MET 61 Introduction to Meteorology - Lecture 8

1
MET 61 Introduction to Meteorology - Lecture 8

• Radiative Transfer
• Dr. Eugene Cordero
• San Jose State University
• Class Outline
• Absorption and emission
• Scattering and reflected light
• Global Energy Balance

2
Radiation Emission

• B? - Monochromatic Irradiance (Planks Law)
• F - Irradiance (Stefan Boltzmann Law)
• ?max Peak emission at a wavelength

3
(No Transcript)
4
Energy distribution

• Radiative energy propagates at speed of light.
• Energy per unit area decrease as square of
  distance from emitter

R1,, R2radius
5
Energy distribution

• Radiative energy propagates at speed of light.
• Energy per unit area decrease as square of
  distance from emitter

R1,, R2radius
6
Example

• Estimate the value of the solar constant the
  irradiance at the top of the Earths atmosphere.
  

7
Solution
earth
sun
8
Example

• Estimate the value of the solar constant the
  irradiance at the top of the Earths atmosphere.
  

S-Solar Constant
9
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

10
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

11
Or in terms of irradiance
12
Or in terms of irradiance
13
Kirchhoffs law

• Describes how good emitters are also good
  absorbers

• This relationship is wavelength dependent.
• Albedo considers the net effect over a range of
  wavelengths.

14
Kirchhoffs law

• Describes how good emitters are also good
  absorbers

• This relationship is wavelength dependent.
• Albedo considers the net effect over a range of
  wavelengths.

15
(No Transcript)
16
(No Transcript)
17

• Activity 7 Inclass question
• If the Earths albedo was to increase by 10
• A) By how much would surface solar radiation
  change?
• B) How would the Earths surface energy budget
  change?
• C) How would the Earths top of the atmosphere
  budget change?

18
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
19
Solution

• E (in solar) E (out terrestrial)

20
Solution

• F (in solar) F (out terrestrial)

S
F
21
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?

22
Solution

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

23
Solution

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

24
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.

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

25

• So the transmissivity of the layer is now

• And neglecting scattering, then the absorptivity
  is

26

• So the transmissivity of the layer is now

• And neglecting scattering, then the absorptivity
  is

27
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.

28
Solution

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

29
Solution

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

• t?0.135
• a?0.865

30
Sun angle
31
(No Transcript)
32
(No Transcript)
33
(No Transcript)
34
What month do you think this graph represents? a)
December b) March c) June d) September
35
What month do you think this graph represents? a)
December b) March c) June d) September
Answer December
36
(No Transcript)
37
Simplified radiative energy cascade for the
Earth-atmosphere climate system
Reflected Extraterrestrial Short Wave Radiation
Planetary Albedo
Energy Output
E-A Climate System
Energy Input
Terrestrial Long Wave Radiation
Extraterrestrial Short Wave Radiation
Planetary Temperature
Solar Temperature
38
Assigned Reading for Feb 14

• Ahrens Ch 2 (continuing)
• Stull Ch 2 Pages 26-28
• Quiz 1 (30 minutes) on Feb 16th from material
  through Feb 14th.

39
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 Earths surface and Earths
  atmosphere assuming that the earths 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 earths
  surface radiates as a blackbody at all
  wavelengths.