The data used in this paper were acquired between April and September 2019 at the Izaña Atmospheric Observatory (IZO). This observatory is located on the island of Tenerife (Spain; 28.3∘ N, 16.5∘ W; 2.4 km a.s.l.), and it is approximately 350 km away from the African continent. This observatory is managed by the Izaña Atmospheric Research Center (IARC) from the State Meteorological Agency of Spain (AEMET; more information at http://izana.aemet.es; last access: 7 November 2019).

In 1984, IZO enrolled in the WMO Background Atmospheric Pollution Monitoring Network (BAPMoN) and the WMO Global Atmosphere Watch (GAW) programme in 1989. IZO collaborates with different international networks, such as the Network for the Detection of Atmospheric Composition Change (NDACC) since 1999 and the GAW–PFR since 2001. In 2003, the Regional Brewer Calibration Center for Europe (WMO–GAW RBCC–E) was established. Furthermore, IZO has been part of AERONET since 2004, as one of the two AERONET–Langley plot calibration sites . Since 2009, IZO has run a Baseline Surface Radiation Network (BSRN) station. In 2014, IZO was appointed by WMO as a Commission for Instruments and Methods of Observation (CIMO) test bed for aerosols and water vapour remote-sensing instruments . More details of IZO programmes can be found in .

An EKO MS-711 grating spectroradiometer used in direct sun-measurement mode has been tested (Fig. ) in the CIMO test bed programme from April to September 2019 (14 706 data points).

The EKO MS-711 was designed to measure global solar spectral radiation within the 300 and 1100 nm wavelength range with an average step of ∼0.4 nm, which exhibits a full width at half maximum (FWHM) <7 nm. It is equipped with built-in entrance optics, and the housing is temperature-stabilized at 25∘C±5∘C . EKO Instruments designed a collimator tube that also allows for the measurement of DNI (see Fig. ).

This spectroradiometer has been mounted on an EKO sun tracker STR-21G-S2 (accuracy of <0.01∘). This set-up performs one spectrum per minute, with an exposure time that changes automatically according to the intensity of the irradiance that varies from 10 ms to 5 s. The main specifications of the EKO MS-711 spectroradiometer are shown in Table .

In this paper, we have used AOD data provided by the permanent AERONET–Cimel CE318-T reference instrument to compare the AOD derived from the EKO MS-711 spectroradiometer. The different Cimel references have been shown to have good AOD traceability with the GAW–PFR worldwide reference . The World AOD reference is maintained by the World Optical Depth Research and Calibration Center (WORCC) .

The Cimel CE318-T photometer is an automatic sun–sky scanning filter radiometer that measures AOD at 340, 380, 440, 500, 675, 870, and 1020 nm (nominal wavelength; extended wavelength versions additionally have 1640 nm), with a full opening angle of 1.2∘. The uncertainty in AOD measurements from Cimel field instruments was estimated to be ±0.01 in the VIS range and near-IR, which increased to ±0.02 in the UV range (340 and 380 nm) . This estimate gives an absolute bias <0.01 for AOD lower than 1.5 . In this study, we have used AERONET version 3.0 level 1.5 AOD data.

The EKO MS-711 spectroradiometer was factory calibrated by EKO Instruments, by making use of a calibrated transfer standard 1000 W quartz tungsten halogen coiled coil filament lamp that is traceable to the National Institute of Standards and Technology (NIST) standard . The instrument's resultant uncertainty is ±17 % for the UV range and <5 % for the VIS range. In November 2016, the EKO MS-711 participated in an intercomparison campaign of spectroradiometers at the National Oceanic and Atmospheric Administration (NOAA) Mauna Loa Observatory (MLO), Hawaii, USA (19.54∘ N, 155.58∘ W; 3397 m a.s.l.; ), where it was calibrated with the Langley method . In 2018 the instrument was deployed at the Physical–Meteorological Observatory and World Radiation Center (PMOD–WRC) for its characteristic use of a tunable laser . Recently, between April and September 2019, the EKO MS-711 was calibrated at the Izaña Atmospheric Observatory by using the Langley method in the 300–1100 nm spectral range. In this study we have used the calibration coefficients with the Langley plot method.

The Langley method used in the IZO Langley calibration is based on the Beer–Lambert–Bouguer law as follows: 1DNI(λ)=DNIo(λ)e-τ(λ)m, where DNI(λ) is the direct normal irradiance at wavelength (λ) measured by the instrument; DNIo(λ) is the top-of-atmosphere irradiance corrected for the Sun–Earth distance at wavelength (λ); m is air mass; and τ(λ) is the optical depth. This expression can be written in the UV–VIS range as follows: 2τ(λ)=τR(λ)+τa(λ)+τNO2(λ)+τH2O(λ)+τO2(λ)+τO3(λ), where τR(λ) is the Rayleigh optical depth , due to the molecular scattering that depends on the station pressure and on the optical air mass (mR) ; τa(λ) is the AOD; and the rest of the terms are the absorption by atmospheric gases in the affected wavelengths . These are defined as follows: 3τR=PPo0.008569λ-41+0.0113λ-2+0.00023λ-4, where P is the pressure at the measurement site within the Earth's atmosphere; Po is the standard pressure at sea level; and λ is the wavelength in micrometres. In situ actual pressure at IZO was used. 4τNO2(λ)=uNO2ANO2, where uNO2 is the reduced path length (in atm cm) taken from the Ozone Monitoring Instrument (OMI) total column NO2 monthly average climatology, and ANO2 is its spectral absorption coefficient . 5τH2O(λ)=(uH2OAH2O)bH2O, where uH2O is the column water vapour content (precipitable water) taken from a global navigation satellite system (GNSS) receiver that considers satellite precise orbits at IZO ; AH2O is the spectral absorption coefficient ; and the bH2O exponent depends on the central wavelength position, instrument filter function, as well as the atmosphere pressure and temperature . We have determined τH2O(λ) from the transmittance for different water vapour and solar zenith angle (SZA) values from the MODerate resolution atmospheric TRANsmission (MODTRAN) model . 6τO2(λ)=(uO2AO2)bO2, where uO2 is the altitude-dependent gaseous-scaled path length taken from the Fourier-transform infrared spectrometer (FTIR) measurements at IZO ; AO2 is the spectral absorption coefficient ; and the bO2 exponent was obtained from the transmittance values simulated with the MODTRAN model for IZO, which obtained a value of 0.454. This value is similar to that obtained by . 7τO3(λ)=uO3AO3, where uO3 is the total column ozone obtained with a reference Brewer spectrophotometer at IZO and AO3 is the ozone absorption cross section .

The Langley plot determines DNIo(λ) (which allows us to derive calibration constant) from a linear extrapolation of DNI(λ) measurements to zero air mass, which is corrected to mean Sun–Earth distance, and plotted on a logarithmic scale versus air mass as follows: 8ln⁡DNI(λ)=ln⁡DNIo(λ)-[τR(λ)mR+τa(λ)ma+τNO2(λ)mNO2+τH2O(λ)mH2O+τO2(λ)mO2+τO3(λ)mO3], where the different air masses have the following expressions: 9mR∼mO2=1cos⁡(θ)+0.50575(96.07995-θ)-1.6364(Kasten and Young, 1989; Gueymard, 2001);10ma∼mH2O=1cos⁡(θ)+0.0548(92.65-θ)-1.452(Kasten, 1966);11mNO2=1sin⁡(θ)+602.30(90-θ)0.5(27.96+θ)-3.4536(Gueymard, 1995); and12mO3=R+h(R+h)2-(R+r)2sin⁡2(θ)(Komhyr et al., 1989), where R (6370 km) is the mean radius of the Earth, r is the station height above mean sea level in kilometres, and h is the mean height of the ozone layer in kilometres (22 km).

The AOD retrievals have been calculated from Eq. (), as follows: 13AOD=1ma[ln⁡DNIo(λ)-ln⁡DNI(λ)-τRmR-τNO2(λ)mNO2+τH2O(λ)mH2O+τO2(λ)mO2+τO3(λ)mO3]. By grouping the gas contributions, such as τgas, the AOD expression is reduced to the following: 14AOD=1ma[ln⁡DNIo(λ)-ln⁡DNI(λ)-τRmR-τgasm].

In this work, we have calculated the EKO AOD at the same nominal wavelengths as those of the Cimel (340, 380, 440, 500, 675, and 870 nm), by integrating the measured irradiance on the considered bandpass (see Table ) and following the methodology used by AERONET (, and references therein). For each wavelength, we have taken the spectral corrections shown in Table  into account. All wavelengths have been corrected by the Rayleigh scattering (see Sect. ). Furthermore the 340, 380, 440, and 500 nm are corrected from nitrogen dioxide (NO2) absorption, with the optical depth being calculated by using the OMI total column NO2 climatological monthly averages and the NO2 absorption coefficient from . The 340, 500, and 675 nm channels are corrected of column ozone, by using the ozone values from the Izaña WMO–GAW reference Brewer spectrophotometer.

The full opening angle and the FOV are normally used indistinctly in the literature, which should not be confused with the viewing angle. Therefore, we use the term FOV for referring to the full opening angle. As we remarked in the introduction, the WMO has recommended the use of instruments with FOV lower than 2.5∘ and slope angle of 1∘ for AOD retrieval. Since the EKO MS-711 was designed for DNI measurements, it has a larger FOV of 5∘, which is twice the WMO-recommended value for AOD retrievals. To account for the different geometries, we have applied a correction to the EKO irradiance measurements. In this section, we explain the methodology applied to the measurements and comparisons with Cimel AOD.

The DNI measurement implies that a certain amount of diffuse radiation is coming from the line of sight of the instrument positioned towards the Sun, and an annular region around it, the so-called circumsolar region, is measured together with the DNI coming from the Sun disc (DNISUN). The source of this diffuse radiation, the circumsolar radiation (CSR), lies in the scattering processes due to the presence of aerosols and clouds in the atmosphere. This CSR has a high dependence on the particle size ; thus large particles (such as desert dust) produce a higher scattering on the incident beam than the smaller particles (e.g. rural background aerosols), which leads this contribution to overestimate the DNI. Thus, the experimental DNI measured by a collimated instrument may be expressed as the sum of both contributions as follows: 15DNI=DNISUN+CSR, where DNISUN is the direct normal irradiance coming from the Sun disc and CSR is the diffuse radiation coming from the sky that is seen by the instrument FOV. This FOV is defined by the instrument geometry and determines the amount of CSR reaching the instrument detector. The value of the DNI measured by the instrument also depends on the atmospheric conditions and the specific instrument characteristics. The most important element that defines the amount of CSR captured by the instrument is the penumbra function P , which defines the fraction of Sun radiation that is captured or not by the collimator, depending on its angle of vision. This penumbra function can be derived from the geometrical features of the instrument as follows: the aperture half-angle α, the slope angle αs, and the limit angle αl (Fig. a). Usually the three angles are known, with the most important being the aperture half-angle α. Thus, the radiation coming from the sky with an angle higher than the αl is outside the collimator and is then not measured by the instrument.

If all the angles are known, then the function P takes the shape of Fig. b; if αs and αl are unknown, then the penumbra function P can be approximated as the shape on Fig. c. In this paper, we used the penumbra function P described in Fig. c because αs and αl are unknown, and we consider that α= FOV/2 =2.5∘.

Since it is not possible to obtain accurate CSR measurements, it has been simulated with the libRadtran radiative transfer model (; more information at http://www.libradtran.org; last access: 7 November 2019), which provides the possibility of simulating the diffuse radiance on sky elements as defined by its azimuthal and polar angles. We briefly describe the method followed to simulate the amount of CSR measured by the EKO MS-711. The first step is to describe the geometry of the problem, as shown in Fig. .

For a sky point defined by the polar angle θ and azimuthal angle φ, the sky radiance on that point is L (θ, φ) in W m-2 sr-1. The angular distance between the considered point and the Sun's position (the green arc in Fig. ) is the so-called scattering angle, ξ. To obtain the angle ξ of each point in the sky in terms of the polar and azimuthal angles, the following equation should be used: 16cos⁡(ξ)=cos⁡(SZA)cos⁡(θ)+sin⁡(SZA)sin⁡(θ)cos⁡(φ-φSUN).

Taking this relation into account, the radiation field L can be expressed in terms of ξ and φ; thus, the irradiance in the solid angle subtended by an angular distance from the Sun's centre ξ, for an instrument with an aperture half-angle α, is as follows: 17I=∫02π∫αoαP(ξ,φ)L(ξ,φ)cos⁡(φ)sin⁡(ξ)⋅dφdξ, where P(ξ,φ) is the penumbra function defined in Sect. . If the Sun is in the angular field considered, the obtained irradiance is the DNI of Eq. (); if not, the result will only be the diffuse radiation. Thus, the key is to simulate the radiances L(ξ,φ) of the points in the FOV that the instrument is “seeing”. In this paper, and taking into account that the instrument is continuously pointing towards the Sun, the integration is performed for ξ values from αo=0.6∘ to α=2.5∘, with the aim of simulating the diffuse radiation coming from a circumsolar ring in order to compare AOD from both instruments using the same CSR.

The input parameters used in the simulations are shown in Table 3. The aerosol contribution has been included in the simulations by using the Optical Properties of Aerosols and Clouds (OPAC software package; ). This library provides the optical properties of the aerosol (and clouds) in the range from 250 to 4000 nm. In our case, we focused the interest on the aerosol mixtures due to the fact that the aerosols in the atmosphere are found as a mixture of different particles. In the libRadtran package the aerosol mixtures described in are included. The following aerosol optical properties stored in the data sets are used: the extinction coefficient, scattering coefficient, absorption coefficient, volume-phase function, single scattering albedo, and asymmetry parameter. Due to the location of the IZO station, we have selected the desert mixtures for the cases of low and high aerosol load.

At this point we should note that the use of 1D simulations with the discrete ordinate method radiative transfer (DISORT; ) solver implies that the Sun is supposed to be a Dirac delta function, while the Sun has an angular radius of 960′′.12±0′′.09 . However, demonstrated that the error in DNISUN simulations, when the Sun is assumed to be a point source, is negligible with respect to the finite sun assumption ; this showed that the simulations of radiances in the vicinity of the Sun that were performed using the DISORT and OPAC aerosols for cloud-free cases gave the same results as the simulations made with the Monte Carlo RTE solver (MYSTIC) included in libRadtran , by taking the angular extent of the solar disc into account. The differences remain under 1 % and even very close to 0 %. Since we want to simulate cloud-free cases, we can use the 1D DISORT without introducing significant errors into the simulations when compared to the more precise Monte Carlo simulations.

Once we have selected the input parameters, we must also select the correct angular grid in the azimuthal and polar coordinates to cover, at least, the angular region previously defined (0.6∘≤α≤2.5∘). By using Eq. () we can calculate the ranges of polar angles θ and azimuthal angles φ needed. The result of a monochromatic simulation, i.e. L(ξ,φ) at 495 nm for the day 26 July 2019 at SZA of ∼14∘, is shown in Fig. a. In Fig. b the penumbra function, i.e. P(ξ,φ), is shown, and in Fig. c the result of multiplying P(ξ,φ) L(ξ,φ) is shown. Note that the angular grid has been selected in steps of 0.1∘.

The expected CSR will be obtained by integrating the radiation field P(ξ,φ) L(ξ,φ) as indicated in Eq. (). The integration is done by using the angres tool that is provided in the libRadtran package, which uses a Monte Carlo integration in 2D to obtain the diffuse radiation in the considered radiation field.

Once the CSR has been determined, we apply the correction to the measured DNI by taking the CSR simulations explained before into account. Thus, from Eq. () the corrected DNI is as follows: 18DNICORR=DNI-CSR. This correction will lead to a DNICORR<DNI with which we can retrieve an AOD with a similar expression to Eq. () as follows: 19AODCORR=1ma[ln⁡DNIoCORR(λ)-ln⁡DNICORR(λ)-τRmR-τgasm].

We must note that in Eq. () that DNIo, calculated with the Langley plot calibration method (see Sect. ), should also be calculated by applying the FOV correction using Eq. () and substituting DNIo with the corrected DNIoCORR. The EKO AODCORR obtained from Eq. () with a DNIoCORR calculated from Eq. () is supposed to be “free” of any CSR contribution, and then it is straight-forward to assume that the AODCORR is closer to the real AOD present in the atmosphere. In order to know the impact of the aerosol load and the FOV size in the values of the CSR simulations, we have calculated the ratio of the simulated CSR with respect to the DNI given by Eq. (). This is the so-called circumsolar ratio (CR) under cloud-free conditions. We have done simulations of DNISUN and CSR to obtain the previously cited CR, by varying the aerosol load in the range [0–0.50] and the FOV in the range [0–5∘]. The rest of the input parameters remain fixed. The results of CR are shown in percentages for a solar zenith angle of 30∘ for the six Cimel channels in Fig. . 20CR(%)=CSRDNISUN+CSR×100.

As seen in Fig. , CR increases for higher FOV and larger AOD, as expected, and for the lower wavelengths. The dashed lines in Fig.  indicate the FOV of the instruments used in this paper with the Cimel (blue line) and EKO (red line) results. In all cases, the CR for the Cimel is lower than 1 % and even 0.5 % for the channels over 440 nm. For EKO, the CR ranges between 2 % in the 870 nm channel and 5 % for the 340 nm channel. Thus, the expected CSR maximum values in Fig.  should be found under these conditions: FOV of 5∘, AOD of 0.50, and wavelength of 340 nm in which a CR of 5 % is found. We have simulated the AOD retrievals as a function of CSR. By combining Eq. () to (), we can vary CR (the value of CSR, in fact) and calculate the AOD retrieved with the corresponding DNIoCORR.

These results indicate that the CSR impacts significantly on the EKO AOD retrievals under relatively high AOD, which leads to AOD underestimation, with the effect being less important for the Cimel AOD retrievals because of its narrower FOV.

These results have been simulated by considering the typical conditions of IZO where mineral dust is practically the only aerosol present . Simulations of the effect on the CR of the eight OPAC mixture aerosols available in the libRadtran model, which include continental (clean, average, and polluted), urban, maritime (clean, polluted, and tropical), and desert aerosols for FOV =5∘ are shown in Fig. 6. For SZA =30∘, with an AOD500nm range between 0 and 2 at sea level, two defined groups are distinguished, namely the continental and urban aerosol mixtures, and the maritime and desert dust mixtures. It should be noted that for stations located in urban or continental (clean and contaminated) environments, which are the majority, the correction that would have to be made to the AOD for a very high aerosol load (e.g. AOD =1) would be much lower, between 1/3 to 1/6, than the correction that would have been performed in the case of dust aerosol (Fig.  and Appendix B).

Based on the experience of and , we have considered that the Langley calibration is suitable if the standard deviation (σ) of the fit (Eq. ) is lower than 0.006, the correlation coefficient (R)>-0.99, the number of valid points >33% of the initial sample, and AOD (500 nm) <0.025. In order to test the Langley method described in Sect. , an example of Langley plots using the UV–VIS near-IR direct Sun measurements on 19 March 2019 at the Izaña Atmospheric Observatory is shown in Fig. .

The comparison between the factory calibration performed by EKO Instruments in 2016 and the IZO Langley plot calibration (2019) is shown in Fig. . These results indicate that the stability of the EKO MS-711 in the range of 300–1100 nm during a 3-year period, between the manufacturer's lamp calibration and the Langley calibrations at IZO, is remarkable. The factory calibration and the IZO Langley plot calibration 3 years later present differences ∼4.8 % between 350 and 1100 nm, and even ≤2.3 % and 3.1 % in the VIS and near-IR range respectively. The larger differences below 350 nm are attributed to the low halogen lamp signal, which was experienced in this region during the factory calibration, and the low instrument sensitivity in this region.

By applying the previous method, DNIo(λ) values and their standard deviations from the EKO MS-711 measurements (from April to September 2019 at the Izaña Atmospheric Observatory), at the nominal wavelengths measured by the Cimel (340, 380, 440, 500, 675, and 870 nm) as a function of time, are shown in Fig. . These DNIo(λ) values have been used in the AOD retrievals.