CLIMATE CHANGE AND ENERGY
Juan Carlos de Obeso
October 12 2013
Climate System
What is Climate?
• Climate is the characteristics of the environment, defined over
a finite time interval, at a given location.
- This includes the mean values or the range of values or even
frequency of events for weather variables, such as wind,
temperature, precipitation, humidity, cloudiness, pressure,
visibility, and air quality.
• A complete description of the climate system and the
understanding of its characteristics and change require the study
of the physical properties of the high atmosphere, deep ocean,
and the land surface, and sometimes the measurement of their
chemical properties.
• Climate is a quantitative science, involving the understanding and
modeling of the transfer of energy from the sun to the earth,
from earth to space, and between atmosphere, ocean, and land,
all under fundamental physical laws such as conservation of
mass, heat, and momentum.
Sept. 9, 2009
What is evident from this graphs?
1958-2012?
1700-2012?
Latest CO2 Reading
393.28 ppm
October 09, 2013
Source:http://keelingcurve.ucsd.
edu/
Modeling the Climate
Sept. 7, 2010
Models
• Conceptual
Illustrate principal relationships or balances
• Empirical/statistical
Describe relationship between observed parameters
(e.g. sea surface temperature and rainfall)
• Numerical/dynamical
Based on set of mathematical equations describing
physical processes, that allow the system to evolve in
time
Sept. 7, 2010
How do we model climate?
[physically]
• Physical/dynamical equations
- 3-D equations of motion (conservation of momentum)
-
Continuity equation (conservation of mass)
Thermodynamic equation (conservation of energy)
Equation of state for air
Balance equation for water vapor
• Parameterizations
Small-scale processes that are treated statistically and their
effects related to average conditions over much longer periods of
time and larger space scales
e.g. clouds, radiative transfer, turbulence
Sept. 7, 2010
Weather & Climate Prediction
Current
Observed
State
Initial & Projected
State of Atmosphere
Sept. 9, 2009
Time Scale, Spatial Scale
Initial &
Projected
State of Ocean
Initial &
Projected
Atmospheric
Composition
Climate Change
Uncertainty
Decadal
Global Climate Change Projections
Source: IPCC 4th Assessment Report, Working Group 1: The Physical Science Basis for Climate Change
Sept. 14, 2009
EESC W4400x
http://www.ipcc.ch/publications_and_data/ar4/wg1/en/contents.html
http://www.ipcc.ch/publications_and_data/ar4/wg1/en/faq-1-3.html
Surface Energy Budget
How is energy/temperature transferred from
surface to atmosphere?
- - - - Radiation - - - -
Conduction/Convection
Net Solar Radiation GH Effect
(LW)
(SW)
Radiative Heat Flux Sensible Heat Flux
T 4
 u(Tsfc  Tair )
Latent Heat Flux
 u ( qsfc  qair )
Atmos.
Ground
Blackbody: Definition
A blackbody is a hypothetical body made up of molecules that
absorb and emit electromagnetic radiation in all parts of the
spectrum
– All incident radiation is absorbed (hence the term black), and
– The maximum possible emission is realized in all wavelength
bands and in all directions
In other words…
A blackbody is a perfect absorber and perfect
emitter of radiation with 100% efficiency at all
wavelengths
Planck Function & Blackbody
Radiation
• The radiation emitted by a blackbody can be described mathematically by the Planck
Function.
• Relates the the intesity of radiation from a bb to it’s wavelength or frequency.
• Mathematically complicated (we will skip).
• But will help us derive a simple model of Earth’s energy balance.
• Wein’s Law (flux of radiation emitted by a bb reachest its peak value at wavelength (picture
b)
• Sun is at ~ 5780 K. What is max wavelength? (Think about this).
Note logarithmic
scales
Blackbody emission curves for the Sun and Earth.
The Sun emits more energy at all wavelengths.
F = sT
4
Electromagnetic Spectrum
Sensitivity of human eyes to EM radiation
 Definition of visible spectrum
st
1
Law of Thermodynamics
ΔEint = Q – W
Earth’s atmosphere: (1) Constant volume: W=0
(in equilibrium) (2) Sun is approx. constant
ΔQin = 0 (although Qin > 0)
(3) dEint = 0, over long time periods,
at least before the anthropocene
If Earth’s [effective] temperature is constant (dE = 0) then how
does surface temperature increase?
Hint: What about Qout?
Blackbody Equilibrium
(Energy Conservation)
Energy In
Sept. 14, 2010
EESC W4400x
Effect of latitude on solar flux
2
1
The solar flux of beam 1 is equal to that of beam 2.
However, when beam 2 reaches the Earth it spreads over
an area larger than that of beam 1. The ratio between the
areas (see figure above) varies like the inverse cosine of The effect of the tilting earth surface
latitude, reducing the energy per unit area from equator is equivalent to the tilting of the
light source
to pole. What happens at the pole?
Blackbody Equilibrium
(Energy Conservation)
Energy In = Energy Out
Emitted
“Earthlight”
4πR2Earth x SEarth
Blackbody Equilibrium
(Energy Conservation)
Energy In = Energy Out
Consider albedo

Sept. 14, 2010
EESC W4400x
Emitted
“Earthlight”
4πR2Earth x SEarth
Reflection of Solar Radiation:
The Earth’s Albedo
Components of the Earth’s albedo and their value in % and the
processes that affect incoming solar radiation in the Earth’s
atmosphere
•The ratio between
incoming and
reflected radiation
at the top of the
atmosphere (TOA)
is referred to as the
planetary albedo.
•The albedo varies
between 0 and 1.
Emission Temperature of a Planet
Solar radiation absorbed = planetary radiation emitted
Ein = Eout = S (1-A) p R2 = T4 4p R2
=>
T4 = S (1-A) / (4)
using: A = 0.3; S = 1370 W/m2;  = 5.67 10-8 W/m2/K4
T ~ 255 °K
~ -18 °C [ T0]
Is that an reasonable answer?
Greenhouse Effect
Energy in = πr2 S, which is spread over the earth having area 4πr2 so we have πr2 S/4πr2 =
S/4 for the incoming radiation (W/m2)
Incoming
solar radiation
Reflection
Atmos. Emission
Transmission
Atmos. Emission
Surface Emission
The simple model has one
layer of greenhouse gases
that are transparent to
short wave radiation but
absorb all long wave
radiation.
The temperature of the
absorbing layer is Te
The temperature at the
surface is Ts
Te is the “effective” or “emitting” temperature of the planet.
Greenhouse Effect
IR-Opaque Atmosphere
Incoming
solar radiation
Reflection
Atmos. Emission
Top of the atmosphere balance:
(S/4) (1-A) = σTe4
Te4 = S (1-A) / (4σ)
IR Absorbing Layer:
2 σ Te4= σ Ts4
Transmission
Atmos. Emission
Surface Emission
Earth’s surface budget:
S (1-A)/4 + σTe4
Ts = 2(1/4) Te
Te is the “effective” or “emitting” temperature of the planet.
= σTs4
Greenhouse Effect
IR-Opaque Atmosphere
End Result
(assuming atmos. absorbs all IR):
Incoming
solar radiation
Ts = 2(1/4) Te =1.19 Te
Reflection
Atmos. Emission
Substituting
previous results
Te4 = S (1-A) / (4)
Transmission
Atmos. Emission
Surface Emission
using: A = 0.3;
S = 1370 W/m2
Te ~ 255 K ~ -18 C  T0
Ts =1.19*Te
~ 303 K ~ 30 C  T1
very warm Earth !
Greenhouse Effect
IR-Opaque Atmosphere
Tobserved  288K = 15 C
so
T0 (-18C) < Tobs < T1 (+30C)
What are we missing?
OK, we are missing almost everything, but what is
important?
Absorption of Infrared (Longwave) Radiation
in Earth’s Atmosphere
Absorption of 100% means that no radiation penetrates the atmosphere. The nearly complete absorption
of radiation longer than 13 micrometers is caused by absorption by CO2 and H2O. Both of these gases
also absorb solar radiation in the near infrared (wavelengths between about 0.7 μm and 5 μm).
16, 2009
TheSept.
absorption
feature at 9.6 micrometers is EESC
causedW4400x
by ozone.
Absorption of Infrared (Longwave) Radiation
in Earth’s Atmosphere
Emissivity
From http://m-w.com
(similar info from wikipedia)
So, if atmosphere behaved like a blackbody,
it would absorb all incoming radiation at all wavelengths,
and emit at all wavelengths (appropriate to its temperature)
Greenhouse Effect
IR-Semi-Opaque Atmosphere
with an atmosphere that is not 100% opaque
4
(1-)σTs
4
4
σTa4
4
𝜀𝑇𝑠
𝜀𝜎𝑇𝑠 4 = 2𝜎𝑇𝑎4 or 𝑇𝑎4 =
2
σTs4
σTs4
𝑆 𝐴𝑆
=
+ 1 − 𝜀 𝜎𝑇𝑠 4 + 𝜎𝑇𝑎4
4
4
σTa4
4
Ts(obs) = 288K, ε=0.77
ε is the atmospheric emissivity
1−𝐴 𝑆
1−𝐴 𝑆
𝜀𝑇𝑠 4
4
4
+ 𝜎𝑇𝑎 = 𝜎𝑇𝑠 𝑜𝑟
+𝜎
= 𝜎𝑇𝑠 4
4
4
2
Earth’s Globally Averaged
Atmospheric Energy Budget
All fluxes are normalized relative to 100 arbitrary units of incident radiation.
Values are approximate.
Figure 3-19
(Kump et al)
Greenhouse Effect
The difference between the longwave radiation from the Earth’s surface and OLR
is the greenhouse effect. Note the strong GH effect in areas which are dominated
by deep tropical clouds that precipitate a lot (above). These clouds reach high
into the atmosphere (more than 10 Km) where the temperature is low, thus the
radiative longwave flux from their tops is relatively small. At the same time the
surface underneath is warm and the surface emitted longwave radiation is
almost entirely trapped in the cloudy atmosphere.
Climate change occurs when either side
of energy balance is perturbed.
Example 1:
• Increase planetary albedo
--
• Decrease absorbed solar
--
• Emitted thermal exceeds
absorbed solar --
• Temperature must decrease
to restore balance.
Climate change occurs when either side
of energy balance is perturbed.
Example 2:
• Increase greenhouse gases

• Decrease IR radiation to
space 
• Absorbed solar exceeds
emitted thermal 
• Temperature must increase
to restore balance.
Climate Feedbacks: The Ice Albedo Feedback
Precipitation Changes
Climate Trends: Sea Level Rise
I present multiple lines of evidence indicating that the Earth’s climate is nearing, but has
not passed, a tipping point, beyond which it will be impossible to avoid climate change with
far ranging undesirable consequences. The changes include not only loss of the Arctic as we
know it, with all that implies for wildlife and indigenous peoples, but losses on a much
vaster scale due to worldwide rising seas. Sea level will increase slowly at first, as losses at
the fringes of Greenland and Antarctica due to accelerating ice streams are nearly balanced
by increased snowfall and ice sheet thickening in the ice sheet interiors. But then the
balance will tip toward ice loss, thus bringing multiple positive feedbacks into play and
causing rapid ice sheet disintegration. The Earth’s history suggests that with warming of 23°C the new equilibrium sea level will ……. raising sea level of the order of 25 meters (80
feet).
Contrary to lethargic ice sheet models, real world data suggest substantial ice sheet and sea
level change in centuries, not millennia. The century time scale offers little consolation to
coastal dwellers, because they will be faced with irregular incursions associated with
storms and with continually rebuilding above a transient water level.
The grim “business-as usual” climate change is avoided in an alternative scenario in which
growth of greenhouse gas emissions is slowed in the first quarter of this century, primarily
via concerted improvements in energy efficiency and a parallel reduction of non-CO2
climate forcings, and then reduced via advanced energy technologies that yield a cleaner
atmosphere as well as a stable climate.
The Ocean induces a lag in
response – as it slowly
warms up and then
releases the heat to the
atmosphere
Approaching the
warmest period in
almost a million years