Solar AOD calculations rely on the sun as a very stable source at top-of-atmosphere (TOA) with earth-sun distance on an annual cycle as the primary cause of changes in expected irradiance. While the sun is ultimately the source of the moon's reflected light, the lunar irradiance for an Earth observer additionally varies as a function of lunar phase angle (LPA), i.e., the fractional illumination as viewed from the surface) on a monthly scale with changes of significance to AOD over much smaller time intervals. The lunar surface itself is comprised of material types correlated with a range of albedos that affect lunar brightness depending on the particular portion of the moon that is illuminated, and the reflected light is further influenced by surface features that also vary with viewing angle. Although solar irradiance varies by ±3.4 % over the course of a year (with an additional small fluctuation due to an 11 year cycle of solar activity of 0.1 %), this is a simple geometric effect that can be corrected accurately and precisely. By contrast, the lunar irradiance can change by a percentage comparable to the annual solar change in 5–6 h or only 2–3 h in the period near a full moon. For the full moon period, this is due to a number of causes including the oppositional effect (“heiligenschein”) where the highly porous lunar regolith structure produces multiple scatter of the returned light that constructively interferes . This phenomenon is further complicated by the occurrence of “shadow-hiding”, a purely geometric effect where the normally incident sunlight causes any shadows cast by lunar material to be hidden by the material itself resulting in substantial (∼ 40 %) increases in lunar brightness in the full moon intervals (LPA: -5 to +5°) which only lasts ∼20 h. The lunar brightness at full moon is 10× or more that at quarter moon representing an extremely large span of values over the range of lunar phase angles in which CIMEL measurements are made. Even outside of the full moon window, the change in signal from near full moon to quarter moon might be a 7:1 ratio which is much larger than expected if one simply assumed a sphere with lambertian scattering (∼3:1), again a consequence of backscatter effects of irregular lunar regolith surface features. Additionally, the variation of earth-moon distance produces a variation of irradiance of ±12 % within 2 weeks from apogee to perigee. While the effects on lunar irradiance related to orbital geometry such as the non-linear phase function can be definitively modeled, computing the lunar signal remains far more challenging than that for the solar signal due the inhomogeneous and structurally complex lunar surface as well as spectral differences in reflectance and much smaller time scales of variation. Lower signal from the lunar source also precludes estimation of AOD for the UV channels and leads to increased triplet variability (variation of AOD taken at three discrete measurement times within a 1 min interval), particularly when both lunar phase angle (LPA) and lunar zenith angle (LZA) are large.

The applied adjustment to lunar irradiance due to the empirical bias correction can often be a large factor (∼10 %) so it's critically important to examine the resulting product for potential bias. For this purpose, the most straightforward standard of comparison would be the associated solar AOD for the same instrument. While the sun and moon measurement periods are mutually exclusive, the transition interval from day to night and vice versa provides an opportunity to quantify differences in this relatively short window for hundreds of sites on a large number of suitable days. Due to the need to avoid solar contamination of the signal, lunar AOD could not be acquired unless the sun was significantly below the horizon (SZA > 98°) which results in at least a couple hours without data following the final solar AOD measurement even if the moon is above the horizon at sunset (likewise lunar measurements will be precluded for some duration prior to sunrise). This transition interval was standardized for all sites by computing the mean and standard deviation of the average AOD difference for all 3 h windows during the period which included an hour of both day and night measurements with at least 6 observations in each day/night average (measurement protocol nominally has observation every 5 min). Since the nighttime calibration accuracy was specifically being examined in this exercise, the hour averaged data were also restricted to cases of low AOD with small standard deviation (AOD440nm≤0.1 and SD<0.01) for both solar and lunar intervals to minimize the effects of potential cloud influence– though the choice of thresholds had little effect on the results. There are many environmental reasons why day and night AOD may differ that are unrelated to calibration such as changes in cloud cover, relative humidity and dominant emission sources. In situations where these factors notably change over the 2–3 h intercomparison window it is not expected that the solar and lunar AOD will agree over this transition. Therefore, these confounding factors have been minimized by looking at low AOD, stable conditions so any bias in calibration can be assessed properly. Figures  and show these transition AOD 440_nm differences from data acquired at 372 sites measured with 454 different CIMELs vs. lunar phase angle (LPA) and lunar zenith angle (LZA). The degree of agreement between solar and lunar AOD is not notably dependent on LZA despite lower signal at large lunar zenith while there is some varying structure to the differences in Fig.  as a function of LPA suggesting the complexities of lunar irradiance are not always perfectly bias-corrected though the deviations are minor, and diminish with increasing wavelength. When assessed in 10° lunar phase angle bins, the mean AOD 440_nm transition differences were within ±0.005 for all bins except [80–90°] (0.0072) which has the lowest lunar signal but also compromises a small fraction of observations (2.7 %). Mean AOD differences for 675 nm and longer wavelengths were within ± 0.002 for all LPA bins. These statistics are presented in Table S3.

The transitions compare solar vs. lunar AOD over a ∼3 h interval when aerosol conditions may have changed, which would degrade the comparison accuracy. So, comparable datasets were produced with a similar comparison of AOD with 3 h lagged AOD for the same measurement type (using only solar AOD and only using lunar AOD). These comparisons would also experience effects due to real aerosol changes within the lagged window and thus provide statistics as a point of reference for the transition AOD differences.

The additional statistical analysis was restricted to 24 h periods containing all three measurement types: daytime solar AOD, nighttime lunar AOD, and transition AOD differences in order to maximize the commonality of the comparison. For every wavelength, the mean AOD differences across the transition from day-night (night-day) are negligibly small and similar or smaller than the differences observed within day or within night periods implying the absence of systematic bias in the lunar AOD (Table ) as well as Ångström exponent (440–870 nm), Precipitable Water Vapor, fine and coarse mode AOD from the Spectral Deconvolution Algorithm (SDA) of . (Table ). While the statistics in these tables are for low AOD conditions, Figs.  and  show the night to day and day to night to day AOD correspondence up to AOD440nm=1.0 which adds data from an additional 50 sites previously excluded by the 0.1 AOD limit.

We are checking for systematic bias between lunar and solar AOD. Even with stability thresholds applied to the 1 h day/night AOD means, the random component of AOD differences increases substantially with increasing AOD due to real atmospheric aerosol variability over the ∼3 h transition interval. To explore this, means of AOD differences binned by the paired measurement mean AOD and associated 95 % confidence intervals were computed by two methods: a standard normal approximation based on the sample mean and standard error, and bootstrap resampling. The bootstrap method is distribution-free, does not assume Gaussian errors, and accommodates asymmetric sampling distributions – considerations particularly relevant at higher AOD where transition pair counts are lower and AOD difference distributions become increasingly skewed due to episodic aerosol loading. The two methods yield nearly identical confidence intervals across all bins through AOD440nm∼0.8, providing mutual validation, with meaningful divergence only at the highest AOD_440 nm bins (≥0.9) where sample sizes are greatly reduced. At low AOD_440 nm (<0.2), the mean solar-lunar AOD differences are negligibly different, ∼0.002 for both 3 h solar-lunar transition interval directions (day to night, night to day), much less than the AERONET instrumental uncertainty of 0.01. Both diurnal transition scatter plots for day AOD vs. night AOD inclusive of all AOD < 1.0 (Figs.  and ) have nearly identical slope ∼0.95 and CCC (concordance correlation coefficient) ∼0.96. A slope slightly below unity is consistent with a tendency for daytime AOD to exceed nighttime AOD_440 nm at elevated aerosol loading. This binned mean difference analysis shows a small but statistically significant higher daytime AOD_440 nm of 0.013 (night-to-day, CI: [0.011, 0.017]) and 0.016 (day-to-night, CI: [0.012, 0.020]) for AOD_440 nm bin [0.6–0.8] which is the highest AOD bin with adequate sample size (n=2138 and n=2988 for day to night and night to day respectively). This should not be interpreted as a calibration or measurement difference between solar and lunar instruments, but rather as a plausible real diurnal aerosol signal, consistent with known daytime aerosol production mechanisms (photochemistry, greater daytime emission of anthropogenic and biomass burning aerosols, etc.) and the absence of any corresponding effect at low AOD.

The AOD measurement absolute accuracy does not depend on AOD level for CIMEL observations. However, the solar/lunar comparison is made after an interval of several hours when aerosol conditions can change. Higher AOD almost without exception occurs in more variable conditions, so the spread of AOD differences across this time window would be expected to increase (greater standard deviation of AOD difference) though this is mitigated to some degree by the stability check on the computed means. Even a small fractional change in AOD at higher aerosol loading over this interval would manifest as larger individual solar/lunar AOD differences – which would not be the case at low AOD (barring cloud-contamination).

The spread of day-night AOD differences, assessed as the standard deviation of linear regression residuals (observed AOD of the lagged interval minus the value predicted by the linear fit), was computed for 0.1 AOD bins for the combined day/night and night/day transitions as well as the corresponding 3 h lagged “within day” and “within night” comparisons (Fig. S2 and Table S4). Notably, all three groups show a progressively increasing standard deviation of AOD differences as AOD increases strongly suggesting this is fundamentally an effect of the increasing aerosol variability. The standard deviation of the AOD differences for the transition data is higher but quite similar to the lagged “within day” and “within night” values. The lagged AOD “night only” trend is comparable to the “day only” trend suggesting the increased scatter is not a product of low lunar signal at higher AOD. Note: The sample sizes are much larger for the “within day”/“within night” than the transition group and sample size drops off dramatically for the highest AOD bins. Good agreement of the solar and lunar AOD (within ± 0.0075) is also observed for individual sites as depicted in Fig. . This histogram shows all AERONET sites with more than 500 transition comparison events acquired from at least 50 different days (N=106 sites) and demonstrates that all these locations had average AOD440nm differences between day and night less than ±0.01.

No dependence of the 3 h transition AOD difference on latitude is observed when the data are binned by latitude (see Table S5). Limited statistics (due to larger day/night time gaps at very high latitudes) at sites with |Latitude|>60° can be computed for four sites: Kuopio (62.9°), Yellowknife_Aurora (62.5°), Narsarsauc (61.2°), and Marambio (-64.2°) which exhibit a very small mean AOD440nm difference of 0.0009±0.014 (N=369).

The cloud-screening protocols for lunar AOD are the same as for solar AOD with one exception. The lunar measurement sequence does not perform the cross-scan scenario (sky radiance measurements across the aureole during solar operation) which is used to identify clouds via the “curvature” check in the cloud-screening algorithm . This is primarily a check for thin cirrus clouds that are relatively uniform in space and time therefore not easily detected by the temporal variance checks in AERONET cloud screening. It's not possible to definitively determine the effect of omitting this check however we have attempted to estimate this by looking at the solar AOD data with only the curvature test disabled (other checks applied normally) and comparing the results to the standard cloud-screened data. The data removed by the curvature check represents only a subset of the total cloud-screened data in that the majority of cloud-influenced observations will have already been removed by triplet variability and daily time series variability checks in the preceding QC processing. calculated that 4.55 % of global solar Level 1.0 AOD observations are eliminated by the curvature check. Further, there is a practical limit to the range where curvature can reliably distinguish thin cirrus clouds from aerosols with effectiveness dropping off as the AOD becomes large, thus isolating the consequences of lacking curvature check is a nuanced assessment.

Both monthly and daily averages of AOD and Ångström exponent (AE) were computed for the solar AOD record at 259 sites with and without curvature check included in the cloud-screening. While there is an expected tendency of reduced AOD and increased AE when curvature check is utilized, the typical monthly differences are negligible (Figs.  and ). Aggregated multi-year monthly average differences by site (curvature-no_curvature) of AOD 440_nm are very small ranging from -0.0004 to -0.0014 and 97 % of the individual monthly means had mean AOD differences of <0.01 while 7 % of months had no difference. The differences shown in Figs.  and are multi-year month averages so individual months would be expected to exceed this. However, even when monthly AOD and AE are considered individually, the statistical differences are typically quite small. Of 14 810 individual months, only 9 months (0.1 %) had a mean AOD difference greater than 0.02 and only 41 (0.3 %) had a mean AE difference greater than 0.1 when removing the curvature check. The potential for significant changes in daily averages is larger but even so only 1.1 % of days had an increase of AOD440nm>0.02 and 2 % had an increase in AE > 0.1 (mean_AOD_diff440nm=0.002, mean_AE_diff=0.0002). Therefore, in general the lack of curvature check would not normally be expected to have notable consequences for the lunar AOD cloud-screening, but note that there are seasonal intervals where changes in Ångström exponent are more pronounced and may be significant in some regions, such as southeast Asia often in association with monsoonal activity and a small number of locations had 5 %–10 % of the data record where day average AE was >0.1 lower without the curvature check. Even when the absence of curvature check does not profoundly affect mean AOD or AE, the additional number of observations removed can be substantial. For instance, at the AERONET site in Singapore the use of curvature removes 8351 more data points during the 2016–2024 interval than are removed without this screening mechanism, a 5.1 % higher exclusion rate.

It should be noted that additional cloud-screening checks are being developed which are only applicable to daytime measurements so it's possible that disparity in cloud-screening efficiency will be greater in future versions of the database. Conversely, additional future cloud screening of AOD and AE time series by AI/ML algorithms may potentially result in a reduction in differences between solar versus lunar cloud screening.

To quantify this measurement limitation, the solar AOD dataset for all sites with significant lunar AOD record were combined and the maximum possible measureable AOD was empirically estimated by finding the largest recorded AOD in airmass bins and an exponential equation was fit (Fig. ). The same process was repeated using the lunar data record, but the lunar data were further divided into 3 lunar phase angle groups since maximal signal is substantially affected by this phase.

Assuming the AERONET operational threshold Vmin, the maximum solar total atmospheric optical depth (Rayleigh plus aerosol plus gaseous) follows from the Beer-Lambert law where m is the optical airmass: 1τmax⁡(m)=1mln⁡V0Vmin⁡⇒τmax⁡(m)=1mln⁡(1500) This limit allows for accurate total OD values up to 7.31 at an airmass of 1 and 1.05 at an airmass of 7 which is consistent with observed 440 nm maxima of 6.91 and 0.99 in this AERONET solar AOD dataset. Note that the Rayleigh optical depth at 440 nm is 0.243 for mean sea level pressure and gaseous absorption OD is typically <0.01 at this wavelength. The maximum AOD limit has also been observed from solar measurements in very high smoke AOD cases in Indonesia in 2015 with a maximum AOD at 675 nm of 7.1 .

The complexities of lunar dynamics make theoretical calculations of lunar maximum measurable AOD more challenging so empirical determination of these potential limits is a useful estimation. Consistent with expectations, the periods with “bright moon” conditions (small LPA; <22.5°; and illumination of lunar disk >96 %) have the largest observed AOD at all airmass ranges. The lunar intervals that represent the minimum illumination allowed for lunar observations (large LPA; >72.5°; 50 %–65 % illumination) have a maximum observable AOD that is approximately half that of the bright moon conditions and 3× less than the corresponding solar AOD maximum. The ordering of these curves directly reflects the lower lunar V0 at larger LPA: a dimmer lunar source at large LPA provides less signal headroom above the noise floor, as aerosol attenuation drives the beam to unacceptably low signal-to-noise levels at lower AOD values than for a brighter moon or the sun.

Figure  shows lunar and solar AOD data from Ilorin, Nigeria an AERONET site that experiences significant Saharan dust as well as seasonal biomass burning aerosol. In this figure, the AOD observations have been partitioned by AOD bin and airmass range. The relative contribution of AOD in each AOD bin is shown and as air mass increases the fraction of higher AOD decreases as available signal decreases (larger zenith angles). While this is observed for each measurement type (solar/lunar), the elimination of the higher AOD components at large airmass is much more pronounced for lunar data. Note that the proportional contribution from each AOD bin range is similar for lunar (top) and solar (bottom) for small airmass (AM<=2). Both solar and lunar measurements see attrition at larger airmass (AM>=4) due to inadequate signal but the lunar fractional contribution from lower AOD increases more substantially and observations from the three bins of largest AOD are entirely excluded while solar observations lose only the two largest AOD bins.

The broader consequence of this signal limitation on the AERONET data record is sampling bias, specifically truncation of large AOD observations as AOD (and airmass) increases, primarily for shorter wavelengths. While truncation is most visually apparent at large airmass, the signal ceiling is active across all airmass values – even at AM =1–2, the highest-AOD episodic events may exceed the lunar measurement ceiling, particularly at large LPA. This aspect is directly reflected in Fig.  which shows AOD440nm histograms composited for common day data from 201 sites based on all 24 h periods with five or more L2 observations from both day and night (>5 million measurements of both lunar and solar data). These lognormal plots show the increasing loss of higher AOD for both solar and lunar observations at larger airmass, with disproportionately larger such effect for the lunar dataset.

For this set of 201 sites, the average lunar removal percentage (from the L2 AOD dataset) for the 440 nm channel is 3.2 %, while the corresponding rates at 675 and 870 nm are quite small (0.3 % or less). However, this does not imply that the longer wavelengths do not also experience loss due to low signal rejection as there are cases when no channels reach Level 2 data status. The lunar data display much larger (3×) removal rates for 440 nm than do solar data as would be expected due to the lower possible maximum AOD for lunar measurements. Although overall the percentage of AOD that are excluded is small, the fractional loss of AOD can be significant for higher AOD locations with some sites excluding more than 8 % of L2 lunar measurements at 440 nm. The general pattern is that more observations are excluded as AOD increases and typically there is greater removal for lunar than solar measurements. The AOD removal rates for solar and lunar observations by wavelength are computed for a selection of individual sites (Table S1).

Figure  presents data from the AERONET site Palangkaraya where high AOD events are frequent. Figure a shows histograms of all L2 AOD870nm which are overlaid with histograms of the AOD870nm measurements from just the subset where AOD440nm values have been excluded. Figure b shows the percentage of L2 data with an AOD measurement at AOD870nm but not at AOD440nm for the solar and lunar datasets. As expected, the absence of AOD440nm is typically found when AOD870nm is large, with an earlier onset of this feature for the lunar data. As AOD increases the fraction of L2 AOD870nm measurements with no associated AOD440nm becomes substantial and is normally greater for the lunar AOD where the Level 2 data often have 100 % of AOD 440 nm observations excluded for the highest aerosol loading cases. AOD at 440 nm will be significantly higher than 870 nm when Angstrom exponent is large so the removal due to the minimum signal threshold is disproportionately impactful resulting in a much higher rate of shorter AOD observations than that experienced at longer wavelengths.

Despite this selective reduction in higher AOD data, the majority of observations at a given site are for the airmass interval from 1–2 (Solar: 58 %, Lunar: 65.5 %) when the available signal is maximal and sampling bias is not impactful. Thus when comparing solar and lunar AOD distributions for all airmass levels, with sites sorted as either low (<AOD440nm><=0.2) or high (>=0.4) AOD sites, the statistics of composited distributions of day and night observations are typically similar for both measurement types (LOW AOD: solar = 0.124 ± 0.137; lunar = 0.118 ± 0.117 HIGH AOD: solar = 0.658 ± 0.492; lunar = 0.636 ± 0.434) (Fig. S3).

AERONET AODs are computed as the mean of a triplet of measurements taken at 30 s intervals over a 1 min period and diminished signal has effects on triplet variability. While the 24-bit ADC resolution of the amplified detector signal (current/voltage) is sufficient at all levels, lunar observations at the very lowest signal levels can experience greater triplet variability as instrumental noise becomes an appreciable fraction of the measured signal which likely results in higher rejection of AOD observations due to triplet variability thresholds. The triplet variability (max–min) is one metric used to screen for cloud presence and if the triplet variability of any longer wavelength (675, 870, 1020 nm) exceeds a dynamically defined threshold it will typically be screened as cloudy. In most cases such measurements are excluded though there is a provision to “add back” a subset of these cases if there are additional factors (such as high Ångström Exponent) providing confidence that the variability is due to aerosol only. Differences exist in the variability of the measurements depending on the type (lunar, solar) with larger triplets observed for dimmer lunar phase periods than during near full moon conditions which may result in larger AOD uncertainty under those conditions (Fig. ). In general, triplet variability is larger for lunar observations than solar observations (Fig. ). These figures present variability of AOD440nm which has no explicit threshold since as noted the filtering for triplet variability is only applied to longer wavelengths. The equivalent plot for 675 nm triplet variability partioned by moon phase is also available (Fig. S4).