Shading Calculations for the Radiation Instruments at Jabiru

Shading calculations for the radiation instruments at Jabiru

D. M. O’Brien, R. M. Mitchell and Reinout Boers CSIRO Atmospheric Research PMB 1 Aspendale Victoria 3195 Australia 2000-05-24

CSIRO Atmospheric Research Internal Paper 18 Document reference: JAB 002A

1 Background

The radiation instruments to be installed at Jabiru include shaded and unshaded pyranometers, a shaded pyrgeometer, a tracking sun-photometer and an all-sky camera (ASC). The pyranometers and pyrgeometer will be installed by the Australian Bureau of Mete- orology as part of a Baseline Surface Radiation Network (BSRN) station, whereas the sun-photometer and all-sky camera will be installed by CSIRO Atmospheric Research. In order to achieve the high quality of data that is demanded by the radiation community from BSRN stations, the instruments must be sited carefully to avoid shading and to min- imize obscuration of the horizon. This report describes the calculations that were carried out for the installation of the radiation instruments in the meteorological enclosure at Jabiru airport. The BSRN instruments are shown in gure 1, taken at the Australian Bureau of Meteorology site in Darwin. The white box in the foreground contains control, data acquisition and communications equipment. Immediately to the right of the box (with its support obscured by the box) is the shaded pyrgeometer mounted on a sun-tracker that positions the shading disc. To the left of the box is the shaded pyranometer, similarly mounted on a sun-tracker with a shading disc. The next post to the left supports the unshaded pyranometer that measures ‘global’ solar radiation. The remaining instruments in the photograph are not part of the BSRN.

Figure 1: Baseline Surface Radiation Network (BSRN) installation at Darwin airport.

The sun-photometer is shown in gure 2, in this case a photograph of the CAR installation at Alice Springs airport. The optics module, to which the sun and sky collimators are attached, is the ‘shotgun’ like object. It is mounted on a compact sun-tracker. The instrument to be deployed at Jabiru will use solar power, rather than mains power as in the instrument shown. Therefore, the Jabiru installation will have a solar panel mounted on the support post. The selection of the site at Jabiru airport was constrained by several factors:

1. access to power and telephone lines;

2 Figure 2: Sun-photometer installation at Alice Springs airport.

2. proximity to the standard meteorological instruments so that all instruments can be serviced daily by sta from Energy Resources Australia (ERA);

3. a row of trees with height varying between 5 m and 10 m about 30 m to the south of the meteorological enclosure limits the horizon;

4. a car park is located immediately to the west of the meteorological enclosure;

5. the unpaved area to the north-west is used by aircraft to taxi to freight containers near the runway, and therefore is subject to dust stirred up by the aircraft propellers;

6. the runway and surrounding apron to the north is susceptible to dust eddies in the dry season.

These factors led to the decision to locate the radiation instruments to the east of the present meteorological enclosure, shown in the photo of gure 3 and the plan of gure 4. This report determines a conguration for the radiation instruments that either eliminates or minimizes the potential for shading. Particular attention is given to shading of the global radiation pyranometer and the sun-photometer by the masts of the automatic weather station (AWS) and the ERA weather station. In addition, the possibility of shading of the sun-photometer by the small shed in the meteorological enclosure and the BSRN station itself is examined carefully.

Method

Several candidate positions for the BSRN (points A{F) and sun-photometer (points G{I) were considered, as indicated on gure 5. Point X was the approximate position for the BSRN determined during a visit to Jabiru in February 2000 using nomographs of the sun’s position. For each candidate position, the distance and bearing to the AWS mast were measured from the site diagram, and the solar elevation at the azimuth of the AWS was computed for every day of the year. To determine whether shading could occur, the solar

3 elevation was compared with the elevation of the top of the mast, based on the standard height of 10 m for the mast and an instrument height of 1.5 m. This process was repeated for the other (potentially) obscuring objects listed in table 1. The heights of the ERA mast and shed were assumed to be 10 m and 2.5 m respectively, while the BSRN shadow arms were assumed to be 1 m higher than the sun-photometer. The program to compute the solar elevation at a specied azimuth as a function of time was written especially for this task, but was based on the general purpose satellite navigation software developed by O’Brien. For each day of the year, the program uses a bisection strategy to determine the universal time when the sun transits the meridian (local solar noon), and then classies the transit according to whether the sun lies to the north or the south. For northern transits, the solar azimuth decreases from its value at dawn, passes through zero at local solar noon, and becomes increasingly negative throughout the afternoon. For southern transits, the solar azimuth decreases from dawn to a minimum in mid-morning, then increases through 180◦ at local solar noon to a maximum in mid- afternoon, and nally decreases again until sunset. Thus, the sun may transit a given azimuth twice in a day. A bisection algorithm is used to nd the times at which the sun transits the specied azimuth, but the update policy in the algorithm depends on whether the transit of the meridian is to the north or the south at local solar noon.

Figure 3: Meteorological enclosure at the Jabiru airport in April 1999. The masts at the left and right of the photo are the AWS and ERA masts. The small shed referred to in the text is the white structure right of centre.

Results

BSRN The site proposed by the Australian Bureau of Meteorology for the global radiation pyranometer is point A on gure 5. Figure 7 shows the solar elevation in the direction of the AWS mast as a function of time throughout the year. The horizontal line in gure 7 is the elevation of the top of the mast. Shading of the pyranometer occurs for approximately six weeks in the middle of the year. Therefore, position A is unacceptable. Figure 8 shows similar calculations for the ERA mast. In this case the sun only transits the mast for approximately fty days at the beginning and again at the end of the year.

4 In the remaining months, the sun transits to the north of the mast and shadowing is impossible. Even when the sun does pass behind the ERA mast, its elevation is so high that the shadow of the mast will not fall on the global pyranometer. Figures 9, 10 and 11 show that shading eliminates points B, C and E, whereas gures 12 and 13 show that points D and F are acceptable. Of the latter, point F is preferable, because it allows more room for the sun-photometer to the south, and because it has marginally better horizon to the south. As a nal check, gure 14 demonstrates that the global pyranometer located at point F will not be shaded by the ERA mast.

Sun-photometer The sun-photometer has three modes of operation:

1. staring directly at the sun;

2. scanning in the principal plane from 6◦ below the sun to the horizon in the back- scattering hemisphere;

3. scanning the almucantar at the zenith angle of the sun.

Measurements made while staring at the sun determine the total optical thickness of the atmosphere, whereas the sky scans determine the size distribution and scattering properties of aerosol. It is clear that the sun-photometer should be sited so that it is not shaded and so that the sun maintains a 6◦ clearance above surrounding objects. The almucantar scans are performed for solar elevations down to a minimum of 10◦, so it is inevitable that some objects will fall into the eld of view. However, measurements are not taken at equal angular increments on the sky scans, but rather are spaced tightly near the sun (where particle size information is most apparent) and are spaced more widely elsewhere. Thus, the probabilty of obscuration by objects not near the solar azimuth is low, and the impact of obscuration on interpretation of the data may be neglected. The possibility of displacing the sun-photometer to the east or west of the north-south line through the BSRN was considered. The argument in favour was that the principal plane scan conducted at local solar noon would not be obscured. However, this argument was rejected for four reasons:

1. on northern transits by the sun, the solar elevation is high and the sun comfortably clears the BSRN by the 6◦ margin; 2. on southern transits, the sun is high and the BSRN will obscure only measurements near the northern horizon, from which little useful information is expected;

3. if the sun-photometer is oset to either the east or the west, the angular width subtended by the BSRN at the sun-photometer is considerably larger than with the sun-photometer to the south, and therefore the BSRN could obscure more sky scans;

4. with the sun-photometer due south of the BSRN, only the noon principal plane scan when the sun is in the south will be aected, and so identication of these events is straightforward, thereby simplifying analysis of the data.

Figures 15{26 show the solar elevation as a function of time at the azimuths of the AWS mast, ERA mast, shed and BSRN (point F) for each of the positions G, H and I. Of these options, point H represents the best compromise, because it lies to the south of the BSRN, because the elevation of the BSRN is lower than at point G, and yet it maintains

5 a reasonable distance to the line of trees to the south. Although point H is shaded by the ERA mast for two brief periods each year, the likelihood of an optical thickness measurement at the time of the shading is low, so the disadvantage is outweighed by the advantage of extra working space between the sun-photometer and the BSRN instruments.

All-sky camera The position of the all-sky camera is not as critical as the positions of the BSRN and sun-photometer, because the solid angle lled by an object such as the AWS mast is small in comparison with the 2π steradians of the sky. However, the camera is best located to the north of the other instruments to ensure that protrusions from the camera (such as support arms) will not shade the global pyranometer of the BSRN. If the maximum height of any protrusion from the camera above the pyranometer is 1 m, then the solar elevation should exceed 9.46◦ at local solar noon for northern transits of the sun. Figure 22 shows that this is always the case.

Recommendation

The global pyranometer should be located at the point marked F in gure 5. Because the layout of the the BSRN instruments on the concrete slab is as shown in gure 6, the power conduit entry point is 1.75 m to the south of point F. This is the point labelled BSRN and marked by + on the site map (gure 4) provided to the contractor selected to cast the slab and install the power. The sun-photometer and all-sky camera should be located at points H and J on gure 5. The coordinates of these points relative to an origin at the south-western corner of the existing meteorological enclosure are indicated in table 2.

Acknowledgement

The authors thank Ian Grant for pointing out that the second transit of the ERA mast had been missed in the original calculations. We all proted from Ian’s intuition and knowledge of astronomy.

6 Label x y Object Distance Bearing Elevation (m) (m) (m) A 23.0 9.2 AWS 23.99 61.08 19.50 − ◦ ◦ ERA 14.92 134.19◦ 29.67◦ B 25.0 8.0 AWS 26.32 60.90 17.77 − ◦ ◦ C 23.0 11.0 AWS 23.17 64.98 3.83 − ◦ ◦ D 25.0 5.0 AWS 27.90 55.51 16.94 − ◦ ◦ E 27.0 9.2 AWS 27.56 65.11 17.14 − ◦ ◦ F 25.0 7.0 AWS 26.82 59.04 17.58 − ◦ ◦ ERA 11.96 133.31◦ 35.40◦ ASC 6.00 0◦ 9.46◦ G 25.0 3.0 AWS 29.08 52.26 16.29 − ◦ ◦ ERA 9.66 115.77◦ 41.34◦ SHED 11.94 94.80 4.79 − ◦ ◦ BSRN 1.75 0◦ 27.94◦ H 25.0 1.0 AWS 30.35 49.28 15.65 − ◦ ◦ ERA 8.97 104.19◦ 43.46◦ SHED 11.94 85.20 4.79 − ◦ ◦ BSRN 3.75 0◦ 14.93◦ I 23.0 1.0 AWS 28.86 46.68 16.41 − ◦ ◦ ERA 10.92 101.62◦ 37.90◦ SHED 9.95 84.23 5.74 − ◦ ◦ BSRN 5.62 20.85◦ 10.09◦

Table 1: Distances, bearings and elevations of potentially obscuring objects from the test points indicated on gure 5.

Point x y All-sky camera 25.0 13.00 Global pyranometer 25.0 7.00 Shaded pyranometer 25.0 6.50 BSRN conduit entry 25.0 5.50 Shaded pyrgeometer 25.0 4.75 Sun-photometer 25.0 1.00

Table 2: Coordinates of the radiation instruments and BSRN power conduit entry point relative to an origin at the south-western corner of the existing meteorological enclosure.

7 Figure 4: Site layout showing the present meteorological enclosure, the buer zone and the recommended locations of the BSRN, sun-photometer and all-sky camera.

8 Figure 5: Site layout showing the candidate positions for the BSRN (A{F) and sun- photometer (G{I).

9 Figure 6: Layout of the three radiation instruments on the BSRN slab.

10 pppp ppp 90 pppp ppppp ppppp ppppp pppp pppp pppp pppp A pppp pppp pppp pppp pppp pppp pppp pppp pppp pppp pppp pppp 60 pppp ppppp ppppp pppp pppp ppppp ppppp ppppp ε ppppp ppppp ppppp ppppp ppppp ppppp pppp ppppp pppppp ppppp 30 pppppp pppppp pppppp ppppppp pppppppp pppppppp pppppppppppppppppppppppppppppppppppp

0 0 50 100 150 200 250 300 350 400 Day of year

Figure 7: Solar elevation ε as a function of time for the transit of the AWS mast as seen from proposed BSRN position A (distance 23.99 m, bearing 61.08 ). The horizontal − ◦ line at 19.51◦ indicates the elevation of the top of the mast from the height of the global radiation sensor.

pp pp 90 pppppp ppppppp ppppppp ppppppp pppppppp pppppppp pppppppppp pppppppppp ppppppppppppp ppppppppppppppppppppApppppppppppp

0 0 50 100 150 200 250 300 350 400 Day of year

Figure 8: Solar elevation ε as a function of time for the transit of the ERA mast as seen from proposed BSRN position A (distance 14.92 m, bearing 134.19◦). The horizontal line at 29.67◦ indicates the elevation of the top of the mast from the height of the global radiation sensor.

11 ppppp pppp 90 pppp ppppp ppppp ppppp pppp pppp pppp pppp B pppp pppp pppp pppp pppp pppp pppp pppp pppp pppp 60 pppp pppp pppp pppp pppp ppppp ppppp pppp pppp ppppp ε ppppp ppppp ppppp ppppp ppppp ppppp pppp ppppp pppppp ppppp 30 pppppp pppppp pppppp ppppppp pppppppp pppppppp pppppppppppppppppppppppppppppppppppp

0 0 50 100 150 200 250 300 350 400 Day of year

Figure 9: Solar elevation ε as a function of time for the transit of the AWS mast as seen from proposed BSRN position B (distance 26.32 m, bearing 60.90 ). The horizontal line − ◦ at 17.77◦ indicates the elevation of the top of the mast from the height of the global radiation sensor.

pppp pppp 90 pppp pppp pppp pppp pppp pppp pppp pppp C pppp pppp pppp pppp pppp pppp pppp pppp pppp pppp 60 ppp pppp pppp pppp pppp pppp pppp pppp ε pppp pppp pppp pppp pppp pppp pppp pppp ppp pppp 30 pppp pppp ppppp pppp ppppp ppppp ppppp ppppp ppppp ppppp pppppp pppppp ppppppp ppppppp ppppppppppppppppppppppppppppppp 0 0 50 100 150 200 250 300 350 400 Day of year

Figure 10: Solar elevation ε as a function of time for the transit of the AWS mast as seen from proposed BSRN position C (distance 23.17 m, bearing 64.98 ). The horizontal − ◦ line at 20.15◦ indicates the elevation of the top of the mast from the height of the global radiation sensor.

12 p p 90 pppp pppp pppp pppp pppp pppp pppp pppp E pppp pppp pppp pppp pppp pppp pppp pppp ppp pppp 60 pppp pppp pppp pppp pppp pppp pppp pppp pppp pppp ε pppp pppp pppp pppp pppp pppp pppp pppp ppp pppp 30 pppp pppp ppppp pppp ppppp ppppp pppp ppppp ppppp ppppp pppppp pppppp ppppppp ppppppp pppppppppppppppppppppppppppppp 0 0 50 100 150 200 250 300 350 400 Day of year

Figure 11: Solar elevation ε as a function of time for the transit of the AWS mast as seen from proposed BSRN position E (distance 27.56 m, bearing 65.11 ). The horizontal − ◦ line at 17.14◦ indicates the elevation of the top of the mast from the height of the global radiation sensor.

p p 90 ppppp ppppp ppppp ppppp ppppp ppppp ppppp ppppp ppppp ppppp D ppppp ppppp ppppp ppppp ppppp ppppp pppp ppppp ppppp ppppp 60 ppppp ppppp ppppp ppppp ppppp ppppp pppppp pppppp ε pppppp pppppp pppppp pppppp pppppp ppppppp pppppppp ppppppp ppppppppp ppppppppp 30 ppppppppppppppppppppppppppppppppppppppppp

0 0 50 100 150 200 250 300 350 400 Day of year

Figure 12: Solar elevation ε as a function of time for the transit of the AWS mast as seen from proposed BSRN position D (distance 27.90 m, bearing 55.51 ). The horizontal − ◦ line at 16.94◦ indicates the elevation of the top of the mast from the height of the global radiation sensor.

13 ppppp ppppp 90 ppppp ppppp ppppp ppppp ppppp ppppp F pppp ppppp ppppp pppp pppp ppppp ppppp pppp pppp pppp pppp ppppp 60 ppppp pppp pppp ppppp ppppp ppppp ppppp ppppp ε ppppp ppppp ppppp ppppp ppppp ppppp pppppp pppppp pppppp pppppp 30 ppppppp ppppppp pppppppp ppppppppp pppppppppppppppppppppppppppppppppppppp

0 0 50 100 150 200 250 300 350 400 Day of year

Figure 13: Solar elevation ε as a function of time for the transit of the AWS mast as seen from proposed BSRN position F (distance 26.82 m, bearing 59.04 ). The horizontal − ◦ line at 17.58◦ indicates the elevation of the top of the mast from the height of the global radiation sensor.

pp ppp 90 ppppppp pppppp ppppppp ppppppp pppppppp pppppppp ppppppppp pppppppppp ppppppppppppp pppppppppppppppppppppFppppppppppp

0 0 50 100 150 200 250 300 350 400 Day of year

Figure 14: Solar elevation ε as a function of time for the transit of the ERA mast as seen from proposed BSRN position F (distance 11.96 m, bearing 133.31◦). The horizontal line at 35.40◦ indicates the elevation of the top of the mast from the height of the global radiation sensor.

14 ppppp ppppp 90 pppppp ppppp ppppp pppppp ppppp ppppp ppppp ppppp G ppppp ppppp ppppp ppppp ppppp ppppp ppppp ppppp ppppp ppppp 60 ppppp ppppp ppppp pppppp pppppp pppppp pppppp pppppp ppppppp ppppppp ε ppppppp ppppppp pppppppp pppppppp ppppppppp pppppppppp pppppppppppppppppppppppppppppppppppppppppppp 30

0 0 50 100 150 200 250 300 350 400 Day of year

Figure 15: Solar elevation ε as a function of time for the transit of the AWS mast as seen from proposed sun-photometer position G (distance 29.08 m, bearing 52.26 ). The − ◦ horizontal line at 16.29◦ indicates the elevation of the top of the mast from a nominal height of 1.5 m.

pp pp 90 pppp pppp pppp pppp pppp pppp pppp ppppp G ppppp pppp ppppp ppppp ppppp pppppp ppppppp ppppppp pppppp ppppppppppppppppppppppppp 60

0 0 50 100 150 200 250 300 350 400 Day of year

Figure 16: Solar elevation ε as a function of time for the transit of the ERA mast as seen from proposed sun-photometer position G (distance 9.66 m, bearing 115.77◦). The horizontal line at 41.34◦ indicates the elevation of the top of the mast from a nominal height of 1.5 m.

15 90 p p p p G

60 p p p p p p ε p p p pp pp p pp pp 30 p p pp pp pp pp pp pp pp pp p pp pp pp pp pp 0 p 0 50 100 150 200 250 300 350 400 Day of year

Figure 17: Solar elevation ε as a function of time for the transit of the meteorological enclosure shed as seen from proposed sun-photometer position G (distance 11.94 m, bearing 94.80 ). The horizontal line at 4.79 indicates the elevation of the top of the shed, − ◦ ◦ reckoned to be 2.5 m high, from a nominal height of 1.5 m.

pppppppp pppppppp 90 pppppppp pppppppp pppppppp pppppppp pppppppp pppppppp ppppppp pppppppp G pppppppp pppppppp pppppppp pppppppp ppppppppp pppppppp ppppppppp pppppppppp ppppppppppp ppppppppppp ppppppppppppp ppppppppppppp 60 ppppppppppppppppppppppppppppppppppppppppppppppppppppppppppp ε

0 0 50 100 150 200 250 300 350 400 Day of year

Figure 18: Solar elevation ε as a function of time for the transit of the BSRN as seen from proposed sun-photometer position G (distance 1.75 m, bearing 0◦). The horizontal line at 29.74◦ indicates the elevation of the top of the nearer BSRN shadow arm, reckoned to be 1.0 m above the sun-photometer.

16 pppp pppp 90 pppppp pppppp pppppp pppppp pppppp pppppp ppppp pppppp H pppppp ppppp ppppp ppppp ppppp pppppp pppppp ppppp ppppp pppppp 60 pppppp pppppp pppppp ppppp pppppp ppppppp ppppppp ppppppp ppppppp ppppppp ε pppppppp pppppppp pppppppppp pppppppppp ppppppppppppppppppppppppppppppppppppppppppppp 30

0 0 50 100 150 200 250 300 350 400 Day of year

Figure 19: Solar elevation ε as a function of time for the transit of the AWS mast as seen from proposed sun-photometer position H (distance 30.35 m, bearing 49.28 ). The − ◦ horizontal line at 15.65◦ indicates the elevation of the top of the mast from a nominal height of 1.5 m.

p pp 90 ppp pp pp pp pp pp pp pp H pp pp pp pp p pp pp p p pp 60 p p p p ε p p p p 30 p p pp pp pp pp pp pp pp pp pp pp pp pp pp pp 0 0 50 100 150 200 250 300 350 400 Day of year

Figure 20: Solar elevation ε as a function of time for the transit of the ERA mast as seen from proposed sun-photometer position H (distance 8.97 m, bearing 104.19◦). The horizontal line at 43.46◦ indicates the elevation of the top of the mast from a nominal height of 1.5 m.

17 p 90 p p p p p pp pp pp H pp pp pp pp pp pp 60 pp pp pp pp pp pp pp pp ε p pp pp pp pp pp pp pp pp pp 30 pp pp pp pp pp pp pp pp pp pp pp pp pp pp pp pp 0 0 50 100 150 200 250 300 350 400 Day of year

Figure 21: Solar elevation ε as a function of time for the transit of the meteorological enclosure shed as seen from proposed sun-photometer position H (distance 11.94 m, bearing 85.20 ). The horizontal line at 4.79 indicates the elevation of the top of the shed, − ◦ ◦ reckoned to be 2.5 m high, from a nominal height of 1.5 m.

pppppppp pppppppp 90 pppppppp pppppppp pppppppp pppppppp pppppppp pppppppp ppppppp pppppppp H pppppppp pppppppp pppppppp pppppppp ppppppppp pppppppp ppppppppp pppppppppp ppppppppppp ppppppppppp ppppppppppppp ppppppppppppp 60 ppppppppppppppppppppppppppppppppppppppppppppppppppppppppppp ε

0 0 50 100 150 200 250 300 350 400 Day of year

Figure 22: Solar elevation ε as a function of time for the transit of the BSRN as seen from proposed sun-photometer position H (distance 3.75 m, bearing 0◦). The horizontal line at 14.93◦ indicates the elevation of the top of the nearer BSRN shadow arm, reckoned to be 1.0 m above the sun-photometer.

18 pppppp pppppp 90 pppppp pppppp pppppp pppppp pppppp pppppp pppppp pppppp I ppppp pppppp pppppp ppppp ppppp pppppp pppppp pppppp pppppp ppppp 60 pppppp pppppp pppppp ppppppp ppppppp ppppppp ppppppp ppppppp pppppppp ppppppppp ε ppppppppppp pppppppppp ppppppppppppppppppppppppppppppppppppppppppppppp 30

0 0 50 100 150 200 250 300 350 400 Day of year

Figure 23: Solar elevation ε as a function of time for the transit of the AWS mast as seen from proposed sun-photometer position I (distance 28.86 m, bearing 46.68 ). The − ◦ horizontal line at 16.41◦ indicates the elevation of the top of the mast from a nominal height of 1.5 m.

90 pp pp pp pp pp pp p pp I pp p p pp p p p p 60 p p p ε p p p p p p p 30 p pp pp p pp pp pp pp p pp pp pp pp pp pp pp 0 0 50 100 150 200 250 300 350 400 Day of year

Figure 24: Solar elevation ε as a function of time for the transit of the ERA mast as seen from proposed sun-photometer position I (distance 10.92 m, bearing 101.62◦). The horizontal line at 37.90◦ indicates the elevation of the top of the mast from a nominal height of 1.5 m.

19 90 p p pp p p pp p p I pp pp pp pp pp pp pp pp 60 pp pp pp pp pp pp p pp pp pp ε pp pp pp pp pp pp pp pp 30 pp pp pp pp pp pp pp pp pp pp pp pp pp pp pp pp pp pp 0 0 50 100 150 200 250 300 350 400 Day of year

Figure 25: Solar elevation ε as a function of time for the transit of the meteorological enclosure shed as seen from proposed sun-photometer position I (distance 9.95 m, bearing 84.23 ). The horizontal line at 5.74 indicates the elevation of the top of the shed, − ◦ ◦ reckoned to be 2.5 m high, from a nominal height of 1.5 m.

ppppp ppppp 90 pppppppp pppppppp pppppppp pppppppp pppppppp pppppppp ppppppp ppppppp I ppppppp pppppppp pppppppp ppppppp pppppppp pppppppp pppppppp pppppppp ppppppppp ppppppppp pppppppppp pppppppppp 60 pppppppppppp ppppppppppppp ppppppppppppppppppppppppppppppppppppppppppppppppppppppppp ε

0 0 50 100 150 200 250 300 350 400 Day of year

Figure 26: Solar elevation ε as a function of time for the transit of the BSRN as seen from proposed sun-photometer position I (distance 5.62 m, bearing 20.85◦). The horizontal line at 10.09◦ indicates the elevation of the top of the nearer BSRN shadow arm, reckoned to be 1.0 m above the sun-photometer.

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