Download What is Kelvin? A Sample Problem Solution * Flux on an angled

What is Kelvin?
A Sample Problem
Kelvin = Absolute temperature scale
An object warms from 0 C to 10 C.
T(Kelvin) = T(Celsius) + 273
What is its fractional increase in temperature?
What is the meaning of absolute zero?
What is its fractional increase in emitted energy
flux?
Can there be negative T on the Kelvin scale?
What is temperature anyway?
Hints:
Stefan-Boltzmann F = σ T4, T in Kelvin
σ = 5.67 X 10 -8 W/m 2/K4
T(K) = T(C) + 273
Flux on an angled surface
Solution
*
Step 1 Convert to T(K):
objects warms from 273 K to 283 K
Step 2 Fractional increase in T:
= ΔT/T O = 10/273 = 0.037 = 3.7%
Step 3 Compute energy from S-B Law:
F(273 K) = 314.9 W/m 2
F(283 K) = 363.7 W/m 2
Step 4 Fractional increase in F:
= ΔF/F O = 48.8/314.9 = 0.155 = 15.5%
Flux on a sphere
Planetary Energy Balance 0
(reason why it is colder at higher latitudes)
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Planetary Energy Balance 1
Planetary Energy Balance 2
Put this together:
•Solar constant S=1370 W/m 2
flux of SW energy at the
radius of Earth’s orbit around
the sun
EIN = S (1-A) πREarth 2
EOUT = σ TE4 4πREarth 2
•Earth intercepts SW energy
with the area of a flat disk
πREarth 2
EIN = E OUT
S (1-A) / 4 = σ TE4
•But Earth emits LW energy
over the entire surface surface of a sphere is
4πR Earth 2
Planetary Energy Balance 3
S (1-A) / 4 = σ TE4
EIN = (1370 W / m2) ( 1 – 0.3 ) / 4 = 240 W / m 2
So σTE4 = 240 W / m 2
In summary
•Earth absorbs F IN = 240 W / m 2 of energy (averaged
over whole earth surface, day and night)
•In the approximation that the earth system radiates
like a blackbody T E = 255 K = -18 C
•But the average surface temperature of Earth is
about 288 K = 15 C
TE4 = ( 240 W / m 2 ) / (5.67 x 10 -8 W / m 2 /K)
Where did we mess up???
TE = 255 K = -18 C
TE = Effective radiating temperature
Greenhouse Effect
One-Layer Model (p43)
S/4
Makes us warmer by
ΔTg = TS - TE = 33 C
(S/4)A
σ TE4
σTs4= 2σTe4
1-layer Atmosphere
(S/4)(1-A)
σ TS4
Earth
TE = 255 K
TS = 303 K
σ TE4
Ts = 2
1/4 T
E
same as without Greenhouse Effect
Now we’re too hot! But you get the idea
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One-Layer Model (p43)
S/4
(S/4)A
Model Assumptions
σ TE4
•Whole atmosphere has
temp TE
1-layer Atmosphere
(S/4)(1-A)
σ TS
Earth
4
σ TE4
Neighboring Planets
Venus - runaway
greenhouse
Earth - “just
right”
Mars - almost no
greenhouse
•Atmosphere absorbs
no SW
•Atmosphere
completely absorbs all
LW emitted by surface
Are any of these correct?
Heat Transfer
Radiation – emission and absorption
Contact – we call this sensible heat (“sense” as
in“touch”) -- results in warm air near surface
Evaporation – we call this latent heat (“latent”
since air heats later, when condensation occurs)
Energy Budget: TOA and surface
One-model atmosphere gives wildly inaccurate
surface temperatures for Venus and Mars
Energy Budget in Climate System
•Complex diagram for complex system
•Based on “100 units” of incoming solar flux
so think of these numbers as %
•Many of these numbers are not that certain!
•But numbers all balance nicely anyway,
because they must!
Energy Budget: Atmosphere
Top of Atmosphere: IN = OUT
Atmosphere: IN = OUT
Surface: IN = OUT
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Main Constituents of Earth’s Atmosphere
N2 Nitrogen
78%
O2 Oxygen
21%
Ar Argon
1%
H2O Water Vapor
0-4%
CO2 Carbon Dioxide
0.037% (increasing)
What is a greenhouse gas?
A greenhouse gas is a gas that absorbs
significantly the radiation emitted by the earth
and its atmosphere.
•N2, O2, & Ar contribute little to the greenhouse effect.
•H2O & CO2 contribute a lot even though their
concentration is low.
Important Greenhouse Gases
Radiation excites vibration and rotation in molecules
most efficiently when molecules are not very
symmetric, such as a triatomic (three atom) or more
molecules
Why does water vapor vary so much?
Tropical
(in ppm)
H2O water vapor
0.1-40,000
CO2 carbon dioxide
370
NH4 methane
1.7
N2O nitrous oxide
0.3
O3 ozone
0.01
CFC chlorofluorocarbons
~0.0007
Sun and Earth emission from space
What is up with Earth?
•Saturation – amount
of H2O vapor in air at
point of condensation
(maximum amount of
vapor air can “hold”)
•Saturation vapor
pressure increases
exponentially with T
Arctic
Most LW radiation emitted by the surface is
absorbed by the atmosphere
Tropical
Arctic
Peak wavelength of
emission from ground
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Thermal structure of the atmosphere
Lapse Rate
Rate at which temperature changes with height
A measure of vertical stability. Why?
Density depends inversely on temperature.
Like Fig 3-9b
Stable – warm fluid on top of cold fluid
About 90% of the atmosphere’s mass is in
the troposphere.
Convection - caused by unstable air
Occurs when heated from below
Like boiling water
Unstable – warm fluid below cold fluid
Cloud types
Cumulonimbus from
Space
Cumulonimbus
Fig 3-10
Stratus and Mist
Why consider clouds?
Thick clouds reflect sunlight well and so
influence planetary albedo
Clouds are also fairly efficient
absorbers/emitters of terrestrial radiation
and so contribute to the greenhouse effect
How do clouds form?
1. Start with air parcel (a volume of air with
similar properties) containing water vapor
2. Lift parcel up
•
Heating at surface, thermals
•
Upslope wind forced by mountains
•
Converge of mass by large scale
circulation
3. Parcel cools by rising
4. Parcel temperature reaches saturation
5. Condensation occurs => cloud forms
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Parcel Saturation
Saturation - amount of H 20
vapor in air at point of
condensation
1. Parcel starts at T0
2. Cools by lifting
3. Reaches saturation
curve at saturation
temperature T1
T1
T0
Evaporation cools
surface and moistens parcel
Why do parcels cool as they rise?
Because atmospheric pressure
decreases with height, the
surrounding air pushes with less
force as parcels rise. This causes
them to expand as they rise.
Parcels do work to increase their
volume, so they lose energy and
they cool.
Think of air escaping from an aerosol can or a tire
Thin High Clouds
Mostly composed of ice crystals and because
they are thin solar radiation passes through,
yet infrared radiation is mostly absorbed.
Contribute more to the greenhouse effect then
the planetary albedo.
Surface Warming
Thin High Cloud
Thick Low Clouds
•Often composed of water
(sometimes ice too)
•Highly reflective so they increase
planetary albedo
•Good blackbody radiators but
their temperature is not very
different from the surface
temperature
Surface Cooling
Thick Low Cloud
Usually reduced absorbed solar dominates
their influence on Earth’s energy budget
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Energy Balance Theory of Climate Change
ΔTS = λ ΔF
Part 2
ΔTS = λ ΔF
Consider feedbacks related to changes in A
(albedo) ALONE
ΔTS = Response (change in surface temp)
λ = Climate sensitivity (determined by
feedbacks)
ΔF = Forcing (change in energy balance)
Get used to this equation!
Remember these Equations?
ΔTEQ = ΔTO + ΔTf
EQ => equilibrium temperature change
with feedback
o => temperature change without feedback
f => temperature change due to feedback
f = ΔTEQ / ΔTO
0 < f < 1 if feedback is negative
f>1
if feedback is positive
Example: Doubled CO2
ΔTO = 1.2 K
ΔTEQ = 1.5 to 4.5 K depends on the model
What is f? Why?
Negative feedback loop
Low sensitivity
Small temperature change
Positive feedback loop
High sensitivity
Large temperature change
Double CO2 Example
f = ΔTEQ / ΔTO
ΔTO = 1.2 K *
ΔTEQ = 1.5 to 4.5 K depends on the model
f is 1.2 to 3.5, so feedback is positive
* How is this computed?
Using planetary energy balance with
higher radiation and convection
responding to doubling CO2.
WARNING book inconsistency!
Examples of Climate Feedbacks
Examples of Climate Feedbacks
Water Vapor Feedback
Ice-Albedo Feedback
Fig 3-20
Fig 3-21
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Cloud Feedback
SW: increasing cloud amount => increasing albedo
=>decreasing temperature
LW: increasing cloud amount => increasing heat
trapping => increasing temperature
Cloud Forcing
What is the effect on the TOA radiation budget
from clouds in the current climate?
Lots of research has shown…
Clouds cool the planet - clouds reduce
incoming SW flux more than they reduce
outgoing LW flux
Big question:What happens to cloud amount
when temperature increases?
Cloud Feedback
If we increase the surface temperature, what
happens?
Don’t know for sure?
What’s the inconsistency?
ΔTO = temperature change “without feedback”
BUT ΔTO actually is computed from a
radiative-convection model which
includes some feedbacks… NAMELY
Run climate model…
IR Flux - Temperature Feedback
Looks like we reduce outgoing LW flux,
reinforcing the surface warming, which would
make cloud feedback negative in a warmer
climate.
Fig 3-22
Most important feedback of all?
IR Flux - Temperature Feedback
Fig 3-22
This strong negative feedback prevents
positive feedbacks from causing runaway
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