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The shade ring correction for diffuse irradiance measurements
Solar Energy Voi. 26, pp. 361-363, 1981 Printed in Great Britain. All rights reserved
0038--092X/81/040361-03502.00/0 Copyright © 1981 Pergamon Press Ltd.
TECHNICAL NOTE The shade ring correction for diffuse irradiance measurements H. E. PAINTER Meteorological Office, Beaufort Park, Easthampstead, Wokingham Berkshire RGI1 3DN, England (Received 30 September 1980; accepted I1 December 1980)
l. INTRODUCTION A widely accepted technique for making measurements of the diffuse solar irradiance on a horizontal surface with a pyranometer is to occult the sun by means of a shade ring mounted on an axis parallel to the polar axis. Because the ring screens a considerable portion of the sky these measurements require corrections which are generally derived from theoretical calculations based on certain assumptions, the most important of which is that the radiance of the sky is isotropically distributed. This assumption is often far from true and leads to considerable errors in the resulting corrected irradiances. A number of experiments have been made to investigate these errors by comparing simultaneous measurements of diffuse irrndiauce by using both a ring and a disc to occult the sun. From a series of comparisons in South Africa Drummond[I] found for a particular site and size of shade ring that for mainly clear skies the measurements with a shade ring needed on average a further increase of 7 per cent, after applying the isotropic sky correction, in order to get agreement with his measurements made with a disc. For overcast skies the extra correction was about 3 per cent; for partly cloudy skies he interpolated between these values and suggested a correction of 5 per cent. Schflepp [2] for a site in Central Mrica and for a different size ring found, by the same method, that an additional correction of 6-.9 per cent was required for clear skies and no additional corrections for overcase skies. More recently Rossi[3] in Finland has obtained experimentally an overall correction (i.e. inclusive of the isotropie correction) for clear sky and overcast conditions and interpolated between these two conditions to obtain the correction for partly cloudy conditions. The United Kingdom Meteorological Office applies only the isotropic correction to routine diffuse irrndiance measurements obtained with a ring. To investigate the deficiencies of this procedure an experiment was mounted to make simultaneous measurements of the diffuse irrndiance using both a ring and a disc. The experiments previously mentioned used discs manually controlled, in our case we used a disc mounted on a very thin arm which could be driven by a small motor. By this means comparisons could be made over a larger range of sky conditions even when the shadow of the disc was not visible, since all that was required was an occasional observation to see that the shadow of the disc was central over the pyranometer dome. Comparisons were therefore possible during partly cloudy conditions. This was considered important as it seemed likely that under certain cloud conditions the anisotropy of the sky would be considerably greater than in clear sky conditions and so giving rise to bigger errors in shade ring diffuse measurements. 2. INSTRUMENTATION The shade ring mounting consisted of the standard Meteorological Office model with a ring 51 cm in diameter and 5.1 cm in width. The occulting disc was 10era in diameter and at a distance of 61 cm from the centre of the receiving surface of the pyranometer. Calculations showed that the arm supporting the disc cut off less than 0.1 per cent of the diffuse irradiance, assuming an isotropic sky. A third pyranometer was mounted to measure the global radiation so that simultaneous irradiance
measurements were made of the global (G), the diffuse by using a ring (R) and the diffuse by using a disc (D). The values of R are the measured values with the theoretical isotropic correction added and the differences hereafter mentioned are the extra corrections needed to equate R to D as a consequence of the anisotropy of the sky. The pyranometers used were the Kipp CM2 model and they were mounted with the line of their thermojunctions directed east and west. All comparisons are for simultaneous irradiations over a period of i hr. Data were not used if the solar elevation was below 10° within the hourly period. This series of comparisons was made at Easthampstead near Brackneil (5102YN; 00"47'W; height above m.s.I. 73 m) from February 1977 to February 1978. 3. ANALYSISOF TIlE DATA The data were analysed to show the difference between the two diffuse measurements D and R and hence the correction necessary to equate the ring measurement to the disc measuremerit for various states of the sky as given by the ratio of RIG. As it was apparent that there was a marked seasonal variation in the magnitude of these corrections the analysis was extended to include their relation to solar declination. The results are given in Table 1; in addition to the mean value of the correction the extreme values are also given for each category. The small negative values arise from small inaccuracies in the performances of the sensors, particularly when taking differences of small quantities. As might be expected, there is a considerable scatter of individual values about the means and this arises from the variety of sky conditions for a given value of R/G. The data were also examined to see whether there was a relationship between D/R and the solar elevation. For this purpose the data when the solar declination was greater than 15° (i.e. summer) and the ratio of R/G less than 0.4 (i.e. the sky was generally clear) were analysed relative to solar elevation; the results are given in Table 2. From these figures there appears to be a relationship between the additional shade ring correction and the solar elevation but because of the small number of observations at low solar elevations this matter is not conclusive; any such relationship is certainly much smaller than the seasonal one shown in Table 1. Because of the limited amount of data it was not possible to further analyse the diffuse measurements with respect to different cloud types. The values in Table 1 have therefore been put into a form suitable for applying mean corrections to R. For each range of solar declination the mean values can be represented by a simple curve consisting of two straight lines; for small values of R/G a line with a constant value o f / ~ R and for larger values of RIG a line in which D/R varies with R/G and indicates zero correction to R when the sky is completely overcast, a fact confirmed by the observations. It was found that the angles of sloping lines could be given a common value for all ranges of solar declination. The lines are given by: D/R = A for O.l < RIG < x
and D/R = 1.215- 0.215 R/G for RIG >1x 361
-15.0 o
-15.0 ° to -5.1 °
- 5 . 0 ° I;o 4.9 °
5.0 ° to 14.9 °
>/ 15.O°
SOLAR DBCLTUATI011
0.9
MI=4---
6.5
]liuilmm
8
linlmm 8
15.3 7.4
No of o1~
11.1
13.8 7.4
14.3 16.8 11..3 12
10.8
11.7 13.3 9.8 10
11
6.8
1.%.9
8.8
16
14.7 6.1
11.4
11.7 20.3 6.3 21
4
6.0
15.7
10.7
12
12
8.0
6.1
31
1.5
12.2
3.3
Ihan
]lean ](axim~ E1niaa= No o f olm
7
9.2 11.2
3
.39
5-3
.3-
2.1
8.2
8.3,
5.8
20
9.7
]l,,:,r4mm=
No o f o1~
6.2
3.9
.29
0.9
.2-
9.2
lie--
No o f o1~
l(:i=im~
Me--
12
9.1
](azimm
]1o o f oi..
4.5
lle~
.1 - .19
9.7
12
2.5
9.7
5-5
26
1.2
7.0
4-5
.49
5
15.5 9.2
12.3
9
8.5 10.5 6.4
9
3.1
16.6
.4-
.59
12
13.1 2.9
7.7
9.3 20.8 3.4 19
10
2.3
16...3
10.5
16
2. 3
12.2
6.0
23
2.2
7.6
4-5
.5-
.69
7
9.0 6.9
8.2
7.6 18.2 4.4 14
9
2.5
11.2
7.0
7
5• 6
13.2
9.0
17
1.8
9.3
4.6
.6-
.79
6
13.1 4.4
7.4
5.9 17.6 2.1 17
12
2.8
11.1
4.9
4
2. 6
9.1
5.3
9
%6
8.0
4.5
.7-
RATIO OF DIFFJSE TO (~.OBAL IRRADIATION (R/G) .89
8
6.5 1.7
4.4
3.9 11.3 1.3 12
9
2.8
11.3
5.1
2
1.8
5.8
3.8
21
-0.4
4.0
2.5
.8-
Table I. Mean and extreme values of the additional shade ring correction (per cent) for different ranges of (i) the ratio of the diffuse to the global irradiation (R/G) and (ii) the solar declination
1.o
16
3.7 -1.7
0.2
1.3 14.2 -1.8 28
9
-1.1
4.4
1.9
18
-0.6
3.1
0.5
24
-0.6
3.3
0.9
.9-
Z o R
g
Technical Note Table 2. Mean values of the addit~nal shade ring correction (per cent) for clear skis for different ranges of solar elevat~n Sol&r elevation
Mean correction %
No. of observations
~-- 20°
2. 5
2
20° to 30 °
2.7
5
30 ° to 40 °
4.3
14
40 o to 50 °
4.6
12
5.4
30
~5o °
where A and x have the values: Solar declination
x
~>15.0~ 0.79 -5.00--4.90 0.71 -5.~5.0 ° 0.55 <-5.0 ~ 0.46
A 1.046 1.063 1.097 I.I16
The values of A give the best fitting line through the relevant points weighted according to the number of observations. No meaningful distinction could be made between the last two ranges of solar declination in Table i so they are combined. 4. DISCUSSION
The results of this series of comparisons are strictly only applicable to the conditions of the experiment; that is to say for a
SE Vol.26. No.
363
CM2 model Kipp pyranometer with a ring with the dimensions given above, at the specific latitude and for the general prevailing state of the sky and atmospheric turbidity. It is possible that another pyranometer with a different cosine response would yield different results and that differences attributed above to anisotropy of the sky may actually include an effect due to the cosine response of the pyranometer. Despite the different locations and sizes of shade rings the results of this comparison are generally in broad agreement with the findings of Drummond[l] who found his additional shade ring corrections were a function of solar declination but not of solar elevation. If the corrections given above are applied to suitable measurements they are only applicable to long term averages since as shown in Table I individual hourly irradiations can still be 10 per cent in error after making these corrections. If more accurate measurements of diffuse irradiances are required then these must be made by either using a disc or by deduction from measurements of global and normal incidence irradiances. It is generally considered that a disc tracking the solar motion is difficult to maintain continuously in all weathers and therefore more thought should be given to the other method. Whichever of these methods is used an automated mechanism is required to track the disc or pyrheliometer with a very high degree of precision and reliability under all weather conditions.
REFERENCES 1. A. J. Drummond, On the measurement of sky radiation. Arch. MeteoroL Geophys. Bioklimatol. BT, 413--435 (1956), 2. W. Schiiepp, Enregistrement S~par~ des Composantes du rayonnement solaire. Bull. Serv. Met~orol., Congo Beige 8, 11-20 (1952). 3. V. Rossi, The shadowing-ring correction for sky radiation pyranometers. Finn. Meteorol. Inst. Contrib. g2, 3-11 (1975).
0038--092X/81/040361-03502.00/0 Copyright © 1981 Pergamon Press Ltd.
TECHNICAL NOTE The shade ring correction for diffuse irradiance measurements H. E. PAINTER Meteorological Office, Beaufort Park, Easthampstead, Wokingham Berkshire RGI1 3DN, England (Received 30 September 1980; accepted I1 December 1980)
l. INTRODUCTION A widely accepted technique for making measurements of the diffuse solar irradiance on a horizontal surface with a pyranometer is to occult the sun by means of a shade ring mounted on an axis parallel to the polar axis. Because the ring screens a considerable portion of the sky these measurements require corrections which are generally derived from theoretical calculations based on certain assumptions, the most important of which is that the radiance of the sky is isotropically distributed. This assumption is often far from true and leads to considerable errors in the resulting corrected irradiances. A number of experiments have been made to investigate these errors by comparing simultaneous measurements of diffuse irrndiauce by using both a ring and a disc to occult the sun. From a series of comparisons in South Africa Drummond[I] found for a particular site and size of shade ring that for mainly clear skies the measurements with a shade ring needed on average a further increase of 7 per cent, after applying the isotropic sky correction, in order to get agreement with his measurements made with a disc. For overcast skies the extra correction was about 3 per cent; for partly cloudy skies he interpolated between these values and suggested a correction of 5 per cent. Schflepp [2] for a site in Central Mrica and for a different size ring found, by the same method, that an additional correction of 6-.9 per cent was required for clear skies and no additional corrections for overcase skies. More recently Rossi[3] in Finland has obtained experimentally an overall correction (i.e. inclusive of the isotropie correction) for clear sky and overcast conditions and interpolated between these two conditions to obtain the correction for partly cloudy conditions. The United Kingdom Meteorological Office applies only the isotropic correction to routine diffuse irrndiance measurements obtained with a ring. To investigate the deficiencies of this procedure an experiment was mounted to make simultaneous measurements of the diffuse irrndiance using both a ring and a disc. The experiments previously mentioned used discs manually controlled, in our case we used a disc mounted on a very thin arm which could be driven by a small motor. By this means comparisons could be made over a larger range of sky conditions even when the shadow of the disc was not visible, since all that was required was an occasional observation to see that the shadow of the disc was central over the pyranometer dome. Comparisons were therefore possible during partly cloudy conditions. This was considered important as it seemed likely that under certain cloud conditions the anisotropy of the sky would be considerably greater than in clear sky conditions and so giving rise to bigger errors in shade ring diffuse measurements. 2. INSTRUMENTATION The shade ring mounting consisted of the standard Meteorological Office model with a ring 51 cm in diameter and 5.1 cm in width. The occulting disc was 10era in diameter and at a distance of 61 cm from the centre of the receiving surface of the pyranometer. Calculations showed that the arm supporting the disc cut off less than 0.1 per cent of the diffuse irradiance, assuming an isotropic sky. A third pyranometer was mounted to measure the global radiation so that simultaneous irradiance
measurements were made of the global (G), the diffuse by using a ring (R) and the diffuse by using a disc (D). The values of R are the measured values with the theoretical isotropic correction added and the differences hereafter mentioned are the extra corrections needed to equate R to D as a consequence of the anisotropy of the sky. The pyranometers used were the Kipp CM2 model and they were mounted with the line of their thermojunctions directed east and west. All comparisons are for simultaneous irradiations over a period of i hr. Data were not used if the solar elevation was below 10° within the hourly period. This series of comparisons was made at Easthampstead near Brackneil (5102YN; 00"47'W; height above m.s.I. 73 m) from February 1977 to February 1978. 3. ANALYSISOF TIlE DATA The data were analysed to show the difference between the two diffuse measurements D and R and hence the correction necessary to equate the ring measurement to the disc measuremerit for various states of the sky as given by the ratio of RIG. As it was apparent that there was a marked seasonal variation in the magnitude of these corrections the analysis was extended to include their relation to solar declination. The results are given in Table 1; in addition to the mean value of the correction the extreme values are also given for each category. The small negative values arise from small inaccuracies in the performances of the sensors, particularly when taking differences of small quantities. As might be expected, there is a considerable scatter of individual values about the means and this arises from the variety of sky conditions for a given value of R/G. The data were also examined to see whether there was a relationship between D/R and the solar elevation. For this purpose the data when the solar declination was greater than 15° (i.e. summer) and the ratio of R/G less than 0.4 (i.e. the sky was generally clear) were analysed relative to solar elevation; the results are given in Table 2. From these figures there appears to be a relationship between the additional shade ring correction and the solar elevation but because of the small number of observations at low solar elevations this matter is not conclusive; any such relationship is certainly much smaller than the seasonal one shown in Table 1. Because of the limited amount of data it was not possible to further analyse the diffuse measurements with respect to different cloud types. The values in Table 1 have therefore been put into a form suitable for applying mean corrections to R. For each range of solar declination the mean values can be represented by a simple curve consisting of two straight lines; for small values of R/G a line with a constant value o f / ~ R and for larger values of RIG a line in which D/R varies with R/G and indicates zero correction to R when the sky is completely overcast, a fact confirmed by the observations. It was found that the angles of sloping lines could be given a common value for all ranges of solar declination. The lines are given by: D/R = A for O.l < RIG < x
and D/R = 1.215- 0.215 R/G for RIG >1x 361
-15.0 o
-15.0 ° to -5.1 °
- 5 . 0 ° I;o 4.9 °
5.0 ° to 14.9 °
>/ 15.O°
SOLAR DBCLTUATI011
0.9
MI=4---
6.5
]liuilmm
8
linlmm 8
15.3 7.4
No of o1~
11.1
13.8 7.4
14.3 16.8 11..3 12
10.8
11.7 13.3 9.8 10
11
6.8
1.%.9
8.8
16
14.7 6.1
11.4
11.7 20.3 6.3 21
4
6.0
15.7
10.7
12
12
8.0
6.1
31
1.5
12.2
3.3
Ihan
]lean ](axim~ E1niaa= No o f olm
7
9.2 11.2
3
.39
5-3
.3-
2.1
8.2
8.3,
5.8
20
9.7
]l,,:,r4mm=
No o f o1~
6.2
3.9
.29
0.9
.2-
9.2
lie--
No o f o1~
l(:i=im~
Me--
12
9.1
](azimm
]1o o f oi..
4.5
lle~
.1 - .19
9.7
12
2.5
9.7
5-5
26
1.2
7.0
4-5
.49
5
15.5 9.2
12.3
9
8.5 10.5 6.4
9
3.1
16.6
.4-
.59
12
13.1 2.9
7.7
9.3 20.8 3.4 19
10
2.3
16...3
10.5
16
2. 3
12.2
6.0
23
2.2
7.6
4-5
.5-
.69
7
9.0 6.9
8.2
7.6 18.2 4.4 14
9
2.5
11.2
7.0
7
5• 6
13.2
9.0
17
1.8
9.3
4.6
.6-
.79
6
13.1 4.4
7.4
5.9 17.6 2.1 17
12
2.8
11.1
4.9
4
2. 6
9.1
5.3
9
%6
8.0
4.5
.7-
RATIO OF DIFFJSE TO (~.OBAL IRRADIATION (R/G) .89
8
6.5 1.7
4.4
3.9 11.3 1.3 12
9
2.8
11.3
5.1
2
1.8
5.8
3.8
21
-0.4
4.0
2.5
.8-
Table I. Mean and extreme values of the additional shade ring correction (per cent) for different ranges of (i) the ratio of the diffuse to the global irradiation (R/G) and (ii) the solar declination
1.o
16
3.7 -1.7
0.2
1.3 14.2 -1.8 28
9
-1.1
4.4
1.9
18
-0.6
3.1
0.5
24
-0.6
3.3
0.9
.9-
Z o R
g
Technical Note Table 2. Mean values of the addit~nal shade ring correction (per cent) for clear skis for different ranges of solar elevat~n Sol&r elevation
Mean correction %
No. of observations
~-- 20°
2. 5
2
20° to 30 °
2.7
5
30 ° to 40 °
4.3
14
40 o to 50 °
4.6
12
5.4
30
~5o °
where A and x have the values: Solar declination
x
~>15.0~ 0.79 -5.00--4.90 0.71 -5.~5.0 ° 0.55 <-5.0 ~ 0.46
A 1.046 1.063 1.097 I.I16
The values of A give the best fitting line through the relevant points weighted according to the number of observations. No meaningful distinction could be made between the last two ranges of solar declination in Table i so they are combined. 4. DISCUSSION
The results of this series of comparisons are strictly only applicable to the conditions of the experiment; that is to say for a
SE Vol.26. No.
363
CM2 model Kipp pyranometer with a ring with the dimensions given above, at the specific latitude and for the general prevailing state of the sky and atmospheric turbidity. It is possible that another pyranometer with a different cosine response would yield different results and that differences attributed above to anisotropy of the sky may actually include an effect due to the cosine response of the pyranometer. Despite the different locations and sizes of shade rings the results of this comparison are generally in broad agreement with the findings of Drummond[l] who found his additional shade ring corrections were a function of solar declination but not of solar elevation. If the corrections given above are applied to suitable measurements they are only applicable to long term averages since as shown in Table I individual hourly irradiations can still be 10 per cent in error after making these corrections. If more accurate measurements of diffuse irradiances are required then these must be made by either using a disc or by deduction from measurements of global and normal incidence irradiances. It is generally considered that a disc tracking the solar motion is difficult to maintain continuously in all weathers and therefore more thought should be given to the other method. Whichever of these methods is used an automated mechanism is required to track the disc or pyrheliometer with a very high degree of precision and reliability under all weather conditions.
REFERENCES 1. A. J. Drummond, On the measurement of sky radiation. Arch. MeteoroL Geophys. Bioklimatol. BT, 413--435 (1956), 2. W. Schiiepp, Enregistrement S~par~ des Composantes du rayonnement solaire. Bull. Serv. Met~orol., Congo Beige 8, 11-20 (1952). 3. V. Rossi, The shadowing-ring correction for sky radiation pyranometers. Finn. Meteorol. Inst. Contrib. g2, 3-11 (1975).