Evaluating mass flux closures using cloud resolving model simulations of deep convection

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Evaluating mass flux closures using cloud
resolving model simulations of deep convection
Evaluating Mass Flux Closures Using Cloud
Resolving Model Simulations of Deep Convection

• Jennifer Fletcher and
• Chris Bretherton
• COGS talk May 7, 2009

Jennifer Fletcher and Chris Bretherton COGS
presentation May
7, 2009
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What does cumulus convection do?

• Makes precipitation and severe weather
• Changes stability
• Generates and redistributes heat and moisture
• Transports tracers
• Makes clouds that affect radiation

Cumulus parameterizations must represent some or
all of these effects
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Two basic types of cumulus parameterization
adjustment and mass flux

• Adjustment temperature and moisture adjust to
  pre-specified profiles over a finite timescale.
• Mass flux a cloud model explicitly calculates
  profiles of cumulus mass flux and thermodynamic
  variables.
• Mass flux more widely used because it can provide
  an internally consistent representation of
  turbulent mixing, updraft dynamics, microphysics,
  and tracer transport

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Three components to a mass flux parameterization

• Trigger will convection occur?
• Closure how much convection?
• Model how will convection distribute heat,
  moisture, etc?

The trigger and the closure may be considered two
parts of the same thing
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Mass flux parameterization

• The closure relates the cloud base mass flux
  to resolved-scale
  variables
• A cloud model
  predicts the
  vertical structure
  of mass flux
  and thermodynamic
  quantities above
  cloud
  base
• My research focuses on a type of mass flux closure

Cloud model predicts cumulus properties per cloud
base mass flux
mcb f(large scale)
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What I am going to show you

• Mass flux closure based on convective inhibition
  (CIN) is well suited for both shallow and deep
  convection.
• This closure takes the form mcbc1Wexp(-c2CIN/TKE)
  
• W is a vertical velocity scale
• TKE mean turbulent kinetic energy in the
  boundary layer

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Mass flux closure fundamental assumptions

• Cumulus cloud base mass flux is a function of
  large scale variables
• Cloud base mass flux has no memory, i.e., it is
  determined by instantaneous forcings.

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Mass flux closure types

• Moisture convergence
• CAPE
• Boundary layer based

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Mass flux closure type 1 moisture convergence

• Mass flux determined so that precipitation
  balances moisture convergence, as observed over
  the tropical oceans.
• Lacking in causality convection cant see
  moisture convergence must ultimately respond to
  local thermodynamic profile
• Performs poorly if the storage term in the
  moisture budget is significant on convective time
  scales (e.g., continental convection).
• Examples Kuo, Anthes
• Popular in the 80s but has largely fallen out of
  favor.

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Mass flux closure type 2 CAPE

• Cumulus base mass flux depends on the
  vertically-integrated parcel buoyancy (adiabatic
  or entraining)
• Causality issue how can
  cloud base mass flux feel
  the deep updraft buoyancy
  profile?
• CAPE and cloud base
  mass flux are inconsistently
  correlated in tropical
  oceanic convection.
• Widely used, e.g.,Arakawa-Schubert (GFS, GFDL),
  Zhang-McFarlane (CAM), Kain-Fritsch (WRF)

From Kuang and Bretherton (2006)
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Mass flux closure type 3 boundary layer
(BL)-based

• Defining characteristic PBL quantities (e.g.,
  surface fluxes, CIN, TKE) determine cloud base
  mass flux.
• Motivation the roots of cumulus updrafts are in
  the boundary layer.
• Applicable to shallow as well as deep convection
• Example UW shallow cumulus scheme (CAM)

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BL closure I CIN closure

• Concept mcb controlled
  by KE of PBL updrafts
  and their potential
  energy barrier (CIN).
  
• Introduced by Mapes (2000)

• mcb c1Wexp(-c2CIN/W2)
• Distribution of CIN W
• Acts as a trigger as well

Plan view of PBL vertical velocity (gray
positive) in LES. From Moeng and Rotunno (1990)
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CIN closure maintains an important feedback
mcb c1Wexp(-c2CIN/W2)

• Keeps PBL top near cloud base
• If PBL top above LCL, CIN small, lots of
  convection, lowers PBL height
• If PBL top far below, lots of CIN, no convection,
  PBL ht increases due to sfc fluxes entrainment

??p
LCL PBL top
??ave
z
1K
???(1 0.61qv-qc)
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BL closure II Grant closure

• Grant and Brown (1999) found in an LES that mcb
  0.03w
• w (B0zPBL)1/3 - the PBL convective velocity
  scale.
• Attractively simple but still requires a trigger.
• This diagnostic relationship is used as a closure
  in the UW shallow convection scheme as
  implemented in the GFDL model.

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Testing BL-based closure

• Strategy use a cloud resolving model to test
• CIN mcbc1Wexp(-c2CIN/W2) and
• Grant (mcb0.03w) closures,
• which were developed for shallow convection.
• Test these closures for deep convection.
• Methods
• Use several different CRM simulations
• Calculate the cloud base cumulus mass flux mcb.
• Test relationships between mcb and PBL variables
  predicted by closure

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Issues with this approach

• 1. Analyzing instantaneous 3-D
  volumes gives sampling uncertainty
• 2. Use of large-scale forcings constrains
  convection.
• But this constraint is identical to that under
  which a cumulus parameterization operates.

-?500
Julian Day
200
260
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System for Atmospheric Modeling (SAM)

• Solves the anelastic equations, 3D geometry,
  bulk microphysics, periodic lateral BCs

Simulated satellite image during KWAJEX
Source http//rossby.msrc.sunysb.edu/7Emarat/SAM
.html
See Khairoutdiov and Randall (2003)
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SAM simulations

• Use well-verified simulations of three intensive
  observing periods
• ARM (Atmospheric Radiation Measurement) Oklahoma
  site, summer 1997
• KWAJEX (Kwajalein Experiment) in West Pacific
  ITCZ, summer 1999
• BOMEX (Barbados Oceanography and Meteorology
  Experiment) in trade Cu environment, June 1969

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SAM simulations ARM (Oklahoma, late June
1997)

• SAM version 6.7
• 192x192 km2 domain, ?x 1 km
• 96 vertical grid levels, ?z ranges from 50-100 m
  in PBL to 250 m in free troposphere, larger above
  tropopause.
• 15 days long
• Features a range of conditions including clear
  sky, shallow convection, and episodic deep
  convection

See Khairoutdiov and Randall (2003)
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SAM simulations KWAJEX (West Pacific ITCZ)

• SAM version 6.3
• 50 days
• 256x256 km2 domain, ?x 1 km
• 64 vertical grid levels, ?z ranges from 100 m in
  PBL to 400 m in free troposphere, larger above
  tropopause.
• Continuously-forced tropical marine deep
  convection.

See Blossey et al (2007)
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SAM simulations BOMEX (trade cumulus
regime)

• SAM version 6.7
• 6 hours
• 192x192x96 grid points
• ?x ?z 40 m everywhere.
• Steadily-forced subtropical shallow cumulus
  convection.
• Non-interactive radiative cooling profile.

See Siebesma et al (2003)
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SAM simulations Cloud Fraction
Note different color vertical scales!
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What I need to test CIN closure
mcb c1Wexp(-c2CIN/W2)

• A definition of cumulus (Cu) updraft saturated
  pixel with w gt 0.5 m/s
• An estimate of Cu updraft base
• Cu- base updraft mass flux
• Average CIN that Cu-base updrafts have overcome
• A vertical velocity scale for Cu updrafts (call
  this W)

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Methods finding cloud base

• Define one representative Cu base height.
• Use a profile-based approach that is consistent
  with what a GCM can do.
• Approach Find lifting condensation level (LCL)
  of a test parcel with similar thermodynamic
  properties to Cu updrafts.
• Parcel originating at 300 m spiked with 1
  horizontal std (?q) of qv works well.
• Cloud reference level 1st grid level above this
  LCL.

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Cloud reference level Cu updraft fraction
Cloud reference level captures Cu base very well
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Analyzing Cu-base mass flux

• Use cloud reference level as proxy for cloud
  base.
• Mass flux Mcb ??cbwcb
• ?cb cloud ref level Cu updraft fractional area.
• wcb Cu updraft vertical velocity
• We often use mcbMcb/? (mcb m/s)
• Well analyze the vertical velocity and cloud
  fraction contributions to mass flux separately.

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Cu updraft mass flux

• Cu base mass flux shows considerable variability
  is somewhat correlated with precip
• But times when no precip plenty of Cu base mass
  flux
• 600 hPa mass flux much better correlated with
  precip

600 hPa mass flux
hello
Cld ref level mass flux
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Calculating cloud ref level CIN
mcb c1Wexp(-c2CIN/W2)
Example KWAJEX day, rain rate 5mm/hr

• At cloud ref level, calculate mean T and qT
  of Cu updrafts.
• Adiabatically
  displace to 300m
• b(z) gT?/T?ave

900
Sounding T?
cloud ref level
Ave Cu updraft T?
Wowwowsa wowsa
Actual cloud base
200
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Calculating Cu-updraft vertical velocity scale W
mcb c1Wexp(-c2CIN/W2)

• Two possibilities I considered TKE1/2 and w
• TKE 1/2(u2 v2w2), PBL large eddies cold
  pool dynamics
• w (implicated by Grant) depends on surface
  fluxes and BL depth.
• In a dry convective BL, the two are linearly
  related.
• Compare these to wcb,, the actual vertical
  velocity of Cu updrafts at cloud ref level.

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CIN, TKE, w

• TKE correlated w/ precip.
• CIN TKE covary
• Cu-base velocity wcb looks like TKE1/2 for
  KWAJEX, w for ARM

TKE1/2
CIN1/2
w
wcb
wcb
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Cu-base vertical velocity scale W
mcb c1Wexp(-c2CIN/W2)

• Try
• W aw bTKE1/2
• Choose a b to minimize sum of (W-wcb)2
  over all times for ARM, KWAJEX, and BOMEX

wcb m/s
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Cu-updraft fractional area
mcb c1Wexp(-c2CIN/W2)

• General form
• ?cbc1exp(-c2CIN/W2)
• But CIN/W2 is often much too large
• CIN/TKE is a much better predictor
• Reflects role of cold pools?

Implied by Grant closure
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Combined results mass flux closure
mcb c1Wexp(-c2CIN/TKE) W aw bTKE1/2
Closure skillfully predicts Cu-base mass flux,
subject to substantial sampling uncertainty
actual
closure
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Can a GCM implement this closure?

• We used CIN of conditionally sampled cu-updrafts
  and the actual BL-mean TKE in these calculations.
• How can this be implemented in a GCM?
• 1 TKE can be calculated from a combination of w
  and precipitation.
• 2 CIN can be calculated from the sounding

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Estimating Cu-updraft CIN from the sounding

• As before, start a parcel at 300m with domain
  mean ? and qvqvmean?qv.
• Lift parcel adiabatically to cloud reference
  level.
• The CIN of this parcel
  is well-correlated with
  the CIN of cloud
  reference level
  Cu-updrafts.

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CIN closure using sounding CIN

• Calculating CIN from the sounding still produces
  a skillful estimate of Cu-base mass flux.
• How to represent TKE and qv std are left as open
  questions.

actual
closure
CIN estimated from sounding
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Conclusion

• CIN closure
• mcb0.03Wexp(-CIN/TKE)
• with Cu-base updraft velocity
• W 0.57w0.24TKE1/2
• skillfully predicts cloud base mass flux for a
  range of realistic CRM simulations of shallow and
  deep convection.

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Future work

• To complete the closure, determine how to
  parameterize ?q and TKE (Cathy Hohenegger).
• These can be specified in terms of surface
  fluxes, precipitation, mean RH, and vertical
  gradient in MSE.

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Thank you
Thanks also to Peter Blossey!
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CIN, TKE, w
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CAPE, entraining CAPE, and mass flux
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Boundary Layer closure I BLQ

• Boundary Layer quasi-equilibrium proposed by
  Raymond (1995) for tropical oceanic deep
  convection
• Closure assumption convection keeps PBL
  ?e near
  a convective
  threshold
• Surface fluxes increase
  PBL ?e while convective
  downdrafts decrease it
• Not applicable to shallow
  or continental deep
  convection

Low ?e downdraft
?ePBL ?ethresh
flux of high ?esurf