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D 2. Effect of Clouds on the Pyrheliometric Measurements
Prepared by G. Major for the BSRN Workshop held in Boulder, Co, 12-16 Aug. 1996
D 2.1 Introduction
In the last BSRN Meeting (Davos, October 1995) the question aroused: how large could be the effect
of variable clouds around the Sun on the pyrheliometric measurements? In this report some results
are presented.
The basic difficulty of making model calculations is the lack of proper radiance distributions around
the Sun for cloudy situations. (For cloudless sky there are radiance distributions for several aerosol
types and optical thickness values from several authors.) In this report "cloudy situation" mean that
there is cloud near to the Sun (in the ring limited by the circles of 1 and 4 degrees from the solar centre)
but not in between the Sun and the measuring pyrheliometer, that is the effect of transmission of cloud
layers is not regarded here. High geometrical resolution radiance measurements were made from
the solar centre up to 3 degrees by the Lawrence Berkeley Laboratory. The data are available from
the National Renewable Energy Laboratory (NREL). They cover all weather situation at one dozen
stations in the U.S.A (Noring et al., 1991). A sample of these data has been involved into this work.
Oversimplified assumptions have been used to derive the radiance distributions applied in calculating
of the effect of clouds.
D 2.2 The geometry
The base height of our rectangular model cloud is 2 km, its geometrical thickness is 0.5 km, optical
thickness is 25, it is 1 km wide and its length is perpendicular to the solar vertical plane, the solar elevation
angle is 45 degrees. The scene is irradiated by the direct and circumsolar beam, the surface irradiance
is seen in Figure D 2.1 (personal communication from T. Varnai, McGill University). The edges of
the cloud shadow are not sharp, since the left lower and right upper edges of the cloud scatter the
solar beam. In this geometrical situation (cloud below or above the Sun) side reflectance into the
pyrheliometer is not possible, the cloud affects the pyrheliometric measurement by scattered radiation
only (edge scattering).
In the other special geometrical situation the cloud length is parallel with the solar vertical plane, that
is the cloud is in the right or left side of the Sun. Now the cloud affects the pyrheliometric measurement
by side reflection only.
D 2.2.1 Cloud edge scattering
For the example calculation, in Figure. D 2.2, the model cloud is above the Sun. In the cloud the
geometrical path length of the radiation beam falling into the pyrheliometer:
The meaning of the symbols is seen in Figure D 2.2.
Taking into account that the optical depth of the cloud is 25, the optical path length of the beam in the
cloud:
It can be supposed that the radiance along the cloud as seen from the pyrheliometer
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