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Atmo II 75. Physics of the Atmosphere II. (4) Radiation Laws 2. Atmo II 76. Wien’s Displacement Law. - PowerPoint PPT Presentation

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Physics of the Atmosphere II

Atmo II 80

• Wiens Displacement LawPlanks Radiation Law (Slides 36 41) already showed us, that the Maximum of the spectral distribution of blackbody radiation is at long wavelengths when temperatures are low (and vice versa). This has already benn known before as Wien's displacement law (Wilhelm Wien, 1893):

max is the wavelength, where the maximal radiation is emitted.Atmo II 81Inserting approximate values (of ~5800 K and ~290 K, respectively) gives:

Sun:max = 0.5 m Visible LightEarth:max = 10 m Thermal InfraredThe Earth radiate predominantly in the infrared part of the spectrum.

• Wiens Displacement LawWe have already seen that the Stefan-Boltzmann law can be derived by integrating the Planks radiation law (Slides 42 44). Also Wien's displacement law follows from Planks law now we need to differentiate it (with respect to ), and we get max by setting the first derivative = 0.Atmo II 82

• Wiens Displacement LawSetting we get

Atmo II 83

• Kirchhoffs LawA black body , by definition, absorbs radiation at all wavelengths completely. Real objects are never entirely black the cannot absorb all wavelengths completely, but show a wavelength-dependent absorptivity () (which is < 1). According to Kirchhoffs law (Gustav Kirchhoff, 1859) the Emission of a body, E (in thermodynamic equilibrium) is:

For a given wavelength and temperature, the ratio of the Emission and the absorptivity equals the black body emission. This shows also, that objects emit radiation in the same parts of the spectrum in which they absorb radiation. Atmo II 84

• We rearrange Kirchhoffs law and see:

At a given temperature, real objects emit less radiation than a black body (since < 1). Therefore we can regard () also as emissivity. Quite often you will thus find Kirchhoffs law in the form:

Emissivity = Absorptivity

Important: it applies wavelength-dependent.

Kirchhoffs LawAtmo II 85In the infrared all naturally occurring surfaces are in very good approximation black even snow! (which is usually not black at all in the visible part of the spectrum).

For the Earth as a whole (in the IR): = 0.95 (gray body)

• Radiation BalanceAt its (effective) surface, a planet will (usually) gain or lose energy only in the form of radiation. In equilibrium we therefore get:Incoming Radiation = Outgoing RadiationPicture credit: NASAAtmo II 86

• Radiation BalanceWe can us this, to build a (very simple!) zero-dimensional radiation balance mode (note here we regard Earth just as a point!). The Earth absorbs shortwave solar radiation with its cross section (= area of a circle), but emits (longwave) terrestrial radiation from its entire surface (= surface of a sphere):which gives the effective temperature of the Earth which is 16 C (!). This is pretty far from Earths mean surface temperature of (meanwhile) +15 C. What is wrong?Atmo II 87

• Infrared Active GasesIf we want to regard the surface on slide 87 as the Earths surface, we need to consider the influence of the Earths atmosphere which is (largely) transparent for solar radiation, but not for terrestrial radiation, since it contains infrared active gases (pictures: C.D. Ahrens). Atmo II 88

• Greenhouse Effect (Basics)Infrared active are (mainly) those gases with three or more atoms, which show rotation-vibration bands in the infrared*: H2O, CO2, O3, N2O, CH4. They are commonly termed greenhouse gases but the term is not a perfect choice (since the main reason, why a greenhouse is warmer that the surrounding, is not the den greenhouse effect). Greenhouse gases also emit infrared radiation, up and down. The part, which is emitted downwards, warms the Earths surface. With increasing temperature the Earths surface emits more IR-radiation (Stefan-Boltzmann law), until an equilibrium temperature is reached, where the part of the IR-radiation, which can leave the Earths atmo-sphere, equals the incoming solar radiation. Atmo II 89

• In our zero-dimensional model we can represent the influence of the infrared active gases with the transmissivity in the infrared (IR): With a value of 0.634 we get the mean surface temperature of +15 C.Without the selective absorption in the IR the Earths surface temperature would be more than 30 C lower (in his model world). Anthropogenic CO2-Emissions enhance the natural greenhouse effect, bei where water vapor H2O dominates (!). But in an atmosphere without greenhouse gases there would not be snow and clouds, the albedo would be less (A = 0.15) an the means surface temperature would by about 2C (still pretty cold).

Greenhouse Effect (Basics)Atmo II 90

• Atmo II 91

Greenhouse Effect (Basics)As soon, as we look a bit closer (later), things get more complicated (NASA).

• More realistic energy balance (IPCC, 2007 after Kiel and Trenberth, 1997).Atmo II 92

Greenhouse Effect (Basics)

• LongwaveRadiationNet-Longwave Radiation = LWdown LWup on the Earths surface. Absolute values but also annual variations are surprisingly small, especially over the ocean: Higher temperatures lead to more emitted radiation (Stefan-Boltzmann) but also to more water vapor (Clausius-Clapeyron) and therefore more back radiation. Atmo II 93