SOLAR RADIATION & THE ENERGY BUDGET
A. Radiation and Global Energy
1. The electromagnetic spectrum
c = λf
c=speed of light, 3x1010 cm/s, λ=wavelength, f=frequency
2. Radiation Laws
a. Wien’s Law
λmax = 2897/ T (oK)
b. Stefan-Boltzman Law
F = σT4 where σ is constant (5.67 x 10-8 Wm-2K-4), T(oK)
c. Kirchoff’s Law
αλ = ελ where αλ is fractional amount energy absorbed, and
ελ is emissivity at that wavelength. Or a good absorber is also a
good emitter.
3. Solar radiation: insolation, spectrum, solar constant, sunspot cycle (about 11 yrs)
From about 150 million km (about 91 mill mi), the amount of insolation intercepted
on a perpendicular plane is called the solar constant, approx. 1367 W/m2 or 1.97
cal/cm2/min. Sun’s energy is 7% UV, 44% VIS, 37% near IR, 11% far IR.
a. sun-earth relationships -later
rotation, revolution-365.25 days, declination-23.5o
b. daily and seasonal variations
sun path exercise; declination changes
c. atmospheric effects on insolation-reflection, absorption, scattering
albedo values (p. 27); Earth-atmosphere albedo about 30%.
Scattering:Rayleigh S proportional to inverse of λ4; and Mie, which scatters all
λ equally producing a white color.
Transmissivity is % incoming solar rad. passing thru atmosphere.
d. Direct vs diffuse (sky) radiation. Scattered rad. Reaching Earth is sky rad.
e. surface incidence, absorption, reflection, measurement
f. applications: architecture, solar nrg, heat load, urban design, comfort
4. Long-wave radiation and atmospheric effects; greenhouse effect
a. Stefan-Boltzman’s Law, I = εσT4 where ε is infrared emissivity usually
between 90-95%. Plants 90-95%, water 92-96%, human skin 95%, dry sand 8590%, wet sand 95%, silver 2%.
b. Though atmosphere nearly transparent to short wave radiation, readily absorbs
terrestrial radiation, with principal absorbers being H2O (5.3-7.7 and 20+
microns), ozone (9.4-9.8 microns), carbon dioxide (13.1-16.9 microns), clouds
(all wavelengths).
c. Only about 9% long-wave rad. escapes directly to space, mainly in
“atmospheric window” (8.5-11 microns); rest absorbed.
d. Atmosphere, in turn, re-radiates absorbed terrestrial radiation, partly to space
and partly back to Earth (counter-radiation). Without counter-rad., Earth’s surface
would be 30-40oC colder than it is. Greenhouse works similarly as opaque glass
cover traps IR radiation.
B. Net Radiation and Energy Budget
1. Incoming radiation that is not reflected or back-radiated is known as the net
radiation.
Qn = (K- -K ) + (L--- L ) = (1-r)K + (L - L ) where r is reflected
insolation, K.
2. Energy gained by Earth that’s not lost thru radiation is transferred to latent and
sensible heat or conducted into the ground as ground storage.
a. Latent heat. Evaporation requires large amounts of energy, which is stored as
latent heat in water vapor until it changes back to liquid. Condensation releases this
energy back to the environment.
b. Sensible heat. Conduction and convection is main heating process in lower
atmosphere, which provides temperatures that we can sense or measure-sensible
heat.
c. Ground storage. Heat flows from warmer to colder. When surface is warmer
than subsurface, heat flows into soil. When colder, heat travels to surface.
3. Conduction and convection. On most scales, most heat is transferred by convection
rather than conduction.
4. Qn = L + H + G is called the energy budget. Net energy gained at the surface is
used in evaporation (L), warming the air (H) and warming the subsurface (G). Over
the year, the Earth gains the same amount of energy as it loses. This is called
steady-state.
Temperatures
1. The seasons and the sun-earth relationships.
a. Rotation is counterclockwise in the N. Hemisphere and takes 24 hrs.
b. Revolution is elliptical orbit that takes 1 yr. Or approx 365 ¼ days to complete.
Perihelion and aphelion are closest and farthest positions of Earth from sun. Distance
between 2 varies from 147 to 152 mill km. or about 1.7%.
c. Declination-tilt of axis of 23 1/2o from vertical. Results in seasonal changes in
daylength, intensity of sunlight.
2. Diurnal temperatures. Max, min.
3. Seasonal lag and temp extremes.
4. Vertical temp. profiles-tropics, arctic; tropopause
5. Horizontal (global) temperatures-controls:
a. latitude
b. elevation
c. surface properties: albedo; land vs. water (p. 51); thermal conductivity
d. aspect and topography
6. Global temp maps; averages, range