A Simple Model of Subtropical Stratocumulus Cloud Feedbacks

1
A Simple Model of Subtropical Stratocumulus Cloud
Feedbacks

• Peter Caldwell and Chris Bretherton
• University of Washington
• 1/22/07

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

• Agreement between models is worst for Sc regions
• GCMs disagree even on the sign of low-cloud
  feedback.

Deep Convection
? 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?
Free-tropospheric T set by ITCZ
12K!
?e
2,000km
1km
BL T set by local SST
5
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
• Havent included realistic STBL
• 2xCO2 response
• -Hadley circulation slows
• Warm-cold ?SST ?
• LTS, Sc cloud ?

from Larson et al. (1999)
6
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

8
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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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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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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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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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 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)

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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
16
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
17
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
18
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
19
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
20
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 v5.9m 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 (40 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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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, increases?ws 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.
32
Not Whole Story

• 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 here by varying droplet concentration (Nd)
  along Cess line
• Less droplets ? average drop larger ? falls
  faster ? more precip
• Results
• Drizzle makes little difference to climate
  sensitivity since LWP low
• Stronger drizzle decreases entrainment, lowering
  zi and zb and increasing LWP (verifies the result
  of Ackerman et al. (2004) under steady state
  conditions)

Nd100/cc
Nd50/cc
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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 opposes the LWP rise
  found in our model, so its inclusion is
  important for a full treatment of Sc feedback
• 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

• Enhanced radiative flux divergence (due to the
  cold BL) significant to ws and ? just above zi.
• Uniform SST increase ? large rise in LWP,
  negative feedback on warming.
• due (in part) to interaction between subsidence
  feedback and increase in entrainment warming with
  BL depth.
• Surface energy balance ? increased LWP shades
  local SST, resulting in slower SSTSc rise,
  decreased zi, and weaker LWP increase.

38
Conclusions (contd)

• Entrainment parameterization details unimportant
• Drizzle decreases entrainment, increasing LWP
• LES of the BL would be a natural and useful
  extension to the current work
• Incorporation of global model data would improve
  our understanding of the large-scale component of
  this model

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Thanks!

• A copy of this presentation as well as a draft of
  Caldwell and Bretherton (2007) are available at
  www.atmos.washington.edu/caldwep/research/researc
  h.htm