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MET 61 Introduction to Meteorology - Lecture 8

“Radiative Transfer”

Dr. Eugene CorderoSan Jose State University

Class Outline:

• Absorption and emission• Scattering and reflected light• Global Energy Balance

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Radiation Emission

• B - Monochromatic Irradiance (Plank’s Law)

• F - Irradiance (Stefan Boltzmann Law)

max – Peak emission at a wavelength

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Energy distribution

• Radiative energy propagates at speed of light.

• Energy per unit area decrease as square of distance from emitter:

2

2

112 R

RFF

R1,, R2=radius

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Example• Estimate the value of the solar constant; the

irradiance at the top of the Earth’s atmosphere.

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Solution

earth

sun

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Example• Estimate the value of the solar constant; the

irradiance at the top of the Earth’s atmosphere.

S-Solar Constant

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Absorption, Reflection and Transmission

- emissivity: Fraction of blackbody that is actually emitted (0-1)• a - absorptivity: fraction of radiation striking an object that is absorbed.• t - transmissivity: fraction of radiation striking an object that is transmitted.• r - reflectivity: fraction of radiation striking an object that is reflected.

• Energy is conserved, so:

a + r + t = 1

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tyabsorptiviB

B

incident

absorbed a

tyreflectiviB

B

incident

reflected r

vitytransmissiB

B

incident

ed transmittt

Or in terms of irradiance

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Kirchhoff’s law

• Describes how good emitters are also good absorbers

a

• This relationship is wavelength dependent.

• Albedo considers the net effect over a range of wavelengths.

incoming

reflected

F

FA

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Activity 7 Inclass question:

If the Earth’s albedo was to increase by 10%:• A) By how much would surface solar radiation change? • B) How would the Earth’s surface energy budget change?• C) How would the Earth’s top of the atmosphere budget change?

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Energy Balance

• Energy at any level must be in balance:

Energy in = Energy out

Example:

Calculate the blackbody temperature of the earth assuming a planetary albedo of 0.3 and that the earth is in radiative equilibrium

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Solution

• F (in; solar) = F (out; terrestrial)

S F

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Example

• A completely gray surface on the moon with an absorptivity of 0.9 is exposed to overhead solar radiation. What is the radiative equilibrium temperature of the surface?

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Solution

• Since the moon has no atmosphere, the incoming solar radiation is the total incident radiation upon the surface. For radiative equilibrium:

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Atmospheric absorption• The amount of radiation that is absorbed by the atmosphere is

proportional to the number of molecules per unit area that are absorbing.

dzkz

sec

)exp(BB

(sigma) – optical depth or optical thickness• k- absorption coefficient (m2/kg) - density (kg/m3)• Angle of incidence (from vertical)

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• So the transmissivity of the layer is now:

)exp(11a t

)exp(tincident

ed transmitt

B

B

• And neglecting scattering, then the absorptivity is:

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Example

• Parallel radiation is passing through a layer 100m in thickness containing a gas with an average density of 0.1 kg/m3. The beam is directed at 60° from normal to the layer. Calculate the optical thickness and transmissivity and absorptivity of the layer at wavelength where the absorption coefficient is 10-1.

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Solution

• Assuming the absorption coefficient and density do not vary within the layer:

• t=0.135

• a=0.865

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Sun angleSun angle

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What month do you think this graph represents?What month do you think this graph represents?a) December b) March c) June d) Septembera) December b) March c) June d) September

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What month do you think this graph represents?What month do you think this graph represents?a) December b) March c) June d) Septembera) December b) March c) June d) September

Answer: DecemberAnswer: December

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Simplified radiative energy cascade Simplified radiative energy cascade for the Earth-atmosphere climate for the Earth-atmosphere climate

systemsystem

Energy Energy InputInput

Energy Energy OutputOutput

E-A E-A Climate Climate SystemSystem

Extraterrestrial Extraterrestrial Short Wave Short Wave RadiationRadiation

Reflected Reflected Extraterrestrial Extraterrestrial Short Wave Short Wave RadiationRadiation

Terrestrial Terrestrial Long Wave Long Wave RadiationRadiation

Planetary AlbedoPlanetary Albedo

Solar TemperatureSolar Temperature Planetary TemperaturePlanetary Temperature

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Assigned Reading for Feb 14

• Ahrens Ch 2 Ahrens Ch 2 (continuing) (continuing)

• Stull Ch 2: Pages 26-Stull Ch 2: Pages 26-2828

• Quiz 1 (30 minutes) on Quiz 1 (30 minutes) on Feb 16Feb 16thth from material from material through Feb 14through Feb 14thth..

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Activity 7: Due March 21st • Question 1: Concrete has an albedo of around .25 and yet the

typical infrared emissivity of concrete is 0.8. Explain why these are different and the implication of this on climate change?

• Question 2: Consider a flat surface subject to overhead radiation. If the absorptivity is 0.1 for solar radiation and 0.8 in the infrared, compute the radiative equilibrium temperature.

• Question 3: Calculate the radiative equilibrium temperature of the Earth’s surface and Earth’s atmosphere assuming that the earth’s atmosphere can be regarded as a thin layer with an absorptivity of 0.1 for solar radiation and 0.8 for terrestrial radiation. Assume the earth’s surface radiates as a blackbody at all wavelengths.