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Longwave radiation on Earth surface. As used in the class of Hydrology at the University of Trento

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2. 2. R. Rigon 2 Or is used for photosynthesis or other chemical reactions Spectral response
3. 3. R. Rigon 3 Earth “is” a gray body Having a temperature emits radiation A.Adams-Partofthesnakeriverpicture Long wave radiation
4. 4. R. Rigon Gray Bodies • Plank’s Law for gray bodies: • The Stefan-Boltzmann equation for gray bodies: W = ✏ 2⇡c2 h 5 e ch KT 1 [Wcm 2 µm 1 ] W = ✏ T4 [Wcm 2 ] 4 where ε is the average emissivity calculated over the entire electromagnetic spectrum. Long wave radiation
5. 5. R. Rigon Gray Bodies The behavior of a real (gray) body is related to that of a black body by means of the quantity ελ, known as the emission coefficient or emissivity, which is defined as: Kirchhoff (1860) demonstrated that a good “radiator” is also a good “absorber”, that is to say: ✏ = W (real body) W (black body) ↵ = ✏ ⇢ + ⌧ + ✏ = 1 5 Long wave radiation
6. 6. R. Rigon Comparison of blackbody and gray body 6 In reality emissivity depends, at least, on wavelength. Earth should be probably defined a selective radiator Long wave radiation
7. 7. R. Rigon See the Earth as gray body a n d g i v e n t h a t t h e temperature of the Earth’s surface is, on average, about 288 K, it obviously e m i t s a s p e c t r u m o f radiation in the infrared band. 7 Long wave radiation
8. 8. R. Rigon Radiation emitted by the Sun and the Earth Yochanan Kushnir 8 Long wave radiation
9. 9. R. Rigon See the Earth as gray body a n d g i v e n t h a t t h e temperature of the Earth’s surface is, on average, about 288 K, it obviously e m i t s a s p e c t r u m o f radiation in the infrared band. A t m o s p h e r e i s n o t anymore transparent to at these wavelengths. 9 Long wave radiation
10. 10. R. Rigon The atmosphere is warmed from below Therefore the temperature is higher at ground level than it is at higher altitudes. 10 Long wave radiation
11. 11. R. Rigon Greenhouse Effect In the absence of atmospheric absorption the average temperature of the Earth’s surface would be about -170C. 11 Long wave radiation
12. 12. R. Rigon Instead the average temperature is about 15 0C Greenhouse Effect 12 Long wave radiation
13. 13. R. Rigon Radiative heating is completed by convective heat transfer, and by water vapor fluxes (latent and sensible heat). 13But this you can see better on the energy budget slides. Long wave radiation
14. 14. R. Rigon But now concentrate on the surroundings of a point 14 AfterHelbig,2009 Any point being at a certain temperature emits long wave radiation which must be accounted for Long wave radiation
15. 15. R. Rigon 15 The atmosphere emits infrared itself bacause of its temperature Long wave radiation
16. 16. R. Rigon Long-wave radiation is given by the balance of incident radiation from the atmosphere and the radiation emitted by the ground. Both values are calculated with the Stefan- Boltzmann law. 16 All the contributions Long wave radiation
17. 17. R. Rigon Longwave radiation coming from surrounding Radiation losses by the area under exam Longwave radiation coming from sky Longwave (infrared) radiation Topographic effects: angle of view 17 Long wave radiation
18. 18. R. Rigon Long-wave radiation The first component should be calculated by integrating the formula over the entire atmosphere, but, given how complex this process is, typically an empirical formula is used that uses the value of air temperature as measured near ground level (2m) and a value of the atmospheric emissivity based on specific humidity, temperature, and cloudiness. The second component, on the other hand, is function of the s u r f a c e t e m p e r a t u r e a n d i t s emissivity. 18
19. 19. R. Rigon The real process: The hydrological parameterisation: Long-wave radiation 19 Long wave radiation Global emissivity of the atmosphere Temperature at 2 m from ground
20. 20. R. Rigon The hydrological parameterisation: εatm = εBrutsaert (1− N6 ) + 0.979N4 Brutsaert (1975) + Pirazzini et al. (2000) εatm = εBrutsaert (1+ 0.26N) εatm = εIdso(1− N6 ) + 0.979N4 εatm = εIdso,corr (1− N6 ) + 0.979N4 Brutsaert (1975) + Jacobs (1978) Idso (1981) + Pirazzini et al. (2000) Hodges et al. (1983) + Pirazzini et al. (2000) Parameterisation of Long-wave radiation 20 Long wave radiation where N is the fraction of sky covered by clouds
21. 21. R. Rigon 21 Net Radiation The sum of longwave and shortwave ratio is called net radiation
22. 22. R. Rigon 22 1Thank you for your attention ! G.Ulrici-2000?