The instrument in focus of this study is the UVPFR sunphotometer, which is a modified version of the precision filter radiometer (PFR) designed and built in the late 1990s at PMOD/WRC in Davos, Switzerland. It measures direct solar irradiance at the four nominal wavelengths 305, 311, 318 and 332 nm at bandwidths of approximately 1.0–1.3 nm at full width at half maximum (FWHM). The detectors are operated in a controlled environment and are exposed to solar radiation only during actual measurements. A Peltier thermostat maintains the ion-assisted deposition filters and silicon detectors at a constant (±0.1 ∘C) temperature of 20 ∘C over an ambient temperature range from -20 to +35 ∘C. A shutter opens for only a few seconds during DS measurements to keep dose-related degradation of the filters and detectors to a minimum. The vacuum tight sensor head is filled with dry nitrogen gas. In addition to the information given here, a more detailed description can be found in Ingold et al. (2001).

A recent improvement of the instrument was the addition of an UG11 low-pass filter at all four channels to remove out-of-band leakage that had been observed in the original version of the UVPFR.

The spectral response functions of the UVPFR no. 1001, used in this study, were measured in the laboratory at PMOD/WRC in February 2016, using an EKSPLA NT 200 tuneable laser (http://www.ekspla.com) as spectral light source. The resulting effective central wavelengths and FWHM are given in Table 1. The spectral response functions have also been convolved (spectral weighting taking into account each filter's spectral response function) with an extraterrestrial solar spectrum and the results are given in column 3 of Table 1. The latter are the wavelengths used for calculating the Rayleigh optical depth for the UVPFR no. 1001. (The differences in Rayleigh optical depth for the two different sets of effective central wavelengths are < 0.0007.) The spectral response functions measured in 2016 were also compared with measurements that were performed at the initial stage of the instrument development, in 1999. The difference in effective central wavelengths was ≤ 0.05 nm at all four wavelengths. For the two shortest and therefore most sensitive wavelengths, the difference was only 0.02 nm.

In order to perform DS measurements, the UVPFR is mounted on a sun tracker so that it is continuously pointing to the Sun. The four photometric channels are measured simultaneously by a commercial data logger system (Campbell Scientific CR10X) with 13 bit resolution. Automatic signal ranging within the PFR and logger system is used to increase the dynamic range to 16 bit. The logger clock is frequently updated to be accurate within 1 s. Signal measurements made at full minutes are averages of 10 samples for each channel made over a total duration of 1.25 s and can be considered as instantaneous values.

The full field of view of the instrument is 2.5∘ and the slope angle is 0.7∘. An optical position sensor monitors the solar pointing within a ±0.5∘ range. Normally, the air pressure at station level is measured with a relative coarse accuracy (±1.0 hPa) barometer (Vaisala PTB101 or Setra Model 278) connected to the UVPFR logger box.

The standard PFR has the same specifications as the UVPFR except that the PFR measures at the nominal wavelengths 368, 412, 500 and 862 nm with a 5 nm FWHM bandwidth. The PFR, together with an evaluation of different calibration methods, has been described in detail by Wehrli (2000).

The Brewer spectrophotometer (Kerr et al., 1985) is an instrument designed for automated measurements of solar UV irradiance and through them for the retrieval of atmospheric ozone (total column and vertical profile) and sulfur dioxide (SO2). A special version of the instrument (Mk IV) is also able to measure (total column of) nitrogen dioxide (NO2) in the VIS range. For the standard TCO measurements direct solar irradiance (DS) is measured quasi-simultaneous at predefined wavelengths in the UV. The Brewers are also equipped with a global entrance port through which global irradiance spectra are measured.

AOD can be retrieved from the standard DS measurements (e.g., Cheymol and De Backer, 2003) or spectral DS measurements (Kazadzis et al., 2007). In the current study AOD retrievals from the double monochromator Brewer MkIII no. 163 at the wavelengths 306.3, 310.1, 313.5, 316.8 and 320.0 have been used.

The UVPFR was calibrated at the Izaña Atmospheric Observatory (IZO) on the island of Tenerife (28.31∘ N, 16.50∘ W) at an altitude of 2373 m. At IZO, the Izaña Atmospheric Research Centre (IARC) manages the Regional Brewer Calibration Center – Europe (RBCC-E) and it is the absolute Sun calibration facility of PHOTONS and the Red Ibérica de medida Fotométrica de Aerosoles (RIMA) networks. PHOTONS and RIMA are federated networks of AERONET. In addition, IZO has been recognized as a World Meteorological Organization Commission for Instruments and Methods of Observation (WMO-CIMO) testbed for aerosol remote sensing instruments including AERONET and GAW-PFR instrumentation.

The home site of the UVPFR is at PMOD/WRC, which is located in Davos in the Swiss Alps (46.81∘ N, 9.84∘ E) at an altitude of 1590 m. At PMOD/WRC several world references for meteorological radiation measurements are maintained. Among others, it hosts the World Optical depth Research and Calibration Centre (WORCC), which maintains the reference triad of PFRs for the global GAW-PFR AOD network.

Calibration of reference sunphotometers with the Langley technique is preferably performed at high-altitude stations since it requires low and stable aerosol load (e.g., Shaw, 1983). Difficulties with Langley calibration at a low-altitude and urban site, when calibration at a high altitude is not possible, have been discussed by Arola and Koskela (2004) and were recently demonstrated by Diémoz et al. (2016). For instruments measuring at wavelengths affected by absorption in ozone, an ideally stable total ozone amount is needed during the Langley related period of measurements. These requirements can be relatively frequently fulfilled at IZO.

During May to August 2015 the UVPFR no. 1001 was operated at the IZO station, with the exception of the time period from the 20 May to 10 June. In September 2016 the next Langley calibration at IZO was performed. In addition to the favorable measurement conditions an advantage of the IZO station is the co-location with other instruments, such as Brewer spectrophotometers and standard PFR sunphotometers. These instruments measure among others TCO and AOD in the 368–862 nm range, respectively. These additional variables are highly valuable and help to determine whether measurement conditions during half days (mornings or afternoons) have been suitable for the so-called Langley plot calibrations.

The classic Langley method to determine the calibration constant V0 of each wavelength channel (V0 being equal to the signal that would have been measured at the top of the atmosphere at mean Sun–Earth distance) has been described in many articles on sunphotometry (e.g., Shaw, 1983) and many variations thereof have been published over the last decades. The method is based on the inversion of the so-called Bouguer–Lambert–Beer law, leading to ln⁡R2V=ln⁡V0-δm,

where the wavelength-dependent quantities ln(V0) and total optical depth δ can be determined by least-squares methods from a number of cloud-free measurements of V taken at different air masses m. R is the actual Sun–Earth distance expressed in fraction to 1 AU. The calibration constant V0 used to be found by linear extrapolation to zero air mass of measurements V, corrected to mean Sun–Earth distance, and plotted on a logarithmic scale versus air mass. This method is historically called Langley plot calibration (Langley, 1903).

Using a single, common air mass m for all components of the total optical depth can lead to significant errors in ln(V0) (e.g., Thomason et al., 1983; Forgan, 1988; Russell et al., 1993; Schmid and Wehrli, 1995; Slusser et al., 2000). Two more accurate variants of the Langley extrapolation used here replace δm by the individual air mass and optical depth components for Rayleigh scattering (r), ozone absorption (o) and aerosol extinction (a), i.e., δrmr+δomo+δama, and solve either of the equations ln⁡R2V+δrmr+δomo=ln⁡V0-δama  orln⁡R2V+δrmr=ln⁡V0-δo+δam2ODw for ln(V0) and aerosol optical depth (Eq. 2) or the sum of the two terms ozone and aerosol optical depth (δo+δa) (Eq. 3). The air mass term m2ODw is the ozone and aerosol optical depth weighted sum of mo and ma, i.e., m2ODw=δomo+δamaδo+δa. The values of ozone optical depth and AOD at IZO used in Eq. (2) and for calculating m2ODw according to Eq. (4) are calculated from total ozone measured by the RBCC-E Brewer spectrophotometer triad (WMO/GAW, 2015) and from the AOD measured by a standard PFR sunphotometer determining AOD at 368, 412, 500 and 862 nm, extrapolated to the actual UV wavelength using the Ångström relation. Langley calibrations based on Eq. (2), sometimes called refined Langley plots (Schmid and Wehrli, 1995), do not require any a priori AOD estimate and ozone changes are taken into account if measured correctly. In contrast, based on numerical tests, V0 results of an individual Langley event using Eq. (3) were found less sensitive to errors in δo. The reason for this should be that when using Eq. (3) the actual value of (δo+δa) is calculated from the linear fit of the Langley plot data and δo is in this case not calculated directly from (uncertain) ozone cross sections and TCO. Values of δo, based on TCO measurements by a Brewer, are still used in the weighting of m2ODw. But since δo at the three shortest UVPFR wavelengths are about 10 times, or more, higher than δa, relatively small errors in δo will not have a large impact on m2ODw and the following determination of V0. For the Langley calibration of the UVPFR at the IZO station, very accurate measurements of both TCO and AOD (368–862 nm) were available. As a result, the average V0's at all UVPFR wavelengths differ 0.2 % or less between the two methods.

From the quality of the linear fit of the Langley plot and using TCO and AOD data from the other instruments, the selection of exact air mass range (within 1.2–2.9) and validity of the Langley plot events were mainly based on subjective judging by the analyst. During the periods when the UVPFR no. 1001 was at IZO, 27 accepted Langley plot occasions were found in 2015 and 11 were found in 2016. The resulting V0's from these events in 2015 for the method in Eq. (3) are shown in Fig. 1. In addition to the requirement of stable AOD, for the UVPFR it is important to have a stable ozone amount over the site. Otherwise, when very accurate ozone measurements are available, as from the RBCC-E Brewer triad, small ozone changes during the Langley plot periods can be accounted for. From the Brewer measurements the ozone change during each Langley event was calculated by fitting a linear function to the available TCO measurement data with respect to air mass. The slope of the fit is the change in ozone per unit air mass. The final V0's are then derived from interpolation to zero ozone change as shown in Fig. 1. From this figure it is also evident that the sensitivity to ozone change is low for the 332 nm channel. The sensitivity increases with decreasing wavelength. For the 305 nm channel there is more than 1 % change in V0 per 1 DU change per unit air mass during a Langley event. Similar results were found for the Langley plots in 2016.

In principle, TCO can also be estimated by the UVPFR itself. It is, however, believed that Brewer spectrophotometers are superior to the UVPFR in TCO determination. At the same time, it is important to remember that the Langley plot calibration of the UVPFR becomes dependent on the ozone measurements when these are used to correct for ozone changes during Langley events. In case there is a small air-mass-dependent error in the Brewer (triad) measurements, there will also be an error in the UVPFR V0's.

As is clear from Fig. 1, taking just a single Langley plot event is not enough, if high accuracy accompanied with uncertainty estimation is aimed for. The (experimental) standard deviation of the V0 of the refined method in 2015 is highest for the shortest wavelength (1.28 %) and smallest for the longest wavelength (0.44 %). The standard deviation of the residuals to the linear fit of V0's from Eq. (3) versus ozone change is 0.99 % at the shortest wavelength and very close to the standard deviation of V0 of the refined method at the other wavelengths. The standard deviations of the V0's in 2016 were slightly lower than for the larger number of Langley plot results in 2015. In addition, the (experimental) standard deviation of the mean V0 for the two periods was 0.25 and 0.23 %, respectively, at the shortest wavelength.

The final calibration values are shown in Table 2. Over the period of slightly more than 1 year between the calibrations at IZO, the decrease in sensitivity was as small as ≤ 0.2 % at the two shortest wavelength channels. For the 332 nm wavelength the change was -1.0 % and for the apparently least stable channel (318 nm) the change was -1.1 %. With only one channel just exceeding the goal stability of ≤ 1 % per year, the stability of the UVPFR no. 1001 is regarded as satisfactory.

Also, the PFR-N24 used in this study was calibrated by the refined Langley method in 2015. This was done at the high-altitude station at the Mauna Loa Observatory, Hawaii. After this calibration, the PFR-N24 was included as a new member in the WORCC PFR triad operated at PMOD/WRC.

Both Brewer no. 163 and the UVPFR no. 1001 participated in the 10th RBCC-E campaign 27 May–4 June 2015 at the INTA (Instituto de Técnica Aerospacial) El Arenosillo station in southern Spain (37.10∘ N, 6.73∘ W; 41 m). In addition to the regular calibration of the ozone measurements, Brewer no. 163 was also absolutely calibrated for AOD determinations versus the UVPFR no. 1001 during this RBCC-E campaign. Using this calibration, UV AOD has been determined from Brewer no. 163 during its measurements at PMOD/WRC in Davos. In addition, as part of the regular operations at PMOD/WRC, the sensitivity of Brewer no. 163 is monitored by taking measurements against reference lamps through the global entrance port. During the period analyzed in this study the irradiance sensitivity of the Brewer varied within ±1.2 %, indicating good stability of the measurements taken through both the global and the direct entrance ports.

Due to the large variation with wavelength of ozone absorption in the UV, spectral transmission measurements need to be performed at well-defined and narrow passbands in this wavelength region. The bandwidth of the UVPFR filters, on the order of 1 nm, is significantly narrower than for standard VIS–NIR sunphotometers, but about twice as wide as the slit functions of Brewer spectrophotometers. Therefore, the effect of finite bandwidths was investigated for the UVPFR. Effective central wavelengths and FWHM are given in Table 1.

Due to the very strong increase in ozone absorption with decreasing wavelength, and hence its stronger change with air mass at the shorter wavelength side of the filter band passes, this leads to an increase in the effective wavelengths seen by the UVPFR when the air mass increases. This in turn leads to errors in the extrapolation to zero air mass during a Langley calibration. The FWHM effect has been quantified with simple but high resolution modeling with the Bouguer–Lambert–Beer law.

Using an extraterrestrial solar spectrum of 0.05 nm resolution with a 0.01 nm increment (Egli et al., 2013), together with ozone absorption coefficients for 223 K from Molecular Spectroscopy Lab, Institute of Environmental Physics (IUP), University of Bremen (Serdyuchenko et al., 2011), direct solar irradiance spectra at the surface were calculated for different air masses and TCO amounts. The IUP ozone cross sections were chosen by convenience since they matched the 0.01 nm resolution of the used extraterrestrial solar spectrum. This was not the case for the cross sections by Bass and Paur (1985) which are used in the operational TCO determinations by the Brewers, as well as for the AOD determinations with both the UVPFR and the Brewer, discussed later in this study. It is assumed that the choice of ozone cross sections does not significantly affect the modeled FWHM effects within their estimated uncertainty.

The aerosol extinction was modeled using the Ångström law, AODλ=βλ-α (Ångström, 1929), with the parameters α=1.3 and β= AOD1000nm=0.012. Ångström (1929) suggested that values of α would normally be within 1.0 to 1.5. From this, and many more recent measurements, the conventional value of 1.3 has emerged; see, e.g., Gueymard (1998). During the Langley calibrations at IZO, α determined from AOD retrievals with standard PFR sunphotometer was always found to be less < 2, with an average value of about 1.5. With parameters α=1.3 and β=0.012 AOD at 305 nm becomes 0.056 and this value was slightly higher than the mean value during accepted Langley plot events. In the end, no matter if α=2 had been used, with the low AOD present at IZO the influence of finite bandwidths due to aerosol extinction varying with wavelength was found to be negligible.

In the calculations a station pressure of 770 hPa was used, which is close to the average value at the IZO station during the evaluated Langley plot events. Effective ozone altitude was set to 25 and 22 km for calculations corresponding to measurements at Izaña and Davos, respectively. These values on ozone altitude were also used for the Langley calibrations at IZO (Sect. 2.2) and for the AOD determinations in Davos (Sect. 5). For the relative optical air mass for ozone absorption the algorithm/formula by Komhyr et al. (1989) was used. Rayleigh optical depth, δr, was calculated according to Bodhaine et al. (1999) and the relative optical air mass for Rayleigh scattering was calculated according to Kasten and Young (1989). The aerosol relative optical air mass, ma, was estimated by an algorithm for water vapor air mass, mw (Gueymard, 1995). The vertical distribution of the aerosol particles is generally not known but also in other AOD calculations the aerosol air mass has been approximated by mw, e.g., for the GAW-PFR network (McArthur et al., 2003; Wehrli, 2008). Finally, the calculated irradiance spectra were convolved with the measured spectral response functions of UVPFR no. 1001.

Results of Langley plots of the simulated UVPFR direct irradiances, V0,λ (Langley), were then compared to the extraterrestrial irradiances calculated by convolving the extraterrestrial spectrum with the UVPFR spectral response functions, V0,λ,true. The FWHM effect is mainly dependent on ozone amount and air mass range. On average the air mass range was 1.3–2.8 and average TCO was 290 DU during the Langley plots at Izaña. For these conditions, the V0 correction factors cFWHM=V0,λ,true/V0,λ(Langley) were estimated to cFWHM= [1.012, 1.003, 1.001, 1.000] for the UVPFR channels from the shortest to the longest wavelength.These values are smaller but in line with corrections calculated for 2 nm FWHM using a more comprehensive model (Slusser et al., 2000). Accordingly, Langley extrapolation corrections found for the Brewer spectrophotometer (Gröbner and Kerr, 2001) are smaller than for the UVPFR at corresponding wavelengths, mainly due to the smaller FWHM (0.5–0.6 nm) of the Brewer.

Not only the derived V0's are affected by the FWHM effect due to the rapidly changing ozone absorption with wavelength. Even if the correct V0's are used, the calculated UVB AOD will still be incorrect if no further correction is applied. With increasing air mass there is an increase in effective central wavelength for the sunphotometer channels as mentioned above. This results in an apparent decrease in ozone optical depth with increasing air mass. This effect was quantified by calculating the ozone optical depth from the modeled UVPFR direct irradiance signals using the Rayleigh and AOD values at their fixed effective central wavelengths. The effect varies slightly with station altitude and pressure. In Fig. 2, results are shown for an approximate pressure level in Davos (p=840 hPa). The changes in effective ozone optical depth are strongest for the shortest wavelengths. The effect is negligible at the 332 nm wavelength.

The apparent change in ozone optical depth is not a perfect linear function with air mass. With little loss in accuracy, the ozone optical depth correction is still estimated as a linear function of mo with the lines passing through the origin. The error in the derived AOD using this simplification is according to the calculations performed here ≤ 0.001 units of AOD at the shortest wavelength and high total ozone amount and considerably smaller at the other wavelengths and/or lower TCO. The resulting ozone optical depth correction factor for 350 DU total column ozone, co,λ,350DU, is given in Table 2. The apparent decrease in ozone optical depth gets stronger with increasing TCO. The ozone optical depth change for 350 DU is taken as reference. Then the ratio of the ozone optical depth change at other ozone amounts at a specific mo is very similar for all wavelengths and can be approximated by a quadratic polynomial as fo,DU=co,λco,λ,350DU=6.1443×10-6×TCO2+0.8518×10-3×TCO-0.0513, where TCO is the total column ozone amount expressed in Dobson units. In this case, the coefficients in Eq. (5) are derived for a pressure of 840 hPa, corresponding to normal conditions in Davos. The resulting difference in fo,DU is negligible both for conditions at IZO (about 770 hPa) and at sea level with differences in calculated AOD being less than 0.0005. Finally, the apparent decrease on ozone optical depth, Δδo,λ, is calculated as Δδo,λ=fo,DUco,λ,350DUmo. The Langley plot and AOD modeling was also made for a case with zero total column ozone. This showed that the FWHM effects accounted for above are practically entirely caused by the rapidly increasing ozone absorption with decreasing wavelength. For example, a similar correction of the Rayleigh optical depth as for the ozone optical depth correction in Eq. (6) would, at any of the UVPFR wavelengths, only be about one-eighth of the Δδo,λ at the 332 nm channel.

All in all, at an air mass of 2 and TCO amount of 350 DU the effect of the FWHM corrections on derived AOD at 305 nm is about +0.015, while it is only about +0.004 at 311 nm. Both these values are much lower than the total uncertainty in the UV AOD (see Sect. 4 below) but since the errors due to the finite FWHM are systematic the relatively small corrections are still performed (GUM, 2008).

A more detailed form of the Bouguer–Lambert–Beer law in Eq. (1), valid at a (monochromatic) UVPFR wavelength λ, is ln⁡R2Vλ=ln⁡V0,λ-mrδr,λ-moδo,λ-maδa,λ-mnδn,λ-msδs,λ. Solving for aerosol optical depth, δa,λ, and neglecting the assumed very small optical depths due to absorption in NO2 (δn,λ) and SO2 (δs,λ), while including the FWHM corrections cFWHM,δ and Δδo,λ described above, leads to AODλ=δa,λ=ln⁡cFWHM,λV0,λR2Vλma-mrmaδr,λ-momaδo,λ+fo,DUco,λ,350DUmo from the measurement of one of the spectral UVPFR output signals Vλ. The V0,λ is the calibration constant at the same wavelength derived from the Langley plot calibrations as described above.

The ozone optical depth, δo,λ, is calculated from ozone absorption coefficients, ko,λ, and TCO amount. To comply with the Brewer's operational TCO determinations, the ozone absorption coefficients are based on ozone cross section data determined by Bass and Paur (1985). The effective ozone temperature and altitude are also approximated in the same way as for the Brewer operational ozone amount determinations, i.e., by the constant values -45  ∘C and 22 km, respectively. Values of ko,λ for the UVPFR no. 1001 are given in Table 2.

Indeed, using different datasets on ozone cross sections would result in different AOD values, especially at the shortest wavelengths. The effect of different cross sections is not further investigated here. In any case the same cross sections should be used for both TCO and AOD determinations.

The ozone amounts taken from a collocated Brewer are calculated with Rayleigh scattering coefficients according to Nicolet (1984), instead of the standard ones used in the operational Brewer program. As an example, for Brewer no. 163 in Davos the corrected TCO values are 2.7 DU lower than the operational ones. Using Rayleigh scattering coefficients calculated according to Bodhaine et al. (1999) gives similar results, within 0.1 DU, as with the coefficients according to Nicolet (1984).

The other parameters on the right-hand side of Eq. (8) are calculated mainly from position and time and the applied air mass formulas were given in Sect. 2.3 above. As above, Rayleigh optical depth, δr,λ, is calculated with the Bodhaine et al. (1999) algorithm. Air pressure, p, is required for the calculation of Rayleigh optical depth and p is also measured at the station. Potential absorption by NO2 and SO2 is not included in Eq. (8). The actual amounts of these gases over the measurement site(s) are assumed to be negligibly small. The potential error of this simplification is quantified in the next section.

AOD values calculated by Eq. (8) are only valid for times when there are no clouds in front of the Sun. The cloud screening applied in this study is based on the method by Alexandrov et al. (2004) with modifications to fit the UVPFR measurements. The Alexandrov et al. (2004) cloud screening algorithm was developed for optical depth measurements at 870 nm wavelength and for a sampling interval of 20 s. Stability tests were performed with a 15-measurement window, which consequently spanned over 5 min. For the cloud screening, optical depth at the longest UVPFR wavelength (332 nm) was used. Since the UVPFR only takes measurements once every minute, only five measurements were used for the stability check. Also, the threshold for the inhomogeneity parameter ε′ was increased from 2×10-4 to 4.5×10-4. A further restriction introduced was that the atmospheric transmission at the shortest UVPFR wavelength (305 nm) had to be > 0.001. This did not result in a perfect cloud screening of UVPFR data but it was considered good enough for the analyses in this study. Remaining cloud-affected data often caused clear outliers in the comparisons with the PFR and Brewer instruments, which then could be removed.

An uncertainty analysis according to GUM (GUM, 2008) has been made for the AOD values retrieved from a UVPFR sunphotometer. Assume we have an arbitrary measurand with its estimated value, y, which is not directly measured but determined from N other estimated quantities x1, x2, ..., xN through a functional relationship y=f(x1, x2, ..., xN). Then the law of propagation of uncertainties for independent variables states that for the combined standard uncertainty of the measurand estimate y, uc(y), uc2(y)=∑i=1N∂f∂xi2u2xi, where u(xi) is the standard uncertainty of each input variable xi (GUM, 2008). For the AODλ=δa,λ calculated according to Eq. (8) this translates to ucδa,λ=1mauV0,λV0,λ2+1mauR2R22+1mauVλVλ2+1mauVCS,λVCS,λ2+mrmauδr,λ2+momauδo,λ2+mnmauδn,λ2++msmauδs,λ2+δa,λumama2+δr,λumrma2+δo,λumoma2+δn,λumnma2+δs,λumsma212. For simplicity, the contribution due to correlated variables has been omitted. The term VCS,λ is the contribution to the measured signal due to additional circumsolar radiation seen within the field of view of the UVPFR, further discussed in Sect. 4.4. Similar AOD uncertainty expressions can be found in the literature (e.g., Russell et al., 1993; Carlund et al., 2003). A slightly different approach was taken by Mitchell and Forgan (2003) where they investigated uncertainty in total optical depth from different sunphotometers measuring at similar wavelengths. When using Eq. (10), uncertainty of cFWHM is included in the u(V0,λ) uncertainty and uncertainty contributions from fo,DU and Δδo,λ,350DU are included in the u(δo,λ) term. To get the expanded uncertainty, U, the combined standard uncertainty (uc(δo,λ)) is multiplied by a coverage factor, k. In this case k=2 is chosen to get an approximate level of confidence of 95 %. So U95=k×ucδa,λ=2×uc(δa,λ) for a number of effective degrees of freedom of uc(δa,λ) of significant size (> 50), which is here the case.