1. A new approach to parameterize ice-phase microphysics
The Predicted Particle Properties (P3) Scheme
Part 1:
A new approach to parameterize
ice-phase microphysics
Jason Milbrandt
Environment and Climate Change Canada (RPN-A)
in collaboration with
Hugh Morrison
National Center for Atmospheric Research (MMM division)
ICEPOP_2018 Meeting
Lakai Sandpine Resort, 6-9 September 2016

2. Roles of Clouds in MODELS
Three main purposes:
optical properties (for radiation scheme)
thermodynamic feedbacks (latent heating/cooling; mass loading)
precipitation (rates and types at surface)

3. Testing the Milbrandt-Yau microphysics scheme in WRF
MOR-hail (only)
MY2 - hail (only)
MOR-graupel (only)
MY2-baseline (g + h)
idealized 1-km WRF simulations (em_quarter_ss)
base reflectivity
Microphysics Schemes:
MOR: Morrison et al. (2005, 2009)
MY2: Milbrandt and Yau (2005)
Morrison and Milbrandt (2011), MWR

4. The simulation of ice-containing cloud systems is often
very sensitive to how ice is partitioned among categories
MOR-hail (only)
MY2 - hail (only)
MOR-graupel (only)
MY2-baseline (g + h)
idealized 1-km WRF simulations (em_quarter_ss)
base reflectivity
Microphysics Schemes:
MOR: Morrison et al. (2005, 2009)
MY2: Milbrandt and Yau (2005)
Morrison and Milbrandt (2011), MWR

5. Cloud Microphysical Processes
BAMS, 1967

6. Microphysics Parameterization Schemes
Hydrometeors are traditionally partitioned into categories
CLOUD
ICE
SNOW
GRAUPEL
RAIN
HAIL
BAMS, 1967

7. Microphysics Parameterization Schemes
The particle size distributions are modeled
e.g.
For each category, microphysical processes are parameterized to predict the evolution of the particle size distribution, N(D)
SNOW
TYPES of SCHEMES:
N (D)
D [ m]
100
[m-3  m-1] 20 40 60 80
101
10-1
10-2
Bin-resolving:
Bulk:
(spectral)

8. BULK METHOD 3rd, 0th, 6th MOMENTS: Nx(D) D Size Distribution Function:
Total number concentration, NTx
Radar reflectivity factor, Zx
Mass mixing ratio, qx
3rd, 0th, 6th MOMENTS:
100 20 40 60 80
101
10-1
10-2
(assuming spheres)
Nx(D)
Hydrometeor
Category x
Hydrometeor
Category x D
Size Distribution Function:
pth moment:

9. BULK METHOD 3rd, 0th, 6th MOMENTS:
Total number concentration, NTx
Radar reflectivity factor, Zx
Mass mixing ratio, qx
3rd, 0th, 6th MOMENTS:
Predict changes to specific moment(s)
e.g. qx, NTx, ...
(assuming spheres)
Implies changes to values of parameters
i.e. N0x, lx, ...
Size Distribution Function:
pth moment:

10. Traditional Approach: PARTITIONING HYDROMETEORS INTO CATEGORIES
BULK METHOD
Traditional Approach:
PARTITIONING HYDROMETEORS INTO CATEGORIES
CLOUD
ICE
SNOW 
HAIL
RAIN
GRAUPEL 

11. Historical development of bulk schemes
began with liquid-only: “cloud” and “rain” (1-moment)
added ice-phase: “ice” and “snow” – analogy to cloud/rain
added more classes (ice-phase) to account for different physical characteristics that affect growth and fall velocities
ICE, SNOW
ICE, SNOW, GRAUPEL
ICE, SNOW, GRAUPEL, HAIL
expansion to 2-moment
expansion to 3-moment
predicted rime fraction
predicted graupel density
predicted crystal axis ratio
combine everything (e.g. Chen et al. 2016, JAS)

12. Bin-resolving coalescence model SOURCE: Berry and Reinhardt (1974)
The warm-rain coalescence process
RAIN
CLOUD
Mass Density [g m-3 (lnr)-1]
Time [min]
DRIZZLE
Bin-resolving coalescence model SOURCE: Berry and Reinhardt (1974)
Radius [cm]
Partitioning of Coalescence Processes:
Autoconversion (cloud to rain)
Accretion (rain collecting cloud)
Self-collection (rain collecting rain)  multi-moment only

13. 2-moment BULK model solution BIN model reference solution
Source: Cohard and Pinty (2000a)

14. Ice Phase Observed crystals: Complex shapes, densities, etc.
growth/decay processes include: deposition/sublimation, riming (wet/dry growth), ice multiplication, aggregation, gradual melting, shedding, …
 Difficult to represent simply

15. Predicted Particle Properties (P3)*
New Bulk Microphysics Scheme:
Predicted Particle Properties (P3)*
NEW CONCEPT
“free” category – predicted properties, thus freely evolving type
vs.
“pre-defined” category – traditional; prescribed properties
Compared to traditional (ice-phase) schemes, P3:
avoids some necessary evils (ad-hoc category conversion, fixed properties)
has self-consistent physics
is better linked to observations
is more computationally efficient
* Morrison and Milbrandt (2015) – Part 1
Morrison et al. (2015) – Part 2
Milbrandt and Morrison (2016) – Part 3
(all in J. Atmos. Sci.)

16. Prognostic Variables: (advected)
Overview of P3
Prognostic Variables: (advected)
LIQUID PHASE: 2 categories, 2-moment:
Qc – cloud mass mixing ratio [kg kg-1]
Qr – rain mass mixing ratio [kg kg-1]
Nc – cloud number mixing ratio [#kg-1]
Nr – rain number mixing ratio [#kg-1]
ICE PHASE: nCat categories, 4 prognostic variables each:
Qdep(n)* – deposition ice mass mixing ratio [kg kg-1]
Qrim(n) – rime ice mass mixing ratio [kg kg-1]
Ntot(n) – total ice number mixing ratio [ # kg-1]
Brim(n) – rime ice volume mixing ratio [m3 kg-1]
* Qtot = Qdep + Qrim , total ice mass mixing ratio (actual advected variable)

17. Prognostic Variables:
Overview of P3
A given (free) category can represent any type of ice-phase hydrometeor
Prognostic Variables:
Qdep – deposition ice mass mixing ratio [kg kg-1]
Qrim – rime ice mass mixing ratio [kg kg-1]
Ntot – total ice number mixing ratio [# kg-1]
Brim – rime ice volume mixing ratio [m3 kg-1]
Predicted Properties:
Frim – rime mass fraction, Frim = Qrim / (Qrim + Qdep) [--]
rim – rime density, rim = Qrim / Brim [kg m-3]
Dm – mean-mass diameter, Dm  Qtot / Ntot [m]
Vm – mass-weighted fall speed, Vm = f(Dm, rim, Frim) [m s-1]
etc.
Diagnostic Particle Types:
Based on the predicted properties (rather than pre-defined)

18. RIME COLLECTION IN CRYSTAL INTERSTICES
Overview of P3
Particle properties (e.g mass-diameter relations*) for process rate calculations are based on conceptual model of particle growth following Heymsfield (1982)
ICE INITIATION
VAPOR GROWTH
RIME COLLECTION IN CRYSTAL INTERSTICES
AGGREGATION D
spherical ice
 = /6 bulk_ice
 = 3
unrimed crystals
 = const
 ~ 2
partially rimed crystal
 = f(Frim, rim)
 ~ 2
spherical graupel
 = /6 grpl
 = 3
* m(D) = D

19. P3 SCHEME – Determining m(D) = D for regions of D:
Predicting process rates ~ computing Mx(p)
P3 SCHEME – Determining m(D) = D for regions of D:
e.g. Frim = 0
conceptual model + algebraic derivation
spherical ice
1 = /6 bulk_ice
1= 3
unrimed, non-spherical crystals
2 = const
2 ~ 2
based on observed crystals

20. P3 SCHEME – Determining m(D) = D for regions of D:
Predicting process rates ~ computing Mx(p)
P3 SCHEME – Determining m(D) = D for regions of D:
General: 1 > Frim > 0; for a given rim
spherical
unrimed
m(D) = 1 D1
non-spherical
unrimed
m(D) = 2 D2
non-spherical,
partially rimed
m(D) = 3 D3
spherical
completely rimed
m(D) = 4 D4

21. P3 SCHEME – Computing N(D) parameters :
Predicting process rates ~ computing Mx(p)
P3 SCHEME – Computing N(D) parameters :
Compute properties Frim = Qrim/(Qdep+Qrim), rim = Qrim / Brim
Determine integral ranges, Dth, Dgr, Dcr
Determine PSD parameters (, N0, μ)
solved numerically (iteratively; pre-computed and stored in look-up table)
4. Also, match A-D parameters to m-D parameters for the various regions of D
based on geometric + empirical relations
for V-D (process rates and sedimentation) and ri_eff (optical properties)

22. P3 SCHEME – Computing the process rates:
Predicting process rates ~ computing Mx(p)
P3 SCHEME – Computing the process rates:
Now, have , N0, μ, and integral ranges Dth, Dgr, Dcr (plus (i), (i), …)
ACTUALLY, FOR P3:
(and X2, …)
Predicting process rates  computing sums (Xn) of partial moments

23. P3 SCHEME – Computing the process rates:
Predicting process rates ~ computing Mx(p)
P3 SCHEME – Computing the process rates:
Now, have , N0, μ, and integral ranges Dth, Dgr, Dcr (plus (i), (i), …)
All process rates are proportional to one or more sums (X1) of sub-moments
Relevant sums of sub-moments are pre-computed (accurately) and stored in a look-up table
At run time, values of X1, X2,.. are accessed (quickly) via look-up table  actual computation of Q|PROC_x is fast

24. Idealized 2D squall line
PROGNOSTIC Variables
DERIVED Physical Properties qr Z qc
Frim ρi qi
qrim
Brim Ni Vm Dm
(Nc and Nr not shown)
Morrison and Milbrandt (2015)
[Part 1]

25. Vertical cross section of model fields (t = 6 h)
Fr ~ 0-0.1
 ~ 900 kg m-3
V ~ 0.3 m s-1
Dm ~ 100 μm
 small crystals
Ice Particle Properties: 
Fr ~ 0
 ~ 50 kg m-3
V ~ 1 m s-1
Dm ~ 3 mm
 aggregates    
Frim ρi   
Fr ~ 1
 ~ 900 kg m-3
V > 10 m s-1
Dm > 5 mm
 hail   Vm Dm
Note – only one (free) category
etc.

26. 1-km WRF Simulations with P3 microphysics (1 category):
Reflectivity
dBZ
Observations
Observations
Morrison et al. (2015) [P3, part 2]

27. WRF Results: Base Reflectivity (1 km AGL, t = 6 h)P3
MOR-H
WDM6
MOR-G
THO
Observations
dBZ
MY2
WSM6
Morrison et al. (2015) [P3, part 2]

28. Timing Tests for 3D WRF Simulations # prognostic variables
Scheme
Squall line case (x = 1 km)
Orographic case (x = 3 km)
# prognostic variables P3
0.436 (1.043)
0.686 (1.013) 7
MY2
0.621 (1.485)
1.012 (1.495) 12
MOR-H
0.503 (1.203)
0.813 (1.200) 9
THO
0.477 (1.141)
0.795 (1.174)
WSM6
0.418 (1.000)
0.677 (1.000) 5
WDM6
0.489 (1.170)
0.777 (1.148) 8
Average wall clock time per model time step (units of seconds.)
Times relative to WSM6 are indicated parenthetically.

29. ICMW* 2016 WORKSHOP CONCLUSION:
BULLET POINT FROM
ICMW* 2016 WORKSHOP CONCLUSION:
In order to advance the parameterization of ice-phase microphysics (in bulk and bin schemes), the modeling community should move towards the paradigm of free ice-phase categories
* International Cloud Modeling Workshop
(summary presented at ICCP 2016, Manchester UK