Climate Sensitivity, Forcings, And
Feedbacks
1
Forcings and Feedbacks in the Climate System
Climate Change 2007: The Physical Science Basis. Working Group I Contribution to the Fourth Assessment Report of the
Intergovernmental Panel on Climate Change, FAQ 1.2, Figure 1. Cambridge University Press. Used with permission.
2
Forcings and Feedbacks
Consider the total flux of radiation through the top of the
atmosphere:
FTOA  Fsolar  FIR
Each term on the right can be regarded as function of the surface
temperature, Ts, and many other variables xi :
FTOA  FTOA Ts , x1 , x2 ,.....xN 
By chain rule,
 FTOA
N
FTOA
FTOA
0
 Ts  
 xi
Ts
i 1 xi
3
Now let’s call the Nth process a “forcing”, Q:
 FTOA
N 1
FTOA
FTOA
0
 Ts  
 xi   Q
Ts
i 1 xi
N 1
FTOA
FTOA xi

 Ts  
 Ts   Q
Ts
Ts
i 1 xi
Then
Ts
1
 R  
N 1

FTOA xi
F
Q
TOA

Ts
Ts
i 1 xi
4
Let
 FTOA 
S  

 Ts 
Ts
 R 
Q
1
Climate sensitivity without
feedbacks
S
N 1
FTOA xi
1 S
Ts
i 1 xi
Climate sensitivity
Feedback factors; can
be of either sign
Note that feedback factors do NOT add linearly in
their collective effects on climate sensitivity
5
Examples of Forcing:
• Changing solar constant
• Orbital forcing
• Changing concentrations of non-interactive
greenhouse gases
• Volcanic aerosols
• Manmade aerosols
• Land use changes
6
Solar Sunspot Cycle
Image courtesy of NASA.
7
Sunspot number
200
150
100
50
0
1600
1700
1800
1900
2000
Year
Image by MIT OpenCourseWare.
8
1370
Srec(Wm-2(
1368
0.2
1366
0.0
-0.2
1364
Temperature anomaly (oC)
0.4
-0.4
1362
1850
1900
1950
2000
Year
Two reconstructions of total solar irradiance combined with measurements, where available
(enclosing the greenshading) and two climate records (enclosing the orange shading) spanning
roughly 150 years.
Reconstructed irradiance
Temperature records
Image by MIT OpenCourseWare.
99
Satellite measurements of solar flux
Climate Change 2007: The Physical Science Basis. Working Group I Contribution to the Fourth Assessment Report of
the Intergovernmental Panel on Climate Change, Figure 2.16. Cambridge University Press. Used with permission.
10
X-Ray Flux
This image has been removed due to copyright restrictions. Please see the
image on page http://sidstation.loudet.org/03-solar-activity/data/flux.png.
11
Normal solar cycle variations in solar radiation
This image has been removed due to copyright restrictions. Please see Foukal, et al. "Variations in
Solar Luminosity and their Effect on the Earth's Climate". Nature 443 (2006): 161-6. The image is
also on page http://blogs.edf.org/climate411/wp-content/files/2007/05/solar_energy.jpg.
12
Inferences based
on Models of
Solar Variability
Climate Change 2007: The Physical Science Basis. Working Group I Contribution to
the Fourth Assessment Report of the Intergovernmental Panel on Climate Change,
Figure 2.17. Cambridge University Press. Used with permission.
13
Eccentricity Cycle (100 k.y.)
Climate
Forcing by
Orbital
Variations
Obliquity Cycle (41 k.y.)
Normal to ecliptic
This image has been removed due to copyright restrictions.
Please see the photo on page http://www.detectingdesign.
com/milankovitch.html.
Precession of the Equinoxes (19 and 23 k.y.)
Northern Hemisphere tilted away from the sun at aphelion.
Northern Hemisphere tilted toward the sun at aphelion.
Milutin Milanković, 1879-1958
Image by MIT OpenCourseWare.
14
Climate Forcing and Response
15
Image courtesy of Global Warming Art.
Strong Correlation between High Latitude Summer Insolation
and Ice Volume
This image has been removed due to copyright restrictions. Please see Figure 2E on page
http://www.people.fas.harvard.edu/~phuybers/Doc/integrated_science2006.pdf.
16
This image has been removed due to copyright restrictions. Please see the image
on page http://en.wikipedia.org/wiki/File:Carbon_History_and_Flux_Rev.png.
17
Variation in carbon
dioxide and
methane over the
past 20,000 years,
based on ice core
and other records
Climate Change 2007: The Physical Science Basis. Working Group I Contribution
to the Fourth Assessment Report of the Intergovernmental Panel on Climate
Change, Figure TS.2. Cambridge University Press. Used with permission.
18
CO2 and Climate
Climate Change 2007: The Physical Science Basis. Working Group I Contribution to the Fourth Assessment Report
of the Intergovernmental Panel on Climate Change, Figure 6.1. Cambridge University Press. Used with permission.
19
Recent History of Volcanic Eruptions
Climate Change 2007: The Physical Science Basis. Working Group I Contribution to the Fourth Assessment Report of
the Intergovernmental Panel on Climate Change, Figure 2.18. Cambridge University Press. Used with permission.
20
Image courtesy of US government.
21
Variation with Time of Natural Climate Forcings:
Climate Change 2007: The Physical Science Basis. Working Group I Contribution to the Fourth Assessment Report of
the Intergovernmental Panel on Climate Change, Figure 6.13. Cambridge University Press. Used with permission.
22
Examples of Forcing Magnitudes:
• A 1.6% change in the solar constant,
equivalent to 4 Wm-2, would produce about
1oC change in surface temperature
• Doubling CO2, equivalent to 4 Wm-2, would
produce about 1oC change in surface
temperature
23
Contributions to net radiative forcing
change, 1750-2004:
Climate Change 2007: The Physical Science Basis. Working Group I Contribution to the Fourth Assessment Report of
the Intergovernmental Panel on Climate Change, Figure 2.20. Cambridge University Press. Used with permission.
24
Examples of Feedbacks:
•
•
•
•
•
Water vapor
Ice-albedo
Clouds
Surface evaporation
Biogeochemical feedbacks
25
Estimates of Climate Sensitivity
Ts
 R 
Q
S
N 1
FTOA xi
1 S
Ts
i 1 xi
 FTOA 
S  

 Ts 
1
Suppose that Ts = Te + constant and that
shortwave radiation is insensitive to Ts:
FTOA   T ,
4
e
FTOA


 Te4  4 Te3  3.8Wm2 K 1
Ts
Ts
S  0.26K Wm

2 1
26
Examples of feedback magnitudes:
• Experiments with one-dimensional radiativeconvective models suggest that holding the
relative humidity fixed,
 FTOA   q 
2
1

Wm
K
2
,



 q   Ts  RH
 FTOA   q 
S
  0.5

 q   Ts  RH
This, by itself, doubles climate sensitivity; with other
positive feedbacks, effect on sensitivity is even larger
27
Ice-Albedo Feedback
ALBEDO RANGE (%)
60
40
20
0
80
60
40
20
0
LATITUDE
ANNUAL RANGE OF ALBEDO
Northern Hemisphere
Southern Hemisphere
Annual range of zonal monthly surface albedo estimates by 2o latitudinal belts.
28
Image by MIT OpenCourseWare.
o
90
60o
0.9
1.0
Neoproterozoic S=0.93
Ice line latitude
Budyko-Sellers type
energy-balance model
(1969)
Solar flux (x present)
1.1
1.2
1.3
No Ice
Present
30o
Eq
All Ice
0.1
1
10
100 1000
Log pCO2 (x present)
Image by MIT OpenCourseWare.
29
Feedbacks in Climate Models
Water
vapor
Cloud
Surface
albedo
Lapse rate Water vapor
+ lapse rate
Climate Change 2007: The Physical Science Basis. Working Group I Contribution to the Fourth Assessment Report of
the Intergovernmental Panel on Climate Change, Figure 8.14. Cambridge University Press. Used with permission.
30
This image (published on Journal of Climate by the American Meteorological
Society) is copyright © AMS and used with permission.
Equilibrium temperature change associated with the Planck response and the various
feedbacks, computed for 12 CMIP3/AR4 AOGCMs for a 2 × CO2 forcing of reference (3.71 W
m−2). The GCMs are sorted according to ΔTes.
From Dufresne and Bony, J. Climate, 2008
31
Cloud Radiative Forcing
2.0
W m-2
1.0
0.0
-1.0
-2.0
-3.0
21 3 11 12 10 16 7 20 15 9
8 14 6
5
4 23 22 19 17 18
Model ID number
Image by MIT OpenCourseWare.
Changes in global mean cloud radiative forcing (W m–2) from individual models
32
MIT OpenCourseWare
http://ocw.mit.edu
12.340 Global Warming Science
Spring 2012
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