Chapter 6
The Greenhouse Effect and Climate Feedbacks
6.1 The greenhouse effect in Earth’s current climate
6.2 Global warming I: example in the global-average
energy balance model
6.3 Climate feedbacks
6.4 The water vapor feedback
6.5 Snow/Ice feedback
6.6 Cloud feedbacks
6.7 Other feedbacks in the physical climate system
6.8 Climate response time in transient climate change
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6.1 The greenhouse effect in Earth’s current climate
Recap (Chap. 2): Pathways of energy transfer in a global average
Recap: Figure 2.8
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6.1a Global energy balance
A one-layer, globally averaged energy balance model
•Repeat essential aspects but in a 1-layer atm
1
2
Figure 6.1
1
2
•For a layer with a single temperature Ta: IRatm=IRatm 2
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Neglect for now!
1
Radiative fluxes: simplified cases where atmosphere absorbs all infrared
For balance, IRatm has
to be 235 (=net solar);
IRatm is same; so sfc
has to be warm enough
to emit 470, double the
solar
Some solar absorbed:
IRsfc has to balance net
solar at sfc + IRatm :
168+ 235=403
Figure 6.2
• Solutions just by energy balance  Large impact of greenhouse effect
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For the 1-layer atm, energy balance solutions
when atmosphere only partly absorbing:
1
Only 10% of IRsfc gets through atm (for “normal” climate, before
increasing greenhouse gases), i.e., atm is absorbing 90%.
Bulk absorptivity for the atm layer, ea=0.90
Energy balance:
Top of the atm
At surface
Input = Output (in Wm-2)
235 = (1-ea) IRsfc + IRatm
168+ IRatm = IRsfc
Eq. 6.2
Eq. 6.3
1
Top of
atmosphere
1
168
1
At surface
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For the 1-layer atm, energy balance solutions
when atmosphere only partly absorbing:
Energy balance:
Input = Output (in Wm-2)
Top of the atm
235 = (1-ea) IRsfc + IRatm
At surface
168+ IRatm = IRsfc
• With IRatm = IRatm (Eq. 6.4), add the 2 eqns to elim IRatm
Gives:
IRsfc = 403/(2-ea)
• For ea= 0.90, IRsfc = 366; Increased ea gives increased IRsfc
Eq. 6.2
Eq. 6.3
Eq. 6.5
• [Note (2-ea) = 1.1; 403 = solar absorbed by sfc + IRatm ]
• [Compare to obs budget: IRatm bigger because atm warmer near surface. i.e., even larger
greenhouse effect that this 1-layer atm.]
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Surface temperature (C) as a function
of absorptivity ea (unitless)
• One-layer global-average energy
balance model
• IRsfc = 403/(2-ea)
Eq. 6.5
• sTs4 = IRsfc
Eq. 6.6
• Use ea =0.9 as “normal” climatology
(open circle)
• Change in GHG  Dea
• gives temperature change DTs
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Figure 6.4
Temperatures from the one-layer energy model
• Get temperatures from
sTs4 = IRsfc
easTa4 = IRatm
Eq. 6.6
Eq. 6.7
gives Ts = 283.5 K = 10.4 C
The atmospheric temperature is considerably colder:
Ta = 249.7 K = -23.5 C
Compare to no atm case (same albedo)
sTs4 = 235 Ts = -19 C
• versus obs avg sfc temp = 15C: a 34 C difference
(i.e., greenhouse effect powerful in current climate)
• Note Ta similar to Ts in no atm case because atm does most of emitting
to space. (If atm absorbs all IRsfc exactly same: the “emission
temperature”)
• Why is 1-layer model Ts colder than obs? In real atm Ta decreases with
height!
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6.2 Global warming I: example in global-avg energy balance model
Increased absorption of infrared radiation by
greenhouse gases leading to surface warming
Figure 6.3
1B
2A
1A
2B
3A
• Steps in conceptual
sequence
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4
3B
6.2b Climate feedback parameter in the one-layer global avg model
Surface temperature (C) as a function
of absorptivity ea (unitless)
• Recall: One-layer global-average
energy balance model
• Use ea =0.9 as “normal” climatology
(open circle)
• x-axis also given as the top of the
atmosphere greenhouse radiative
forcing G in Wm-2
• DTs (temperature change)
• Linear approximation is shown as
dashed line
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Figure 6.4
• In a more complex model, equivalent of ea not a single number:
absorptivity is calculated at many levels, depends on various
greenhouse gases, …
… so express radiative change effects in terms
of changes in top of atm radiative balance
• In simple model, increase of greenhouse gas,
corresponds to increase in absorptivity Dea
(trapping more upgoing IR in atm)
• Before any temp change occurs there will be a
deficit G in the outgoing IR  imbalance at top
of atm G (in Wm-2) good measure of the
greenhouse radiative forcing* (as a change from
normal climatology. Note G is independent of the
particular gas that does the absorbing)
*Forcing: Something that causes an effect.
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• Simple model details:
Keep Ts, Ta (temporarily) fixed at
climatological values (Ts, Ta): reduction in
outgoing IR due to change in absorptivity
Dea is:
G = DeasTs4 -
DeasTa4
Reduced a bit by
increased
(labeled 1B in fig 6.3) emissivity. Smaller
since Ta < Ts
Increased IR
absorption
For more complex models similar
proceedure: for Ts, Ta, fixed, compute
reduction in outgoing IR due to change in
GHG
Temperature must warm to bring outgoing IR back into balance.
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• G  4 Wm-2, for doubled CO2; G increases with increasing GHG
• Linear approximation for sufficiently
small DTs
aTDTs = G
Eq. 6.10
• aT climate feedback parameter (Wm-2K-1)
that arises only from changes in
temperature (without any changes in water
vapor, snow ice clouds, etc. (next section!))
• DTa can be obtained from DTs
• aT: increase in outgoing IR at top of atm
per unit increase in sfc temp.
• aT corresponds to inverse slope of linear
approx. in fig 6.4, about 2.2 (Wm-2K-1)
• aT approx. independent of G
• Eq. 6.10 is for equilibrium (time dependence of warming in section 6.8)
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aTDTs = G
G: imbalance in outward IR, (before
temperature increases) increased
absorption of IR in atm by
aTDTs: increase in outward IR to space
due to warmer temperatures
• balances the heating effects of the
forcing G
• negative feedback
• if forcing disappeared negative
feedback would cause temperatures
to go back toward normal
•larger G balanced by larger DTs;
aT determines how much larger
•“basic greenhouse effect”
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6.3 Climate feedbacks
• Climate feedbacks modify changes due to basic greenhouse effect
• Some may amplify warming considerably
Main feedbacks:
1. The water vapor feedback: assoc. with increases in water vapor
with temp., since water vapor is a GHG
2. The snow/ice feedback: decreases in snow and ice  global
albedo decreases (less solar radiation reflected)
3. Cloud feedbacks: due to changes in cloud cover, which affect
both cloud contribution to the greenhouse effect and to albedo
More details on each below. First use framework from globalaverage energy balance model indicate relative importance of
feedbacks
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6.3a Climate feedback parameter
• Generalize the climate feedback parameter a
aDTs = G
Eq. 6.11
• To calculate G from a complex model:
• Hold temperature, moisture, clouds, etc. fixed
• Increase greenhouse gas concentrations & calculate global
average changes in outgoing IR
•To measure the effects of different feedbacks:
• hold different parts of the climate system constant
•e.g., aT: hold water vapor, ice, snow and clouds fixed but allow
temp to vary. Measure increased IR to space as temp increases
•Then let water vapor vary  aH2O, …
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6.3a Climate feedback parameter (cont.)
• Contributions to a are approx. additive
a = aT + aH2O + aice + acloud
aH2O contribution of water vapor feedback, aice contribution of
snow/ice feedback, acloud net contribution of the cloud feedback
atm
IR
[formally, a =
Ts
_ S , where S is the net solar flux]
Ts
• In practice, contributions of various feedbacks do not add as neatly
but gives sense of contributions  some caveats
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6.3b Contributions of climate feedbacks to global avg temp response
a = aT + aH2O + aice + acloud
e.g.,

a = 4.0 – 1.8 -0.2 -0.6* = 1.4 Wm-2K-1
DTs = G/a = 3.1 K
for G = 4.3 Wm-2
• Compare to if aH2O = aice = acloud = 0
a = aT = 4.0  DTs = 1.1 K
• global average warming increases substantially when positive
feedbacks are included
• but these feedbacks include complex parts of climate system 
different models give a range of values!
*Note: positive feedbacks tend to amplify. But have a negative contribution to a
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Table 6.1
Feedback
Radiative flux to
space per degree inc.
in Ts [Wm-2K-1]
Cumulative climate
feedback parameter,
a [Wm-2K-1]
Cumulative change
in equil. temp, DTs
[K]
Infrared cooling
(negative feedback)
aT 3.7 to 4.4
3.7 to 4.4
1.0 to 1.2
Water vapor
(positive feedback)
aH2O  -2.0 to -1.5
2.0 to 2.4
aT + aH2O
1.8 to 2.1
Sea ice/land snow
(positive feedback)
aice  -0.3 to -0.1
1.7 to 2.3
aT + aH2O + aice
1.9 to 2.5
Clouds
(positive/negative?)
acloud  -1.2 to -0.1
0.9 to 1.6
aT + aH2O + aice + acloud
2.7 to 4.8
aT
Contributions of various feedbacks to climate feedback parameter a
and surface temperature increase DTs=G/a (using G=4.3 Wm-2 for doubled CO2)
Sign is positive for negative feedback, (i.e., energy loss that opposes warming)
Based on 12 models (Soden & Held, 06). Note a range is from actual model values sum of lowvalues to sum
of high values. e.g., aT = 3.7 is not from same model as aH2O = -2.0
Thus, climate feedbacks:
(i) amplify the warming
(ii) increase the uncertainty in the estimate of this warming
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6.3b Climate sensitivity
Mean, standard deviation, and range of doubled-CO2
climate sensitivity for a number of models
Table 6.2
Publication
Number of
models
Mean
Standard
deviation
Range
IPCC (1996)
IPCC (2001)
IPCC (2007)
17
15
18
3.8
3.5
3.2
0.8 C
0.9 C
0.7 C
1.9 to 5.2 C
2.0 to 5.1 C
2.1 to 4.4 C
Different approach: define a standardized experiment:
Double CO2 & run the simulation to new equilibrium climate state.
Change in the long term average defines doubled-CO2 response.
Global-average surface temperature response DT2x used as a
measure of climate sensitivity: doubled-CO2 climate sensitivity.**
[**Terminology alert: sometimes a-1 is also called climate sensitivity]
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6.4 The water vapor feedback
Water vapor feedback in the greenhouse effect
2B
2A
3
1
6
4
5
Figure 6.5
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Water vapor (as measured by vapor pressure)
versus temperature
Figure 6.6
As T increases in atm, if* RH range
similar, water vapor increases
* RH limited by evap. near surface, condensation, but can depend on circulation
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6.5 Snow/Ice feedback
Snow/ice feedback in the global energy balance
Figure 6.7
5B
3
2
5A
4
1
Complications: e.g., cloud cover, albedo of aging snow/ice,…
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6.6 Cloud feedbacks
Cloud feedback challenges:
1. Small scale motions. Average effects at the grid size must
be parameterized
2. Opposing effects in infrared and solar contributions to
energy budget
3. Several cloud properties can affect radiation, e.g.: cloud
fraction, cloud top height, cloud water and ice content.
Different cloud types thus have different net feedback.
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6.6 Cloud feedbacks
Effects of cloud amount in the global energy balance
Figure 6.8
Tend to cancel
Warming tendency
IR
solar
Net Cooling tendency
Increased
reflection
of solar
IR
• Effects of cloud fraction increases (for given cloud type)
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Small
Cooling tendency
Cloud top feedback
Figure 6.9
Warming tendency
• Cloud top feedback: low-level moisture and temperature increase
cloud top tends to reach higher IR emissions decrease
(from colder cloud top)
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6.7 Other feedbacks in the physical climate system
Stratospheric cooling
• Surface and troposphere warm when GHG increase, but
stratosphere tends to cool
• GHG increase in the stratosphere absorption and emission of
IR both increase, but emission exceeds absorption
• Energy budget of layer of temp. Tstrat
2estratT4strat = Qozone + estratIRtrop
has to decr.
increase
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about the same
6.8 Climate response time in transient climate change
Schematic of an equilibrium response experiment
Figure 6.10
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Schematic of greenhouse warming
with time-dependent forcing
Figure 6.11
Warming if
equilibrated
with forcing
Transient
response
experiment
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Greenhouse warming with time-dependent forcing:
ensemble of simulations
Ensemble: runs
with different
natural climate
variability
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Greenhouse warming with time-dependent forcing:
ensemble of simulations
Ensemble: runs
with different
natural climate
variability
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A transient response experiment where greenhouse gas concentrations
are capped at time ts, so the forcing stabilizes (upper panel)
Figure 6.12
Idealized case: cap GHG at given level (i.e., stop emissions suddenly!)
Temperature was less than equilibrium due to lag so continues to
rise for several decades
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6.8b A doubled-CO2 equilibrium
response experiment
6.8c The role of oceans in slowing
warming
Figure 6.13
Equilibrium
temperature response
Annual average
Years 60-80 of
surface air
time-dependent
temperature response temperature
response
from an earlier version
of the GFDL climate
model comparing
equilibrium response Ratio of timedependent
to time-dependent
response to
response
equilibrium
response
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After Manabe et al., 1991, J. Climate.
6.8 Climate sensitivity in transient climate change
∂DTs
C
+ aDTs = G
∂t
Ocean heat storage IR to space Radiative forcing (GHG)
due to Ts
increase
• Extend simple globally averaged energy balance model of Eq. 6.11
to include heat storage in ocean surface layer of depth, H
• Heat capacity per unit area C = cwH
where  - density; cw- heat capacity of sea water
[Details for following example: G reaches 4 W m-2 in 70 years, roughly like 1%/yr CO2 incr.; high/low a from
Table 6.1 (1.6, 0.9 Wm-2K-1); =1000 kg m-3, cw=4200 J kg-1, H=200m gives 17, 30 yr lag]
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A transient response experiment by climate models of different
climate sensitivities to forcing (upper panel)
Simple example:
linearly increasing
radiative forcing
starting in 1970
lag due to ocean,
depends on a
Figure 6.14
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G
DTs = a in equilibrium
High
sensitivity
model
(smaller a)
Low
sensitivity
model
A transient response experiment by climate models of different
climate sensitivities to forcing
Initially small
∂DTs
C
+ aDTs = G
∂t
Ocean heat storage IR to space Radiative forcing (GHG)
due to Ts
increase
*to see this try DT = g(t - ) in Eq. 6.15 using G = gt
s
a
C lag due to ocean,
a depends on a
Hard to distinguish
high a from low
ainitially
*=
Heat storage balances GHG initially
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G
DTs = a in equilibrium
High
sensitivity
model
(smaller a)
Low
sensitivity
model
A transient response experiment by climate models of different
climate sensitivities to forcing
• Climate models agree fairly well in the early stages of Ds increase
and predicted warming for next few decades. But doesn’t yet
constrain size of eventual warming for given GHG concentrations
C lag due to ocean,
a depends on a
Hard to distinguish
high a from low
ainitially
*=
Heat storage balances GHG initially
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High
sensitivity
model
(smaller a)
Low
sensitivity
model