Jason Milbrandt

Recherche en Prévision Numérique [RPN]Meteorological Research Division, Environment Canada

GEM Workshop, June 12, 2007

A New

Multi-Moment Cloud Multi-Moment Cloud

Microphysics PackageMicrophysics Package

for the GEM-LAM

Why develop a new cloud scheme for GEM?

• Computer resources increasing

• High-resolution NWP grids are becoming mainstream

• Important to predict cloud processes as well as possible

• GEM-LAM-2.5 has systematic problems with the precipitation forecasts

1. Background on bulk schemes

2. Description of the new microphysics package

3. Some advantages of the multi-moment approach

OUTLINE

One of the goals of NWP model:

Predict the effects of the clouds

MODEL GRID:(hypothetical NWP model)

PARTLYCLOUDY(RH < 100%)

CLOUDY(RH = 100%)

CLOUD-FREE

CPS

EXPLICITSCHEME

Single cloudy grid element:

CLOUDY(RH = 100%)

EXPLICITSCHEME

INPUT:w, T, p, qv

Single cloudy grid element – interaction with NWP model:

MICROPHYSICAL PROCESSES in the cloudy grid element

Single cloudy grid element – interaction with NWP model:

Changes to

w, T, p, qv

and

qc, qr, qi, ...

Advectionand

Turbulent Mixing

MICROPHYSICALPROCESSES

OUTPUT:• Latent heating• Hydrometeors (cloud, rain, ice,…) qc, qr, qi, ...

INPUT:w, T, p, qv

qc, qr, qi, ...

Single cloudy grid element: Slight magnification

= cloudy (saturated) air

Single cloudy grid element: Extreme magnification

Single cloudy grid element: Extreme magnification

1 m3

(unit volume)

[e.g. Cloud droplets]

(not to scale)

N (D)

D [ m]

100

[m-3 m-1]

20 40 60 800

101

100

10-1

10-2

1 m3

(unit volume)

[e.g. Cloud droplets]

(not to scale)

(Example of observed

cloud droplet spectrum)

N (D)

D [ m]

100

[m-3 m-1]

20 40 60 800

101

100

10-1

10-2

1 m3

(unit volume)

[e.g. Cloud droplets]

(not to scale)

DISCRETE SIZE BINS

SPECTRAL 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

(unit volume)

[e.g. Cloud droplets]

(not to scale)

1 m3

(unit volume)

BULK METHOD

N (D)

D [ m]

100

[m-3 m-1]

20 40 60 800

101

100

10-1

10-2

ANAYLTICAL FUNCTION

[e.g. Cloud droplets]

(not to scale)

Representing the size spectrum

Gamma Distribution Function:

DeDNDN 0)(

* Q = q (mass content)

INCREASINGVALUES(of , N0 and )

log N(D) log N(D) log N(D)

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

Varying :(N0 and constant)

Varying :(Q* and N0 constant)

Varying N0:( and constant)

BULK METHOD

Size Distribution Function:

Dxx

xxeDNDN 0)(

pth moment:

xpx

xxx

px

pNdDDNDpM

100

1)()(

N (D)

D10020 40 60 800

101

100

10-1

10-2

HydrometeorCategory x

Total number concentration, NTx

)0()(0

xxTx MdDDNN

Radar reflectivity factor, Zx

)6()(0

6xxx MdDDNDZ

Mass mixing ratio, qx

)3(6

)(6 0

3x

xx

xx MdDDNDq

Example of Moments:

BULK METHOD

Size Distribution Function:

Dxx

xxeDNDN 0)(

pth moment:

xpx

xxx

px

pNdDDNDpM

100

1)()(

Total number concentration, NTx

)0()(0

xxTx MdDDNN

Radar reflectivity factor, Zx

)6()(0

6xxx MdDDNDZ

Mass mixing ratio, qx

)3(6

)(6 0

3x

xx

xx MdDDNDq

Example of Moments:Predict changes to specific moment(s) e.g. qx, NTx, ...

Implies changes to values of

parameters

i.e. N0x, x, ...

* (May contain traces of supercooled water)

T < 0C *

T < 0C

= ICE CRYSTAL

(May contain traces of supercooled water)

T < 0C

= ICE CRYSTAL

= SNOW CRYSTAL / AGGRETATE

(May contain traces of supercooled water)

T < 0C

= ICE CRYSTAL

= SNOW CRYSTAL / AGGREGATE

= GRAUPEL

(May contain traces of supercooled water)

T < 0C

= ICE CRYSTAL

= SNOW CRYSTAL / AGGREGATE

= GRAUPEL

= HAIL

(May contain traces of supercooled water)

= ICE CRYSTAL

= SNOW CRYSTAL / AGGREGATE

= GRAUPEL

= HAIL

= LIQUID WATER

T < 0C

ICE SNOW

GRAUPEL HAIL

LIQUID WATER

PARTITIONING THE HYDROMETEOR SPECTRUM

ICE SNOWCLOUD

GRAUPEL HAILRAIN

PARTITIONING THE HYDROMETEOR SPECTRUM

ICE SNOWCLOUD

GRAUPEL HAILRAIN

BULK METHOD

Drr

rr eDNDN 0)(

Dii

iieDNDN 0)( Dss

sseDNDN 0)(

Dgg

gg eDNDN 0)(D

hhhheDNDN 0)(

ccc DDNDN ccc exp)( 1)1(

0

PARTITIONING THE HYDROMETEOR SPECTRUM

Full TRIPLE-MOMENT Version:

• Six hydrometeor categories:– 2 liquid: cloud and rain– 4 frozen: ice, snow, graupel and hail

• ~50 distinct microphysical processes

• Warm-rain scheme based on Cohard and Pinty (2000a)

• Ice-phase based on Murakami (1990), Ferrier (1994), Meyers et al. (1997), Reisner et al. (1998), etc.

• Predictive equations for Zx added for triple-moment*

*Milbrandt and Yau (2005a,b) [J. Atmos. Sci.]

Milbrandt-Yau Cloud Scheme *

Diagnostic-Dispersion DOUBLE-MOMENT Version:

Identical to full version except:

• Diagnostic-x relations added for double-moment*

Milbrandt-Yau Cloud Scheme *

Recall:Size Distribution Function:

Dxx

xxeDNDN 0)(

CURRENT VERSIONS AVAILABLE FOR GEM:

GEM_v3.2.2 / PHY_4.4 available upon request**

GEM_v3.3.0 / PHY_4.5 part of official RPN/CMC library

Single-moment version– Six hydrometeor categories

– Single-moment (Qx) for each

Double-moment version– Six hydrometeor categories– double-moment (Qx,, Nx) for each

– fixed-x

Milbrandt-Yau Cloud Scheme

**(also available for MC2_v4.9.8)

UPCOMING VERSION AVAILABLE FOR GEM:

Prototype cloud scheme for the 2010 Winter Olympics

“Olympic” version *CLOUD double-moment (Qc, Nc)

RAIN double-moment (Qr, Nr) [diagnostic-r ]

ICE/SNOW double-moment (Qi, Ni) [hybrid category]

GRAUPEL single-moment (Qg)

HAIL double-moment (Qh, Nh) [diagnostic-h ]

Milbrandt-Yau Cloud Scheme

* To be implemented in GEM-LAM 2.5 km AUTUMN 2007

Prognostic Nc

Double-Moment “CLOUD” Category:

• Condensation rate based on saturation adjustment

• Nc initialization is air-mass (CCN) dependent

Advantages of multi-moment approach:

CCN-dependent Nc nucleation:

MARITIME

CONTINENTAL

103

100

10-1

0.01 0.1 1.00 10.0

SUPERSATURATION (%)

101

NCCN

(cm-3)

102

Advantages of multi-moment approach:

Qc (Cloud Mixing Ratio)

Nc (Cloud Number Concentration)

Dc (Cloud Mean-Mass Diameter)

The warm-rain coalescence process

Radius [cm]

Bin-resolving coalescence modelSOURCE: Berry and Reinhardt (1974)

RAINCLOUD

DRIZZLE

Mas

s D

ensi

ty [

g m

-3 (

lnr)

-1]

Tim

e [m

in]

Advantages of multi-moment approach:

0.1–1 mm

RAIN

DRIZZLE

STRATIFORM RAIN

Qr

Mass Content[g m-3]

Dr

Mean Diameter[mm]

Advantages of multi-moment approach: DRIZZLE vs. RAIN

z[km]

Q [g m-3] Dm [mm]NT [m-3] Ze [dBZ]

Contours every 5 min

MassContent

Total NumberConcentration

EquivalentReflectivity

Mean-MassDiameter

5 min

10 min

15 min

20 min

INITIAL

Analytic bin model calculation: (1D column)

Advantages of multi-moment approach: SEDIMENTATION

z

Vq

t

q xqx

SEDI

x

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

SEDIMENTATION: Bulk scheme

SINGLE-moment scheme (SM):

ANALYTIC BIN model (ANA):

z[km]

Q [g m-3] Dm [mm]NT [m-3] Ze [dBZ]

z[km]

Q [g m-3] Dm [mm]NT [m-3] Ze [dBZ]

5 min

10 min

15 min

20 min

INITIAL

DOUBLE-moment scheme, FIXED DISPERSION ( = 0):

ANALYTIC BIN model (ANA):

z[km]

Q [g m-3] Dm [mm]NT [m-3] Ze [dBZ]

z[km]

Q [g m-3] Dm [mm]NT [m-3] Ze [dBZ]

5 min

10 min

15 min

20 min

INITIAL

ANALYTIC BIN model (ANA):

DOUBLE-moment scheme, DIAGNOSTIC DISPERSION, = f (Dm):

z[km]

Q [g m-3] Dm [mm]NT [m-3] Ze [dBZ]

z[km]

Q [g m-3] Dm [mm]NT [m-3] Ze [dBZ]

5 min

10 min

15 min

20 min

INITIAL

TRIPLE-moment scheme:

ANALYTIC BIN model (ANA):

z[km]

Q [g m-3] Dm [mm]NT [m-3] Ze [dBZ]

z[km]

Q [g m-3] Dm [mm]NT [m-3] Ze [dBZ]

5 min

10 min

15 min

20 min

INITIAL

MassContent

Bulk schemes:

Analytic model:z

[km]

Q [g m-3]

5 min

10 min

15 min

20 min

INITIAL

Q [g m-3] Q [g m-3] Q [g m-3]

z[km]

DOUBLE-MOMENT

Fixed SINGLE-MOMENT

DOUBLE-MOMENT

Diagnosed

Q [g m-3]

TRIPLE-MOMENT

Prognosed

Advantages of multi-moment approach: SEDIMENTATION

0.1 - 4 mm

SNOW (large crystals / aggregates)

Qs

Mass Content[g m-3]

Ds

Mean Diameter[mm]

(equivalent sphere)

Advantages of multi-moment approach: MASS ≠ SIZE

SUMMARY

• Efficient single-moment and double-moment versions of the Milbrandt-Yau scheme are available for GEM-LAM

• Single-moment version will be proposed as the operational scheme for GEM-LAM_2.5 by fall 2007

• New version (“semi-double-moment”) will be developed and tested for implementation by spring 2007

• Large-scale version (diagostic cloud-fraction; fewer prognostic variables) to be developed soon

• For code, support, bug reports, or question:

Jason.Milbrandt@ec.gc.ca

MERCIMERCI