Tue 2/23/2016Convective parameterization:

• Parameterized convective momentum transport• Adjustment scheme conceptual design

Reminders/announcements:- Convective parameterization assignment (due today)- Short “progress report”, due Th 2/25, to allow feedback- Midterm Thu 3/3 (2014 exam posted on www page)

• Considering take-home portion, summarizing CP papers• See BMJ “lab review exercise” on class web page: Practice for exam

- Project hypothesis assignment, due (presented) Tue 3/15

Convective ParameterizationOutline for convective parameterization (CP) section:

A. Concept 1.) Thought experiment2.) Concepts and processes

B. Why CP schemes are needed and matter1.) Types of NWP problems affected by CP schemes2.) Convective momentum adjustment

C. CP Scheme Fundamentals1.) Adjustment versus mass-flux schemes2.) The Betts-Miller-Janjic CP scheme3.) The Fritsch-Chappell and Kain-Fritsch schemes4.) Tiedtke and Arakawa-Schubert schemes

D. Modifications to CP schemes, model experiments

Convective parameterization (CP) exhibits some similarities to turbulence parameterization, but important differences too (e.g., upscale growth of convective systems, MCS)

CP also requires scale separation between resolved, parameterized processes

Weisman et al. (1997) show that 4-km grid length sufficiently matches 1-km grid length to justify omission of CP

Bryan et al. (2003) suggest that much higher resolution (order 100 m grid) required for research-grade simulations

Summary from last class

• Cloud-resolving models have used LES to parameterize subgrid terms for decades; literature review suggests that the appropriateness of using traditional LES closures for this purpose has never been established

• The statistical properties of the simulated squall lines are still not converged between the 250- and 125-m runs

• It is clear that simulations with O(1 km) grid spacing should not be used as benchmark or control solutions for resolution sensitivity studies

• The simulations also support the contention that a minimum grid spacing of O(100 m) is required for traditional LES closures to perform appropriately for their design

• For the research community, O(100 m) grid spacing is recommended for most applications, because a modeling system that is well founded should be desired for most purposes (!)

A few quotes from Bryan et al. (2003)

CP papers of interest

CP Thermodynamic tendency

1st Law: )(_

convectioncumulust

What physical processes need to be represented on the right side of this equation?

What environmental factors would influence the strength of these processes?

In exercise, take a try at developing a simple parameterization

CP Thermodynamic tendency

1st Law:

pdtdqL

t convectioncumulus _

Include latent effects and grid-averaged convective heat flux convergence

Must parameterize and similarly in moisture equation q

Cumulus ConvectionHow is the cumulus field on this day changing the larger-scale environment in which it is embedded?

- Stabilize environment (warming aloft, cooling below)

- Compensating subsidence warms, dries air outside convective towers

- Moistens air aloft, transports water vapor upward

- Produces cloud cover aloft (anvil material) if Cumulonimbus, alters grid-cell albedo

- Alters momentum (especially with large shear)

- Generates precipitation, results in net drying in column

Cumulus ConvectionWhat processes and motions are involved?

- Convective up and downdrafts• Vertical advection, adiabatic expansion/compression

- Compensating subsidence (outside convection)

- Associated turbulent motions (entrainment, detrainment)

- Water substance phase changes• Condensation, evaporation, perhaps freezing, melting, etc.

• Cloud formation – interactions with microphysics, radiation

- Precipitation; vapor removed from atmosphere, net drying on grid scale

Processes represented by CP scheme

Indirect radiative effects

Precipitation onset Cloud mixing, etc. stratocumulus

Temperature tendencies

Moisture tendenciesConvective QPF

Convective Parameterization thought experiment

What is the impact of sub-grid scale convection on the grid-scale atmosphere over the Southeast?

Radar mosaic (Composite)

GFS forecast for this case

Blue: Total 6-h precipitationGreen: CP 6-h precipitation

Convective precipitation is implicit

About CP PrecipitationConvective precipitation does not generally require:

- Any grid-scale ascent or vertical motion

- Any production of grid-scale clouds or precipitation

- Any portion of the vertical profile to reach saturation

CP precipitation must be evenly distributed over grid cells

Thus, spatial coverage of convective precipitation is greater than observed, and unrealistically homogeneous

This is perfectly consistent with CP design, but users must understand the distinction

Two Approaches to Convective Parameterization

• Adjustment Schemes (e.g., BMJ)– Nudge vertical profile toward empirical reference profile – Tendency profile related to difference between moist

adiabat inside cloud and ambient moist adiabat

• Mass Flux Schemes (e.g., KF)– Attempt to explicitly model convective feedback

processes in each grid cell

Convective momentum transport

• Many CP schemes only alter temperature, moisture (e.g., KF, BMJ), not momentum

• Several newer schemes do account for this (Tiedtke, Zhang McFarlane, SAS)

Can we neglect CP momentum transport?

Real convection alters both thermodynamic & momentum fields

Thermodynamic parameterization is relatively straightforward

Momentum adjustments currently range from complete neglect to inclusion of mesoscale pressure forces

Convective Momentum Transport (CMT) included in many climate and global model CP schemes

Historically, less attention to CMT in mesoscale models – why?

See earlier studies from Moncrieff, LeMone, Wu, Zhang, Gregory, Stevens, Shapiro, Mechem, Houze, Holton, Grubisic, Mahoney and others

Why is subgrid-scale CMT often neglected in mesoscale models?

Often run with sufficiently small grid spacing to omit convective parameterization (CP) scheme

Grid lengths in question often partially resolve organized convective systems (e.g., 12-km grid length)

Complicated because momentum doesn’t mix like a scalar! Must account for pressure effects

Previous observational and modeling work demonstrate importance of subgrid CMT on wind field

Current Treatments of CMTAdded to GFS to help squelch spurious hurricanes (Han & Pan 2006)

Climate models: Including CMT improves representation of ITCZ (Wu, Zhang, and others)

Mesoscale models: Older Fritsch-Chappell scheme included CMT formulation; Kain-Fritsch mass-flux scheme designed for inclusion, but omitted

WRF-ARW: CP scheme only passed thermodynamic (T, q) tendencies to solver until V3.3 (fairly recently)

Former student Megan Mallard (now EPA) and I modified WRF-ARW Kain-Fritsch CP scheme to compute, pass horizontal momentum tendencies

What does organized convection do to grid scale wind field?

Examine output from high-resolution idealized MCS simulation (1-km grid)

Zonal wind cross section normal to convective line

See Mahoney et al. (2009, MWR) for details

CMT ConfigurationModified routines to pass RUCUTEN, RVCUTEN to solver from

KF scheme

Included CMT formulation in module_cu_kfeta.F

2 2 2 1 1 11~ u d u d u d m u um d dm

conv

u u u u u ut p

Similar for v wind component; is this a “local” or “non-local” formulation?

KF computes updraft, downdraft mass flux, corresponding u, d andentrainment and detrainment rates, and

Overbars denote grid-scale values, subscripts 1 and 2 indicate top, bottom of grid cell for which momentum tendency computed

See Kain and Fritsch (1990) for details

Environment: Pseudo-Idealized

What “should” parameterized

convection do in this environment?

Cross-line zonal wind speed for simulation of idealized MCS with dx = 1 km

12 km

10 km

8 km

6 km

4 km

2 km

Sfc

Model ConfigurationQuasi-idealized squall line in idealized environment in

thermal wind balance, with westerly shear

WSM6 microphyics, no PBL, TKE closure, no radiation

Triggered convection with warm bubble

KF CP scheme, with and without CMT

12-km grid length for CP runs, also 1.3 km grid later interpolated to 12-km grid for comparison

NoCMT CMT

Convective precipitation (hourly)

NoCMT CMT

EC simulation (1.3 km grid)

U wind field, 1.3 km, ~250 mb1.3 km run interpolated to 12-km grid

How did the 12-km CP runs compare?

12-km KF NOCMT 12-km EC

12-km KF with CMT 12-km EC

KF NOCMT minus KF CMT (~250 mb level, m/s, zonal wind component)

What does RUCUTEN look like?

Parameterized zonal momentum tendency isosurfaces, 2 h

Westerly acceleration not parameterized, grid

scale pressure gradient

Deceleration is related to

parameterized CMT

12-km EC

Cross section, time difference, EC12 run, 2 hours

Time difference, NOCMT KF run, 2 hours

Time difference, CMT KF run, 2 hours

Difference (u, m/s) between KF CMT and KF NOCMT 2 h

250-mb height anomaly and wind

NoCMT CMT

CMT simulation produces stronger ridging aloft on grid scale

Conclusions

Adding CMT to KF scheme produced zonal wind field closer to that obtained from explicit simulation

Stronger deceleration aloft due to CMT parameterization

Stronger acceleration downstream of MCS related to stronger meso-high aloft in CMT run

Results sufficiently promising to proceed with other tests (e.g., disorganized convection)

Subsequent implementation in Navy COAMPS didn’t increase skill scores, however

Acknowledgements

Megan Gentry (now Mallard) for work in passing tendencies to WRF solver

Jack Kain for initial discussions on CMT implementation

Jason Nachamkin, US Navy, testing with COAMPS

NSF grant ATM-0603760, awarded to North Carolina State University

The Betts-Miller Janjic (BMJ) Convective Parameterization (CP) Scheme

• Used in NCEP NAM model (12-km domain)• References:

• Betts and Miller, 1986 (QJRMS)• Janjic, 1994 (Mon. Wea. Rev.)• Manikin et al. 2000 (tech memo on mods)• Baldwin et al. 2002 (Wea. Forecasting)

• Step 1: In each individual grid cell, find most unstable parcel within ~ 130 mb of surface

• Step 2: Lift parcel to LCL (cloud base) & beyond– If parcel not buoyant anywhere, deep scheme aborts– If buoyancy found, continue lifting parcel to EL– Highest model level at which parcel still buoyant defined

as cloud top

• Step 3: Check cloud depth:– If cloud depth < 200 mb, deep convection aborts &

scheme checks for shallow convection– If cloud depth > 200 mb, check for deep convection

BMJ Scheme

• Step 4 (if cloud > 200 mb deep): Determine reference profiles for T, q

• Step 5 (if cloud > 200 mb deep): Enthalpy constraint:– If net warming/drying would result, allow deep convection,

nudge , q profiles toward reference value over many time steps, precipitate

– If net cooling/moistening would result (negative precipitation), abort deep convection, check shallow convection

BMJ Scheme

BMJ Scheme

Deep Convection in BMJ Scheme:

Intensity of BMJ highly sensitivity to moisture –More moist columns, more intense convection

–Dry reference profiles yield more precipitation

BMJ: 1- Check cloud depth

BMJ: 2- Compute reference profiles

It is possible to recognize where the BMJ deep convective parameterization scheme has been active by the well-defined reference profile.

BMJ Example (COMET)

Precisely how are “reference profiles” determined?– Why do we need to know this? So we can recognize

“footprint” of BMJ scheme in model forecast soundings, among other reasons

– Once deep cloud is found, construct 1st guess profile

– Then correct to satisfy enthalpy constraint

– First guess theta profile determined up to freezing levelas fraction of slope of moist adiabat from LCL

0.85 ( )

m

ref LCL m LCL

p

P P

BMJ Scheme

BMJ Scheme

Precisely how are “reference profiles” determined?

– First guess theta profile determined up to freezing level as fraction (.85 or .9) of slope of moist adiabat from LCL

– Above freezing level, profile returns to moist adiabat at cloud top via quadratic interpolation

- Quadratic interpolation: (note that at p = ptop, y=1)

)(85.0 PPLCLmLCLref

2( ) [ ( ) ( ) ] 1ref cloud ref frz cloud frz

fzl

fzl top

T p T T p T p y

p py

p p

BMJ: construction of 1st guess T profile

Moist adiabat passing through LCL for lifted

air triggering deep cloud

Freezing level

.85 slope of moist adiabat

Return to moist adiabat at cloud top (quadratic interpolation)

LCL

Cloud top

REFERENCE TEMP PROFILE

How are moisture profiles determined?– 1st guess moisture profile computed from temperature

profile

– Value set at 3 levels: cloud base, freezing level, cloud top

– Assume linear gradients between

– Then, iteratively adjust both temperature, moisture profiles to satisfy enthalpy constraint

See Janjic (1994, MWR) for more details

BMJ: construction of 1st guess Td profile

BMJ 1st guess moisture profile

Freezing level

First-guess temperature profile as before

Original LCL

Cloud top

Dry adiabat

p = -38.75mb

p = -58.75mb

p = -18.75mb

Dew point profile Mixing ratio

MODULE MODULE_CU_BMJ!-----------------------------------------------------------------------

USE MODULE_MODEL_CONSTANTS!-----------------------------------------------------------------------

REAL,PARAMETER :: && DSPC=-3000. && ,DTTOP=0.,EFIFC=5.0,EFIMN=0.10,EFMNT=0.20 &

! & ,DTTOP=0.,EFIFC=5.0,EFIMN=0.20,EFMNT=0.70 & & ,ELIVW=2.72E6,ENPLO=20000.,ENPUP=15000. && ,EPSDN=1.05,EPSDT=0. && ,EPSNTP=100.0,EPSNTT=100.,EPSPR=5.E-5 && ,EPSUP=0.95 && ,FR=1.00,FSL=0.85,FSS=0.85 && ,FUP=1./200000. && ,PBM=13000.,PFRZ=15000.,PNO=1000. && ,PONE=2500.,PQM=2500. && ,PSH=20000.,PSHU=45000. && ,RENDP=1./(ENPLO-ENPUP) && ,RHLSC=0.60,RHHSC=1. &

!REAL,PARAMETER :: DSPBFL=-3875.*FR*1.333 &

& ,DSP0FL=-5875.*FR*1.333 && ,DSPTFL=-1875.*FR*1.333 && ,DSPBFS=-3875.*FR && ,DSP0FS=-5875.*FR && ,DSPTFS=-1875.*FR

(FR = 1.00)

WRF model code- in WRFV3/phys directory

MODULE MODULE_CU_BMJ!-----------------------------------------------------------------------

USE MODULE_MODEL_CONSTANTS!-----------------------------------------------------------------------

REAL,PARAMETER :: && DSPC=-3000. && ,DTTOP=0.,EFIFC=5.0,EFIMN=0.10,EFMNT=0.20 &

! & ,DTTOP=0.,EFIFC=5.0,EFIMN=0.20,EFMNT=0.70 & & ,ELIVW=2.72E6,ENPLO=20000.,ENPUP=15000. && ,EPSDN=1.05,EPSDT=0. && ,EPSNTP=100.0,EPSNTT=100.,EPSPR=5.E-5 && ,EPSUP=0.95 && ,FR=1.00,FSL=0.85,FSS=0.85 && ,FUP=1./200000. && ,PBM=13000.,PFRZ=15000.,PNO=1000. && ,PONE=2500.,PQM=2500. && ,PSH=20000.,PSHU=45000. && ,RENDP=1./(ENPLO-ENPUP) && ,RHLSC=0.60,RHHSC=1. &

!REAL,PARAMETER :: DSPBFL=-3875.*FR*1.333 &

& ,DSP0FL=-5875.*FR*1.333 && ,DSPTFL=-1875.*FR*1.333 && ,DSPBFS=-3875.*FR && ,DSP0FS=-5875.*FR && ,DSPTFS=-1875.*FR

WRF model code- in WRFV2/phys directory

WRF 2.1

Does this modification make the scheme

more or less active?

MODULE MODULE_CU_BMJ!-----------------------------------------------------------------------

USE MODULE_MODEL_CONSTANTS!-----------------------------------------------------------------------

REAL,PARAMETER :: && DSPC=-3000. && ,DTTOP=0.,EFIFC=5.0,EFIMN=0.20,EFMNT=0.70 & & ,ELIVW=2.72E6,ENPLO=20000.,ENPUP=15000. && ,EPSDN=1.05,EPSDT=0. && ,EPSNTP=.0001,EPSNTT=.0001,EPSPR=1.E-7 && ,EPSUP=1.00 && ,FR=1.00,FSL=0.85,FSS=0.85 && ,FUP=0. && ,PBM=13000.,PFRZ=15000.,PNO=1000. && ,PONE=2500.,PQM=20000. && ,PSH=20000.,PSHU=45000. && ,RENDP=1./(ENPLO-ENPUP) && ,RHLSC=0.00,RHHSC=1.10,ROW=1.E3 & & ,STABDF=0.90,STABDS=0.90 && ,STABS=1.0,STRESH=1.10 && ,TREL=2400. & REAL,PARAMETER :: DSPBFL=-3875.*FR &

& ,DSP0FL=-5875.*FR && ,DSPTFL=-1875.*FR && ,DSPBFS=-3875. && ,DSP0FS=-5875. && ,DSPTFS=-1875.

WRF model code- in WRFV2/phys directory

“FUP” is related to updraft entrainment, evidently turned off in this version, not before

Also, now land, sea profiles are the same, but were not before!

WRF 2.2

WRF model code- in WRFV3/phys directory

WRF 3.2

BMJ CP• Time scale for convective adjustment

PTCsTCEefficiencycloudisEwhere

EFtTTT

JanjicModifiedqforsimilar

schemeoriginaltTTT

p

steptimeofstref

steptimeofstref

;

)()(

:)1994(

)()(

Betts-Miller-Janjic CP• Two time scales for adjustment:

– One for “faster, drier” adjustment (large E)– One for “slower, more moist” adjustment (small E)

• Moisture profile is altered for fast or slow adjustment– For slow adjustment, p values proportional to those in

fast, except scaled by a factor of 0.6

• We may do some BMJ experiments:– Experiment #1: Adjust convective scheme to turn off fast profiles

– Experiment #2: Reduce p values below those for “fast” profile

• Shallow scheme: designed to represent pre-convective environment by transporting heat downward, moisture upward

• Allows for cloud-layer mixing parameterization in situations with shallow or non-precipitating cloud

• Mimics condensation near cloud base (warming, drying) & evaporation near cloud top (cooling, moistening); net change results in no precipitation

BMJ Shallow Mixing Scheme

• Shallow portion of BMJ scheme triggers if1.) Cloud depth (from lifting the most unstable

parcel) < 200 mb, but covers 2+ model levels

2.) Deep clouds are found, but enthalpy constraint not satisfied (negative precipitation would result)

3.) Several other checks satisfied (e.g., upward heat transport)

BMJ Shallow Scheme

BMJ Shallow Scheme• How does shallow convection modify environment?

– Similar to deep clouds, except over restricted vertical layer (< 200 mb deep) and no precipitation allowed

– Primes environment for deep convection (too much?)– Does not facilitate grid-scale convection

• Shallow reference profiles computed differently:– use “mixing line” between cloud base, top (200-mb limit)– Moisture line: no net moisture change, linear function of

reference temperature– Result: moisture profile tails off toward cloud top

Shallow Convection in BMJ

• Shallow portion of BMJ scheme triggers if– “Cloud” depth (resulting from lifting the most

unstable parcel)–> 10 hPa deep –< 200 hPa deep–Covers at least two model layers

Example of BMJ shallow reference profiles

Cross-sections of CP, PBL T tendencies

BMJ + MYJ

BMJ-NS + MYJBMJ + YSU

Summary: Betts-Miller-Janjic• Key assumptions:

– Environment moved toward a quasi-equilibrium structure defined in terms of a “reference profile” (an “adjustment scheme”)

– Not necessary to explicitly represent heating, moistening due to sub-grid updrafts, downdrafts, entrainment, and detrainment

– Closure assumes that rate of grid scale destabilization determines how rapidly grid-scale profile is pushed toward reference profile

– Relaxation time for adjustment is roughly 2 hours (less for fine grid)

• Strengths: – Well designed for tropical oceans, coarse grids, cases with slow

environmental response

Betts Miller Janjic CP

Strengths (cont.)• Works well in moist environments with little cap

• Effectively precludes “gridscale overturning”

• Implicitly includes effects on cloud layers of downdrafts, latent heat of fusion from freezing in updrafts, melting of falling precipitation

• Runs quickly; computationally cheap, stable and robust

Betts-Miller-Janjic CPWeaknesses:

– Only indirect account of downdraft effects; trouble generating mesoscale convective signatures, e.g., outflow

– Reference profiles are derived from tropics, not necessarily relevant for explosive midlatitude convection

– Shallow convection scheme can be overactive (e.g. CAD)

– Not designed to facilitate grid-scale precipitation

– Only triggered with deep moisture (problem for loaded-gun soundings)

– Doesn’t account for the strength of cap-inhibiting convective development

BMJ in tomorrow’s NAM soundings

BMJ in tomorrow’s NAM soundings

Precip generated, drying column, little change below base

Plan view plots show active CP at

this time