Elements of the Sun; Solar Radiation

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Chapter 9 Climate Sensitivity and Feedback
Mechanisms

• This chapter discusses
• Climate feedback processes
• Climate sensitivity and climate feedback
  parameter
• Examples
• (Materials are drawn heavily from D. Hartmanns
  textbook and online materials by J.-Y. Yu of UCI.
  Guo-Yue Niu contributed significantly to the
  preparation of this lecture.)

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Climate Feedback and Sensitivity
Feedback is a circular causal process whereby
some proportion of a system's output is returned
(fed back) to the input.
?Q
input
?Qfinal
Climate System
output
?T
?Tfinal
?Qfinal ?Q ?Qfeedback
?Qfeedback can be either negative or positive
?Tfinal ?T ?Tsensitivity
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An objective measure of climate feedback and
sensitivity
The strength of a feedback depends on how
sensitive the change in input (Q) responds to the
change in output (T) Feedback
strength ? ?Q / ?T Climate
sensitivity ?-1 ?T / ?Q 1. Positive values ?
negative feedbacks, stable Negative values ?
positive feedbacks, unstable ?BB 4sT3
3.75Wm-2K-1 2. The larger ?, the stronger
feedback.
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Stefan-Boltzmann feedback
Outgoing longwave radiation F
sT4 s 5.67x10-8
The strength of the feedback
?BB ?F / ?T 4s T3 3.75 Wm-2K-1
1. A negative feedback, stable 2. 1K increase in
T would increase F by 3.75 Wm-2 (see Fig.
9.1)
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Water vapor feedback
Clausius-Clapeyron relationship es
f(T) 1 increase in T would increase 20 in
es Water vapor is the principal greenhouse gases.
The feedback strength ?v 1.7
Wm-2K-1 1. A positive feedback, unstable 2.
Weaker than ?BB 3. ?BB ?v 2.05 Wm-2K-1 (see
Fig. 9.1)
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Ice (snow) albedo feedback
Striking contrast between ice-covered and
ice-free surfaces In ice-covered regions, more
solar energy reflected back to space Feedback
strength ?ice 0.6 Wm-2K-1 1. Positive
feedback, unstable 2. ?BB ?v ?ice1.45 Wm-2K-1
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An example of climate feedback
Global Temperature Anomalies
?T
Northern Hemisphere Snow Cover Anomalies
?Q
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Snow cover change ? Temperature change
Chapin et al. (2005), Science 1. Decrease in
snow-cover and snow season 2. Tundra ? trees
Snow (ice)-albedo climate feedback
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Total feedback
?total 1.45 Wm-2K-1
Positive feedback
negative feedback
?total
3.75 Wm-2K-1
Doubling of atmospheric CO2 ? 2.9 K Without
ice-albedo feedback ? 2.0 K
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Cloud feedback

• It is unclear what is the strength and even
  directions (negative or positive). From GCM
  simulations, ?cloud 0 - -0.8.
• 2. Could effects can be either umbrella or
  blanket.
• umbrella
  blanket

Low cumulus clouds Negative feedback
High cirrus clouds Positive feedback
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Cloud feedback (con.)
3. It is uncertain whether an increased
temperature will lead to increased or decreased
cloud cover. 4. It is generally agreed that
increased temperatures will cause higher rates of
evaporation and hence make more water vapor
available for cloud formation, the form (e.g.,
type, height, and size of droplets) which these
additional clouds will take is much less
certain.
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Energy-balance climate models

• Zero-dimensional EBMs
• (1-a) S0 /4 sTe4

shortwave in Longwave out
The surface T Ts Te ?T (greenhouse
effects) The Erath S0 1376 Wm-2, a 0.3, Te
255 K, Ts 288 K Venus S0 2619 Wm-2, a
0.7, Te 242 K, greenhouse
gases Ts 730 K
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Energy balance climate models (con.)
2. One-dimensional EBMs (Sellers and Budyko in
1969) Shortwave in Transport out
Longwave out S(x) 1 - a(x) C T(x) -
Tm A B T(x) S(x) the mean annual
radiation incident at latitude (x) S0/4
s(x) a(x) the albedo at latitude (x)
for ice-free (Ts gt -10C) 0.3 for
ice (Ts lt -10C) 0.62 C the
transport coefficient (3.81 W m-2 C-1) T(x)
the surface temperature at latitude (x) Tm
the mean global surface temperature A and B are
constants A 204.0 W m-2 and B 2.17 W m-2 K-1
This B is equivalent to ?BB (3.75)
or ?BB ?v 2.05 (see Fig. 9.1)
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Energy balance climate models (con.)

• Changeable parameters
• S0
• a(x) (0.62)
• C (3.81 W m-2 C-1)
• A and B are (B 2.17 W m-2 K-1)
• The model contains four kinds of climate
  feedbacks
• Ice-albedo feedback (Tsgt - 5C 0.8) (see Fig.
  9.5)
• Stefan-Boltzmann feedback B (?BB) 3.75
• water-vapor feedback B (?BB ?v) 2.05 1.45
  (Budyco, 1969) 1.6 (Cess, 1974)
• dynamical feedbacks and zonal energy transport
  C0 means no such a feedback
• You may also add cloud feedbacks by changing B
  smaller (positive feedbacks)
• 
  B larger (negative
  feedbacks)
• Try Toy Model 4 at the course website

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Biogeochemical feedbacks A Daisyworld model
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Biogeochemical feedbacks A Daisyworld model
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Biogeochemical feedbacks A Daisyworld model
Growth Factorwhite 1 - 0.003265(295.5K
-Twhite)2
Global mean temperature sTe4 S0 (1
ap) /4 apAgag Awaw Abab
Local temperature sTi4 S0 (1 ai)
/4 Ti4 ?(ap ai) Te4 where
0lt? lt S0/(4s) represents the allowable range
between the two extremes in which horizontal
transport of energy is perfectly efficient (0)
and least efficient S0/(4s).
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A Daisyworld model
Global mean emission temperature is remarkably
stable for a wide range of solar constant values.
(see Fig. 9.9d) Run Toy Model 1 at the course
website.
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Climate Trend 1976 to 2000

• Increase in T ? melting of snow and frozen soil ?
  larger area of wetlands
• more soil carbon released as CH4 ? increase in T
• Together with ice-albedo feedback, the warming
  trend will be
• accelerated

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Other feedbacks at regional scales
Albedo
Increase in albedo
SW radiation absorbed decreases
Rn decreases
H, LE decreases
Increase in albedo
Increase in Rn
Reduction in Cloudness Precipitation convergence
Reduction in Soil moisture
Increase in insolation
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Other feedbacks at regional scales
Soil Moisture
Decrease in soil moisture
LE decreases H Increases Ts Increases Rn decreases
Decrease in soil moisture
Increase in Rn
Reduction in Cloudness Precipitation convergence
Increase in insolation
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Equilibration times of the climate systems
Radiative forcing
Climate System
Atmosphere 10 days
Atmosphere boundary layer 1day
Ocean
Land
Mixed layer mths-yrs
Sea ice days to 100 y
Ice/snow 10 days
Lakes 10 days
glacier 100s yrs
Biosphere 10 d to 100 yrs
Deep ocean 1000 years
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Three-dimensional atmospheric general circulation
models (AGCMs)

• 1. Computer programs
• Describing atmosphere at gt150,000 grid cells
• 2. Operate in two alternate stages
• Dynamics for whole global array, simultaneously
  solves
• Conservation of Energy
• Conservation of Momentum
• Conservation of Mass
• Ideal Gas Law
• Physics for each independent column, computes
  mass/energy divergences, surface inputs, buoyant
  exchange, e.g.,
• Radiation Transfer Boundary Layer
• Surface Processes Convection (cloud)
• Precipitation
• 3. Coupling with
• Ocean, Land, Biosphere, Sea Ice, and Ice Sheets

Grid spacing 33 horizontally
meters/km vertically Time step 30 minutes
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Concluding Remarks

• The inclusion or exclusion of a feedback
  mechanism could dramatically alter the climate
  modeling results.
• Some important feedbacks may have not been
  included in GCMs.
• Global climate models are getting more complex as
  more feedback mechanisms are included.
• Analyses on climate feedbacks and sensitivity can
  help
• understand the mechanisms of climate change.
• select important processes and limit the
  complexity of climate models.