2008Simulation 36hcomparing only

the last 24h(spin-up)


+ Observations CloudSat/Calipso

Calipso + CloudSat=

LiDAR + RaDAR + Modis (IR)=

DARDAR CLOUD products(J. Delanoe, R. Hogan, 2008, 2010)

vertical profile of cloud mask,IWC, effective radius,

extinction, optical thickness, ...horizontal resolution = 1.1 km

vertical resolution = 60 m


Intercomparaison case study December 20th 2008

Daily Mean Non-Convective Cloud Cover (NARR)

25%

50%

75%

100%

Precipitation

Temperature

Meteo


Intercomparaison

2

2345

67

8

9

3 4 5 6 7 8 9

Chaque profil DARDAR de chaque traversée est comparé au profil des simulations GEM le plus proche en temps et en lieu.

2 3 4 5 6 7 8 9

DARDAR

Sundqvist

M&Y+SCPF

M&Y

DARDAR

Sundqvist

M&Y+SCF

M&Y

0.0 0.125IWC (g/m3)

0.25 0.375 0.5 0.625 0.75 0.875 1.0

Intercomparison

2345

67

8

9

Cloud Fraction

along tracksmean IWC

(g/m3)

in-cloud mean IWC(g/m3)

LAM-2.5km LAM-REG

GLOBAL


15km

CRMLES

CRM

PROBLEM NUMBER 1: Spatial resolutionPROBLEM NUMBER 2: Temporal resolution

LAM-2.5km LAM-REG




SCPF

SUND ∆t=450s

LAM Arctic Basin ∆x=15km

Test with POLAR-GEMPROBLEM NUMBER 2: temporal resolution

MY2 450s

SUND ∆t=450sSUND ∆t=60s

MY2 ∆t=450s



MY2 ∆t=60s

PROBLEM NUMBER 2: temporal resolution

Microphysical sub-time step

sedmicradv t

q

t

q

t

q

t

q

t

F

ρ

1ssq.U

t

q io

Equation to solve for each microphysical variable qfor each model time-step ∆t, for each model tile:

problem: computed

sequentially, no interaction

3 steps+updates

qVF tsedimentationflux


∆t>t

Sundqvistdiagnostic precip.

Milbrandt and Yauprognostic precip.

+ separated sedimentation

long time step issue concernsinteractions between particles during sedimentation

therefore concerns mainly precipitations

collectionOK

nocollection

collection

t ∆t

Reality:collection process

during sedimentation

Prognostic precipitation + separate sedimentation requires small time step, requires courant number = 1, but in large scale model, time steps are large too...The trick simply consists in iterate over the whole microphysics scheme (M&Y) within each atmospheric model time step, in order to simulate a series of small time step.


seeder-feeder effect

sed

r

micr

rr

t

q

t

q

t

q

0

sedmicradv t

q

t

q

t

q

t

q

n

i sedimicriadvi t

q

t

q

t

q

t

q

1

Each model time step ∆t is divided in n microphysicssub-time step ∆ti such as : ∆t = n∆ti It has been chosen ∆ti ≈60s as a good compromise cost/precision.

Equation to solve for each microphysical variable q, for each model time-step ∆t, for each model tile:

(discretized form)





SUND 450sSUND 60s

MY2 450s

MY2 60sMY2 450s sub-time step at 60s

The problem that resists

Numerical cost!

∆t = 450 sec

reference

x 1.2Other avenues?

x 2.3 !

∆t = 450 sec

dtmicro=60 sec

∆x = 15km Sundqvist

Milbrandt& Yau


∆x= 15km

Can’t afford !

Cost-efficient sedimentation scheme?PROBLEM NUMBER 2: temporal resolution

t

F

ρ

1ssq.U

t

q io

Eulerian

qVF t

1

z

tVC t tV is terminal

fall velocitysedimentationCourant number

numerical

scheme evolution ofECMWF IFS verticalresolution...

60 levels 91 levels(137 since 2013)

The combination of thehighest terminal fall velocity,

the finest model level and thelong model time step will determine

the number of sedimentationsub-steps to use on the whole column!

Can’t afford !

Only one solution: sub-stepping the sedimentation part!

Cost-efficient sedimentation scheme?PROBLEM NUMBER 2: temporal resolution

t

F

ρ

1ssq.U

t

q io

Lagrangian

Box-Lagrangian(Teruyuki Kato, 1995, J. Meteor. Soc. Japan)

qVF t

Theoretically no CFL criteriabut practically so diffusivethat it limits C to about 2-3knowing that Lagrangian treatment is heavierresult is alwaysmore expensive than Eulerian sedimentation.

numericalscheme

Bad news never come alone!

Mass qx and concentration Nx have different fall velocities Vq > VN

(they are proportional and the proportion p depends on the assumed shape of the size distribution).

t t+∆t


Vq

VN

The goal is to mimic size sorting: bigger particles falls faster


t t+∆t


Vq

VN

N Q D

Milbrandt and McTaggart-Cowan,

2010, J.A.S.

rain drops


t t+∆t


Vq

VN

N Q D

N Q D

Milbrandt and McTaggart-Cowan,

2010, J.A.S.


Solutions:rain drop spontaneous break-up?

yes, but... how about ice particles?Limiting mean mass diameter?

yes, but... that implies inventing new particles



We will never avoid:•ghost particles removing at cloud top

overall loss of column particles number•mass without number = evaporation at leading edge of precip

overall loss of column total condensate mass•Courant number that increases during sub-stepping

Eulerian sedimentation can become unstable!

t t+∆t

Vq

VN

Size sorting is one of the main benefit from the use of double moment schemesit’s also causing its doom at large time step...


c

1D model comparison: sedimentation only of a collection of graupel particles

Euleriansedimentat.

scheme

dt=10s dt=30s dt=60s dt=90s

dt=2min dt=3min dt=4min dt=8min

DgMax=6mm Initial CFL conditionfullfilled!

c


Box-Lagrangiansedimentat.

scheme


dt=2min dt=3min dt=4min dt=8min

DgMax=6mm Initial CFL conditionfullfilled!

Cost-efficient sedimentation scheme!PROBLEM NUMBER 2: temporal resolution

We have a Solution for You!

Cost-efficient sedimentation scheme

io ssz

F

t

q

1

mass flux: qVF t

source tendenciessink tendenciesBudget

equation(no advec.)

Upstreamforwardscheme

)( iojj sstFF

z

tqq

1

Assumption: so/si terms and fluxes constant during ∆t Layer j

Layer j-1 1jF

jF

io SS

Remainsat the end

of time-step)()()()( io

j sstPFz

tPqPq

3121 111

Layer j+1

Line1minusLine2

)( iojj sstPF

z

tPqPF

z

t

3121

condensate flux falling below layer j :

bounded between 0 (no negative sedim.)and total available condensate

after source/sink termsknown

(after advection)known known -- computed using (q- + Fj-1 )

... And similarly for number concentration NStill have to determine proportions P1 P2 P3 ...


iojjj SSPFz

tPqPF

z

t

3121

V∆tV∆t ∆z

Layer j

1jF

∆z

P1=

Cost-efficient sedimentation schemePROBLEM NUMBER 2: temporal resolution

Probabilities (proportions)and sedimentation fluxesare aware of the Courant

number. So must be sourcesink terms. Sedimentation

fluxes take into accountsource/sink terms :

full interaction!


Lets fix a maximum mean mass diameter so that D ≤ Dmax (from obs., tunable). It follows that there is a maximum terminal fall velocity It follows that both moment outgoing sedimentation fluxes are related and bounded:

t t+∆t

dqN Dc

pFF

max

Avoiding excessive size sorting



t t+∆t

dqN Dc

pFF

max

dNq DcNqFF minminmin

Lets fix a minimum mean particle diameter id est D > Dmin . It follows that there is a minimum terminal fall velocity It follows that outgoing mass sedimentation flux is bounded so that the remaining particles (if any, constrained by FN) are always bigger than this minimum.

Lets fix a maximum mean mass diameter so that D ≤ Dmax (from obs., tunable). It follows that there is a maximum terminal fall velocity It follows that both moment outgoing sedimentation fluxes are related and bounded:

Avoiding excessive size sorting



dt=10sdt=10s DgMax=6mm DgMin=noneBox-Lagrangian

or Euleriansedimentat.

schemeincluding

Dgmax

Newsedimentat.

scheme

DgMax=6mm DgMin=200μmdt=10s DgMax=6mm


dt=10sdt=10s DgMax=50mm DgMin=noneBox-Lagrangian

or Euleriansedimentat.

scheme

Newsedimentat.

scheme

DgMin=200μm

includingDgmax

dt=10s DgMax=50mm

cdt=2min dt=3min dt=4min dt=8min


Newsedimentat.

schemeDgMax=6mm DgMin=200μm


dt=8min

dt=8min

dt=8min

Box-Lagrangiansedimentat.

scheme

Newsedimentat.

scheme

Euleriansedimentat.

scheme

1D kinematic model comparison:full microphysics + Subgrid Cloud Fraction

c

1D kinematic modelWeak and slow Up

and downdraft.With subgrid cloud fraction.

New SedimentationScheme

c



EulerianSedimentation

Scheme

c



Box-LagrangianSedimentation

Scheme

High performance, low cost!

Cheap!

Specia

lpric

e!

Adapting multi-moments microphysics models across all resolutions

Two-fold issue


15km

CRMLES

Spatial resolution ∆x :Subgrid Cloud and


Temporal resolution ∆t :Sedimentation related

issue

11

,mintV

zss

z

qV

t

q io

Cost-efficient sedimentation schemeConclusions:

• Advantage 1: much lighter scheme that mimics Eulerian/Lagrangian schemes at short ∆t.• Advantage 2: much faster scheme.• Advantage 3: able to get rid of excessive size sorting, at any time step.• Advantage 4: theoretically able to take into account source/sink terms and sedimentation at the same time.• Advantage 5: stable (able to avoid loss of precipitations that was the problem for long time steps).• Disappointment 1: results are not time-step independent• Disappointment 2: at large time step, staggering (diffusion) of precipitation close to “diagnostic precipitation” schemes effect (limit of the continuous fluxes and source/sink terms assumption).• Disappointment 3: up to now, at large time step, source/sink terms do not take into account sedimentation in a satisfying way.

→ Possibility to mix our microphysical sub-stepping approach with the new sedimentation at lower cost.

Double moment microphysics schemes for Numerical Weather

Prediction models: why and how?

Will you buy it?


Box-Lagrangianor Eulerian

sedimentat.scheme

Newsedimentat.

scheme

Newsedimentat.

scheme

DgMin=200μm DgMin=25μm

DgMax=6mm DgMax=6mm DgMax=6mm

c

DgMin=none

dt=10s

dt=10s

dt=10s

tq

Avoid too high cloud fraction of high altitude clouds:Correction for Cirrus Ice Clouds

q21

tq qq t qq t qs,i qs,w

>90% of qs,w

001 Uqq s

ices

liqs

hos q

qRHUqq ,min1 00

8.207583.2

TRHho

Kärcher and Lohmann, 2002homogeneous freezing of supercooled aerosols


(ECMWF approach)

Link to aerosols: activation schemes

Cohard and Pinty,2000: kNwSfNc CCNwact ,,,,

function of supersaturation,vertical velocity, concentrationof CCN, physico-chemical properties of aerosols (2 kinds)

Cloud Condensation Nuclei (CCN) activation at cloud base:

Predict the number concentration of cloud droplets.Two kinds of aerosol type:

“polluted” (hydronium sulfate) and “pristine marine” (sea salt).

DeMott et al.,2010:

cTc NT cdb

act INaNi

5.0

based on 9 studies and field campaigns.Focus on mix-phase clouds above sat. w.r.t. liquid. Increases notably mix-phase clouds.

Meyers et al.,1992:

639.0196.12exp1000 iSactNi function of supersat.w.r.t. ice

Ice Nuclei activation in pure ice clouds:

Link to aerosols: activation schemes

Presently used:

New:

Predict the number concentration of small ice particles throughprimary ice nucleation.

5.0INN is the number concentration of giant IN of diameter larger than 0.5 microns

Documents

Double moment microphysics schemes for Numerical Weather Prediction models: why and how? F. Chosson M.K. Yau