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(2) Radiation Laws 1

Atmo II 31. Physics of the Atmosphere II. (2) Radiation Laws 1. Wiki. Atmo II 32. Angle and Solid Angle. www.greier-greiner.at. Radian (rad) is the standard unit for angular measures. In a circle (with radius r ) 1 rad corresponds to an arc length = r .

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(2) Radiation Laws 1

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  1. Atmo II 31 Physics of the Atmosphere II (2) Radiation Laws 1

  2. Wiki Atmo II 32 Angle and Solid Angle www.greier-greiner.at Radian (rad) is the standard unit for angular measures. In a circle (with radius r) 1 rad corresponds to an arclength = r. The whole circumference is therefore 2π rad = 6.2832 rad. Steradian (sr) is the standard (SI) unit for solid angles. On a sphere (with radius r) 1 sr corresponds to an area = r2. The whole surface area is therefore 4π sr = 12.5664 sr.

  3. Atmo II 33 Solid Angles on Earth Wiki Solid angles of different areas on Earth (Zimbabwe, Algeria + Libya, Switzerland – or Austria)

  4. Atmo II 34 Radiation Units Try not to be confused! Radiant energy: Energy [J] Radiant flux: Energy per time [J s–1] = [W] (power) Radiant flux density = Irradiance: Energy per time per area [Js–1m–2] = [Wm–2] Radiance: Energy per time per area per solid angle [Wm–2sr–1] Spectral radiance Spectral radiance with respect to wavelength [Wm–2sr–1m–1] = [Wm–3 sr–1] or Spectral radiance with respect to frequency: [Wm–2sr–1Hz–1]

  5. Atmo II 35 Strahlungsgrößen Vorsicht – Verwirrungsgefahr! Strahlungsenergie: Energie [J] Strahlungsfluss: Energie pro Zeit [J s–1] = [W] (also eine Leistung) Strahlungsflussdichte = Irradianz: Energie pro Zeit pro Fläche [Js–1m–2] = [Wm–2] Strahldichte = Radianz: Energie pro Zeit pro Fläche pro Raumwinkel [Wm–2sr–1] Spektrale Dichte der Strahldichte:Strahldichte bezogen auf die Wellenlänge [Wm–2sr–1m–1] = [Wm–3 sr–1] oder Strahldichte bezogen auf die Frequenz [Wm–2sr–1Hz–1]

  6. Atmo II 36 Planck’s Law According to Planck’s Law (Max Planck, 1900) the energy emitted by a black body (un-polarized radiation) per time, area, solid angle and wave length λequals: c0 = Speed of light (in vacuum) = 299 792 458 m s–1 h = Planck constant = 6.626 069 57·10–34 Js kB = Boltzmann constant = 1.380 6488·10–23 J K-1 According to our last slides this has to be – right: Spectral radiancewith respect to wavelength [Wm–2 sr–1 m–1]

  7. Atmo II 37 Planck’s Law Planck’s Law (last slide) refers to un-polarized radiation per solid angle. In case of linear polarization we would just get half of it. If you should miss a factor π– this comes be integrating over thehalf space. Planck‘s law often comes in frequency formulation:

  8. Atmo II 38 Planck–Function Black-Body Radiation (Planck Functions) for different temperatures (wikimedia). Note the large dynamic range due to the extremely strong wavelength dependence.

  9. Atmo II 39 Planck–Function Planck Functions in double logarithmic representation (wikimedia). Note that black bodies with higher temperatures emit more energy at all wavelengths.

  10. Atmo II 40 Planck–Function – Sun Planck Function for the temperature of our Sun (yes, the sun can indeed be regarded as a blackbody !) (Meteorology Today, C. D. Ahrens). 44 % of the total energy is emitted in the visible part of the spectrum. But also in the thermal infrared the suns emits way more energy (per m2) than the Earth.

  11. Atmo II 41 Planck–Functions? But how about pictures like this? (LabSpace). These are scaled representations, showing λBλ on the y-axis – and the solar radiation intercepted by the Earth (and not emitted by the Sun).

  12. Atmo II 42 Integrating Planck’s Law If we want just to know the total power emitted per square meter, we need to integrate the Planck law twice – over the half space and over all wavelengths. The integral over the half space gives: K. N. Liou Effective area: Black body radiation is isotropic(independent of the direction):

  13. Atmo II 43 Stefan–Boltzmann Law The integral over all wavelengths gives: But this is nothing else than:

  14. Atmo II 44 Stefan–Boltzmann Law The famous Stefan–Boltzmann Law (after Josef StefanandLudwig Boltzmann): σ = Stefan–Boltzmann constant σ = 5.670 373 · 10–8 W m–2 K–4 The Stefan–Boltzmann constant is therefore related to even more fundamental constants: (Please try it without calculator)

  15. Atmo II 45 Solar Constant How much solar radiation reaches the Earth? Looking at a point-source, and considering energy conservation, we see that concentric spheres must receive the same energy (blackboard). Die radiant flux density (irradiance), at the mean distance Earth – Sun(= Astronomical Unit – AU) per square meter is termed Solar Constant and has (probably) the value: where the Solar RadiusRSun = 695990 km (about.0.7 Mio km), and the Astronomical UnitrS–E = 149597871 km (about 150 Mio. km). but S0 is not constant. The brightness temperature of the Sun is 5776 K.

  16. Atmo II 46 Measuring the Solar Constant Total Solar Irradiance (TSI) measurements – composite of different satellite measurements (World Radiation Center).

  17. Atmo II 47 Measuring the Solar Constant TSI measurements – original measurements (source: WRC). Systematic difference ~ anthropogenic radiative forcing. Trend estimation impossible without data overlap.

  18. Atmo II 48 Changing Solar Constant Changes in thetotalsolar irradiance due to the ~11 year solar cycle (about 1 W/m2 or 1 ‰) are comparatively small (NASA GISS). Note the pronounced latest minimum.

  19. Atmo II 49 Changing Solar UV Radiation Changes in the UV part of the spectrum are much more distinct (NASA).

  20. Atmo II 50 Solar Insolation W & K In general, a square meter on Earth will not receive the full solar constant, since the solar radiation will not hit at right angle (keywords – seasons, night). With the zenith angle of the sun, θ, we get S = S0 cosθ (Lambert’s Cosine Law). And not all the radiation will reach the ground.

  21. Atmo II 51 Solar Insolation Daily mean solar insolation as a function of latitude and day of year in units of Wm−2 based on a solar constant of 1366 Wm−2. The shaded areas denote zero insolation. The position of vernal equinox (VE), summer solstice (SS), autumnal equinox (AE), and winter solstice (WS) are indicated with solid vertical lines. Solar declination is shown with a dashed line (K. N. Liou).

  22. Atmo II 52 Solar Radiation at the Surface At the “top of the atmosphere“ the solar irradiance is still close to that of a black body (R.A. Rhode). Even under “clear sky” conditions a part of the incoming radiation will be scattered and absorbed (the latter – about 20 % mainly due to Ozone and Water Vapor).

  23. Atmo II 53 Albedo Albedo is the percentage of the solar radiation, which is directly reflected. Die Albedo depends on the surface properties. The Albedo is particularly high for (dense) clouds and (fresh) snow. The Earthas a whole reflects 31% of the incoming solar radiation (A = 0.31). The Earth-surface therefore only absorbs about 50 % of the solar radiation. Surface Albedo Clouds 45-90 % Fresh snow (3) 75-95 % Glaciers 20-45 % Sea Ice 30-40 % Rock, soil (2) 10-40 % Forests (1) 5-20 % Water 5-10 % Planetary Albedo 31%

  24. Atmo II 54 Albedo Annual mean of the top of the atmosphere (toa) Albedo (Raschke & Ohmura*)

  25. Atmo II 55 Shortwave-Radiation Net-Short-Wave Radiation = SWdown – SWup at the Earth‘s surface.

  26. Atmo II 56 Shortwave-Radiation Annual mean toa Net Shortwave Radiation (Raschke & Ohmura*)

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