Theor. Appl. Climatol. 51, 97-104 (1995)
Theoretical and Ap21ied Climatology © Springer-Verlag 1995 Printed in Austria
Universitfit ffir Bodenkultur, Institut ffir Meteorologie und Physik, Vienna, Austria
Calibration of Sunphotometer for Measurements of Turbidity P. Weihs, I. Dirmhirn, and I. M. Czerwenka-Wenkstetten With 6 Figures Received March 16, 1994 Revised January 6, 1995
Summary This study investigates an alternative method to the Langley plot, a widely used but complex calibration method for sunphotometers. A sunphotometer has been calibrated using two different methods: the Langley method, a calibration to the extraterrestrial irradiance, and second by comparison to a standard instrument. The standard instrument used for these studies is spectrophotometer. The relative difference between the calibration factors obtained by the two methods is between 0.13°,ofor the channel with the greatest sensitivity (500 nm) and 2°/; for the channel with the lowest signal (368 nm). The accuracy of both calibrations is of the same order of magnitude with relative errors between 1.2 and 7°0 for the Langley method and 2.9 to 5.3 3{;for the standard instrument method. Analyses of the origin of possible errors show the sensitivity of the Langley method to less than ideal weather conditions, which could cause an error in calibration of up to 45~,; under'extreme conditions and when too few measurements are made. This studies are made only for the UV and the visible range, investigations about the application of this technique in the near IR have still to be done and would also require spectrometers with a wider sensitivity range. These investigations do not alter the fact that frequent calibrations are still needed due to sensitivity changes like filter degradation.
1. Introduction Spectral m e a s u r e m e n t s of turbidity can give inf o r m a t i o n on the c o m p o s i t i o n of the atmosphere, e.g. q u a n i t y of water vapor, c o n c e n t r a t i o n s of aerosols (Holben a n d Eck, 1990; T h o m e et al., 1992).
W o b r o c k and Eiden's (1988) e q u a t i o n describes the spectral dependence of turbidity:
G=2/(a22 + b2 + c)
(1)
where ra is the aerosol optical depth, a,b,c are constants and 2 is wavelength. M e a s u r e m e n t s of turbidity at a m i n i m u m of two wavelengths are required to determine the constants a , b and c. I n s t r u m e n t s used to measure turbidity should therefore have as m a n y channels as possible at wavelengths outside atmospheric a b s o r p t i o n bands, where only Rayleigh scattering a n d aerosol extinction occur (Shaw, 1976). L a m b e r t Bouguer's law, which allows for the d e t e r m i n a t i o n of extinction of direct solar radiation t h r o u g h the atmosphere, is given by:
E~ = E~, o e-~;."
(2)
where E~ is the measured solar irradiance at wavelength 2 at the point of observation, r~ is optical depth, m is the relative air mass and E~, 0 is the extraterrestrial irradiance. (2) allows for the calculation of optical depth after the determination of the atmospheric transmission E~jE;..o. The extraterrestrial irradiance is k n o w n from the literature (e.g., Neckel and Labs, 1984). Therefore, to determine the optical depth, the spectral irradiance E;. has to be accurately measured. T a k i n g into a c c o u n t the rapid changes in sensitivity due
98
P. Weihs et al.
to filter degradation and other instabilities occurring in some sunphotometers, a recent calibration of the instrument is the best way to avoid inaccuracies in measurement. Turbidity instruments can be calibrated in two ways: first by using the Langley method, and second by calibrating to a standard instrument.
0.6-
0.5~ ~" 0.4>, 0.3 0.2 0.1 0 30O
2. Instrumentation
I
i
400
500
2.1 Sunphotometer The sunphotometer M A I N Z II manufactured by N O L L which has been used for these studies has five spectral channels (368 nm, 500 nm, 675 nm, 778 nm, and 862 nm) (Fig. 1) with halfwidths between 3 and 5 nm. Unfortunately only the first 3 channels are in the spectrophotometer's wavelength range and can be calibrated by both methods. The sunphotometer sensor is photodiode, which has a spectral sensitivity dependance as shown in Fig. 2. Due to the narrow transmittance of filters and the smooth sensitivity of the diode a constant sensitivity within the halfwidth of the filters can be assumed. The field of view of the instrument is 2 ° . Measurements are made pointing the instrument towards the sun. A diopter with a focussing screen allows the instrument to be aligned along the direct solar beam. The measured value indicated by the instrument is the average of the values recorded during 500 milliseconds. A program option logs only the highest measured value during the time of measurement; thus, inaccuracies due to unsteady holding of the instrument during sun-tracking are minimized. During the measurements the raw voltage (mV), the channel number and the amplification must be recorded. Before and after the measurement pe-
i
i
i
i
I
I
i
600 700 800 900 1000 1100 1200 Wavetength (nm)
Fig. 2. Spectral sensitivity of the sunphotometer's photodiode
riod the temperature of the instrument must also be recorded in order to make temperature sensitivity correction during subsequent processing.
2.2 Spectrophotometer A spectrophotometer was used as a standard instrument for a second, independent calibration of the sunphotometer. This instrument was built at Utah State University (Dirmhirn et al., 1992), and improved afterwards at Institut ftir Meteorologie und Physik der Universit~it ftir Bodenkultur in Vienna, Austria. It allows measurements of the spectral irradiance, has a bandwidth of 1.4 nm and a minimum wavelength increment of 0.1 nm. The optics are composed of an integrating sphere and a Jobin-Yvon doublemonochromator. The detector is a Hamamatsu photomultiplier which is only sensitive between 200 and 700 nm (Fig. 3). The spectrophotometer was calibrated with a 1000 W FEL NIST standard lamp, the irradiance of which is known to 1.35% at 350 nm and to 1.01% at 654 nm. The fluctuations of the sensitivity of the instrument caused by a 100
0.25
/
f
0.2
"
i~
"~ 0.1 5
~o
-
re"
I 0.2
0.3
0.4
0.5 0.6 0.7 Wavetength (,rim)
0.8
0.9
1
Fig. 1. Comparison of 5 channels of the MAINZ II sunphotometer with the spectral extraterrestrial irradiance
0.1 100
200
300
t A00 500 600 Wavelength (nm)
700
800
900
Fig. 3. Spectral sensitivity of the spectrometer's photomultiplier
Calibration of Sunphotometer for Measurements of Turbidity
temperature dependence of the photomultiplier and of the electronics are determined by measurements with a standard 37 W calibration lamp in the field between scans. A correction to the measured values is applied during subsequent data processing. Each measurement series consists of global and diffuse irradiance measurements. The diffuse irradiance is measured before and after each scan of the global irradiance using a shading disc. This shading disc has a 2 cm radius and is held 15 cm from the opening of the integrating sphere. This shading disc is mounted on a 1 mm thick rod. The diffuse irradiance is measured before and after each scan of the global irradiance. The direct irradiance Ex is determined by subtracting the average of the before and after diffuse irradiance scans from the global irradiance measurement: E~ = (Gx --(HI.,~ q- H2,;)/2Ksak)
(3)
Where H1, x and H2, x are the measurements of the diffuse irradiance for the wavelength 2 before and after the global irradiance scans and K1a k is the factor for the correction of the sensitivity fluctuations of the spectrophotometer using the field calibration. 3. Calibration Methods
An extrapolation of this line to air mass 0 is done statistically by using the "root mean square method". The extrapolated values for air mass 0 are those given by Neckel and Labs (1984) corrected for Earth-Sun distance. The spectral extraterrestrial irradiance is not constant over the halfwidth of the filters, therefore it should be weighted with the filter function.
+ Eo,;.+~;.Qx+~x + ... 22
-=y
This method has been discussed in Kremser et al. (1984) and Dunkelmann and Scolnik (1959). The direct solar radiation is measured during a cloudless day at as many zenith angles as is possible. The logarithm of the intensity is plotted on a graph as a function of the relative air mass. A constant optical depth during the measurement period is required in order for this method to give accurate results in which case the x - y graph is a straight line with a slope equal to: d = (ln(V1) - l n ( V 2 ) / ( m 2 - m l )
(4)
Where V1 and V2 are the raw voltage and m2 and ml are the relative air masses at the respective times of successive measurements. The slope d is equal to the optical depth; although, as will be mentioned in Section 5.1, a straight line may also result in case of optical depth changing at a constant rate.
(S)
21
Eo,n is the weighted extraterrestrial intensity for channel n, Eo, x is the actual extraterrestrial Jrradiance at the wavelength 2 where 21 and 22 are the two limits of the wavelength interval and Qa is the part of the transmitted irradiance in the interval [ 2 - d2/2, 2 + d2/2] relative to the total irradiance transmitted by the filter. Q;, is given by Qx = A)./Atot
(6)
where Ato, is the total irradiance transmitted by the filter and A;~ is the irradiance transmitted in the wavelength interval [2 + d2/2; 2 - d2/2]. Finally, the calibration factor for channel n is calculated using the following equation Cn = Eo. ,'Ken,f/exp(Vo)
3.1 The Langley Method Using the Extraterrestrial Irradianee
99
(7)
When E0. n is the weighted averge of the extraterrestrial irradiance for channel n, Kentf is the factor for the correction of the earth-sun distance and V0 is the raw value extrapolated to air mass 0. The calibration constant is given in W c m - 2 g m - 1 m V - 1 and has to be multiplied with the sunphotometer raw output in order to give the measured solar irradiance E;. By inversion of Eq. (2) the optical depth may be calculated.
3.2 The Comparison of Sunphotometer and Spectrophotometer The values of the direct solar irradiance measured using the spectrophotometer obtained from (3) first have to be corrected to match the filter function of the sunphotometer by means of Eq. (5), and are then compared to the vertical component of the sunphotometer values given by: I~,h = cos(Z) I~
(8)
where Z is the zenith angle, I;..h is the correspon-
100
P. Weihs et al.
ding vertical component and Ix is the measured direct slant path irradiance. The spectrophotometer values (x in [mW/(mZnm)]) and the sunphotometer values (y in [mV]) referred to a horizonal surface can then be compared graphically where the inverse of the slope (a) of their linear relationship. (9)
y = ax
give the desired calibration factor (= 1/a).
-2
.-.
4. Results 4.1 Results from the Langley Plot Calibration
The places that are most suitable for calibration to the extraterrestrial irradiance are high altitude locations where no large fluctuations of optical depth occur during the period of measurement. Our calibration was made on the Zugspitze at 2960m elevation, between 3 and 12 October 1992. The smallest relative air mass for this time
Table 1. Results of the Calibrations of 3 Channels of the
-2.5
M A I N Z It Sunphotometer, a) Channel I, b) Channel 2, c) Channel 3
a)
~" -3.5 C
-~-~
"~..., i "~
-J -4.5
2 = 368 nm
A Langley Method
B Comparison Method
Ratio B/A
N u m b e r of measurements Corr. Coeff. Rel. error Calibration Factors I0 6 W/(cmZ.mV)
10
16
-
0.9869 7% 75.95
0.9789 5.8% 77.64
1.02
2 = 500 n m
A Langley Method
B Comparison Method
Ratio B/A
N u m b e r of measurements Corr. Coeff. Rel. error C a l i b r a t i o n Factors 10- 6 W/(cm2. mV)
10
14
-
-5 -5.5 -6 0
1
2
4 Ret. a i r m a s s
a) Channel 1
7 5.75 "" - . . . 6.5
"~
.E
b)
"7,
6.25 6
c
.-~ 5.75 5.5 5.25 5 0
1
2
3
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6
Ret. a i r m a s s
b) Channel 2 0.5
0.9985 1.2% 0.85
0.9939 2.9% 0.8489
0.9987
0./-,5 "" ..~ 0.4 .-7.
0.35
c)
0.3
~ 0.25
"!.....
5 0.2
2 = 675 n m
A Langley Method
B Comparison Method
Ratio B/A
N u m b e r of measurements Corr. Coeff. Rel. error C a l i b r a t i o n Factors 10- 6 W/(cm 2. mV)
10
17
-
.J
0.15 0.1 0.05 0 0
1
2
3 z. 5 Re[. a i r m a s s
6
7
8
c) Channel 3
Fig. 4. a - c ) Langley plots for channels 1, 2 a n d 3 of the M A I N Z II s u n p h o t o m e t e r , Zugspitze (9. Oct. 1992)
0.9629 5% 4.816
0.9873 4.1% 4.766
0.9895
Calibration of Sunphotometer for Measurements of Turbidity
of the year is 1.85. The best conditions from several day's attempts were selected. Favourable conditions were only available on a few days and we have chosen to concentrate on the set of most reliable data. The Langley plots for three channels can be seen in Fig. 4a-c. The calibrations were truncated at air mass 3 due to changing conditions, which may already have occurred between air mass 3 and 4. However the data quality is quite satisfactory between air mass 8 and air mass 4. The values have been plotted as a function of the relative air mass, and the correlation factor has
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J= Q.
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50
100 150 200 Spectrometer [mW/(m2nm)]
250
300
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~7
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101
been calculated. The calibration factors have been determined using Eqs. 4 to 7. These are listed in Table 1.
4.2 Calibration with Respect to the Spectrophotometer The calibration determined by comparing the sunphotometer with the spectrophotometer has been made using Eqs. 5, 8 and 9. The raw data of the sunphotometer referenced to the horizontal have been compared to the weighted spectrophotometer data. Figure 5a-c show the comparison of the sunphotometer data with the spectrophotometer values. The data used in these graphs were recorded at different sites (Zugspitze, 2960 m and Saloniki, 300 m) having different altitudes above sea level and also at different sun elevations, thus cover a wide range of intensities. Only data with no possible changes, during the scan, due to clouds were implemented into our study. This reduces the amount of data considerably and this was an additional reason to use a second set of measurements, from a different site. To avoid any errors due to a possible deviation from the ideal cosine response of the spectrophotometer only measurements with solar elevations greater than 20 ° were used. The calibration factors were calculated using the method described in Section 3.2.
~6 E5
0
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5. Comparison and Comments Regarding the two Calibration Methods
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If ""
5.1 Considerations of Accuracy 0
100
200 300 Z,O0 500 600 S p e c t r o m e t e r [mW/(m2 nm)]
700
800
b) Channel 2 1.8 ~" 1.6 E 1.4 ~OJ 1.2
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#
oE 0.8 ~ 0.6
s f ~"
~'0.4
Y, o.2 0 n , j J "''~ ] 0 100
200 300 400 500 600 Spectrometer [mW/(m2nm]]
700
800
c) Channel 3 Fig. 5. a-c) Calibration of the 3 channels of the sunphotometer by comparison with the spectrophotometer
Before showing the results of calibrations we should classify and estimate the origins of possible errors in both calibration methods (Table 2) differentiating between systematic and nonsystematic errors. Systematic errors arise from uncertainties associated with the calibration source. Neckel and Labs (1984) estimated the accuracy of the given extraterrestrial irradiance to be 1%. The accuracy of calibration lamps varies with the type of the lamp (Walker, 1987); lamps of the FEL type have an accuracy of 1.35~ at 350 nm and 1.01 ~o at 654 nm, respectively. The error due to the reproducibility is 0.99% at 350 nm and 0.88% at 654 nm, respectively giving a possible error during the calibration of the spectrophotometer of up to 2.34% at 350 nm and 1.89% at 654 nm.
102
P. Weihs et al.
Table 2. Sources and Dimensions of the Errors of both Calibration Methods LANGLEY M E T H O D A System. error
Calibration Source
B Non system, errors Weather
COMP: TO STANDARD
Extraterrestrial irradiance
1%
according to (1)
Changin9 opt. depth steady change falsified line according to (3) Extrapolation with few air masses according to (5)
Instrument - Optics
-Sensitivity
Calibration lamp system, err. 350 nm 654 nm Reproducibility 350 nm 654 nm Accord. to (2)
up to 10~o Comparisonon thefield due to the optic
1.35~ 1.01 0.99~ 0.88~o 0.5~o
up to 45~o
Sunphotometer
Spectrophotometer
opening angle according to (5)
< 0.001
Shade disc According to (4) Cosine effect
Electronics + Sensor according to (5) and (6)
1~o
Sunphotometer Sensitivity correction
0.5~o up to 6~o
< 0.001
Spectrophotometer Correction of sensitivity
2~o
Sunphotometer Electronics + sensor
1~o
(1) Neckel and Labs (1984) (2) Walker et al. (1987) (3) Dunkelman and Scolnik (1959) (4) Chai and Green (1976) (5) Shaw (1976)
The second kind of errors, the non-systematic ones, result from random individual false measurements that tend to broader the error band of the values and, hence, the uncertainty of the regression fit. Sources of errors in the Langley method are primarily due to changes in the weather and inaccuracies of the instrument. Changing optical depth due to haze occurring during measurements made during periods that appear to have constant conditions can in the case of an extrapolation over air masses not bigger than 3 cause maximum errors up to 45~ (Dunkelman and Scolink, 1959). Also, in the case of an apparently linear regression function, the optical depth may have changed continuously during the day in agreement to a parabolic function causing an error up to 10~o (Shaw, 1976; Kremser et al., 1984). To avoid such errors it is best to use the Langley method only during times when the aerosol optical depth is exceedingly small and when conditions are j udged to be stable over time, as in the case of highaltitude observations made during anticyclonic
conditions and during morning hours when local convection is minimal. Errors in measurements, related to instrument performance, can have two cause: the optics and the sensitivity fluctuations of the instrument (Table 2). A large source of error of the optics of the sunphotometer may be the view angle. Shaw (1976) showed, that the error with a 5° view angle caused by the circumsolar radiation can be ignored (the view angle of the sunphotometer used in this study is 2°). The error due to nonlinearity of the amplification, due to bad reproducibility and inaccuracy of the digital reading, is given by the manufacturing firm N O L L as 1}/o. No indication of nonlinearity was observed. Other sources of accuracy given in the literature are of the same order of magnitude (Shaw, 1976). For the spectrophotometer we can differentiate between errors due to the optics and errors due to fluctuations in the sensitivity of the instrument. The error due to the shading disc, given by Chai
Calibration of Sunphotometer for Measurements of Turbidity
und Green (1976) as 0.5~, is however dependent on the turbidity. The cosine error measured in the laboratory of the Institute of Meteorology and Physics is shown on Fig. 6. The values were normalized to 30 ° incidence, the maximum relative errors were - 3 and + 3 ~ respectively between the zenith angles 70 ° and O °. As discussed above fluctuations of the sensivity of the instrument are checked and corrected with a current regulated 37 W lamp in the field. This has been tested with a quantum sensor and the reproducibility was found to be 2~.
5.2 Comparison of the two Calibration Methods In order to make a comparison of both calibrations techniques the calibration factors, the relative errors (of the intercept at Y and of the reciprocal of the slope of the regression line respectively), the correlation coefficient of the regression line as well as the number of measurements of both calibration methods are compared for the three channels in Table 1. For the calibration on the basis of the Langley method the relative error (in a 9 5 ~ confidence interval) in the calibration factor is equal to the relative error of the extrapolated extraterrestrial, zero airmass value (point of intersection with the Y axis). The extrapolated voltage value may be found with 9 5 ~ confiderence between the given confidence interval. The relative error of the calibration based on comparisons with the spectrophotometer equals the error (in a 95~o confidence interval) of the reciprocal of the slope of the linear regression line. The correlation coefficient is a measure of the fit of the regression line and it is dependent on the
3 I
jJ'
2
j-
1
j
% -1
J
-2
-3
-/
-5 0
10
20
30 z,O 50 Angle of incidence
60
Fig. 6. Cosine error of the intergrating sphere of the spectrophotometer
70
103
variance (variation of the points around the regression line). A better correlation factor reduces the relative error of the calibration factor and these two values are a measure for the quality of the correlation. In channel 2 the ratio between the calibration factors is acceptable at 0.9987. The relative error of the calibration factor is also very small indicating a good calibration in both cases. The calibrations of channels 1 and 3 however, have larger relative errors and larger deviations of the calibration factors. Channel 1 shows the biggest deviation (2~o) and the largest relative error. Because the atmospheric conditions were, identical for the three channels the differences between the relative errors of the three channels must be attributed to the accuracy of the measurements within the respective channels. One reason for these differences are differences in channel sensitivities. This can be seen by looking at the dimensions of the calibration factors (Table 1). The lower sensitivity of channel 1 and 3 compared to channel 2 is due to a decrease of the photodiode sensitivity in the UV (Fig. 2) at channel 1 and to the small transmission of filter 3, respectively. In addition the weak solar irradiance in channel 1 causes low signals and, hence a greater inaccuracy (Fig. 1). The mean variation of the measurements around the regression line for the second calibration method is dependent on the performance of both instruments. In addition to the smaller accuracy of the sunphotometer measurements in channel 1 and 3, decreasing sensitivity of the spectrophotometer at 675 nm (Fig. 3) and weaker irradiance of the sun in the UV contribute to the greater deviations noted for the second method. The strong turbidity during some of the measurement periods at (Saloniki) with a strong circumsolar radiation may have caused a nonnegligible error resulting from the shadow method used. Despite all these possible errors the agreement between the calibration factors (Table 1) is reasonable, the largest deviation (2~) for channel 1 being of the same order of magnitude as the systematic errors of the calibration source.
104
P. Weihs et al.: Calibration of Sunphotometer for Measurements of Turbidity
6. Conclusions
The probability of a good regression will of course increase if a greater number of measurements is used. However non-tolerable errors may occur with the Langley Plot calibration method due to circumstances which cannot be controlled such as changing optical depth and weather which does not allow enough measurements. The second method of calibration by comparison does not suffer from these disadvantages. Nevertheless, the comparison of the two methods showed reasonably good agreement despite the several possible sources of errors. Unfortunately, these calibrations were only performed for the 3 channels in the UV and in the visible range. The application of this technique in the important near IR wavelength range would require spectrometers with a much wider sensitivity range. The development of such alternative calibration methods do not alter the fact that possible sensitivity changes (like filter degradation) of sunphotometers still afford frequent calibrations. In principle it should be expected that in the future measurements in the laboratory will have a greater accuracy and will replace the calibration outdoors. Acknowledgments
Dirmhirn, I., 1984: Spektrale UV-Strahlung im Gebrige. Proceedings Rauris ITAM 1986, 400 405. Dirmhirn, I., Sreedharan, C. R., Venugopal, G., 1993: Spectral ultraviolet radiation instrument and preliminary measurements in mountainous terrain. Theor. Appl. Climatol., 46(4), 219-228. Dunkelman, L., Scolnik, R. 1959: Solar spectral irradiance and vertical atmospheric attenuation in the visible and ultraviolet. J. Opt. Soc. Amer., 49, 356-367. Holben, B. N., Eck, T. F., 1990: Precipitable water in the Sahel measured using sun photometry. Aoric. Forest Met., 52, 95-107. Kremser, K., Koepke, P., Quenzel, H., 1984: Aersol optical thickness from direct solar radiation improved Langley method applied to measured data. In: Fieco, G. (ed.) I.R.S. 84 Current problems in Atmospheric Radiation. Hampton Virginia U.S.A.: A. Deepak. Krfiger, O., 1989: Atmosph~irenkorrektur yon Thematic Mapper-Messungen fiber Wattengebieten der Deutschen Bucht, Bericht GKSS-Forschungszentrum Geesthacht GmBH. Neckel, H., Labs, D., 1984: The solar radiation between 330 and 12500 A. Solar Physics., 90, 205-258. Shaw, G. E., 1976: Error analysis of multi-wavelength sun photometry. Pure Appl. Geophys., 114, 1-14. Thome, K. J., Herman, B. M., Reagan, J. A., 1992: Determination of precipitable water from solar transmission. J. Appl. Meteor., 31, 157 165. Walker, J. H., Saunders, R. D., Jackson, J. H., McSparron, D.A., 1987: Spectral irradiance calibrations. NBS Spec. Publ. 250-20. Wobrock, W., Eiden, R., 1988: Direct solar radiation: spectrum and irradiance derived from sunphotometer measurements. Appl. Opt., 27(11), 2253-2260.
The authors thank the Institute of Meteorology of the University of Miinich for the loan of the sunphotometer. The study was made as part of the UV-investigations funded by the "Bayrisches Klima Forschungsprojekt Bay FORKLIM".
References Chai, A. T., Green, A. E. S., 1976: Ratio Measurement of diffuse to direct solar irradiance in the middle ultraviolet. Appl. Opt., 15(5), 1182-1187.
Authors' address: P. Weihs, I. Dirmhirn and I. M. CerwenkaWenkstetten, Universit~it fiir Bodenkultur, Institut fiir Meteorologic und Physik, Tiirkenschanzstrasse 18, A-1180 Wien, Austria.
