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6 h-coping withterrain

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Distribution of solar radiation in a rugged (tilted) terrain. As used in the class of Hydrology at the University of Trento

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6 h-coping withterrain

  1. 1. Riccardo Rigon IlSole,F.Lelong,2008,ValdiSella Solar Radiation Coping with terrain
  2. 2. R. Rigon Finally the residual radiation hits the terrain The terrain is not a plane but it is inclined. Therefore, besides correcting radiation for latitude, longitude and hour, it is necessary to account for slope and aspect 2 Hitting the terrain
  3. 3. R. Rigon In the presence of topographic surfaces In the northern hemisphere, slopes that face South receive a greater insolation and, therefore, the water in the soil evaporates more quickly or the snow melts faster. Slopes with differing aspects are often characterized by different species and densities of plants and trees. 3 Hitting the terrain
  4. 4. R. Rigon Projection of radiation onto an inclined surface AfterCorripio,2003 First we calculate the normal to the surface 4 Hitting the terrain
  5. 5. R. Rigon ⇧nu = 1 |⇧nu| ⇧ ⇧ ⇧ ⇧ ⇤ 1/2 (z(i,j) z(i+1,j) + z(i,j+1) z(i+1,j+1)) 1/2 (z(i,j) + z(i+1,j) z(i,j+1) z(i+1,j+1)) l2 ⇥ ⌃ ⌃ ⌃ ⌃ ⌅ where z are the elevations of the four points used and l2 is the are of the cell - of side l. Projection of radiation onto an inclined surface Unit normal vector: 5 AfterCorripio,2003 Hitting the terrain
  6. 6. R. Rigon AfterCorripio,2003 6 Representation of the vector normal to the surface of Mount Bianco Hitting the terrain
  7. 7. R. Rigon AfterCorripio,2003 Projection of radiation onto an inclined surface And we compare with the solar vector, indicating the direction of the Sun 7 Hitting the terrain
  8. 8. R. Rigon 8 ⌥s = ⇤ sin ⇥ cos sin ⇤ cos ⇥ cos cos ⇤ cos cos⇤ cos ⇥ cos + sin ⇤ sin ⇥ ⌅ Projection of radiation onto an inclined surface Where all the quantities were already defined previously Hitting the terrain
  9. 9. R. Rigon AfterCorripio,2003 Projection of radiation onto an inclined surface 9Then we calculate the angle between the sun vector and the normal s Hitting the terrain
  10. 10. R. Rigon We can define then the angle of solar incidence AfterCorripio,2003 Projection of radiation onto an inclined surface 10 s Hitting the terrain
  11. 11. R. Rigon Projection of radiation onto an inclined surface Angle of solar incidence cos s = ⌅s · ⌅nu ⇧nu = 1 |⇧nu| ⇧ ⇧ ⇧ ⇧ ⇤ 1/2 (z(i,j) z(i+1,j) + z(i,j+1) z(i+1,j+1)) 1/2 (z(i,j) + z(i+1,j) z(i,j+1) z(i+1,j+1)) l2 ⇥ ⌃ ⌃ ⌃ ⌃ ⌅ ⌥s = ⇤ sin ⇥ cos sin ⇤ cos ⇥ cos cos ⇤ cos cos⇤ cos ⇥ cos + sin ⇤ sin ⇥ ⌅ 11 Hitting the terrain
  12. 12. R. Rigon s = cos 1 nu.z Aspect (from the North anti-clockwise) Projection of radiation onto an inclined surface Slope The above angles needs to be compared with those of the terrain: 12 Hitting the terrain
  13. 13. R. Rigon 13 Projection of radiation onto an inclined surface Remarkably the form of formula for the incident radiation is the same that for a flat surface when the projection angle is accounted: Hitting the terrain
  14. 14. R. Rigon Solar radiation transmitted to the ground under clear sky conditions Therefore, for the direct shortwave radiation: Corripio,2002 14 S as, it was before Hitting the terrain
  15. 15. R. Rigon 15 However, it is not just matter of light but also of shadows Hitting the terrain
  16. 16. R. Rigon Incident radiation Topographic effects: shading 16 More schematically shadow light Hitting the terrain
  17. 17. R. Rigon Incident radiation Topographic effects: shading 17 More schematically light shadow Hitting the terrain
  18. 18. R. Rigon Incident radiation DetailsinCorripio,2003 18 Therefore the direct solar radiation must be corrected to include shading Hitting the terrain
  19. 19. R. Rigon sky view factor diffuse radiation due to Rayleigh scattering diffuse radiation due to aerosols diffuse radiation due multiple scattering What about diffuse radiation ? Topographic effects: angle of view 19 Hitting the terrain
  20. 20. R. Rigon Incident radiation Topographic effects: angle of view 20 Any point in a rugged landscape see just a part of the sky sphere. Its fraction says which portion of the sky contribute to diffuse shortwave radiation. Hitting the terrain
  21. 21. R. Rigon Incident radiation Topographic effects: angle of view 21 Different points view a different sky Hitting the terrain
  22. 22. R. Rigon 22 The sum Hitting the terrain
  23. 23. R. Rigon AfterCorripio,2003 23 Now it really hits the terrain and, in part, it is reflected away Hitting the terrain
  24. 24. R. Rigon AfterCorripio,2003 24Insolation received by Mont Blanc at Spring Equinox Finally a map Hitting the terrain
  25. 25. R. Rigon Typical albedo values 25 http://en.wikipedia.org/wiki/Albedo Albedo
  26. 26. R. Rigon Typical albedo values 26 http://en.wikipedia.org/wiki/Albedo Albedo
  27. 27. R. Rigon 51 The percentage of radiation that is reflected (reflectance) depends on wavelength of the radiation, and on the geometry, nature, and structure of the surface under investigation. Spectral Signature (or Response) 27 Spectral response
  28. 28. R. Rigon •In the case of solar radiation, the spectral signature is defined as the reflectance of the surface in function of the wavelength. 28 Spectral response
  29. 29. R. Rigon 29 •Every type of surface can be statistically characterised by a spectral signature. Spectral response
  30. 30. R. Rigon •The spectral signature of a specific element of a territory will vary due to the variability of local environmental factors. •Given a certain type of ground cover, static elements, such as slope and exposition, and dynamic elements, such as surface ground humidity, the phenological state of the vegetation, the atmospheric transparence, etc., will cause variations in the spectral signature curve. Factors 30 Spectral response
  31. 31. R. Rigon Radiation that hits the terrain, heats it. Or causes changes of phase water to vapor ice to water 31 Spectral response

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