met 61 introduction to meteorology - lecture 7

MET 61

1 MET 61 Introduction to MET 61 Introduction to MeteorologyMeteorology

MET 61 Introduction to Meteorology - Lecture 7

“Warming the Earth and Atmosphere”

Dr. Eugene CorderoSan Jose State University

W&H: pg 113-122Stull: Chapter 2

Ahrens: Chapter 2

Class Outline:

Nature of energyRadiation in the atmosphereRadiation laws (relationships)

Conduction Convection

Density andpressuregradients

Temperature and moisture gradients

Airflow, friction andcloud development

The air

Radiantenergy

Thermalenergy

Potentialenergy

Kineticenergy

Figure 1.4 Energy forms and transformations in the atmosphere.

The Nature of Energy in the Atmosphere

• Radiant Energy is energy associated with electromagnetic waves propagating through space

• Thermal Energy is energy associated with the ability of one body or substance to raise the temperature of a cooler one

• Potential Energy is energy due to position, e.g. moisture in a cloud about to fall as rain

• Kinetic Energy is energy due to motion, e.g. air in motion

While there are four forms of energy in While there are four forms of energy in the atmosphere, there are only three the atmosphere, there are only three

modes of energy transmissionmodes of energy transmission

• By Radiation

• By Conduction or the

• By Convection or the

While there are four forms of energy in While there are four forms of energy in the atmosphere, there are only three the atmosphere, there are only three

modes of energy transmissionmodes of energy transmission

• By Radiation of electromagnetic waves propagated through space

• By Conduction or the transfer of energy in a substance by means of molecular excitation without any net external motion

• By Convection or the transfer of energy by mass motions within a fluid or gas, resulting in actual transport of energy.

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Energy flow through a simple Energy flow through a simple climate systemclimate system

First Law of Thermodynamics states that energy can neither be created nor destroyed. This leaves only two possibilities; either

Energy Energy InputInput

Energy Energy OutputOutput

Climate Climate SystemSystem

Basic Radiation Concepts

Electromagnetic radiation

• Radiation is the transfer of energy by rapid oscillations of electromagnetic fields.

• The most important general characteristic is its wavelength (), ____________________________.

• Frequency, and wave speed, c are related as:=c/; c=3.0x108m/s

• Wavenumber is defined as # waves/unit of measure.=1/ (m-1) ; note difference in book notation

Defined as the crest-to-crest distanceDefined as the crest-to-crest distance

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Spectrum of electromagnetic radiation

Figure 2.5 Full spectrum of electromagnetic radiation.

0.770.39 m

Visible

C os m ic ray s

R ad io w a ve s

S ola r ra ys toE ar th

1010 10 10 10 10 10 10 10 10-10

-10-12-14 -8 -6 -2 0 2 4

Wavelength m

Wavelength cm

In fra- red

Ultraviolet

X -ray s

G am m a ray sV

iole

tIn

digo

Blu

e

Gre

en

Yel

low

Ora

nge

Red

-8 -6 -4 -2 0 642 8

10 10 10 10 1010 101010

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The Earth-Sun relationship

Sun Earth

Atmosphere

Io = 1 3 6 7 ± 2 W m

Io

d

–2

Figure 2.7 Earth-Sun relationship; I° is the solar constant which is measured perpendicular to the solar

beam, and d is the mean Earth-Sun distance.

Io

4 x 1026 Watts

Mean d = 149.5 x 106 km

What emits electromagnetic radiation?

• All bodies that possess energy [i.e. whose temperatures are > 0 Kelvin (-273.2 C)] emit radiation

• Efficiency of emission is dependent on its emissivity (

• Where a body emits the maximum radiation for its temperature it is called a black body

• Less efficient radiators have varying between 0 and 1.

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Energy absorption and emission

• Molecules can absorb and emit discrete amounts of energy (photons).– These discrete amounts of energy are associated with

electron orbits, rotational changes and vibrational rates.

• Certain objects are selective absorbers: – They absorb (and emit) only certain wavelengths.

• Absorption and emission properties are described in terms of – ‘line spectrum’.

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Absorption spectra for CO2

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Absorption spectra for H2O

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Absorption spectra for O2and O3

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Total Atmospheric Absorption SpectraCO2+H2O+O3 etc.

Wavenumber

Go to the 200 mb height/Isotach (GFS) and identify the approximate

wavenumber for the jet stream using the analysis field.

Two fundamental facts about e-m radiation

• The higher the temperature of the object emitting radiation:– the shorter the wavelength of radiation

emitted– the greater the amount of radiation

emitted

• These relationships are defined by the Planck and Stefan-Boltzmann Law

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Blackbody Radiation

• A blackbody emits it’s maximum possible radiation for that temperature.

• A blackbody is a theoretical concept.

• Plank’s law states that the irradiance of monochromatic (at one wavelength) radiation emitted by a blackbody at temperature T is:

1λT)cexp(λ

cB

25

1

c1=3.74x10-16 W m2; c2=1.44x10-2 m ºK

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0 .2 0 . 4 0 . 6 0 . 8 1 . 0 1 . 2 1 .4

0

5

1 0

0

1 0

2 0

3 0

2 82 42 01 61 284( m) (T = 300 K)

(m) (T = 6000 K)

Ene

rgy

in u

nit

wav

elen

gth

(

107

Wm

–2 p

er

m)

Ene

rgy

in u

nit

wav

elen

gth

(

Wm

–2 p

er

m)

( a )

(Wavelength)

Ene

rgy

in u

nit w

avel

engt

h

( b )

T1

T2T3

T1 > T2 > T3

max

max

Figure 2.6 Energetic characteristics and spectral responses of radiatingobjects showing (a) the spectral distribution of radiant energy from a blackbody at a temperature of 6000 K (left-hand vertical and lower axes) and 300K (right-hand vertical and upper axes); (b) the generalised changes in energyoutput and wavelength distribution with varying temperatures (modifiedafter Oke 1987, and Preston-Whyte & Tyson 1988).

Planck’s Curve

Top Diagram• 300 K object top and

right hand axes, 6000 K object left and bottom axes

• Note massive increase in energy and decrease in wavelength for the hotter object

Lower Diagram• Generalised curves

showing changes in wavelength and energy emission with temperature

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Stefan-Boltzmann law

• Relates the blackbody irradiance to the temperature.

• Integrates the monochromatic irradiance over all wavelengths

4F T is Stefan-Boltzmann constant: 5.57x10-8 W m-2 deg-4.

For non-black bodies a value (between 0 - unity) for emissivity must be included, e.g. F = T4

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Wien’s Displacement Law

• Relates the wavelength of peak emission for a blackbody at temperature T.

T/2897m

where is in m and T in K

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Solar Energy

• Radiant Flux of solar energy is ~ 3.9x1026 W

• Irradiance (E*) : energy/m2

• The Sun’s irradiance at the outer portion of solar disk is (radius=7x108) is:

27

28

26

/1034.61074

109.3mWx

mx

WxF

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Solar Energy (2)

• The average temperature of the sun is about:– 5780°K

• From the Stefan-Boltzmann relationship:

Irradiance is: F =T4 = (5.67x10-8 W m-2 K-4) (5780)4

F= 6.33 x 107 W/m2

• This is another way to calculate the Sun’s irradiance at the outer portion of the solar disk

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In Class QuestionsIn Class Questions

In the following diagram the profile of radiation intensity is given for the Sun and the Earth. Using the previously discussed radiation laws, calculate a) the approximate values of the wavelengths of maximum emissions for the sun and earthb) The maximum radiation intensity for both the sun and the earth.

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Solution

• Calculate the wavelength of maximum radiation for the sun and the earth?

• For the Sun (max) = 2897/6000 = 0.483 m

• For the Earth (max) = 2897/288 = 10.01 m

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Solution

B) Use below

1λT)cexp(λ

cB

25

1λ

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Short and longwave radiation

• All objects emit radiation:

– Sun emits radiation mostly at shorter wavelengths; ultraviolet (UV) and visible:

– Earth emits radiation mostly at longer wavelengths; infrared (IR)

• Difference based on temperature of emitting body.

–(shortwave or solar radiation)

–(Longwave or terrestrial radiation)

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Solar Energy

• Radiant Flux of solar energy is ~ 3.9x1026 W

• Irradiance (E*) : energy/m2

• Derive the solar constant (the irradiance at the top of the earth’s atmosphere): S

2

29

26

/1388105.1494

109.3mW

x

WxF

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Activity 6 (Due March 14Activity 6 (Due March 14thth) )

1. Red light has a wavelength of 0.7 m. Find the corresponding frequency and wavenumber.

2. If you were trying to identify changes in the Earth’s surface temperature, what clues would you look for from a space-based observing system (hint radiation…)?

3. Calculate and plot out (using a computer) the blackbody irradiance for the sun and earth.

4. 4.125. 4.14

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Some relationships…T/2897m

4F T

1λT)cexp(λ

cB

25

1

= 5.57x10-8 W m-2 ºK -4. c1=3.74x10-16 W m2; c2=1.44x10-2 m ºK

0 .2 0 . 4 0 . 6 0 . 8 1 . 0 1 . 2 1 .4

0

5

1 0

0

1 0

2 0

3 0

2 82 42 01 61 284( m) (T = 300 K)

(m) (T = 6000 K)E

nerg

y in

uni

t w

avel

eng

th

(10

7 W

m–2

per

m

)

Ene

rgy

in u

nit

wav

elen

gth

(

Wm

–2 p

er

m)

( a )

(Wavelength)

Ene

rgy

in u

nit w

avel

engt

h( b )

T1

T2T3

T1 > T2 > T3

max

max

Figure 2.6 Energetic characteristics and spectral responses of radiatingobjects showing (a) the spectral distribution of radiant energy from a blackbody at a temperature of 6000 K (left-hand vertical and lower axes) and 300K (right-hand vertical and upper axes); (b) the generalised changes in energyoutput and wavelength distribution with varying temperatures (modifiedafter Oke 1987, and Preston-Whyte & Tyson 1988).

met 61 introduction to meteorology - lecture 7

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