2.1 Site and instrumentation

2.2 GRASP methodology

GRASP contains mainly two independent modules: the “forward model” and the “numerical inversion”. The first one is a radiative transfer model (RTM) used to simulate atmospheric remote sensing observations for a characterized atmosphere. The second module, based on the multi-term least squares method (Dubovik and King, 2000), is used in combination with the RTM for a statistically optimized fitting of the observations to retrieve aerosol properties from radiometric measurements (Dubovik et al., 2014). This provides the algorithm with high flexibility since different constrains can be applied to the retrieval and can be modified to adapt the retrieval for each specific situation. It is important to mention that GRASP works with normalized radiances (I_GRASP), which are related with the measured radiances as

where I_meas is the radiance measured by the instrument and E₀ is the extraterrestrial solar irradiance, both expressed in the same units. The standard ASTM-E490 solar spectrum has been used in this work for the normalization of Eq. (1). This spectrum was calculated for moderate solar activity and medium Sun–Earth distance; therefore, it has been corrected from Sun–Earth distance for each day of the year. This way, the normalization factor must be applied when using data in radiance units as input to GRASP and to transform the output-normalized radiances from GRASP into radiance units.

3.1 Dark-signal correction

For the dark-signal (DS) evaluation, the instrument was fully covered with a black piece and introduced into a thermal chamber in the GOA-UVa facilities. The instrument was subjected to a temperature variation in the range from −10 to 50 ^∘C in darkness conditions. The dark signal registered by each channel at each temperature is shown in Fig. 1. It shows a constant behaviour for 440 and 500 nm filters. On the contrary, for the other wavelengths a staggered exponential behaviour can be seen. To characterize this behaviour, the logarithm of the ZEN dark signal has been fitted to a polynomial of degree 3. This fitting is afterwards rounded up to the unit to obtain a staggered fitting. The modelled dark signal is also represented in Fig. 1 by the black lines. This modelling has been used to subtract the corresponding dark-signal value from the raw signal, obtaining dark-signal-corrected ZSR (ZSR_DSC). The residuals between the modelled and real DS are shown in Fig. S2 in the Supplement; these residual values are within the instrument resolution for all channels. It has also been verified that the dark-signal behaviour has remained constant over time, comparing the modelled DS against the nighttime measurements. In this work, the DS has been characterized in the laboratory to cover a wide range of temperatures, but it could be calculated from the nighttime measurements (dark sky) or even from daytime measurements (covering the instrument with a black piece), when a thermal chamber is not available.

Figure 1ZEN-R52 dark signal (DS) in analogue-to-digital units (ADUs) against the temperature (coloured dots) at 440, 500, 675 and 870 nm. Black lines represent the DS for each channel.

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3.2 Quality control filtering criteria

With the dark signal corrected, we compared the field measurements of ZSR_DSC against the simulated ZSR (ZSR_SIM). This first comparison is shown in the left panels of Fig. 2. The colour of the points in the scatter plots of Fig. 2 represents the density of points per pixel as defined by Eilers and Goeman (2004); all the density scatter plots of this paper were done in this manner. The determination coefficient (r²) is also added in the panels of Fig. 2, showing in general good agreement for each channel between ZSR_DSC and ZSR_SIM but with some outliers regarding the linear trend (see left panels a, c, e and g). These outliers present higher ZSR_DSC values than expected, and they could be caused by the presence of clouds in the zenith, instrument malfunction or other reasons.

Figure 2Density scatter plot of the measured zenith sky radiances corrected from dark signal (ZSR_DSC), in analogue-to-digital units (ADUs), against the zenith sky radiances simulated by GRASP (ZSR_SIM), both at 440 (a, b), 500 (c, d), 675 (e, f) and 870 nm (g, h). Left (a, c, e, g) and right (b, d, f, h) panels show these data before and after applying a quality control filtering, respectively. Determination coefficient (r²) and number of data pairs (N) are also shown.

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The ZEN-R52 measurements can be affected in different ways. For example, a possible stray sunlight intromission when the Sun is very elevated can increase the measured signal, the presence of clouds can also affect it, or the variation in temperature can introduce some dependency. To identify and reject the cloud-contaminated or wrong measurements, different thresholds have been identified after the visual analysis of some parameters in the scatter plots. For the SZA, the signal of the instrument is higher than the expected for SZA values below 30^∘, which could be explained by solar stray sunlight intromission. Then, ZSR_DSC values recorded under SZAs below 30^∘ were discarded, as well as the values with SZAs above 80^∘ due to the low signal registered for these SZAs (see Fig. S3 in the Supplement for a clear overview). The ZEN variability parameter (Sect. 2.1.3) can be assumed as a cloud presence indicator, since measurements affected by clouds should register a high ZEN variability due to the high fluctuation of the sky radiances during the 1 min measurement. An evaluation of Fig. 2 but with points classified by its ZEN variability at 440 nm led us to establish a threshold of 4 % for this parameter at the four channels (see Fig. S4 in the Supplement).

No other clear dependence of the outliers has been observed. The results after applying the mentioned filters ($\mathrm{30}{}^{\circ }<\mathrm{SZA}<\mathrm{80}{}^{\circ }$; ZEN  variability<4 %) are represented in the right panels (b, d, f and h) of Fig. 2. The number of coincident measurements is reduced to 4369 points after applying the quality control, but a significant improvement in the determination coefficients is observed, rising from 0.97, 0.93, 0.85 and 0.8 to 0.99, 0.99, 0.96 and 0.95 for 440, 500, 675 and 870 nm, respectively. From now on, all the ZSR_DSC measurements will satisfy this quality control unless otherwise specified.

3.3 Temperature correction

In order to check the dependence with temperature of each channel, the ZSR_DSC $/$ ZSR_SIM ratio normalized by the mean ratio has been plotted against the temperature in Fig. 3. In the left panels (a, c, e and g) of Fig. 3, all data points are represented together with the linear fit, showing a negligible dependence on temperature for 440 and 500 nm. For the 675 and 870 nm channels, this dependency presents slopes of the linear fitting of 0.008 and 0.0036 ${}^{\circ }{\mathrm{C}}^{-\mathrm{1}}$, respectively. These values are higher than the 0.0002 ${}^{\circ }{\mathrm{C}}^{-\mathrm{1}}$ obtained for the other two channels, which led us to consider a temperature correction for 675 and 870 nm. In order to disregard outliers, the ratios were grouped by 2 ^∘C bins, and its median was calculated whenever the group had at least 40 points. These median values are plotted against the mean temperature of the group's temperatures in Fig. 3 right panels (b, d, f and h). The corresponding linear fit coefficients obtained in Fig. 3f and h are used for the temperature dependency correction following Eq. (2):

where ZSR_DSC is the ZEN signal after dark-signal correction, and ZSR_TC is this signal with the temperature correction applied; a and b represent the intercept and slope of the final linear fits, respectively; y₂₀ is the correspondent y-axis value of the linear fit at the temperature T of 20 ^∘C (arbitrary value chosen to normalize). For 440 and 500 nm, ZSR_DSC and ZSR_TC are equivalent since no temperature correction is applied.

Figure 3Left panels (a, c, e, g): density scatter plots for the normalized ratios ZSR_DSC $/$ ZSR_SIM in arbitrary units (AU) against the temperature at (a) 440, (c) 500, (e) 675 and (g) 870 nm. Right panels (b, d, f, h): scatter plots of the median value for the ratios ZSR_DSC $/$ ZSR_SIM grouped in 2 ^∘C ranges against mean temperature of the group at (b) 440, (d) 500, (f) 675 and (h) 870 nm. The Linear fit (red line), its equation, determination coefficient (r²) and number of data points (N) are also shown.

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3.4 Calibration coefficients

The calibration factors can be directly obtained by comparing the dark and temperature-corrected ZSR from the ZEN-R52 against the values simulated by GRASP. The density scatter plots between ZSR_SIM values and ZSR_TC are shown in Fig. 4. The slope of the linear fit directly represents the calibration coefficients obtained to transform the ZSR_TC signal into radiance units ($\mathrm{W}{\mathrm{m}}^{-\mathrm{2}}{\mathrm{nm}}^{-\mathrm{1}}{\mathrm{sr}}^{-\mathrm{1}}$) for each channel. The calibrated ZSR data are named ZSR_ZEN hereafter.

Figure 4Density scatter plot of the zenith sky radiance simulated (ZSR_SIM) in radiance units against the ZEN-R52 measurements in arbitrary units (AU) corrected in dark signal and temperature (ZSR_{DSC_TC}) at (a) 440, (b) 500, (c) 675 and (d) 870 nm. The Linear fit (red line) and its equation, determination coefficient, (r²), and number of data points (N) are also shown.

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These calibration coefficients are compared to the ones obtained by intercomparison with a calibrated integrating sphere at IARC facilities in Table 1. Table 1 also presents the relative differences between both calibration coefficients using the coefficients from IARC as reference; the uncertainty involved in the latter calibration method procedure is estimated to be 5 % by Walker et al. (1991). These differences are 1.39 %, −6.54 %, −6.72 % and −5.89 % for 440, 500, 675 and 870 nm, respectively. The proposed calibration method uses the standard ASTM-E490 solar spectrum to transform the unitless output radiances from GRASP, as indicated in Eq. (1). This fact can increase the relative differences between the two calibration methods, together with the lack of temperature correction in the second one. However, when using the calibration method developed in this study, the same normalization factor applied to the ZSR simulated by GRASP (ZSR_SIM) can be applied to the calibrated ZEN-R52 measurements when using them as input to GRASP for the inversion. This way, the introduction of a systematic error due to the normalization required by the GRASP inversion algorithm can be avoided. This means that this calibration method is better suited when using the ZSR_ZEN values as input for GRASP to retrieve aerosol properties, since we could work directly with the normalized radiances from GRASP. For this work, it has been assumed that during the period of study the calibration has not decayed, since it is not a long dataset. Nevertheless, a recalibration must be considered, especially if there is any maintenance or repair task. From now on, ZSR_ZEN will stand for the calibrated zenith sky radiances measured by the ZEN-R52, satisfying the stabilized quality controls ($\mathrm{30}{}^{\circ }<\mathrm{SZA}<\mathrm{80}{}^{\circ }$; ZEN  variability<4 %).

Table 1Calibration coefficients obtained using simulations of zenith sky radiance (Coef-SIM) and the ones obtained at the IARC against a calibrated integrating sphere (Coef-IARC). The relative difference (Δ) between both coefficients is included assuming Coef-IARC as reference.

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3.5 ZEN-R52 vs. CE318 photometer comparison

In order to check the goodness of the calibrated ZEN-R52 measurements, the ZSR_ZEN observations have been compared against measurements recorded by co-located CE318 instruments for the whole available dataset of ZEN-R52 measurements (April 2019 to September 2021). For the comparison, measurements extracted from two different scenarios are used: the cloud mode (CM) and principal plane (PPL) scanning.

3.5.1 Cloud mode

The CE318 Sun–sky photometer allows us to perform measurements in the “cloud mode” scenario. It is carried out when the direct Sun measurement indicates an obscured Sun and therefore the aerosol retrieval is not possible. This scenario orientates the sensor head into the zenith direction and takes zenith radiance measurements at 9 s intervals for each wavelength, which are obtained by successively rotating an interference filter in front of the detector. The cloud mode scenario was originally implemented to obtain, during this idle time, cloud optical depth from zenith sky radiances at the spectral wavelengths employed by the Sun–sky photometer (Chiu et al., 2010) as suggested by Marshak et al. (2000) and Barker and Marshak (2001).

The zenith sky radiances measured under the cloud mode (ZSR_CM) have been directly downloaded from the AERONET web page. For the comparison with ZEN-R52, quasi-coincident (the closest within ±1 min) ZSR_ZEN and ZSR_CM measurements have been paired and plotted in Fig. 5, showing a good correlation between both datasets. The deviation between them is high, likely due to the short-time variation in the cloud radiative field. Figure 5 includes all the ZSR_ZEN measurements; the filtering to SZA values and ZEN variability is not applied, since the cloud mode measurements are under cloud presence. In this case, there is no dependence on SZA; outliers do not appear for $\mathrm{SZA}<\mathrm{30}{}^{\circ }$ values. Hence, the ZSR_ZEN values do not correlate with reference values for $\mathrm{SZA}<\mathrm{30}{}^{\circ }$ when the Sun is cloud free, which confirms the suggested explanation that ZSR_ZEN measurements are contaminated by stray sunlight under cloud-free conditions when the Sun elevation is high ($\mathrm{SZA}<\mathrm{30}{}^{\circ }$). In addition, it was checked that 86 % of the ZEN-52 measurements used in this comparison (which are known to be affected by clouds) present a ZEN  variability>4 % at least for one channel. This also validates the proposed use of the ZEN variability as a rough “cloud screening”.

Figure 5Scatter plot of the calibrated ZEN-R52 measurements (ZSR_ZEN) against coincident measurements from AERONET cloud mode (ZSR_CM) at (a) 440, (b) 500, (c) 675 and (d) 870 nm. The Linear fit (red line) and its equation, determination coefficient (r²), and number of data points (N) are shown. The median (Md) and standard deviation (SD) of the Δ differences are also shown. Point colours represent the SZA.

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This comparison against the cloud mode measurements will not be used to quantify the uncertainty of the ZEN measurements; this is because clouds are very variable and, therefore, so is the recorded signal. Therefore, we should compare both measurements carried out at exactly the same time, but this is not the case since ZEN measurements are 1 min averages, while CE318 photometer measurements are quasi-instantaneous. In addition, for the retrieval of aerosol properties, it is necessary to employ measurements under cloud-free conditions; therefore, the results obtained in the following comparison will be the reference ones.

3.5.2 Principal plane scan

CE318 Sun–sky photometers allow us to perform three different scanning scenarios for sky radiance measurements. One of these scanning scenarios is the principal plane (PPL) geometry, where the azimuth angle is equal to the solar azimuth angle while the zenith angle varies, measuring sky radiances. This is done sequentially once for each channel starting at 870 nm, followed by 675, 500 and 440 nm channels for each PPL scenario. The PPL geometry allows us to extract the ZSR by linear interpolation of the PPL points to the zenith position. A cloud screening of PPL points has been made by checking the smoothness of the PPL curve as described in Holben et al. (1998). The smoothness criterion analyses the second derivative of the PPL radiances with respect to the scattering angle. This way the PPL measurement is classified as cloud contaminated if the second derivative is negative (the threshold is not 0 but $-\mathrm{1}\times {\mathrm{10}}^{-\mathrm{7}}$ as empirically determined) at any scattering angle between 2 and 90^∘ (Almansa et al., 2020). The obtained ZSR from this method, based on the interpolation of cloud-screened CE318 sky radiances measured in the PPL geometry, has been labelled as ZSR_PPL.

Figure 6(a–d) Density scatter plot of the calibrated ZEN-R52 measurements (ZSR_ZEN) against coincident zenith sky radiances derived from AERONET PPL measurements (ZSR_ZEN−PPL) at (a) 440, (b) 500, (c) 675 and (d) 870 nm. The Linear fit (red line), its equation, determination coefficient (r²) and number of data pairs (N) are shown. (e–h) Frequency histograms of the ΔZSR_ZEN−PPL differences in AOD from ZEN-R52 and AERONET PPL at (e) 440, (f) 500, (g) 675 and (h) 870 nm are shown. The mean bias error (MBE), median (Md) and standard deviation (SD) of the differences are also shown.

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The PPL dataset is not directly available in the AERONET web page; thus, it has been extracted from the CÆLIS database (Fuertes et al., 2018; González et al., 2020). ZSR_ZEN and ZSR_PPL measurements within ±1 min are compared in Fig. 6. Upper panels (a–d) of Fig. 6 show the density scatter plots of ZSR_ZEN against the reference ZSR_PPL, where a high correlation between both datasets can be observed for all the channels, varying the determination coefficients between 0.94 (at 870 nm) and 0.99 (at 440 and 500 nm). In general, the number of outliers is higher for longer wavelengths.

In order to evaluate the uncertainty of the ZSR_ZEN measurements using ZSR_PPL as reference, the relative differences between ZSR_ZEN and ZSR_PPL(ΔZSR_ZEN−PPL) have been evaluated and represented in frequency histograms in the bottom panels (e–h) of Fig. 6. These panels also include the mean (mean bias error; MBE), median (Md) and standard deviation (SD) of ΔZSR_ZEN−PPL. The median values, less sensitive to outliers, are close to zero (Md=1.36 %, −1.39 % and −0.22 % for 440, 500 and 675 nm, respectively), indicating that the ZSR_ZEN values are accurate regarding the reference ZSR_PPL values, except for the 870 nm channel, whose Md value of 4.99 % points out an overestimation of the reference ZSR values. The precision decreases for longer-wavelength channels, from SD values of 3.00 % and 4.62 % for 440 and 500 nm, respectively, to SD=12.54 % and 21.37 % for 675 and 870 nm, respectively. These accuracy and precision values will be used in the convergence criteria mentioned in Sect. 2.2.2.

All these statistical parameters have been calculated by also considering the calibration coefficients, without temperature correction, obtained at IARC with a calibrated integrating sphere. These parameters and those previously obtained by the proposed method of this work are shown in Table 2 to check which calibration provides ZSR values closer to the reference ZSR_PPL values. The results of Table 2 show that the ZSR obtained with the proposed calibration method, based on intercomparison with ZSR simulations, is, in general, more accurate and precise except for 440 nm. Although the results of Table 2 for 440 nm are worse for the proposed calibration than for the IARC calibration, the results are still good for the proposed method with MBE close to 0 (1.96 % and respectively 0.73 % for IARC) and a low value of SD (3 % and respectively 2.95 % for IARC). The ZSR_ZEN values from the IARC calibration are not temperature corrected, which could partially explain the observed differences.

Table 2Determination coefficient (r²) between ZSR_ZEN and ZSR_PPL,the mean (MBE), median (Md) and standard deviation (SD) of the Δ differences between ZSR_ZEN and ZSR_PPL at 440, 500, 675 and 870 nm using the calibration coefficient obtained in this paper with simulated ZSR values and the ones obtained with an integrating sphere at IARC in parenthesis. N represents the number of coincident ZSR_ZEN and ZSR_PPL data pairs.

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These results indicate that the ZEN-R52 measurements are more reliable at shorter wavelengths and, therefore, should be given more importance than those corresponding to longer ones in the retrieval of aerosol properties. The inversion module from the GRASP code considers the importance of each measurement through the so-called “noises”, allowing us to associate a different noise or reliability to each channel, considering them as normal distributions. The standard deviations collected in Table 2 (using the calibration proposed in this work), associated with the ZSR_ZEN uncertainty, are used to this end in the GRASP-ZEN method.

4.1 Scenarios from the combination of five aerosol types

In this test the aerosol scenarios are formed by a random mixture of the five aerosol types used by the models GRASP inversion strategy (see Sect. 2.2.2). Here we aim to assess the capabilities of the retrieval of aerosol properties if the observed aerosol was actually a pure mixture of these five types of aerosol. To this end, random fractions of each aerosol type are selected together with a random total aerosol concentration chosen in the interval from 0.01 to 0.15 µm³ µm⁻², which will be used in combination with the fixed aerosol properties from each model, creating a total of 1000 scenarios. The simulations have been made for three different SZAs (30, 50 and 70^∘), but we will focus here on the $\mathrm{SZA}=\mathrm{50}{}^{\circ }$ situation, which would represent a halfway solution and common scenario for the latitude of Valladolid.

Figure 7 shows the AOD_INV retrieved for SZA equal to 50^∘, against the original synthetic AOD (AOD_SYN). The same graphs for SZA at 30 and 70^∘ are shown in Fig. S6 in the Supplement. In general, the data deviation increases for high AOD values, which are less frequent. For SZA equal to 50^∘, the method overestimates the aerosol load for all the wavelengths, with MBE ranging from 0.23 at 440 nm to 0.11 at 870 nm. The best results are obtained for $\mathrm{SZA}=\mathrm{30}{}^{\circ }$, with absolute mean bias errors lower than 0.002 for all wavelengths and the lowest uncertainty (standard deviation lower than 0.66), while for $\mathrm{SZA}=\mathrm{70}{}^{\circ }$ the method slightly underestimates the AOD with MBEs ranging from −0.004 to 0. It is important to point out that the convergence capability of the method decreases for high SZAs, with the convergent inversions being a total of 43.2 % and 43.6 % at SZA=30 and 50^∘, respectively, but only 27.1 % for $\mathrm{SZA}=\mathrm{70}{}^{\circ }$ (considering that there are initially 1000 scenarios). These results could be related to the dependence of the ZSR sensitivity on the SZA, which is higher for lower SZA, and therefore would make it easier for the method to find a solution.

Figure 7Density scatter plot of the AOD retrieved by GRASP after the inversion of synthetic ZSR (AOD_INV) against the initial AOD (AOD_SYN) obtained for synthetic scenarios created from the combination of five aerosol types for $\mathrm{SZA}=\mathrm{50}{}^{\circ }$ at (a) 440, (b) 500, (c) 675 and (d) 870 nm. The Linear fit (red line) with its equation, determination coefficient (r²) and number of data points (N) are shown. Mean bias error (MBE), median (Md) and standard deviation (SD) of the absolute and Δ (between round brackets) differences between the inverted and synthetic AOD are also included.

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Figure 8Frequency histograms of the absolute differences in the aerosol size distribution properties retrieved by GRASP after the inversion of synthetic ZSR (INV) and the ones initially obtained (SYN) for synthetic scenarios created from the combination of five aerosol types at $\mathrm{SZA}=\mathrm{50}{}^{\circ }$. The mean bias error (MBE), median (Md) and standard deviation (SD) as well as their corresponding values for the Δ differences (between round brackets) are also shown. These size distribution properties are volume median radius of fine (RF) and coarse (RC) modes, standard deviation of log-normal distribution for fine (σF) and coarse modes (σC), and aerosol volume concentration for fine (VCF) and coarse (VCC) modes as well as the total (VCT).

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For the size distribution, the frequency histograms of the absolute differences between the inverted and the synthetic parameters are shown in Fig. 8 for a clear overview of the results obtained (the direct scatter plot comparison can be seen in Fig. S7 in the Supplement). For the current synthetic test, the retrieval of size distribution properties is very accurate and precise, showing Md values very close to zero for all the properties. For the volume median radius and standard deviation of the log-normal distribution, the precision is high, with SD<10 % for both fine and coarse modes. In the case of the aerosol volume concentration, the uncertainty is higher, with SD values of 0.03 (34.6 %), 0.01 (20.4 %) and 0.02 µm³ µm⁻² (53.9 %) for the total, fine and coarse modes, respectively. These results could be, at least in part, due to the fixed size distributions for the models, which present similar RF, RC, σF and σC values; therefore, they will not show an important variation when combining them, but on the contrary, the aerosol volume concentration is an extensive property and therefore can have a higher variation.

4.2 AERONET scenarios

The same procedure is developed in this test but using real aerosol scenarios retrieved at Valladolid by AERONET. In this case, the AERONET-retrieved aerosol properties (size distribution, refractive indices, etc.) are used directly as input in the GRASP forward module to simulate the ZSR values. For this new test, all the available inversions (almucantar and hybrid scans) from AERONET for the coincident ZEN-R52 measurement period (2019–2021) with a sky error < 5 % have been used, obtaining a total of 5321 synthetic scenarios. With this test, we aim to assess the capabilities of the method to retrieve the aerosol properties when the aerosol scenario corresponds to real aerosol conditions and not necessarily to a mixture of the five mentioned aerosol types. In this situation, the ZSR_SYN simulations are made for the corresponding date and time at which the AERONET inversion product was retrieved, achieving a wide variety of SZA values ($\mathrm{18}{}^{\circ }<\mathrm{SZA}<\mathrm{78}{}^{\circ }$).

Figure 9 presents the comparison between the AOD_INV, obtained from the inversion of the perturbed ZSR_SYN with GRASP-ZEN, and AOD_SYN from AERONET scenarios. This comparison reveals a clear overestimation of the inverted AOD values compared to the original ones for the four wavelengths, ranging the MBE values from 0.01 to 0.04 and the Md from 0.01 to 0.03 for the differences between both datasets. These results could be related with the previous results of AOD overestimation at $\mathrm{SZA}=\mathrm{50}{}^{\circ }$, but in this situation it is not related with the SZA, since it has been checked that points with different SZAs are homogeneously distributed. Therefore, the overestimation occurs for all SZA. The standard deviation values of the AOD differences, which can be associated with a “theoretical uncertainty” of the method, are 0.05 for 440 and 500 nm, 0.03 for 675 nm, and 0.02 for 870 nm.

Figure 9Density scatter plot of the AOD retrieved by GRASP after the inversion of synthetic ZSR (AOD_INV) against the initial AOD (AOD_SYN) obtained for synthetic scenarios created from AERONET retrievals at (a) 440, (b) 500, (c) 675 and (d) 870 nm. The Linear fit (red line) with its equation, determination coefficient (r²) and number of data points (N) are shown. Mean bias error (MBE), median (Md), and standard deviation (SD) of the absolute and Δ (between round brackets) differences between the inverted and synthetic AOD are also included.

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The reason for the observed overestimation could be in the limitations of the GRASP-ZEN method based on the models approach, which only allows us to retrieve aerosol properties within the properties of the five aerosol types. This means that, for example, if the real aerosol has a median radius of fine mode bigger than the ones of the five models, then the GRASP-ZEN retrieval will underestimate the real median radius of fine mode, and this difference will be compensated for by unbalancing other aerosol properties to fit the measured ZSR and the synthetic ZSR values of the retrieved aerosol scenario (to reduce the residual differences in ZSR values).

Figure 10Frequency histograms of the absolute differences in the aerosol size distribution properties retrieved by GRASP after the inversion of synthetic ZSR (INV) and the ones initially obtained (SYN) for synthetic scenarios created from AERONET retrievals. The mean bias error (MBE), median (Md) and standard deviation (SD) as well as their corresponding values for the Δ differences (between round brackets) are also shown. These size distribution properties are volume median radius of fine (RF) and coarse (RC) modes, standard deviation of log-normal distribution for fine (σF) and coarse modes (σC), and aerosol volume concentration for fine (VCF) and coarse (VCC) modes as well as the total (VCT).

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To explore this hypothesis, the retrieved size distribution properties have been compared with the synthetic ones. The frequency histograms for the absolute differences between the inverted and the synthetic properties are shown in Fig. 10 (the direct scatter plot comparison can be seen in Fig. S8 in the Supplement). The retrieved volume concentrations present median differences regarding the synthetic ones about 0.01 µm³ µm⁻² for VCF and VCT and very close to zero for the VCC. Similarly to the AOD, the volume concentration data present a theoretical uncertainty of 0.01 µm³ µm⁻² for the fine mode and 0.02 µm³ µm⁻² for the coarse mode and the total. The retrieved intensive properties underestimate the reference values, with the median values of their differences being about −14 % and −10 % for RF and σF, respectively, and −10 % and −4 % for RC and σC, respectively.

This lack of accuracy is the main difference between the results of Figs. 10 and 8. As mentioned before, we would expect a higher accuracy and precision in the retrieved values of the volume median radius and standard deviation for the model combination scenarios test (Sect. 4.1), since the scenario can be perfectly reproduced by GRASP-ZEN because it is a combination of the same models used in the inversion module; however, for a real aerosol scenario (the test for AERONET scenarios of this subsection), these properties would be impossible to obtain with enough accuracy since they present a wider range of size distributions than the one offered by the models approach. Similar results are expected for the real and imaginary refractive index and other optical properties, due to the limitations of the models approach.

The results of this section conclude that the GRASP-ZEN method is useful for the retrieval of AOD but not for some size distribution properties, like the volume median radius and standard deviation of fine and coarse modes. Therefore, we will focus on the retrieval of AOD at 440, 500, 675 and 870 nm as well as VCF, VCC and VCT.

5.1 Aerosol optical depth

The AOD retrieved by GRASP-ZEN using the ZSR_ZEN measurements (AOD_{GRASP_ZEN}) has been compared against independent AOD measurements from AERONET (AOD_AERONET) derived from CE318 Sun–sky photometers co-located with the ZEN-R52 at Valladolid. Figure 11 shows the complete time series evolution of AOD_{GRASP_ZEN} together with AOD_AERONET, both at 440 nm. Despite some AOD_{GRASP_ZEN} outliers which are not reproduced by the AOD_AERONET, both datasets show in general a similar temporal evolution. Figure 12 shows a more detailed view of these data in a shorter period, from 16 to 22 June 2020, with high availability of data from both GRASP-ZEN and AERONET datasets for the four wavelengths. A lack of AOD values in the GRASP-ZEN dataset around midday is observed; it is explained by the rejection of ZEN-R52 measurements for SZAs below 30^∘, which, in the analysed period and latitude, occurs around midday. In Fig. 12 (panels a–d), it can also be observed that both GRASP-ZEN and AERONET datasets vary with time in a similar way for all the wavelengths, with AOD values from GRASP-ZEN slightly overestimating the AOD values from AERONET at all wavelengths.

Figure 11Time series evolution of aerosol optical depth (AOD) at 440 nm retrieved by GRASP-ZEN and by AERONET at Valladolid for all the ZEN-R52 available dataset (April 2019 to September 2021).

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Figure 12(a–d) Time series evolution of aerosol optical depth (AOD) at (a) 440, (b) 500, (c) 675 and (d) 870 nm retrieved by GRASP-ZEN and by AERONET at Valladolid for a week period in summer 2020 (16 to 22 June). (e) AOD retrieved by GRASP-ZEN for all ZEN-R52 channels are plotted together.

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Figure 13(a–d) Density scatter plots of the AOD retrieved by GRASP-ZEN (AOD_{GRASP_ZEN}) against coincident measurement from AERONET (AOD_AERONET) at (a) 440, (b) 500, (c) 675 and (d) 870 nm. The Linear fit (red line), its equation, determination coefficient (r²) and number of data pairs (N) are shown. (e–h) Frequency histograms of the absolute differences in AOD from GRASP-ZEN and AERONET at (e) 440, (f) 500, (g) 675 and (h) 870 nm. The mean bias error (MBE), median (Md) and standard deviation (SD) are also shown.

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To perform a more quantitative analysis of the correlation between these datasets, a matchup of AERONET AOD (AOD_AERONET) with GRASP-ZEN AOD (AOD_{GRASP_ZEN}) values within 1.5 min has been made, obtaining a total of 37 787 coincident points per wavelength. The AOD data from GRASP-ZEN are represented against the coincident AOD from AERONET in a density plot in Fig. 13 for each wavelength (panels a–d). This figure (panels e–h) also shows in the bottom panels the frequency histograms for the differences between both AOD datasets. AOD_{GRASP_ZEN} presents a higher correlation with AOD_AERONET for shorter wavelengths, with r² ranging from 0.86 at 440 nm to 0.72 at 870 nm. In general, the AOD at 675 nm and especially at 870 nm presents more deviation between the data pairs than for the shorter wavelengths. Some outliers presenting high AOD_{GRASP_ZEN} values can be appreciated, especially at shorter wavelengths; this could be caused by some spurious measurements likely contaminated by clouds that pass the cloud-screening criteria or measurements recorded with dirtiness, rain droplets or dust over the instrument (it must be frequently cleaned). AOD from GRASP-ZEN generally overestimates the AERONET values, as the sensitivity study of Sect. 4.2 pointed out, with median values of the differences of AOD_{GRASP_ZEN} with respect to AOD_AERONET between 0.01 and 0.02 for all wavelengths; similar values appear for MBE, ranging from 0.01 to 0.03. The uncertainty in the retrieved AOD_{GRASP_ZEN} is estimated by SD to be 0.03 for 440 and 500 nm and 0.02 for 675 and 870 nm, using as reference the values provided by AERONET, which are within the theoretical uncertainty obtained in the previous section for the AOD.

5.2 Aerosol volume concentration

Regarding the total aerosol volume concentration, the values retrieved with GRASP-ZEN and the ones from AERONET for the whole period are shown in Fig. 14. The time evolution shows generally a similar behaviour for both datasets with the exception of some VCT extreme values more frequent in the GRASP-ZEN database. Here it can also be seen that for this parameter there is a higher temporal coverage from GRASP-ZEN than from AERONET.

Figure 14Time series evolution of the total volume concentration (VCT) retrieved by GRASP-ZEN and by AERONET at Valladolid for all the ZEN-R52 available dataset (April 2019 to September 2021).

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Figure 15Time series evolution of volume concentration for fine (VCF) and coarse (VCC) modes as well as the total (VCT) retrieved by GRASP-ZEN and by AERONET at Valladolid for a week period in summer 2020 (16 to 22 June).

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The VCF, VCC and VCT values from both datasets are shown in Fig. 15 for the week from 16 to 22 June 2020 (same days than in Fig. 12), showing again a similar behaviour for the two datasets. Figure 15 also reveals that the GRASP-ZEN values are noisier and higher than the AERONET values, especially for the fine mode.

For a more quantitative analysis of the correlation between VCF, VCC and VCT from the GRASP-ZEN and AERONET datasets, a synchronization with a time window of ±5 min was done, obtaining a total of 4356 coincident points for each volume concentration. A higher temporal range is selected here because the inversion products are less frequent than AOD. In addition, we assume that these aerosol properties should not change significantly in 5 min.

Figure 16(a–c) Density scatter plot of the volume concentration for fine (VCF) and coarse (VCC) modes and total (VCT) retrieved by GRASP-ZEN against coincident retrievals from AERONET. The Linear fit (red line), its equation, determination coefficient (r²) and number of data points (N) are shown. (d–f) Frequency histograms of the absolute differences between both datasets. The mean bias error (MBE), median (Md) and standard deviation (SD) are also shown.

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The GRASP-ZEN volume concentrations are represented against the coincident AERONET ones in the density scatter plots of the upper panels of Fig. 16 for fine, coarse and total values. Bottom panels of Fig. 16 also show the frequency histograms of the differences between GRASP-ZEN and AERONET values of VCF, VCC and VCT. The best correlation is obtained for the total volume concentration, with an r² of about 0.66, while for fine and coarse volume concentration the determination coefficients are 0.57 and 0.56, respectively. Despite the low correlation coefficients, the retrieved volume concentrations are rather precise, with median values of the differences between GRASP-ZEN and AERONET datasets of 0.006 and 0.005 µm³ µm⁻² for fine and coarse modes, respectively, and 0.010 µm³ µm⁻² for the VCT. The highest dispersion of the differences in volume concentrations is obtained for the VCT, which presents a SD value about 0.020 µm³ µm⁻², while for fine and coarse modes these values are 0.009 and 0.016 µm³ µm⁻², which are close to the uncertainty of AERONET products (0.01 µm³ µm⁻²). These results are again within the theoretical uncertainty obtained in the previous section.

All the results of this paper have been obtained using the GRASP-ZEN methodology based on the models approach, which is a suitable option for the current study due to the reduced number of radiometric observations provided by the ZEN-R52. However, the versatility of the GRASP code allows for different strategies for the retrieval of aerosol properties. In this sense, we have considered other strategies in this study to choose the one which provides the best results. These strategies are based on the temporal multi-pixel approach offered by GRASP (Lopatin et al., 2021), which constrains the variation of aerosol properties in time, forcing them to vary smoothly. The multi-pixel approach was firstly used in combination with the models approach. In order to avoid the problems derived by having fixed aerosol models with fixed aerosol properties, the temporal multi-pixel was also used by assuming the size distribution as a bimodal (fine and coarse modes) log-normal distribution and the refractive indices have no dependence on wavelength. None of these methods significantly improved the retrieval of aerosol properties, but they did reduce the computation time (the data of a full day are inverted all at the same time). Nevertheless, these strategies could be considered for future aerosol retrievals.