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C 3. Annex 2 to the Diffuse Geometry WG Report: Optimization of Diffusometers to Pyrheliometers
Prepared by G. Major and M. Putsay,Hungarian Meteorological Service
C 3.1 Introduction
The instrument most commonly used to measure global radiation is the pyranometer. The sensitivity
of pyranometers depend on several factors. To avoid several accuracy decreasing effects the following
suggestion arises: measure the global radiation as sum of the diffuse radiation and of the vertical
component of the direct radiation. The measured direct radiation always includes and the measured
diffuse radiation always excludes some circumsolar radiation. To minimize the bias in the global radiation
values, these two kind of circumsolar radiation should be as close to each other as is possible. The
full equivalence can not be achieved (Major 1992). In this work geometrical parameters of diffusometers
are derived to fit them to some selected pyrheliometers.
C 3.2 Basic considerations
The direct + diffuse method of measuring of global radiation is based on the following equation:
G = I sin(h) + D (1)
where I = the direct radiation coming from the solar disc,
h = the solar elevation angle,
D = the diffuse radiation, defined by (1).
The pyrheliometer measured direct radiation:
p dir
I = I + C
(2)
dir
whereC = the circumsolar radiation received by the pyrheliometric sensor.
The diffusometer measured diffuse radiation:
d dif
D = G – (I + C ) sin(h) (3)
dif
where C = the circumsolar radiation excluded by the diffusometer.
Our purpose is the minimization of the following difference:
d p dif dir
DE = G – (D + I sin(h)) = sin(h) (C – C ) (4)
Taking into account the formulae of calculating the circumsolar radiation (Major 1994, p. 34), the difference
is:
dif pyr
DE = sin(h) B I L(z) sin(2z) (F – F ) dz, (5)
where z = the angle measured from the solar center,
the I extends from the smaller of the slope angles to the larger of the
limit angles of the two instruments,
L(z) = the radiance distribution along the circumsolar sky (sky function),
F(z) = the penumbra function for the diffusometer and pyrheliometer respectively.
p yr d if
For any pyrheliometer F is a definite function of its geometry, while in the case of diffusometers F
is a function of the geometry and of the solar elevation as well. L(z) sin(2z) plays the role of a weighting
function in integrating the difference of the penumbra functions. It weights the “circumstances” of the
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