Calibrating Broadband UV Instruments: Ozone and Solar Zenith Angle Dependence

Barry A. Bodhaine NOAA Climate Monitoring and Diagnostics Laboratory, Boulder, Colorado

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Ellsworth G. Dutton NOAA Climate Monitoring and Diagnostics Laboratory, Boulder, Colorado

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Richard L. McKenzie National Institute of Water and Atmospheric Research, Lauder, New Zealand

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Paul V. Johnston National Institute of Water and Atmospheric Research, Lauder, New Zealand

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Abstract

A UV spectroradiometer was installed at Mauna Loa Observatory (MLO), Hawaii, in July 1995. This instrument has been employed to characterize several broadband UV instruments of a type commonly used to estimate erythemal irradiance at many sites around the globe. One year of clear-sky data from MLO has been analyzed for solar zenith angles (SZAs) of 5°–85°, in steps of 5°, and for total ozone values in the range 220–310 DU measured with a Dobson spectrophotometer. Because the spectral responses of various broadband instruments can be quite different, and particularly because the erythemal response defined for human skin is significantly different than that of many broadband instruments, the calibration of a broadband instrument reporting in erythemal units is strongly dependent on total ozone and SZA. When a broadband instrument is placed in the field it is necessary to know the calibration as a function of ozone and SZA to determine accurate erythemal irradiance. However, the manufacturers of broadband instruments do not generally provide information on the ozone dependence of the calibration. A procedure is described here for determining the calibration of a broadband UV instrument by comparison with a calibrated spectroradiometer. This procedure does not require precise knowledge of the spectral response of the broadband instrument. This analysis shows that if, for example, total ozone concentration decreased from 300 to 200 DU, the calibration constant of a broadband instrument should be increased by almost 20%. Therefore, the broadband instrument would significantly underestimate the increase of erythema.

Corresponding author address: Barry Bodhaine, NOAA/CDML, R/E/CG1, 325 Broadway, Boulder, CO 80303.

Email: bbodhaine@cmdl.noaa.gov

Abstract

A UV spectroradiometer was installed at Mauna Loa Observatory (MLO), Hawaii, in July 1995. This instrument has been employed to characterize several broadband UV instruments of a type commonly used to estimate erythemal irradiance at many sites around the globe. One year of clear-sky data from MLO has been analyzed for solar zenith angles (SZAs) of 5°–85°, in steps of 5°, and for total ozone values in the range 220–310 DU measured with a Dobson spectrophotometer. Because the spectral responses of various broadband instruments can be quite different, and particularly because the erythemal response defined for human skin is significantly different than that of many broadband instruments, the calibration of a broadband instrument reporting in erythemal units is strongly dependent on total ozone and SZA. When a broadband instrument is placed in the field it is necessary to know the calibration as a function of ozone and SZA to determine accurate erythemal irradiance. However, the manufacturers of broadband instruments do not generally provide information on the ozone dependence of the calibration. A procedure is described here for determining the calibration of a broadband UV instrument by comparison with a calibrated spectroradiometer. This procedure does not require precise knowledge of the spectral response of the broadband instrument. This analysis shows that if, for example, total ozone concentration decreased from 300 to 200 DU, the calibration constant of a broadband instrument should be increased by almost 20%. Therefore, the broadband instrument would significantly underestimate the increase of erythema.

Corresponding author address: Barry Bodhaine, NOAA/CDML, R/E/CG1, 325 Broadway, Boulder, CO 80303.

Email: bbodhaine@cmdl.noaa.gov

1. Introduction

Broadband UV sensors are widely used for routine measurements of UV-B irradiance, particularly to estimate the erythemal response of the human skin and to detect spatial and temporal changes in that quantity. Several commercial versions of the popular Robertson–Berger (RB) type of meter (Berger 1976) are available, and their spectral characteristics are generally somewhat similar to each other. The manufacturers of these instruments usually provide conversion factors for estimating various portions or weighted integrals of the UV spectrum, such as total UV-B (280–315 nm or 280–320 nm), Diffey action spectrum, Parrish action spectrum, or the DNA-weighted spectrum. However, these estimates can be significantly in error since the actual spectral response of the instrument can be significantly different from the portion of the spectrum being estimated, which in turn causes strong ozone dependence of the measurements. This occurs because of the strong variation of ozone absorption of UV in the UV-B region of the spectrum.

The principle of operation of the RB type of instrument depends on a UV-sensitive phosphor that absorbs radiation in the UV-B region and reemits it in the green region. Radiation from the whole sky passes through a quartz dome and is incident on a horizontal UV broadband filter that transmits the UV to the phosphor. The green light emitted by the phosphor passes through a green filter and is measured by a photodiode that has its peak response in the green part of the spectrum. The instrument used in this study is a Model UVB-1 obtained from Yankee Environmental Systems. The UVB-1 is temperature stabilized at 45°C.

The absolute calibration of RB-type meters, including detailed theoretical studies of these instruments, has been treated by DeLuisi and Harris (1981, 1983) and more recently by Grainger et al. (1993), Mayer and Seckmeyer (1996), and Leszczynski et al. (1998). All of these authors compared broadband instruments to a collocated spectroradiometer. Spectral data from the spectroradiometers were then integrated using various weighting functions to approximate erythemal or other biological responses, and the results were compared to the broadband measurements. The spectral data were also weighted by various instrument functions in some of these studies (Mayer and Seckmeyer 1996; Leszczynski et al. 1998). The response of a broadband instrument is strongly dependent on both solar zenith angle (SZA) and total ozone. SZA is important because of the cosine dependence of horizontal incidence-type sensors, the distribution of total irradiance between direct and diffuse components, and, to some extent, the variation of these with wavelength. Their response depends on ozone because various instruments have different spectral responses. Thus, the advantage of using spectroradiometers to calibrate broadband instruments is that various spectral weighting functions can be used in processing the data to simulate the spectral responses of broadband instruments at various SZAs and ozone values.

This paper describes a procedure to calibrate a UVB-1 broadband instrument using one year of spectroradiometer measurements made at the Mauna Loa Observatory, Hawaii (MLO). It is found that this calibration is strongly dependent on both SZA and ozone. A procedure is developed for transferring the calibration of a reference broadband instrument to other broadband instruments. This procedure is based entirely on instrumental results, whereas previous studies have depended to some extent on model results, particularly for the ozone dependence (Mayer and Seckmeyer 1996; Leszczynski et al. 1998).

2. The Mauna Loa Observatory site

Mauna Loa Observatory is located on the island of Hawaii (19.53°N, 155.58°W; 3.4 km) and is operated by the Climate Monitoring and Diagnostics Laboratory (CMDL) of the National Oceanic and Atmospheric Administration (NOAA). A large number of measurements are conducted at this site, including carbon dioxide, carbon monoxide, methane, ozone, aerosols, and solar and thermal radiation. Clear mornings occur at MLO more than 50% of the time, which makes MLO an excellent site for solar radiation measurements and especially Langley plot calibrations. Relative atmospheric transmission in the visible (broad band) has been measured at MLO since 1958 and optical depth since 1982, yielding an excellent optical depth record (Dutton 1992; Dutton et al. 1994). The CMDL series of annual reports (e.g., Hofmann et al. 1996b) provides an excellent summary of these and many other activities at MLO. Bodhaine (1983) provided a brief history of the station. Because of the Dobson spectrophotometer ozone measurement record at MLO (1957 to the present) and the annual ozone cycle (220–310 DU in this study), the opportunity exists to obtain well-calibrated UV spectroradiometer measurements and to relate them to the ozone record. It would be desirable to perform similar studies at sites experiencing larger ozone variations.

A scanning UV spectroradiometer was installed at MLO in July 1995. This instrument was developed and operated by the National Institute for Water and Atmospheric Research (NIWA) at Lauder, New Zealand, and has been included in a number of spectroradiometer intercomparisons (McKenzie et al. 1991; McKenzie et al. 1993; Seckmeyer et al. 1995). The first year of data was presented by Bodhaine et al. (1996) and Bodhaine et al. (1997). These studies have shown that short-term variations of UV-B irradiance are inversely correlated with variations in total ozone (McKenzie et al. 1991; Hofmann et al. 1996a; Bodhaine et al. 1996; Bodhaine et al. 1997). Other studies of the relationship between ozone and spectral UV measurements have been reported by Lubin and Frederick (1991) in the Antarctic Peninsula, by Booth et al. (1994) in Antarctica, and by Frederick et al. (1993) in southern Argentina. However, a detailed study of the effects of ozone on the calibration of broadband UV sensors has not been published.

3. Instrumentation

The UV spectroradiometer was described by McKenzie et al. (1992), and its operation at MLO was described by Bodhaine et al. (1997). This instrument uses a horizontally mounted diffuser designed to view the whole sky and minimize cosine error. The entrance slit to the spectrometer is located 4.5 cm below the diffuser. A shading disk can be mounted on the instrument to separate the diffuse and direct radiative components. Stepper-motor-driven gratings cover the spectral range of 290–450 nm with a bandpass of about 1 nm. A complete scan requires about 200 s. The spectroradiometer is programmed to begin measurements at dawn and perform scans at 5° SZA intervals throughout the day beginning and ending at 95°; during the middle of the day, however, the system switches to a scan every 15 min.

Calibration of the spectroradiometer is performed on site using a standard 1000-W FEL lamp, with calibration traceable to the National Institute of Standards and Technology (NIST), at approximately 6-month intervals. A wavelength calibration using a mercury lamp and a stability test using a 45-W lamp are performed weekly for quality control. The cosine response of the sensor was characterized by McKenzie et al. (1992), and all data have been corrected for cosine errors.

A Yankee UVB-1 (SN950208) broadband instrument has been in operation at MLO since August 1995. This instrument is operated according to the instructions provided by the manufacturer, and all data are recorded as 3-min mean voltages on a Campbell Scientific data acquisition system. The spectral response of the UVB-1 was taken from the calibration sheet supplied by the manufacturer for this particular instrument and is shown in Fig. 1. Also shown in Fig. 1 is the International Commission of Illumination (CIE) erythema weighting function provided by McKinlay and Diffey (1987) to represent the response of human skin to UV irradiance. The two spectra in Fig. 1 were used to construct two datasets from the spectroradiometer data by weighting and integrating over wavelength. The three datasets are referred to here as
i1520-0426-15-4-916-eq1
Note that if the manufacturer’s spectral response of the UVB-1 is accurate, then the UVB1 and S(UVB1) datasets should be in close agreement (after scaling to irradiance units) because S(UVB1) attempts to simulate the response of the broadband instrument. Also, a comparison of S(UVB1) and S(CIE) is a method of simulating the different responses of the UVB-1 and the CIE spectra using spectroradiometer data. Here we will use the comparison of the UVB1 and S(CIE) datasets to form the basis of the development of calibration expressions for the UVB-1 broadband instrument. By examining Fig. 1 note that the UVB-1 instrument spectral response falls off at about the same rate as the CIE curve but is displaced by about 10 nm toward longer wavelengths in the steep falloff region. Therefore, the UVB-1 spectrum will be less responsive to ozone changes than the CIE spectrum.

4. Data analysis

Typical clear-sky scans were shown by Bodhaine et al. (1997) in their Fig. 1 along with a discussion of how weighted and integrated irradiances are derived for certain action spectra. For the following analyses, UV spectroradiometer data for SZA ≥ 45° were chosen for clear mornings at MLO during the July 1995–July 1996 time period. This gives one full year of data, amounting to 132 data points, allowing the study of an annual cycle and giving ozone values in the DU 220–310 range. Clear mornings at MLO were determined by examining other solar radiation records obtained at MLO and also Dobson spectrophotometer observer notes. A day was accepted as a clear day in this study if the sky was cloudless from dawn through the time of the 45° scan, if all scans were acceptable up through the 45° scan, and if Dobson ozone data were available for that morning. Afternoon data were not considered because clear afternoons seldom occur at MLO. A 45° SZA occurs at about 0900 LST in summer and about 1100 LST in winter. It is interesting to note that because of the 19.5° latitude of MLO 43° is the smallest SZA that occurs every day throughout an entire year at MLO. However, the sun is approximately at zenith at solar noon on 18 May and 26 July each year and passes to the north of zenith between those dates. Data for SZAs smaller than 45° (sun higher in the sky) were obtained from days when morning clear conditions extended long enough and during those times of the year when the sun was high enough in the sky. Because of these limitations, the datasets for the smaller SZAs were more limited (e.g., the 5° dataset has only five points in it). An important limitation in this regard, which will be discussed in more detail later, is that the wintertime days were missing from the smaller SZA datasets, giving smaller ranges of ozone variation and larger average ozone for those datasets. All Dobson spectrophotometer total ozone data were derived from A–D, direct sun, ground quartz plate observations (using 305.5–325.0- and 317.5–339.9-nm wavelength pairs), which are considered the most reliable for Dobson observations (Komhyr et al. 1993).

To ensure that the spectroradiometer and UVB-1 data were simultaneous, the spectroradiometer data were first weighted and integrated for the two spectra (CIE and UVB1) at each 5° SZA, and times were assigned to the center effective wavelengths of the integrated spectra. Next, the effective time of each 3-min mean UVB-1 voltage was assigned at the center of the 3-min interval. A linear interpolation was performed on the UVB-1 voltage time series in order to assign values coincident in time with spectroradiometer-weighted irradiance values. In this way the three datasets could be compared at the same effective times. Finally, the three ratios (UVB1)/S(CIE), (UVB1)/S(UVB1), and S(UVB1)/S(CIE) were formed in preparation for regression against the ozone dataset.

The calibration factors recommended by the manufacturer of the broadband instrument are functions of SZA. However, for small SZAs the manufacturer recommended a value of 0.141 W m−2 V−1 for erythema measurements. For a preliminary look at the dataset, the calibration constant (0.141 W m−2 V−1) was applied to all UVB-1 voltages, and the UVB1 dataset was regressed against the S(CIE) dataset for SZA ≥ 45° (see Fig. 2). Note that the units of irradiance have been expressed in μW cm−2 for convenience. This simulates the most common application of the RB type of broadband instrument—that is, the estimation of erythema according to the CIE definition. At first glance the calibration of the broadband instrument looks fairly good;however, this is not surprising since the manufacturer’s standard was actually calibrated against this same spectroradiometer in Lauder, New Zealand. A closer inspection of Fig. 2 reveals groupings of data (by SZA) that do not lie on the regression line. Figure 3b shows the ratio (UVB1)/S(CIE) plotted as a time series for the SZA 45° data. If the instruments were in exact agreement, the ratio would be equal to 1 everywhere. However, the time series shows not only an offset but also an annual cycle that appears to correlate very well with the MLO ozone time series shown in Fig. 3a. This correlation with ozone suggests that the calibration of the broadband instrument depends significantly on total ozone.

Based on the apparent dependence of the ratio (UVB1)/S(CIE) on total ozone, the following procedure was developed for the calibration of the UVB-1 broadband instrument in CIE erythema units. An example for SZA 45° is shown in Fig. 4. First the UVB1 voltages were plotted against S(CIE) and any obvious outliers were removed (Fig. 4a). Note that the datasets are well correlated but that the regression line does not pass through the origin. Next, the ratio (UVB1)/S(CIE) was regressed against the ozone dataset to produce a linear equation describing the relationship (Fig. 4b). Some scatter exists about the regression line, but the correlation is still fairly high. The equation relating the ratio (UVB1)/S(CIE) and ozone was then used to recover estimated erythema values, given UVB-1 voltages at the prescribed SZA (45° in this case), where total ozone is the independent variable. These estimated erythema values are compared to those measured by the spectroradiometer in Fig. 4c where the slope is close to 1, the intercept is close to 0, and the correlation is very high. In this example the predicted erythema was calculated from the relation
i1520-0426-15-4-916-e1
This process was repeated for SZAs from 5° to 85° in steps of 5°, giving a family of linear calibration equations depending only on ozone, similar to (1). Examples of some of these regressions for various SZAs are shown in Fig. 5. Note that the slope of the regression line is positive for small SZAs but is negative for large SZAs. This curious behavior will be discussed in more detail later. The regression equations may be expanded into an array of calibration factors depending on SZA and ozone, as shown in the contour plot in Fig. 6. This plot shows a strong dependence on ozone for the smaller SZAs, a minimum dependence on ozone at about 65°, and also a strong SZA dependence at larger SZAs. For any given ozone and SZA the necessary calibration factor can be read from this plot. Figure 7 shows the calibration factors as a function of SZA, portrayed as a family of curves where different curves are given for different values of total ozone. This revealing figure shows that the ozone dependence is positive for small SZAs, becomes 0 at SZA 65°, and becomes negative at large SZAs. Why is there an inflection point with sign reversal at SZA 65°?

To understand the strange reversal at 65° in Fig. 7, it is necessary to consider the fact that the UVB-1 spectral response and the CIE spectrum differ somewhat and therefore respond differently to total ozone. A convenient way of expressing the dependence of an action spectrum on ozone is the radiative amplification factor (RAF). The RAF, defined as the percent change of UV (erythemal) irradiance divided by the percent change of total ozone, was introduced to estimate the effects of ozone depletion on the incident UV irradiance. It is called an amplification factor because it is frequently greater than 1, so that if large ozone changes occur, even larger changes in erythemal radiation can occur. The concept of an RAF has been discussed by many authors (e.g., DeLuisi and Harris 1983; McKenzie et al. 1991) and more recently by Bodhaine et al. (1997). Here we use the power-law formulation of Madronich (1993) to calculate RAFs for the UVB1, S(CIE), and S(UVB1) datasets. The RAF is simply the slope of the power-law regression between ozone and irradiance.

Figure 8 shows the results of these RAF calculations. Note that the S(CIE) RAFs are significantly higher than the UVB1 RAFs for small SZAs and significantly lower for large SZAs. The crossover point is 65°, which confirms that the slope of the ozone dependence for S(CIE) is greater than that of UVB1 for SZA < 65° and less than that of UVB1 for SZA > 65°. Because the correction factor is the ratio of (UVB1)/S(CIE), the dependence of the correction factor on ozone is positive for SZA < 65° and negative for SZA > 65°. The reader should note that the RAF calculations have been corrected for earth–sun distance (discussed by Bodhaine et al. 1997) but have not been normalized to compensate for the larger average ozone at smaller SZAs due to the reduced number of data points available for the smaller SZAs. The reduced number of data points for SZA < 45° is also responsible for the somewhat noisy behavior of the RAFs for SZA < 45°.

To obtain a more complete understanding of the effects discussed here, two additional similar sets of analyses were performed. To show that the dependence on ozone is due to the different spectral responses of UVB-1 and CIE, the entire analysis was repeated using the UVB1 and S(UVB1) datasets, which presumably have the same spectral response. The ozone dependence should become small in this case. An example of the process for SZA = 45° is shown in Fig. 9 (similar to the three-step process in Fig. 4). Here the UVB1 voltages are plotted against the S(UVB1) irradiances (Fig. 9a) to test for outliers, and the ratio (UVB1)/S(UVB1) is regressed against ozone to derive a correction factor as a function of ozone for SZA = 45° (Fig. 9b). Finally, estimated irradiances derived from UVB1 measurements, after having been corrected for ozone, are compared to those measured by the spectroradiometer (Fig. 9c). Assuming that the spectral response of the broadband instrument provided by the manufacturer is accurate, the ozone effects should be greatly reduced. The results of the analysis for all SZAs are presented in Fig. 10, which shows a family of correction factor curves for different values of ozone similar to those previously shown in Fig. 7. The main difference between the two figures is that the ozone dependence is now negligible for the smaller SZAs, as expected. Also, although there is still some ozone dependence in Fig. 10 at large SZAs, it is much smaller than the ozone dependence in Fig. 7. In other words, the simulation of the UVB1 spectrum by constructing S(UVB1) and comparing it to actual UVB1 voltages reveals only a small ozone dependence. The residual effects are most likely due to cosine errors, which are responsible for the large overall increase in correction factor at the larger SZAs. The small ozone dependence remaining at the largest SZAs could also be caused by inaccuracies in the manufacturer’s UVB-1 spectral response or by spectral effects in the cosine response of the UVB-1 instrument. A close inspection of Fig. 10 reveals an inflection point at about SZA = 59° and a systematic reversal in the residual ozone dependence for SZA > 59°. Figure 8 shows clearly that the RAF behavior is consistent with these results. Note that the UVB1 and S(UVB1) RAF curves in Fig. 8 are in good agreement for small SZAs; however, they cross over at about SZA = 59° and they diverge slightly for large SZAs.

Since the cosine errors of the spectroradiometer are small (and corrected), the cosine response of the broadband instrument as a function of SZA may be estimated from Fig. 10, as shown by the scale on the right. Assuming that the cosine response is 1 in the range SZA = 5°–15°, the scale was derived by ratioing the values of calibration factors to a value of 70 along the vertical axis. The implied cosine correction required for the broadband instrument (comparing the family of curves to the cosine response scale) is about 1.3–1.4 at SZA = 85°. Typical cosine errors of the broadband instrument according to the manufacturer for the direct beam component are shown in Fig. 10 (longer dashed line). According to the manufacturer’s calculations, this results in a much smaller cosine correction of total irradiance at larger SZAs because most of the irradiance normally arrives as diffuse skylight, which is assumed to be isotropic (longest dashed line). However, at MLO our results show that a much larger fraction of the irradiance is in the direct beam. Thus, the requirements for a good cosine response are more demanding at the high altitude of MLO, and the transfer of calibration to an instrument operated at lower altitudes would lead to some errors at large SZAs because of this effect.

For our third analysis of the behavior of the ozone dependence of this calibration procedure, the spectroradiometer data processed by the two different weighting functions were compared to each other. Note that this is an excellent method of modeling the behavior of different action spectra through the use of real measured solar spectra and can be used to check the validity of the computer models commonly in use to study these kinds of effects. In this final case study we compared S(CIE) and S(UVB1). Since the same sensor is used for these two datasets, by treating the ratio S(UVB1)/S(CIE) we minimize instrumental effects, although there could be some residual spectral cosine errors because of the two different spectral responses. Thus, this test should reveal the true ozone dependence that results from comparing the two different spectra.

Figure 11 shows the derivation of the calibration factors, similar to those in Figs. 4 and 9, for SZA = 45°. The two datasets S(CIE) and S(UVB1) were compared directly to check for outliers (Fig. 11a). Next, the ratio S(UVB1)/S(CIE) was regressed against ozone to derive the correction factor as a function of ozone for SZA = 45° (Fig. 11b). Next, the predicted values derived from S(UVB1) corrected for ozone were compared to the measured values of S(CIE) (Fig. 11c). Finally, the entire process was repeated for the other SZAs, and the results are shown in Fig. 12 as a family of curves that give the correction factor as a function of SZA for various values of ozone. Therefore, Fig. 12 shows the idealized behavior of the ozone dependence on the use of two different spectra for calibration purposes and is quite similar to Fig. 7. That is, the ozone dependence is almost wholly due to the two different spectra and is not significantly influenced by the use of two different sensors. The inflection point and reversal of ozone dependence for this case occurs at about SZA = 69°. This also can be seen in Fig. 8, in which the S(CIE) RAF is greater than the S(UVB1) RAF for SZA < 69° and is less than S(UVB1) for SZA > 69°.

5. Model results

To investigate the results of the instrument comparison given above, radiative transfer (RT) calculations simulating the above measurements were performed. Solar UV irradiances with spectral resolution similar to that of the MLO spectroradiometer were calculated for MLO atmospheric conditions encountered during the instrument comparison. The RT calculations were done using a version of Discrete Ordinate Radiative Transfer (DISORT) (Stamnes et al. 1988) that was implemented at CMDL and used previously for various other applications (Dutton and Cox 1995; Dlugokencky et al. 1996). The RT model as used for the current study allows for 10 streams of radiation and 34 atmospheric layers. The model accounts for Rayleigh and Mie multiple scattering and absorption of oxygen and ozone in the UV-B region of the spectrum. Since there is only a minimal effect of the atmospheric-state variables, the tropical mean atmospheric profile of McClatchey et al. (1972) was used. The model’s spectral results for various SZAs and ozone amounts were weighted by the S(CIE) and S(UVB1) spectra to simulate the measurements given in Fig. 12, and the results of the model calculations are shown in Fig. 13. The model calculations agree with the measurements in Fig. 12 within about 7%, and the general shape of the curves is replicated. Model calculations of a somewhat similar nature were performed by Leszczynski et al. (1998).

A close look at Fig. 13 shows that the crossover point of ozone dependence is slightly different for different values of ozone, whereas the crossover point in Fig. 12 is a single point. The singular crossover point at about SZA = 69° in Fig. 12 is derived from using straight-line functions in the linear regression relating S(CIE)/S(UVB1) to ozone for the various values of SZA. (SZA = 45° is shown as an example in Fig. 11b.) Because there is some curvature in these functional relations, a parabolic function fit to the data can give a better fit in some cases, with the result that the inflection point in Fig. 12 gets spread over a range of SZAs in a manner similar to that shown in the model results of Fig. 13.

6. Conclusions

Because broadband UV sensors, such as the RB-type instrument, are commonly used to estimate erythemal irradiance, it is extremely important to develop a calibration procedure applicable under a full range of field conditions. The best method of calibrating a broadband sensor is to compare it directly to a well-calibrated spectroradiometer and to integrate the resulting spectra over the same spectral response as the broadband instrument. However, if the spectral response of the broadband instrument is not well known or if it is not the same as the particular action spectrum that is to be estimated, a given calibration factor is good only for a particular value of SZA and a particular value of total atmospheric ozone. The above analysis shows that errors as high as 10% or more can result if the effects of ozone are not taken into account. A correct calibration of a broadband instrument must include a field comparison with a spectroradiometer over a sufficient time period to include total ozone values covering the range that will be observed at the operational site of the broadband instrument. Assuming that the spectroradiometer is properly cosine characterized (as it is here), then cosine errors of the broadband instrument will also be taken into account using the above analysis. The results of the calibration described here for SZA ≥ 45° are shown in Fig. 14 and may be compared directly to the raw data initially presented in Fig. 2, before corrections were applied. The linear regression in Fig. 14 shows a slope close to 1, an intercept close to 0, and r2 close to 1, clearly indicating very good ozone and SZA correction.

After a calibrated broadband instrument is placed at a field site, the daily values of ozone at that site must also be known in order to properly interpret the data. Although climatological ozone values are not accurate enough, satellite ozone coverage is sufficiently widespread and accurate enough to allow derivation of a correction factor for a broadband instrument at a particular site.

Generally speaking it is not practical to characterize every individual broadband instrument using the above procedure, although it would be desirable to do so at regular intervals, such as once per year. Although there are some obvious limitations, our recommended procedure for routine broadband instrument calibration is to select one instrument as a “secondary” standard and to characterize it by comparison with a spectroradiometer over a wide range of SZA and ozone values according to the above procedure. Other broadband instruments of the same type may then be compared to the secondary standard over a short time period and single calibration constants may be derived for each of the additional instruments through simple linear regression. A sufficiently accurate calibration may then be applied to each working broadband instrument through the application of the correction factor analysis involving SZA and ozone for the secondary instrument and to the single calibration constant for the working instrument.

It should be emphasized that the above procedure will be satisfactory for a given family of similar instruments—that is, those that have similar spectral responses. However, different types of instruments—for example, different models—must be individually characterized by comparison to a spectroradiometer over a wide range of SZA and ozone values. It is, of course, possible that two instruments of the same type could have somewhat different spectral responses. Finally, it is worth noting that if the spectral response curve of a particular broadband instrument is known, then its calibration may be established at a given site by comparison to a spectroradiometer over a range of SZAs, and then the ozone dependence of the calibration could be estimated through the use of modeling. It should be mentioned that the above analysis and discussion is valid only for clear-sky conditions. In addition, some residual effects, possibly due to other atmospheric quantities such as aerosols, may remain in the data. While this is not a problem at a clean site, such as MLO, it could possibly show up as a small error in calibration at a more polluted site. Furthermore, the results derived here for MLO may not be strictly applicable at other sites because cosine errors may differ at other locations where the diffuse component is relatively more important, due to more molecular and aerosol scattering at lower altitudes.

For some applications of broadband instruments the effects of SZA may be of lesser importance, particularly when total daily irradiances are of interest. In this case, although cosine errors are large at large SZAs, the actual magnitude of the irradiance is small, so that the contribution to the overall daily total irradiance is still small. However, for studies in which the irradiance as a function of SZA is important, such as RAF or diffuse–direct studies, the above calibration procedure is necessary.

This analysis shows that if, for example, total ozone concentration decreased from 300 to 200 DU, the calibration constant of a broadband instrument should be increased by almost 20%. Therefore, the broadband instrument would significantly underestimate the increase of erythema.

Acknowledgments

We thank Mike Kotkamp, John Barnes, and Steve Ryan for maintaining the instrumentation; Gloria Koenig for providing the MLO Dobson ozone data; Bob Uchida for building the calibration facility; and John DeLuisi, Bob Stone, and Joyce Harris for their helpful comments.

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    • Crossref
    • Export Citation
  • DeLuisi, J. J., and J. M. Harris, 1981: Characteristics of ultraviolet radiation in the human erythema band measured with a Robertson–Berger meter and a double monochromator. NOAA Tech. Memo. ERL ARL-99, Air Resources Laboratories, Silver Spring, MD, 43 pp.

  • ——, and ——, 1983: A determination of the absolute radiant energy of a Robertson–Berger meter sunburn unit. Atmos. Environ.,17, 751–758.

    • Crossref
    • Export Citation
  • Dlugokencky, E. J., E. G. Dutton, P. C. Novelli, P. P. Tans, and K. A. Masarie, 1996: Changes in CH4 and CO growth rates after the eruption of Mt. Pinatubo and their link with changes in tropical troposphere UV flux. Geophys. Res. Lett.,23, 2761–2764.

    • Crossref
    • Export Citation
  • Dutton, E. G., 1992: A coherence between the QBO and the amplitude of the Mauna Loa atmospheric transmission annual cycle. Int. J. Climatol.,12, 383–396.

    • Crossref
    • Export Citation
  • ——, and S. K. Cox, 1995: Tropospheric radiative forcing from El Chichon and Mt. Pinatubo: Theory and observations. Atmospheric Science Paper 586, Colorado State University, Ft. Collins, CO, 209 pp.

  • ——, P. Reddy, S. Ryan, and J. J. DeLuisi, 1994: Features and effects of aerosol optical depth observed at Mauna Loa, Hawaii: 1982–1992. J. Geophys. Res.,99, 8295–8306.

    • Crossref
    • Export Citation
  • Frederick, J. E., P. F. Soulen, S. B. Diaz, I. Smolskaia, C. R. Booth, T. Lucas, and D. Neuschuler, 1993: Solar ultraviolet irradiance observed from southern Argentina: September 1990 to March 1991. J. Geophys. Res.,98, 8891–8897.

    • Crossref
    • Export Citation
  • Grainger, R. G., R. E. Basher, and R. L. McKenzie, 1993: UV-B Robertson–Berger meter characterization and field calibration. Appl. Opt.,32, 343–349.

    • Crossref
    • Export Citation
  • Hofmann, D. J., and Coauthors, 1996a: Record low ozone at Mauna Loa Observatory during winter 1994–1995: A consequence of chemical and dynamical synergism? Geophys. Res. Lett.,23, 1533–1536.

    • Crossref
    • Export Citation
  • ——, J. T. Peterson, and R. M. Rosson, 1996b: Climate Monitoring and Diagnostics Laboratory, No. 23, Summary Rep. 1994–1995. Environmental Research Laboratories, Boulder, CO, 161 pp.

  • Komhyr, W. D., C. L. Mateer, and R. D. Hudson, 1993: Effective Bass–Paur 1985 ozone absorption coefficients for use with Dobson ozone spectrophotometers. J. Geophys. Res.,98, 20 451–20 465.

    • Crossref
    • Export Citation
  • Leszczynski, K., K Jokela, L. Ylianttila, R. Visuri, and M. Blumthaler, 1998: Erythemally weighted radiometers in solar UV monitoring:Results from the WMO/STUK intercomparison. Photochem. Photobiol.,67, 212–221.

    • Crossref
    • Export Citation
  • Lubin, D., and J. E. Frederick, 1991: The ultraviolet radiation environment of the Antarctic peninsula: The roles of ozone and cloud cover. J. Appl. Meteor.,30, 478–493.

    • Crossref
    • Export Citation
  • Madronich, S., 1993: The atmosphere and UV-B radiation at ground level. Environmental UV Photobiology, A. R. Young, Ed., Plenum Press, 1–39.

    • Crossref
    • Export Citation
  • Mayer, B., and G. Seckmeyer, 1996: All-weather comparison between spectral and broadband (Robertson–Berger) UV measurements. Photochem. Photobiol.,64, 792–799.

    • Crossref
    • Export Citation
  • McClatchey, R. A., R. W. Fenn, J. E. A. Selby, F. E. Volz, and J. S. Garing, 1972: Optical properties of the atmosphere. Rep. AFCRL-7-0497, Air Force Cambridge Research Laboratory, Bedford, MA, 108 pp.

    • Crossref
    • Export Citation
  • McKenzie, R. L., W. A. Matthews, and P. V. Johnston, 1991: The relationship between erythemal UV and ozone, derived from spectral irradiance measurements. Geophys. Res. Lett.,18, 2269–2272.

    • Crossref
    • Export Citation
  • ——, P. V. Johnston, M. Kotkamp, A. Bittar, and J. D. Hamlin, 1992:Solar ultraviolet spectroradiometry in New Zealand: Instrumentation and sample results from 1990. Appl. Opt.,31, 6501–6509.

    • Crossref
    • Export Citation
  • ——, M. Kotkamp, G. Seckmeyer, R. Erb, C. R. Roy, H. P. Gies, and S. J. Toomey, 1993: First Southern Hemisphere intercomparison of measured solar UV spectra. Geophys. Res. Lett.,20, 2223–2226.

    • Crossref
    • Export Citation
  • McKinlay, A. F., and B. L. Diffey, 1987: A reference action spectrum for ultraviolet induced erythema in human skin. J. Int. Comm. Illum.,6, 17–22.

  • Seckmeyer, G., and Coauthors, 1995: Geographic differences in the UV measured by intercompared spectroradiometers. Geophys. Res. Lett.,22, 1889–1892.

    • Crossref
    • Export Citation
  • Stamnes, K., S.-C. Tsay, W. Wiscombe, and K. Jayaweera, 1988: Numerically stable algorithm for discrete-ordinate-method radiative transfer in multiple scattering and emitting layered media. Appl. Opt.,27, 2502–2509.

    • Crossref
    • Export Citation

Fig. 1.
Fig. 1.

Spectral response of the UVB-1 SN950208 (manufacturer’s specifications) compared to the CIE approved spectrum for the response of human skin.

Citation: Journal of Atmospheric and Oceanic Technology 15, 4; 10.1175/1520-0426(1998)015<0916:CBUIOA>2.0.CO;2

Fig. 2.
Fig. 2.

Erythemal irradiance calculated from spectroradiometer data using CIE-weighted spectra vs erythema measured by UVB-1 SN950208 using the manufacturer’s recommended calibration factor of 0.141 W m−2 V−1. The solid line is a least squares straight-line fit to the data.

Citation: Journal of Atmospheric and Oceanic Technology 15, 4; 10.1175/1520-0426(1998)015<0916:CBUIOA>2.0.CO;2

Fig. 3.
Fig. 3.

The time series of (a) total ozone (Dobson) and (b) the ratio of UVB-1 erythema to spectroradiometer erythema (CIE-weighted spectra) at SZA = 45°. UVB-1 erythema values were calculated using the manufacturer’s suggested calibration factor (0.141 W m−2 V−1). Note that the average of the erythema ratios appears to be close to the slope of the regression line in Fig. 2.

Citation: Journal of Atmospheric and Oceanic Technology 15, 4; 10.1175/1520-0426(1998)015<0916:CBUIOA>2.0.CO;2

Fig. 4.
Fig. 4.

Calibration analysis of the UVB-1 broadband instrument voltages compared to the CIE-weighted spectroradiometer data (erythema) as a function of ozone for SZA = 45°. (a) The top graph shows the raw data plotted against each other for visual inspection. (b) The middle graph shows the ratio (UVB1)/S(CIE) regressed against ozone. Note the strong dependence on ozone and the high correlation coefficient. (c) The bottom graph shows the predicted erythema values calculated by applying the equation in the middle graph to the original UVB1 voltages and then by plotting them against the S(CIE) data, showing that the ozone correction accounts for nearly all of the variability.

Citation: Journal of Atmospheric and Oceanic Technology 15, 4; 10.1175/1520-0426(1998)015<0916:CBUIOA>2.0.CO;2

Fig. 5.
Fig. 5.

Regressions of the ratio (UVB1)/S(CIE) against ozone for various values of SZA. Note that the slope of the regression line is positive for small SZA, near 0 for SZA = 65°, and negative for larger SZA.

Citation: Journal of Atmospheric and Oceanic Technology 15, 4; 10.1175/1520-0426(1998)015<0916:CBUIOA>2.0.CO;2

Fig. 6.
Fig. 6.

The contour plot of the calibration factor to be applied to UVB-1 voltages as a function of SZA and ozone to predict the erythema from UVB-1 voltage measurements. Mathematically, the calibration factor is S(CIE)/(UVB1) μW cm−2 V−1.

Citation: Journal of Atmospheric and Oceanic Technology 15, 4; 10.1175/1520-0426(1998)015<0916:CBUIOA>2.0.CO;2

Fig. 7.
Fig. 7.

The family of calibration factor curves as a function of SZA for various values of ozone. The calibration factor is essentially S(CIE)/(UVB1), so that multiplying the UVB-1 voltage by the calibration factor for the proper SZA and ozone value gives the predicted erythema for the broadband instrument.

Citation: Journal of Atmospheric and Oceanic Technology 15, 4; 10.1175/1520-0426(1998)015<0916:CBUIOA>2.0.CO;2

Fig. 8.
Fig. 8.

The power-law RAFs as a function of SZA for S(CIE)(solid), S(UVB1) (short dashes), and UVB1 (long dashes). All irradiance data were corrected for the eccentricity of the earth’s orbit. Note that for SZA < 45° the datasets were shorter and the average ozone values for the datasets were larger than for SZA > 45°.

Citation: Journal of Atmospheric and Oceanic Technology 15, 4; 10.1175/1520-0426(1998)015<0916:CBUIOA>2.0.CO;2

Fig. 9.
Fig. 9.

Calibration analysis of the UVB-1 broadband instrument voltages compared to the S(UVB1) data as a function of ozone for SZA = 45°. (a) The top graph shows the raw data plotted against each other for visual inspection. (b) The middle graph shows the ratio (UVB1)/S(UVB1) regressed against ozone (note the lack of dependence on ozone). (c) The bottom graph shows the predicted erythema values calculated by applying the equation in the middle graph to the original UVB1 voltages and then by plotting them against the S(UVB1) data.

Citation: Journal of Atmospheric and Oceanic Technology 15, 4; 10.1175/1520-0426(1998)015<0916:CBUIOA>2.0.CO;2

Fig. 10.
Fig. 10.

The family of calibration factor curves as a function of SZA for various values of ozone. The calibration factor is essentially S(UVB1)/(UVB1), so that multiplying the UVB-1 voltage by the calibration factor for the proper SZA and ozone value gives the predicted erythema for the broadband instrument. Note that the ozone dependence is small, as expected. Superposed on this graph is the cosine response of the broadband instrument supplied by the manufacturer for the direct beam (longer dashed line) and total irradiance (longest dashed line).

Citation: Journal of Atmospheric and Oceanic Technology 15, 4; 10.1175/1520-0426(1998)015<0916:CBUIOA>2.0.CO;2

Fig. 11.
Fig. 11.

The calibration analysis of the S(UVB1) data compared to the S(CIE) data as a function of ozone for SZA = 45°. (a) The top graph shows the raw data plotted against each other for visual inspection. (b) The middle graph shows the ratio S(UVB1)/S(CIE) regressed against ozone. Note the strong dependence on ozone and the high correlation coefficient. (c) The bottom graph shows the predicted erythema values calculated by applying the equation in the middle graph to the original S(UVB1) data and then by plotting them against the S(CIE) data, showing that the ozone correction accounts for nearly all of the variability.

Citation: Journal of Atmospheric and Oceanic Technology 15, 4; 10.1175/1520-0426(1998)015<0916:CBUIOA>2.0.CO;2

Fig. 12.
Fig. 12.

The family of calibration factor curves as a function of SZA for various values of ozone. The calibration factor is essentially S(CIE)/S(UVB1), so that multiplying the S(UVB1) data by the calibration factor for the proper SZA and ozone value gives the predicted erythema for the broadband instrument.

Citation: Journal of Atmospheric and Oceanic Technology 15, 4; 10.1175/1520-0426(1998)015<0916:CBUIOA>2.0.CO;2

Fig. 13.
Fig. 13.

Model calculations of the family of calibration factor curves as a function of SZA for various values of ozone using the CMDL version of DISORT to simulate S(CIE)/S(UVB1). This figure may be compared directly to Fig. 12.

Citation: Journal of Atmospheric and Oceanic Technology 15, 4; 10.1175/1520-0426(1998)015<0916:CBUIOA>2.0.CO;2

Fig. 14.
Fig. 14.

Erythemal irradiance calculated from Yankee UVB-1 data for CIE-weighted spectra vs voltages measured by UVB-1 SN950208, using the ozone and SZA correction procedure outlined in this paper. These results may be compared to the raw data prior to corrections shown in Fig. 2.

Citation: Journal of Atmospheric and Oceanic Technology 15, 4; 10.1175/1520-0426(1998)015<0916:CBUIOA>2.0.CO;2

Save
  • Berger, D. S., 1976: The sunburning ultraviolet meter: Design and performance. Photochem. Photobiol.,24, 587–593.

    • Crossref
    • Export Citation
  • Bodhaine, B. A., 1983: Aerosol measurements at four background sites. J. Geophys. Res.,88, 10 753–10 768.

  • ——, and Coauthors, 1996: New ultraviolet spectroradiometer measurements at Mauna Loa Observatory. Geophys. Res. Lett.,23, 2121–2124.

    • Crossref
    • Export Citation
  • ——, E. G. Dutton, D. J. Hofmann, R. L. McKenzie, and P. V. Johnston, 1997: UV measurements at Mauna Loa: July 1995 to July 1996. J. Geophys. Res.,102, 19 265–19 273.

    • Crossref
    • Export Citation
  • Booth, C. R., T. B. Lucas, J. H. Morrow, C. S. Weiler, and P. A. Penhale, 1994: The United States National Science Foundation/Antarctic Program’s Network for monitoring ultraviolet radiation. Ultraviolet Radiation in Antarctica: Measurements and Biological Research, C. S. Weiler and P. A. Penhale, Eds., AGU Antarctic Research Series, Vol. 62, American Geophysical Union, 17–32.

    • Crossref
    • Export Citation
  • DeLuisi, J. J., and J. M. Harris, 1981: Characteristics of ultraviolet radiation in the human erythema band measured with a Robertson–Berger meter and a double monochromator. NOAA Tech. Memo. ERL ARL-99, Air Resources Laboratories, Silver Spring, MD, 43 pp.

  • ——, and ——, 1983: A determination of the absolute radiant energy of a Robertson–Berger meter sunburn unit. Atmos. Environ.,17, 751–758.

    • Crossref
    • Export Citation
  • Dlugokencky, E. J., E. G. Dutton, P. C. Novelli, P. P. Tans, and K. A. Masarie, 1996: Changes in CH4 and CO growth rates after the eruption of Mt. Pinatubo and their link with changes in tropical troposphere UV flux. Geophys. Res. Lett.,23, 2761–2764.

    • Crossref
    • Export Citation
  • Dutton, E. G., 1992: A coherence between the QBO and the amplitude of the Mauna Loa atmospheric transmission annual cycle. Int. J. Climatol.,12, 383–396.

    • Crossref
    • Export Citation
  • ——, and S. K. Cox, 1995: Tropospheric radiative forcing from El Chichon and Mt. Pinatubo: Theory and observations. Atmospheric Science Paper 586, Colorado State University, Ft. Collins, CO, 209 pp.

  • ——, P. Reddy, S. Ryan, and J. J. DeLuisi, 1994: Features and effects of aerosol optical depth observed at Mauna Loa, Hawaii: 1982–1992. J. Geophys. Res.,99, 8295–8306.

    • Crossref
    • Export Citation
  • Frederick, J. E., P. F. Soulen, S. B. Diaz, I. Smolskaia, C. R. Booth, T. Lucas, and D. Neuschuler, 1993: Solar ultraviolet irradiance observed from southern Argentina: September 1990 to March 1991. J. Geophys. Res.,98, 8891–8897.

    • Crossref
    • Export Citation
  • Grainger, R. G., R. E. Basher, and R. L. McKenzie, 1993: UV-B Robertson–Berger meter characterization and field calibration. Appl. Opt.,32, 343–349.

    • Crossref
    • Export Citation
  • Hofmann, D. J., and Coauthors, 1996a: Record low ozone at Mauna Loa Observatory during winter 1994–1995: A consequence of chemical and dynamical synergism? Geophys. Res. Lett.,23, 1533–1536.

    • Crossref
    • Export Citation
  • ——, J. T. Peterson, and R. M. Rosson, 1996b: Climate Monitoring and Diagnostics Laboratory, No. 23, Summary Rep. 1994–1995. Environmental Research Laboratories, Boulder, CO, 161 pp.

  • Komhyr, W. D., C. L. Mateer, and R. D. Hudson, 1993: Effective Bass–Paur 1985 ozone absorption coefficients for use with Dobson ozone spectrophotometers. J. Geophys. Res.,98, 20 451–20 465.

    • Crossref
    • Export Citation
  • Leszczynski, K., K Jokela, L. Ylianttila, R. Visuri, and M. Blumthaler, 1998: Erythemally weighted radiometers in solar UV monitoring:Results from the WMO/STUK intercomparison. Photochem. Photobiol.,67, 212–221.

    • Crossref
    • Export Citation
  • Lubin, D., and J. E. Frederick, 1991: The ultraviolet radiation environment of the Antarctic peninsula: The roles of ozone and cloud cover. J. Appl. Meteor.,30, 478–493.

    • Crossref
    • Export Citation
  • Madronich, S., 1993: The atmosphere and UV-B radiation at ground level. Environmental UV Photobiology, A. R. Young, Ed., Plenum Press, 1–39.

    • Crossref
    • Export Citation
  • Mayer, B., and G. Seckmeyer, 1996: All-weather comparison between spectral and broadband (Robertson–Berger) UV measurements. Photochem. Photobiol.,64, 792–799.

    • Crossref
    • Export Citation
  • McClatchey, R. A., R. W. Fenn, J. E. A. Selby, F. E. Volz, and J. S. Garing, 1972: Optical properties of the atmosphere. Rep. AFCRL-7-0497, Air Force Cambridge Research Laboratory, Bedford, MA, 108 pp.

    • Crossref
    • Export Citation
  • McKenzie, R. L., W. A. Matthews, and P. V. Johnston, 1991: The relationship between erythemal UV and ozone, derived from spectral irradiance measurements. Geophys. Res. Lett.,18, 2269–2272.

    • Crossref
    • Export Citation
  • ——, P. V. Johnston, M. Kotkamp, A. Bittar, and J. D. Hamlin, 1992:Solar ultraviolet spectroradiometry in New Zealand: Instrumentation and sample results from 1990. Appl. Opt.,31, 6501–6509.

    • Crossref
    • Export Citation
  • ——, M. Kotkamp, G. Seckmeyer, R. Erb, C. R. Roy, H. P. Gies, and S. J. Toomey, 1993: First Southern Hemisphere intercomparison of measured solar UV spectra. Geophys. Res. Lett.,20, 2223–2226.

    • Crossref
    • Export Citation
  • McKinlay, A. F., and B. L. Diffey, 1987: A reference action spectrum for ultraviolet induced erythema in human skin. J. Int. Comm. Illum.,6, 17–22.

  • Seckmeyer, G., and Coauthors, 1995: Geographic differences in the UV measured by intercompared spectroradiometers. Geophys. Res. Lett.,22, 1889–1892.

    • Crossref
    • Export Citation
  • Stamnes, K., S.-C. Tsay, W. Wiscombe, and K. Jayaweera, 1988: Numerically stable algorithm for discrete-ordinate-method radiative transfer in multiple scattering and emitting layered media. Appl. Opt.,27, 2502–2509.

    • Crossref
    • Export Citation
  • Fig. 1.

    Spectral response of the UVB-1 SN950208 (manufacturer’s specifications) compared to the CIE approved spectrum for the response of human skin.

  • Fig. 2.

    Erythemal irradiance calculated from spectroradiometer data using CIE-weighted spectra vs erythema measured by UVB-1 SN950208 using the manufacturer’s recommended calibration factor of 0.141 W m−2 V−1. The solid line is a least squares straight-line fit to the data.

  • Fig. 3.

    The time series of (a) total ozone (Dobson) and (b) the ratio of UVB-1 erythema to spectroradiometer erythema (CIE-weighted spectra) at SZA = 45°. UVB-1 erythema values were calculated using the manufacturer’s suggested calibration factor (0.141 W m−2 V−1). Note that the average of the erythema ratios appears to be close to the slope of the regression line in Fig. 2.

  • Fig. 4.

    Calibration analysis of the UVB-1 broadband instrument voltages compared to the CIE-weighted spectroradiometer data (erythema) as a function of ozone for SZA = 45°. (a) The top graph shows the raw data plotted against each other for visual inspection. (b) The middle graph shows the ratio (UVB1)/S(CIE) regressed against ozone. Note the strong dependence on ozone and the high correlation coefficient. (c) The bottom graph shows the predicted erythema values calculated by applying the equation in the middle graph to the original UVB1 voltages and then by plotting them against the S(CIE) data, showing that the ozone correction accounts for nearly all of the variability.

  • Fig. 5.

    Regressions of the ratio (UVB1)/S(CIE) against ozone for various values of SZA. Note that the slope of the regression line is positive for small SZA, near 0 for SZA = 65°, and negative for larger SZA.

  • Fig. 6.

    The contour plot of the calibration factor to be applied to UVB-1 voltages as a function of SZA and ozone to predict the erythema from UVB-1 voltage measurements. Mathematically, the calibration factor is S(CIE)/(UVB1) μW cm−2 V−1.

  • Fig. 7.

    The family of calibration factor curves as a function of SZA for various values of ozone. The calibration factor is essentially S(CIE)/(UVB1), so that multiplying the UVB-1 voltage by the calibration factor for the proper SZA and ozone value gives the predicted erythema for the broadband instrument.

  • Fig. 8.

    The power-law RAFs as a function of SZA for S(CIE)(solid), S(UVB1) (short dashes), and UVB1 (long dashes). All irradiance data were corrected for the eccentricity of the earth’s orbit. Note that for SZA < 45° the datasets were shorter and the average ozone values for the datasets were larger than for SZA > 45°.

  • Fig. 9.

    Calibration analysis of the UVB-1 broadband instrument voltages compared to the S(UVB1) data as a function of ozone for SZA = 45°. (a) The top graph shows the raw data plotted against each other for visual inspection. (b) The middle graph shows the ratio (UVB1)/S(UVB1) regressed against ozone (note the lack of dependence on ozone). (c) The bottom graph shows the predicted erythema values calculated by applying the equation in the middle graph to the original UVB1 voltages and then by plotting them against the S(UVB1) data.

  • Fig. 10.

    The family of calibration factor curves as a function of SZA for various values of ozone. The calibration factor is essentially S(UVB1)/(UVB1), so that multiplying the UVB-1 voltage by the calibration factor for the proper SZA and ozone value gives the predicted erythema for the broadband instrument. Note that the ozone dependence is small, as expected. Superposed on this graph is the cosine response of the broadband instrument supplied by the manufacturer for the direct beam (longer dashed line) and total irradiance (longest dashed line).

  • Fig. 11.

    The calibration analysis of the S(UVB1) data compared to the S(CIE) data as a function of ozone for SZA = 45°. (a) The top graph shows the raw data plotted against each other for visual inspection. (b) The middle graph shows the ratio S(UVB1)/S(CIE) regressed against ozone. Note the strong dependence on ozone and the high correlation coefficient. (c) The bottom graph shows the predicted erythema values calculated by applying the equation in the middle graph to the original S(UVB1) data and then by plotting them against the S(CIE) data, showing that the ozone correction accounts for nearly all of the variability.

  • Fig. 12.

    The family of calibration factor curves as a function of SZA for various values of ozone. The calibration factor is essentially S(CIE)/S(UVB1), so that multiplying the S(UVB1) data by the calibration factor for the proper SZA and ozone value gives the predicted erythema for the broadband instrument.

  • Fig. 13.

    Model calculations of the family of calibration factor curves as a function of SZA for various values of ozone using the CMDL version of DISORT to simulate S(CIE)/S(UVB1). This figure may be compared directly to Fig. 12.

  • Fig. 14.

    Erythemal irradiance calculated from Yankee UVB-1 data for CIE-weighted spectra vs voltages measured by UVB-1 SN950208, using the ozone and SZA correction procedure outlined in this paper. These results may be compared to the raw data prior to corrections shown in Fig. 2.

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