1) Signal offset components

The overall signal offset consists of the dark current signal plus an electronic offset and a stray light contribution. The dark current arises from thermally generated electrons in the CCD and depends mainly on the instrument’s temperature. In contrast to the electronic offset, the stray light and dark current depend on the integration time. Stray light signals include undesired signals originating from other wavelengths or from misguided radiation within the instrument caused by. For example, reflections on the spectrometer walls.

(ii) Stray light

Spectral filters are used for stray light measurements. These filters block certain wavelength regions. Spectral radiation that is measured out of the blocked wavelength range is considered as the stray light contribution (after subtraction of the d + e current). Stray light measurements were performed in the laboratory [using a 1000-W standard tungsten irradiance lamp, traceable to the Physikalisch Technische Bundesanstalt (PTB)] and in atmospheric conditions (using the sun as the radiation source). Atmospheric measurements of the stray light contribution have the advantage that the spectral pattern of the stray light is measured in real conditions. On the other hand, laboratory measurements provide more constant and controlled circumstances. The stray light of the two spectroradiometers was quantified using spectral cutoff filters (manufactured by LOT Oriel, Darmstadt, Germany). Visible (VIS) longwave pass filters (cutting wavelengths λ_c: 400, 600, and 700 nm) have been employed. Here, λ_c is defined as the wavelength where the spectral filter transmission is 50%. A rejection of radiation of ≤99% is reached at 0.9λ_c. If the spectroradiometer measures a signal that differs from the d + e current below 0.9λ_c, then the difference between the measured counts I_Filter and the d + e current I_d+e using a longwave pass filter with λ_c is defined as the stray light signal:

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Figures 3a, 3c and 3e show the spectral stray light signals I_SL for the AFDM-CCD derived from the laboratory experiments using different longwave pass filters. For comparison, results for the AFDM-PDA are depicted in Figs. 3b, 3d and 3f, respectively. Additionally, the counts (minus I_d+e) of the lamp spectrum measurement (with no filter) are displayed (I_Lamp). The different sensitivities of the AFDM-PDA and the AFDM-CCD cause significantly different spectral courses of the filtered and nonfiltered measurements (Figs. 3a and 3b) even though the same lamp was used. Figures 3c and 3d display the stray light counts I_SL in a limited wavelength range (280–450 nm) on a logarithmic scale. Note that the curves in Figs. 3c–f are plotted up to a wavelength that corresponds with the filter cutting wavelength 0.9λ_c. It is shown that the level of stray light counts below the cutoff wavelength of the filter depends on the filter that is used for the following reasons. (a) The measured signal using a filter results in a generally lower signal due to the transmission of the filter (not identical to one) even in the spectral range larger than the cutting wavelength. (b) The broader the filter range is, the more the signal decreases. It is quite evident that lower signals cause lower stray light. However, the spectral shape of the stray light contribution can be studied from this type of figure. In contrast to the AFDM-PDA, the AFDM-CCD shows a distinct wavelength dependence of the stray light counts I_SL with a maximum around 340–350 nm. The influence of the stray light contribution on F_a and J values is discussed in section 3.

In Figs. 3d and 3e the stray light counts I_SL are scaled to the lamp spectrum. Here, I_SL influences the total signal mainly in the UV spectral range below 320 nm (contribution up to 30%). For the AFDM-CCD the stray light contribution is less than 5% between 330 and 580 nm. Above 580 nm the stray light contribution slightly increases again due to the decreased sensitivity of the AFDM-CCD in this spectral range (see next subsection). In contrast, the stray light contribution of the AFDM-PDA decreases rather continuously with increasing wavelength up to a value of less than 0.1% (see Fig. 3f). However, the stray light contribution related to the lamp spectrum for the critical UV range is quite comparable for both spectroradiometers for wavelengths below 400 nm.

Field measurements were analyzed with the stray light spectra derived from the laboratory data and were compared with spectra analyzed with the stray light spectrum obtained from the atmospheric measurements. A difference of ±3% was derived mainly in the first nanometer of the actinic flux density spectrum. For wavelengths above 304 nm the difference between the I_SL spectra obtained in the laboratory to those from field measurements decreased to less than 1%. In addition, J(O¹D) values calculated with the two stray light distributions were compared. An overall difference of less than 2% was quantified, which justifies the use of a predefined stray light spectrum from the laboratory measurements for the evaluation of field data.

2) Sensitivity

The sensitivity D(λ) of the AFDM-CCD spectroradiometer (and the AFDM-PDA) is quantified by the conversion factor that transforms the measured spectral counts (I) into the actinic flux density:

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The procedure to determine D(λ) is called absolute calibration where a standard irradiance lamp with known values of F(λ) is used. For an incident angle of radiation of θ = 0°, F_a and F are equivalent. The absolute calibration was performed with a standard 1000-W lamp (traceable to PTB). The standard irradiance is certified for a distance of 700 mm between the calibration lamp and the optical inlet of the spectroradiometer. To improve the calibration accuracy the procedure is carried out with two calibration distances. The first set of measurements was done at the calibration distance of 700 mm (given in the manual of the manufacturer). A second set of calibration measurements was collected at a closer distance (≈400 mm) between the lamp and the optical inlet. The latter increases the signal magnitude, which helps to improve the accuracy of the sensitivity measurement in particular in the spectral region of the CCD with low sensitivity. Each set of measurements consists of a series of lamp measurements I_Lamp(λ); filter scans with a longwave pass filters of F320 and F700; and d + e measurement I_d+e(λ) (with obscured optical inlet).

The stray light counts using a longwave pass filter with λ_c = 320 nm (I_SL320) and λ_c = 700 nm (I_SL700) were determined via Eq. (3). As shown above, the stray light of the CCD instrument is slightly wavelength dependent (see Fig. 3c). The stray light counts are derived from the averaged counts between 270- and 305-nm wavelength using a longwave pass filter with λ_c = 320 nm. This average serves as a reference signal to scale the filter measurement using the filter with λ_c = 700 nm, which defines the spectral shape of the stray light, with a scaling factor (s₁):

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The spectral counts calculated with

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are determined for both distances. In this way a second scaling factor (s₂) is derived that links the measurements of the “near” and “far” calibrations. The factor is calculated by dividing the direct signals for each pixel. In theory the ratio should be independent of wavelength. However, due to the low sensitivity, in particular below 320 nm and above 520 nm, the measured scaling factor s₂ is noisy. Hence, the final scaling factor s₂ is determined by the ratio of the wavelength-averaged signals between 370 and 430 nm (range with lowest noise of s₂) of the near and far calibrations:

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Now the scaling factor s₂ enables a conversion of the near signals to signals at 700-mm distance. Finally, the revised far signals are used to determine the calibration factors.

Figure 4 displays the spectral sensitivities [given in units of counts per (photons cm⁻² s⁻¹ nm⁻¹)] of the AFDM-PDA spectroradiometer and the AFDM-CCD with and without using a bandpass filter (UG5, manufactured by SCHOTT AG, Mainz, Germany). Here, D(λ) includes the sensitivity of the detector and the transmission characteristics of the optical inlet and the optical fiber. The UG5 transmission ranges from 89% at wavelengths around 350 nm to 0.7% at 580 nm. In the UV spectral range the AFDM-CCD has a sensitivity in the order of 10⁻⁹ counts per (photons cm⁻² s⁻¹ nm⁻¹), whereas the sensitivity of the AFDM-PDA is one order of magnitude lower [10⁻¹⁰ counts per (photons cm⁻² s⁻¹ nm⁻¹)]. The spectral patterns of the AFDM-PDA and AFDM-CCD (without the UG5 filter) sensitivities are quite homogeneous over the entire spectral range. The sensitivity of the AFDM-CCD with the UG5 filter exhibits a strong wavelength dependence. This bandpass filter reduces the sensitivity mainly in the VIS spectral range by two orders of magnitude from 10⁻⁹ to 10⁻¹¹ counts per (photons cm⁻² s⁻¹ nm⁻¹). In this way the bandpass filter avoids rapid saturation of the detector in the VIS range even during measurements with low integration times (20 ms). Hence, the main purpose of this UG5 bandpass filter is the adjustment of the sensitivity considering the entire wavelength range with respect to the available solar radiation. The loss of sensitivity in the VIS is negligible due to the gain of solar radiation in the VIS by five orders of magnitude compared to the UV-B. The second advantage of using the UG5 filter is the reduction of stray light by about 50%.

3) Noise and detection limit

The precision of spectroradiometer measurements is defined by the noise of the measured signals for constant measurement conditions. A quantitative measure of the noise is the signal-to-noise ratio (SNR), which is defined by

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Here, I is the average of the raw counts and sdv is the standard deviation. The precision of a spectroradiometer measurement is defined as P = 1/SNR, where P gets smaller with an increased SNR.

Using a calibration lamp for the measurement of SNR causes additional noise due to the limited stability of the lamp output. Therefore, d + e measurements with an obscured optical inlet were performed instead of measurements with a lamp to quantify the SNR. The SNR of the AFDM-CCD was determined by the mean and standard deviation of 1000 d + e measurements using different integration times (5–400 ms). In contrast to the AFDM-PDA (σ = 2 counts), the standard deviation σ of the AFDM-CCD measurements depends on the integration time as shown in Fig. 5a. The 1000 d + e measurements for each integration time were averaged, and afterward the mean spectrum was averaged over all wavelengths. The error of the latter calculation is considered by the standard deviation. The corresponding error bars are less than the symbol size in Fig. 5a; therefore, they are not plotted in this figure. The integration time dependence of σ has an effect on the SNR, which results in a decrease of the AFDM-CCD SNR with integration time (see Fig. 5b). For typical integration times between 100 and 300 ms, values of SNR between 450 and 550 are obtained. In contrast to the AFDM-CCD, the AFDM-PDA has an SNR ranging between 150 and 180 for the same integration times. Consequently, an improvement of the SNR (AFDM-CCD) in the range of a factor of 3 is obtained compared to the SNR of the AFDM-PDA.

The limit of detection, also called the noise equivalent irradiance (NEI), describes the lowest meaningful actinic flux density that can be reasonably measured. NEI is determined by the standard deviation of the d + e current σ and is calculated with

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NEI depends on the wavelength mainly due to the wavelength dependence of the sensitivity D(λ). A calculation of NEI is not well defined due to the variation of σ with integration time. Therefore, NEI was determined for two assumed values of σ (three and five counts). The spectrally dependent detection limit of the AFDM-CCD with the UG5 filter ranges between 10⁹ photons cm⁻² s⁻¹ nm⁻¹ (UV-B) and 5–10¹¹ photons cm⁻² s⁻¹ nm⁻¹ (VIS). It is improved in the UV-B by one order of magnitude compared to the NEI of the AFDM-PDA system (UV-B, 10¹⁰ photons cm⁻² s⁻¹ nm⁻¹; VIS, 3–10¹⁰ photons cm⁻² s⁻¹ nm⁻¹), which is more spectrally homogeneous.

4) Effects of spectral resolution and FWHM

The influence of the spectral resolution and full width at half maximum (FWHM) with respect to the photolysis frequency of ozone, J(O¹D), which is particularly sensitive to the spectral resolution and FWHM, was investigated using radiative transfer simulations. The calculations were performed with the “uvspec” model from the libradtran package (Mayer and Kylling 2005). Actinic flux density spectra were computed using the extraterrestrial spectrum with 0.1-nm resolution (Kurucz 1992). These spectra were adjusted to the spectral resolution of the AFDM-PDA and the AFDM-CCD (both 0.8 nm) and convoluted with different slit functions according to the FWHM of both spectrometers (AFDM-PDA, ∼2.6 nm; AFDM-CCD, ∼1.5 nm). Finally, J(O¹D) data were derived from the adjusted actinic flux density spectra and compared to J(O¹D) values derived from nonconvoluted spectra using absorption cross-section data published by Daumont et al. (1992) and quantum yields taken from Matsumi et al. (2002). An improvement of the J(O¹D) accuracy in the range of 2%–4% was found for the AFDM-CCD spectroradiometer compared to the AFDM-PDA.

The impact of the spectral resolution on the accuracy of J(O¹D) was also studied. As reported by Madronich and Weller (1990), the deviation between J(O¹D) derived for Δλ = 0.1 nm and Δλ = 0.8 nm can get as high as 1% depending on the SZA.

5) Uncertainty estimation

The main sources of measurement uncertainties of the AFDM-CCD are quantified in Table 2. They are taken from Jäkel (2005). The largest uncertainty arises from the absolute calibration. The temporal drift of the absolute calibration and the uncertainty due to disconnection and reconnection of the optical fibers with the spectrometer are continuously observed with the transfer calibration. These transfer calibrations are performed in the laboratory and during field campaigns using different 200-W lamps. For the transfer lamps an uncertainty of ±3% is estimated. The determination of the certified distance from the irradiance standard to the receiving plane of the optical inlet leads to an uncertainty of less than ±1%. In addition to the absolute calibration the spectral calibration represents the second major source of uncertainty in the UV spectral range. The manufacturer specifies an absolute wavelength accuracy of about 0.3 nm. To calculate the related uncertainty, spectra were artificially shifted by 0.3 nm. The ratio of the original spectra and the shifted spectra was calculated, and an uncertainty of ±5% in the UV range and of less than ±1% in the VIS range was observed. The error due to the nonideal angular response of the optical inlet was considered in the angular correction of the data depending on various parameters. A remaining uncertainty for that kind of correction can only be estimated (±2%). The uncertainty resulting from the signal offset components mainly affect the lowest wavelength of the measured spectra (first 3 nm). They were estimated to be ±5% for the d + e current and ±3% for the stray light contribution. These results yield a total uncertainty estimate of ±10% in the UV range and ±5% in the VIS range, calculated with Gaussian error propagation.

In terms of the J(O¹D) [J(NO₂)] uncertainty, the stray light determination results in an uncertainty contribution of <±2% [<±1%]. Small-scale variations of the d + e current cause an uncertainty of ±3.5% [<±1%]. Furthermore, the FWHM and spectral resolution contribute with <±1% each. The contribution of the spectral calibration uncertainty is <±1%. It results in an overall J(O¹D) [J(NO₂)] uncertainty of ±8% [±6%] including the calibration and angular response uncertainties presented in Table 2.

1) Actinic flux densities

Figure 7a shows the artificial spectra of the PDA spectroradiometer DEM, the AFDM-CCD, as well as the ATI and GBM spectra in a logarithmic plot measured on 6 May 2004 (1030–1051 UTC) at SZA = 33°. The spectral range of between 294 and 310 nm is considered the most crucial range with regard to the sensitivity of the spectroradiometers. For wavelengths larger than 310 nm (to 500 nm), all results agree within ±10%. The double-monochromator spectra (ATI and GBM) are considered to be the measurements with the lowest uncertainty in the UV-B spectral range due to their high quality of stray light rejection. Nevertheless, the mean ratio between GBM and ATI (λ = 297–310 nm) of 1.03 ± 0.07 indicates an increased uncertainty compared to the average range of λ = 310–500 nm (GBM/ATI = 0.99 ± 0.01). The DEM spectrum starts at a larger wavelength (301 nm) compared to the double-monochromator spectra (294.5 and 295.5 nm, respectively). The AFDM-CCD spectrum shows an underestimation below 298.5 nm compared to the ATI and GBM spectra. The reason is the problematic determination of the offset. The offset represents a small difference of two signals with a high number of counts (measured signal minus d + e current) and this is highly error prone.

The spectral ratios of the actinic flux density spectra of all spectroradiometers and the ATI double monochromator for both measurements are plotted in Fig. 7b. With minor exceptions all spectra agree with the ATI data above 305 nm within ±10%. The deviations exceeding ±10% possibly originate from (i) an insufficient 0.5-nm interpolation of the spectra, (ii) uncertainties in the wavelength calibration, or (iii) an inaccurate time synchronization. Interpolation uncertainties are considered as negligible due to the fact that the GBM data are not interpolated. Nevertheless, a spectral structure of the GBM–ATI is obvious that is similar to the AFDM-CCD/ATI ratio. The uncertainty of wavelength shifts was estimated by shifting a simulated F_a spectrum by 0.2 nm. Systematic deviations of up to 10% were found, which decreased with increasing wavelength. The main effect on the spectral course of the ratios was attributed to insufficient time synchronization. This results in increasing variations between different measurements, in particular for variable cloud conditions. This fact emphasizes the need for temporal high-resolution data collection. Exemplarily, two F_a spectra taken by the AFDM-CCD within 3 s were compared. Deviations of ±20% were noticed in this short period of time.

The ratio between the double-monochromator spectra and the AFDM-CCD spectrum clearly shows the increased uncertainty of the AFDM-CCD below 300-nm wavelength (Fig. 7b). However, compared to the DEM spectroradiometer, the AFDM-CCD follows best the spectra of the double monochromators toward lower wavelengths as a result of the higher sensitivity in this spectral range.

In Fig. 8 the diurnal pattern of the ratios between the double monochromator and AFDM-CCD is depicted. For this purpose these ratios were calculated for each measurement (all in all, 32 ratios). Figure 8 shows the ratios for different wavelengths from 300 nm up to 350 nm. Additionally, the SZA is plotted. In addition to the dependence on the SZA, the atmospheric conditions also influence the accuracy of the AFDM-CCD measurements. For large SZA and overcast conditions the intensity of the downwelling radiation is reduced and a higher sensitivity of the detector is required. The improved agreement between AFDM-CCD and the two double monochromators with increasing wavelength is obvious. Exemplarily for 300-nm wavelength, the ratio between GBM and AFDM-CCD ranges between 0.7 and 1.4, whereas for 301 nm the ratios are mostly concentrated around the ±10% range. One has to keep in mind that wavelength shifts and time synchronization problems may have an impact on these results. A closer look at Fig. 8a shows that even the differences between the two double monochromators for 300 nm can reach 10%.

2) Photolysis frequencies

Photolysis frequencies of O₃ and NO₂ were calculated from the corrected AFDM-CCD and PDA actinic flux density spectra and from the double-monochromator spectra. For J(NO₂) [J(O¹D)], absorption cross-section data were taken from Merienne et al. (1995) (Daumont et al. 1992), while the quantum yield data stem from Troe (2000) (Matsumi et al. 2002). The use of J(NO₂) and J(O¹D) investigates the AFDM-CCD’s capability to determine J values in the UV-A and UV-B compared to the PDA and to the double-monochromator measurement method.

The ratios of the J values derived from AFDM-CCD/DEM/GBM measurements and the J values with respect to the ATI were calculated. A time series of the ratios for J(O¹D) and J(NO₂) is plotted in Fig. 9. The smallest deviations of J(O¹D) values are found for the GBM (average ratio, 0.97; standard deviation, 0.19) and the AFDM-CCD data (0.99 ± 0.20). The PDA spectroradiometer underestimates J(O¹D) (0.90 ± 0.20), caused by the underestimation of the UV-B radiation and the shift of the start wavelength of the DEM spectra to larger wavelengths (see Fig. 7). Figure 9b displays the ratio of the J(NO₂) values. Nearly all ratios are within the ±10% range, whereby the best agreement was found for the GBM and AFDM-CCD, each with a mean ratio of 0.99 (±0.01). The ratio of the DEM spectroradiometer shows again a small underestimation compared to the ATI data (0.97 ± 0.29).

The advantage due to the high temporal resolution of the AFDM-CCD is demonstrated by comparing the derived J values with ATI results, using different scan times (ATI, 21 min per spectrum; AFDM-CCD, 200 ms per spectrum). For this comparison the J values of the AFDM-CCD were averaged over the time interval, when the ATI spectroradiometer scanned the corresponding wavelength range [for J(O¹D), 290–330 nm; for J(NO₂), 290–420 nm]. Table 4 summarizes the results for the measurements on 6 May 2004. The averaged values from the AFDM-CCD agree with the ATI data within ±3%. The standard deviations of the AFDM-CCD values show the variability that is missed by the low temporal resolution measurements. The variability of J_AFDM-CCD during one ATI measurement is greater for J(NO₂) (4%–24%) than for J(O¹D) (2%–10%), because clouds impact upon the UV-A and VIS portions of the spectrum more than they do upon the UV-B (Seckmeyer et al. 1996; Crawford et al. 2003).