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Calculating diffuse radiation values Diffuse irradiance refers to all the solar radiation coming from the sky except for solar radiation coming directly from the sun and the circumsolar irradiance within approximately three degrees of the sun.
Measurement of diffuse radiation is difficult
because one needs to shade the pyranometer from the direct normal and the circumsolar
irradiance. Until the development of high quality automatic trackers, diffuse
measurements were made with shadowbands that not only shaded the instrument from
the sun but also shaded other parts of the sky. A fair estimate of the diffuse
irradiance can be obtained by subtracting the direct normal beam radiation projected
onto a horizontal surface from the global irradiance.
The product of the direct normal beam irradiance
times the cosine of the zenith angle yields the amount of solar radiation striking the
earth coming from the sun. If the global pyranometer had a perfect cosine response, the
difference between the projected beam irradiance and the global irradiance would be
equal to the diffuse irradiance. This is true instantaneously, but over longer time
intervals this becomes an approximation because the beam radiation changes in a
systematic way over the day. We use a beam weighting function to average the cosine
of the zenith angle over an hour. For more details see Frank Vignola and D. K. McDaniels,
"Transformation of Direct Solar Radiation to Tilted Surfaces", Proceedings of
the American Section of the International Solar Energy Society, Anaheim,
California, p. 651, June 1984.
Unfortunately pyranometers do not have a perfect
cosine response and subtracting the beam radiation from the global does lead to
systematic errors in the calculated diffuse values. This is shown in the figure below.
The data shown in the figure were taken on a clear day. The diffuse was measured with
an Eppley PSP and a shade ball. The calculated diffuse data are from five minute global
and beam data measured with an Eppley PSP and NIP, respectively. In September in
Eugene, the cosine response of the PSP is nearly correct during the middle of the day
but underestimates the solar radiation during the morning and evening hours. This is
typical of the cosine error associated with a PSP. Another source of error is that the thermopile of the PSP radiates to the sky and this reduces the amount of solar radiation counted by 10 to 20 watts per square meter. For global values, this difference is relatively small, but for diffuse values this can represent a 20° error. We adjust for part of this re-radiation by the sensor by adding the average nighttime values of this re-radiation to the daytime values. This works for the early morning and late evening hours fairly well, but for the middle of the day, the diffuse values measured with an Eppley PSP still have systematic values that are approximately 10 watts per square meter too low.
In August, 2000, we began measuring the diffuse
radiation with a Schenk star type pyranometer. A star type pyranometer alternates
black and white wedges and the incident solar radiation is the difference between
the temperatures of the white and black wedges. Since the thermal re-radiation is
about equal for the different wedges, the effect of re-radiation is nil. This makes
star type pyranometers ideal for the measurement of diffuse radiation. © 2000, UO Solar Radiation Monitoring Laboratory. Last
revised: December 11, 2000.
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