.

REPRESENTING CLOUD AND PRECIPITATION

IN

NWP MODELS IN CANADA

(Peter) M.K. Yau1 and Jason Milbrandt2

1McGill University, Montreal, Canada2Environment Canada [RPN], Dorval, Canada

Environment Canada's forecast model

GEM (Global Environmental Multiscale)

Global Uniform Global Variable Limited Area (LAM)

Grid configurations:

• medium-range (10-d)

• x = 35 km → 25 km

• t = 15 min

• short-range (48-h)

• x = 15 km → 10 km

• t = 7.5 min

• experimental

• short-range (24-h)

• x = 2.5 km → 1 km

• t=1 min (t=30s)

Simple Cloud SchemeDetailed Microphysics

Scheme

The simple cloud scheme (Sundqvist)

• Cloud-cover fraction is diagnosed (function of RH)

• Condensation occurs when RH exceeds a threshold (80% near

surface)

• Total condensate (cloud water/ice) is prognostic (advected)

• Precipitation falls instantly to the ground – there is no

advection of precipitation

Global Uniform Global Variable

Multi-moment scheme

Milbrandt and Yau (JAS 2005 a,b)

Milbrandt and Yau (JAS, 2006 a,b)

Gultepe and Milbrandt

(Pure App. Geoph.,2007)

Milbrandt et al. (MWR, 2008)

Milbrandt et al. (MWR, 2010)

Dawson et al. (MWR, 2010)

Six hydrometeor categories:

2 liquid: cloud, rain

4 frozen: ice, snow, graupel, hail

Scheme implemented in

GEM-LAM, Global variable (Canada)

ARPS (U Oklahoma, US)

WRF 3.2 (US)

RAIN

GRAUPEL HAIL

SEDIMENTATIONSEDIMENTATION

VAPOR

ICECLOUD

VDvr VDvs

NUvi,

VDvi

CLci, MLic, FZci

CLcs

CNig CNis,

CLis

CLri

CLih

CLsh

CLir-g

CLsr-h

CLir-g

CLsr-g

CLch

CNsg

CNgh

MLgr

CLcg

VDvg

CLir

VDvh

self-

collection

self-

collection

CLrh,

MLhr,SHhr

NUvc,

VDvc

CNcr,

CLcr

CLsr CLrs

MLsr, CLsrSNOW

The detailed microphysics scheme

Limited Area Model

•Overview of the scheme

•Testing and improvement in IMPROVE-2

(GEM-LAM)

•Forecast in winter Olympics 2010

(GEM-LAM)

•Testing over Arctic (GEM-Global Variable)

ANAYLTICAL FUNCTION

BULK METHOD

Representing the size spectrum

N(D)

D [ m]

100

[m-3 m-1]

20 40 60 800

101

100

10-1

10-2

1 m3

Gamma Distribution Function:

DeDNDN 0)(

* Q = r q (mass content)

INCREASING

VALUES(of , N0 and )

log

N(D

)

log N

(D)

log N

(D)

D [mm] D [mm]D [mm]

Varying (slope) (N0 and constant)

Varying (shape) (Q* and N0 constant)

Varying N0 (intercept) ( and constant)

BULK METHOD

pth moment:(

xp

x

xxx

p

x

pNdDDNDpM

10

0

1)()(

Size Distribution Function:

D

xxxx eDNDN

0)(

Total number concentration, NTx

)0()(0

xxTx MdDDNN

Radar reflectivity factor, Zx

)6()(0

6

xxx MdDDNDZ

Mass mixing ratio, qx

densityairDcDmwhere

Mc

dDDNDc

q

xx

xx

xx

x

r

rr

,)(

),3()(

3

0

3

Predict evolution of

specific moment(s)

e.g. qx, NTx, ...

Implies prediction of evolution

of parameters

i.e. N0x, x, ...

BULK METHOD

pth moment:(

xp

x

xxx

p

x

pNdDDNDpM

10

0

1)()(

Size Distribution Function:

D

xxxx eDNDN

0)(

Predict evolution of

specific moment(s)

e.g. qx, NTx, ...

Implies prediction of evolution

of parameters

i.e. N0x, x, ...

For every predicted moment, there

is one prognostic parameter.

The remaining parameters are

prescribed or diagnosed.

Two-moment scheme:

qx and NTx are predicted;

x and N0x are prognosed;

(x is specified)

Three-moment scheme:

qx, NTx and Zx are predicted;

x, N0x and x is prognosed

One-moment scheme:

qx is predicted;

x is prognosed

(N0x and x are specified)

e.g.

CLOSURE OF SYSTEM

( densityairandcDDmwhere

Gq

ZNc T

r

r

,

,)1)(2)(3(

)4)(5)(6()(

)(

3

2

2

Solve for shape parameter α from

3

1

)1(

)4(

r

q

cNT

Solve for slope parameter λ from

)1(

1

0

TN

N

Solve for intercept parameter N0 from

→ NT and q vary monotonically in a 1-moment scheme

Diagnostic closure for α in 2-

moment scheme

)(

,3

1

m

T

m

Df

cN

qD

r

r

r = M (p,αest) / M(p,αcorr)

Verification and

improvement of Multi-

moment scheme in GEM-

LAM (1 km) in IMPROVE-2

CASE STUDY

November-December 2001: IMPROVE-2 Observational Campaign

Improvement of Microphysical Parameterization through

Observational Verification Experiment

Cresswell

Sounding

150 km

13-14 Dec 2001 case:

• chosen for study at W.M.O. International Cloud Modeling Workshop,

Hamburg (July 2004)

• special issue of J. Atmos. Sci. (October 2005) dedicated to IMPROVE-2

GOES – IR: 2239 UTC 13 Dec 2001

CASE STUDY

Precipitation in IOP region:

• prefrontal showers;

• moderate to heavy stratiform rain

(associated with mid-level baroclinic

zone);

• surface frontal rain-band;

• transition to sporadic showers

Characteristics:

• large-scale baroclinic system

• strong low-level cross-barrier flow

OBSERVED PRECIPITATION1600 UTC 13 Dec – 0800 UTC (18 h)

BIAS SCORES4-km MM5 Simulation

UNDER-Predicted

OVER-Predicted

CASE STUDY: MM5 Simulations

Source: Garvert et al. (2005a) [J. Atmos. Sci.]

13-14 Dec 2001 case:

• MM5 runs at 4-km and 1.3 km exhibited errors in surface precipitation

attributed to problems associated with the microphysics (SM Reisner-2)

S-Pol

1.5 PPI

R 150 km

Portland

0.5 PPI

R 200 km

4km-GEM

700 hPa

1-km GEM

E. Reflectivity

No pronounced over prediction along lee side of Cascade

Source: Stoelinga et al. (2003) [Bull. Amer. Meteor. Soc.]

MICROPHYSICS: Observations

Aircraft flight tracks (2200 – 0200 UTC)

Convair-580

NOAA P-3

MICROPHYSICS: Observations

Source: Wood et al. (2005) [J. Atmos. Sci.]

NO

AA

P-3

Co

nva

ir-5

80

Mean size inc. with dec. height

Z>4.5 km - single ice xtal

3<Z<4 km – dendrite

2<Z<3 km – column &

aggregate

13-14 Dec 2001 CaseA B

MICROPHYSICS: Observations

Source: Garvert et al. (2005b) [J. Atmos. Sci.]

Combined Observations for 2200–0200 UTC

Cloud liquid water along P-3 flight legs

Under prediction of vertical

extent of cloud water

Ice/snow content along Corvair flight legs

Over prediction of concentration of snow

mass

→ too large deposition and/or riming

IMPROVEMENTS OF SNOW CATEGORY

•Diffusional growth

•Growth by riming

“The electrostatic analogy of the capacitance theory of

ice crystal growth is highly flawed and does not produce

the observed growth rates of ice crystals.

It severely overpredicts the growth rates in almost all

cases [by a factor of 3 to 8+ for plates and 2 to 4 for columns]

involving even simple hexagonal shapes.”

Bailey and Hallet (2006)

Electrostatic Analogy for

Diffusional Growth of Ice Crystals

i

i

AB

SC

dt

dm )1(4

i

i

AB

SC

dt

dm )1( 4

Add CORRECTION FACTOR to DIFFUSIONAL GROWTH EQUATION

i

icorr

AB

SfC

dt

dm )1( 4

where fcorr must be < 1, with value justified by results

fcorr = 0.50

With decreasing fcorr,

SNOW content (qs) is reduced

and

CLOUD LWC (qc) is increasedfcorr = 0.25

fcorr = 1.0Sensitivity Tests for

IMPROVE-2:qs

qc

g kg-1

g kg-1

g kg-1

C = 0.5D

C = 0.25D

C = 0.125D

Other evidence:

Field et al. (2008)

Westbrook et al. (2008)

• For the collection efficiency, Ecs = 1 is often assumed (for collection of cloud by snow)

• If Ecs < 1, the snow riming rate will be overestimated

( xyxxyyyxxyyyyxyyxxyx dDdDDNDNDDEDmDDDVDVCL )()(),()()()(

4

1 2

0 0

r

RIMING of SNOW

Stochastic collection equation: (for category x collecting category y)

COLLECTION

EFFICIENCY

Approximation:

• Works for Dc ~ 15-30 m,

and Ds ~ 150-1500 m

• Reduces riming rate 10-80%

(vs. Ecs = 1)

5.0

1000

1000,min(

30

)30,min(),(

m

mD

m

mDDDE sc

sccs

500

m

225

m

150

m

700

m

950

m

Ds

0.5Dc

Ec

s(D

c,D

s)

17

00

m

RIMING of SNOW

*Wang and Ji, 1992

Test of 2-moment microphysics in

Vancouver Olympics 2010 in 1 km

GEM-LAM

1.0 km

Whistler

• 3 nested LAM integrations twice daily

from 0000 and 1200 UTC GEM-Regional

forecasts:

LAM-15 km → 2.5 km → 1 km

Vancouver

15 km

2.5 km

Nesting strategy for

LAM-V10 system

Verification for

LAM-V10

Olympic Autostation Network (OAN):

• approx. 40 standard and special surface observing

sites (hourly or synop available on GTS)

• large number (relatively) of surface stations

• concentrated in small region

Verification Examples

Observations courtesy of George Isaac

SNOW

PELLETS

FLUFFY

SNOWFLAKES

Observed:*

*Forecaster:

Michael Gélinas

Experimental field:Solid-to-Liquid ratio

Testing of 2-moment microphysics in

Global GEM variable 15 km over the

Arctic

30 day simulation – July 2008 over Arctic

Polar-GEM:

•x = 15 km

Sundqvist

Two-MomentOne-Moment

GPCP merged obs

PRECIPITATION

GPCPmerged

obs

Sundqvist

Two-Moment

One-Moment

Cloud Scheme:

SENSITIVITY TO TIME STEP

t = 450s

t = 225s

t = 120s

t = 60s

Sundqvist

Two-Moment

One-Moment

Cloud Scheme: GPCPmerged

obs

60-h Simulation

Sundqvist

Two-Moment

One-Moment

Cloud Scheme:

GPCPmerged

obs

SENSITIVITY TO TIME STEP

60-h Simulation (t = 60 s)

SUMMARY

1) Multi-moment mixed phase bulk cloud microphysical

schemes have been developed and implemented in

GEM-LAM and GEM-Global Variable

2) Comparison with in-situ field measurements allows

improvements in the scheme

3) Implementation in GEM-Global Uniform is planned but

still needs work to address

a) time splitting for microphysics

b) subgrid scale cloud fraction

c) simplification to allow for a mixture of

higher and lower moment hydrometeor

categories

( z

Vq

t

q xqx

SEDI

x

rr

SEDIMENTATION: Bulk scheme

xqV = mass-weighted fall velocity

SM

( z

VN

t

N xNx

SEDI

x

xNV = number-weighted fall velocity

DM

( z

VZ

t

Z xZx

SEDI

x

xZV = reflectivity-weighted fall velocity

TM

For a given size distribution, xNxqxZ VVV

ANA

TM

DM0SM

Effects on sedimentation terms

(Q = r q)

z

[km]

Q [g m-3]

TM better than DM0 better than SM

DIFFERENCE RELATED TO SIZE SORTING

Disadvantages of 1-moment scheme

a) Inconsistency in modeling physical processes

From closure relation, NT and q vary monotonically → NT increases

or decreases with q, but

in breakup, NT increases but q = constant, and

in diffusional growth, q increases but NT = constant.

c) Inconsistency in modeling size sorting in sedimentation

→ mean size increases with decreasing height, but not necessarily

true in 1-moment as mean diameter is

3

1

T

mcN

qD

r

Disadvantages of 2-moment fixed α scheme in

sedimentation

Rate of change of Dmx (size sorting)

proportional to fallspeed ratio

From TRIPLE- MOMENT sedimentation profiles:

Diagnosed α → sedimentation results in larger mean size (larger Dm) but

narrower spectrum (larger α )

0

2)(

4dDDNDqE

dt

dqxb

cxc

CL

x r

...21

proc

x

proc

x

S

x

dt

dq

dt

dq

dt

dq

MICROPHYSICAL

PROCESSES

How well do the various bulk scheme

predict sources/sinks?

0

)()(

dDDNdt

Ddm

dt

dq

CLCL

x CONTINUOUS COLLECTION

OF CLOUD WATERe.g.

xb

cxccxc

CL

DqEqEDVD

dt

Ddm

22

4)(

4

)(r

r

pth moment:

0

)()( dDDNDpM x

p

x

)2( xx

CL

x bMdt

dq

xb

xx DaDV )(

How well do the various bulk scheme predict

sedimentation and sources/sinks?

TM and DIAG DM schemes

better than

SM AND FIXED DM schemes