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Summary of Chapter 2 of FW Taylor's Elementary Climate Physics book
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A select few Derivations of Climate Physics
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H2 Solar radiation and the energy budget of the Earth2.1 Sun and climate
99,97% of the energy arrives from the Sun in the form of electromagnetic radiation
The remainder are negligible for most purposes:
o Interior of the Earth
o Space: energetic particles
o Cosmic rays
o Human power production: fossil and radioactive fuels
The Sun does behave like a hot, solid sphere emitting radiation at a constant
temperature of about 6000K (5780K precise)
Sun is a ball of hot, ionized gas or plasma
The radiation it emits into space originates from different depths in the outermost
layers, which are at different temperatures
2.2 Solar physics
The Sun is a star of the spectral class G2 on the main sequence of the Hertzsprung-Russel
diagram: it is a scatter plot of stars showing the relationship between the stars’ absolute
magnitudes or luminosities versus their stellar classifications or effective temperatures.
Simple: it plots each star on a graph measuring the star’s brightness against its
temperature (color).
The Sun is larger than the average star; top 10%
Radius: 696000 km (100X radius of Earth)
Mass: 2x1030kg
Density at centreL 160000 kg m-3
Consist mostly of hydrogen (91.2%) en helium (8.7%)
4.5 billion years old middle aged
Most mass concentrated in core; T: 15000000K pressure: 10 Mbar
Rotates with a 25-day period at the solar equator, slowing around 35 days near the poles
Photosphere: visible surface
Sunspots: lower T of 4000K; the number fluctuates randomly
2.3 Source of the Sun’s energy
Gravitational collapse: last stadium of a star, if everything is fused to iron, the inherent
gravity is greater than the force outward implode
2.4 The radiation laws
Planck’s radiation law: describes the radiant energy (radiance) emitted from a perfectly
black object as a function of wavelength for a given temperature
A ‘black’ object: perfect absorber with zero reflectivity
2ℎ𝑐 2 1
𝑅(𝜆, 𝑇) = 𝜆5 ℎ𝑐 W-3 sr-1
𝑒 𝜆𝑘𝑇 −1
Radiance is the amount of energy per unit time, per unit area, per unit spectral interval,
and per unit solid angle, passing through a point.
Stefan-Boltzmann law: total power leaving as radiation at all wavelengths from unit area
of a surface at temperature T
𝐹 = 𝜎 𝑇 4 𝑊𝑚−2
𝜎 = 𝑆𝑡𝑒𝑓𝑎𝑛′ 𝑠 𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡
Wiens law: wavelength of the maximum rate of emission at a given temperature
2897
𝜆𝑚𝑎𝑥 = 𝑇 𝜇𝑚
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