Climate Change, the Sun and Greenhouse Gases

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Climate Change, the Sun and Greenhouse Gases by
K.K. Tung Department of Applied Mathematics
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Chapter 8 Snowball Earth and Global Warming 8.1
Introduction 1268.2 Simple ClimateModels
128Incoming Solar Radiation 129Albedo
130Outward Radiation 130Ice Dynamics
132Transport 132TheModel Equation 1338.3 The
Equilibrium Solutions 134Ice-Free Globe
135Ice-Covered Globe 136Partially Ice-Covered
Globe 137Multiple Equilibria 1388.4 Stability
139The Slope-Stability Theorem 140The Stability
of the Ice-Free and Ice-Covered Globes
141Stability and Instability of the Partially
Ice-Covered Globe 141How Does a Snowball Earth
End? 1438.5 Evidence of a Snowball Earth and Its
Fiery End 1448.6 The GlobalWarming Controversy
1468.7 A Simple Equation for Climate
Perturbation 1508.8 Solutions 153Equilibrium
GlobalWarming 153Time-Dependent GlobalWarming
154Thermal Inertia of the Atmosphere-Ocean
System 1558.9 Exercises 157
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As constant as the sun?

• Distant Past One billion years ago, our suns
  radiation is about 6 weaker. Snowball Earth.
  Glacier at sea level in the tropics. Four such
  episodes, each lasting 10 million years. The end
  of last one 600 million years ago led to the
  Cambrian Explosion of multicellular life forms.
• Recent Past Naked eye and telescope observation
  of the suns surface. 11th-12th century, Medieval
  Maximum, Vikings colonies flourished in
  Greenland. Late 17th century, Maunder Minimum,
  Little Ice Age in Europe and North America.
• Present Satellite measurement of the changes in
  the solar constant. Detection of the
  atmosphere-oceans response to solar variability.
  Proposed mechanism of how the Earths climate
  responds to variations of solar radiation.
• Future Predictions of global warming. How much
  of the warming is caused by the greenhouse gases,
  and how much by the sun?

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Importance of Ice-Albedo Feedback

• Ice covered surface reflects more sunlight back
  to space, less solar energy received, hence
  colder. Then glaciers advance more equatorward.
• The reverse In a warmer climate, more ice melts,
  exposing darker surface underneath, which absorbs
  more solar radiation, hence warmer, and more ice
  melts. Glaciers retreat.

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As constant as the sun?

• Distant Past
• Recent Past Naked eye and telescope observation
  of the suns surface. 11th-12th century, Medieval
  Maximum, Vikings colonies flourished in
  Greenland. Late 17th century, Maunder Minimum,
  Little Ice Age in Europe and North America.
• Present Satellite measurement of the changes in
  the solar constant. Detection of the
  atmosphere-oceans response to solar variability.
  Proposed mechanism of how the Earths climate
  responds to variability of solar radiation.
• Future Predictions of global warming. How much
  of the warming is caused by the greenhouse gases,
  and how much by the sun?

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Until recently the variability of the solar
radiation was not measured directly, but sunspot
Observation has a long history.
You are mistaken, my son. I have
studied Aristotle and he nowhere mentions spots.
Try changing your spectacles.
Sunspots and Faculae
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Past reports of solar-weather connection

• Pittock (1978) reviewed many such reports. None
  can be shown to be real.
• 1600s, cold temperatures were associated with
  sunspots.
• 1676, Robert Hook arrived at opposite conclusion.
• 1801, Sir William Herschel noted that high wheat
  prices occur when sunspots are few, and concluded
  that lower solar activity means less light and
  therefore less wheat.
• 1870s, 20 papers on rainfall when sunspots are
  numerous, rainfall is more plentiful, and vice
  versa.
• 1882, Balfour Stewart noted an 11-year cycle in
  Nile River flow.
• 1889, D. E. Hutchins claimed an 11-year solar
  cycle in African droughts
• 1987, Robert Currie examined drought records from
  China, North America and South America, and found
  118 locations (61 of those examined) had 10-11
  year cycles.

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Climate response attributable to the suns
variability Not yet proven.

• To establish Sun-Earth Climate Connection we need
  three scientific components
• (1) accurate measurement of the change in
  the suns irradiance at the top of the Earths
  atmosphere (the so-called solar constant),
• (2) measurement of the atmospheres response
  (warming) attributable to (1) in the presence of
  larger noise, and
• (3) a theory connecting (1) and (2).
• Until recently all three components were missing.
  Sun-weather connections were unproven
  conjectures. Many previous reports were no
  different from coincidences.
• Starting 1979, satellites can now measure the
  variability in the solar constant, thus
  satisfying (1) on decadal time scales.
• This talk concerns our work on (2) and (3).

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                                                                                                          Record of TSI observations since 1978 from 9 independent instruments. The instruments agree in the amount of variation during each solar cycle, but the averages over each solar cycle disagree because of different calibration scales of the instruments. Disagreements are getting smaller as calibration methods improve.

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ACRIM TSI composite by Willson and Mordvinov
2003 and an update of the PMOD TSI composite by
Fröhlich and Lean 1998. The black lines are the
TSI averages in the periods 19801991 and
19912002.
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Quantitative analysis
Total solar radiation varies by 0.1 from solar
min to solar max, as detected by satellite at the
top of the atmosphere. More at UV, uncertain at
longer wavelengths. A variation of the solar
constant S On 11-year time scale of about
dS0.90 watts m-2 . Ozone in the stratosphere
absorbs 15, 85 of the remaining gets to the
troposphere. dQdS(0.85)/4 0.19 watts
m-2. This 1/20 that due to a doubling of CO2,
with dQ 3.7 watts m-2. Equivalent to a 1 per
year increase in greenhouse gases for 5-6 years
from solar min to solar max.
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Compare with Projections of Future Changes in
Climate
Projected warming in 21st century expected to
be greatest over land and at most high
northern latitudes and least over the Southern
Ocean and parts of the North Atlantic Ocean
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• The reality of solar cycle response near surface
  is established.
• Can we explain a near surface global warming of
  0.2 K from 0.1 solar variation?
• Too large to be explainable by direct radiative
  calculations need an unknown amplifier.
• Many strange theories.

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• Soon and Baliunas (2000)Climate
  Hypersensitivity to Solar Forcing
• The hypersensitive response of the climate
  system to solar UV forcing is caused by strongly
  coupled feedback involving vertical static
  stability, tropical thick cirrus ice clouds and
  stratospheric ozone
• No need for new mechanisms same mechanisms as
  studied for decades in the global warming
  problem.

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Solar cycle and Global Warming

• Radiative forcing from solar-min to solar-max
• 0.19 watts m-2.
• Periodic warming0.2K.
• If real, can be used to calibrate climate
  sensitivity.

• Radiative forcing for double CO2
• 3.7 watts m-2
• Equilibrium warming
• Current range1.5K 4.5K,
• depending on models climate sensitivity,
  which is uncertain.

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The Global Warming Controversy

• There is no disagreement that the CO2 in the
  atmosphere is steadily increasing, and that it is
  a greenhouse gas.
• The controversy lies instead in the magnitude of
  the predicted warming, which is model dependent
  Is it 1.5 C? Or is it 4.5 C? The magnitude
  depends on how sensitive the climate is to
  radiative forcing. The factor of 3 uncertainty is
  caused by the positive feedback processes
  involving water in its various forms. Without
  water the warming is only 1.5 C at equilibrium at
  doubled CO2.
• The solar cycle response can help determine the
  magnitude of earths climate sensitivity.

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Human and Natural Drivers of Climate Change

• CO2, CH4 and N2O Concentrations
• - far exceed pre-industrial values
• - increased markedly since 1750
• due to human activities

Relatively little variation before the industrial
era
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Attribution of global warming to greenhouse gases
uses models
Observations

• are observed changes consistent with
• expected responses to forcings
• inconsistent with alternative explanations

All forcing
Solarvolcanic
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S1367 Watts/m2
Suns radiation
Total radiation intercepted by the circular
disk S times pR2 total received by earth Q
pR2/4. QS/4.
Average radiation Received by earth Q s(y),
ysinq
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Time-dependent Held Suares climate model with
dynamical transport (annually averaged)
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Perburbation Equationsmall perturbation, linear
response
Note that for small perturbations, different
feedback (fs) can be superimposed, i.e. fSfi.
But gains (gs) cannot.
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Feedback processes

• f1 water-vapor feedback more water vapor in the
  upper troposphere more greenhouse effect.
• cloud feedback more convection more
  clouds, traps more heat or reflects more to
  space.
• f2 ice-snow albedo feedback less ice/snow
  cover, lower albedo, earth absorbs more heat.
• More feedback processes.

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Global warming problemdifferent dQ, different t,
possibly the same g.
Common treatment of the problem double CO2 run
model to equilibrium, find equilibrium dT
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Implication for global warming predictions

• Can be used to calibrate climate sensitivity
  related to water-vapor feedback. GCMs will
  always have large uncertainty unless calibrated
  against observation. Model climate sensitivity
  1.5-4.5K g1-3. The range of uncertainty has
  not narrowed in over two decades. Which is
  right? 3 K g2.