AERONET-OC L WN Uncertainties: Revisited

: The Ocean Color Component of the Aerosol Robotic Network (AERONET-OC) aims at supporting the assessment of satellite ocean color radiometric products with in situ reference data derived from automated above-water measurements. This study, applying metrology principles and taking advantage of recent technology and science advances, revisits the uncertainty estimates formerly provided for AERONET-OC normalized water-leaving radiances L WN . The new uncertainty values are quanti ﬁ ed for a number of AERONET-OC sites located in marine regions representative of chlorophyll-a-dominated waters (i.e., Case 1) and a variety of optically complex waters. Results show uncertainties typically increasing with the optical complexity of water and wind speed. Relative and absolute uncertainty values are provided for the various sites together with contributions from each source of uncertainty affecting measurements. In view of supporting AERONET-OC data users, the study also suggests practical solutions to quantify uncertainties for L WN from its spectral values. Additionally, results from an evaluation of the temporal variability characterizing L WN at various AERONET-OC sites are presented to address the impact of temporal mismatches between in situ and satellite data in matchup analysis.


Introduction
In situ reference measurements are essential to any ocean color program for system vicarious calibration of satellite sensors, assessment of primary and derived data products, and development of bio-optical algorithms.The primary ocean color product is the spectral normalized water-leaving radiance L WN : the radiance emerging from below the sea surface derived from the top-of-atmosphere radiance after correction for atmospheric perturbations, normalized with respect to the illumination conditions and viewing geometry, and finally corrected for in-water bidirectional effects.The quantification of the accuracy of L WN , or of the equivalent remote sensing reflectance R RS , is essential to successively determine that affecting derived data products [e.g., chlorophyll-a concentration (Chla)].For this reason, primary satellite radiometric products are matter of extensive validation programs aiming at verifying the compliance of their uncertainties with mission requirements.Often these requirements entail generic uncertainty targets of 5% for satellite-derived L WN or R RS (e.g., Hooker et al. 1992;Drinkwater and Rebhan 2007).Recalling that the 5% uncertainty value is considered achievable in oligotrophic/mesotrophic oceanic waters in the blue-green spectral region (GCOS 2011), its assessment implies access to highly accurate in situ reference data exhibiting uncertainties quantified in agreement with metrology principles.
The Ocean Color Component of the Aerosol Robotic Network (AERONET-OC) was specifically conceived to support the assessment of satellite L WN products through automated in situ measurements performed from offshore fixed structures in a variety of water types (Zibordi et al. 2009(Zibordi et al. , 2021)).A best effort to quantify uncertainties affecting AERONET-OC L WN was made by Gergely and Zibordi (2014).Following the "Guide to the Expression of Uncertainty in Measurement" (GUM; JCGM 2008), they determined AERONET-OC L WN uncertainties accounting for the main uncertainty sources affecting the quantities included in the measurement equation.Specifically, they considered contributions from (i) absolute radiometric calibration, (ii) instrument sensitivity change during deployment, (iii) data reduction minimizing the impact of wave perturbations, (iv) environmental variability, and (v) corrections for illumination conditions and bidirectional effects.Results showed uncertainty values ranging from 5% in the blue-green spectral region in moderately turbid waters up to about 30% in the blue in highly absorbing waters.Using these results, Zibordi et al. (2022) defined a site-and wavelengthindependent linear function relating L WN to its uncertainty values.This solution aimed at providing a practical, albeit approximate, solution to the operational use of AERONET-OC L WN for the quantification of uncertainties affecting satellitederived radiometric products.
This work primarily aims at revisiting the AERONET-OC L WN uncertainties formerly quantified by Gergely and Zibordi (2014) benefitting of advances in measurement protocols allowed by the recent CE-318T 12-band radiometers and additionally by new investigations on CE-318T calibration and data processing.In particular, unlike the former CE-318 9-band radiometers, the new CE-318T 12-band instruments allow for multiple consecutive above-water measurement sequences, which permit better addressing environmental perturbations in L WN .Moreover, recent studies on uncertainties affecting the CE-318T absolute calibration and corrections for bidirectional effects allow for a more accurate determination of their contributions to the uncertainty budget.
Finally, this work also investigates the potential for improved relationships making it possible to statistically estimate uncertainties for L WN regardless of site and ideally of wavelength.
Further objective of this work is an evaluation of the impact of temporal variations affecting L WN at a number of AERONET-OC sites in view of more comprehensively supporting the analysis of in situ and satellite matchups naturally exhibiting temporal mismatches.

Materials and methods
a. AERONET-OC instrument and measurement model AERONET-OC (Zibordi et al. 2021) allows for the determination of the spectral water-leaving radiance L W by exploiting in situ measurements of the total radiance from the sea L T and of the sky radiance L i , according to where u (set to 408) is the sensor sea-viewing angle, u (with u 5 1808 2 u) the sensor sky-viewing angle, u the sensor relative azimuth angle with respect to the sun (set to 908), and u 0 the sun zenith angle.The term r indicates the sea surface reflectance factor applied to quantify the sky radiance reflected by the sea surface into the field of view of the sensor.Its value is a function of the viewing and illumination geometries, and of the sea state conveniently expressed through the wind speed W (Mobley 1999).In the current AERONET-OC processing, W is extracted from the National Centers for Environmental Prediction (NCEP) data products with 6-h temporal resolution, and interpolated to the acquisition time of each AERONET-OC measurement sequence.
The normalized water leaving radiance L WN , which is the primary radiometric product for ocean color applications, is determined from where C Q is the correction applied to normalize L W for the in-water bidirectional effects as a function of the viewing and illumination geometries, wind speed, atmospheric and marine optical properties expressed through the aerosol optical depth t a and the water inherent optical properties IOP, respectively.
In the AERONET-OC version 3 database, L WN is corrected with C Q values determined applying two distinct methods leading to the generation of diverse data products.The first method, with corrections identified by the term C Chla Q and water IOPs exclusively expressed by Chla iteratively estimated from R RS band ratios, is specific for Case-1 waters (see Morel et al. 2002).The second method, with corrections identified by the term C IOP Q and IOPs determined from L W itself, is likely applicable to any water type (see Lee et al. 2011).Finally, the term C A is used to minimize the dependence on illumination conditions and it is computed as where t d is the diffuse atmospheric transmittance and D the sun-Earth distance.CE-318 and CE-318T instruments perform spectral measurements of (i) direct solar irradiance E applied to quantify t a and (ii) radiance from the sea and sky to determine L T and L i .Each measurement sequence, which comprises spectrally asynchronous measurements of 11 values of the total radiance from the sea and 3 values of the sky radiance, is performed in approximately 3 min for the CE-318 instruments and 4 min for the CE-318T ones.Then L i is determined by averaging the 3 sky radiance values while L T is determined by the averaging of the lowest 2 values of the total radiance from the sea.Rationale for this specific data reduction, supporting the determination of L T and aiming at minimizing the impact of wave perturbations, is provided in Zibordi (2012) andin D'Alimonte et al. (2021).Comprehensive details on AERONET-OC data handling, processing, quality assurance and control are available in Zibordi et al. (2021).

b. AERONET-OC data
Version 3 level 2.0 (i.e., fully quality controlled) L WN data from CE-318T instruments for the following sites were considered in the study: (i) Casablanca Platform (CPL) in the western Mediterranean Sea exhibiting frequent occurrence of Case-1 waters; (ii) Acqua Alta Oceanographic Tower (AAOT) in the northern Adriatic Sea and, Galata Platform (GLT) and Section-7 Platform (ST7) in the Black Sea, all characterized by optically complex waters with varying concentrations of sediments and chromophoric dissolved organic matter (CDOM); (iii) Gustaf Dalen Lighthouse Tower (GDLT) and Irbe Lighthouse (ILT) in the Baltic Sea, also characterized by optically complex waters, but exhibiting very high concentrations of CDOM.
To minimize the impact of changes in illumination conditions mainly affecting L i , the analysis was restricted to the data acquired with u 0 , 708 within 62 h from local noon.The time interval around 1200 local time comprises the overpass time of most of the ocean color satellites.Nevertheless, the ST7 and GLT time windows were centered at 1300 and 1100 local time, respectively.This choice was imposed by the need to minimize the impact of the small number of data available at these sites around 1200 local time due to deployment restrictions preventing optimal viewing geometries with respect to the superstructure around local noon.
The uncertainties characterizing L WN data products corrected for bidirectional effects through the Chla-based and the IOP-based approaches, hereafter identified as L Chla WN and L IOP WN , were both evaluated.Still, the symbol L WN is used when discussing uncertainties independent from specific corrections for bidirectional effects.

c. Background on measurement uncertainties
The methodology applied in this study for the quantification of L WN uncertainties relies on GUM guidelines and is equivalent to that implemented by Gergely and Zibordi (2014).The basic elements of the methodology are hereafter summarized for completeness.
The standard uncertainty u c (y) associated with a measurand y indirectly determined from other quantities through a measurement model y 5 f(x 1 , … , x N ), can be obtained propagating the uncertainties of each model input quantity through the first-order expansion of Taylor series: where ũ2 c (y) is the square of u c (y) when neglecting any correlation among input variables.f /x i and u(x i ) indicate the partial derivative respect to x i and the uncertainty of the model input quantity x i , respectively.When nonnegligible correlations characterize pairs of input quantities x i , x j , Eq. ( 4) becomes where f /x j and u(x j ) indicate the partial derivative respect to x j and the uncertainty of the model input quantity x j , respectively.Last, r(x i , x j ) is the correlation coefficients between x i and x j .
d. Determination of the combined uncertainties u c (L W ) for L W and u c (L WN ) for L WN Excluding correlations and nonlinearity contributions, the combined uncertainty ũc (L W ) for the spectral values of L W were determined from the uncertainties affecting L T , L i , and r [hereafter indicated by u(L T ), u(L i ), and u(r)], according to Considering all possible correlations, the combined uncertainty u c (L W ) was computed as Alternatively, when restricting correlations to L T and L i only (considered as the major correlation, mj), the related combined uncertainty u c,mj (L W ) was determined with The value of u c (L WN ) was instead determined considering the additional uncertainties affecting C Q and C A , hereafter defined as u(C Q ) and u(C A ), respectively.When neglecting correlations, the equation expressing the combined uncertainties for L WN becomes while, when including only the correlations between L T and Alternatively, when including all correlations Eq. ( 9) becomes e. Uncertainty values applied for the determination of u c (L W ) and u c (L WN ) Figure 1 shows the uncertainty sources accounted for in the calculation of the combined uncertainties for L WN .Both u(L T ) and u(L i ) depend on (i) the uncertainty affecting instrument calibration u ac , (ii) the decay of instrument sensitivity u sc , and (iii) the environmental perturbations u en .The uncertainty u(r) also depends on multiple contributions: (i) the uncertainty affecting wind speed u WS (r), (ii) the uncertainty u dr (r) resulting from the filtering applied to L T , and finally, (iii) the intrinsic uncertainty in the theoretical determination of r.
The approaches used to estimate all these quantities, and those used for u(C A ) and u(C Q ) related to C A and C Q , are described in the following subsections.
It is anticipated that the L WN uncertainties were determined with coverage factor k 5 1 (JCGM 2008).2014) used the constant value of 2.7% to quantify the relative uncertainty affecting the absolute radiometric calibration of AERONET-OC radiometers.This value was suggested by a comprehensive investigation on calibration uncertainties for in situ ocean color sensors (Hooker et al. 2002).A reanalysis of relative uncertainties affecting AERONET-OC absolute calibrations indicated much lower values varying between 0.6% and 1.0% in the 400-670 nm spectral interval (see Table 1) as derived from the quadrature sum of the various uncertainty sources (see appendix A).The use of these updated values to determine u ac , which is supported by laboratory calibration intercomparisons (Johnson et al. 2021), leads to a reduction of the combined uncertainties with respect to the previous analysis from Gergely and Zibordi (2014).Still, the newly applied values of u ac need to be considered a best estimate for AERONET-OC radiometric calibrations, which are operationally performed at the Goddard Space Flight Center (GSFC) of the National Aeronautics and Space Administration (NASA), but subject to continuous intercalibrations with the JRC Marine Optical Laboratory (Zibordi et al. 2009(Zibordi et al. , 2021)).
Additional instrument related sources of uncertainty such as temperature sensitivity and spectral transmittance of sensor filters, which were evaluated by Giles et al. (2019) and Johnson et al. (2021), respectively, were not considered because their effects are likely negligible in the 400-667 nm spectral region of major interest for ocean color applications.Conversely, sensitivity decay during deployments u sc was considered, but assumed constant across spectral bands and sites (see Table 1).Its value was estimated from the analysis of sensitivity changes observed for diverse CE-318T through various deployments.
2) ENVIRONMENTAL PERTURBATIONS Environmental perturbations u en are mostly due to sea surface roughness and on a lesser extent to changes in in-water optical properties or illumination conditions during measurement sequences.Gergely and Zibordi (2014) quantified u en as the median of the coefficient of variation (CV) of replicate values of spectral L T and L i from measurements performed within a 30 min interval.In this work, benefitting of the higher measurement frequency of CE-318T instruments, relative u en values were quantified through the median of CVs calculated with triplicates (triplets) of spectral L T and L i values determined within a time interval typically shorter than 10 min.This solution makes it possible to more precisely quantify the impact of environmental perturbations occurring during measurement sequences and consequently those perturbations strictly related to the measurement methodology.
3) UNCERTAINTY FOR THE r FACTOR Due to the few data available at level 2.0 for most of the AERONET-OC sites, Gergely and Zibordi (2014) determined a median u(r)/r of approximately 3.2% solely using the AAOT data: this uncertainty value was then applied to each site.Conversely, in this work u(r)/r was calculated for each measurement.This leads to an increase of u(r)/r with respect  400 412 443 490 510 560 620 667 u ac (L T,i )/L T,i 1.04 0.76 0.72 0.68 0.68 0.65 0.65 0.61 u sc (L T,i )/L T,i 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 to the former estimate.The increase is more marked for sites characterized by a median wind speed higher than that characterizing the AAOT site.
Recalling that wind speed W is from NCEP products (W NCEP ), the impact of uncertainties in its value was estimated accounting for actual in situ wind speeds (W ins ) available for AERONET-OC measurements performed at the AAOT site between 2017 and 2020.Specifically, the standard deviation s(W) of differences between W NCEP and W ins , exhibiting values of 2.16 m s 21 , was applied to quantify r[W 6 s(W)] for each measurement sequence from individual AERONET-OC sites.The values of u WS (r)/r were then computed from the mean of CVs determined for the pairs r(W) and r[W 1 s(W)], and the pairs r(W) and r[W 2 s(W)].
As already anticipated, the AERONET-OC processing determines L T by averaging the lowest 2 out of 11 measurements of the total radiance from the sea from each measurement sequence.This filtering process implies that the computed L T may not be statistically represented by the associated W value, but rather by a lower one (Zibordi 2012).The impact of such a data reduction process is quantified through u dr (r)/r defined by the median of the CVs between r calculated with W 5 W NCEP and alternatively with W 5 0. D'Alimonte et al. ( 2021) recently showed that the values of r computed with Hydrolight (Mobley 1994(Mobley , 1999) ) and applied in the processing of AERONET-OC data are underestimated.This underestimate increases with wind speed and in particular with low sun zenith angles (see Fig. 11 in their article).The data reduction method applied in AERONET-OC data processing partially compensates for the impact of the underestimate of r values.Consequently, to avoid overestimating u(r), the specific contribution to uncertainties brought by the underestimate of r was not accounted for in this study.

4) UNCERTAINTIES FOR THE C A AND C Q FACTORS
The uncertainty u(C A ) related to C A largely depends on that assigned to t d (t a ).In this study, as in Zibordi et al. (2009), u(C A )/C A was empirically set to 1.5% (which is probably an underestimated value).The value of u(C Q ) was also expressed by a percent of C Q value.In former analyses, the relative uncertainties u(C Chla Q )/C Chla Q were assumed spectrally constant and equal to 25%.Recently, the uncertainties related to bidirectional effects were experimentally determined for both the Chla-based and IOP-based approaches for diverse water types (see Talone et al. 2018), even though limited to the correction for the nonnadir viewing geometry, which however represents the major contribution to the overall correction.The values of u(C Chla Q )/C Chla Q for Chla-based corrections, which spectrally vary between 30% and 80%, were determined from a second-order polynomial fit of the uncertainties provided in Talone et al. (2018) for diverse water types.Conversely, u(C IOP Q )/C IOP Q for the IOP-based method was set to a spectrally constant value of 25% also estimated from data by Talone et al. (2018).The applied values of 1.It is finally mentioned that the uncertainty contribution to C Q due to the uncertainties in W was neglected because it only marginally affects the determination of the air-water transmission function (Gordon 2005).

5) CORRELATIONS AMONG INPUT QUANTITIES
Many of the uncertainty results reported by Gergely and Zibordi (2014) indicated as u c,mj (L WN ) were determined only accounting for variables exhibiting significant correlations.In particular, recognizing that correlations among input variables should not be ignored, Gergely and Zibordi (2014) included in the computation of u c,mj (L WN ) any correlation term larger than 0.5.Noting that correlations may lead to a significant decrease in uncertainties, in this work major correlations were restricted to the one between L i and L T .This choice was supported by the rich correlation observed between L i and L T measurements, generally higher that that shown by other quantities.In particular, L i and L T exhibit correlations which are higher when the contribution of the reflected sky radiance to L T is more pronounced (i.e., in the blue) or when L WN is very low (e.g., in the red).This is clearly shown by the results displayed in Fig. 2 and summarized in Table 2.The lowest correlations are reported for the AAOT in the green spectral region.When compared to u c (L WN ), which accounts for all    reported for both L Chla WN and L IOP WN data products.Combined uncertainties are provided by either neglecting any correlation ( ũc ), including all correlations among variables (u c ), and finally only including the major correlation between L i and L T (u c,mj ).Additionally, the values of the L WN uncertainty that are obtained considering only a single uncertainty source at a time, are reported for each site: these are denoted as u x (L WN )/L WN with x indicating the uncertainty source considered.Median values of W, u 0 , and t a at the 412 nm center wavelength, Chla (as determined from regional algorithms embedded in the AERONET-OC processing), and r are shown in Table 3 for the various sites, even though restricted to the time interval considered in the analysis.The site-dependent relative uncertainty values of various model input quantities are provided in appendix B for each site.

Mean values of L Chla
WN and L IOP WN for CPL, which is frequently representative of Case-1 waters, are provided in Table 4 and in Fig. 3

c. GLT and ST7
The GLT and ST7 Black Sea sites exhibit median L Chla WN spectra with maxima at 490 and 560 nm, respectively (see the left panels in Fig. 5).The relative combined uncertainties summarized in Tables 6 and 7 vary from 4.5% at 490 and 510 nm to 11.9% at 667 nm for GLT, and from 5.8% at 510 nm to 12.4% at 400 nm for ST7.These values are slightly lower when considering L IOP WN data and further reduced when considering correlations.Absolute combined uncertainties are also slightly higher than those determined for the AAOT site.Due to the higher wind speed characterizing these two Black Sea sites with respect to AAOT, u(r)/r (see appendix B) exhibits larger values than any other site [except for ILT showing the maximum median wind speed and consequently a maximum value of u(r)/r)].However, beyond 443 nm, except at the 667 nm center wavelength for GLT, the largest uncertainty contribution is from u(C Chla Q ) (see the right panels in Fig. 5).Opposite to the previous sites, the values of u c,mj (L Chla WN )/L Chla WN at blue bands for ST7 are lower than those obtained including all correlations among the input variables.This is due to the contribution of negative correlation terms exceeding in value the contribution from the positive ones.

d. GDLT and ILT
Figure 6 shows the median spectra of L Chla WN for the GDLT and ILT sites in the Baltic Sea.These spectra exhibit very similar shapes, with slightly higher values for ILT and extremely low values in the blue for both sites.As expected, relative uncertainties are very high in correspondence of these minima with median values exceeding 20% at 400 nm.Combined uncertainties rapidly decrease with wavelength, with minima in the 510-560 nm spectral region (see Tables 8 and 9).When considering the absolute uncertainty values, u c,mj (L Chla WN ) exhibit the maximum at 560 nm, still lower than that determined for other sites.As for ST7, also for these sites the values of u c,mj (L Chla WN )/L Chla WN [and additionally u c,mj (L IOP WN )/L IOP WN for GDLT only] at blue bands are lower than those obtained including all correlations among the input variables.

e. Temporal variability
The temporal variability over 1, 2, or 3 h u tv (L Chla WN )/L Chla WN was determined from pairs of L WN .The computed values of u tv (L Chla WN )/L Chla WN were combined in quadrature with u c,mj (L Chla WN )/L Chla WN to estimate the expected overall uncertainty u mu (L Chla WN )/L Chla WN affecting AERONET-OC L Chla WN data applied for the construction of matchups, thus attempting to account for the temporal mismatch between in situ and satellite data.Results from this specific analysis are summarized in Table 10.With a time difference Dt 5 1 h, the increase of u mu (L Chla WN )/L Chla WN with respect to u c,mj (L Chla WN )/L Chla WN is generally confined to 3%.It naturally increases when considering Dt 5 2 and Dt 5 3 h.Still, the increase is small for CPL and AAOT at the blue and green center wavelengths.In particular, for CPL the values u mu (L Chla WN )/L Chla WN between 412 and 510 nm are confined below the ideal uncertainty target of 5%.It must be however considered that the number of values available for the analysis may appreciably vary with Dt and likely affect the statistical significance of results (see ST7 for which the values obtained with Dt 5 3 h are lower than those obtained with Dt 5 2 h).This work is a revisitation of the former analysis of AERONET-OC uncertainties carried out by Gergely and Zibordi (2014).It was suggested by a number of technological and science advances.In particular the recent adoption of CE-318T radiometers allows for a reevaluation of environmental perturbations u en (L T ) and u en (L i ), and a quantification of the temporal variability u tv (L WN ).These latest radiometers are in fact capable of performing consecutive measurement sequences (e.g., triplets) leading to the determination of successive values of L T and L i a few minutes apart from each other.As expected, the new u en (L T ) and u en (L i ) exhibit much lower values with respect to those characterizing the previous analysis.
In view of assessing the impact of the other methodological changes introduced in the current study, relative combined uncertainties u c,mj (L Chla WN )/L Chla WN were also calculated applying the values of u(r)/r, u(C Chla Q )/C Chla Q , and u ac used in Gergely and Zibordi (2014).These results (not shown) indicate that the lower combined values of u ac applied in the current analysis heavily contribute to a decrease of u c,mj (L Chla WN )/L Chla WN .However, this reduction is compensated by the higher median values of u(r)/r obtained from estimates determined for each measurement opposite to the use of a constant value adopted by Gergely and Zibordi (2014).This is particularly evident at those sites exhibiting high median wind speed, such as GDLT, showing a significant increase of u c,mj (L Chla WN )/L Chla WN .When looking at the spectral values, the increase is more marked in the blue due to the larger impact of u(r)/r.

b. Data reduction
A major contribution to combined uncertainties comes from u(r) and u(C Q ).To investigate the possibility of minimizing their contributions, in agreement with Gergely and Zibordi (2014), uncertainties have been reevaluated only including data alternatively characterized by W # 3 m s 21 , Chla # 0.7 mg m 23 , u 0 # 458, and t a (412) # 0.2.Results proposed for the sole AAOT site are summarized in Table 11.As expected, limiting the input data to conditions determined by W # 3 m s 21 leads to a substantial decrease of u(r)/r.This decrease (not shown) is more pronounced at those sites exhibiting the highest median wind speed [e.g., with u(r)/r decreasing by 1.1% for AAOT, and up to approximately 3.5% and 4.2% for ST7 and ILT].Consequently, the combined uncertainties u c,mj (L Chla WN )/L Chla WN diversely decrease at various sites: up to 1.2% for AAOT and slightly above 12% in the blue for ILT and GDLT (not shown).
Imposing Chla # 0.7 mg m 23 leads to a decrease of u(C Chla Q )/C Chla Q and consequently of the combined uncertainties (except in the red), mostly for the Black Sea sites.However, the lack of suitable data for ILT and GDLT prevents any assessment for these sites.
The uncertainties determined for the temporal variability appear smaller when simultaneously imposing t a (412) # 0.2 and u 0 # 458, as shown in Table 12.Consequently, the values of u mu (L Chla WN )/L Chla WN also reduce with respect to those provided in Table 10.In particular, also for time differences Dt 5 2 and 3 h, they become lower than 5% at the blue and green center wavelengths for CPL and between 443 and 560 nm for AAOT and GLT.Nevertheless, only a few sites exhibit a statistically significant number of data to allow evaluating the case with Dt . 1 h.).The diverse symbols represent the various sites, whereas their color identifies the wavelength.The purple and red dashed lines indicate the linear regressions determined solely using the Black and Baltic Sea "blue bands" and, alternatively, all the remaining data.For L Chla WN , r 2 is 0.81 and 0.50 for the red and purple lines, respectively (both exhibiting p value , 0.01).For L IOP WN , r 2 is 0.92 and 0.50 for the red and purple lines, respectively (in this case too, both showing p value , 0.01).
contributions, which generally leads to uncertainty values slightly lower than those determined neglecting correlations.The following conclusions are based on the uncertainties determined solely accounting for the major correlations between L i and L T .
Results were produced for AERONET-OC sites representative of a variety of water types: Casablanca Platform (CPL) exhibiting frequent occurrence of Case-1 waters; the Acqua Alta Oceanographic Tower (AAOT), the Galata Platform (GLT), and the Section-7 Platform (ST7) characterized by optically complex waters with varying concentrations of sediments and CDOM; finally, the Gustaf Dalen Lighthouse Tower (GDLT) and Irbe Lighthouse (ILT), characterized by very high concentrations of CDOM.
The quantified uncertainties exhibit values varying from above 3% at 490 nm for CPL, and up to approximately 25% at 400 nm in CDOM-dominated waters.Uncertainties are higher for L Chla WN with respect to L IOP WN due to the assumption of higher uncertainties for Chla-based corrections than for the IOP-based ones applied to remove bidirectional effects.
Overall, the revisited uncertainties determined for L Chla WN do not significantly differ from the previous proposed by Gergely and Zibordi (2014).This is largely explained by compensations enacted in their quantification by the increase or decrease of diverse contributions.
The largest contribution to uncertainties is the sea surface reflectance factor r.This finding is explained by the uncertainties in wind speed estimation and in the data reduction method leading to the determination of L T .This is particularly evident at those sites characterized by larger median values of wind speed.For the remaining sites such as CPL and AAOT, a large fraction of the total uncertainty is explained by the contributions due to correction factors for bidirectional effects determined with the Chla-based method.
The study shows that restricting the uncertainty analysis to cases characterized by W # 3 m s 21 , or u 0 # 458, or Chla # 0.7 mg m 23 , leads to a reduction of the uncertainties.
In agreement with Zibordi et al. (2022) the possibility to estimate absolute uncertainties as a linear function of L Chla WN , or alternatively L IOP WN , was investigated.The analysis confirmed the solution formerly proposed by Zibordi et al. (2022), still at the expense of applying two different linear relationships, to accommodate an increased spectral dispersion between radiances and uncertainties.Nevertheless, a single linear relationship is instead applicable for measurement conditions characterized by W # 3 m s 21 , due to a reduction of the dispersion between median spectral radiances and related uncertainties.
Finally, the impact of temporal variability was investigated for the various AERONET-OC sites in view of best supporting matchup analysis between in situ and satellite data by accounting for temporal mismatches.Simply considering a time difference Dt 5 1 h between satellite and in situ data, the combined values accounting for L WN uncertainties and contributions due to temporal variability are generally confined below 5% in Case-1 and moderately optically complex waters (i.e., at CPL and AAOT) in the blue-green center wavelengths.Conversely, they exceed 5% at the other AERONET-OC sites considered in the study, or for larger Dt.

FIG. 1 .
FIG. 1. L WN measurement model and uncertainty sources included in the calculation of combined uncertainties.See the text for symbols explanation.
FIG. 2. Scatterplot of L i vs L T (in units of mW cm 22 sr 21 mm 21 ) from all sites at (left) 412 and (right) 560 nm.The density of points increases from blue to yellow.
f. Site-dependent temporal variability CE-318 9-band instruments, characterized by the capability of producing a single measurement sequence every 30 min, were operated at the considered AERONET-OC sites up to fall 2017.Due to these instruments intrinsic limitations,Gergely and Zibordi (2014) determined values of u en (L T ) or u en (L i ) across temporal intervals of 30 min well exceeding the duration of a measurement sequence generally restricted to 3 min for CE-318 instruments.Still, such a determination including contributions by temporal variability was shown relevant for the application of AERONET-OC L WN in the evaluation of uncertainties affecting satellite-derived L WN by making it possible to partially account for temporal mismatches between in situ and satellite data(Zibordi et al.  2022).Even though not strictly connected with measurement uncertainties, the temporal variability characterizing L WN at various AERONET-OC sites was quantified benefitting of measurements from CE-318T 12-band instruments with the objective to assist future analysis of in situ and satellite matchups.This was accomplished by determining CVs from pairs of L WN obtained with 1, 2, or 3 h delay, where L WN indicates values of L WN from the average of triplets performed around local noon.The use of large time differences is not affected by changes in illumination being L WN normalized with respect to the illumination conditions.
FIG. 3. (left) Median L Chla WN at CPL and (right) u x (L WN )/L WN for selected center wavelengths for each uncertainty source (see text for symbols).The black and red error bars in the left panel indicate the median absolute deviation m and u c,mj (L Chla WN ), respectively.
together with the computed uncertainties.With reference to Table 4, the median values of relative combined uncertainties ũc (L Chla WN )/L Chla WN and ũc (L IOP WN )/L IOP WN exhibit their minima at 490 nm, whereas higher values affect the blue and red bands.Maxima are observed in the red because of the signal close to nil.As expected, due to the assumption of larger uncertainties for C Chla Q than for C IOP Q , the computed relative combined uncertainties are higher for L Chla WN than for L IOP WN .Also predictable, the median values of relative combined uncertainties determined accounting for all correlations, u c (L Chla WN )/L Chla WN and u c (L IOP WN )/L IOP WN , exhibit values appreciably lower than ũc (L Chla WN )/L Chla WN and ũc (L IOP WN )/L IOP WN .However, those lower estimates may be questioned by the statistical significance of some correlations often exhibiting values well below 0.5.Unsurprisingly, when considering the sole major correlation between L T and L i , the related median relative combined uncertainties u c,mj (L Chla WN )/L Chla WN and u c,mj (L IOP WN )/L IOP WN show values slightly lower than those of ũc (L Chla WN )/L Chla WN and ũc (L IOP WN )/L IOP WN .Figure 3 (right panel) displays the value of u x (L WN )/L WN for selected center wavelengths calculated for each uncertainty source independently (with x denoting the uncertainty source considered in the calculation).Notably, the highest contributions are those associated with r and exhibit a spectral dependence opposite to that of L Chla WN and L IOP WN .The second main source of uncertainty is the environmental variability.

l
(nm) N 400 412 443 490 510 560 620 667 W # 3 m s 21 FIG. 7. Scatterplot of median (left) L Chla WN and (right) L IOP WN values vs median absolute combined uncertainties u c,mj (L Chla WN ) and u c,mj (L IOP WN ).The diverse symbols represent the various sites, whereas their color identifies the wavelength.The black solid line indicates the linear regression.The gray dashed line indicates the regression proposed by Zibordi et al. (2022).The determination coefficient (r 2 ) is 0.62 and 0.60 for L Chla WN and L IOP WN , respectively (p value , 0.01).

TABLE 1 .
Site-independent relative uncertainty values (in %) of various model input quantities applied for the computation of L W and L WN combined uncertainties.See text for symbols' explanations.

TABLE 2 .
Correlation coefficients between L i and L T for all sites.

TABLE 3 .
Median and median absolute deviation of W, u 0 , t a (412), Chla, and r determined for each site for data falling within 62 h from 1200 local time (or 1100 and 1300 local time for GLT and ST7, respectively).N is the number of measurements, whereas the associated value in parentheses indicates the number of actual triplets available for the analysis.input quantities, u c,mj (L WN ) is expected to show higher values, even if some exceptions may occur due to negative correlation values.This means that the choice of including only major correlations generally provides conservative results with respect to the inclusion of all correlation terms.

TABLE 4 .
Relative (in %) and absolute (in units of mW cm 22 sr 21 mm 21 ) combined uncertainties at different center wavelengths (l) for the CPL site (see text for symbols' explanation).The median values of L Chla WN and L IOP WN are reported together with their median absolute deviation m (in units of mW cm 22 sr 21 mm 21 ).

TABLE 5 .
As in Table 4, but for AAOT.

TABLE 6 .
As in Table 4, but for GLT.

TABLE 9 .
As in Table 4, but for ILT.

TABLE 10 .
Median relative uncertainty u mu (L Chla WN )/L Chla WN (in %) for diverse time differences Dt.N is the number of pairs used to determine u tv (L Chla WN )/L Chla WN .

TABLE 12 .
Median relative uncertainty u mu (L Chla WN )/L Chla WN (in units of %) for diverse Dt, obtained from triplets satisfying t a (412) # 0.2 and u 0 # 458.N is the number of pairs of triplets used to determine u tv (L Chla WN )/L Chla WN .Results are only reported for those cases exhibiting a number of pairs N exceeding 80, heuristically assumed statistically relevant.