Georg Grell

NOAA / Earth Systems Research Laboratory

Parameterizing Convection: from mass flux

schemes to an ensemble/stochastic scheme (Grell-

Devenyi, GD) to fully stochastic scale- and aerosol-

aware approaches

Overview • Some general aspects on mass flux type

convective parameterizations

• Parameterizing convection on “gray-scales”

• The G3D and GF schemes

• Applications

– Scale awareness

– Aerosol awareness

– Stochastics

– Latest results on using GF in NOAA’s Next Generation

Global Prediction System (NGGPS)

• Towards more unified parameterizations

The G3D scheme, developed more

than a decade ago

• Remove AS closure (SAS GFS)

• Add an ensemble to look at the min/max/average values of the other ensembles within the nearest neighbor grid points (could be nine or 25 grid points)

• Add a random number generator to arbitrarily pick some ensemble values out of the “pack”

– Random number generators that come with compilers

– Other modeling system that are using G3 (global FIM as well as Brazilian RAMS model) also use arbitrary random modifcations

More changes: G3 versus GD

The G3 scheme has additional features that may be

turned on or off:

• Horizontal and vertical smoothing of tendencies

• A similar ensemble/stochastic approach to

shallow convection

• Option for tracer transport and some aqueous

phase chemistry and scavenging

• Direct coupling with atmospheric radiation (and

photolysis) through outputting clw/ice mix

ratios and cloud fraction

Cumulus

induced

compensating

subsidence

Downdraft

detrainment

Updraft

detrainment

Lateral

entrainment

and

detrainment

G3d modification for gray scales: nine grid boxes

Subsidence spreading – a 3D

application • Mass detrainment at top and bottom are spread over

neighboring grid cells

• No preferred directional choice in spreading, all grid

points are treated equally

• No other direct dependence of one grid point on

another (e.g., subsidence or other terms will not impact

unresolved convection through additional

forcing/suppression)

• Like a running average over a larger grid area!

We consider this a somewhat clumsy initial step towards.

It is, however, decreasing the subsidence heating and

leads to a shift of unresolved versus resolved

precipitation, increasing the resolved part

A step further: using Arakawa’s approach in

Grell-Freitas (GF)

8

Grell-Freitas Convective Param

• Scale-aware/Aerosol-aware (Grell and Freitas, 2014, ACP) • Stochastic approach adapted from the Grell-Devenyi

schem • Originally many parameters could be perturbed • In 2014 version only 2 were kept (closures and

capping inversion threholds) • Scale awareness through Arakawa approach (2011) • Aerosol awareness is implemented with empirical

assumptions based on a paper by Jiang and Feingold • Separate shallow scheme also exists with modifications

by Joe Olson – another version is used in Joe’s MYNN moist EDMF approach (towards a unified approach)

1. Spreading of subsidence? This is equivalent to applying the parameterization over a larger area – G3- scheme (in WRF and BRAMS)

2. Letting the model do the subsidence? What then is the understanding of “vertical eddy fluxes” ?

3. Arakawa et al., 2011 simply define a setup that will lead to convergence to an explicit solution and get

4. Problem: Define fractional coverage (σ) = area covered by active updraft and downdraft plume

5. In GF, we define very simple relationship between σ and entrainment rate (which is related to radius of plume) – but any other approach may easily be used

6. Initial entrainment rate determines when σ is becoming important (when scale awareness kicks in),

– Maximum allowable fractional coverage determines when scheme transforms itself to a shallow convection parameterization

– This effect can be turned off

The scale awareness: Our adaptation of Arakawa’s approach

Variable Resolution Tests

using the Grell-Freitas Convection Scheme (Laura Fowler, Bill Skamarock, GF group)

MPAS Physics:

• WSM6 cloud microphysics

• Grell-Freitas convection scheme

• Monin-Obukhov surface layer

• YSU PBL

• Noah land-surface

• RRTMG lw and sw.

MPAS mesh:

50 – 3 km variable resolution.

CONUS is the 3 km region.

Very smooth transition to the 50 km

region.

MPAS results for South America runs

CONVECTIVE HEATING RATE (K day-1) GRID-SCALE HEATING RATE (K day-1)

Variable Resolution Tests

with the Grell-Freitas Convection Scheme

MPAS 50-3 km mesh, Grell-Freitas convection scheme

10-13 January 2014 forecasts, 3-day average heating rates

Model Setup

WRF-ARW is initialized with a weak axisymmetric vortex

disturbance in an idealized tropical environment that is

favorable for the vortex disturbance to develop into a

hurricane. The initial mass and wind fields associated with the

weak vortex disturbance are obtained by solving the nonlinear

balance equation for the given wind distributions of the initial

vortex (Wang 1995, MWR), and the prescribed background

thermal sounding and winds.

• f-plane located at 12.5ºN

• A prescribed axisymmetric vortex:

— maximum surface tangential wind: 15 ms-1

— radius of surface maximum wind: 90 km

• Quiescent environment thermally corresponding

to the Jordan sounding with a constant sea

surface temperature of 29ºC

• The models are run with 2 domains, a 9 km

outer domain with a vortex-following 3-km nest and 43

vertical levels

All experiments use a Monin-Obukhov surface layer, the unified

Noah land-surface model, 3dTKE mixing and no cumulus

parameterization on the 3 km grid.

The control configuration for radiation is the RRTM scheme for

longwave and Dudhia scheme for shortwave radiative forcing.

Model setup for full 3d idealized tests

• A prescribed weak axisymmetric vortex:

— maximum surface tangential wind: 15 ms-1

— radius of surface maximum wind: 90 km

• initial mass and wind fields associated with the weak vortex disturbance are obtained

by solving the nonlinear balance equation for the given wind distributions of the initial

vortex (Wang 1995, MWR)

• Idealized environment thermally corresponding

to the Jordan sounding with a constant sea

surface temperature of 29ºC (favorable for hurricane development)

• f-plane located at 12.5ºN

• 4 different resolutions are used, 27-9-3-1km. There is no 2-way interaction. 43 vertical levels

All experiments use a Monin-Obukhov surface layer, the unified Noah land-surface

model, modified 3dTKE mixing

Tropical Cyclone scale awareness fully 3d simulations

total precipitation convective precipitation

27km

3km 9km 3km 9km

27km

Early stage of storm development

Heating and drying tendencies at 36hr ( deg/day) – averaged inner part of 3km domain

He

igh

t (k

m)

Cloud tops at ~7km

Heating tendencies Drying tendencies

Heating tendencies (contours) Drying tendencies (contours)

Crossection through center of storm, dx=3km, vertical velocity in color (m/s)

Parameterization can not handle tilt, could be a significant problem if tendencies would not be so miniscule

Cross-section through center of storm, dx=1km, vertical velocity in color (m/s)

Heating tendencies (contours) W (m/s) in color

Drying tendencies (contours) W (m/s) in color

Actually looks better on dx=1km!

Adding a 1km resolution simulation

Domain averaged (3km resolution domain) precipitation rate (mm/h) and fraction of convective to total rain

Heating profiles from convective parameterization for idealized tropical cyclone simulations at 27km, 9km, and 3km

Average cloud top at 7km

Average cloud top at 3km

Drying profiles from convective parameterization for idealized tropical cyclone simulations at 3km and 1km (!) resolution

Idealized 3d tropical cyclone simulation

Scale-awareness seems to work fine with the very simple Arakawa (2011) approach, as well as other

very simple assumptions to estimate a fractional coverage.

Including the effect of aerosols – Why?

• Aerosol interactions are an important link for climate,

weather, and air quality. Considering their interactions by

using coupled approaches maybe an important next step in

future modeling systems (Grell and Baklanov, 2011)

24

Aerosol awareness

Change 2: Modified evaporation of

raindrops (Jiang and Feingold)

based on empirical relationship

Change 1: Change constant

autoconversion rate to aerosol

(CCN) dependent Berry conversion

¶rrain

¶t

æ

èç

ö

ø÷

autoconversionBerry, 1968

=rr

c( )2

60 5+0.0366 CCN

rrcm

æ

èç

ö

ø÷

Change 2 introduces a proportionality between precipitation

efficiency (PE) and total normalized condensate (I1), requiring

determination of the proportionality constant Cpr

25

Aerosol awareness

The dependency introduced through precipitation efficiency

• can have a strong effect on downdrafts, but is

• limited by other environmental conditions (e.g., if the precipitation

efficiency is already very low, it cannot get much lower, and vice

versa)

How do we get CCN? 1. Most sophisticated approach:

directly from complex model results (WRF-Chem) 2. Simplest approach:

from observed Aerosol Optical Thickness (AOT) at 550 nm (global or regional analysis), following Rosenfeld et al. (2008) and Andreae et al (2008), using

3. Or anywhere in between – depending on complexity of model setup

Typical vertically averaged PM25 distribution

Systematic and random SW differences (Chem – Met)

(almost every run, 20 runs, 3-day forecasts)

Random changes, caused by different

location of clouds, not interesting at this

point

Apparently random changes, interesting

because of high aerosol concentrations,

usually less SW radiation reaching the ground

Systematic changes, in almost every run

g/kg

Differences in integrated cloud water and ice concentrations, 36 hour

simulations starting Sep 9, 12Z. DX=5km, displayed is Sep 10, 12Z

MET - Chem

More cloudwater in the met run! But only in the lowest levels!

Results from 5km resolution simulation, T2m differences,

CHEM - MET

Sep 10, 12Z

Next: 1.7km resolution, convection: WRF-Chem simulation over 30hr period, initialized at 18Z, Sep 9

Low level clouds in NE corner do not exist in run with indirect effect included…

T2M differences, Chem-Met, 12Z, Sep 10

Hourly precipitation difference

T2M, 18Z, Sep 10

Box averaged vertical profile of CLW+ICE

RNW+SNOW at different locations

Averaging in areas with significant convection

RNW unpredictable: Convection has

different strength

Lat = -4.5 to -6.5 Lon -68 to -72

CLW and ICE appear to have a signal

1.E6*kg/kg

1.E6*kg/kg

1.E6*kg/kg

PM2.5 (μg/m3)

PM2.5 (μg/m3)

PM2.5 (μg/m3)

So what if you try this with aerosol-awareness

turned on in the GF convective

parameterization

Previous 1-d tests • much more detrainment of

cloud water and ice at cloud top

• less suspended hydrometeors, especially in lower part of parameterized clouds

• stronger downdrafts. Leading to less drying in and just above the boundary layer, but stronger cooling in lowest levels

Polluted (AOD=1.)

clean (AOD=.01)

33

T2M difference fields, September 10, 1200UTC- mid-morning. Positive (red) is

warmer compared to MET – simulation with convective parameterization

DIR +IND

Convection

permitting

simulations

DX=5km DX=1.7km

Using convective

parameterization

with and without

aerosol

awareness

Why should this be related to convective parameterization?

Direct effect only

Aerosol tests – initial conclusions

• Tropical environments may be the most likely to see an impact – signal strength also very important (very low or very high AOD)

• Strength of convection at this point, and with our model setup, may be difficult to correlate to aerosols

• Initial results for aerosol aware convective parameterization indicate more tests needed

– Shallow convection

– Use CCN from model

• 3d impacts will depend on environmental conditions

– Because of the dependence of precipitation efficiency on wind shear and subcloud humidity in addition to CCN, impacts in middle latitudes may be much more mixed

Stochastic parameter perturbation: example

using GF scheme

• For stochasticism: significantly different from original approach

through bringing in temporal and spatial perturbations, but still

possible to perturb the ensembles

• Apply directly to closure assumptions – for location and strength of

convection

• In GF, apply to skewness and sharpness of vertical mass flux PDF’s: an

easy way to significantly alter vertical heating and drying profiles, but

conserving mass

• Momentum transport

Using SPP to perturb normalized vertical

mass flux PDF’s

• Perturbed 8-member RAP ensemble. Mean is compared against deterministic

RAP – initial results are for 4 days only

• July 1, 3, 5, and 8, initial time 00Z

Preliminary results produced by Isidora Jankov, only looking at

direct forecast impacts, no data assimilation for this experiment.

Temperature Bias and RMSE profiles for 24hr lead time

stochastic

deterministic

SPP: Opportunities, but much work remains

• Simple initial test for perturbing normalized vertical mass flux PDF’s: For most

of the variables similar or improved performance from the ensemble mean

(including RH, winds and precipitation)

• Coupling with SKEBS (J. Berner)

• Sensitivity: much to learn with “best” stochastic fields, but also limits to

perturbation of PDF’s

• Can any of this be tied in a meaningful way to physics?

• Are other stochastic approaches (Cellular Automaton, Markov Chain) an option?

• Momentum and closures

• Momentum transport (as in SAS and/or ECMWF)

• Additional closure for deep convection: Diurnal cycle effect (Bechtold)

• Impacts of mixed phase physics

• PDF approach for normalized mass flux profiles was implemented

• Originally to fit LES modeling for shallow convection

• allows easy application of mass conserving stochastic perturbation of vertical

heating and moistening profiles

• Provides smooth vertical profiles

• Third type of cloud (congestus type convection)

• Changed cloud water detrainment treatment

• Changed cloud water/rain conversion

• Impacts of memory (impacting PDF’s, entrainment, cloud water detrainment

• Stochastic part now coupled to Stochastic Parameter Perturbation (SPP), and

Stochastic Kinetic Energy Backscatter (SKEBS) approach (J. Berner )

• Inversion detection routine used to determine top heights of shallow and mid level

convection

• Additional closures for shallow convection (Boundary Layer Equilibrium (BLQE,

Raymond 1995; W*, Grant 2001, Heat Engine, Renno and Ingersoll, JAS 1996)

Versions now used in WRF, FIM, GFS, GEOS-5, MPAS, FV3

Recent (since ACP paper) new implementations into GF scheme

Effect of cloud scale horizontal pressure gradients (Gregory et al. 1997, Zhang

and Wu, 2000) is to adjust the in-cloud winds towards those of the large scale

flow. For the ECMWF approach (follows Gregory et al., 1997), the entrainment

rate is simply adjusted

E(u,v)up=Eup +λDup

D(u,v)up=Dup +λDup λ can be perturbed stochastically. Or used for tuning.

Where E(u,v) and D(u,v) are simply the entrainment/detrainment rates.

For SAS approach equations follow directly Zhang and Wu, 2003,

• The pressure gradient force across the updraft is proportional to the

product of mass flux and vertical shear of the mean wind,

• Proportionality constant is -.55 for Zhang and Wu,

• Gregory at al at first assumed the constant to be -.7

Tuning of momentum transport will not change HAC’s, but may help with

wind biases, especially in the tropics. Also appears important for TC’s.

Momentum transport

As in ECMWF, we also include an additional heat source representing

dissipation of kinetic energy (Steinheimer et al 2007)

Momentum

transport

Changing the vertical

mass flux PDF’s

• Large changes in vertical

redistribution of heat and

moisture

• Mass conserving for

stochastic approaches

• significant impact on HAC’s

Large impact for tuning: normalized mass flux PDF’s

Heating Drying Clw + Ice

deg/day kg/kg/day kg/kg/day

GF – lower atmos. maximum of mass flux

GF – maximum of mass flux higher in

atmos. SAS

Playing with the mass flux PDF’s in HWRF/GF: Keeping

the maximum normalized profile lower in the atmosphere

leads to very similar profiles as SAS

Shown is only a comparison on domain 1

Changing momentum

transport constants:

• large impact on comparison

of global wind speed biases

• Improving wind bias has

significant impact on HAC’s

but does not necessarily

improve HAC’s

Diurnal Cycle implementation,

120 hour forecasts:

• precipitation averaged over

Amazon basin is improved

• HAC’s little impacted

Impact of momentum transport and diurnal cycle

implementation

By far largest impact in GFS physics is

from clw detrainment profiles

Small changes in clw/ice detrainment can cause

large impact in biases – from microphysics

Small changes in clw/ice detrainment can cause large impact in biases – interaction with microphysics

Large impact in physics from clw detrainment profiles

Red using old GF

Blue using new GF

FIM, 120hr forecasts, 30

days, only change is a slight

modification of clw

detrainment

WRF, 12hr forecasts, RAP with cycling for

10 days, many other changes

BIAS RMSE

FIM-BIAS

Tuning: usually done within a physics suite, will

determine statistical performance for operational

applications!

• WRF version of GF was originally tuned to meet RAP standards

(RAP/HRRR physics suite), focus on US, short range storm

scale type verification

• Use in other suites requires significant knowledge of other

physics parameterizations used

RAP CSI/BIAS Precipitation Summer (Three Weeks Jul 2016)

6 hr 1 hr 12 hr

Red using old GF

Blue using new GF

Latest results using FV3GFS, C384, June 2016

average of 30 forecasts out to 10 days

Time series of Day 7 Height anomaly correlation

NH SH

Precipitation verification over CONUS, 24hrly accumulations

DAY 2

DAY 3

CSI Bias

High bias for low

thresholds: We think we

can fix this if caused

from convective

parameterization

Total

precipitation

(mm/day)

Convective

precipitation

SASAS 3.33 2.07 (62.2%)

GF 3.55 1.99 (56.1%)

Global precipitation

average: Still little too high

Monthly averaged short wave

radiation, compared to NASA’s

Clouds and the Earth's Radiant

Energy System (CERES)

and globally average precipitation

Shallow Convection parameterization (work in collaboration with Saulo Freitas)

• envisions bubbles rising from PBL into free atmosphere

• feedback through strong lateral mixing and subsidence

• “ensemble” version

variations of size of bubbles

different closure assumptions to determine strength and location of convection

feedback of ensemble-mean-changes to the model

so far computational requirements of ensemble version significantly increased

• scheme is similar to deep convection parameterization, but no downdrafts, no rain, different detrainment as well as closure assumptions, and different choices of ensembles

Scale-Aware Requirements for a Turbulent Mixing Scheme

Boundary Layer-Cloud Physics Development

1)Reduction of parameterized mixing as dx -> 0. 2)Change in the behavior of the scheme as dx -> 0.

• Mass-flux (shallow-cu) scheme – represent smaller plumes as dx -> 0. • Eddy Diffusivity scheme – transforms to 3D mixing as dx -> 0.

3)Addition of stochastic physics when an ensemble of processes are no longer represented.

Subgrid clouds in the MYNN-EDMF Scheme • Stratus component from partial-condensation scheme within

the eddy diffusivity component. • Shallow-cumulus component from mass-flux component.

Towards unified schemes: Looking at shallow convection as

a part of Boundary Layer physics (PBL), coupled with

microphysics and radiation schemes

MYNN Boundary Layer Scheme Modifications

1.Mass-flux component (MYNN-EDMF) – Dynamic Multi-Plume: dynamic number/sizes of plumes.

• Adapts to different mode grid spacing • Adapts to growth of PBL.

– Options to transport momentum, TKE, and chemical species. – Option to activate stochastic lateral entrainment rates (Suselj et al. 2013). – Total mixing (mass-flux transport & eddy diffusivity) is solved simultaneously and

implicitly (Suselj et al. 2013).

2.Subgrid-scale clouds – Chaboureau and Bechtold (2002 & 2005) convective & stratus components. – Diagnostic-decay method implemented. – Coupled to the radiation schemes.

57

Dynamic Multi-Plume (DMP)

A) The maximum number of plumes available (Nmax) is determined by the model grid spacing. Max plume width = 0.75*dx

Boundary Layer-Cloud Physics Development

1 2 3 4 5 6 7 8 9 10 (#) 100 200 300 400 500 600 700 800 900 1000 (m)

1 2 3 4 5 6 7 (#) 100 200 300 400 500 600 700 (m)

B) Number of plumes (N) is further limited by the PBLH. For example, at dx = 1000 meters, a maximum of 7 plumes are available, but the number used grows as the PBLH grows:

Taken from Neggers et al. 2003, JAS

58

• For each set of the LAM simulations (at grid spacings of 1, 2, 4, 8, 16 km), two permutations were run:

1. GF deep-cu scheme OFF GF shallow-cu scheme OFF.

2. GF deep-cu scheme ON GF shallow-cu scheme ON.

• 36 hour simulations are done using ECMWF analyses beginning at 12 UTC 30 Jan 2010, and used every 6h to generate LBCs for the coarsest domains.

• Two set of 1-way nested domains are used:

• 16-4-1 km grids • 8-2 km grids

The Grey Zone Project (headed by UK Met Office) aims to systematically explore convective transport and cloud processes in NWP models at resolutions ranging from 1 to 16 km.

Integrated Cloud Water & Ice

Grey Zone Project to test scale awareness