A Simple Model of Subtropical Stratocumulus Cloud Feedbacks

1
A Simple Model of Subtropical Stratocumulus Cloud
Feedbacks

• Peter Caldwell and Chris Bretherton
• UW Clouds Precip Seminar
• 4/12/07

2
Motivation
a).ISCCP Inferred Stratus Cloud Amount
b). ERBE Net Cloud Radiative Forcing
(graphics courtesy Dennis Hartmann)

• Low clouds cover large regions of the globe

and have the strongest cloud radiative forcing.
Cloud radiative forcing clear-sky flux
observed flux (both at top of atmosphere)
3
Motivation
Stratocumulus
Deep Convection

• Model uncertainty is worst in Sc regions

? Cloud Forcing (W m-2 K-1)
Subsidence Rate ? _at_ 500mb (mb day-1)
Cloud forcing sensitivity from 15 coupled GCMs
binned by subsidence rate ? (Fig. 2a from Bony
Dufresne, 2005). Red values are from 8
high-sensitivity models, blue are for the
remaining 7 low-sensitivity models.
4
Why this Uncertainty?
12K!
?e
Entrainment the rate of incorporation of
free-tropospheric air into the BL by turbulent
eddies
1km
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Why this Uncertainty?
Free-tropospheric T set by ITCZ
12K!
?e
2,000km
1km
BL T set by local SST
6
Simple Models

• Why a Simple Model Might Work
• Free-tropospheric T throughout the tropics is
  controlled by deep convection in the
  Intertropical Convergence Zone (ITCZ)
• RH is insensitive to small climate perturbations
  (IPCC 2001)
• A simple energy balance permits calculation of
  the stratus-region subsidence profile.
• Previous studies (e.g. Betts and Ridgway (1989),
  Pierrehumbert (1995), Miller (1997), Larson et
  al. (1999))
• Have exploited these features
• 2xCO2 response
• -Hadley circulation slows
• Warm-cold ?SST ?
• LTS ? ? Sc cloud ?

from Larson et al. (1999)
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Our Model

• Shared with previous studies
• - free-tropospheric temperature
• - moisture
• - subsidence
• Differs by
• Using a more realistic BL model
• NOT parameterizing Sc influence on ITCZ (gives
  extra free parameter)
• Accounting for radiative effect of cold BL on air
  just above cloud top.

from Larson et al. (1999)
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Outline

• Motivation
• Model Introduction
• Validation Data
• Explanation/Validation of Model Components
• Temp
• Moisture
• Subsidence
• Mixed Layer Model (MLM)
• Results
• SST assumptions
• Minimal Model
• Sensitivity Studies
• Future Work
• Conclusions

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Data Observations _at_ 20S, 85W

• EPIC East Pacific Investigation of Climate
  (Oct. 2001)
• http//www.atmos.washington.edu/caldwep/research
  /ScDataset/sc_integ_data_fr.htm
• 2. PACS 03 Pan-American Climate Studies
  (Nov. 2003)
• Similar, but 6 hourly radiosondes, no scanning
  radar, and better aerosol measurements.
• 3. PACS 04 Pan-American Climate Studies
  (Dec. 2004)
• Similar, but 11 days of 6 hourly radiosonde
  data.

6 days of 3 hrly radiosondes, vertical and
scanning radar, microwave radiometer, shipboard
measurements obtained aboard the NOAA vessel
Ronald H. Brown.
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Tropical Temperature Structure
EPIC Region (20S, 85W)

• Observationally, tropical temperature follows the
  virtual moist adiabat (Betts, 1982).

Virtual Moist Adiabat - the virtual temperature
profile traced out by a parcel rising moist
adiabatically and without fallout of condensed
moisture.
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Lapse Rate Feedback

• qs increases increasingly rapidly with increasing
  T, so d?/dz is larger at warmer T.
• This means that temperature perturbations
  increase with height.
• This feedback is well studied (e.g. Hansen et
  al. 1984).

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Free-Tropospheric Moisture
EPIC Region (20S, 85W)
Param

• 10 RH fits the EPIC data reasonably well
• Moisture is highly variable in time

Obs
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Free-Tropospheric Subsidence
Outside of the BL, radiation is the only
energetic forcing on a parcel, so
In steady state
0, leaving
where horiz. advection,
subsidence rate
net radiative heating rate
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Subsidence Parameterization
Radiative heating calculated from
free-tropospheric profiles using BUGSrad, a
2-stream correlated-k scheme
where horiz. advection,
subsidence rate
net radiative heating rate
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Subsidence Parameterization
Potential Temp is virtual moist adiabatic
Radiative heating calculated from
free-tropospheric profiles using BUGSrad, a
2-stream correlated-k scheme
where horiz. advection,
subsidence rate
net radiative heating rate
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Subsidence Parameterization
Horiz. advection idealized from Sept-Nov average
ERA40 data at 20S, 85W. Assumed independent of
climate change.
Potential Temp is virtual moist adiabatic
Radiative heating calculated from
free-tropospheric profiles using BUGSrad, a
2-stream correlated-k scheme
where horiz. advection,
subsidence rate
net radiative heating rate
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Subsidence Parameterization
Horiz. advection idealized from Sept-Nov average
ERA40 data at 20S, 85W. Assumed independent of
climate change.
Potential Temp is virtual moist adiabatic
Residual is subsidence rate!
Radiative heating calculated from
free-tropospheric profiles using BUGSrad, a
2-stream correlated-k scheme
where horiz. advection,
subsidence rate
net radiative heating rate
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Detail 1
The previous method neglects BL effects, so it
doesnt satisfy ws(0)0.
To correct for this, we force ws to decrease
linearly from its calculated value at z 1.8km
(z smallest zgtzi in all runs) to 0 at the
surface
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Detail 2
Proximity to the cold BL significantly enhances
radiative flux divergence just above zi. This

• decreases ?
• increases ws

This effect is parameterized by computing the ws
and ? perturbations induced by the radiative
enhancement assuming linear hydrostatic f-plane
dynamics and sinusoidal latitudinal variation in
diabatic heating.
EPIC Obs
Uncorrected
Corrected
All enhancement ? cooling
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Subsidence Feedback
Subsidence should decrease as the planet warms

• Recent papers supporting this conclusion Knutson
  and Manabe (1995), Zhang and Soon (2006), Held
  and Soden (2006), Vecchi et al. (2006)

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BL Model details

• Cloud-topped mixed layer model (MLM) fully
  consistent model of BL dynamics if
• -Liquid water potential temperature and total
  water mixing ratio are constant in height
• -Horizontally homogenous (cloud fraction 0 or 1)
• Bulk surface fluxes with v6.2m s-1 (tuned to
  get ocean heat flux right)
• BL advection fixed with
• Fully interactive 2-stream correlated-k radiation
  (BUGSrad)
• Comstock et al. (2004) drizzle parameterization
  with Rodgers and Yau (1989) Stokes flow droplet
  sedimentation
• Turton-Nicholls entrainment closure with
  Bretherton et al. (2007) sedimentation correction
• MLM run to steady state.

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How to Read Results
Balanced Surface Budget
Contours of constant zi
Current Climate
Equal Warming
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Results

• Black line (Cess) equal SSTstrat and SSTITCZ
  warming.
• BL deepens and LWP increases

?Negative feedback on global warming
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Results

• Red line (slab ocean) model forced to obey
  surface energy balance, ocean transport fixed at
  current conditions (37 W m-2 into ocean).

Assume constant

• Decrease in surface insolation with rising LWP
  now allowed to feed back, causing
• local SST to rise more slowly than ITCZ SST
• BL depth to decrease
• weaker LWP rise than in Cess case.

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Compare w/ GCMs
From Zhu et al. 2007 J Climate in press.
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Minimal Model
Our model is still too complex to provide an
intuitive explanation for LWP increase.

• Can the general features of this model be
  reproduced via simple analytic formulae?
• Will this simple model shed light on the physical
  processes?

• Provide approximate solutions for
• Entrainment
• Cloud Base
• Cloud Top
• Explain model behavior in this setting

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Subsidence and Entrainment

• The cloud-top subsidence rate is
• The cloud-top evolution equation gives

Assume constant
Assume negligible
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Cloud Base

• Using Clausius-Clapeyron,
• Assuming TSSTSc-4K (fixed in height) yields
• The BL moisture budget gives
• Combining,

Assume negligible
Assume negligible
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Cloud Top

• BL energy balance is
• Assuming and combining
  with we,

Use energy-balance we closure no air-sea ?T
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Understanding LWP increase along Cess line

• As SSTs rise, lapse rate increases ? ws(z)
  decreases (subsidence feedback)
• Since we-ws(zi), entrainment warming decreases
• To restore balance, zi increases.

Since this increases entrainment flux by
entraining warmer air in addition to entraining
more vigorously, equilibrium is reestablished at
lower we.

• Since zb decreases with decreasing we, cloud base
  decreases with uniform SST increase.

Thus LWP increases along Cess line.
We call this the subsidence lapse-rate feedback.
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Not Whole Story
Full Model Full model, Fixed G

• Full-model zi not constant when lapse rate fixed
  (though rise rate is decreased)

• zb actually increases along Cess line in full
  model
• (though at a slower rate than zi rises)

? Simple model physics contributes to, but
doesnt completely describe full model behavior
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Effect of Entrainment Param.
Nicholls-Turton
Nicholls-Turton
Nicholls-Turton
Lewellen
Lewellen
Lewellen
-Entrainment parameterization has little effect
on dynamics.
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Effect of Drizzle

• Tested by varying droplet concentration (Nd)
  since
• Less droplets ? average drop larger ? falls
  faster ? more precip

1st indirect aerosol effect

• Results
• Small ctrl-run drizzle rates ? weak response to
  Nd changes
• Cloud response to Nd depends on LWP

Decreasing drizzle INCREASES LWP
LWPNd100/cc LWPNd50/cc LWPNd100/cc
Decreasing drizzle DECREASES LWP (Ackerman et al.
2004)
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Effect of Drizzle
Fractional change in optical depth due to
changing Nd


1st indirect aerosol effect
Effect of spreading given LWP over more
droplets (1st indirect aerosol effect)
Effect due to changing LWP (2nd indirect aerosol
effect)
LWPNd100/cc LWPNd50/cc LWPNd100/cc
2nd indirect aerosol effect much weaker than 1st
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Future Work

• Problem LWP increases with zi, counter to
  observations.
• Cause MLM neglects stratification, which is
  increasingly important in deeper BLs
• Impact Stratification decreases LWP, so our
  model overestimates LWP rise.
• Solution Substitute an LES instead of the MLM
• (straightforward to do, problemrun time)

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Future Work

• Problem Some aspects of the large-scale model
  component are uncertain (e.g. advection)
• Solution Use global model output as surrogate
  large-scale forcing. By acting as an
  alternative version of the large-scale model
  component, a sense of the uncertainty due to
  representation of the large scale will be
  obtained
• Timeline Someday!

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Conclusions

• Check your presentation before starting
• Enhanced radiative flux divergence (due to the
  cold BL) significant to ws and ? just above zi
• If SST increases uniformly, LWP rises rapidly and
  Sc have a strong negative feedback on warming
• Uniform SST increase ? large rise in LWP,
  negative feedback on warming.
• due (in part) to subsidence lapse-rate feedback
• MLM neglects stratification and large-scale
  feedbacks (which could be important)

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Conclusions (contd)

• If SST obeys a surface energy balance, cloud
  shading results in
• weaker LWP rise
• little change in local SST
• decreased BL depth
• Entrainment parameterization details unimportant
• Drizzle increases LWP for thin clouds and
  decreases LWP for thick clouds, though impact on
  cloud albedo is relatively small.

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Thanks!

• A copy of this presentation as well as drafts of
  the papers we wrote about this are available at
  www.atmos.washington.edu/caldwep/research/researc
  h.htm

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Data - Models

• Reanalysis
• ERA15/ERA40
• NCEP
• GCMs (monthly climatologies)
• GFDL AM2.12b, 2.0x2.5, 26 levels, 5/10yrs
• CAM CAM 3.0 rio33, 2.8x2.8, 26 levels,
  5/10yrs
• SP-CAM 2d CRM w/ 4km horiz. res, 28 levels
  embedded in each grid cell of T42 CAM 3.
• Techniques
• Annual averaging
• data interpolated to 20S, 85W

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Validation of Temp Param
EPIC Region (20S, 85W)

• The virtual moist adiabat fits the observations,
  reanalyses quite well.
• GCMs have too strong a lapse rate (-dT/dz too
  large so d?/dz is too weak).

GCMs
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Free-Tropospheric Moisture
EPIC Region (20S, 85W)

• 10 RH fits the EPIC data reasonably well
• Moisture is highly variable in time
• qv overestimated in large-scale models
• As expected, qv increases rapidly with ITCZ SST
  (e.g. Held and Soden, 2006)