Procedure for creating topographically correct radiation coverages
(toporad.csh shell script)
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All of the following steps are taken at 20-minute intervals throughout the day
when the sun is above the horizon.  The 15th of each month is chosen for each
month's representative day.

1.  Run ELEVRAD to get clear sky total radiation.

2.  Split total radiation into direct (beam) and diffuse components.  (ELEVRAD's
      direct beam radiation is figured normal to the sun's position, unlike 
      TOPORAD, which works with direct beam radiation normal to a horizontal 
      surface on the earth).

3.  Convert beam radiation from 'sun-normal' to 'horizontal-normal' orientation 
      by multiplying by the cosine of the zenith angle; zenith angle is measured
      from true vertical (0 degrees) to true horizontal (90 degrees).

4.  Multiply the direct beam radiation by a horizon mask made up of ones (pixels
      on which the direct beam is shining) and zeros (pixels which are 
      topographically shadowed, on which the direct beam is not shining).

5.  Multiply the diffuse radiation by the sky view factor, which for each pixel
      is the percentage of the sky which is visible.

6.  Add these direct beam and diffuse radiation amounts together to get the 
      total clear sky radiation treating each pixel as a flat horizontal 
      surface.  This coverage is exactly what TOPORAD would produce in a clear 
      sky situation, except the slope and aspect of the pixels is not 
      considered.  This is wanted at this point because we going to use observed
      insolation values to calibrate optical depth and attenuation variables,
      and insolation field measurements are taken with horizontal sensors.

7.  Repeat steps 1-6 with different values for the optical depth (a variable 
      which greaty affects ELEVRAD's output).  Compare the resulting curves to 
      UPLMET's observed clear sky envelope to determine which optical depth
      value gives the best fit.  An optical depth of 0.42 was found to be the 
      best.

8.  For each month, divide the average UPLMET insolation value by ELEVRAD's
      clear sky value on a horizontal surface (at the UPLMET pixel) to get that 
      month's 'cloud factor'.  (Resulting cloud factors range from 0.83 in 
      August to 0.51 in January).

9.  Multiply ELEVRAD's clear sky radiation on a horizontal surface by the 
      cloud factor for each month to get cloud-corrected ELEVRAD radiation.

10. Compute extra-terrestrial radiation on the region considering each pixel
      as a flat horizontal surface. This is simply the amount of insolation
      in the absence of atmospheric attenuation, or potential radiation.

11. Compute the 'transmission coefficient' by dividing the cloud-corrected
      ELEVRAD radiation by the extra-terrestrial radiation (tt).

12. Using Bristow and Campbell's equation, determine the diffuse fraction of
      ELEVRAD's cloud-corrected radiation (equation hinges upon tt value).

13. Multiply the diffuse fraction by ELEVRAD's cloud-corrected radiation to
      get the actual amount of diffuse radiation.

14. Subtract this diffuse radiation from the total ELEVRAD cloud-corrected
      radiation to get the amount of direct beam radiation.

15. Convert this direct beam radiation from 'horizontal-normal' orientation
      back to 'sun-normal' orientation by dividing by the cosine of the zenith
      angle; this is what TOPORAD expects as direct beam input.

16. Run TOPORAD using these direct beam and diffuse radiation amounts, and 
      add up all of the 20-minute intervals throughout each day to get a daily
      total. The result is a set of topographically correct radiation coverages,
      with values in MJ.m^-2.day^-1.

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ISSUES:

When the sun is below the horizon, no calculations are performed, because the 
program assumes that there is no solar radiation hitting any part of the 
region.  In fact, there is diffuse radiation before sunrise and after sunset.
However, the amount of diffuse radiation from the sky at such times is minimal
compared to when the sun is above the horizon, so it can be negated.

In steps 1-6 (running ELEVRAD to get clear sky radiation on a flat, horizontal
surface), terrain configuration factor and albedo (two factors which TOPORAD
uses to compute topographically-correct radiation images) are ignored.  This 
is admissable because neither of these two factors plays a significant role in
determining the insolation regime, especially using a low albedo of 0.1, which 
is approximately that of an evergreen forest.


toporad_procedure.txt     11/01