Sun-Earth Geometry, and a factor of 4
Lecture 13
Today:
• Planetary energy balance
• Atmospheric structure revisited
Next lecture:
-What makes some gases greenhouse gases?
- Snow, water vapor, clouds
From last time:
If the Sun’s emitting surface layer (the “photosphere”) were to warm up by 10%, by
how much would the solar flux increase (as a fractional increase)?
Energy balance
EIN = EOUT
S0(1-A) pr2 = s Te4 4pr2
Te = the “effective temperature”. Now divide both sides by the
surface area of the Earth, 4pr2. This will give the energy averaged
over the Earth's surface.
S0
(1-A) = s T e4
4
S0 = 1370 W m-2 ; s = 5.67 ¥10 -8 W m-2 K-4
The average albedo of the Earth is 0.30
Calculate input of solar energy/sec averaged over Earth’s
surface
EIN = 240 W m -2
The average flux of solar energy absorbed by the Earth system.
(averaged over entire surface, including day/night)
The solar constant, S0 = the flux of solar energy passing
through space at the Earth's orbital distance.
S0 = 1370 W/m2
The Earth intercepts the same
amount of solar energy as flat
disc of area pr2
r
pr2
The Earth emits longwave
radiation over the surface area of
a sphere, 4pr2
E IN [Watts] = EOUT [Watts]
[S0(1-A)] pr2 = s Te4 4pr2
i.e. [Solar flux absorbed] ¥ (disc area) = terrestrial flux ¥ (sphere area)
Effective Radiating Temperature -1
EIN = EOUT
S0
(1-A) = s T e4
4
where S0 is the solar constant
A is the planetary albedo
s is the Stephan-Boltzmann constant
and
Te is the "effective radiating temperature"
Given values for S0, A, and s, we can solve for Te:
S
Te4 = 4s0 (1-A)
[S
]
Te = 4s0 (1-A)
1/4
1
Effective Radiative Temperature -2
[S
Greenhouse Effect
If the Earth had no atmosphere (and still had an albedo of 0.30),
its surface temperature would be 255 K.
]
Te = 4s0 (1-A)
0.25
s = 5.67 x 10-8 W m-2 K-4 [universal constant]
For Earth: solar constant, S0 = 1370 W m-2
albedo A = 0.30
Calculate T e
The atmosphere acts like a blanket, trapping heat near the surface
and keeping the surface much warmer than it would otherwise be.
The magnitude of this "greenhouse effect" (DTg) is:
DTg = Ts - Te = 288 K - 255 K
T e = 255 K (or -18 C)
"The Earth radiates as if it were a blackbody at 255 K”, i.e. gives
out a spectrum characteristic of a body at 255K
but...
the Earth's actual surface temperature (Ts) is 288 K (or +15 C).
DTg = 33 K
DTg is a property of the atmosphere.
(Should really be called "the atmosphere effect".)
How do we reconcile this?
Sister planets
Energy Balance and Climate Change
You cannot "predict" surface temperature Ts from knowledge of Te.
Energy balance equation (F is energy flux, W/m2)…
Te is a function of S0 and A
Ts = Te + DTg
where, DTg is a property of the atmosphere of a planet
Venus
(runaway
greenhouse)
Earth
("just right")
Mars
(little
greenhouse)
FIN
energy absorbed
by Earth
=
FOUT
energy emitted
by Earth
“Energy Balance Theory of Climate Change”
if
FOUT < FIN
then
Tsurface will go up until balance is restored
[imbalance]
i.e., the case with global warming
2
Color-coded energy budget: top of atmosphere and surface
Energy Budget: in the atmosphere
Top-of-Atmosphere budget: IN = OUT
Atmosphere budget: IN = OUT
Fig 3-19
Fig 3-19
Surface budget: IN = OUT
Satellite View of Energy Budget
visible satellite
infrared satellite
Vertical structure of the atmosphere
Pressure: the weight of air overhead (e.g. psi = lbs/in2)
Note log scale on pressure graph.
a. At what height are you above 99% of the atmospheric mass?
b. What fraction of atmospheric mass is in the Troposphere?
a. 30 km
b. 90%
c. 6 km
Lapse rate: The rate at which temperature changes with height in the
atmosphere. A measure of vertical stability.
c. What height corresponds to Te?
3
Lapse rate and convection
A dialectic on atmospheric vertical structure
KKC Fig 3-9
Lapse rate: The rate at which temperature changes with height in the
atmosphere. A measure of vertical stability.
Stable: Warm fluid on top of cold fluid.
Unstable: Warm fluid below cold fluid.
Fig. 3-10
Weather (clouds, rain) happens
in the troposphere because the
troposphere is unstable.
Why is the troposphere unstable?
Because temperature decreases with height.
Yes, but why does temperature decrease with height?
3 forms of heat
transfer:
- conduction
- convection
- radiation
Because it is heated from below.
Yes, but how does it come about that it is heated from below?
Because the atmosphere is mostly transparent to solar
(shortwave) radiation, and this is absorbed by the ground
Atmospheric constituents
• main gases (O 2, N2, Ar are 99.9% of dry volume of atmosphere)
• variable gas (water vapor)
• trace gases (CO2, O3, CFCs, SO2, etc, etc, etc)
• particles (dust, seasalt, sulfate, soot, organics)
Greenhouse gases
ppmv = parts per million by volume:
molecules of trace gas per million molecules of air
4