A Simple Model of Subtropical Stratocumulus Cloud Feedbacks

1
A Simple Model of Subtropical Stratocumulus Cloud
Feedbacks

• Peter Caldwell
• Chris Bretherton
• 2/06/06

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

• Stratocumulus (Sc) 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, in press). 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
Our Model
Constant relative humidity
Free-tropospheric T horizontally uniform
subsidence balances radiative cooling
qT
?e
stratus? ITCZ coupling
ITCZ SST sets T profile
BL Cloud Model (Mixed Layer Model)
Stratus Region
ITCZ Region
6
Historical Context

• Previous focus has been on 2-way models
  (Pierrehumbert 1995, Miller 1997, Larson et al.
  1999)
• Similarities
• Idealize tropics as ITCZ cold pool
• Assume homogenous free-tropospheric T
• Assume subsidence rate set by radiative cooling.
• Differences
• Previous models include let stratus feed back on
  ITCZ state
• ? need additional assumptions about
  stratus?ITCZ coupling,
• but results in solutions w/ 1 less free
  parameter than our model.
• Currently, the Global Cloud Systems Study -
  Climate Processes Team is examining this 1-way
  coupling for a model intercomparison study.

7
Outline

• Motivation
• Model Overview
• Explanation of BL forcings
• Temp
• Moisture
• Subsidence
• Advection
• Results
• Conclusions

8
Data Observations _at_ 20S, 85W

• EPIC East Pacific Investigation of Climate
  (Oct. 2001)
• 6 days of 3 hrly radiosondes, vertical and
  scanning radar, microwave radiometer, shipboard
  measurements.
• 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.

9
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
• Displaying either
• data interpolated to 20S, 85W -or-
• ocean grid cells between /-30 lat composited by
  SST anomaly.

10
Temp Parameterization

• Horizontal T gradients in tropics are weak. Why?

11
Why is tropical Temp constant?
Persistent deep convection in the ITCZ sets the
temp profile to moist adiabatic, decreasing
column relative density.
ITCZ
stratus
?v (K)
12
Why is tropical Temp constant?
Density differences between the ITCZ column and
elsewhere cause buoyancy imbalance, resulting in
gravity waves.
ITCZ
stratus
?v (K)
13
Why is tropical Temp constant?
Since ITCZ forcing is constant, equilibrium is
only possible when all columns match the ITCZ
profile.
In the extra tropics, coriolis turning
allows for steady solutions with significant
horizontal T gradients.
ITCZ
stratus
?v (K)
14
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.
15
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
16
Validation of 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.

17
Moisture Param

• Studies suggest RH may remain constant
• as the planet warms (2001 IPCC report, Soden et
  al. 2002, etc).
• This feature is evident in the plots to the left.

18
Validation of Moisture Param

• Above 3km, 10 RH fits the EPIC data well
• Between 3km and cloud top, qv is constant.

EPIC Region (20S, 85W)
19
Validation of Moisture Param

• Above 3km, 10 RH fits the EPIC data well
• Between 3km and cloud top, qv is constant.
• This quantity is highly variable in time.

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

• Above 3km, 10 RH fits the EPIC data well
• Between 3km and cloud top, qv is constant.
• This quantity is highly variable in time.
• And overestimated in models.

EPIC Region (20S, 85W)
Param
Obs
Reanalyses
GCMS
21
Subsidence Parameterization
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
22
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
23
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
24
Subsidence Parameterization
Potential Temp is virtual moist adiabatic
Horiz. advection is assumed constant. Its value
is derived by solving this equation for current
conditions assuming the ERA40 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
25
Subsidence Parameterization
Potential Temp is virtual moist adiabatic
Residual is subsidence rate!
Horiz. advection is assumed constant. Its value
is derived by solving this equation for current
conditions assuming the ERA40 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
26
Subsidence Validation Current Climate
Composite of cells w/ SST anomalylt-5K
85W, 20S (EPIC) grid cell

• Good agreement between our parameterization,
  models
• Compositing by SST anomaly gives results similar
  to 20S, 85W.

27
Subsidence Validation Climate Change
Composite of cells w/ SST anomalylt-5K
85W, 20S (EPIC) grid cell

• Subsidence rates decrease in a warmer climate.

GCM Ctrl
constant
constant
increases
GCM SST2K
Pres (mb)
Pres (mb)
28
Temperature Advection
Temperature Advection (K day-1,
positivewarming effect)

• Methodology
• These values are averaged over
• a). lowest 2 model levels (1000mb and
• 925mb)
• b). all SST-anomaly bins w/ center lt -5K
• (this corresponds to 100 cells/model)
• Computed as product of annual-mean winds and
  annually-mean T gradients.

Including an advection scheme tied to the
difference in SST between regions does not
substantially change the results.
29
Moisture Advection
Moisture Advection (g kg-1 day-1, positivedrying
effect)
Numbers derived by averaging over a). lowest 2
model levels (1000mb and 925mb) b). all
SST-anomaly bins w/ center lt -5K (this
corresponds to 100 cells/model)
Including an advection scheme tied to the
surface qs gradient makes negligible difference.
30
Mixed Layer Model

• Assumes moist static energy h and total water
  mixing ratio qT are constant in height
  (well-mixed).
• Employs bulk surface fluxes with 7m/s surface
  wind speed.
• Uses Nicholls-Turton entrainment
  parameterization.
• Includes Turton drizzle parameterization
  including a sedimentation flux.
• Equilibrium solutions obtained by running to
  steady state.

31
Outline

• Motivation
• Model Overview
• Parameterizations and their validation
• Results
• Basic behavior (and why)
• Sensitivity studies
• Challenges
• Conclusions

32
How to Read Results
Balanced surface budget (more later)
Contours of constant LWP
11 line
Current climate
33
How to Read Results
Balanced surface budget (more later)
Contours of constant LWP
11 line
Current climate
When virtual static energy fluxlt0, mixed layer
hypothesis falls apart.
34
How to Read Results
Balanced surface budget (more later)
Contours of constant
11 line
Current climate
When virtual static energy fluxlt0, mixed layer
hypothesis falls apart.
35
A Path through Parameter Space

• Uniform Warming (black line)
• BL deepens, LWP ?
• Negative cloud feedback
• Balanced Surface Energy Budget (red line)
• Ocean surface energy budget is
• so if in equilibrium with unchanged ocean heat
  flux (26 W m-2 in model),
• Radiative term dominates, necessitating constant
  LWP to maintain balance.
• No cloud feedback.
• zi is forced to decrease to maintain LWP.
• Stratus SST increases less than in ITCZ.

36
What controls Entrainment Rate?
Put these results on overhead so I can
bullet/diagram my way through w/ computer?
Idea

• Entrainment inversely proportional to inversion
  strength

37
What controls Inversion Height?

• Idea
• we balances ws since
• For given SSTITCZ, ws determines zi.

• Increased we must be balanced by increased ws,
  which can only happen if zi. ? (so zi follows
  we).
• ws (z) ? as SSTITCZ ? (lapse rate feedback), so
  zi increases slightly along constant we paths.

38
What controls Cloud Base?
Air in the BL is a linear mixture of air from the
surface and air from above the BL, so
small
If qs(Tsurf) qs(SST),
RHsurf

Cloudbase occurs where RH1, so
Since CTv is constant, zb tracks we.
39
What controls LWP?

• LWP reflects the more rapid rise in zi than in zb.

40
Effect of Entrainment Param.
Nicholls-Turton
Nicholls-Turton
Nicholls-Turton
Lewellen
Lewellen
Lewellen
-Entrainment parameterization does NOT affect
dynamics.
41
What is effect of drizzle param?
Liquid Water Path (g kg-1)
Inversion Height (m)

• Inversion height increases (since precip
  decreases subcloud buoyancy flux, decreasing we).
• LWP increases (since precip removes qT).
• Basic feedbacks unchanged.

Turton drizzle
Turton drizzle
No drizzle
No drizzle
42
Challenges Doesnt reproduce current climate at
20S, 85W

• Obs place zi at 1.2km, while model gives
  zi800m.
• Due to error in modeled ? in the 3km nearest the
  BL. Reasons
• Stratified adjustment weaker over shallower
  layer.
• Radiative cooling enhanced by proximity to cold
  BL.
• Current climate well simulated with 4K additional
  cooling.
• BL-induced cooling should depend on LWP,
  inversion strength, zi.
• Must continue to satisfy energy budget

43
More Challenges

• Modeled LWP, SWCF increase with zi, counter to
  observational evidence.
• - Deep BLs tend to decouple and have lower
  cloud fraction. These effects cant be simulated
  with a MLM.
• - Currently working on LES simulations to
  circumvent this problem.

44
Conclusions Parameterization

• Observations/Reanalyses/GCMs support our
  parameterizations.
• Entrainment parameterization doesnt matter.
• Inclusion of drizzle changes the mean state, but
  not model response.

45
Conclusions Modeling Results

• Uniform SST increase ? negative cloud feedback.
• Surface energy balance ? no cloud feedback, ITCZ
  SST warms faster, and BL depth decreases.
• Both scenarios suggest a more negative
  stratocumulus cloud feedback than most current
  GCMS, suggesting that warming may be less drastic
  than predicted.

46
Conclusions - Challenges

• Uncertain parameterizations
• moisture
• ocean upwelling
• temperature just above the BL
• Cloud fraction/well-mixedness not addressed by
  MLM (fix by using LES)

47
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48
Number of columns in SST bins.
49
Temperature Advection
EPIC Region Temp. Advection
K day-1, positivewarming effect
Numbers derived by averaging over a). lowest 2
model levels (1000mb and 925mb) b). all
SST-anomaly bins w/ center lt -5K (this
corresponds to 100 cells/model)
50
Is direct effect of CO2 important?

• No.

51
Our Model
10 RH above 3km
Convection fixes ? to virtual moist adiabat
subsidence balances radiative cooling advection
constant qv to 3km
qT
?e
stratus? ITCZ coupling
BL Cloud Model
Stratus Region
ITCZ Region
52
Mixed Layer Model

• Assumes moist static energy h and total water
  mixing ratio qT are constant in height
  (well-mixed).
• Prognoses h, qT, and BL depth zi. Diagnoses cloud
  base zb and liquid water path LWP.
• Uses BUGSrad radiative transfer code with zenith
  angle51.5o and a solar constant reduced by a
  factor of 0.48 to emulate diurnally-averaged
  radiation for Oct. 16th at 20S, 85W.

• 2K of cooling is applied to entrained air to
  account for enhanced radiative cooling near zi.
• Employs bulk surface fluxes with 7m/s surface
  wind speed.
• Assumes fixed zi advection of -0.49mm/s.
• Uses Nicholls-Turton entrainment
  parameterization.
• Includes Turton drizzle parameterization
  including a sedimentation flux
• Equilibrium solutions obtained by running to
  steady state.

53
Results
Put these results on overhead so I can
bullet/diagram my way through w/ computer?

• Cloud forcing parallels LWP.
• Contours of LWP roughly parallel to probable path
  of SST increase.
• Surface T almost independent of ITCZ SST.

54
Validation of Temp Param
EPIC Region (20S, 85W)

• The virtual moist adiabat fits the observations
  quite well.
• Reanalysis data
• also follows the virtual moist adiabat.

55
Tropical SST-binned Temp
Cols Used GFDL 15 CAM 11 SPCAM11
Cols Used GFDL 181 CAM 110 SPCAM108
Cols Used GFDL 438 CAM 268 SPCAM267
-Deviation in lapse rate due to poor propagation
of gravity waves?
56
Tropical SST-binned Temp
Cols Used GFDL 15 CAM 11 SPCAM11
Cols Used GFDL 181 CAM 110 SPCAM108
Cols Used GFDL 438 CAM 268 SPCAM267
-Profiles do show lapse-rate feedback
57
What sets model behavior?
Applied Change
stratus SST increases 1K
-1K
0.9g kg-1
1K
ITCZ/stratus T gradient ?
qs(surf) ?
SST ?
Direct Effects
9W m-2
-0.03g kg-1 day-1
19W m-2
Model Response
SHF ?
LHF ?
advective drying ?
0.4m s-1
0.8g kg-1 day-1
0.9K day-1
0.1m s-1
BL warms
we ?
BL moistens
-0.3g kg-1 day-1
0.7K day-1
200m
Entrainment warming ?
Entrainment drying ?
zi ?
0.2g kg-1 day-1
-1.2K day-1
BL mass ? so fluxes less effective
BL ? ?
BL qt ?
58
ITCZ SST increases
Applied Change
1.01K
1K
0.1g kg-1
0.1K km-1
T of entrained air ?
Lapse rate steepens
qv of entrained air ?
ITCZ/stratus T gradient ?
Direct Effects
1.01K
3.4W m-2
0.06g kg-1 day-1
0.7W m-2
-0.06mm s-1
Model Response
Inversion strength ?
Evap we enhancement ?
BL Qrad ?
-ws(z) ?
dry advect ?
25m
-0.3mm s-1
-0.4mm s-1
-0.2mm s-1
zi ?for given we
we ?
-125m
zi ?, but less than predicted by we
-0.8K day-1
0.5g kg-1 day-1
Entrainment drying ?
Entrainment warming ?
BL mass ? so fluxes more effective
1K day-1
0.2g kg-1 day-1
constant BL ?
BL moistens
59
Why does ws decrease?

• Increasing moisture in the atmosphere means that
  at lower levels, more radiation is trapped,
  lowering the cooling rate slightly.
• Decrease in cooling rate and increase in d?/dz
  must be balanced by decreased ws.

60
What Controls Cloud Base?

• BL moisture responds to
• surface qv
• above-BL qv
• drying by we, by advection, and by drizzle

• Cloud base increases as the BL warms, dries.
• Based on surface T, BL qT, (see RHS), zb follows
  zi.

Decreased drying, by we,, advection, drizzle