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Aug 10, 2007 - World Radiation Center (PMOD/WRC), Davos [4,5]. In response to concerns raised by the observed de- cline in the stratospheric ozone layer, ...
Characterization and calibration of ultraviolet broadband radiometers measuring erythemally weighted irradiance Gregor Hülsen* and Julian Gröbner Physikalisch-Meteorologisches Observatorium Davos, World Radiation Center, Dorfstrasse 30, CH-7260 Davos Dorf, Switzerland *Corresponding author: [email protected] Received 24 April 2007; accepted 7 June 2007; posted 20 June 2007 (Doc. ID 82344); published 9 August 2007

An ultraviolet calibration center has been established in Davos, Switzerland. It provides a laboratory for characterizing the spectral and angular response of broadband radiometers. The absolute calibration of these instruments is performed through the comparison to the reference spectroradiometer QASUME. We present what we believe to be a novel calibration methodology that explicitly includes the information of the angular and spectral response functions. From the results of the latest broadband intercomparison campaign, the typical uncertainties of these instruments could be obtained. Most radiometers have an expanded uncertainty of approximately 7%. The angular response introduces an uncertainty of 0.9%–7.2%, depending on the cosine error of the radiometer. © 2007 Optical Society of America OCIS codes: 010.1290, 120.0120, 120.3940, 120.5630, 120.6200, 260.7190.

1. Introduction

Measurements of solar UV radiation have a long history, starting in 1907 with the first measurements by Dorno using cadmium cells [1]. Subsequent developments of instruments and methodologies have led to major improvements in the measurement of solar UV radiation, and have increased our knowledge of the factors influencing this part of the solar spectrum [2,3]. State of the art instruments to measure solar UV radiation are spectroradiometers. These instruments are very delicate and require constant maintenance and substantial man power to produce solar UV measurements of the required quality. Thus, only a few stations exist world-wide that monitor spectral solar UV radiation on a routine basis, and the spatial coverage is therefore rather poor. Essentially, these stations are used as reference points for the validation of satellite derived surface UV radiation products or for the calibration of filter radiometers. In Europe, the quality assurance of these UV monitoring stations is done through site visits by the transportable reference spectroradiometer QASUME, which provides a 0003-6935/07/235877-10$15.00/0 © 2007 Optical Society of America

traceability for spectral solar UV irradiance to a stable and reliable reference, and is maintained at the Physikalisch Meteorologische Observatorium Davos, World Radiation Center (PMOD兾WRC), Davos [4,5]. In response to concerns raised by the observed decline in the stratospheric ozone layer, and the expected increase in solar UV radiation, a number of regional and national networks were established in Europe to monitor solar UV radiation on a continuous basis [6,7]. The majority of these networks consists of broadband filter radiometers with a sensitivity that is close to the sensitivity of human skin to UV radiation [8]. The main purpose of these networks is to provide UV radiation information to the public. Even though these instruments are simple to operate, the quality of the measurements crucially depends on the characterization and calibration procedures implemented by each network. To provide some general guidelines and improve the comparability of UV products derived by these networks, the World Meteorological Organization (WMO) has produced a report on broadband instruments that measure erythemally weighted solar irradiance [9]. In addition, working group four of COST Action 726 has devised a practical guide on how to derive erythemally weighted solar UV irradiance from measurements with these broadband filter radiometers [10]. 10 August 2007 兾 Vol. 46, No. 23 兾 APPLIED OPTICS

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This paper will describe the UV Calibration Center established at PMOD兾WRC, and the methodologies used to characterize and calibrate broadband filter radiometers used to measure solar UV irradiance. Finally, some practical examples from a recent broadband radiometer intercomparison campaign within the activities of COST Action 726 will be used to demonstrate the accuracies that are achievable with these types of instruments. 2. Methods and Measurements

Radiation measurements with broadband filter radiometers fundamentally depend on the relationship between the measured spectral radiation spectrum and the spectral responsivity of the radiometer. Indeed, different spectral radiation distributions will produce results that not only depend on the amount of radiation received by the detector, but also depend on their relative spectral shape. Furthermore, the detector spectral response will not usually be identical to the nominal spectral sensitivity for which the radiometer was designed as with, for example, the erythemal action spectrum. This implies that the calibration of such a radiometer will depend on the spectral source function and the spectral filter response. In addition, suitable correction functions will be required to convert from the detector weighted radiation to the one representative for the desired weighting function. In a similar context, irradiance measurements require the detector to weight incoming radiation with the cosine of the incoming angle relative to normal incidence. Deviations from this angular response will usually result in diurnal variations, and may also depend on the atmospheric state. This is especially true for measurements in the UV wavelength region where the relative changes of the direct unscattered solar radiation to the diffuse radiation change substantially during the day, and depend significantly on the solar zenith angle. This section will describe the laboratory facilities used to characterize broadband filter radiometers, and the methodology that is used to produce erythemally weighted solar irradiance from the measurements with broadband radiometers. A.

Laboratory Characterization

1. Spectral Response The relative spectral response facility has been described in [11]. It consists of a Bentham double monochromator DM-150 with gratings of 2400 lines兾mm. The wavelength can be selected within the range of 250–500 nm, and the slit width was chosen to yield a nearly triangular slit function with a full width at half maximum of 1.9 nm. A 300 W xenon lamp positioned in front of the entrance slit acts as a radiation source, and has been adjusted to maximize the radiation at the exit slit. Behind the exit slit, a quartz plate mounted at 45° vertically transmits about 92% of the radiation toward the test detector, while about 8% of the radiation is deflected toward a photodiode, which is used to check the stability of the monochro5878

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mator output signal. An iris with a diameter of 6 mm is placed in the beam path in front of the test detector to define the beam spot size. The signals from the radiometer are recorded by a Hewlett–Packard 34420A voltmeter. The wavelength scale of this monochromatic source facility was initially determined by measurements of selected spectral emission lines of a mercury lamp placed in front of the entrance slit of the monochromator. Uncertainties, due to the reproducibility of this setup, limit this approach to an uncertainty of about ⫾0.2 nm. We finally characterized the monochromatic source facility in its usual operating state using the QASUME reference spectroradiometer as a reference detector. For the spectral response function (SRF) measurement of a filter radiometer, the transmission function T共␭兲 of the system must be known. We will describe three complementary measurement techniques to determine T. The first method uses the reference spectroradiometer QASUME. The diffuser head of this instrument was placed at the output of the monochromatic source facility, and the spectral throughput of the complete system was scanned in 5–10 nm increments with the reference spectroradiometer. Thus, the slit function and the transmission of the system were determined at each wavelength increment, and were combined to produce a relative transmission function and a spectral wavelength offset based on the calibration of the QASUME spectroradiometer. The slit function of the monochromatic light source (defined as the full width at half maximum) was determined to be 1.92 nm with a wavelength uncertainty of ⫾0.1 nm over the whole measurement range of 260–500 nm. The relative spectral transmission function of the system was measured with two additional instruments to check the consistency between the various methodologies: Y A photodiode (METAS certificate 116-00434) calibrated for absolute spectral responsivity. Y A pyroelectric detector with a very uniform spectral responsivity and high sensitivity. Figure 1(a) shows the relative spectral transmission function determined with these methods, and Fig. 1(b) shows the relative differences. It can be seen in the figure that the agreement is excellent for wavelengths that are longer than approximately 300 nm, with differences that are less than 5%. On the other hand, differences of the order of 10% can be seen below 300 nm between the measurements of the photodiode and the two other determinations. The reason for this discrepancy has not been found so far. A possible explanation is the polarization of the output radiation, which could influence the photodiode (naked photosensitive surface), while the QASUME spectroradiometer has a diffusing surface to depolarize the output radiation, and the pyroelectric detector is insensitive to it (temperature measurement). The calibration of the monchromatic light source using the

Fig. 2. Dependence of the ARF on the light spectrum. The ratios of the ARFs are measured with and without a WG305 filter.

Fig. 1. Transmission function of the monochromator B3388 measured with a pyroelectric radiometer, a calibrated photodiode, and the reference spectroradiometer QASUME: (a) results of the measurements; (b) ratio of the different methods to the last method.

QASUME spectroradiometer was chosen as the method of choice. The SRF is obtained from

SRF共␭兲 ⫽ 共ir ⫺ idark兲兾T共␭兲,

(1)

where ir and idark are the signal and the dark signal of the radiometer, respectively. The SRF is normalized to its maximum. The overall relative measurement uncertainty of the SRF is estimated to be 5% for SRF values that are larger than 5 ⫻ 10⫺4. SRF values below 5 ⫻ 10⫺4 have a higher uncertainty of 15% due to the higher measurement variability, due to the extremely low sensitivity of the test radiometer. 2. Angular Response The angular response function (ARF) of a radiometer is measured on a 3 m long optical bench. A 1000 W xenon lamp mounted at one end of the optical bench serves as radiation source. The detector is mounted on a goniometer at the other end of the optical bench with the vertical rotation axis passing through the plane of the receiving surface of the radiometer. The resolution of the rotation stage is 29,642 steps兾deg, or 0.12 arc sec. A baffle placed in the beam path reduces stray light within the dark room from reaching the radiometer, and a WG305 filter with a 50% cutoff at 303 nm removes radiation below approximately 300 nm. A mirror glued onto the rotation stage reflects some of radiation back on the xenon-lamp

source and is used to determine the zero-position of the goniometer to better than 0.1 deg. The radiometer signals are recorded by an Agilent 34970A data acquisition switch unit. The homogeneity of the light radiation at the reference surface of the radiometer was determined in a cube of 25 mm ⫻ 25 mm ⫻ 25 mm. In the plane normal to the light beam, the deviation from the maximum signal was less than 1% and the decrease in intensity along the beam path is less than 2%. The relative uncertainty of the measurement is estimated to be less than 2% for zenith angles less than 80 deg. The influence of the WG305 filter on the measured angular response was studied for three different radiometer types. For all instruments the results shown in Fig. 2 suggest that the use of a filter to suppress radiation at wavelengths below 300 nm is necessary to produce results consistent with solar radiation measurements. B.

Absolute Calibration

The absolute calibration of a broadband filter radiometer should be performed with a radiation source that has a similar spectral distribution to the radiation for which the radiometer will be used. For the case of solar measurements this requirement implies that the calibration has to be done using the sun as a source, since the spectral distribution and variability of the surface solar radiation cannot be simulated in the laboratory with the required accuracy. 1. Reference Spectroradiometer The instrument of choice for the measurement of absolute spectral solar radiation is a well characterized spectroradiometer. At PMOD兾WRC the reference instrument is the transportable reference spectroradiometer QASUME [4]. The absolute spectral irradiance measurements of the QASUME spectroradiometer are traceable to the primary irradiance standard of the Physikalisch-Technische Bundesanstalt (PTB), Germany, through a set of 1000 W FEL transfer stan10 August 2007 兾 Vol. 46, No. 23 兾 APPLIED OPTICS

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dards, which form the QASUME reference [12]. The irradiance reference of this instrument has become the de-facto standard for spectral UV measurements in Europe.

3. Data Analysis To calculate erythemally weighted irradiance from the raw data of a broadband radiometer, the individual detector characteristics need to be taken into account:

2. Solar Irradiance Measurement Figure 3 shows a setup of broadband instruments for the absolute calibration at the roof platform of PMOD兾WRC besides the entrance optic of the QASUME spectroradiometer. The spectroradiometer itself and the electronic readout of the radiometers are installed below the roof platform. The platform is located at latitude 46.8 N, longitude 9.83 E, and an altitude 1610 m above sea level. Digital-type radiometers from Solar Light come with their own data acquisition system; for the calibration these loggers are set to the maximum resolution and fastest sampling rate. For most of these data loggers the fastest storage rates are one minute averages of the UV signal. A 30 channel multimeter (Agilent 34970A) is used to acquire the radiation and temperature signals of analog-type instruments. The sampling rate of the analog recorder is set to a few seconds. Simultaneously the reference spectroradiometer measures a solar spectrum between 290 and 400 nm with a wavelength step of 0.25 nm and an integrating time of 0.7 s. The procedure is repeated every 15 minutes, which leads to around 40 solar spectra兾day.

Y Detector spectral response function: the conversion function, f, which translates from detector weighted solar irradiance to erythemal weighted irradiance is calculated as

f共SZA, TO3兲 ⫽

冕 冕

CIE共␭兲Erad共␭兲d␭ ,

(2)

SRF共␭兲Erad共␭兲d␭

where Erad is a set of solar spectra calculated with a radiative transfer model for different solar zenith angles (SZA) and total ozone column 共TO3兲 [13,14]. The SRF is obtained from the laboratory measurement described in Subsection 2.A.1, and CIE is the erythemal action spectrum [8]. Examples of the conversion function for three different types of radiometers are shown in Figs. 4(a)– 4(c). Y Angular response function: any deviations of the angular response of the detector entrance optic from the nominal cosine response will result in systematic measurement errors depending on the current atmospheric conditions. This error is usually called the cosine error, and can partially be corrected using the methodology described in [15,16]. The cosine error of an instrument depends on the radiance distribution of the incident radiation, which is usually separated into the direct and diffuse radiation components, Edir and Edif. These components can be derived either by actual measurements, or they can be calculated with a radiative transfer model. Then, the standard procedure to correct for a detector cosine error is based on the following equation: Coscor ⫽

1 , fglo

fglo ⫽ fdir

Edir Edif ⫹ fdif , Eglo Eglo

(3)

(4)

where fglo is the global cosine error and Eglo is the sum of Edir and Edif; fdir represents the direct cosine error, which is equal to the ARF obtained in the laboratory, and fdif is called the diffuse cosine error and is calculated by assuming a homogeneous radiance distribution integrated over the whole hemisphere,



␲兾2

fdif ⫽ 2

ARF共⌰兲sin共⌰兲d⌰.

(5)

0

Fig. 3. Absolute calibration platform on the roof of PMOD兾WRC, which can carry about 30 broadband radiometers. 5880

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The broadband radiometer is calibrated against the reference spectroradiometer to obtain the abso-

Fig. 5. Solar spectrum measured with the QASUME spectroradiometer (solid curve), radiometer SRF (dashed dotted curve), and spectral detector weighted irradiance (dashed curve). The circles represent radiometer readings during the scan time of the spectroradiometer.

ED共␭兲 ⫽ SRF共␭兲E共␭兲.

(6)

The integral of ED共␭兲 over the wavelength yields the detector weighted irradiance ED. The representative time TD of this value is the integral over all of the time stamps of each spectroradiometer recording t共␭兲 weighted by the detector response function and normalized by ED: TD ⫽

Fig. 4. Conversion function to transform from detector weighted to erythemally weighted solar irradiance. The function is normalized to its value at SZA ⫽ 40 deg and TO3 ⫽ 300 DU: (a) Solar Light SL501 (normalization factor f0 ⫽ 0.53), (b) YES UVB-1 共f0 ⫽ 0.20兲, and (c) Kipp & Zonen UV radiometer 共f0 ⫽ 0.27兲.

lute calibration factor. During one scan of the spectroradiometer many data points from the test instrument are recorded. To match these different measurements one has to take into account the changing atmospheric conditions during the time of one spectroradiometer scan (SZA and the cloud variability), using the following method. The solar spectrum as measured by the spectroradiometer, E共␭兲, is weighted with the detector spectral response SRF共␭兲 to produce a spectral detector weighted solar irradiance ED共␭兲 as illustrated in Fig. 5:

1 ED



SRF共␭兲E共␭兲t共␭兲d␭.

(7)

This effectively means that the radiation contribution of each wavelength weighted with the detector sensitivity is used as a measure of the “relative importance” of each recording relative to the total measured irradiance. The radiometer readings U关t共␭兲兴 during the time of the solar spectrum scan are correspondingly weighted to calculate an average radiometer signal for each solar irradiance scan:

UD ⫽

1 ED



SRF共␭兲E共␭兲U关t共␭兲兴d␭.

(8)

To calculate the erythema weighted irradiance from the raw data of a broadband radiometer, the following equation is used [10]: ECIE ⫽ 共U ⫺ Uoffset兲Cfn共SZA, TO3兲Coscor,

(9)

where U and Uoffset are the raw and dark signals respectively, and C represents the absolute calibration factor. The conversion function fn is calculated according to Eq. (2), and is normalized to its value at SZA ⫽ 40 deg and TO3 ⫽ 300 DU. The cosine error of 10 August 2007 兾 Vol. 46, No. 23 兾 APPLIED OPTICS

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the instrument is corrected by the Coscor-function [Eq. (3)]. The dark signal Uoffset is the average of a large number of nighttime readings of the radiometer. The calibration factor C is calculated for each solar irradiance scan by the comparison of the weighted spectroradiometer measurement ED with the average radiometer signal UD: C⫽

ED 1 1 ⫻ ⫻ , UD ⫺ Uoffset Coscor f0

(10)

where f0 is the normalization factor of the conversion function. An average calibration factor is obtained from all measurements satisfying a predefined set of criteria, i.e., measurement conditions without precipitation and SZA smaller than 75 deg. 3. Results and Discussion

In August of 2006 a large set of broadband radiometers were calibrated at PMOD兾WRC in the frame of the activities of working group four of COST 726 [17]. In this section results of this campaign are shown as practical examples for the three main types of radiometer currently in use: the Kipp & Zonen UV radiometers, the SL501 radiometers from Solar Light, and the UVB-1 radiometers from Yankee Environmental Incorporated (YES). A.

of each individual broadband radiometer should be measured to obtain reliable results [18]. B.

Cosine Error

In Fig. 7 examples of the cosine error for the three types of instruments and the reference spectroradiometer are shown. The quality of the angular response of an input optic can be summarized by quoting the diffuse cosine error, which is a representative quantity for instruments measuring solar irradiance. The diffuse cosine error fdif was between 0.98 and 1.03 for Kipp & Zonen UV radiometers, between 0.91 and 1.12 for SL501 radiometers from Solar Light, and between 0.83 and 0.90 for UVB-1 radiometers from Yankee Environmental Incorporated. These values give an indication of the magnitude of the required cosine correction needed for each particular type of instrument. Since any cosine correction depends on the generally unknown diffuse radiance distribution and the fraction of direct and diffuse irradiance, such a correction has a great deal

Spectral Response Function

Figure 6 shows examples of the SRF as a function of wavelength ␭. The SRF is substantially different for each radiometer type, and even within one type the variation is not negligible. The wavelength of the 50% value of the SRF can vary by ⫾1 nm, and the variability of the SRF value for wavelengths larger than 330 nm can be more than ⫾30%. Therefore the SRF

Fig. 6. Examples of spectral response functions. Displayed are the mean and standard deviation of the SRFs of five Kipp & Zonen and two Scintec, nine YES UVB-1, and ten Solar Light SL501A radiometers. 5882

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Fig. 7. Examples of angular response functions: (a) mean and standard deviation of the ARFs of sets of different radiometer types (same as in Fig. 6) and the reference spectroradiometer QASUME; (b) cosine error of these instruments.

of uncertainty, which becomes a significant source of error for instruments with a bad angular response. The variation in the cosine correction can be of the order of ⫾15% for certain radiometers, especially for broken cloud conditions with rapid changes in the relative direct and diffuse irradiance components. C. Absolute Calibration

Figure 8 shows the absolute calibration factors for two sample radiometers, a UVB-1 from Yankee Environmental Incorporated and a Scintec radiometer. To illustrate the effect of the cosine correction on the determination of the calibration factor, it was neglected during the calculation of C in Eq. (10), but added to the figures as a separate function. Figure 8 shows that on a clear sky day the diurnal variability of the calibration factor C is remarkably similar to

Fig. 8. Inverse absolute calibration factor for (a) a YES UVB-1 and (b) a Scintec radiometer normalized to the mean value of C (circles). A lower inverse C means a lower measured signal with the radiometer. Displayed is the data from a clear sky day (DOY 227), a diffuse day (DOY 224), and a day with rapidly changing cloud conditions (DOY 231). The cosine correction functions calculated from the ARF of the instruments are added to the figures as solid lines.

the cosine error of the instrument, which is otherwise compensated by applying the cosine correction function Coscor in Eq. (10). On the diffuse day, the calibration factor C shows no diurnal trend, which is also consistent with a constant cosine correction that is identical to the diffuse cosine error term only. However, on a day with rapidly changing cloud conditions, as illustrated in Fig. 8, the variability of C is significantly higher for the instrument with a large cosine error due to the uncertainty in applying a reliable cosine correction for these atmospheric conditions. In this specific case the cosine correction is equal to the diffuse cosine error term. Figure 9 shows the comparison between the UVindex measured with two broadband radiometers relative to the reference spectroradiometer. The raw data of the radiometers were converted to UV-index using Eq. 9. The calibrated data of the radiometer fit very well to the reference for clear sky days, with a

Fig. 9. Comparison between the UV index measured with the reference spectroradiometer for (a) a YES UVB-1 and (b) a Scintec radiometer. The calibrated data of the radiometer fit very well to the reference measurement for clear and diffuse sky days. A significant variation remains after the data correction for DOY 231 only for the instrument with a large cosine error. 10 August 2007 兾 Vol. 46, No. 23 兾 APPLIED OPTICS

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standard deviation of usually less than 5%. For cloudy days the instruments with low cosine errors still show low variabilities of the order of ⫾5%, while instruments with high cosine errors show variabilities of more than ⫾10%. D. Uncertainty Budget

The uncertainty of erythemally weighted irradiance obtained with a broadband radiometer can be split into the uncertainty resulting from the calibration and the uncertainty from applying the full conversion Eq. (9) that is introduced in Subsection 2.B.3. 1. Calibration Uncertainty The uncertainty resulting from the calibration is essentially composed of the uncertainty of the primary reference, which in our case is the traveling reference spectroradiometer QASUME, with an uncertainty of 2.5% [4]. Additional uncertainty components result from the various calibration steps that are required to obtain the calibration factor C using Eq. (10). These include the determination of the dark offset Uoffset, the determination of the reference values ED from the spectroradiometer using the spectral response function SRF measured in the laboratory, the cosine correction function Coscor to correct the cosine error of the instrument, and finally the normalization factor of the conversion function f. All of these parameters in turn depend on laboratory measurements of the SRF and the ARF, and on the choice of the cosine correction function, which is applied to the measurements. Due to the complex interaction between these parameters, we have decided to use the variability of the calibration factor during the whole calibration period as representative uncertainty for the calibration. Any uncertainties in any of these parameters might result in constant offsets or diurnal variations, which will increase the variability of the calibration factor. The largest variability is expected from the diurnal changes of the solar zenith angle and the resulting absolute and spectral changes in the solar radiation. Thus the observed variability of C during several days will be representative for conditions that are encountered during its routine deployment. Using a large set of 36 radiometers deployed during the PMOD兾WRC-COST 726 campaign in August 2006 we have determined a relative standard deviation of C of the order of ⫾2% using more than 100 solar spectra obtained between three and nine days for stable and well maintained radiometers (see Fig. 8). 2. Uncertainty of the Derived Erythemally Weighted Irradiance The uncertainty of the derived erythemally weighted irradiance of a broadband radiometer is composed of the uncertainties of the parameters involved in Eq. (10). The uncertainty of the calibration factor C was discussed in the Subsection 3.D.1 and is of the order of 2% for a standard radiometer of any of the three types investigated during the intercomparison. The uncertainty resulting from the conversion of detector weighted irradiance to erythemally weighted irradi5884

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Fig. 10. Conversion function is influenced (a) by the uncertainty of the SRF measurement and (b) by the input parameters to the radiative transfer model 共TO3 ⫽ 300 DU兲.

ance fn depends, on one hand, on the uncertainty of the measured SRF and, on the other hand, on the radiative transfer model calculations used to establish the conversion function. The effect of these parameters on the conversion function fn is shown in Figs. 10(a) and 10(b). Thus, uncertainties in the determination of the SRF will lead to an uncertainty of, at most, 1% depending on the SZA (at a SZA below 50 deg the error is below 0.1%). The uncertainty in fn resulting from atmospheric conditions that differ from the radiative transfer model assumptions and the real situation (different albedo, aerosol optical depth, site elevation, . . .) are less than 0.1% for SZAs lower than 60° and may reach 1.5% at a SZA of 75°. An additional uncertainty of at most 1.2% is introduced if the total ozone column TO3 is known only to a precision of ⫾10 DU. The greatest uncertainty results from the cosine correction function Coscor due to the difficulty in accurately characterizing the radiation field at the time

Table 1. Uncertainty Budget for the Calibration of Broadband Radiometers (SZA < 75 deg)

Contribution

Relative Standard Uncertainty (%)

Uncertainty of C Variability Reference spectroradiometer

1.8 2.5

Combined calibration uncertainty

3.1

Uncertainty of the erythemal weighted irradiance Conversion function fn–SRF 0.7 uncertainty Conversion function fn–model 0.9 uncertainty Conversion function fn–TO3 1.2 uncertainty (⫾10 DU) Cosine correction 0.9–7.2 Combined total uncertainty Total expanded uncertainty (k ⫽ 2)

3.6–8.0 7.2–16.0

of the measurement. Under clear sky situations the assumption of homogeneous sky radiance in UV is approximately fullfilled [15], while for broken cloud conditions the inhomogeneity of the sky radiance and the rapid changes of the direct and diffuse irradiance pose formidable challenges to a reliable cosine correction. Due to these difficulties we estimate the uncertainty of the cosine correction function as the full magnitude of the cosine correction variability for clear sky situations, which represents an upper bound for the expected variability between totally diffuse and clear skies. Thus, the uncertainty strongly depends on the quality of the angular response function of a particular instrument. From the set of instruments present at the PMOD兾WRC-COST 726 intercomparison, we could derive typical uncertainties for the following three main types of instruments: (1) Kipp and Zonen, Scintec: less than 0.9%; (2) SL501: between 1.7% and 4.3%; and (3) YES UVB-1: between 4.0% and 7.2%. The resulting uncertainties are presented in Table 1. We show that stable instruments with low cosine errors can reach expanded uncertainties of 7.2%, while instruments with large cosine errors show much higher uncertainties of the order of 16.0%. The reported expanded uncertainty of measurement is stated as the standard uncertainty of measurement multiplied by the coverage factor k ⫽ 2, which for a normal distribution corresponds to a coverage probability of approximately 95%. 4. Conclusion

The PMOD兾WRC has established a UV calibration center (UVC) in Davos, Switzerland, which consists of instrumentation previously domiciled at the Joint Research Centre of the European Commission in Ispra, Italy. The laboratory infrastructure is comprised of two setups, one for characterizing the relative spectral response, and one to determine the angular re-

sponse of filter radiometers. The absolute calibration of these filter radiometers is performed by simultaneous outdoor measurements of solar irradiance by the test radiometers and the reference spectroradiometer QASUME. The absolute irradiance scale is traceable to the QASUME irradiance reference. A novel calibration methodology has been introduced, which takes the angular response function and the spectral response of the broadband radiometer explicitly into account. The typical uncertainties of broadband radiometers measuring erythemally weighted solar irradiance were investigated using results from the PMOD兾WRC-COST 726 campaign held in August 2006 in Davos, Switzerland. It could be shown that well maintained and stable radiometers could be calibrated with an expanded uncertainty of 7.2%. This uncertainty is composed of the uncertainty due to the calibration procedure itself, 3.1%, the uncertainty resulting from converting from detector weighted irradiance to erythemally weighted irradiance, 1.7%, and the uncertainty due to the cosine correction. The latter depends significantly on the angular response of each individual radiometer, and varies between 0.9% and 7.2%. The instrumentation of the UVC is made available by the Joint Research Centre of the European Commission in Ispra, Italy under the cooperation agreement 2004-SOCP-22187. M. Blumthaler, J. Gil Roca, J. Vilaplana Guerrero, L. Vuilleumier, and D. Walker assisted us in the calibration campaign in August 2006. G. Hülsen acknowledges support from the Coopération Europènne dans le Domain de la Recherche Scientifique et Technique (COST), SBF C05.0068. References 1. C. Dorno, “Dauerregistrierung der Ortshelligkeit von Davos, Oktober 1919 bis Oktober 1920, mittels der photoelektrischen Zellenmethode,” Meteorol. Z 1, 1– 8 (1921). 2. P. Bener, Investigation on the Spectral Intensity of Ultraviolet Sky and Sun ⫹ Sky Radiation Under Different Conditions of Cloudless Weather at 1590 m a.s.l., Technical Summary Rep. 1 [Contract AF 61(052)–54, 1960]. 3. J. B. Kerr, “Observed dependencies of atmospheric UV radiation and trends,” in Solar Ultraviolet Radiation: Modelling, Measurements and Effects, C. S. Zerefos and A. F. Bais, eds. (Berlin, Heidelberg, 1997), pp. 259 –266. 4. J. Gröbner, J. Schreder, S. Kazadzis, A. F. Bais, M. Blumthaler, P. Görts, R. Tax, T. Koskela, G. Seckmeyer, A. R. Webb, and D. Rembges, “Traveling reference spectroradiometer for routine quality assurance of spectral solar ultraviolet irradiance measurements,” Appl. Opt. 44, 5321–5331 (2005). 5. J. Gröbner, M. Blumthaler, S. Kazadzis, A. Bais, A. Webb, J. Schreder, G. Seckmeyer, and D. Rembges, “Quality assurance of spectral solar UV measurements: results from 25 UV monitoring sites in Europe, 2002 to 2004,” Metrologia 43, 66 –71 (2006). 6. M. Blumthaler, “Quality assurance and quality control methodologies within the Austrian UV monitoring network,” Radiat. Prot. Dosim. 111, 359 –362 (2004). 7. B. Johnsen, O. Mikkelborg, M. Hannevik, L. T. Nilsen, G. Saxebol, and K. G. Blaasaas, “The Norwegian UV-monitoring program,” ISSN 0804-4910 (Norwegian Radiation Protection Authority, 2002), http://www.nrpa.no. 10 August 2007 兾 Vol. 46, No. 23 兾 APPLIED OPTICS

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