The PFR (Wehrli, 2000) is a sun photometer that measures DSI at four wavelengths nominally centred at 368, 412, 501 and 862 nm; it is mounted on an independent tracking system to follow the motion of the Sun. The entrance window of the instrument is protected by a quartz window, and the internal parts are fully protected from outside conditions. It is filled with dry nitrogen at approximately 2 bar, and the internal temperature is kept constant by an active Peltier system at approximately 20 °C, with an accuracy of 0.1 °C. Radiation passes through the quartz window and interference filters to allow solar radiation from only a narrow spectral region to reach the silicon photodiode detector. The full-width-at-half-maximum (FWHM) bandwidth of the filters varies from 3 to 5 nm, and its field-of-view (FOV) angle is approximately 2° at FWHM. Measurements occur every minute when a shutter opens for 10 s to perform the 10 sequential measurements at each wavelength. This minimizes the exposure time of the filters to solar radiation and hence minimizes their degradation. The stability of the travelling-standard PFRs is validated by calibration before and after each campaign.

The PREDE POM (Estelles et al., 2012; Prede Co. Ltd., Japan: https://prede.com/english/skyradio.html, last access: 10 April 2024) is a sun and sky radiometer with a two-axis stepping motor as a tracking system to perform observations of both direct sun and diffuse sky irradiance. The step is 0.0036° per pulse. There are two major versions of the instrument with different wavelengths. POM-01 measures direct solar irradiance and diffuse sky irradiance at seven wavelengths centred at 315, 400, 500, 675, 870, 940 and 1020 nm. POM-02 is an extended version measuring at 315, 340, 380, 400, 500, 675, 870, 940, 1020, 1627 and 2200 nm. In both cases, the FWHM bandwidth is 2–10 nm depending on the channel. The wavelengths are isolated using filters mounted on a filter wheel, and the detector is a silicon photodiode, except for the case of wavelengths above 1600 nm in the POM-02, which are measured by an InGaAs photodiode. The FOV of the instrument is approximately 1° and includes a temperature control system to maintain an internal temperature of 30 °C, a four-element silicon Sun sensor and a rain sensor. In this study, we used a standard POM-01 instrument, while the rest of the instruments used were modified POM-01 versions to measure at 340 nm instead of 315 nm.

The CIMEL sun and sky photometer (Giles et al., 2019) is an instrument including a two-axis robotic tracking system. This tracking system allows it to perform direct sun and sky scans in order to measure either DSI or diffuse sky radiance. There are different versions measuring at different wavelengths. The smallest wavelength is 340 nm, and the largest wavelength is 1640 nm, although for some versions it is 1020 nm. The number of wavelengths is up to 10. In this study, we used CIMELs with at least eight interference filters centred at 340, 380, 440, 500, 675, 870, 940 and 1020 nm. The FWHM is 10 nm, except for 340, 380 and 1640 nm (2, 4 and 25 nm, respectively). A silicon detector is used to measure the radiation. Filters are mounted on a filter wheel that moves every second to switch to a different wavelength until all channels are measured in a measurement sequence. The sequence is then repeated three times within 30 s to provide triplet observations. The instrument has an FOV of 1.2°. It also has a four-quadrant detector, which detects the point of maximum solar-radiation intensity, enabling it to correctly point to the Sun before the measurement sequence starts. AERONET AOD data are publicly available at three levels (1.0, 1.5 and 2.0). In this study, we only used level 2.0, which included cloud screening, the final calibration and quality assurance.

The ILP method (Campanelli et al., 2004; Nakajima et al., 2020; Campanelli et al., 2024) is a modification of the conventionally used SLP. The basic principle in both methods is to use the solar radiation measured at the ground during at least a half-day, as well as the Beer–Lambert–Bouguer law: 1I=I0e-mτ, where I is the DSI measured at the ground, I0 is the calibration constant (solar irradiance at the top of the atmosphere in the units of the instrument), m is the air mass coefficient, and τ is the total optical depth of the atmosphere. The solar irradiance is measured in the instrument's units as the SLP and ILP methods do not require conversion to units of Wm-2. The total optical depth is the sum of the scattering and absorption optical depths of the atmospheric constituents.

For the case of no clouds, in front of the solar disc, 2τ=τR+τg+τa, where τR is the Rayleigh scattering optical depth, τg is the gas absorption optical depth, and τa is the extinction aerosol optical depth.

Equation () can be written as follows: 3aln⁡I=ln⁡I0+mτ or 3bln⁡I=ln⁡I0-mτR-mgτg-maτa.

The value of τR is calculated using the atmospheric pressure. The value of τg is calculated from the total column of gases absorbing at a certain wavelength. The values of mg and ma are the air masses corresponding to gases and aerosols, respectively.

The SLP method uses Eq. (), and by measuring DSI during the day at several known air masses, we can perform a linear fitting procedure assuming that the total optical depth of the atmosphere is constant for at least several hours (slope of the linear fit). However, the optical depth can vary under real atmospheric conditions. At wavelengths where gas absorption is minor or where the gases that absorb radiation show no rapid variability, AOD dominates the total optical depth. The SLP method (sun photometers use carefully selected wavelengths to avoid strong absorption) is applicable with high accuracy at high-altitude locations where the AOD is usually very low and where its fluctuations do not have a significant effect on the total optical depth over timescales of a few hours. On the other hand, the SLP method cannot be used at sites with aerosol pollution (Shaw et al., 1983; Toledano et al., 2018). In order to avoid the shipment of instruments to such locations, to increase the frequency of calibration and to monitor their status, we require a method that is usable at any type of station. The ILP method was developed for this purpose. Instead of using Eq. (), a modified version of Eq. () is used, which is now described.

The Rayleigh scattering and gas absorption optical depths can be calculated, and so AOD is the only parameter to be retrieved before deriving the calibration constant. In the ILP method, instead of AOD, the scattering aerosol optical depth (sc-AOD) is used as a parameter. If ω is the single scattering albedo (SSA), τa is​​​​​​​ the AOD and τsc is the sc-AOD then τsc=ωτa, and Eq. () takes the following form: 4ln⁡I+mτR+mτg=ln⁡I0-mτscω.

Assuming y=ln⁡I+mτR+mτg and x=mτsc, we obtain a straight line y=ax+b, where the slope is a=-1ω and b=ln⁡I0.

Therefore, calculating τsc for several times during the day, we can apply a linear fit to all pairs of x and y values and calculate the calibration constant. This method takes into account the variability of the AOD but assumes constant SSA during the measurement period instead. Therefore, large variability of SSA can affect the accuracy of the method.

The estimation of τsc is possible through inversion modelling (Skyrad pack code version 4.2 in our case) applied to the angular distribution of normalized sky radiance (NSR) (Eq. ) observed in almucantar geometry at scattering angles up to 30°. The NSR is defined in Eq. (): 5R(θ)=E(θ)mΩI, where E is the measured diffuse sky irradiance, θ is the scattering angle, m is the air mass, Ω is the solid-view angle (SVA) of the instrument, and I is the direct solar irradiance.

The model estimates sc-AOD and the aerosol phase function by retrieving the size distribution with an a priori refractive index. To model the radiative transfer and to retrieve sc-AOD, the surface albedo (SA), the total ozone column (TOC) and the surface pressure (P) are also required as inputs.

The Skyrad code also derives SSA and therefore AOD, but it is not used in the ILP calibration. However, it is used for a screening criterion as all values corresponding to AOD ≥ 0.4 are rejected before the final calibration.

To evaluate ILP, we calibrated the POMs using a PFR as a reference for the campaign. We begin by assuming that two co-located instruments (a PFR and a POM) measure DSI at the same wavelength. If I1 is the DSI at the ground measured with a PFR, I2 is the DSI measured with a POM at the same time, I01 is the PFR calibration constant and I02 is the POM calibration constant then the irradiances satisfy the following equation: 6aI1(λ,t)I2(λ,t)=I01(λ)I02(λ).

The POM calibration constant is 6bI02=I01I2I1.

Therefore, we used the raw signal ratio of the instruments for measurements with a maximum of 30 s time difference and the known calibration of the PFR to calculate the calibration for the POM. The calibration constants and raw signals are in the instrument units (different for each instrument) and were corrected for an Earth–Sun distance of 1 au.

The signal ratios were cloud-screened with the PFR AOD cloud-screening algorithm (Kazadzis et al., 2018a) and were visually filtered for outliers and days with erroneous measurements. Due to diurnal variation of the signal ratios, we only used data from 09:00–13:00 UTC. We also excluded all days with fewer than 20 measurements in this time interval and calculated a point-to-point calibration for the remaining data. We checked whether the 2 standard deviations (σ) of all points during each day fell below or were equivalent to 0.5 % of the daily median calibration. If the 2σ values were above 0.5 % of the daily calibration, we repeatedly removed all points outside the 2σ range until the day satisfied this criterion. If the remaining points of that day fell below 20 during this procedure, the day was rejected. Finally, we further examined the point calibrations and their corresponding AODs to reject any remaining days with erroneous calibrations. From the quality-assured datasets, we calculated the POM daily median calibrations and their monthly average (since ESR calculates the calibration with ILP on a monthly basis).

To calculate the AOD, we used the following procedure (used by ESR): for the first month of each campaign, we used the monthly calibration constant for all measurements of the month. For the rest of the months, we assumed that the monthly calibrations correspond to the last day of each month at 12:00 UTC. For measurements between two monthly calibrations, we used linear interpolation to calculate the calibration at the time of the measurement. The interpolation is only based on these two consecutive monthly calibrations. We only used two wavelengths, 500 and 870 nm, as they are directly comparable between the instruments. For the second channel, the nominal wavelength of the PFR is 862 nm, while for the POM, it is 870 nm. Despite the difference of 8 nm in wavelength, Rayleigh and Mie scattering are weaker at longer wavelengths so the effect of the difference is less significant in this spectral region.

There were three campaigns per location, and we present the AOD differences between the PFR and POMs or CIMEL. In Fig. , we show the median AOD differences and standard deviations (box size), as well as the 5th and 95th percentiles of the differences (error bars). A noticeable feature is that the ESR AOD calculated with the ILP method is systematically lower than the PFR AOD. In Davos, the median differences are between -0.006 and -0.01 at 500 nm and 0.000 to -0.005 at 870 nm. In Rome, the median differences range from approximately -0.014 to -0.034 at 500 nm, with the vast majority of differences being < -0.01. At 870 nm, QUATRAM I in Rome shows a median difference of -0.005, and the other campaigns show a median difference of < -0.01. For QUATRAM II in Rome, which was the longest campaign and the one with the largest differences in terms of the POM master (POMCNR), we included a second POM (POMSPZ). This shows a performance similar to the POM master (POMCNR^∗) during QUATRAM III in Rome.

When using a PFR calibration transfer to recalculate the AOD for POMs, the absolute median differences are < 0.005 for all cases. The CIMEL–PFR comparison shows similar results with all median AOD differences below 0.01. In addition, the majority of the 5th–95th percentiles for either CIMEL–PFR or POM–PFR using the calibration transfer are within 0.01.

Regarding the WMO traceability criteria, the data within the WMO limits for POM AOD with an ILP calibration are below 95 % for all cases at 500 nm, as well as for QUATRAM II and III in Rome at 870 nm (Table ). However, there is a large deviation between both locations: while at 500 nm, the percentage in Davos is above 60 %, and it is below 4 % in Rome. Using the calibration transfer to calculate POM AOD, > 98 % of data are within the WMO limits (Table ). The CIMEL–PFR comparison (Table ) also shows percentages mainly above 98 %. Exceptions are QUATRAM I and II in Rome at 500 nm and QUATRAM I in Rome at 870 nm. All CIMEL–PFR comparisons show at least ∼ 60 % differences within the WMO limits.

Recalculating the AOD with the same post-processing algorithm and for the same instrument (once for each POM) for both POM calibrations (ILP and calibration transfer), we can more clearly observe the effect of just the calibration on AOD. In this case, the median AOD difference is similar to the difference between the original POM and PFR datasets shown by the green boxes in Fig. . The results of the comparison, showing the calibration effect along with the “original” differences, are in Fig. S1 in the Supplement (Sect. S1). The median AOD differences attributed to the calibration deviate from the “original” AOD differences by < 0.003, except for three cases. It is approximately 0.005 for QUATRAM III in Rome at 500 nm and in Davos at 870 nm. A larger value of 0.01 was observed for QUATRAM II in Rome at 500 nm for only one of the POMs (POM_CNR). These deviations are not systematically larger or smaller than the “original” at 870 nm, but they are smaller for most campaigns at 500 nm.

The variability of AOD differences for the comparison between both recalculated POM AOD datasets (which just show the calibration effect) is a result of the dependence of the calibration effect on the air mass. Therefore, it depends on the magnitude of the calibration difference, its month-to-month variability and the air mass distribution present in the data.

These results suggest that the overall contributions of the post-processing algorithm and instrument differences between the networks result in AOD differences that are within the PFR AOD retrieval uncertainty. For ESR, the calibration method dominates the overall AOD difference.

In the previous section, we showed that the major source of AOD differences was due to differences in the PFR and POM calibration methods. The calibration differences between the ILP method and the PFR-based transfer can be found in Table S1 (Sect. S1). The values in the Supplement show some minor differences compared to Campanelli et al. (2024) for some months, mainly due to differences in the selected days. The difference is larger for August 2018 in Davos. During this month, we observed an abrupt shift of daily calibrations early in the month. Hence, we removed the days before the shift as the monthly calibration is attributed to the end of the month when retrieving the AOD. In this section, we discuss the stability and the uncertainties of the different calibrations.

The ILP calibrations show either positive or negative fluctuations for consecutive months at the same location, lying in the 0.17 %–2.3 % range with a median absolute value of 0.55 % and a standard deviation of 0.87 %. These calibration fluctuations can be attributed either to changes in the instruments' response or to the random component of the ILP method uncertainty. The coefficient of variation (CV%) of the daily ILP calibrations per month (Campanelli et al., 2024, Table 2a) is an estimate of the ILP monthly calibration uncertainties. CV% is the percentage of the standard deviation of daily calibration constants during the month divided by the monthly calibration constant. The CV% for the ILP calibrations used in this study lies in the 0.18 %–2.87 % range at 500 and 870 nm.

The PFR calibration differences between consecutive calibrations are in the 0.00 %–0.45 % range at 500 and 870 nm (Table S3), with all calibrations having an uncertainty below 0.4 % (Table S2).

The PFR-based calibration transfers of POMs show fluctuations for consecutive months at the same locations in the 0.00 %–1.72 % range, with a median absolute value of 0.19 % and a standard deviation of 0.56 %. The uncertainties of the calibration transfers calculated as the combination of the PFR calibration uncertainty σPFR and the standard deviation of the daily calibrations σd are calculated as follows: 8σTR=σPFR2+σd2.

Applying Eq. (8) shows that the calibration transfer uncertainties are in the 0.27 %–0.8 % range (Table S2).

The month-to-month variabilities of the ILP method and the transfer-based calibrations do not coincide. This is reflected in the month-to-month variability of the calibration differences between both methods, which is in the 0.01 %–1.93 % range. Their median absolute value is 0.55 %, and their standard deviation is 0.96.

However, not all calibration fluctuations can be explained by the uncertainties in the present section. A particularly interesting case is the calibration change from July to August 2019 in Rome for POMCNR at 870 nm. The CV% of the ILP calibrations of these 2 months is below 0.5 % (Campanelli et al., 2024), while their calibration difference is 1.3 %. The calibration transfers from the PFR for the same months differ by only 0.2 %, providing no evidence of changes in the instrument response. The same months show an ILP calibration change above 2 % for POMSPZ, with the calibration transfers differing by 0.3 %. At 500 nm for the same months, the ILP differences are above 1 %, while the calibration transfer differences are 0 %. Therefore, the ILP differences between these 2 months are attributable to the overall uncertainty of the ILP calibration.

Three parameters are discussed in this section, namely AOD, SSA and the Angström exponent (AE). According to Nakajima et al. (2020), the level of AOD affects the ILP performance. Also, the ILP method uses a pre-assigned refractive index value and assumes a stable SSA (which is connected with IRI) during the half-day in which the ILP is performed (Eq. ). Therefore, the SSA value and variability may affect the calibration. Due to the above, we assess whether there is an association of the levels or the variability of AOD and SSA with the differences between the ILP method and the calibration-transfer-based calibrations. For the AOD, we used the PFR dataset. For the SSA, we used the AERONET level-1.5 retrievals due to lack of data availability in terms of the quality-assured level 2.0. Because of the limited SSA dataset and the larger uncertainty (compared to level 2.0), we also used the AE from the PFR in the investigation. AE is related to the size of aerosols, and a change in AE reflects a change in aerosol composition that may affect IRI and SSA. For the AOD and AE, we used only data corresponding to the half-days used for ILP calibrations. In addition, we removed all points corresponding to AOD ≥ 0.4 at 500 nm and air masses ≥ 3 according to the screening criteria of the ILP method. For the SSA, we used all data during the campaign months except values < 0.1 corresponding to AOD at 440 nm and a very small number of outliers. Since ESR provides monthly calibrations, we used the monthly median values as indicators of the AOD, SSA and AE average levels. Each monthly median is the median of the daily medians. As indicators of the variability during the ILP method, we use the discrepancies between the monthly medians of the daily 5th, 20th, 80th and 95th percentiles.

Here, we investigate whether there is any systematic difference between Davos and Rome with respect to AOD, SSA and AE values or variabilities that could potentially be associated with the larger calibration differences in Rome for all months. We use AOD and AE from the PFR data during the half-days and full days of the ILP calibrations. SSA is from the AERONET data obtained during the QUATRAM campaigns. We used monthly median statistics as the average level and monthly medians of the daily percentiles (5th, 20th, 80th and 95th) as a variability indicator, as described in Sect. .

Figure  shows the PFR AOD values for all months of the campaigns at both locations. For most months, it is evident that the AOD is higher and more variable in Rome, but there are exceptions, such as for the QUATRAM I (DAV17/ROM17) campaign. Also, we can see that the highest AOD corresponds to QUATRAM III in Rome (ROM21) (Fig. ), while the largest calibration and AOD differences between PFR and POM were in QUATRAM II (ROM19) (Fig. , Table S1). Both AOD values and AOD variability vary at the same location and between both locations from month to month, showing no consistency between AOD (Fig. ) and calibration differences (Table S1).

The ILP method assumes a constant SSA as the inverse slope of the linear fit (Sect. ) and uses an a priori refractive index (selected by the operator). These assumptions potentially reduce the accuracy of the method. Here, we present the SSA values provided by AERONET, along with their variability during the campaign months (Fig. ), at 440 nm (green) and 870 nm (red). For the Davos 2018 campaign, there are 3 months instead of 4 as there was a lack of data during the first month, July 2018, due to the fact that the campaign started towards the end of the month. In general, there is no evidence of either any systematic difference between both locations or an association between the calibration and AOD differences, even for the same location. In Rome, the largest SSA variability corresponds to QUATRAM I (ROM17) (Fig. ), where we observed the smallest calibration and AOD differences during the Rome campaigns (Fig. , Table S1). Similarly, the largest variability is during QUATRAM III (DAV21) in Davos, which also exceeds the Rome SSA variability. However, we did not observe larger differences between ILP and the calibration transfer in Davos during QUATRAM III (DAV21) compared to during QUATRAM II (DAV18). In terms of median SSA, depending on the month, either Rome or Davos may have larger SSA. The fluctuations of SSA do not seem to significantly affect the calibration differences. However, we acknowledge that the limitations of the SSA dataset (Sect. ) limit the confidence in the conclusions.

Due to the limitations of the SSA dataset (Sect. ), we included a comparison of the AE medians and variabilities during the campaigns as an additional indicator of aerosol composition. During QUATRAM I (DAV17/ROM17), both locations have similar median AE values, but Davos shows the largest variability. During QUATRAM II (DAV18/ROM19), the AE in Davos is the largest, while the variability varies significantly between the months. Similarly, during QUATRAM II in Rome, AE is lower, and each variability largely depends on the month. Finally, during QUATRAM III (DAV21/ROM21), Rome shows the largest AE and variability. Again, there is neither a systematic difference between both locations nor an association of calibration differences and AE at the same location.

In the first sub-study, we focus separately on each a priori parameter of the ILP calibration. All other parameters are left at their original values except for one that is variable. The goal is to recalculate the ILP calibrations for the local station conditions. Therefore, for each parameter under study, we select a value based on observations at the measurement site. Specifically, TOC and P are present in the PFR data. The TOC used in the PFR algorithm corresponds to the OMI satellite product (aura_omi_l2ovp_omto3_v8.5, https://acd-ext.gsfc.nasa.gov/anonftp/toms/omi/data/overpass/, last access: 25 January 2024), and P was measured with a Setra barometer (uncertainty of less than 10 mbar). The refractive index values (RRI and IRI) are available from datasets of the AERONET almucantar scans (only at 440, 675, 870 and 1020 nm). SA is also taken from the AERONET datasets at the same wavelengths. Over land, this originates from a Ross-Li bidirectional reflectance distribution function (BRDF) model (Lucht and Roujean, 2000) based on MODIS (or Moderate Resolution Imaging Spectroradiometer) satellite observations (Sun et al., 2017). For the rest of the wavelengths (340, 400 and 500 nm), we had to select values based on the existing wavelengths. For RRI and IRI, we used linear interpolation and extrapolation to estimate their values at those three missing wavelengths. The SA selection at 340, 400 and 500 nm is based on its observed values and its spectral dependence in the IGBP library from the libRadtran package (Emde et al., 2016). SVA is provided by ESR.

For each parameter, we used three different values to calculate three different ILP calibration constants. We calculated one ILP calibration using the median (RRI, IRI) or the mean (TOC, P and SA) value during all the months of the three QUATRAM campaigns. The other two calibrations correspond to values equivalent to 1 standard deviation above and below each average. For SVA, we used the values provided by ESR for the first ILP calibration. The other two values are based on the maximum difference observed between ESR SVA and other SVA calibration methods for POMs presented in Campanelli et al. (2024). In the Supplement (Sect. S3–S5 and Tables S4–S6), we present all the values used for the six input parameters.

Here, we present the results of the ILP calibration using different values for the input parameters of Skyrad 4.2. The selection is described in the subsection of Sect. 4.2.1 referring to the methodology.

The RRI average observations from AERONET were similar to the pre-assigned input of Skyrad pack 4.2 (1.5 for all wavelengths), while the standard deviation was small. Hence, we used the original, minimum and maximum values (1.33, 1.5 and 1.6). The calibration difference due to this change in RRI was in the 0.00 %–0.21 % range.

For P, we used the values 0.8, 0.83 and 0.85 atm for Davos and 0.97, 1 and 1.02 atm for Rome (the original values for ILP were 0.83 and 1). Most differences were below 0.05 %. In 1 month at 870 nm, we obtained a maximum difference of 0.2 %.

For TOC, we used 260, 300 and 400 DU for both locations, which resulted in differences of up to 0.43 %. The comparisons for RRI, P and TOC are available in more detail in Tables S8–S10.

For IRI, SA and SVA, we show the ILP calibration differences in Figs. –. For the majority of the cases, the calibration differences due to IRI are smaller than 0.5 % (Fig. ). For specific months (August 2018 for Davos and July 2019 for Rome), they are 1 % or higher.

Using SA from AERONET noticeably reduces the calibration difference (Fig. ) at 500 nm for most months at both locations, but the effect can explain a calibration difference of up to 0.75 %, approximately (September 2019, Rome), while the calibration differences in Rome are in the 2.5 %–3.5 % range (Table S1).

For SVA, there are also noticeable differences of 0.5 %–1 % from the central value (Fig. ). SVA, like IRI, also shows a particularly high sensitivity during the second month (August 2018, Davos). The central SVA value corresponds to identical input parameters with respect to the original calibration; therefore, we expect the magenta line (original) in Fig.  and the blue line (central SVA) to be identical. Some differences below 0.1 % are probably present in most months due to the use of different compilers and versions of the Skyrad pack 4.2. However, for September 2019 in Rome at 500 nm, they differ by up to 0.5 %, and for August 2018 in Davos at 870 nm, they differ by > 1 %. This may be a result of computational instability. For the other months, such differences are below 0.1 %.

In the second sub-study, we alter the values of all parameters simultaneously except SVA (we used the value provided by ESR). Again, the goal is to adapt the input parameters to the site conditions. We calculated the ILP calibration for two separate cases: a.

Average case. This included one calibration per month using the monthly average values used in the first sub-study for all five parameters being tested (RRI, IRI, P, TOC and SA).

In this section, we present the results of the second sub-study is described in the subsection of Sect. 4.2.2 referring to the methodology. There are two calibration cases that we tested in the whole QUATRAM II campaign.

The results in Table  show changes of < 0.5 % for the average case with the exception of August 2018 in Davos. Due to the large sensitivity in the IRI, the calibration changed by > 1 %.

Under the “selected” case (selected conditions for all parameters that increase the ILP calibration), there is a larger increase in the calibration in Davos compared to in Rome at both wavelengths (Table ), but all differences are below 1 %.

In the third sub-study, we tested the IRI, SA and SVA for a more extensive number of values (seven fixed values regardless of the location) to assess the behaviour of the calibration. For IRI and SA, the selection is based on the three values of the first sub-study, the 5th–95th percentiles of the observations, and the minimum and maximum values. We also added semi-arbitrary values between the observed and two extreme values (one very small and one very large) to test the performance of the method over a wider range of inputs. For SVA, we use values based on the differences between the different SVA calibration procedures appearing in Campanelli et al. (2024). The actual values for each parameter are in Sect. S10; see Table S11.

In this section, we present the results of the third sub-study described in the subsection of Sect. 4.2.3 referring to methodology, where we only test IRI, SA and SVA for seven values over a larger range. We only selected 1 month per location, avoiding August 2018 and July 2019 due to the behaviour presented in the subsections of Sect. 4.2.1 and 4.2.2 referring to the results. Figures – show the results for each parameter.

Changing only IRI (while it is < 0.05) shows that ILP changes by < 0.25 % for both wavelengths and locations (Fig. ). Increasing IRI > 0.05 or to other rare and unrealistic values has no effect on the calibration. Therefore, IRI appears to either have a significant or a small effect on the ILP calibration, depending on the month.

Changing only SA (Fig. ) shows a monotonic but nonlinear dependence of the ILP calibration, where larger SA leads to a smaller calibration constant. At 870 nm, there is a maximum calibration constant at SA = 0.04, with approximately 0.07–0.08 being the average values from AERONET and 0.1 being the value used by ESR. At 500 nm, the difference between the ILP calibrations in Davos and Rome is also smaller at lower SA, showing that ILP in Rome is affected to a larger extent by the SA value at 500 nm. However, even when using an SA value as low as 0.02, the remaining calibration difference between the calibration transfer and ILP at 500 nm is approximately 2 % in Rome and 0.7 % in Davos. At 870 nm, the difference is at least 0.95 % for Davos and 1.7 % for Rome for all SA values used as input.

Finally, for SVA (Fig. ), there is a monotonic decreasing dependency in terms of the calibration constant and SVA at 500 nm, while some fluctuations occur at 870 nm. The minimum calibration difference at 500 nm is approximately 0.58 % for Davos and 1.7 % for Rome, while at 870 nm, the results are 0.78 % for Davos and 1.6 % for Rome.

Since the ILP method is performed using a linear fit of the logarithm of DSI with respect to the product of the air mass coefficient and sc-AOD (Eq. ), errors from the retrieval of sc-AOD will transfer errors to the calibration. Since there is no reference dataset available for sc-AOD, we tried to indirectly investigate potential errors using available data.

The Skyrad code retrieves both sc-AOD and SSA through inversion modelling and calculates the corresponding AOD as additional information. Therefore, we initially compare the AOD dataset with the PFR AOD for potential differences. However, systematic underestimation or overestimation of both the sc-AOD and SSA retrievals can result in opposing errors to the corresponding AOD that cancel each other. Due to the limitations of the AERONET SSA dataset (lack of level-2.0 data and limited number of retrievals per day), we cannot evaluate the SSA retrieved by Skyrad 4.2 with confidence. Also, part of the SSA difference between the AERONET product and the output of the Skyrad code for the ILP calibration may be attributed to the fixed refractive index and the different scattering angles in the almucantar geometry used for the sky radiance measurements (ILP uses only forward scattering, having a maximum angle of 30°).

Another indirect method to investigate the effect of the sc-AOD retrievals on the calibration performance is to use a different inversion model to retrieve sc-AOD and to re-calibrate the instrument with the ILP method. We therefore used the inversion model Skyrad pack MRI version 2 (Kudo et al., 2021). MRI allows the modelling of non-spherical particles in contrast to Skyrad pack 4.2 retrievals. It also introduces stability constraints on the edges of the size distribution, as well as other smoothness constraints (see Kudo et al., 2021, for a detailed description). As mentioned in Kudo et al. (2021), the MRI method is more accurate at high AOD. Under low-AOD conditions in Davos, a noticeable portion of data showed large retrieval errors and unrealistic sc-AOD and/or AOD values. However, there were sufficient data at both locations to recalculate the ILP calibration, and, hence, it was applied to the QUATRAM II data.

We also investigated whether the variability of the SSA corresponding to the Skyrad 4.2 and MRI retrieval shows any association with the calibration differences. All retrieved AOD, sc-AOD and SSA data retrieved by MRI are screened according to the ILP criteria: keeping only data corresponding to AOD at 500 nm < 0.4 and air masses at < 3.

As discussed in Sect. , the ILP method can have significant random uncertainty as individual ILPs for half-days can lead to different average monthly values. However, the vast majority of daily calibration constants are lower than the calibration transfers from PFR, most of them by > 0.5 %–1 % (Table ), for both locations and wavelengths. One way to obtain such biased results is a systematic underestimation in sc-AOD by the inversion of NSR or an underestimation of sc-AOD in the small air masses and overestimation in large air masses.

In this section, we investigate the effect of the sc-AOD retrieval through inversion of the ILP calibration. As there were two inversion algorithms available, we compare the calibration and the sc-AOD calculated by Skyrad pack 4.2 with the calibration and sc-AOD from Skyrad MRI.

The AOD from Skyrad 4.2 is retrieved through the inverted sc-AOD and may show similar errors. Since we do not have an sc-AOD reference dataset, we compared the Skyrad AOD with PFR AOD.

The differences between the AOD retrieved from the Skyrad pack 4.2 using almucantar scans of POM and the PFRs show a systematic underestimation as expected, except for the comparison at 870 nm for Davos (Table ). The differences are also higher in Rome than in Davos. However, the median differences are significantly smaller than those corresponding to the ESR direct-sun AOD product compared to the same PFRs, and the percentage of differences within the WMO limits is higher. The AOD differences also increase with smaller air masses in Rome but not in Davos. For air masses below 1.5, the median AOD difference is -0.012/-0.004 at 500/870 nm in Rome and 0.000/0.001 at 500/870 nm in Davos. For air masses above 2, the median AOD difference is -0.005/-0.000 at 500/870 nm in Rome and -0.003/0.000 at 500/870 nm in Davos. More details including linear fitting of the air mass dependencies are available in Sect. S12 and Table S15.

Using the sc-AOD from MRI as an input to the ILP method instead of Skyrad 4.2 in Davos 2018 and Rome 2019, we obtained different calibration constants for each month, but there is no consistent improvement (Table ). At 500 nm, 6 out of 9 months show a calibration closer to the calibration transfers by between 0.29 % to 0.96 % (negative differences in Table ), while at 870 nm, the calibration constant is larger for only 3 months (0.04 %–1.39 %). However, the AOD median differences are very small (up to 0.002), and there is no consistency between sc-AOD and calibration differences (Table ). Due to the fact that the datasets are different, there is also a different selection of individual sc-AOD inversions and days that pass the criteria for the final ILP calibration. The combination of using randomly different sc-AOD points and half-day selections results in the observed calibration differences that are mainly < 1 %. Such random differences are similar to the magnitude of ILP CV% values (defined in Sect. ) in Campanelli et al. (2024).

The ratio of the provided sc-AOD and AOD in the ILP output allows us to calculate the corresponding SSA. The number of available QUATRAM II common measurements between Skyrad 4.2 and MRI is 1114 for Davos and 4434 for Rome. For ILP-retrieved SSA from both Skyrad 4.2 and MRI, we mainly observe a larger median in Davos (0.952/0.926 for 500/870 nm from Skyrad 4.2 and 0.959/0.939 from MRI) compared to Rome (0.934/0.917 from Skyrad 4.2 and 0.942/0.927 from MRI). The monthly values are in Table S12. The difference between the 80th and 20th percentiles in terms of the SSA is, overall, larger in Rome at 500 nm (0.03/0.02 from Skyrad 4.2 at 500/870 nm and 0.025/0.015 from MRI) and larger in Davos at 870 nm (0.021/0.029 from Skyrad 4.2 nm and 0.014/0.02 from MRI). However, there are month-to-month variations. In Table S13, we show the monthly medians of the daily differences between the 80th and 20th percentiles. Depending on the month, either Rome or Davos shows a larger variability.