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measurement, namely the atmospheric conditions (scattering) and the solar elevation. For a given
pyrheliometer and given circumstances several such diffusometers could be composed that would
result in zero DE. For a given pyrheliom eter + diffusometer system, DE varies with varying circumstances.
To obtain small DE values in each condition, the two penumbra functions should be as close to each
other as possible. The construction of a diffusometer that (together with the pyrheliometer) gives yearly
zero-bias global radiation, requires that the yearly combined probability distribution of:
1. solar elevation,
2. turbidity (scattering),
3. diffuse radiation,
4. sunshine
be taken into account when minimizing the standard deviation of DE around its zero mean.
Examples
The above considerations will be applied for:
1. a very wide range of sky functions,
2. 20, 45 and 60 degrees of solar elevation,
3. geometrically different pyrheliometers,
4. pyranometers used in radiation stations
to find the diameter of shading disk and the length of arm that diffusometers require for optimal
performance.
C 3.2.1 Sky functions
The sky functions (only cloudless atmosphere is considered) depend on:
1. the type and amount of atmospheric aerosol,
2. the humidity (size distribution of aerosol and appearance of haze particles),
3. the solar elevation angle (optical path length).
For the least scattered radiation, a mountain aerosol model was used with an optical depth of 0.05
The middle conditions are represented by continental aerosol with an optical depth of 0.23. Also for
these conditions a measured sky function is used. It is a mean of circumsolar measurements made
in Boardman (USA) at 45 degrees solar elevation. This function is quite close to the one calculated
for rural aerosol plus haze particles with an optical depth of 0.02. The radiation flux with the greatest
scattering is represented by a summertime desert aerosol of 1.0 optical depth. For desert conditions
there have been reports of optical depth as high as 4, but even in the case of 1 optical depth, direct
radiation hardly could be measured. Table C 3.1 provides the direct beam irradiance for each of the
model and solar elevation combinations.
The calculation of the sky functions has been made by M. Putsay.
Solar elevation
(deg)
Mountain
aerosol
Continental
aerosol
Summer
desert aerosol
Measured
60 1041 863 343
45 983 785 253 770
20 727 470 45
Table C 3.1. Direct radiation (W m ) for the 10 sky functions.
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