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6 e-coping withearthsurface


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Solar radiation when hits a place on Earth according the place's longitude and latitude. Used in the class of Hydrology at the University of Trento

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6 e-coping withearthsurface

  1. 1. Riccardo Rigon IlSole,F.Lelong,2008,ValdiSella Solar Radiation Coping with Earth Surface
  2. 2. R. Rigon Radiation intensity Solar intensity governs seasonal climatic changes and the local climatic niches which are linked to the apparent height of the Sun. 2 Copying with Earth surface
  3. 3. R. Rigon Insolation and latitude Incoming solar radiation is not evenly distributed across all lines of latitude, creating a heating imbalance. Figure3.7 3 Copying with Earth surface
  4. 4. R. Rigon Radiative imbalance 4 Copying with Earth surface
  5. 5. R. Rigon decreases towards the poles and it is reduced in areas where clouds form frequently For example, the complete energy balance is greater at the equator but the greatest amount of insolation is in the subtropical deserts Average annual radiation is < 80 W/m2 in the cloudy parts of the arctic and the antarctic >280 W/m2 in the subtropical deserts Radiation received from the Sun 50 Copying with Earth surface
  6. 6. R. Rigon From a subjective point of view, the Sun varies its height in the sky seasonally. This is the subject of interest in the study of the geometry of radiation. The geometry of radiation 6 Copying with Earth surface
  7. 7. R. Rigon Calculations of the incident radiation onto the surface of the Earth need to take account of the geometry of the interaction between the Sun’s rays and the surface of the Earth, which is curved and therefore variably exposed with respect to the direction of the Sun in function of latitude, time of day (longitude) and, naturally, day of the year. Moreover the Earth rotation is inclined with respect to its orbit around the Sun , and this causes seasons to happen. To sum up 7 Copying with Earth surface
  8. 8. R. Rigon The geometry of radiation To calculate the aforementioned quantities it is usual to use a topocentric coordinate system, that is, with the origin in the geographic position of the observer, which is right-handed and positioned on the plane tangent to the Earth’s surface in the considered point. N.B. - A coordinate system located at the centre of the Earth id called geocentric. NauticAlmanacOffice,1974 8 Copying with Earth surface
  9. 9. R. Rigon The geometry of radiation The X-axis is, therefore, tangent to the earth and positive in a West-East direction. The Y-axis is tangent in the North-South direction and is directed towards the South. The Z-axis lies on the segment joining the centre of the Earth with the point being considered on the surface. It is assumed that the Sun lies in the ZY plane at the solar noon. NauticAlmanacOffice,1974 9 Copying with Earth surface
  10. 10. R. Rigon Solar Vector The solar vector can be expressed as a function of the angles that have been defined. The resulting trigonometric expression is: Therefore, to determine the position of the Sun one needs to know the latitude, t h e h o u r a n g l e , a n d t h e s o l a r declination. ⌥s = ⇤ sin ⇥ cos sin ⇤ cos ⇥ cos cos ⇤ cos cos⇤ cos ⇥ cos + sin ⇤ sin ⇥ ⌅ 10 Copying with Earth surface X Y Z
  11. 11. R. Rigon Hour angle The hour angle can be easily calculated as: ⇥ = t 12 1 ⇥ if t is the solar hour 11 Copying with Earth surface
  12. 12. R. Rigon Solar declination The solar declination is a function of the day of the year (and the era). It requires complex calculations that take account of the precession movements of the Earth. There are, however, various approximations. The one that is presented here is due to Bourges, 1985: where is the day of the year 12 Copying with Earth surface Is the angular height of Sun from the horizon at equator at noon* *
  13. 13. R. Rigon X Y Z 13 Projection on a plane at a certain latitude is the solar vector ⌥s = ⇤ sin ⇥ cos sin ⇤ cos ⇥ cos cos ⇤ cos cos⇤ cos ⇥ cos + sin ⇤ sin ⇥ ⌅ If is the vertical unit row-vector corresponding to the Z axis: and Copying with Earth surface
  14. 14. R. Rigon 14 Projection on a plane at a certain latitude with the symbols explained above Then the projection of the solar irradiation on the plane YX is reduced by the factor where: or: Copying with Earth surface X Y Z
  15. 15. R. Rigon 15 To sum up: Was: Is now: The solar constant can be modified as follows. Copying with Earth surface