Lecture 5: Solar radiation and the seasons (Ch 2)

• energy transfer mechanisms

• thermal radiation emission spectra of sun and earth

• earth’s seasons

RadiationRadiation. Emission-flight-absorption of “photons” (energy packets). Ultimately, radiative energy transfer “drives” the atmosphere.

ConductionConduction. Local exchange of energy by molecule-to-molecule interaction. Not very important in atmosphere except at boundaries, where mass motion of the air is impeded.

ConvectionConvection. Transport due to “bulk motion” ie. “mass movement” of the air. Rate of transport is proportional to air velocity... and transport flux is parallel to velocity vector. Convective fluxes of “sensible” and “latent” heat are enormously important in the atmosphere.

Energy Transfer MechanismsEnergy Transfer Mechanisms

Electromagnetic radiationElectromagnetic radiation

… generated by the acceleration of charges in matter at any temperature above absolute zero (thermal motion guarantees such accelerations)

Black bodyBlack body

Object or medium that perfectly absorbs all radiation striking it (need not be visually black) and emits radiation at the maximum possible rate for a given temperature

Fig. 2-5

Wien (Germany, 1864-1928; experimentalist)

Wien’s Lawgives the wavelength at which peak emission occurs:

]K[

2900]μm[max T

Sun, T 6000 K

Earth, T 300 K

Black body emission spectrumBlack body emission spectrumFig. 2-7

Boltzmann (Austria,1844-1906; theoretician)Stefan (Austria, 1835-

1893; experimentalist)

Stefan-Boltzmann Law gives the area I under the curve, the total energy emitted per second per square metre of emitter surface:

4TI 4

422 1 KKm

WmW

Emissivity equals 1 for a “black body”… for most terrestrial surfaces > 0.9

810x67.5

Black body emission spectrumBlack body emission spectrumFig. 2-7

Interaction of radiation and matterInteraction of radiation and matter

• individual atoms and molecules of a gas are “selective” emitters and absorbers, whereas solids and liquids emit and absorb over a wide and continuous range of wavelengths (see Sec. 2-1, p38)

• emission and absorption of photons by atmospheric gases is confined to just those wavelengths that cause the participating molecule (or atom) to move from and to an allowable energy state. Thus the atmosphere is not a black (or gray) body

• later we’ll come back to interaction of radiation with the atmosphere

A.H. Compton, Nobel prize winner (1927), interaction of light and matter (USA)

Sun’s radius is about R=700,000 km and surface temperature is about T=6000 K. How much radiant energy Esun does the sun produce in one second, assuming it may be treated as a black body?

)4( 2sun RAIAE

4TI

Having computed Esun, and given earth is at distance r =1.5 x 108 km from the sun, can you compute the intensity S0 [W m-2] of the solar bean at the top of our atmosphere?

Problem:Problem:

Solar (= shortwave) radiation bandSolar (= shortwave) radiation band

μm4μm4.0

Longwave (= terrestrial = thermal infrared) radiation bandLongwave (= terrestrial = thermal infrared) radiation band

μm100μm4

The “NIR”

about half sun’s emission

μm4μm7.0

Two-band decomposition of environmental radiation commonly Two-band decomposition of environmental radiation commonly used in earth science…used in earth science…

Solar constant (Solar constant (SS0 0 ))

Strength (ie. intensity) of the solar (shortwave) beam measured outside the atmosphere.

Seen from planets, sun is a distant point source: so

On earth,S0 =1367 W m-2

201

rS

r

Fig. 2-9

The seasons are regulated by the amount of solar radiation received per unit of ground area per day at earth’s surface. This is affected by sun-earth geometry which controls:

• noon solar elevation & daylength• beam spreading (controlled by solar elevation)• beam depletion (solar pathlength through atmosphere)

Fig. 2-10

If earth’s spin axis lay in the ecliptic plane…(it doesn’t)

spin axis // to sun-earth radius: 24-hour day in S.H.

spin axis to sun-earth radius: 12-hour day everywhere

Fig. 2-11

spin axis to sun-earth radius: 12-hour day everywhere

spin axis 23.5o from being to sun-earth radius

Fig. 2-12

“Solar declination” – latitudinal position of the sub-solar point (negative during N.H. winter). It depends only on time of year

“Subsolar point” – position on earth’s surface where solar beam meets surface at incidence

Tropic of Cancer

Configuration during summer solstice…

Tropic of Capricorn

Fig. 2-13

Edmonton, Dec 21:

=90–53.5–23.5= 13o

Noontime solar elevation angle (p48):

= 90o – latitude + solar declination

Edmonton, Jun 21:

=90–53.5+23.5=60o

(taken as +ve in both hemispheres)

annual migration of the sub-solar point

Fig. 2-14

Sydney, Australia (34oS), Jun 21: =90 – 34 – ( 23.5) = 32.5o

Dec 21: =90 – 34 – (-23.5) = 79.5o

Solar elevation =90o , sin(90)=1, so ignoring absorption/scattering of the solar beam, intensity at surface is 1367 W m-2

Solar elevation =30o, sin (30)=1/2, so ignoring absorption/scattering of the solar beam, intensity at surface is 684 W m-2…i.e. oblique incidence spreads the incident energy over a greater area, reducing intensity

Intensity of the incident beam proportional to Intensity of the incident beam proportional to sin(sin(), i.e. to the “sine” of the solar elevation angle ), i.e. to the “sine” of the solar elevation angle

Fig. 2-16