The Cimel CE318-TS (Tables  and ) is the standard instrument in AERONET, a radiometer manufactured by Cimel Electronique that measures direct solar and lunar radiation together with sky radiance using a sensing head mounted on a two-axis tracker and a control unit . The sensing head is equipped with two types of detectors: silicon photodiode and InGaAs (indium gallium arsenide) detectors. The radiation reaching the detectors is filtered by a set of optical bandpass filters with different wavelengths centered at 340, 380, 440, 500, 675, 870, 940, 1020, and 1640 nm, with a FWHM of 2 nm for 340 nm, 4 nm for 380 nm, 25 nm for 1640 nm, and 10 nm for the rest of the channels. The 1020 nm spectral band is measured twice, using two detectors, hereafter referred to as the 1020 and 1020i measurements. The tolerance interval for central wavelength and FWHM is ±0.5 nm, which means that the spectral response might vary between Cimel photometers, even in the case of those with the same version and model. The field of view (FOV) of the instrument is approximately 1.3∘ , and a removable collimator is used to minimize stray light, which is especially necessary for sky radiance measurements near the solar aureole.

Solar tracking is performed using time-based ephemerides, latitude, and longitude and is enhanced using a four-quadrant sensor present in the sensor head. According to , the pointing error of the Cimel CE318 is less than 0.1∘. The measurements of direct solar radiation for all the current filters are performed in triplets, consisting of sequences of three measurements taken every 30 s, with a total duration of 1 min for each triplet. Direct solar/lunar measurements are performed every 5 min (this is the default value in the last firmware version, but it can be adjusted between 2 and 15 min) between 09:00 and 15:00 LT (local time), with a variable frequency depending on the air mass outside those hours. During periods when the radiometer is not in use, the tracker is positioned facing downwards, to minimize any potential damage to the optical filters from solar radiation. Microphysical and optical parameters of the aerosols can be retrieved with spectral radiance measurements together with the AOD; AERONET uses the code developed by , with some improvements introduced in . Recently, new inversion methods have emerged, among which GRASP stands out.

Typical uncertainties in AOD products for reference instruments are expected to range between 0.002 and 0.009 , which are higher for shorter wavelengths. Uncertainties in AOD values in the case of field instruments are expected to be higher, between 0.010 and 0.020, with higher values for UV spectral bands .

The CE318-TV12-OC (Table ) is another version of the CE318-T photometer specifically designed for ocean color applications. Equipped with 12 optical filters centered at 400, 412.5, 442.5, 490, 510, 560, 620, 665, 779, 865, 937, and 1020 nm, this photometer is utilized by the AERONET Ocean Color (AERONET-OC) global network, installed on offshore platforms to measure the radiance emerging from the sea, a critical parameter for satellite ocean color validation .

Cimel data used in this study have been screened for clouds by matching our dataset with AERONET version 3 level-2.0 quality-assured data. This technique ensures that our data are free of clouds and are filtered for instrumental problems and that the final post-field instrument calibration has been applied.

The PFR (Table ) is an instrument manufactured by PMOD/WRC, consisting of a sensor head and a control unit. Unlike the Cimel CE318, it does not have its own tracker, and it is usually mounted on commercial trackers that always point towards the sun. The sensor head has four independent channels with bandpass optical filters centered at 368, 412, 500, and 862 nm, with a 5 nm FWHM and four 3-angled silicon photodiodes to avoid reflections between filters and detectors. The FOV of the PFR is determined by two diaphragms of 3 and 7 mm in diameter, separated by 160 mm, resulting in a FOV of 2.5∘. The system is hermetically sealed with a slightly pressurized internal atmosphere (2000 hPa) of dry nitrogen and temperature stabilized with a Peltier-type thermostat system that maintains the sensor head temperature at 20.0±0.5 ∘C for an ambient temperature range between -20.0 and 35.0 ∘C. This system eliminates the need for temperature corrections to the sensor signal and also prevents accelerated aging of the filters, ensuring the high stability of the PFR . The detectors are only exposed for short periods of time, as an automatic shutter opens every minute for 10 s to take measurements of direct solar radiation, minimizing filter degradation related to exposure. The expected uncertainty in AOD depends on the uncertainty in the calibration and air mass . estimated the uncertainty in the PFR calibration constant to be between 0.2 % (500 nm) and 1 % (368 nm), which leads to an uncertainty in the AOD between 0.002 and 0.01 for a relative air mass equal to 1.

Cloud flagging for PFRs follows some of the basic features that CIMEL uses as well as additional ones based on the high (1 min) measurement frequency of the PFR described in .

IZO (Tenerife, Canary Islands, Spain; 28.309∘ N, 16.499∘ W; 2373 m a.s.l.) is a high-mountain subtropical station managed by the Izaña Atmospheric Research Center (IARC), belonging to the State Meteorological Agency of Spain (AEMET). This station predominantly represents the background atmospheric conditions of the subtropical lower troposphere due to its location above a strong, quasi-permanent layer of thermal inversion resulting from general subsidence processes in the troposphere (descending branch of the Hadley cell) and the presence of trade winds at lower levels . However, the proximity to the Sahara introduces an important influence of mineral dust in its aerosol climatology, making IZO a key location for dust transport monitoring .

Aerosol characterization at the site is dominated by free-troposphere conditions throughout the year, with remarkably low aerosol loading (AOD500nm of 0.03 or lower and average Ångström exponent, AE440−870nm, values of 1.01) and a predominant impact of fine-mode aerosols . Dust-laden conditions are predominantly observed in summer, with AOD500nm of 0.15 and AE440−870nm of 0.54 . The predominance of extremely clean atmosphere throughout the year makes IZO a calibration site for GAW-PFR and AERONET-Cimel networks, providing an advantage when comparing the two instruments since it eliminates, to a great extent, the errors caused by turbidity or atmospheric instability.

IZO is an ACTRIS calibration facility, a member of ACTRIS/CARS (Center for Aerosol Remote Sensing), and is responsible for the QA/QC of the automatic sun/sky/moon photometer measurements.

Valladolid station (Valladolid, Castilla Leon, Spain; 41.664∘ N, 4.706∘ W; 705 m a.s.l.) is an urban site located in the north-central part of the Iberian Peninsula. This site is characterized by a continental clean aerosol climatology with hot and dry summers and cold winters. However, Valladolid can be influenced by both local and regional sources of pollution. The high variability in temperature and humidity leads to a dynamic aerosol environment, with changes in sources and transport pathways over time.

Valladolid is an AERONET calibration center, providing accurate and precise AOD measurements for use in climate and air quality work. Several studies have shown that Valladolid has relatively low AOD values compared to other urban areas, likely due to the city's location and transport patterns with monthly mean AOD values (AOD440nm) ranging from 0.10 to 0.24 and AE440−870nm from 0.9 to 1.5 . However, the city experiences occasional episodes of elevated AOD associated with transported dust from North Africa and forest fires. For example, found that the highest AOD values in Valladolid occurred during dust episodes from the Sahara, with AOD440nm above 0.3 and reaching values as high as 1–2. These dust events modulate the annual climatology of the aerosols in this area with a total contribution of about 11.5 % to the total AOD.

Valladolid station is also a member of ACTRIS CARS and is responsible for the QA/QC of the automatic sun/sky/moon photometer measurements.

In this section, we present the results of transferring calibration from the GAW-PFR, which is considered the reference instrument for AOD measurements by the WMO, to an AERONET-Cimel (CE318-TS) photometer. Although the GAW-PFR and AERONET-Cimel have distinct characteristics such as different optics, sun-tracking systems, relatively different fields of view, and spectral bands with varying FWHMs and λc, several comparison studies have been carried out in the past to make these different datasets comparable (, among others). For example, conducted an exhaustive, long-term comparison in terms of AOD, which showed excellent traceability of AERONET-Cimel AOD with the GAW-PFR AOD reference at the 440, 500, and 870 nm channels, with poorer traceability results in the UV range. These authors also showed the important effect that the different FOVs between the two photometers have on the AOD monitoring, with an important AOD underestimation in the case of PFR under the presence of coarse particles due to the enhanced forward aerosol scattering, especially at the shorter wavelengths.

Our study was conducted at two different locations, IZO and Valladolid, where co-located PFR and Cimel instruments were used to collect measurements almost simultaneously (within 1 min) over a period of 6 months. The time period encompassed measurements with the AERONET photometer no. 1089 between 1 July and 31 December 2021 in the case of IZO and with the AERONET photometer no. 904 between 1 July and 31 December 2022 in the case of Valladolid. The different aerosol regimes at these two sites allowed us to assess the new LR calibration method under different atmospheric conditions: one pristine high-altitude site, suitable for performing the standard Langley calibration, and an urban site with a moderate impact of aerosol variability, used in AERONET as a cross-calibration station. The 6-month period was chosen because it is the common recalibration interval of reference instruments in GAW-PFR and AERONET-Cimel networks . According to Sect. , these instruments have been quality assured, including two independent cloud screening steps (GAW-PFR and AERONET-Cimel level 2.0 algorithms). During the analysis period, the AOD at 500 nm (τ500,a) varied between 0.008 and 0.583 at IZO, with an average of 0.093, and between 0.017 and 0.845 at Valladolid, with an average of 0.123.

Daily V0,λ values retrieved with the LR method (V0,λLR) over the 6-month period at the two sites were computed using the ratio (expressed as in Eq. ) of coincident PFR (VλMM) and Cimel (VλFF) measurements (i.e., VλFF/VλMM) for an air mass range from 2 to 5, with two daily V0,λLR values associated with the morning and afternoon branches. We have considered the closest spectral bands between the two photometers, i.e., 1020/862, 1640/862, 870/862, 675/500, 440/412, 500/500, 1020i/862, 380/368, and 340/368. It means a Δλ between instruments (Cimel versus PFR) ranging from 778 nm (for Cimel 1640 nm spectral band) down to zero at 500 nm. The Cimel exo-atmospheric output voltage data obtained by using the standard Langley method V0,λSL for the no. 1089 and no. 904 Cimel photometers at IZO were used as a reference. The two V0,λSL values, one per photometer, were considered valid for the 6-month period of measurements used in the present study, considering the extraordinarily high temporal stability of Cimel masters found by . Figures  and  show the daily relative differences (in %) between V0,λSL and V0,λLR for the different CE318 spectral bands (except 937 nm) at the two sites, respectively.

At IZO, Fig.  and Table  show that, on average, the relative differences in the calibration constant retrieved by the standard Langley technique and the LR (ΔV0‾) and their standard deviation (σ(ΔV0)) are generally low for spectral bands outside the UV range: below 0.45 % and 0.77 %, respectively. The high σ(ΔV0) values observed at the 1640 nm spectral band (0.77 %) are attributed to the significant Δλ used in the LR, which employs the photometric information obtained by the master PFR at the spectral band centered at 862 nm to calibrate this Cimel spectral band in the NIR (Δλ of 778 nm). In the UV range, these values are found to be higher, up to 0.78 % for ΔV0‾ and 1.41 % for σ(ΔV0). It is well known that there are higher uncertainties and temperature dependence in the Cimel photometers in this spectral range . Although the CE318-TS signal is typically corrected in AERONET for temperature across most wavelengths using standard integrating spheres, such temperature calibration is not performed for the UV filters due to limited source power in this spectral range. These results are also consistent with the expected increase in variation in the Δτ term due to the more significant aerosol extinction in this spectral range. Looking at Fig. , two different time periods affecting the V0 differences can be observed, with more scatter and higher σ(Δτ) in the first period between July and September 2022. This period corresponds to the frequent dust outbreaks affecting IZO during summertime ; therefore, there is more of an effect of dust forward scattering in AOD retrieval uncertainty due to the different instrument FOVs . The impact of circumsolar irradiance on the higher FOV of the PFR radiometer was already studied by , who found an underestimation of AOD by PFR, which is more significant at lower wavelengths, depending on dust particle radius and AOD load and is considered non-negligible for τ500,a values >0.1. This effect will directly translate into the Δτ′ term in the slope of the LR analysis (Eq. ).

To investigate the performance of the LR method for different aerosol regimes, we included two different time periods in Table : the period from July to September 2022 (a summertime period with a significant amount of dust), denoted as the first period, and from October to December, denoted as the second period (which was expected to have clean conditions at the site). Mean τ500,a values of 0.12 (with a standard deviation of 0.09) and 0.03 (with a standard deviation of 0.03) were retrieved for these two periods, respectively. We found considerably lower ΔV0‾ and σ(ΔV0) values in the second period when the influence of mineral dust and the possible impact of the different FOV on the LR method through the term Δτ were minimized. Under these non-dusty conditions, we observed ΔV0‾ values between -0.20 % and 0.30 % and σ(ΔV0) values up to 0.46 % for spectral bands outside the UV range. In the UV range, ΔV0‾ and σ(ΔV0) values reached up to 0.84 % and 1.25 %, respectively, for the second period.

In the case of the Valladolid station, Fig.  and Table  depict the time evolution of ΔV0 and their mean and standard deviation values. A lack of ΔV0 seasonal dependence was found at this station, indicating a lower impact of aerosol seasonality at Valladolid in comparison to the IZO high-mountain station. However, some periods with higher ΔV0 values associated with higher values of σ(Δτ) can be observed in Fig. , especially at longer-wavelength spectral bands. These periods, observed in July and August and not related to the increase in AOD conditions, may be caused by instrumental issues such as calibration problems or dirtiness in one of the photometers. Additionally, an important bias in the ΔV0 values in the Cimel 675, 500, and 440 nm spectral bands (Fig. d, e, and f) was also observed, up to 1.61 %. This difference could also be due to possible instrumental problems. ΔV0‾ values up to 0.68 % were found in the longer wavelengths (1640–870 nm), with σ(ΔV0) ranging from 0.50 % to 0.93 % in 1640 nm due to the high wavelength difference between spectral bands involved in the LR method. Similarly to IZO, comparatively higher differences and standard deviations were found in the UV range (up to 1.44 % and 1.83 %, respectively).

The results from Figs.  and  show that the major differences in V0 are primarily due to variability in Δτ (σ(Δτ)), excluding different instrumental factors. As mentioned in Sect. , the variability in Δτ is mainly driven by the variability in the aerosol component Δτa. According to Eq. (), Δτa depends on τλM,a and α. To estimate the combined effect of these two variables on the V0 obtained with the LR method, a sensitivity study was conducted. This study is not explicitly presented in this section but is included as supplementary material in the Supplement. The study showed that a similar variation in both variables has a comparable influence on calibration, although α is more influential due to its greater variability. Finally, this study revealed that the LR method exhibits uncertainties greater than 1 % for τ500,a≥0.25 and α≥1.0; therefore, it should not be applied under these conditions.

One important application of the LR method is its use in calibrating different versions of the CE318-T when the spectral bands between them are different. This is the case for the CE318-TS and CE318-TV12-OC photometers, which are standard instruments in AERONET and AERONET-OC, respectively. As in the previous section, each of the 12 spectral bands of the CE318-TV12-OC has been compared to the nearest CE318-TS spectral band using the ratios VλFF/VλMM. This involves a comparison between 1020/1020, 865/870, 779/870, 665/675, 620/675, 560/500, 510/500, 1020i/1020i, 490/500, 442/440, 412/440, 400/440, with a Δλ up to 91 nm (at 779 nm). These two instruments were used to measure at IZO for a period of 20 d, from 9 to 29 January 2023. The reference calibration value in this case is the standard Langley calibration (V0,λSL) of the CE318-TV12-OC photometer, which is compared to the daily V0,λLR values in Fig.  and Table . The temporal evolution of the V0,λ relative differences (in %) has been split into the morning (blue circles) and afternoon (orange circles). With the exception of 1020 (Fig. a), low ΔV0‾ and σ(ΔV0) values were obtained over the time period. The considerably higher differences in the 1020 nm spectral band measured with the silicon detector are related to the considerably important temperature dependence of the silicon detectors needed at this wavelength range and the lack of temperature characterization of the CE318-TV12-OC photometers. In the rest of the spectral bands, ΔV0‾ ranged between 0.17 and 0.69 in the morning and between 0.02 and 1.13 during the afternoon, with minimum differences in the longest wavelength channel (1020i nm) and maximum in the shortest wavelength channel (400 nm). A similar behavior was observed for σ(ΔV0), with remarkably lower values ranging from 0.01 to 0.21 during the morning and slightly higher (0.04–0.19) in the afternoon excluding the 1020 filter. The difference between morning and afternoon in terms of variability is attributed to the effect of atmospheric turbulence during the afternoon period, while the mean differences observed at shorter wavelengths are attributed to the joint effect of Cimel tracking (no pointing refinement in the last measurements performed at shorter wavelengths) and optical differences between instruments.

In this section, we demonstrate the application of the LR method to detect and correct possible instrumental issues in our photometers. In Sect.  and , we demonstrated the suitability of the LR method to transfer the calibration between instruments with different spectral bands. However, we have not checked the calibration error that the use of the conventional ratio cross-calibration approach in these Δλ conditions can imply. We also observed the impact of different FOVs between instruments and possible instrumental issues such as calibration, temperature dependence in some spectral bands (1020 nm measured with the silicon detector and UV filters), and the joint effect of the lack of refinement during the Cimel tracking and the possible optics differences between similar spectral bands.