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Annex D Pyrheliometers and Pointing
D 1. On the Pointing Error of Pyrheliometers
Prepared by G. Major for the BSRN discussion held in Davos, Switzerland, in October of 1995
D 1.1 Introduction
The direct radiation is the solar radiation coming from the solid angle determined by the solar disk.
The pyrheliometers are designed to measure the direct radiation. Their view limiting angles (slope,
opening and limit angle) are larger than the visible radius of the solar disk. This is partly due for the
easier tracking of the Sun: if the limiting angles are larger than the solar disk, it is not necessary to
follow the Sun quite precisely.
How large pointing errors or inaccuracies occur in the everyday practice? Let us take a hand-operated
pyrheliometer. If its adjustments are made once in a minute, its largest mispointing in azimuth angle
would be one quarter of a degree. The deviation from the right position in elevation angle is in the same
order. Regarding the pointing devices of the pyrheliometers, 1 mm deviation of the illuminated spot
from its proper position could be regarded as large mispointing. Depending on the length of the pointing
path, this deviation means about half a degree of pointing error.
The purpose of this document is to present calculated values of the errors in the output of pyrheliometers
caused by pointing uncertainty up to 2 degrees. Two atmospheric conditions are taken into account:
-- mountain aerosol, optical depth: 0.07, solar elevation: 60 degrees, direct radiation: 1000 W m ;
-2
-- continental background aerosol, optical depth: 0.23, solar elevation: 20 degrees, direct radiation:
461 W m .
-2
The calculations have been made for 3 pyrheliometers: the PacRad size cavity instrument (ABS), the
KIPP and NIP pyrheliometers. Their slope angles are: 0.75, 1.0 and 1.78 degrees respectively.
D 1.2 The method of calculation
The calculation is based on the Pastiels` theory (see for example in Major 1994). The irradiance given
by a circular pyrheliometer can be written as:
where = the output of the pyrheliometer,
= the average sensitivity of the receiver,
= the area of the receiver,
= the limit angle of the pyrheliometer,
= the penumbra function of the pyrheliometer,
= the radiance (=sky function)
= the angle between the direction of radiance and the optical axis of the
pyrheliometer.
Circular pyrheliometer means that all the view limiting diaphragms and the receiver are circular in shape,
that is the whole pyrheliometer has a rotational symmetry around its optical axis. In the equation the
same rotational symmetry is supposed for the solar disk and the circumsolar sky.
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