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C 2. Annex 1 to Diffuse Geometry WG Report: The effect of diffusometer shading geometry

Prepared by G. Major, Z. Nagy and M. Putsay for the BSRN Meeting, May 1-5, 2000, Melbourne

C 2.1 Introduction

The diffuse radiation is the solar radiation received by the horizontal surface from the above 2p solid

angle except the solid angle of solar disk. To exclude the solar disk from the whole sky some kind

of shading device should be used. Several years ago, when computer controlled solar trackers were

not available, shading rings were used. These rings covered much larger part (varying with the solar

declination) of the sky than the solar disk, therefore so called “ring correction” had to be applied to

the measured diffuse radiation values. The modern solar trackers keep both the pyrheliometers and

the shading disks or shading spheres of diffusometers in the proper position, that is they move altogether

with the apparent m ovement of the Sun. However the shading devices cover somewhat larger solid

angle than that of the solar disk (but much less than the shading rings), moreover this extra coverage

might be different for different diffusometers, this way the scattered solar radiation coming from the

covered (circumsolar) part of the sky might also be different.

The purpose of this work is to give estimation of the difference of diffuse radiation values

measured by diffusometers of different geometry.

For this end geometrical data of some diffusometers have been collected. The number of involved

diffusometers is not large, but it is believed that their range covers that of the most frequently used

ones.

The irradiance arising from the circumsolar radiation can be calculated knowing the geometry of the

instrument and the distribution of circumsolar radiance (sky function). Since the measurement of the

latter one is not a common practice, therefore measurements were made in Budapest by using 3 shading

sphere of different size, to obtain a 18 months time series that contains large range of possible natural

environmental conditions.

Geometrical data of diffusometers

The data were provided in 1997 and 1998 by the colleagues operating the instruments in the countries

named in Table C 2.1 and by John Hickey of Eppley Co. The used pyranometers are: KippZonen (10

mm), Eppley (5.64 mm) and Star (16 mm). Larger variability is seen in the case of shaders and arm

lengths. The shaded solid angle is characterized by the slope and limit angles (the (half)opening angle

is their mean value) calculated for the “vertical position”, that is when the Sun would be in the zenith.

Their slope angles are larger than that of most pyrheliometers (Major 1995), this is due to that, that

the shaders should be larger than the (outer) glass dome of the pyranometers used in the diffusometer

set. On the other side, the long arm of the disffusometers results less limit angles than that of modern

pyrheliometers. In most cases it is seen that the dimension of diffusometers were determined so, that

the (half)opening angle would fit to that of one of the standard pyrheliometers. The two experimental

shading spheres used in the Hungarian diffusometers have been designed so that they would cover

the expected range of geometry of BSRN station diffusometers. The same size shading sphere and

shading disk have almost the same effect (Major 1994).

C 2.2 The calculation method

To calculate the irradiance measured by a diffusometer from the circumsolar belt, we have to know

the circumsolar sky function and the penumbra function of the instrument (Pastiels method). The penumbra

function describes the fraction of the sensing surface seen from a given direction. For the directions

that decline less from the optical axis (pointed to the solar center) than the slope angle, the penumbra

function is equal to 1 (the whole sensor is seen). For the directions that decline more from the optical

axis than the limit angle, the penumbra function is equal to 0 (no part of the sensor is seen). The

circumsolar sky function describes the distribution of radiance around the Sun (up to some degrees

from the solar center).

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