Lecture 8
Climate Feedback Processes
GEU 0136
Forcing, Response, and Sensitivity
• Consider a climate forcing
(e.g., a change in TOA net radiation balance, dQ)
• and a climate response
(e.g., a resulting change in the globally averaged annual
mean surface air temperature, dTs)
• We can define a climate sensitivity parameter
• To know (i.e., forecast) expected climate change
resulted from a forcing of DQ, simply multiply by lR
• Then the central question of “know how”:
What determine the magnitude of
lR?
Response, Sensitivity, and Feedback
S0: solar constant; yj = yj(S0)
DOLR
DS0
DTS
Dalbedo
Dvapor
• Sensitivity parameter
depends on direct and
indirect effects of forcing
• Changes in TS will also
affect:
– Outgoing longwave (sTe4)
– Planetary albedo
(ice, snow, clouds)
– Water vapor absorption
• Total sensitivity must take
all these indirect effects
into account
• Some will amplify
sensitivity, and some will
damp sensitivity
3 Basic Radiative Feedback
Processes
Stefan-Boltzmann Feedback
• Simplest possible model of
planetary radiative
equilibrium
• Outgoing longwave
radiation will increase to
partly offset any increase
in incoming radiation
Water Vapor Feedback
• As surface warms, equilibrium vapor
pressure will increase (Clausius-Clapeyron)
• Increasing q increases LWdown (higher e),
so Ts warms even more
• Air is not always saturated, but we can
assume relative humidity remains fixed as
Ts increases, and calculate new Ts from
radiative-convective equilibrium
Water Vapor Feedback (cont’d)
lR)FRH ~ 2 lR)BB
• Water
vapor is a
positive
feedback
mechanism
• OLR is only
linear wrt
TS, not
quartic as
predicted
by BB
curves
Ice-Albedo Feedback
• Cold temperatures make the surface turn
white due to increased sea ice and snow
cover on land
• White (high-albedo) surfaces reflect more
SWdown, decrease energy absorbed , leading
to colder surface temperatures
• Warmer temperatures tend to reduce
planetary albedo, allowing more energy to
be absorbed
• Positive feedback … tends to amplify
changes in TS resulting from any forcing
Ice-Albedo Feedback
• SH: ice sheet at
pole, sea-ice
from 50º to 80º
• NH: sea-ice at
pole, seasonal
snow from 40 º
northward
Ice Age Changes
Ice age surface albedo was
much higher than present!
Budyko Ice-Albedo Climate Model
• Solar rad is
distribted
according to
latitude
• Energy
transport is
diffusive
• OLR is linear
with TS
• Albedo
switches
between two
values,
depending on
ice or no ice
Budyko Ice-Albedo Climate Solutions
• Stronger sun
causes ice
edge to
retreat to
higher lat,
& vice versa
• Below 97%
of current
value, model
produces a
white Earth!
Budyko Feedback Sensitivities, 1
d = g/B
• Ratio of
meridional
energy
transport to
longwave
cooling
• Budyko used
2.6 … modern
measurements
suggest 1.7
• Less sensitive
using recent
data
Budyko Feedback Sensitivities, 2
• Ice-free
albedo
decreases
toward the
poles to
account for
cloud masking
of surface
• Ice transition
makes less
difference
Tropical SST and LW Feedback
• Tropical SSTs didn’t
vary much during ice
ages … why?
• Near 300 K, LW
cooling decreases very
fast with increasing
SST
• Positive feedback
should make tropical
SSTs sensitive and
variable …
• but they’re not!
Longwave and Evaporation Feedbacks
• Tropical SST energy balance:
SWdown –
(200 W m-2)
-
LWup =
H
+
LE
+
DF
(60 W m-2) = (10 W m-2 ) + (120 W m-2) + (20 W m-2)
Compensating Tropical SST
Feedbacks
Changes in LE with SST balance positive
feedback with respect to longwave down
Biophysical Feedback: “Daisyworld”
• Consider a planet populated by two kinds of plants:
white “daisies” and black “daisies.”
• Write an energy balance for the planet, assuming
– (1) it emits as a blackbody
– (2) the albedo is an area-weighted average of the albedos of
bare ground, white, and black daisies
• The daisies grow at temperature-dependent rates
(optimum at 22.5º C, zero at 5 º and 40º), and also
proportional to the fraction of bare ground
• The daisies also die at a specified rate c
• Solve for areas Ai and temperatures Ti of each surface
(white daisies, black daisies, and bare ground)
Daisyworld
h = 0 : transport is perfect
More generally,
h = (S0/4) : transport is zero
Biophysical Feedback: “Daisyworld”