radiation budget_greenhouse effect

7/27/2019 Radiation Budget_Greenhouse Effect

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greenhouse effect, radiation budget,


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Solar Spectrum

The sun emits radiation at all wavelengths

Most of its energy is in the

IR-VIS-UV

portions of the spectrum

~50% of the energy is in the visible region

~40% in the near-IR

~10% in the UV


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Wavelength (m)


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Blackbody Radiation

Blackbody radiationradiation emitted by a body that

emits (or absorbs) equally well at all wavelengths

Planck

function


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Basic Laws of Radiation

1) All objects emit radiant energy.

2) Hotter objects emit more energy than colder objects. The amount of energyradiated is proportional to the temperature of the object raised to the

fourth power.

This is the Stefan Boltzmann Law

F = T4F = flux of energy (W/m2)

T = temperature (K)

= 5.67 x 10

-8

W/m

2

K

4

(a constant)


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Basic Laws of Radiation

1) All objects emit radiant energy.

2) Hotter objects emit more energy than colder objects (per unit area).The amount of energy radiated is proportional to the temperature of

the object.

3) The hotter the object, the shorter the wavelength () of the peak in

emitted energy.

This isWiens Law:

.)(2898

maxT

Km


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Stefan-Boltzmann law

F = T4F = flux of energy (W/m2)

T = temperature (K)

= 5.67 x 10-8 W/m2K4 (a constant)

Wiens law

.)(2898

maxT

Km


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We can use these equations to calculate properties of energy radiating from

the Sun and the Earth.

6,000 K 300 K


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T(K)

max(m)

region inspectrum F

(W/m2)

Sun 6000

Earth 300


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T(K)

max(m)

region inspectrum F

(W/m2)

Sun 6000 0.5

Earth 300 10


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Electromagnetic Spectrum

(m)

1000 100 10 1 0.1 0.01

ultraviolet

visible

lightinfraredmicrowaves x-rays

High

Energy

Low

Energy


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T(K)

max(m)

region inspectrum F

(W/m2)

Sun 6000 0.5 Visible

(yellow?)

Earth 300 10 infrared


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Blue light from the Sun is removed from the beam

by Rayleigh scattering, so the Sun appears yellow

when viewed from Earths surface even though its

radiation peaks in the green


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T(K)

max(m)

region inspectrum F

(W/m2)


(green)

Earth 300 10 infrared


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Stefan-Boltzman law

F = T4F = flux of energy (W/m

2

)T = temperature (K)

= 5.67 x 10-8 W/m2/K4 (a constant)


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T(K)

max(m)

region inspectrum F

(W/m2)


(green)

7 x 107

Earth 300 10 infrared 460


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Solar Radiation and Earths Energy Balance


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Planetary Energy Balance

We can use the concepts learned so far to

calculate the radiation balance of the Earth


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Some Basic Information:

Area of a circle = r2Area of a sphere = 4 r2


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Energy Balance:

The amount of energy delivered to the Earth is equal to the energy lost

from the Earth.

Otherwise, the Earths temperature would continually rise (or fall).


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Energy Balance:

Incoming energy = outgoing energy

Ein

= Eout

Ein

Eout


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How much solar energy reaches the Earth?


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As energy moves away from the sun, it is spread over a greater and

greater area.


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As energy moves away from the sun, it is spread over a greater and

greater area.

This is the Inverse Square Law


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Define So as the energy flux reaching

the Earth from the Sun.

We can calculate So:

So = L / A,

where L = The Suns luminosity

and A = area of a sphere with a radius

equal to Earths orbital distance


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So is the solar constant for Earth

.W/m1370

105.14

W109.34

W109.3

2

211

26

0

2

26

0

S

RA

LS


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It is determined by the distance between Earth (rs-e) and the Sun and the Sun

luminosity.

.W/m1370105.14W109.3

4

W109.3

2

211

26

0

2

26

0

S

RA

LS

E h l t h it l t t


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Each planet has its own solar constant


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Assuming solar radiation covers the area of a circle defined by the radius of

the Earth (re)

Einre


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Assuming solar radiation covers the area of a circle defined by the radius of

the Earth (re)

Ein = So (W/m2) x re2 (m2)

Einre


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How much energy does the Earth emit?

300 K


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Eout = F x (area of the Earth)


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F = T4

Area = 4 re2


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F = T4

Area = 4 re2

Eout = ( T4) x (4 re2)


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(m)

1000 100 10 1 0.1 0.01

Hotter objects emit more

energy than colder objects

Earth

Sun


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(m)

1000 100 10 1 0.1 0.01



F = T4

Earth

Sun


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(m)

1000 100 10 1 0.1 0.01

Earth

Sun

Hotter objects emit at shorter

wavelengths.

max = 3000/T



F = T4

h d h h i ?


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Eout

H h d h E h i ?


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F = T4

Area = 4 re2

Eout = ( T4) x (4 re2)

Eout


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Ein


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We can assume solar radiation covers the area of a circle defined by the radius

of the Earth (re).

Einre


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of the Earth (re).

Ein = So x (area of circle)

Ein

re


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It is determined by the distance between Earth and the Sun (R) and the Sunsluminosity (L).

Remember

.W/m1370

105.14W109.3

4

W109.3

2211

26

0

2

26

0

S

RA

LS


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of the Earth (re).

Ein = So x (area of circle)

Ein = So (W/m2) x re2 (m2)

Ein

re


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Ein = So re2BUT THIS IS NOT QUITE CORRECT!

**Some energy is reflected away**

Ein

re


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Albedo (A) = % energy reflected away

Ein = So re2 (1-A)

Ein

re


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Albedo (A) = % energy reflected away

A= 0.3 today

Ein = So re2 (1-A)Ein = So re2 (0.7)

re

Ein

Energy Balance:


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Incoming energy = outgoing energy

Ein = Eout

Eout

Ein

Energy Balance:


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Ein = Eout

Ein = So re2 (1-A)

Eout

Ein

Energy Balance:


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Ein = Eout

Ein = So re2 (1-A)Eout = T4(4 re2)

Eout

Ein


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Energy Balance:


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Ein = Eout

So re2 (1-A) = T4 (4 re2)

Eout

Ein

Energy Balance:


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Ein = Eout

So (1-A) = T4 (4)

Eout

Ein

Energy Balance:


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Ein = Eout

So (1-A) = T4 (4)T4 = So(1-A)

4

Eout

Ein


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T4 = So(1-A)

4If we know So and A, we can calculate the temperature of the Earth.

We call this the expected temperature (Texp). It is the temperature we

would expect if Earth behaves like a blackbody.

This calculation can be done for any planet, provided we know its

solar constant and albedo.


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T4 = So(1-A)

4For Earth:

So = 1370 W/m2

A = 0.3 = 5.67 x 10-8 W/m2K4


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T4 = So(1-A)

4For Earth:

So = 1370 W/m2

A = 0.3 = 5.67 x 10-8

T4 = (1370 W/m2)(1-0.3)

4 (5.67 x 10-8 W/m2K4)


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T4 = So(1-A)

4For Earth:

So = 1370 W/m2

A = 0.3

= 5.67 x 10-8

T4 = (1370 W/m2)(1-0.3)

4 (5.67 x 10-8 W/m2K4)

T4 = 4.23 x 109 (K4)

T = 255 K


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Expected Temperature:

Texp = 255 K

(oC) = (K) - 273


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Expected Temperature:

Texp = 255 K

(oC) = (K) - 273

So.

Texp= (255 - 273) = -18oC

(which is about 0 oF)


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Is the Earths surface really -18 oC?


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NO. The actual temperature is warmer!

The observed temperature (Tobs) is 15 oC, or about 59 oF.


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NO. The actual temperature is warmer!

The observed temperature (Tobs) is 15 oC, or about 59 oF.

The difference between observed and expected temperatures

(T):

T = Tobs - Texp

T = 15 - (-18)

T = + 33 oC


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T = + 33 oCIn other words, the Earth is 33 oC warmer than expected based on

black body calculations and the known input of solar energy.


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T = + 33 oCIn other words, the Earth is 33 oC warmer than expected based on


This extra warmth is what we call the GREENHOUSE EFFECT.


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T = + 33 oC

In other words, the Earth is 33 oC warmer than expected based on



It is a result of warming of the Earths surface by the absorption of

radiation by molecules in the atmosphere.


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The greenhouse effect:

Heat is absorbed or trapped by gases in

the atmosphere.

Earth naturally has a greenhouse effect of

+33 oC.


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The concern is that the amount of greenhouse warming will increase with the

rise of CO2 due to human activity.


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T = + 33 oC

In other words, the Earth is 33 oC warmer than expected based on



It is a result of warming of the Earths surface by the absorption of

radiation by molecules in the atmosphere.


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Earths Radiation transfer

It is easier to visualize earth's radiation heat transfer with the diagram. The units used to measure the radiant flux energy are the same watts

that are used for electricity; at the top of the atmosphere, the inputenergy is 341 watts per square meter (Wm-2),

which is exactly balanced by a return of that radiant energy; 102 Wm-2 isreflected by the clouds or the surface and 239 Wm-2 is returned as a net

result of the earth-atmosphere heat exchange interaction - and 102 +239 = 341.

The heated atmosphere sends 333 Wm-2of infrared radiation back to theearth, called back radiation.

The key to the global warming issue is that the earth must heat up sothat it can return 396 Wm-2 to restore the balance.

As the greenhouse gases build up, more infrared rays are absorbed inthe atmosphere, and more are sent back to the earth as back radiation.Since greenhouse gases are causing the problem, the only solutionafforded by physics is to reduce them.

radiation budget_greenhouse effect

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