A method to calibrate a solar pyranometer for measuring reference diffuse irradiance

Solar Energy 74 (2003) 103–112

A method to calibrate a solar pyranometer for measuring reference diffuse irradiance Ibrahim Reda*, Tom Stoffel, Daryl Myers National Renewable Energy Laboratory, 1617 Cole Boulevard, Golden, CO 80401, USA Accepted 7 March 2003

Abstract Accurate pyranometer calibrations, traceable to internationally recognized standards, are critical for solar irradiance measurements. One calibration method is the component summation, where the pyranometers are calibrated outdoors under clear sky conditions, and the reference global solar irradiance is calculated as the sum of two reference components, the diffuse and subtended beam solar irradiances. The beam component is measured with pyrheliometers traceable to the World Radiometric Reference, while there is no internationally recognized reference for the diffuse component. In the absence of such a reference, we present a method to consistently calibrate pyranometers for measuring the diffuse component with an estimated uncertainty of 6(3% of reading11 W/ m 2 ). The method is based on using a modified shade / unshade method, and pyranometers with less than 1 W/ m 2 thermal offset errors. We evaluated the consistency of our method by calibrating three pyranometers four times. Calibration results show that the responsivity change is within 60.52% for the three pyranometers. We also evaluated the effect of calibrating pyranometers unshaded, then using them shaded to measure diffuse irradiance. We calibrated three unshaded pyranometers using the component summation method. Their outdoor measurements of clear sky diffuse irradiance, from sunrise to sundown, showed that the three calibrated pyranometers can be used to measure the diffuse irradiance to within 61.4 W/ m 2 variation from the reference irradiance. Published by Elsevier Science Ltd.

1. Introduction Accurate broadband shortwave (solar) irradiance measurements are important to renewable energy resource assessments and climate change research. Since 1977, the National Renewable Energy Laboratory (NREL) has been working to improve the calibration and characterization of pyranometers and pyrheliometers. NREL developed the Broadband Outdoor Radiometer Calibration (BORCAL) process to semi-automate the calibration of radiometers in the natural environment. BORCAL is used to calibrate and characterize up to 100 radiometers at a time, under clear sky conditions. BORCAL results can be used to reduce solar irradiance uncertainties by applying correction algorithms to account for the radiometer’s responses to solar position, aerosol optical depth, and other meteorological conditions documented during the calibration effort from sunrise to sundown (Myers et al., 2002). *Corresponding author. E-mail address: ibrahim [email protected] (I. Reda). ] 0038-092X / 03 / $ – see front matter Published by Elsevier Science Ltd. doi:10.1016 / S0038-092X(03)00124-5

The BORCAL process uses the component summation method where the global solar irradiance (G) is calculated from sunrise to sundown as: G 5 B cos Q 1 D

(1)

where B is the direct normal (beam) irradiance, Q is the solar zenith angle, and D is the diffuse irradiance (Coulson, 1975; ISO, 1993; Myers et al., 2002). B is measured using an absolute cavity radiometer (ACR) traceable to the World Radiometric Reference (WRC / PMOD, 2000). Q is calculated using the standard local time, traceable to the national standard (Michalsky, 1988; Muriel et al., 2001). However, there is no internationally recognized reference for D. In the absence of such a standard we introduce a method to calibrate pyranometers for measuring the clear sky diffuse irradiance. These pyranometers are then used to measure the diffuse component in BORCAL process (as a reference) or in the field. In our method, we use a pyranometer with a black and white thermopile design that consistently demonstrates

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thermal offset errors less than 61 W/ m 2 . Pyranometers with single black detector pyranometers (SBDP) have been shown to have thermal offset errors from 230 W/ m 2 to 25 W/ m 2 . These errors can exceed 40% in measuring the rather small clear sky diffuse irradiance (Drummond and Roche, 1965; Gulbrandsen, 1978; Dutton et al., 2001; Baseline historical data, 1985–2002). The thermal offset errors are a result of the temperature difference between the sky and the case of the shaded pyranometer. These errors are typically negative because the temperature of the clear (blue) sky is always lower than the pyranometer case temperature. Algorithms based on the sky net longwave radiation and night time thermal offset can be used to minimize the thermal offset errors during daylight (Bush et al., 2000; Heaffelin et al., 2001; Dutton et al., 2001; Philipona, 2002). However, these corrections are not ideal because the daylight thermal offset is larger than that of the night time, specially for clear sky diffuse measurement (Philipona, 2002). Because the uncertainty resulting from the non-ideal corrections for thermal offsets is unknown, we selected The Eppley Laboratory, Inc. model 8-48 pyranometers to measure the diffuse reference for their low thermal offset errors (,1 W/ m 2 ). Even though these pyranometers may have errors larger than 7% when tilted (Nast, 1983), their tilt error can be minimized when they are calibrated at their intended tilt angle. In this article, we begin by defining the diffuse responsivity for a solar pyranometer, then describing the shade / unshade method, where the pyranometer is periodically shaded and unshaded from the beam irradiance to calculate its responsivity, then describing our modified shade / unshade method and its uncertainty. Then in later sections we show the consistency of the calibration results for three pyranometers using our method. We also present the results of an outdoor comparison between two pyranometers that were calibrated using our method (to measure the diffuse reference) and three other pyranometers that were calibrated (unshaded) using BORCAL. The comparison shows that once we established the diffuse reference component, the summation method (through BORCAL) can be used to calibrate unshaded pyranometers (intended to be used shaded for diffuse measurements), as long as the pyranometers have thermal offset errors less than 1 W/ m 2 .

2. The diffuse responsivity Many researchers have observed that the responsivity of a pyranometer is a function of solar zenith and azimuth angles because of the nonuniformity of their receiving surfaces (Mohr et al., 1979; Nast, 1983; NREL BORCAL Reports, 1977–2002; Myers et al., 2002). Thus when a pyranometer is shaded from the solar (sun) disk to measure the diffuse irradiance, its diffuse responsivity, RSd , for a diffuse irradiance distribution, D(Q, F ), and a pyranome-

ter responsivity, RS(Q, F ), is calculated (after Forgan, 1979) as: 2p p / 2

E E RS(Q, F )D(Q, F ) sin(2Q ) dQ dF 0

0

RSd 5 ]]]]]]]]]] 2p p / 2

(2)

E E D(Q, F ) sin(2Q ) dQ dF 0

0

where Q and F are the zenith and azimuth angles, respectively, and RS(Q, F ) is determined by using BORCAL or any recognized calibration method. From Eq. (2), RSd will change in value with the change of D(Q, F ). Because D(Q, F ) is ever changing, depending on the sky conditions and cloud distribution, it is difficult to calculate RSd . Its value, however, will always lie between the extreme values of RS(Q, F ). Thus, for all sky conditions, RSd can be considered as: RSmax (Q, F ) 1 RSmin (Q, F ) RSd 5 ]]]]]]] 2

(3)

Then under any sky condition, the percentage uncertainty, Ud , in measuring the diffuse irradiance can be considered as: [RSmax (Q, F ) 1 RSmin (Q, F )]100 Ud 5 ]]]]]]]]] 2RSd

(4)

where RSmax (Q, F ) and RSmin (Q, F ) are the maximum and minimum responsivities. For the clear sky condition, where D(Q, F ) is approximately uniform, the effective RSd should equal the responsivity at Q approximately 458 (without the effect of circumsolar around the sun disk). Thus Eq. (2) yields: 2p

RSd 5

E RS(458, F ) dF

(5)

0

However, when a pyranometer is shaded to measure the diffuse irradiance, the shading disk does not shade a portion of the circumsolar around the sun disk. The irradiance resulting from this unshaded circumsolar will bias the effective responsivity toward the responsivity that corresponds to Q and F of the unshaded circumsolar. For NREL latitude and longitude (408N and 1058W) a reasonable assumption is that the effective diffuse responsivity, for the clear sky conditions combined with the unshaded circumsolar effect, will equal the responsivity at Q 5 458 when the circumsolar is at Q 5 458. Another reasonable assumption is that the responsivity will vary in the range from RS(308, F ) to RS(608, F ) from sunrise to sundown, where 308 is the zenith angle of the effective responsivity at solar noon, estimated from the net clear sky diffuse irradiance at Q 5 458 being biased towards the unblocked circumsolar at Q 5 208 (minimum zenith at solar noon for NREL site), and 608 is the zenith angle of

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the effective responsivity at sunrise and sundown, estimated from the net clear sky diffuse irradiance at Q 5 458 being biased towards the unblocked circumsolar at Q 5 908. This will result in smaller variation in the responsivity and consequently Eq. (4) will yield smaller uncertainty in the measured diffuse irradiance during clear sky conditions than that measured during all sky conditions. From this we decided to consistently calibrate our pyranometers at Q 5 458 and their uncertainties are calculated using Eq. (4) in the zenith range from 308 to 608 when measuring the clear sky diffuse irradiance. Using consistent zenith angle for calibration will allow evaluating the responsivity change from calibration to calibration because the responsivity will always be reported at Q 5 458. It will also allow comparing our calibration results with other methods with reported responsivities at Q 5 458. Also when a diffuse reference is established and internationally recognized, it is easier to correct our diffuse reference in all past calibrations. Eq. (5) implies the difficult task to calculate the 458 zenith responsivity at each azimuth angle from 08 to 3608. It requires many clear sky calibrations to cover the whole range of azimuth angles. Because it is impractical and time consuming, we decided to calculate the 458 zenith responsivity at six azimuthal positions using the calibration method described in Section 3.2. This will quantify most of the azimuth response of the pyranometer’s sensor. The positions were chosen at azimuth positions of 08, 608, 1208, 1808, 2408, and 3008. Position 08 is the origin position where the pyranometer signal connector is at a reference marked position, and 608 is the horizontal clockwise angle from position 08, and so on. The diffuse responsivity is then calculated as the average of the six resulting responsivities.

3. Calibration procedure In this section we describe the classical shade / unshade method to calculate the responsivity at any given time, then we describe its errors. Then in a step by step procedure, we introduce the modified shade / unshade method and its calibration uncertainty.

3.1. The shade /unshade method For a pyranometer with responsivity RS, the global irradiance equals U /RS and the diffuse irradiance equals S /RS, where U and S are the pyranometer output voltages when it is unshaded (exposed to the beam irradiance) or shaded from the beam irradiance, respectively. Thus at a specific time, Eq. (1) yields, U S ] 5 B cos Q 1 ] RS RS

(6)

105

Thus, U 2S RS 5 ]] B cos u

(7)

Eq. (7) is deemed correct if, and only if, the terms U and S are measured at the same time, which is impossible because the pyranometer cannot measure global and diffuse (unshaded and shaded) irradiance at the same time. Decades ago, in order to implement a practical calibration technique, a simple version of the shade / unshade method was developed using Eq. (7), known then as the shade / unshade equation (Iqbal, 1983; ISO, 1993; Myers et al., 2002; ASTM-913). In this method the pyranometer is unshaded and U, B, and Q are measured after a settling time, then it is shaded and S is measured after a settling time. The basic assumption of this method is that during calibration, under clear sky conditions, the diffuse irradiance will be stable enough that its value will not change from the time when the pyranometer is unshaded (when U, B, and Q are measured) to the time when the term S is measured at the end of the shade period. Then S can be used safely in Eq. (7) to calculate the pyranometer responsivity. Next we address the question, how long to shade and unshade? For different pyranometer types, the time for the signal change to reach 95% of its value is between 4 s and 23 s or 4t and 3t, where t is the time constant (1 / e) and its value is between 1 s and 7.5 s (Brinkworth and Hughes, 1976). Pyranometers also have multiple time constants as a result of the thermal inertia of their sensors, longwave radiation exchange between their protective domes and sensors, and change in their cases’ (bodies’) temperature (Shen and Robinson, 1992; Zemel, 1993). These influences may cause a pyranometer to take more than 12 min to reach stability (Shen and Robinson, 1992). Evaluation of different pyranometer types shows that model 8-48, for example, reaches stability in 120 s (or 24t, where its t 55 s) for less than 0.1% error levels (Nast, 1983). From this the American Society for Testing and Materials (ASTM) recommends that the shade and unshade periods, for any pyranometer, are equal to 30t and 60t, respectively (ASTM E-913). This method is simple but introduces the following errors in calculating a responsivity: • During the shade period the pyranometer’s thermal offset error will be algebraically added to the term S in Eq. (7). Because this error is proportional to irradiance in the order of 230 W/ m 2 to 25 W/ m 2 depending on pyranometer type and the clear sky conditions during calibration, the term S might be less than its actual value, while the value of U, B, and cos Q might remain the same. This will cause the nominator in Eq. (7) to increase, which will result in an over estimated responsivity. For example, if during the unshaded period the term U is proportional to global irradiance in the order of 700 W/ m 2 , then one can conclude that a

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230 W/ m 2 to 25 W/ m 2 thermal error in the diffuse irradiance will result in increasing the resultant responsivity by 4.3% to 0.7%, respectively. Because the irradiance (global or diffuse) is calculated as the pyranometer output voltage divided by the responsivity, the over estimated responsivity will result in under estimating the irradiance measured by the pyranometer in the field. • The assumption of the diffuse irradiance being stable during the shade / unshade periods might introduce small errors for pyranometers with t , 1 s (i.e. shade period ,30 s), while it will introduce larger errors of unknown magnitude for pyranometers with longer time constant such as model 8-48, where t equals 5 s (i.e. shade period equal 150 s). To reduce the first error, we chose model 8-48 for its low thermal offset (errors would be less than 0.1% in the responsivity calculation), and for the second error we introduce the modified shade / unshade method as described in Section 3.2.

3.2. The modified shade /unshade method To minimize the errors resulting from the change of the diffuse irradiance during the long shade and unshade periods for model 8-48 pyranometers, we use a control pyranometer that is continuously shaded while the pyranometer that needs calibration (test pyranometer) is periodically shaded and unshaded. The ratio (R) of the test and control pyranometer output voltages is calculated at the end of each shade period, then fitted to a straight line function. The function is then used, as described in step 3.2.2, to monitor and correct for the change in the diffuse irradiance during the rather long shade / unshade periods.

3.2.1. Set up and data collection protocol • Mount the test and control pyranometers and a calibrated ACR on sun trackers. Mount the pyranometers horizontally and shade them with shading disks to block the direct sun beam during the shading episodes. The shading disks are mounted so that they subtend an angle of 58, which is the ACR field of view. This will allow the pyranometer to exactly measure the irradiance that is not measured by the ACR. • Collect data simultaneously from the test and control pyranometers, and from the ACR. • Calculate the reading of each instrument by averaging the last three data points in each shade or unshade period to allow for pyranometer settling time after every signal change. • Repeat the shade / unshade sequence three times. • Begin the sequences so that the data set includes zenith angles in the range from 408 to 508 to make sure that RS at Q 5 458 can be calculated.

3.2.2. Shade /unshade timing and step by step procedure: (see Fig. 1 for details) • Begin the first shade / unshade sequence by shading the test and control pyranometers for at least 150 s (30t ), the test pyranometer is at position 08. • While the control pyranometer is continuously shaded and at its original position, unshade the test pyranometer for a settling time of 300 s (60t ) at position 08. Then record the zenith angle, the output signals of the test and control pyranometers, and the beam irradiance measured by the ACR as: Qu,0 , Utest,0 , Scontrol,0 and Bu,0 , respectively. • Every 60 s of settling time, rotate the unshaded test pyranometer clockwise from position 08 to positions 608, 1208, 1808, 2408, then 3008. Then record Qu,i , Utest,i , Scontrol,i , and Bu,i , where i is the ith position. • End the shade / unshade sequence by rotating the test pyranometer to position 08, then shading it for a settling time of at least 150 s. Then record Q1 and the ratio R 1 , Stest,1 R 1 5 ]] Scontrol,1

(8)

where Stest,1 and Scontrol,1 are the output shade voltages of test and control pyranometers. • Repeat the shade / unshade sequence two times and at the end of each sequence, where the test pyranometer is shaded, record Q2 and Q3 then R 2 and R 3 (calculated by Eq. (8)). • Using curve fitting, fit data points (R 1 , Q1 ), (R 2 , Q2 ), and (R 3 , Q3 ) to the straight line function (R 5 a 1 bQ, where a and b are its offset and slope). Knowing Q at the end of the six unshade positions (08, 608, 1208, 1808, 2408, and 3008), calculate the shade ratios R sh,i , then from Eq. (8), calculate the shade voltage of the test pyranometer (Stest,i ) at each ith position, Stest,i 5 R sh,i Scontrol,i

(9)

• For each of the three sequences, calculate the responsivity at each position, RStest,u,i, Utest,i 2 Stest,u,i RStest,u,i 5 ]]]] Bu, j cos Qu,i

(10)

This will result in three responsivities versus zenith angle for each of the six positions. • Fit the three responsivities to a straight-line function of zenith angle RS(Q ). Then by using RS(Q ), the responsivity at 458 zenith for each of the six positions is calculated. The average of the six responsivities is the diffuse responsivity for the test pyranometer at 458 zenith (RSd,test,45 ) , and half the range of the six responsivities is then added to the total uncertainty of the calibration as described in Section 3.2.3. • Calculate the diffuse responsivity of the control

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107

Fig. 1. Schematic timing diagram for one sequence of the shade / unshade method to calibrate EPLAB Model 8-48.

pyranometer (RSd,control,45 ) as follow: If the diffuse irradiance is measured at the same time by the test and control pyranometers, then Stest /RStest 5 Scontrol / RScontrol . This will yield RScontrol 5 RStest /R, where R is the ratio Stest /Scontrol . Then to calculate the diffuse responsivity at Q 5 458, the ratio R is calculated at Q 5 458 (R 45 ), then, RSd,test,45 RSd,control,45 5 ]]] R 45

(11)

3.2.3. Calculating the calibration uncertainty The following equation is used to calculate the calibration uncertainty with 95% confidence level, u 95 , (Dieck, 1995): u 95 5 ]]]]]]]]]]]]]] 2 2 2 2 6œu 2ACR 1 u 2DAQ 1 u 2u 1 u RS, Q 1 u RS,D Q 1 u RS, F 1 (Ku R ) (12) where the uncertainties are: uACR 5absolute cavity radiometer [|0.4% of Reading (Rdg)] (IPC-IX report, 2000); u DAQ 5data acquisition system [|0.05% Rdg]

(DAQ Specifications); uQ 5zenith angle calculation [|0.02% Rdg] (Michalsky, 1988); u RS,D Q 5effective responsivity resulting from its change in the zenith angle range from 308 to 608 [|1.5% to 2.5% Rdg], RSmax 2 RSmin uRS,D Q 5 ]]]]100 2RSd

(13)

where RSmax and RSmin are the maximum and minimum responsivities in the zenith angle range from 308 to 608. This can be estimated or obtained from historical calibration of the test pyranometer (BORCAL reports, 2000 to 2002; ASTM E-913); u RS, F 5responsivity change resulting from the six azimuthal positions [|0.5% Rdg], maxhRSi j 2 minhRSi j uRS, F 5 ]]]]]]100 2RSd

(14)

uR 5shaded ratio (R sh ) change resulting from fitting the ratios to a function of Q [ | 0.6% Rdg]; K5shade / unshade fraction (S /U ), where S and U are the shade and unshade output voltages of the test pyranometer at any position [|0.1]. The total calibration uncertainty is calculated as:

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108

]]]] Ucontrol,95 5 6(œ(u test,95 )2 1 (u R )2 % Rdg 1 u off )

Table 1 Historical responsivities (mV/(W m 21 )) for test and control pyranometers model 8-48 Calibration event

32858

May 1, 2000 shade / unshade (3 azimuth positions) April 25, 2001 shade / unshade (3 azimuth positions) April 26, 2001 shade / unshade (3 azimuth positions) May 8, 2001 shade / unshade (3 azimuth positions) April 4, 2002 shade / unshade (6 azimuth positions) % of half range (shade / unshade only) a

32871

(16)

2

resulting in [|6(2.6% Rdg11 W/ m )].

32331

4. Calibration results

9.06 9.14

8.92

8.90 a

9.14

8.94

8.93 a

9.15

8.92

8.95 a

9.07

8.96

8.94 a

60.52

60.27

Two test pyranometers (serial numbers 32858 and 32871) and a control pyranometer (serial number 32331) were calibrated four times (32858 five times) from May 2000 to April 2002 using the modified shade / unshade method. The calibration results in Table 1 show that the change in the calculated responsivity at Q 5 458 varied from 60.25% to 60.52% for the three pyranometers, which is within 60.94% to 61.35% (uncertainties at Q 5 458 from Table 2). Table 2 shows that the total calibration uncertainty is from 2.96% to 3.29%. It also shows the magnitudes of different uncertainties encountered during the shade / unshade event on April 4, 2002. The uncertainty of the responsivity at Q 5 458 (u 95 at 458 ) is calculated using the root sum square (RSS) of all uncertainties except u RS,D Q , and the last column is the total calibration uncertainty at any Q, calculated using the RSS of u 95 at 458 and u RS,D Q . Fig. 2 shows the magnitude of ratio change versus zenith angle, on April 4, 2002, for each of the two test pyranome-

60.25

Shaded continuously.

Utest,95 5 6(u test,95 % Rdg 1 u off )

(15)

where u off is the uncertainty resulting from the thermal effect, equals approximately 61 W/ m 2 for model 8-48 [|6(2.5% Rdg11 W/ m 2 )] (Baseline historical data, 2002 to 2002). The control pyranometer uncertainty will then be:

Table 2 Percentage calibration uncertainty (6) for the test and control pyranometers model 8-48 Serial number

%uACR

%u DAQ

%uu

%u RS,

32858 32871 32331

0.40 0.40 0.40

0.05 0.05 0.05

0.02 0.02 0.02

0.76 1.07 N /A

az

%u R

%u 95

0.39 0.60 N /A

0.94 1.29 1.35

at 458

%u RS,D Q

Total %u 95

2.5** 3*** 2.5***

2.67 3.27 3.29

**Estimated. ***From BORCAL.

Fig. 2. Output voltage ratios of test pyranometers divided by control pyranometer S / N 32331.

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Fig. 3. Responsivity of test pyranometers at position 08.

Fig. 4. Responsivity of test pyranometers at position 608.

ters to the control pyranometer. It also shows how well the straight line function is fitting the three data points for each pyranometer. Figs. 3–8 show the change of responsivity versus zenith

angle, on April 4, 2002, for each of the six azimuth positions. They also show how well the straight line function is fitting the three data points for each of the six positions.

Fig. 5. Responsivity of test pyranometers at position 1208.

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Fig. 6. Responsivity of test pyranometers at position 1808.

Fig. 7. Responsivity of test pyranometers at position 2408.

5. Outdoor comparison with three calibrated 8-48s using BORCAL We calibrated two model 8-48 pyranometers (serial numbers 32858 and 32871), using the modified shade / unshade method. Then we used them to measure the reference diffuse component in BORCAL to calibrate three

unshaded model 8-48 pyranometers (serial numbers 32331, 32872, and 32873). The responsivities at 458 of the three pyranometers were calculated as the average of the morning and afternoon responsivities at 458 zenith from BORCAL results. We installed the five pyranometers outdoors on trackers and shaded. The reference diffuse irradiance was calculated as the average irradiance measured by

Fig. 8. Responsivity of test pyranometers at position 3008.

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111

Fig. 9. Difference between diffuse irradiances measured by the reference and three shaded 8-48s.

pyranometers 32858 and 32871. Fig. 9 and Table 3 show that, 95% of the time, the difference between the reference diffuse irradiance and the irradiance measured by the three pyranometers is from 60.81 W/ m 2 to 61.39 W/ m 2 or 61.62% to 62.7% of the reading from sunrise to sundown which is within the calibration uncertainty. Fig. 9 shows that, at approximately 10:00 and 14:00 where AM & PM zenith angles equal 458, the errors between the reference irradiance and the irradiance measured by each of the three pyranometers are within 0.5 W/ m 2 (which is on the order of thermal offset magnitude). This is because all responsivities are calculated at Q equals 458. This concludes that pyranometers can be calibrated unshaded then used shaded to measure the diffuse irradiance. Fig. 9 also shows that the errors diverge as the zenith angle departs from Q equals 458. This is a result of the combined zenith and azimuth response errors, resulting from the change of the diffuse responsivity [RS(Q, F )] of each pyranometer when the diffuse irradiance distribution [D(Q, F )] changes at each data point. These errors are difficult to correct because the errors in the reference diffuse irradiance can not be separated from the three pyranometers errors, because RS(Q, F ) and D(Q, F ) must be known at each data point. RS(Q, F ) might be obtained by many pyranometer calibrations, but D(Q, F ) requires

Table 3 Difference between diffuse irradiances measured by the reference and 3 shaded 8-48s 32872

32873

32331

Mean square error Standard deviation U 95 (W/ m 2 )

Error in W/ m 0.51 0.63 0.99 0.75 60.81 61.10

0.85 1.02 61.39

Mean square error Standard deviation U 95 (%)

Error in percentage (%) 0.98 1.38 1.43 1.98 61.62 62.26

2.03 2.89 62.73

2

dividing the sky into small pixels, then measuring the irradiance in each pixel by a device that has enough resolution to measure very small irradiances (for the blue sky pixels). Unfortunately, at present such a device does not exist.

6. Conclusions 1. Measuring the clear sky diffuse irradiance with uncertainty of 6(3% of reading11 W/ m 2 ) with respect to the (WRR) can be achieved using model 8-48 pyranometers when calibrated using the modified shade / unshade method. This uncertainty results in smaller uncertainty when the pyranometer is used to measure the diffuse component during BORCAL, because under clear skies the ratio of the diffuse to the global irradiance is on the order of 1 / 10, which will result in uncertainty of 60.1(3%11 W/ m 2 ) or 6(0.3% 10.3 W/ m 2 ) in the reference global irradiance calculation, see Eq. (1). 2. Using the shade / unshade method with a control pyranometer gives consistent results from calibration to calibration, 6(0.25% to 0.52%) from Table 1. 3. Using the control pyranometer reduces and quantifies the errors resulting from the sky instability and the pyranometer time constant, during the shade / unshade periods, see ratio uncertainty (uR ) in Table 2. 4. This method can be used to calibrate any pyranometer for measuring the clear sky diffuse irradiance. Nevertheless it can introduce a bias error in the calculated responsivity from 0.7% to 4.3%, depending on the pyranometer type and the sky conditions during the calibration, if the appropriate thermal offset corrections are not taken into consideration. In some cases spectral correction might be considered (e.g. silicon detectors). 5. If a model 8-48 pyranometer is calibrated horizontally, it must be used horizontally because it can result in .7% errors when tilted (Nast, 1983). If it is required to be installed tilted in the field, then this procedure must

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be performed with the control and test pyranometers at the same tilt angle of the field setup. 6. This method can be used at any site, but care should be taken in estimating the zenith angle corresponding to the effective diffuse responsivity, using the technique described in Section 2 (for NREL site it is estimated to be 4586158). If tilt is required to reach the effective zenith angle, then the appropriate tilt uncertainty should be added to the total calibration uncertainty. 7. Once the reference diffuse irradiance is established, the summation method can be used to calibrate pyranometers unshaded. The pyranometers can then be used shaded for diffuse measurements, as long as their thermal offset errors are corrected.

Acknowledgements The authors thank NREL staff members: Afshin Andreas, Bev Kay, Peter Gotseff, and Steve Wilcox for their continuous support to BORCAL and NREL baseline data quality.

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