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

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)

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

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

Cloud Microphysical Processes BAMS, 1967

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

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)

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:

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:

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

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)

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

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

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

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.)

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)

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)

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

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

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

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)

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

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

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]

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.

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

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]

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.

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