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AERONET-OC LWN Uncertainties: Revisited

AERONET-OC LWN Uncertainties: Revisited APRIL 2023 CA ZZ A N I G A A N D ZI BO R D I 411 AERONET-OC L Uncertainties: Revisited WN a a ILARIA CAZZANIGA AND GIUSEPPE ZIBORDI Joint Research Centre, European Commission, Ispra, Italy (Manuscript received 8 June 2022, in final form 7 December 2022) ABSTRACT: 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 .The WN new uncertainty values are quantified 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 from its spectral WN values. Additionally, results from an evaluation of the temporal variability characterizing L at various AERONET-OC WN sites are presented to address the impact of temporal mismatches between in situ and satellite data in matchup analysis. KEYWORDS: Ocean; In situ oceanic observations; Remote sensing; Uncertainty 1. Introduction in situ measurements performed from offshore fixed struc- tures in a variety of water types (Zibordi et al. 2009, 2021). A In situ reference measurements are essential to any ocean best effort to quantify uncertainties affecting AERONET-OC color program for system vicarious calibration of satellite sen- L was made by Gergely and Zibordi (2014). Following the WN sors, assessment of primary and derived data products, and “Guide to the Expression of Uncertainty in Measurement” development of bio-optical algorithms. The primary ocean (GUM; JCGM 2008), they determined AERONET-OC L WN color product is the spectral normalized water-leaving radi- uncertainties accounting for the main uncertainty sources af- ance L : the radiance emerging from below the sea surface WN fecting the quantities included in the measurement equation. derived from the top-of-atmosphere radiance after correction Specifically, they considered contributions from (i) absolute for atmospheric perturbations, normalized with respect to the radiometric calibration, (ii) instrument sensitivity change dur- illumination conditions and viewing geometry, and finally cor- ing deployment, (iii) data reduction minimizing the impact rected for in-water bidirectional effects. The quantification of wave perturbations, (iv) environmental variability, and of the accuracy of L , or of the equivalent remote sensing WN (v) corrections for illumination conditions and bidirectional reflectance R , is essential to successively determine that af- RS effects. Results showed uncertainty values ranging from 5% in fecting derived data products [e.g., chlorophyll-a concentra- the blue-green spectral region in moderately turbid waters up tion (Chla)]. For this reason, primary satellite radiometric to about 30% in the blue in highly absorbing waters. Using products are matter of extensive validation programs aiming these results, Zibordi et al. (2022) defined a site- and wavelength- at verifying the compliance of their uncertainties with mission independent linear function relating L to its uncertainty WN requirements. Often these requirements entail generic uncer- values. This solution aimed at providing a practical, albeit ap- tainty targets of 5% for satellite-derived L or R (e.g., WN RS proximate, solution to the operational use of AERONET-OC Hooker et al. 1992; Drinkwater and Rebhan 2007). Recalling L for the quantification of uncertainties affecting satellite- WN that the 5% uncertainty value is considered achievable in derived radiometric products. oligotrophic/mesotrophic oceanic waters in the blue-green This work primarily aims at revisiting the AERONET-OC spectral region (GCOS 2011), its assessment implies access to L uncertainties formerly quantified by Gergely and WN highly accurate in situ reference data exhibiting uncertainties Zibordi (2014) benefitting of advances in measurement proto- quantified in agreement with metrology principles. cols allowed by the recent CE-318T 12-band radiometers The Ocean Color Component of the Aerosol Robotic Net- and additionally by new investigations on CE-318T calibra- work (AERONET-OC) was specifically conceived to support tion and data processing. In particular, unlike the former the assessment of satellite L products through automated WN CE-318 9-band radiometers, the new CE-318T 12-band instru- ments allow for multiple consecutive above-water measurement sequences, which permit better addressing environmental Denotes content that is immediately available upon publica- tion as open access. This article is licensed under a Creative Commons Attribution 4.0 license (http://creativecommons.org/ Corresponding author: Ilaria Cazzaniga, ilaria.cazzaniga@ec. europa.eu licenses/by/4.0/). DOI: 10.1175/JTECH-D-22-0061.1 Ó 2023 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses). 412 J OUR N A L O F A T M O S P H E R I C A N D O C E A N I C T E C H N O L OGY VOLUME 40 perturbations in L . Moreover, recent studies on uncertainties likely applicable to any water type (see Lee et al. 2011). Fi- WN affecting the CE-318T absolute calibration and corrections for nally, the term C is used to minimize the dependence on illu- bidirectional effects allow for a more accurate determination of mination conditions and it is computed as their contributions to the uncertainty budget. 2 21 C (l, u , t , D) 5 [D t (t )cosu ] , (3) Finally, this work also investigates the potential for improved A 0 a d a 0 relationships making it possible to statistically estimate uncer- where t is the diffuse atmospheric transmittance and D the tainties for L regardless of site and ideally of wavelength. WN sun–Earth distance. Further objective of this work is an evaluation of the impact of CE-318 and CE-318T instruments perform spectral meas- temporal variations affecting L at a number of AERONET- WN urements of (i) direct solar irradiance E applied to quantify t OC sites in view of more comprehensively supporting the and (ii) radiance from the sea and sky to determine L and analysis of in situ and satellite matchups naturally exhibiting T L . Each measurement sequence, which comprises spectrally temporal mismatches. i asynchronous measurements of 11 values of the total radiance from the sea and 3 values of the sky radiance, is performed in 2. Materials and methods approximately 3 min for the CE-318 instruments and 4 min a. AERONET-OC instrument and measurement model for the CE-318T ones. Then L is determined by averaging the 3 sky radiance values while L is determined by the averaging of AERONET-OC (Zibordi et al. 2021) allows for the deter- the lowest 2 values of the total radiance from the sea. Rationale mination of the spectral water-leaving radiance L by exploit- forthisspecific data reduction, supporting the determination of ing in situ measurements of the total radiance from the sea L L and aiming at minimizing the impact of wave perturbations, and of the sky radiance L , according to T is provided in Zibordi (2012) and in D’Alimonte et al. (2021). L (l, u, u, u , u ) 5 L (l, u, u, u ) W 0 T 0 Comprehensive details on AERONET-OC data handling, processing, quality assurance and control are available in 2 r(u, u, u , W) L (l, u , u, u ), (1) 0 i 0 Zibordi et al. (2021). where u (set to 408) is the sensor sea-viewing angle, u (with b. AERONET-OC data u 5 1808 2 u) the sensor sky-viewing angle, u the sensor rela- Version 3 level 2.0 (i.e., fully quality controlled) L data 8 WN tive azimuth angle with respect to the sun (set to 90 ), and from CE-318T instruments for the following sites were con- u the sun zenith angle. The term r indicates the sea surface sidered in the study: reflectance factor applied to quantify the sky radiance re- flected by the sea surface into the field of view of the sensor. (i) Casablanca Platform (CPL) in the western Mediterranean Its value is a function of the viewing and illumination geome- Sea exhibiting frequent occurrence of Case-1 waters; tries, and of the sea state conveniently expressed through the (ii) Acqua Alta Oceanographic Tower (AAOT) in the wind speed W (Mobley 1999). In the current AERONET-OC northern Adriatic Sea and, Galata Platform (GLT) and processing, W is extracted from the National Centers for Section-7 Platform (ST7) in the Black Sea, all character- Environmental Prediction (NCEP) data products with 6-h ized by optically complex waters with varying concentra- temporal resolution, and interpolated to the acquisition time tions of sediments and chromophoric dissolved organic of each AERONET-OC measurement sequence. matter (CDOM); The normalized water leaving radiance L , which is the WN (iii) Gustaf Dalen Lighthouse Tower (GDLT) and Irbe primary radiometric product for ocean color applications, is Lighthouse (ILT) in the Baltic Sea, also characterized determined from by optically complex waters, but exhibiting very high concentrations of CDOM. L (l) 5 L (l, u, u, u , u ) C (l, u, u, u , W, t , IOP) WN W 0 Q 0 a To minimize the impact of changes in illumination condi- 3 C (l, u , t , D) , (2) A 0 a tions mainly affecting L , the analysis was restricted to the data acquired with u , 708 within 62 h from local noon. The where C is the correction applied to normalize L for the 0 Q W time interval around 1200 local time comprises the overpass in-water bidirectional effects as a function of the viewing and time of most of the ocean color satellites. Nevertheless, the illumination geometries, wind speed, atmospheric and marine ST7 and GLT time windows were centered at 1300 and 1100 optical properties expressed through the aerosol optical depth local time, respectively. This choice was imposed by the need t and the water inherent optical properties IOP, respectively. In the AERONET-OC version 3 database, L is corrected to minimize the impact of the small number of data available WN with C values determined applying two distinct methods at these sites around 1200 local time due to deployment re- strictions preventing optimal viewing geometries with respect leading to the generation of diverse data products. The first Chla to the superstructure around local noon. method, with corrections identified by the term C and wa- The uncertainties characterizing L data products cor- ter IOPs exclusively expressed by Chla iteratively estimated WN rected for bidirectional effects through the Chla-based and from R band ratios, is specific for Case-1 waters (see Morel RS Chla et al. 2002). The second method, with corrections identified the IOP-based approaches, hereafter identified as L and WN IOP IOP by the term C and IOPs determined from L itself, is L , were both evaluated. Still, the symbol L is used W WN Q WN APRIL 2023 CA ZZ A N I G A A N D ZI BO R D I 413 when discussing uncertainties independent from specific cor- rections for bidirectional effects. c. Background on measurement uncertainties The methodology applied in this study for the quantifica- tion of L uncertainties relies on GUM guidelines and is WN equivalent to that implemented by Gergely and Zibordi (2014). The basic elements of the methodology are hereafter summarized for completeness. The standard uncertainty u (y) associated with a measur- and y indirectly determined from other quantities through a measurement model y 5 f(x , … , x ), can be obtained 1 N propagating the uncertainties of each model input quantity through the first-order expansion of Taylor series: FIG.1. L measurement model and uncertainty sources in- WN N 2 ­f cluded in the calculation of combined uncertainties. See the text 2 2 u ˜ (y) 5 ∑ u (x ) , (4) for symbols explanation. ­x i51 where u ˜ (y) is the square of u (y) when neglecting any corre- c correlations, the equation expressing the combined uncertain- lation among input variables.­f /­x and u(x ) indicate the par- i ties for L becomes WN tial derivative respect to x and the uncertainty of the model 2 2 2 2 2 ˜ ˜ input quantity x , respectively. When nonnegligible correla- u (L ) 5 (C C ) u (L ) 1 (L C ) u (C ) c WN Q A c W W A Q tions characterize pairs of input quantities x , x , Eq. (4) i j 2 2 1 (L C ) u (C ), (9) W Q A becomes N21 N while, when including only the correlations between L and ­f ­f T 2 2 u (y) 5 u ˜ (y) 1 2 ∑ ∑ u(x )u(x )r(x , x ), (5) 2 2 c c i j i j L , u ˜ (L ) is replaced by u (L ): ­x ­x i i51 j5i11 c W c,mj W i j 2 2 2 2 2 u (L ) 5 (C C ) u (L ) 1 (L C ) u (C ) c,mj WN Q A c,mj W W A Q where­f /­x and u(x ) indicate the partial derivative respect to x and the uncertainty of the model input quantity x , respec- 1 (L C ) u (C ): (10) j j W Q A tively. Last, r(x , x ) is the correlation coefficients between x i j i and x . Alternatively, when including all correlations Eq. (9) becomes d. Determination of the combined uncertainties u (L ) c W 2 2 2 u (L ) 5 u (L ) 1 2C C L r(C , C ) u(C )u(C ) c WN c WN Q A W Q A Q A for L and u (L ) for L W c WN WN 1 2C C L r(L , C ) u (L )u(C ) A W W A c W A Excluding correlations and nonlinearity contributions, the combined uncertainty u ˜ (L ) for the spectral values of L 1 2C C L r(L , C ) u (L )u(C ): (11) c W Q A W W Q c W Q were determined from the uncertainties affecting L , L , and T i r [hereafter indicated by u(L ), u(L ), and u(r)], according to T i e. Uncertainty values applied for the determination 2 2 2 2 2 2 u ˜ (L ) 5 u (L ) 1 u (L )r 1 u (r)L : (6) W T i i of u (L ) and u (L ) c W c WN Figure 1 shows the uncertainty sources accounted for in Considering all possible correlations, the combined uncer- the calculation of the combined uncertainties for L . Both tainty u (L ) was computed as WN c W u(L )and u(L ) depend on (i) the uncertainty affecting in- T i 2 2 u (L ) 5 u ˜ (L ) 2 2r r(L , L ) u(L ) u(L ) 2 2L r(L , r) c c W W T i T i i T strument calibration u , (ii) the decay of instrument sensi- ac tivity u , and (iii) the environmental perturbations u .The sc en 3 u(L )u(r) 2 2L r(L , r) u(L ) u(r): (7) T T i i uncertainty u(r) also depends on multiple contributions: (i) the uncertainty affecting wind speed u (r), (ii) the WS Alternatively, when restricting correlations to L and L only T i uncertainty u (r) resulting from the filtering applied to L , dr T (considered as the major correlation, mj), the related com- and finally, (iii) the intrinsic uncertainty in the theoretical bined uncertainty u (L ) was determined with c,mj W determination of r. 2 2 u (L ) 5 u ˜ (L ) 2 2r r(L , L ) u(L ) u(L ): (8) The approaches used to estimate all these quantities, and c,mj W c W T i T i those used for u(C ) and u(C ) related to C and C , are de- A Q A Q The value of u (L ) was instead determined considering the scribed in the following subsections. c WN additional uncertainties affecting C and C , hereafter de- It is anticipated that the L uncertainties were deter- Q A WN fined as u(C ) and u(C ), respectively. When neglecting mined with coverage factor k 5 1(JCGM 2008). Q A 414 J OUR N A L O F A T M O S P H E R I C A N D O C E A N I C T E C H N O L OGY VOLUME 40 TABLE 1. Site-independent relative uncertainty values (in %) Additional instrument related sources of uncertainty such of various model input quantities applied for the computation of as temperature sensitivity and spectral transmittance of sensor L and L combined uncertainties. See text for symbols’ W WN filters, which were evaluated by Giles et al. (2019) and explanations. Johnson et al. (2021), respectively, were not considered be- cause their effects are likely negligible in the 400–667 nm l (nm) spectral region of major interest for ocean color applications. 400 412 443 490 510 560 620 667 Conversely, sensitivity decay during deployments u was con- sc u (L )/L 1.04 0.76 0.72 0.68 0.68 0.65 0.65 0.61 sidered, but assumed constant across spectral bands and sites ac T,i T,i u (L )/L 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 sc T,i T,i (see Table 1). Its value was estimated from the analysis of sen- u(C )/C 1.5 1.5 1.5 1.5 1.5 1.5 1.5 1.5 A A sitivity changes observed for diverse CE-318T through various Chla Chla 58 52 41 32 31 35 55 80 u(C )/C Q Q deployments. IOP IOP 25 25 25 25 25 25 25 25 u(C )/C Q Q 2) ENVIRONMENTAL PERTURBATIONS Environmental perturbations u are mostly due to sea sur- en 1) UNCERTAINTIES FOR ABSOLUTE RADIOMETRIC face roughness and on a lesser extent to changes in in-water CALIBRATIONS optical properties or illumination conditions during measure- ment sequences. Gergely and Zibordi (2014) quantified u as en Gergely and Zibordi (2014) used the constant value of the median of the coefficient of variation (CV) of replicate 2.7% to quantify the relative uncertainty affecting the abso- values of spectral L and L from measurements performed T i lute radiometric calibration of AERONET-OC radiometers. within a 30 min interval. In this work, benefitting of the higher This value was suggested by a comprehensive investigation on measurement frequency of CE-318T instruments, relative u en calibration uncertainties for in situ ocean color sensors values were quantified through the median of CVs calculated (Hooker et al. 2002). A reanalysis of relative uncertainties af- with triplicates (triplets) of spectral L and L values deter- T i fecting AERONET-OC absolute calibrations indicated much mined within a time interval typically shorter than 10 min. lower values varying between 0.6% and 1.0% in the 400–670 nm This solution makes it possible to more precisely quantify the spectral interval (see Table 1) as derived from the quadrature impact of environmental perturbations occurring during mea- sum of the various uncertainty sources (see appendix A). The surement sequences and consequently those perturbations use of these updated values to determine u , which is supported ac strictly related to the measurement methodology. by laboratory calibration intercomparisons (Johnson et al. 2021), leads to a reduction of the combined uncertainties with respect 3) UNCERTAINTY FOR THE r FACTOR to the previous analysis from Gergely and Zibordi (2014). Still, Due to the few data available at level 2.0 for most of the the newly applied values of u need to be considered a best esti- ac mate for AERONET-OC radiometric calibrations, which are AERONET-OC sites, Gergely and Zibordi (2014) determined operationally performed at the Goddard Space Flight Center a median u(r)/r of approximately 3.2% solely using the (GSFC) of the National Aeronautics and Space Administration AAOT data: this uncertainty value was then applied to each (NASA), but subject to continuous intercalibrations with the site. Conversely, in this work u(r)/r was calculated for each JRC Marine Optical Laboratory (Zibordi et al. 2009, 2021). measurement. This leads to an increase of u(r)/r with respect 22 21 21 FIG. 2. Scatterplot of L vs L (in units of mW cm sr mm ) from all sites at (left) 412 and i T (right) 560 nm. The density of points increases from blue to yellow. APRIL 2023 CA ZZ A N I G A A N D ZI BO R D I 415 TABLE 2. Correlation coefficients between L and L for all sites. 4) UNCERTAINTIES FOR THE C AND C FACTORS i T A Q The uncertainty u(C ) related to C largely depends on l (nm) A A that assigned to t (t ). In this study, as in Zibordi et al. (2009), d a 400 412 443 490 510 560 620 665 u(C )/C was empirically set to 1.5% (which is probably an A A CPL 0.9 0.8 0.8 0.8 0.8 0.7 0.9 0.9 underestimated value). The value of u(C ) was also ex- AAOT 0.5 0.5 0.3 0.1 0.1 0.1 0.3 0.4 pressed by a percent of C value. In former analyses, the rela- GLT 0.7 0.7 0.6 0.5 0.5 0.5 0.6 0.7 Chla Chla tive uncertainties u(C )/C were assumed spectrally Q Q ST7 0.6 0.6 0.5 0.4 0.4 0.4 0.4 0.5 constant and equal to 25%. Recently, the uncertainties re- GDLT 0.7 0.7 0.7 0.5 0.4 0.3 0.4 0.4 lated to bidirectional effects were experimentally determined ILT 0.8 0.8 0.8 0.6 0.5 0.4 0.6 0.6 for both the Chla-based and IOP-based approaches for di- verse water types (see Talone et al. 2018), even though limited to the correction for the nonnadir viewing geometry, which to the former estimate. The increase is more marked for sites however represents the major contribution to the overall cor- characterized by a median wind speed higher than that charac- Chla Chla rection. The values of u(C )/C for Chla-based correc- Q Q terizing the AAOT site. tions, which spectrally vary between 30% and 80%, were Recalling that wind speed W is from NCEP products determined from a second-order polynomial fit of the uncer- (W ), the impact of uncertainties in its value was estimated NCEP tainties provided in Talone et al. (2018) for diverse water accounting for actual in situ wind speeds (W ) available for ins IOP IOP types. Conversely, u(C )/C for the IOP-based method Q Q AERONET-OC measurements performed at the AAOT site was set to a spectrally constant value of 25% also estimated between 2017 and 2020. Specifically, the standard deviation from data by Talone et al. (2018). The applied values of s(W) of differences between W and W , exhibiting val- NCEP ins Chla Chla IOP IOP 21 u(C )/C and u(C )/C are provided in Table 1. Q Q Q Q ues of 2.16 m s , was applied to quantify r[W 6 s(W)] for It is finally mentioned that the uncertainty contribution to each measurement sequence from individual AERONET-OC C due to the uncertainties in W was neglected because it sites. The values of u (r)/r were then computed from the WS only marginally affects the determination of the air–water mean of CVs determined for the pairs r(W)and r[W 1 s(W)], transmission function (Gordon 2005). and the pairs r(W)and r[W 2 s(W)]. As already anticipated, the AERONET-OC processing 5) CORRELATIONS AMONG INPUT QUANTITIES determines L by averaging the lowest 2 out of 11 meas- Many of the uncertainty results reported by Gergely and urements of the total radiance from the sea from each Zibordi (2014) indicated as u (L ) were determined only measurement sequence. This filtering process implies that the c,mj WN accounting for variables exhibiting significant correlations. In computed L may not be statistically represented by the asso- particular, recognizing that correlations among input variables ciated W value, but rather by a lower one (Zibordi 2012). The should not be ignored, Gergely and Zibordi (2014) included impact of such a data reduction process is quantified through in the computation of u (L ) any correlation term larger u (r)/r defined by the median of the CVs between r calcu- c,mj WN dr than 0.5. Noting that correlations may lead to a significant de- lated with W 5 W and alternatively with W 5 0. NCEP crease in uncertainties, in this work major correlations were D’Alimonte et al. (2021) recently showed that the values of restricted to the one between L and L . This choice was sup- r computed with Hydrolight (Mobley 1994, 1999) and applied i T ported by the rich correlation observed between L and L in the processing of AERONET-OC data are underestimated. i T measurements, generally higher that that shown by other This underestimate increases with wind speed and in parti- cular with low sun zenith angles (see Fig. 11 in their article). quantities. In particular, L and L exhibit correlations which i T The data reduction method applied in AERONET-OC data are higher when the contribution of the reflected sky radiance processing partially compensates for the impact of the un- to L is more pronounced (i.e., in the blue) or when L is T WN derestimate of r values. Consequently, to avoid overesti- very low (e.g., in the red). This is clearly shown by the results mating u(r), the specific contribution to uncertainties brought displayed in Fig. 2 andsummarizedin Table 2. The lowest cor- by the underestimate of r was not accounted for in this relations are reported for the AAOT in the green spectral re- study. gion. When compared to u (L ), which accounts for all c WN TABLE 3. Median and median absolute deviation of W, u , t (412), Chla, and r determined for each site for data falling within 0 a 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. 21 23 Site NW (m s ) u (8) t (412) Chla (mg m ) r (}) 0 a CPL 4841 (616) 3.1 6 1.2 41.7 6 13.9 0.12 6 0.06 0.2 6 0.1 0.027 6 0.8 3 10 AAOT 9516 (1281) 2.4 6 1.0 39.2 6 10.4 0.20 6 0.10 0.9 6 0.4 0.026 6 0.6 3 10 GLT 4920 (653) 3.6 6 1.2 40.7 6 9.4 0.18 6 0.07 0.6 6 0.2 0.027 6 0.9 3 10 ST7 2471 (309) 4.2 6 1.2 43.3 6 8.0 0.18 6 0.06 1.2 6 0.6 0.028 6 1.0 3 10 GDLT 956 (47) 3.8 6 1.4 42.0 6 4.3 0.13 6 0.05 2.8 6 0.8 0.027 6 0.9 3 10 ILT 1426 (186) 4.6 6 1.5 40.0 6 3.7 0.17 6 0.07 2.8 6 0.7 0.028 6 1.1 3 10 416 J OUR N A L O F A T M O S P H E R I C A N D O C E A N I C T E C H N O L OGY VOLUME 40 22 21 21 TABLE 4. Relative (in %) and absolute (in units of mW cm sr mm ) combined uncertainties at different center wavelengths (l) Chla IOP for the CPL site (see text for symbols’ explanation). The median values of L and L are reported together with their median WN WN 22 21 21 absolute deviation m (in units of mW cm sr mm ). l (nm) 400 412 443 490 510 560 620 667 Chla Chla L 6 m(L ) 0.81 6 0.23 0.94 6 0.27 0.98 6 0.24 0.95 6 0.14 0.65 6 0.07 0.30 6 0.04 0.06 6 0.02 0.03 6 0.01 WN WN IOP IOP 0.82 6 0.22 0.95 6 0.26 0.99 6 0.23 0.96 6 0.12 0.65 6 0.07 0.30 6 0.04 0.05 6 0.02 0.03 6 0.01 L 6 m(L ) WN WN Chla Chla 4.7 4.4 3.9 3.6 4.0 5.4 14.1 18.7 u ˜ (L )/L WN WN Chla Chla u (L )/L 4.2 3.8 3.3 2.9 3.0 4.0 12.3 16.6 c WN WN Chla Chla 4.5 4.2 3.8 3.5 3.9 5.1 12.5 16.4 u (L )/L WN WN c,mj Chla 0.036 0.039 0.036 0.03 0.023 0.015 0.008 0.006 u (L ) c,mj WN IOP IOP ˜ 4.3 3.9 3.4 3.1 3.5 4.4 13.8 18.1 u (L )/L c WN WN IOP IOP 2.8 2.5 2.1 1.7 1.9 2.8 11.9 16.0 u (L )/L WN WN IOP IOP 3.9 3.6 3.3 3.0 3.3 4.2 12.2 15.8 u (L )/L c,mj WN WN IOP u (L ) 0.034 0.037 0.034 0.028 0.022 0.014 0.007 0.005 c,mj WN correlations among the input quantities, u (L ) is expected mismatches between in situ and satellite data (Zibordi et al. c,mj WN to show higher values, even if some exceptions may occur due 2022). Even though not strictly connected with measurement to negative correlation values. This means that the choice of in- uncertainties, the temporal variability characterizing L at WN cluding only major correlations generally provides conservative various AERONET-OC sites was quantified benefitting of results with respect to the inclusion of all correlation terms. measurements from CE-318T 12-band instruments with the objective to assist future analysis of in situ and satellite match- f. Site-dependent temporal variability ups. This was accomplished by determining CVs from pairs of CE-318 9-band instruments, characterized by the capability L obtained with 1, 2, or 3 h delay, where L indicates WN WN of producing a single measurement sequence every 30 min, values of L from the average of triplets performed around WN were operated at the considered AERONET-OC sites up to local noon. The use of large time differences is not affected by fall 2017. Due to these instruments intrinsic limitations, changes in illumination being L normalized with respect to WN Gergely and Zibordi (2014) determined values of u (L )or en T the illumination conditions. u (L ) across temporal intervals of 30 min well exceeding the en i duration of a measurement sequence generally restricted to 3. Results 3 min for CE-318 instruments. Still, such a determination in- Results from the uncertainty analysis are summarized in the cluding contributions by temporal variability was shown rele- vant for the application of AERONET-OC L in the following subsections for each site by providing both absolute WN evaluation of uncertainties affecting satellite-derived L by [e.g., u(L )] and relative [e.g., u(L )/L ] combined uncer- WN WN WN WN making it possible to partially account for temporal tainties together with the related median L values. Results are WN Chla FIG.3.(left) Median L at CPL and (right) u (L )/L for selected center wavelengths for each uncertainty WN x WN WN source (see text for symbols). The black and red error bars in the left panel indicate the median absolute deviation m Chla and u (L ), respectively. c,mj WN APRIL 2023 CA ZZ A N I G A A N D ZI BO R D I 417 TABLE 5. As in Table 4, but for AAOT. l (nm) 400 412 443 490 510 560 620 667 Chla Chla 0.57 6 0.14 0.70 6 0.17 0.84 6 0.22 1.10 6 0.28 1.06 6 0.28 0.93 6 0.28 0.21 6 0.09 0.13 6 0.06 L 6 m(L ) WN WN IOP IOP 0.55 6 0.13 0.68 6 0.16 0.83 6 0.20 1.08 6 0.27 1.06 6 0.27 0.93 6 0.29 0.21 6 0.09 0.13 6 0.06 L 6 m(L ) WN WN Chla Chla 5.9 5.4 4.7 4.3 4.3 4.9 7.3 9.6 u ˜ (L )/L WN WN Chla Chla 5.3 4.9 3.9 3.2 2.9 3.1 5.1 7.2 u (L )/L c WN WN Chla Chla 5.6 5.2 4.6 4.3 4.3 4.9 7.2 9.2 u (L )/L WN WN c,mj Chla 0.032 0.037 0.04 0.047 0.045 0.045 0.015 0.012 u (L ) WN c,mj IOP IOP ˜ 5.4 5.0 4.4 4.0 4.0 4.1 5.6 6.5 u (L )/L c WN WN IOP IOP 3.7 3.3 2.6 2.1 2.1 2.3 4.0 5.2 u (L )/L c WN WN IOP IOP 5.1 4.8 4.4 4.0 4.0 4.1 5.5 6.2 u (L )/L c,mj WN WN IOP u (L ) 0.029 0.034 0.037 0.044 0.042 0.036 0.012 0.009 c,mj WN Chla IOP reported for both L and L data products. Combined un- signal close to nil. As expected, due to the assumption of WN WN Chla IOP certainties are provided by either neglecting any correlation (u ˜ ), larger uncertainties for C than for C , the computed rel- c Q Q Chla including all correlations among variables (u ), and finally only ative combined uncertainties are higher for L than for WN IOP including the major correlation between L and L (u ). Addi- i T c,mj L . Also predictable, the median values of relative com- WN tionally, the values of the L uncertainty that are obtained con- WN bined uncertainties determined accounting for all correla- Chla Chla IOP IOP sidering only a single uncertainty source at a time, are reported tions, u (L )/L and u (L )/L , exhibit values c WN WN c WN WN for each site: these are denoted as u (L )/L with x indicat- Chla Chla IOP IOP ˜ ˜ x WN WN appreciably lower than u (L )/L and u (L )/L . WN WN WN WN c c ing the uncertainty source considered. Median values of W, u , However, those lower estimates may be questioned by the and t at the 412 nm center wavelength, Chla (as determined statistical significance of some correlations often exhibiting from regional algorithms embedded in the AERONET-OC values well below 0.5. Unsurprisingly, when considering the processing), and r are shown in Table 3 for the various sites, sole major correlation between L and L , the related T i even though restricted to the time interval considered in the anal- Chla Chla median relative combined uncertainties u (L )/L and WN WN c,mj ysis. The site-dependent relative uncertainty values of various IOP IOP u (L )/L show values slightly lower than those of c,mj WN WN model input quantities are provided in appendix B for each site. Chla Chla IOP IOP ˜ ˜ u (L )/L and u (L )/L . c WN WN c WN WN Figure 3 (right panel) displays the value of u (L )/L a. CPL x WN WN for selected center wavelengths calculated for each uncer- Chla IOP Mean values of L and L for CPL, which is frequently WN WN tainty source independently (with x denoting the uncertainty representative of Case-1 waters, are provided in Table 4 and source considered in the calculation). Notably, the highest in Fig. 3 together with the computed uncertainties. With refer- contributions are those associated with r and exhibit a spec- ence to Table 4, the median values of relative combined un- Chla IOP Chla Chla IOP IOP tral dependence opposite to that of L and L .The ˜ ˜ certainties u (L )/L and u (L )/L exhibit their WN WN c WN WN c WN WN second main source of uncertainty is the environmental minima at 490 nm, whereas higher values affect the blue and red bands. Maxima are observed in the red because of the variability. FIG.4.As Fig. 3, but for AAOT. 418 J OUR N A L O F A T M O S P H E R I C A N D O C E A N I C T E C H N O L OGY VOLUME 40 FIG.5. As Fig. 3, but for (top) GLT and (bottom) ST7. b. AAOT reduce the combined uncertainty values, except in the green Chla IOP spectral region where the correlation between L and L is i T Mean values of L and L for AAOT are provided in WN WN the lowest. Comparing the uncertainty values of the various Table 5 and in Fig. 4 together with the computed uncertainty Chla sources (see appendix B) with those previously obtained by values. The L median spectrum shows much lower values WN Gergely and Zibordi (2014), notably lower values are ob- in the blue and much higher in the red (up to 4 times at served for u (L )/L and u (L )/L , now estimated consider- 667 nm) with respect to those from CPL. The combined un- en i i en T T ing a time window lower than 10 min instead of 30 min. certainties show the same spectral dependence observed for Conversely, the values of u(r)/r are larger than those deter- CPL, but the relative uncertainties exhibit much lower values Chla in the red because of the higher L . Similar results are ob- mined by Gergely and Zibordi (2014) solely using mean spec- WN Chla tained by including major correlations effects, which slightly tral values of L . WN TABLE 6. As in Table 4, but for GLT. l (nm) 400 412 443 490 510 560 620 667 Chla Chla 0.31 6 0.10 0.41 6 0.13 0.55 6 0.16 0.79 6 0.23 0.74 6 0.21 0.60 6 0.18 0.12 6 0.04 0.07 6 0.03 L 6 m(L ) WN WN IOP IOP 0.31 6 0.09 0.40 6 0.12 0.54 6 0.15 0.78 6 0.22 0.74 6 0.20 0.59 6 0.17 0.11 6 0.04 0.07 6 0.03 L 6 m(L ) WN WN Chla Chla ˜ 10.2 8.5 6.1 4.7 4.6 4.9 9.3 12.5 u (L )/L c WN WN Chla Chla 9.9 8.3 5.9 4.1 3.8 3.8 8.0 11.2 u (L )/L c WN WN Chla Chla 9.5 8.1 5.9 4.5 4.5 4.8 8.8 11.9 u (L )/L c,mj WN WN Chla 0.031 0.035 0.035 0.036 0.034 0.029 0.012 0.009 u (L ) c,mj WN IOP IOP u ˜ (L )/L 9.9 8.2 5.7 4.2 4.2 4.3 8.1 10.3 c WN WN IOP IOP 8.3 6.9 4.5 3.0 3.0 2.9 6.7 9.0 u (L )/L WN WN IOP IOP u (L )/L 9.2 7.8 5.5 4.1 4.1 4.2 7.6 9.5 c,mj WN WN IOP 0.03 0.033 0.033 0.034 0.032 0.025 0.01 0.008 u (L ) c,mj WN APRIL 2023 CA ZZ A N I G A A N D ZI BO R D I 419 TABLE 7. As in Table 4, but for ST7. l (nm) 400 412 443 490 510 560 620 667 Chla Chla 0.26 6 0.07 0.33 6 0.08 0.43 6 0.10 0.63 6 0.13 0.66 6 0.15 0.66 6 0.22 0.17 6 0.08 0.11 6 0.05 L 6 m(L ) WN WN IOP IOP 0.26 6 0.06 0.33 6 0.08 0.43 6 0.09 0.65 6 0.13 0.67 6 0.16 0.69 6 0.24 0.18 6 0.08 0.11 6 0.05 L 6 m(L ) WN WN Chla Chla 13.0 11.2 8.2 6.2 5.9 6.4 9.8 12.5 u ˜ (L )/L WN WN Chla Chla 12.7 11.0 8.0 5.8 5.4 5.5 7.9 10.8 u (L )/L c WN WN Chla Chla 12.4 10.8 8.0 6.1 5.8 6.3 9.6 12.3 u (L )/L WN WN c,mj Chla 0.035 0.039 0.036 0.039 0.04 0.044 0.017 0.013 u (L ) WN c,mj IOP IOP ˜ 12.2 10.3 7.1 5.0 4.8 4.7 6.5 7.7 u (L )/L c WN WN IOP IOP 10.1 8.5 5.6 3.8 3.5 3.3 5.2 6.7 u (L )/L WN WN IOP IOP 11.5 9.9 6.9 4.9 4.7 4.6 6.2 7.3 u (L )/L c,mj WN WN IOP u (L ) 0.033 0.036 0.033 0.033 0.033 0.033 0.013 0.01 c,mj WN c. GLT and ST7 are also slightly higher than those determined for the AAOT site. Due to the higher wind speed characterizing these Chla The GLT and ST7 Black Sea sites exhibit median L WN two Black Sea sites with respect to AAOT, u(r)/r (see spectra with maxima at 490 and 560 nm, respectively (see the appendix B) exhibits larger values than any other site [ex- left panels in Fig. 5). The relative combined uncertainties cept for ILT showing the maximum median wind speed and summarized in Tables 6 and 7 vary from 4.5% at 490 and consequently a maximum value of u(r)/r)]. However, be- 510 nm to 11.9% at 667 nm for GLT, and from 5.8% at yond 443 nm, except at the 667 nm center wavelength for 510 nm to 12.4% at 400 nm for ST7. These values are slightly Chla IOP GLT, the largest uncertainty contribution is from u(C ) lower when considering L data and further reduced when WN considering correlations. Absolute combined uncertainties (see the right panels in Fig. 5). FIG.6.As Fig. 3, but for (top) GDLT and (bottom) ILT. 420 J OUR N A L O F A T M O S P H E R I C A N D O C E A N I C T E C H N O L OGY VOLUME 40 TABLE 8. As in Table 4, but for GDLT. l (nm) 400 412 443 490 510 560 620 667 Chla Chla 0.09 6 0.04 0.12 6 0.05 0.18 6 0.05 0.31 6 0.06 0.37 6 0.07 0.46 6 0.11 0.17 6 0.04 0.11 6 0.03 L 6 m(L ) WN WN IOP IOP 0.10 6 0.04 0.13 6 0.05 0.19 6 0.05 0.32 6 0.06 0.39 6 0.07 0.49 6 0.12 0.17 6 0.04 0.11 6 0.03 L 6 m(L ) WN WN Chla Chla 27.0 20.3 12.2 7.5 6.9 7.6 9.4 11.9 u ˜ (L )/L WN WN Chla Chla 26.7 20.1 12.2 6.9 6.1 6.3 8.0 10.6 u (L )/L c WN WN Chla Chla 24.6 19.2 11.7 7.4 6.9 7.6 9.3 11.7 u (L )/L WN WN c,mj Chla 0.025 0.026 0.023 0.026 0.028 0.037 0.017 0.014 u (L ) WN c,mj IOP IOP ˜ 26.6 19.7 11.5 6.0 5.1 4.4 5.6 6.6 u (L )/L c WN WN IOP IOP 25.8 18.8 10.1 4.5 3.4 2.8 4.5 5.8 u (L )/L WN WN IOP IOP 24.0 18.5 10.9 5.9 5.0 4.4 5.5 6.5 u (L )/L c,mj WN WN IOP u (L ) 0.024 0.025 0.022 0.022 0.023 0.024 0.011 0.008 c,mj WN Chla Chla Opposite to the previous sites, the values of u (L )/L e. Temporal variability c,mj WN WN at blue bands for ST7 are lower than those obtained including all Chla Chla The temporal variability over 1, 2, or 3 h u (L )/L tv WN WN correlations among the input variables. This is due to the contri- was determined from pairs of L . The computed values WN bution of negative correlation terms exceeding in value the con- Chla Chla of u (L )/L were combined in quadrature with WN WN tv tribution from the positive ones. Chla Chla u (L )/L to estimate the expected overall uncertainty c,mj WN WN Chla Chla Chla u (L )/L affecting AERONET-OC L data applied mu WN WN WN d. GDLT and ILT for the construction of matchups, thus attempting to account Chla Figure 6 shows the median spectra of L for the GDLT for the temporal mismatch between in situ and satellite data. WN and ILT sites in the Baltic Sea. These spectra exhibit very sim- Results from this specificanalysis are summarized in Table 10. Chla Chla ilar shapes, with slightly higher values for ILT and extremely With a time difference Dt 5 1h, the increaseof u (L )/L mu WN WN Chla Chla low values in the blue for both sites. As expected, relative un- with respect to u (L )/L is generally confined to WN WN c,mj certainties are very high in correspondence of these minima 3%. It naturally increases when considering Dt 5 2and with median values exceeding 20% at 400 nm. Combined un- Dt 5 3 h. Still, the increase is small for CPL and AAOT at certainties rapidly decrease with wavelength, with minima in the blue and green center wavelengths. In particular, for Chla Chla the 510–560 nm spectral region (see Tables 8 and 9). When CPL the values u (L )/L between 412 and 510 nm mu WN WN Chla considering the absolute uncertainty values, u (L ) ex- are confined below the ideal uncertainty target of 5%. It WN c,mj hibit the maximum at 560 nm, still lower than that determined must be however considered that the number of values for other sites. As for ST7, also for these sites the values available for the analysis may appreciably vary with Dt and Chla Chla IOP IOP of u (L )/L [and additionally u (L )/L for likely affect the statistical significance of results (see ST7 c,mj WN WN c,mj WN WN GDLT only] at blue bands are lower than those obtained in- for which the values obtained with Dt 5 3 h are lower than cluding all correlations among the input variables. those obtained with Dt 5 2h). TABLE 9. As in Table 4, but for ILT. l (nm) 400 412 443 490 510 560 620 667 Chla Chla L 6 m(L ) 0.13 6 0.04 0.16 6 0.04 0.23 6 0.05 0.39 6 0.06 0.46 6 0.07 0.58 6 0.09 0.22 6 0.05 0.14 6 0.04 WN WN IOP IOP 0.13 6 0.03 0.16 6 0.04 0.23 6 0.04 0.41 6 0.06 0.48 6 0.07 0.61 6 0.09 0.22 6 0.05 0.14 6 0.03 L 6 m(L ) WN WN Chla Chla ˜ 24.0 20.1 12.4 7.5 6.9 7.4 9.2 11.7 u (L )/L c WN WN Chla Chla 22.3 19.3 12.5 7.6 6.6 6.3 7.8 10.5 u (L )/L c WN WN Chla Chla 22.8 19.3 11.9 7.3 6.8 7.4 9.1 11.5 u (L )/L c,mj WN WN Chla 0.030 0.032 0.028 0.029 0.032 0.042 0.02 0.016 u (L ) c,mj WN IOP IOP u ˜ (L )/L 23.5 19.6 11.7 6.1 5.2 4.5 6.0 7.0 c WN WN IOP IOP 20.7 17.3 10.7 5.7 4.7 3.7 5.3 6.6 u (L )/L WN WN IOP IOP u (L )/L 22.3 18.7 11.1 5.9 5.1 4.5 5.8 6.7 c,mj WN WN IOP 0.029 0.031 0.027 0.025 0.026 0.027 0.013 0.009 u (L ) c,mj WN APRIL 2023 CA ZZ A N I G A A N D ZI BO R D I 421 Chla Chla Chla Chla TABLE 12. Median relative uncertainty u (L )/L (in TABLE 10. Median relative uncertainty u (L )/L mu WN WN mu WN WN units of %) for diverse Dt, obtained from triplets satisfying (in %) for diverse time differences Dt. N is the number of pairs Chla Chla t (412) # 0.2 and u # 458. N is the number of pairs of triplets used to determine u (L )/L . a 0 tv WN WN Chla Chla used to determine u (L )/L . Results are only reported for tv WN WN l (nm) those cases exhibiting a number of pairs N exceeding 80, heuristically assumed statistically relevant. Site Dt (h) 400 412 443 490 510 560 620 667 N l (nm) CPL 1 5.0 4.6 4.2 3.8 4.4 5.7 15.4 20.1 1478 2 5.4 4.9 4.5 4.1 4.7 6.3 17.6 22.1 812 Site Dt (h) 400 412 443 490 510 560 620 667 N 3 5.5 5.0 4.5 4.2 4.9 6.4 18.7 24.5 418 CPL 1 3.5 3.3 3.0 2.8 3.0 4.1 11.3 14.4 366 AAOT 1 6.2 5.7 5.1 4.7 4.7 5.4 8.2 10.3 2558 2 3.9 3.7 3.2 3.1 3.2 4.4 12.1 15.1 188 2 6.9 6.4 5.7 5.2 5.2 6.0 9.5 11.6 1666 AAOT 1 3.9 3.7 3.3 3.1 3.2 4.1 9.9 12.5 483 3 7.3 6.7 6.2 5.6 5.8 6.8 10.8 12.9 952 2 6.3 5.6 4.9 4.7 4.7 5.6 7.9 9.0 260 GLT 1 10.8 9.1 6.7 5.1 5.1 5.2 9.9 13.4 984 3 6.4 5.9 5.2 4.8 5.4 6.2 9.3 10.0 104 2 13.1 11.2 8.4 6.2 6.2 6.2 11.5 15.2 516 GLT 1 7.4 6.3 4.8 3.8 3.8 4.0 7.0 9.4 250 3 19.6 19.1 13.2 9.7 9.1 9.3 16.2 19.3 186 ST7 1 9.3 7.9 6.3 5.0 4.7 4.9 7.1 8.7 144 ST7 1 12.5 10.9 8.1 5.7 5.6 5.5 10.4 13.3 786 GDLT 1 17.9 15.1 10.8 6.9 7.0 7.4 9.1 11.4 82 2 18.7 15.4 11.8 7.9 6.9 6.7 12.9 16.5 374 ILT 1 20.4 17.4 11.6 7.1 6.7 7.4 9.3 11.2 121 3 14.6 13.0 10.3 7.3 7.2 6.8 12.0 15.2 354 GDLT 1 27.8 21.8 13.5 8.2 7.5 8.0 10.0 12.5 316 2 31.1 24.5 14.8 9.2 8.4 8.3 11.3 13.5 224 and Zibordi (2014). These results (not shown) indicate that 3 37.4 26.7 17.1 11.3 9.5 9.4 12.2 14.4 164 the lower combined values of u applied in the current analy- ILT 1 24.9 20.9 13.2 8.0 7.3 7.8 9.7 12.1 337 ac Chla Chla 2 26.5 22.0 13.7 8.0 7.4 8.1 10.1 12.6 211 sis heavily contribute to a decrease of u (L )/L . How- c,mj WN WN 3 29.2 22.3 14.2 8.4 7.7 8.5 10.2 12.6 110 ever, 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 4. Discussion by Gergely and Zibordi (2014). This is particularly evident at a. Comparison of results from the current and previous those sites exhibiting high median wind speed, such as GDLT, Chla Chla uncertainty analyses showing a significant increase of u (L )/L . When WN WN c,mj looking at the spectral values, the increase is more marked in This work is a revisitation of the former analysis of the blue due to the larger impact of u(r)/r. AERONET-OC uncertainties carried out by Gergely and Zibordi (2014). It was suggested by a number of technological b. Data reduction and science advances. In particular the recent adoption of A major contribution to combined uncertainties comes CE-318T radiometers allows for a reevaluation of environ- from u(r) and u(C ). To investigate the possibility of mini- mental perturbations u (L ) and u (L ), and a quantifi- en T en i mizing their contributions, in agreement with Gergely and cation of the temporal variability u (L ). These latest tv WN Zibordi (2014), uncertainties have been reevaluated only radiometers are in fact capable of performing consecutive including data alternatively characterized by W # 3m s , measurement sequences (e.g., triplets) leading to the determi- Chla # 0.7 mg m , u # 458, and t (412) # 0.2. Results pro- nation of successive values of L and L a few minutes apart 0 a T i posed for the sole AAOT site are summarized in Table 11.As from each other. As expected, the new u (L ) and u (L ) en T en i expected, limiting the input data to conditions determined by exhibit much lower values with respect to those characteriz- W # 3m s leads to a substantial decrease of u(r)/r. This ing the previous analysis. decrease (not shown) is more pronounced at those sites exhi- In view of assessing the impact of the other methodological biting the highest median wind speed [e.g., with u(r)/r changes introduced in the current study, relative combined Chla Chla decreasing by 1.1% for AAOT, and up to approximately uncertainties u (L )/L were also calculated applying c,mj WN WN Chla Chla 3.5% and 4.2% for ST7 and ILT]. Consequently, the com- the values of u(r)/r, u(C )/C , and u used in Gergely ac Q Q Chla Chla bined uncertainties u (L )/L diversely decrease at c,mj WN WN Chla Chla various sites: up to 1.2% for AAOT and slightly above 12% TABLE 11. Values of u (L )/L (in %) determined by c,mj WN WN partitioning the AAOT dataset applying thresholds to the values in the blue for ILT and GDLT (not shown). of W, u , t (412), and Chla. N is the number of cases satisfying Imposing Chla # 0.7 mg m leads to a decrease of 0 a Chla Chla the thresholds. u(C )/C and consequently of the combined uncertain- Q Q ties (except in the red), mostly for the Black Sea sites. How- l (nm) ever, the lack of suitable data for ILT and GDLT prevents 400 412 443 490 510 560 620 667 N any assessment for these sites. Alarge influence on combined uncertainties is also W # 3m s 4.9 4.5 4.1 4.0 3.9 4.4 6.3 8.0 6173 brought by imposing u # 458. This has a large impact on u # 458 5.1 4.7 4.1 3.9 3.8 4.3 6.2 7.7 5931 0 Chla Chla t (412) # 0.2 5.9 5.5 4.8 4.5 4.5 5.1 6.6 8.5 4740 u(C )/C , which is halved at CPL. Nevertheless, the Q Q Chla # 0.7 mg m 4.5 4.2 3.6 3.4 3.4 3.8 7.6 10.3 3215 IOP IOP impact is negligible on u(C )/C . Q Q 422 J OUR N A L O F A T M O S P H E R I C A N D O C E A N I C T E C H N O L OGY VOLUME 40 Chla IOP FIG. 7. Scatterplot of median (left) L and (right) L values vs median absolute combined uncertainties WN WN Chla IOP u (L ) and u (L ). The diverse symbols represent the various sites, whereas their color identifies the c,mj WN c,mj WN wavelength. The black solid line indicates the linear regression. The gray dashed line indicates the regression pro- 2 Chla IOP posed by Zibordi et al. (2022). The determination coefficient (r ) is 0.62 and 0.60 for L and L , respectively WN WN (p value , 0.01). Finally, imposing t (412) # 0.2 leads to a slight reduction of the Gloria Platform (GLR; located close to ST7 and no longer u (L )/L (typically decreasing by less than 0.2%) without operated), GLT, GDLT, and Helsinki Lighthouse (HLT; in en i i any significant change in the combined uncertainty values, ex- the Baltic Sea) sites, to produce a linear relationship between cept for a reduction of approximately 2%–4% in the blue Chla Chla u (L ) and L regardless of wavelength and site. That WN WN c,mj spectral region for GDLT. statistical relationship applied to estimate absolute uncertain- The uncertainties determined for the temporal variability ap- Chla ties for each L spectral value was mostly explained by the WN pear smaller when simultaneously imposing t (412) # 0.2 and weight of uncertainty contributions linearly varying with u # 458, as shown in Table 12. Consequently, the values of Chla L , such as those resulting from the absolute radiometric WN Chla Chla u (L )/L also reduce with respect to those provided in WN WN mu calibration and corrections for bidirectional effects. Improve- Table 10. In particular, also for time differences Dt 5 2and 3 h, ments in the quantification of uncertainties introduced in this they become lower than 5% at the blue and green center wave- Chla work lead to a decreased correlation between L and WN lengths for CPL and between 443 and 560 nm for AAOT and Chla Chla Chla u (L ). The scatterplots in Fig. 7 display median L c,mj WN WN GLT. Nevertheless, only a few sites exhibit a statistically signifi- IOP (left panel) and L (right panel) values, versus the corre- WN cant number of data to allow evaluating the case with Dt . 1h. Chla IOP sponding median u (L ) and u (L ). The regression c,mj WN c,mj WN c. Uncertainty as a function of L (l) WN lines for the plotted values are displayed together with the re- Chla gression line proposed by Zibordi et al. (2022) for L , i.e., Zibordi et al. (2022) applied the median uncertainty values WN Chla Chla determined by Gergely and Zibordi (2014) for the AAOT, u (L ) 5 0:0091 1 0:0405L . c,mj WN WN Chla IOP Chla FIG. 8. Scatterplot of median (left) L and (right) L values vs the corresponding uncertainties u (L ) and WN WN c,mj WN IOP u (L ). The diverse symbols represent the various sites, whereas their color identifies the wavelength. The purple c,mj WN and red dashed lines indicate the linear regressions determined solely using the Black and Baltic Sea “blue bands” Chla and, alternatively, all the remaining data. For L , r is 0.81 and 0.50 for the red and purple lines, respectively (both WN IOP exhibiting p value , 0.01). For L , r is 0.92 and 0.50 for the red and purple lines, respectively (in this case too, both WN showing p value , 0.01). APRIL 2023 CA ZZ A N I G A A N D ZI BO R D I 423 Chla IOP Chla FIG.9.Scatterplots of median (left) L and (right) L values vs the corresponding uncertainties u (L ) WN WN c,mj WN IOP and u (L ) for data restricted to cases characterized by W # 3m s . The diverse symbols represent the various c,mj WN sites, whereas their color indicates the wavelength. The black solid line indicates the linear regression. The determina- 2 Chla IOP tion coefficient (r )is0.72 and 0.85 for L and L , respectively (both exhibiting p value , 0.01). WN WN Definitively, the data in Fig. 7 are much more scattered than for the normalized water leaving radiance L . The main ele- WN those shown by Zibordi et al. (2022). This is largely explained ments indicating the need for such a reevaluation of uncer- tainties were (i) the availability of time series produced with by a significant reduction of u and the application of values ac Chla CE-318T 12-band instruments exhibiting higher measurement of u(r) determined for each single L measurement. This WN leads to a separation of the median uncertainties at the blue frequency when compared to those performed with CE-318 center wavelengths (i.e., from 400 to 443 nm) from all other 9-band instruments, and consequently allowing a more accu- rate determination of environmental perturbations; (ii) a re- spectral values for those sites characterized by higher median cent rigorous quantification of uncertainties affecting absolute wind speed such as the Black Sea and Baltic Sea ones. By sep- radiometric calibrations; (iii) the potential for a more accurate arating these “blue-bands” data from the others, two distinct estimate of the uncertainties affecting corrections for the linear relations can be defined as displayed in Fig. 8. in-water bidirectional effects, performed with either the so- As already stated, wind speed has a major impact on uncer- called Chla-based and IOP-based approaches; and (iv) the tainties and specifically leads to their increase for the Baltic determination of uncertainties affecting the sea surface reflec- and Black Sea sites. Because of this, the relationships between Chla IOP Chla IOP tance factor on a measurement by measurement basis. u (L ) and u (L ) with median L and L ,re- c,mj WN c,mj WN WN WN Uncertainties were determined for the AERONET-OC spectively, were redetermined restricting the analysis to cases Chla IOP L and L data products generated by applying the Chla- characterized by W # 3m s . This reduced dataset appears WN WN based and IOP-based corrections for in-water bidirectional ef- less scattered, as shown in Fig. 9: a single regression line well Chla IOP fects, respectively. Uncertainties were computed following describes the relation between median L or L and the WN WN Chla IOP GUM (JCGM 2008) and proposed in relative and absolute corresponding uncertainties u (L ) and u (L ). c,mj WN c,mj WN units by (i) neglecting correlations among input quantities de- fining the measurement equation, which leads to the largest 5. Summary and conclusions uncertainties; (ii) accounting for each correlation term in the Advances in AERONET-OC suggested to revisit the un- measurement equation, which usually leads to the lowest un- certainties formerly quantified by Gergely and Zibordi (2014) certainties; and finally (iii) only including major correlation TABLE A1. Sources and related relative uncertainties (in %) contributing to absolute radiometric calibration uncertainties. l (nm) 400 412 443 490 510 560 620 667 Lamp (NPL #1333) 0.90 0.55 0.55 0.50 0.50 0.45 0.45 0.40 Lamp fit 0.30 0.30 0.20 0.20 0.20 0.20 0.20 0.20 Lamp aging (with 25 h of use) 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 Plaque 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 Shunt 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 Power supply (with a 7.5 mA bias) 0.07 0.07 0.07 0.06 0.06 0.05 0.05 0.04 Lamp–plaque distance 0.20 0.20 0.20 0.20 0.20 0.20 0.20 0.20 Lamp positioning 0.30 0.30 0.30 0.30 0.30 0.30 0.30 0.30 Plaque repositioning 0.10 0.10 0.10 0.10 0.10 0.10 0.10 0.10 Sensor alignment 0.10 0.10 0.10 0.10 0.10 0.10 0.10 0.10 424 J OUR N A L O F A T M O S P H E R I C A N D O C E A N I C T E C H N O L OGY VOLUME 40 contributions, which generally leads to uncertainty values TABLE B1. Median relative uncertainties (in %) for individual sources at different center wavelengths (l)for the various slightly lower than those determined neglecting correlations. AERONET-OC sites: CPL, AAOT, GLT, ST7, GDLT, and ILT. The following conclusions are based on the uncertainties de- termined solely accounting for the major correlations between l (nm) L and L . i T 400 412 443 490 510 560 620 667 Results were produced for AERONET-OC sites represen- tative of a variety of water types: Casablanca Platform (CPL) CPL exhibiting frequent occurrence of Case-1 waters; the Acqua u (L )/L 0.5 0.6 0.6 0.7 0.7 0.9 1.0 1.1 en i i Alta Oceanographic Tower (AAOT), the Galata Platform u (L )/L 1.2 1.2 1.1 1.2 1.2 1.6 2.7 3.2 en T T u (r)/r 3.9 3.9 3.9 3.9 3.9 3.9 3.9 3.9 (GLT), and the Section-7 Platform (ST7) characterized by dr u (r)/r 3.8 3.8 3.8 3.8 3.8 3.8 3.8 3.8 optically complex waters with varying concentrations of sedi- WS u(r)/r 5.6 5.6 5.6 5.6 5.6 5.6 5.6 5.6 ments and CDOM; finally, the Gustaf Dalen Lighthouse Tower (GDLT) and Irbe Lighthouse (ILT), characterized by AAOT very high concentrations of CDOM. u (L )/L 0.6 0.6 0.7 0.8 0.8 1.0 1.1 1.2 en i i The quantified uncertainties exhibit values varying from u (L )/L 1.3 1.3 1.2 1.1 1.1 1.2 1.8 2.1 en T T above 3% at 490 nm for CPL, and up to approximately u (r)/r 2.3 2.3 2.3 2.3 2.3 2.3 2.3 2.3 dr 25% at 400 nm in CDOM-dominated waters. Uncertainties u (r)/r 3.2 3.2 3.2 3.2 3.2 3.2 3.2 3.2 WS Chla IOP u(r)/r 4.2 4.2 4.2 4.2 4.2 4.2 4.2 4.2 are higher for L with respect to L due to the assump- WN WN tion of higher uncertainties for Chla-based corrections GLT than for the IOP-based ones applied to remove bidirec- u (L )/L 0.7 0.8 0.8 0.9 0.9 1.1 1.2 1.3 en i i tional effects. u (L )/L 1.8 1.7 1.6 1.3 1.4 1.3 2.2 2.4 en T T Chla Overall, the revisited uncertainties determined for L do WN u (r)/r 4.3 4.3 4.3 4.3 4.3 4.3 4.3 4.3 dr not significantly differ from the previous proposed by Gergely u (r)/r 3.9 3.9 3.9 3.9 3.9 3.9 3.9 3.9 WS and Zibordi (2014). This is largely explained by compensa- u(r)/r 6.3 6.3 6.3 6.3 6.3 6.3 6.3 6.3 tions enacted in their quantification by the increase or de- ST7 crease of diverse contributions. u (L )/L 0.8 0.9 0.9 0.9 1.0 1.2 1.2 1.3 en i i The largest contribution to uncertainties is the sea surface u (L )/L 2.1 2.1 1.9 1.7 1.6 1.7 2.2 2.5 en T T reflectance factor r. This finding is explained by the uncertain- u (r)/r 5.5 5.5 5.5 5.5 5.5 5.5 5.5 5.5 dr ties in wind speed estimation and in the data reduction u (r)/r 4.0 4.0 4.0 4.0 4.0 4.0 4.0 4.0 WS method leading to the determination of L . This is particu- u(r)/r 7.0 7.0 7.0 7.0 7.0 7.0 7.0 7.0 larly evident at those sites characterized by larger median values of wind speed. For the remaining sites such as CPL GDLT u (L )/L 0.5 0.5 0.5 0.6 0.7 0.7 0.8 0.8 and AAOT, a large fraction of the total uncertainty is ex- en i i u (L )/L 2.7 2.0 1.7 1.6 1.4 0.9 1.6 2.1 en T T plained by the contributions due to correction factors u (r)/r 4.4 4.4 4.4 4.4 4.4 4.4 4.4 4.4 dr for bidirectional effects determined with the Chla-based u (r)/r 3.7 3.7 3.7 3.7 3.7 3.7 3.7 3.7 WS method. u(r)/r 5.9 5.9 5.9 5.9 5.9 5.9 5.9 5.9 The study shows that restricting the uncertainty analysis to cases characterized by W # 3m s ,or u # 458, or Chla # 0 ILT 0.7 mg m , leads to a reduction of the uncertainties. u (L )/L 0.5 0.5 0.6 0.7 0.7 0.8 1.0 1.1 en i i u (L )/L 2.1 2.0 1.9 1.6 1.4 1.3 1.9 2.3 In agreement with Zibordi et al. (2022) the possibility to es- en T T Chla u (r)/r 6.0 6.0 6.0 6.0 6.0 6.0 6.0 6.0 timate absolute uncertainties as a linear function of L ,or dr WN IOP u (r)/r 4.3 4.3 4.3 4.3 4.3 4.3 4.3 4.3 WS alternatively L , was investigated. The analysis confirmed WN u(r)/r 7.6 7.6 7.6 7.6 7.6 7.6 7.6 7.6 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 ra- optically complex waters (i.e., at CPL and AAOT) in the diances and uncertainties. Nevertheless, a single linear rela- blue-green center wavelengths. Conversely, they exceed tionship is instead applicable for measurement conditions 21 5% at the other AERONET-OC sites considered in the characterized by W # 3m s , due to a reduction of the study, or for larger Dt. dispersion between median spectral radiances and related uncertainties. Acknowledgments. The authors thank the AERONET Finally, the impact of temporal variability was investi- Team for the effort to include and sustain the Ocean Color gated for the various AERONET-OC sites in view of best component in the AERONET observational network. They supporting matchup analysis between in situ and satellite also acknowledge the Centro Previsioni e Segnalazioni data by accounting for temporal mismatches. Simply con- Maree of Comune di Venezia for providing the in situ wind sidering a time difference Dt 5 1 h between satellite and in data. They finally thank the anonymous reviewers for their situ data, the combined values accounting for L uncer- WN tainties and contributions due to temporal variability are precious contribution. This work has received funding from generally confined below 5% in Case-1 and moderately the EMPIR programme (Grant 19ENV07 for METEOC-4) APRIL 2023 CA ZZ A N I G A A N D ZI BO R D I 425 Automated near-real-time quality control algorithm with cofinanced by the participating states and from the European improved cloud screening for sun photometer aerosol optical Union’s Horizon 2020 research and innovation programme. depth (AOD) measurements. Atmos. Meas. Tech., 12, 169– The support provided by DG DEFIS, i.e., the European 209, https://doi.org/10.5194/amt-12-169-2019. Commission Directorate-General for Defence, Industry and Gordon, H. R., 2005: Normalized water-leaving radiance: Revisit- Space, and the Copernicus programme is also gratefully ing the influence of surface roughness. Appl. Opt., 44, 241– acknowledged. 248, https://doi.org/10.1364/AO.44.000241. Hooker,S. B., W. E. Esaias,G. C.Feldman, W.W. Gregg,and Data availability statement. All AERONET-OC data used C. R. McClain, 1992: An overview of SeaWiFS and during this study are contributed by the International Ocean Color. NASA Tech. Memo. 104566, Vol. 1, 24 pp., AERONET Federation and available from AERONET-OC https://oceancolor.gsfc.nasa.gov/SeaWiFS/TECH_REPORTS/ archive at https://aeronet.gsfc.nasa.gov/cgi-bin/draw_map_ vol1_abs.html. display_seaprism_v3. Please refer to the AERONET-OC }}, and Coauthors, 2002: The seventh SeaWiFS Intercalibration web page for complete information on data policy. Round-Robin Experiment (SIRREX-7), March 1999. NASA Tech. Memo. NASA/TM-2002-206892, Vol. 17, 78 pp., https://ntrs.nasa.gov/api/citations/20020045342/downloads/ APPENDIX A 20020045342.pdf. JCGM, 2008: Evaluation of measurement data}Guide to the Uncertainty Sources for Absolute Radiometric expression of uncertainty in measurement. International Calibration Uncertainties Organization for Standardization Tech. Rep. JCGM 100:2008, Table A1 shows the uncertainty sources and their typical 134 pp., https://www.bipm.org/documents/20126/2071204/ relative values applied for the computation of the uncer- JCGM_100_2008_E.pdf/cb0ef43f-baa5-11cf-3f85-4dcd86f77bd6. Johnson, B. C., G. Zibordi, S. W. Brown, M. E. Feinholz, M. G. tainty budget for the absolute radiometric calibrations per- Sorokin, I. Slutsker, J. T. Woodward, and H. W. Yoon, 2021: formed at the JRC Marine Optical Laboratory. It is noted Characterization and absolute calibration of an AERONET- that contributions due to the determination of actual center OC radiometer. Appl. Opt., 60, 3380–3392, https://doi.org/10. wavelengths and spectral responses of sensor bands are not 1364/AO.419766. included. Lee, Z. P., K. Du, K. J. Voss, G. Zibordi, B. Lubac, R. Arnone, and A. Weidemann, 2011: An inherent-optical-property- APPENDIX B centered approach to correct the angular effects in water- leaving radiance. Appl. Opt., 50,3155–3167, https://doi.org/10. Relative Uncertainty of Input Variables for 1364/AO.50.003155. AERONET-OC Sites Mobley, C. D., 1994: Light and Water: Radiative Transfer in Natu- ral Waters. Academic Press, 592 pp. The median relative values of each uncertainty source }}, 1999: Estimation of the remote-sensing reflectance from contributing to the combined uncertainties of L are re- WN above-surface measurements. Appl. Opt., 38, 7442–7455, ported for each site in Table B1. Note that u(r)/r has been https://doi.org/10.1364/AO.38.007442. calculated as the root of the sum of squares of u (r)/r WS Morel, A., D. Antoine, and B. Gentili, 2002: Bidirectional reflec- and u (r)/r for each measurement. For this reason, u(r)/r dr tance of oceanic waters: Accounting for Raman emission and values in the following tables may differ from the root of varying particle scattering phase function. Appl. Opt., 41, the sum of squares of median u (r)/r and u (r)/r. WS dr 6289–6306, https://doi.org/10.1364/AO.41.006289. Talone, M., G. Zibordi, and Z. Lee, 2018: Correction for the non- nadir viewing geometry of AERONET-OC above water radi- REFERENCES ometry data: An estimate of uncertainties. Opt. Express, 26, A541–A561, https://doi.org/10.1364/OE.26.00A541. D’Alimonte, D., T. Kajiyama, G. Zibordi, and B. 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Sorokin, 2021: Advances in the Ocean Color based products for climate: 2011 update. WMO Doc. GCOS- Component of the Aerosol Robotic Network (AERONET- 154, 138 pp., https://library.wmo.int/doc_num.php?explnum_ OC). J. Atmos. Oceanic Technol., 38,725–746, https://doi.org/ id=3710. 10.1175/JTECH-D-20-0085.1. Gergely, M., and G. Zibordi, 2014: Assessment of AERONET- }}, M. Talone, and F. Mélin, 2022: Uncertainty estimate of OC LWN uncertainties. Metrologia, 51,40–47, https://doi.org/ 10.1088/0026-1394/51/1/40. satellite-derived normalized water-leaving radiance. IEEE Giles, D. M., and Coauthors, 2019: Advancements in the Aerosol Geosci. Remote Sens. Lett., 19, 1502905, https://doi.org/10. Robotic Network (AERONET) version 3 database} 1109/LGRS.2021.3134876. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Journal of Atmospheric and Oceanic Technology American Meteorological Society

AERONET-OC LWN Uncertainties: Revisited

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Abstract

APRIL 2023 CA ZZ A N I G A A N D ZI BO R D I 411 AERONET-OC L Uncertainties: Revisited WN a a ILARIA CAZZANIGA AND GIUSEPPE ZIBORDI Joint Research Centre, European Commission, Ispra, Italy (Manuscript received 8 June 2022, in final form 7 December 2022) ABSTRACT: 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 .The WN new uncertainty values are quantified 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 from its spectral WN values. Additionally, results from an evaluation of the temporal variability characterizing L at various AERONET-OC WN sites are presented to address the impact of temporal mismatches between in situ and satellite data in matchup analysis. KEYWORDS: Ocean; In situ oceanic observations; Remote sensing; Uncertainty 1. Introduction in situ measurements performed from offshore fixed struc- tures in a variety of water types (Zibordi et al. 2009, 2021). A In situ reference measurements are essential to any ocean best effort to quantify uncertainties affecting AERONET-OC color program for system vicarious calibration of satellite sen- L was made by Gergely and Zibordi (2014). Following the WN sors, assessment of primary and derived data products, and “Guide to the Expression of Uncertainty in Measurement” development of bio-optical algorithms. The primary ocean (GUM; JCGM 2008), they determined AERONET-OC L WN color product is the spectral normalized water-leaving radi- uncertainties accounting for the main uncertainty sources af- ance L : the radiance emerging from below the sea surface WN fecting the quantities included in the measurement equation. derived from the top-of-atmosphere radiance after correction Specifically, they considered contributions from (i) absolute for atmospheric perturbations, normalized with respect to the radiometric calibration, (ii) instrument sensitivity change dur- illumination conditions and viewing geometry, and finally cor- ing deployment, (iii) data reduction minimizing the impact rected for in-water bidirectional effects. The quantification of wave perturbations, (iv) environmental variability, and of the accuracy of L , or of the equivalent remote sensing WN (v) corrections for illumination conditions and bidirectional reflectance R , is essential to successively determine that af- RS effects. Results showed uncertainty values ranging from 5% in fecting derived data products [e.g., chlorophyll-a concentra- the blue-green spectral region in moderately turbid waters up tion (Chla)]. For this reason, primary satellite radiometric to about 30% in the blue in highly absorbing waters. Using products are matter of extensive validation programs aiming these results, Zibordi et al. (2022) defined a site- and wavelength- at verifying the compliance of their uncertainties with mission independent linear function relating L to its uncertainty WN requirements. Often these requirements entail generic uncer- values. This solution aimed at providing a practical, albeit ap- tainty targets of 5% for satellite-derived L or R (e.g., WN RS proximate, solution to the operational use of AERONET-OC Hooker et al. 1992; Drinkwater and Rebhan 2007). Recalling L for the quantification of uncertainties affecting satellite- WN that the 5% uncertainty value is considered achievable in derived radiometric products. oligotrophic/mesotrophic oceanic waters in the blue-green This work primarily aims at revisiting the AERONET-OC spectral region (GCOS 2011), its assessment implies access to L uncertainties formerly quantified by Gergely and WN highly accurate in situ reference data exhibiting uncertainties Zibordi (2014) benefitting of advances in measurement proto- quantified in agreement with metrology principles. cols allowed by the recent CE-318T 12-band radiometers The Ocean Color Component of the Aerosol Robotic Net- and additionally by new investigations on CE-318T calibra- work (AERONET-OC) was specifically conceived to support tion and data processing. In particular, unlike the former the assessment of satellite L products through automated WN CE-318 9-band radiometers, the new CE-318T 12-band instru- ments allow for multiple consecutive above-water measurement sequences, which permit better addressing environmental Denotes content that is immediately available upon publica- tion as open access. This article is licensed under a Creative Commons Attribution 4.0 license (http://creativecommons.org/ Corresponding author: Ilaria Cazzaniga, ilaria.cazzaniga@ec. europa.eu licenses/by/4.0/). DOI: 10.1175/JTECH-D-22-0061.1 Ó 2023 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses). 412 J OUR N A L O F A T M O S P H E R I C A N D O C E A N I C T E C H N O L OGY VOLUME 40 perturbations in L . Moreover, recent studies on uncertainties likely applicable to any water type (see Lee et al. 2011). Fi- WN affecting the CE-318T absolute calibration and corrections for nally, the term C is used to minimize the dependence on illu- bidirectional effects allow for a more accurate determination of mination conditions and it is computed as their contributions to the uncertainty budget. 2 21 C (l, u , t , D) 5 [D t (t )cosu ] , (3) Finally, this work also investigates the potential for improved A 0 a d a 0 relationships making it possible to statistically estimate uncer- where t is the diffuse atmospheric transmittance and D the tainties for L regardless of site and ideally of wavelength. WN sun–Earth distance. Further objective of this work is an evaluation of the impact of CE-318 and CE-318T instruments perform spectral meas- temporal variations affecting L at a number of AERONET- WN urements of (i) direct solar irradiance E applied to quantify t OC sites in view of more comprehensively supporting the and (ii) radiance from the sea and sky to determine L and analysis of in situ and satellite matchups naturally exhibiting T L . Each measurement sequence, which comprises spectrally temporal mismatches. i asynchronous measurements of 11 values of the total radiance from the sea and 3 values of the sky radiance, is performed in 2. Materials and methods approximately 3 min for the CE-318 instruments and 4 min a. AERONET-OC instrument and measurement model for the CE-318T ones. Then L is determined by averaging the 3 sky radiance values while L is determined by the averaging of AERONET-OC (Zibordi et al. 2021) allows for the deter- the lowest 2 values of the total radiance from the sea. Rationale mination of the spectral water-leaving radiance L by exploit- forthisspecific data reduction, supporting the determination of ing in situ measurements of the total radiance from the sea L L and aiming at minimizing the impact of wave perturbations, and of the sky radiance L , according to T is provided in Zibordi (2012) and in D’Alimonte et al. (2021). L (l, u, u, u , u ) 5 L (l, u, u, u ) W 0 T 0 Comprehensive details on AERONET-OC data handling, processing, quality assurance and control are available in 2 r(u, u, u , W) L (l, u , u, u ), (1) 0 i 0 Zibordi et al. (2021). where u (set to 408) is the sensor sea-viewing angle, u (with b. AERONET-OC data u 5 1808 2 u) the sensor sky-viewing angle, u the sensor rela- Version 3 level 2.0 (i.e., fully quality controlled) L data 8 WN tive azimuth angle with respect to the sun (set to 90 ), and from CE-318T instruments for the following sites were con- u the sun zenith angle. The term r indicates the sea surface sidered in the study: reflectance factor applied to quantify the sky radiance re- flected by the sea surface into the field of view of the sensor. (i) Casablanca Platform (CPL) in the western Mediterranean Its value is a function of the viewing and illumination geome- Sea exhibiting frequent occurrence of Case-1 waters; tries, and of the sea state conveniently expressed through the (ii) Acqua Alta Oceanographic Tower (AAOT) in the wind speed W (Mobley 1999). In the current AERONET-OC northern Adriatic Sea and, Galata Platform (GLT) and processing, W is extracted from the National Centers for Section-7 Platform (ST7) in the Black Sea, all character- Environmental Prediction (NCEP) data products with 6-h ized by optically complex waters with varying concentra- temporal resolution, and interpolated to the acquisition time tions of sediments and chromophoric dissolved organic of each AERONET-OC measurement sequence. matter (CDOM); The normalized water leaving radiance L , which is the WN (iii) Gustaf Dalen Lighthouse Tower (GDLT) and Irbe primary radiometric product for ocean color applications, is Lighthouse (ILT) in the Baltic Sea, also characterized determined from by optically complex waters, but exhibiting very high concentrations of CDOM. L (l) 5 L (l, u, u, u , u ) C (l, u, u, u , W, t , IOP) WN W 0 Q 0 a To minimize the impact of changes in illumination condi- 3 C (l, u , t , D) , (2) A 0 a tions mainly affecting L , the analysis was restricted to the data acquired with u , 708 within 62 h from local noon. The where C is the correction applied to normalize L for the 0 Q W time interval around 1200 local time comprises the overpass in-water bidirectional effects as a function of the viewing and time of most of the ocean color satellites. Nevertheless, the illumination geometries, wind speed, atmospheric and marine ST7 and GLT time windows were centered at 1300 and 1100 optical properties expressed through the aerosol optical depth local time, respectively. This choice was imposed by the need t and the water inherent optical properties IOP, respectively. In the AERONET-OC version 3 database, L is corrected to minimize the impact of the small number of data available WN with C values determined applying two distinct methods at these sites around 1200 local time due to deployment re- strictions preventing optimal viewing geometries with respect leading to the generation of diverse data products. The first Chla to the superstructure around local noon. method, with corrections identified by the term C and wa- The uncertainties characterizing L data products cor- ter IOPs exclusively expressed by Chla iteratively estimated WN rected for bidirectional effects through the Chla-based and from R band ratios, is specific for Case-1 waters (see Morel RS Chla et al. 2002). The second method, with corrections identified the IOP-based approaches, hereafter identified as L and WN IOP IOP by the term C and IOPs determined from L itself, is L , were both evaluated. Still, the symbol L is used W WN Q WN APRIL 2023 CA ZZ A N I G A A N D ZI BO R D I 413 when discussing uncertainties independent from specific cor- rections for bidirectional effects. c. Background on measurement uncertainties The methodology applied in this study for the quantifica- tion of L uncertainties relies on GUM guidelines and is WN equivalent to that implemented by Gergely and Zibordi (2014). The basic elements of the methodology are hereafter summarized for completeness. The standard uncertainty u (y) associated with a measur- and y indirectly determined from other quantities through a measurement model y 5 f(x , … , x ), can be obtained 1 N propagating the uncertainties of each model input quantity through the first-order expansion of Taylor series: FIG.1. L measurement model and uncertainty sources in- WN N 2 ­f cluded in the calculation of combined uncertainties. See the text 2 2 u ˜ (y) 5 ∑ u (x ) , (4) for symbols explanation. ­x i51 where u ˜ (y) is the square of u (y) when neglecting any corre- c correlations, the equation expressing the combined uncertain- lation among input variables.­f /­x and u(x ) indicate the par- i ties for L becomes WN tial derivative respect to x and the uncertainty of the model 2 2 2 2 2 ˜ ˜ input quantity x , respectively. When nonnegligible correla- u (L ) 5 (C C ) u (L ) 1 (L C ) u (C ) c WN Q A c W W A Q tions characterize pairs of input quantities x , x , Eq. (4) i j 2 2 1 (L C ) u (C ), (9) W Q A becomes N21 N while, when including only the correlations between L and ­f ­f T 2 2 u (y) 5 u ˜ (y) 1 2 ∑ ∑ u(x )u(x )r(x , x ), (5) 2 2 c c i j i j L , u ˜ (L ) is replaced by u (L ): ­x ­x i i51 j5i11 c W c,mj W i j 2 2 2 2 2 u (L ) 5 (C C ) u (L ) 1 (L C ) u (C ) c,mj WN Q A c,mj W W A Q where­f /­x and u(x ) indicate the partial derivative respect to x and the uncertainty of the model input quantity x , respec- 1 (L C ) u (C ): (10) j j W Q A tively. Last, r(x , x ) is the correlation coefficients between x i j i and x . Alternatively, when including all correlations Eq. (9) becomes d. Determination of the combined uncertainties u (L ) c W 2 2 2 u (L ) 5 u (L ) 1 2C C L r(C , C ) u(C )u(C ) c WN c WN Q A W Q A Q A for L and u (L ) for L W c WN WN 1 2C C L r(L , C ) u (L )u(C ) A W W A c W A Excluding correlations and nonlinearity contributions, the combined uncertainty u ˜ (L ) for the spectral values of L 1 2C C L r(L , C ) u (L )u(C ): (11) c W Q A W W Q c W Q were determined from the uncertainties affecting L , L , and T i r [hereafter indicated by u(L ), u(L ), and u(r)], according to T i e. Uncertainty values applied for the determination 2 2 2 2 2 2 u ˜ (L ) 5 u (L ) 1 u (L )r 1 u (r)L : (6) W T i i of u (L ) and u (L ) c W c WN Figure 1 shows the uncertainty sources accounted for in Considering all possible correlations, the combined uncer- the calculation of the combined uncertainties for L . Both tainty u (L ) was computed as WN c W u(L )and u(L ) depend on (i) the uncertainty affecting in- T i 2 2 u (L ) 5 u ˜ (L ) 2 2r r(L , L ) u(L ) u(L ) 2 2L r(L , r) c c W W T i T i i T strument calibration u , (ii) the decay of instrument sensi- ac tivity u , and (iii) the environmental perturbations u .The sc en 3 u(L )u(r) 2 2L r(L , r) u(L ) u(r): (7) T T i i uncertainty u(r) also depends on multiple contributions: (i) the uncertainty affecting wind speed u (r), (ii) the WS Alternatively, when restricting correlations to L and L only T i uncertainty u (r) resulting from the filtering applied to L , dr T (considered as the major correlation, mj), the related com- and finally, (iii) the intrinsic uncertainty in the theoretical bined uncertainty u (L ) was determined with c,mj W determination of r. 2 2 u (L ) 5 u ˜ (L ) 2 2r r(L , L ) u(L ) u(L ): (8) The approaches used to estimate all these quantities, and c,mj W c W T i T i those used for u(C ) and u(C ) related to C and C , are de- A Q A Q The value of u (L ) was instead determined considering the scribed in the following subsections. c WN additional uncertainties affecting C and C , hereafter de- It is anticipated that the L uncertainties were deter- Q A WN fined as u(C ) and u(C ), respectively. When neglecting mined with coverage factor k 5 1(JCGM 2008). Q A 414 J OUR N A L O F A T M O S P H E R I C A N D O C E A N I C T E C H N O L OGY VOLUME 40 TABLE 1. Site-independent relative uncertainty values (in %) Additional instrument related sources of uncertainty such of various model input quantities applied for the computation of as temperature sensitivity and spectral transmittance of sensor L and L combined uncertainties. See text for symbols’ W WN filters, which were evaluated by Giles et al. (2019) and explanations. Johnson et al. (2021), respectively, were not considered be- cause their effects are likely negligible in the 400–667 nm l (nm) spectral region of major interest for ocean color applications. 400 412 443 490 510 560 620 667 Conversely, sensitivity decay during deployments u was con- sc u (L )/L 1.04 0.76 0.72 0.68 0.68 0.65 0.65 0.61 sidered, but assumed constant across spectral bands and sites ac T,i T,i u (L )/L 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 sc T,i T,i (see Table 1). Its value was estimated from the analysis of sen- u(C )/C 1.5 1.5 1.5 1.5 1.5 1.5 1.5 1.5 A A sitivity changes observed for diverse CE-318T through various Chla Chla 58 52 41 32 31 35 55 80 u(C )/C Q Q deployments. IOP IOP 25 25 25 25 25 25 25 25 u(C )/C Q Q 2) ENVIRONMENTAL PERTURBATIONS Environmental perturbations u are mostly due to sea sur- en 1) UNCERTAINTIES FOR ABSOLUTE RADIOMETRIC face roughness and on a lesser extent to changes in in-water CALIBRATIONS optical properties or illumination conditions during measure- ment sequences. Gergely and Zibordi (2014) quantified u as en Gergely and Zibordi (2014) used the constant value of the median of the coefficient of variation (CV) of replicate 2.7% to quantify the relative uncertainty affecting the abso- values of spectral L and L from measurements performed T i lute radiometric calibration of AERONET-OC radiometers. within a 30 min interval. In this work, benefitting of the higher This value was suggested by a comprehensive investigation on measurement frequency of CE-318T instruments, relative u en calibration uncertainties for in situ ocean color sensors values were quantified through the median of CVs calculated (Hooker et al. 2002). A reanalysis of relative uncertainties af- with triplicates (triplets) of spectral L and L values deter- T i fecting AERONET-OC absolute calibrations indicated much mined within a time interval typically shorter than 10 min. lower values varying between 0.6% and 1.0% in the 400–670 nm This solution makes it possible to more precisely quantify the spectral interval (see Table 1) as derived from the quadrature impact of environmental perturbations occurring during mea- sum of the various uncertainty sources (see appendix A). The surement sequences and consequently those perturbations use of these updated values to determine u , which is supported ac strictly related to the measurement methodology. by laboratory calibration intercomparisons (Johnson et al. 2021), leads to a reduction of the combined uncertainties with respect 3) UNCERTAINTY FOR THE r FACTOR to the previous analysis from Gergely and Zibordi (2014). Still, Due to the few data available at level 2.0 for most of the the newly applied values of u need to be considered a best esti- ac mate for AERONET-OC radiometric calibrations, which are AERONET-OC sites, Gergely and Zibordi (2014) determined operationally performed at the Goddard Space Flight Center a median u(r)/r of approximately 3.2% solely using the (GSFC) of the National Aeronautics and Space Administration AAOT data: this uncertainty value was then applied to each (NASA), but subject to continuous intercalibrations with the site. Conversely, in this work u(r)/r was calculated for each JRC Marine Optical Laboratory (Zibordi et al. 2009, 2021). measurement. This leads to an increase of u(r)/r with respect 22 21 21 FIG. 2. Scatterplot of L vs L (in units of mW cm sr mm ) from all sites at (left) 412 and i T (right) 560 nm. The density of points increases from blue to yellow. APRIL 2023 CA ZZ A N I G A A N D ZI BO R D I 415 TABLE 2. Correlation coefficients between L and L for all sites. 4) UNCERTAINTIES FOR THE C AND C FACTORS i T A Q The uncertainty u(C ) related to C largely depends on l (nm) A A that assigned to t (t ). In this study, as in Zibordi et al. (2009), d a 400 412 443 490 510 560 620 665 u(C )/C was empirically set to 1.5% (which is probably an A A CPL 0.9 0.8 0.8 0.8 0.8 0.7 0.9 0.9 underestimated value). The value of u(C ) was also ex- AAOT 0.5 0.5 0.3 0.1 0.1 0.1 0.3 0.4 pressed by a percent of C value. In former analyses, the rela- GLT 0.7 0.7 0.6 0.5 0.5 0.5 0.6 0.7 Chla Chla tive uncertainties u(C )/C were assumed spectrally Q Q ST7 0.6 0.6 0.5 0.4 0.4 0.4 0.4 0.5 constant and equal to 25%. Recently, the uncertainties re- GDLT 0.7 0.7 0.7 0.5 0.4 0.3 0.4 0.4 lated to bidirectional effects were experimentally determined ILT 0.8 0.8 0.8 0.6 0.5 0.4 0.6 0.6 for both the Chla-based and IOP-based approaches for di- verse water types (see Talone et al. 2018), even though limited to the correction for the nonnadir viewing geometry, which to the former estimate. The increase is more marked for sites however represents the major contribution to the overall cor- characterized by a median wind speed higher than that charac- Chla Chla rection. The values of u(C )/C for Chla-based correc- Q Q terizing the AAOT site. tions, which spectrally vary between 30% and 80%, were Recalling that wind speed W is from NCEP products determined from a second-order polynomial fit of the uncer- (W ), the impact of uncertainties in its value was estimated NCEP tainties provided in Talone et al. (2018) for diverse water accounting for actual in situ wind speeds (W ) available for ins IOP IOP types. Conversely, u(C )/C for the IOP-based method Q Q AERONET-OC measurements performed at the AAOT site was set to a spectrally constant value of 25% also estimated between 2017 and 2020. Specifically, the standard deviation from data by Talone et al. (2018). The applied values of s(W) of differences between W and W , exhibiting val- NCEP ins Chla Chla IOP IOP 21 u(C )/C and u(C )/C are provided in Table 1. Q Q Q Q ues of 2.16 m s , was applied to quantify r[W 6 s(W)] for It is finally mentioned that the uncertainty contribution to each measurement sequence from individual AERONET-OC C due to the uncertainties in W was neglected because it sites. The values of u (r)/r were then computed from the WS only marginally affects the determination of the air–water mean of CVs determined for the pairs r(W)and r[W 1 s(W)], transmission function (Gordon 2005). and the pairs r(W)and r[W 2 s(W)]. As already anticipated, the AERONET-OC processing 5) CORRELATIONS AMONG INPUT QUANTITIES determines L by averaging the lowest 2 out of 11 meas- Many of the uncertainty results reported by Gergely and urements of the total radiance from the sea from each Zibordi (2014) indicated as u (L ) were determined only measurement sequence. This filtering process implies that the c,mj WN accounting for variables exhibiting significant correlations. In computed L may not be statistically represented by the asso- particular, recognizing that correlations among input variables ciated W value, but rather by a lower one (Zibordi 2012). The should not be ignored, Gergely and Zibordi (2014) included impact of such a data reduction process is quantified through in the computation of u (L ) any correlation term larger u (r)/r defined by the median of the CVs between r calcu- c,mj WN dr than 0.5. Noting that correlations may lead to a significant de- lated with W 5 W and alternatively with W 5 0. NCEP crease in uncertainties, in this work major correlations were D’Alimonte et al. (2021) recently showed that the values of restricted to the one between L and L . This choice was sup- r computed with Hydrolight (Mobley 1994, 1999) and applied i T ported by the rich correlation observed between L and L in the processing of AERONET-OC data are underestimated. i T measurements, generally higher that that shown by other This underestimate increases with wind speed and in parti- cular with low sun zenith angles (see Fig. 11 in their article). quantities. In particular, L and L exhibit correlations which i T The data reduction method applied in AERONET-OC data are higher when the contribution of the reflected sky radiance processing partially compensates for the impact of the un- to L is more pronounced (i.e., in the blue) or when L is T WN derestimate of r values. Consequently, to avoid overesti- very low (e.g., in the red). This is clearly shown by the results mating u(r), the specific contribution to uncertainties brought displayed in Fig. 2 andsummarizedin Table 2. The lowest cor- by the underestimate of r was not accounted for in this relations are reported for the AAOT in the green spectral re- study. gion. When compared to u (L ), which accounts for all c WN TABLE 3. Median and median absolute deviation of W, u , t (412), Chla, and r determined for each site for data falling within 0 a 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. 21 23 Site NW (m s ) u (8) t (412) Chla (mg m ) r (}) 0 a CPL 4841 (616) 3.1 6 1.2 41.7 6 13.9 0.12 6 0.06 0.2 6 0.1 0.027 6 0.8 3 10 AAOT 9516 (1281) 2.4 6 1.0 39.2 6 10.4 0.20 6 0.10 0.9 6 0.4 0.026 6 0.6 3 10 GLT 4920 (653) 3.6 6 1.2 40.7 6 9.4 0.18 6 0.07 0.6 6 0.2 0.027 6 0.9 3 10 ST7 2471 (309) 4.2 6 1.2 43.3 6 8.0 0.18 6 0.06 1.2 6 0.6 0.028 6 1.0 3 10 GDLT 956 (47) 3.8 6 1.4 42.0 6 4.3 0.13 6 0.05 2.8 6 0.8 0.027 6 0.9 3 10 ILT 1426 (186) 4.6 6 1.5 40.0 6 3.7 0.17 6 0.07 2.8 6 0.7 0.028 6 1.1 3 10 416 J OUR N A L O F A T M O S P H E R I C A N D O C E A N I C T E C H N O L OGY VOLUME 40 22 21 21 TABLE 4. Relative (in %) and absolute (in units of mW cm sr mm ) combined uncertainties at different center wavelengths (l) Chla IOP for the CPL site (see text for symbols’ explanation). The median values of L and L are reported together with their median WN WN 22 21 21 absolute deviation m (in units of mW cm sr mm ). l (nm) 400 412 443 490 510 560 620 667 Chla Chla L 6 m(L ) 0.81 6 0.23 0.94 6 0.27 0.98 6 0.24 0.95 6 0.14 0.65 6 0.07 0.30 6 0.04 0.06 6 0.02 0.03 6 0.01 WN WN IOP IOP 0.82 6 0.22 0.95 6 0.26 0.99 6 0.23 0.96 6 0.12 0.65 6 0.07 0.30 6 0.04 0.05 6 0.02 0.03 6 0.01 L 6 m(L ) WN WN Chla Chla 4.7 4.4 3.9 3.6 4.0 5.4 14.1 18.7 u ˜ (L )/L WN WN Chla Chla u (L )/L 4.2 3.8 3.3 2.9 3.0 4.0 12.3 16.6 c WN WN Chla Chla 4.5 4.2 3.8 3.5 3.9 5.1 12.5 16.4 u (L )/L WN WN c,mj Chla 0.036 0.039 0.036 0.03 0.023 0.015 0.008 0.006 u (L ) c,mj WN IOP IOP ˜ 4.3 3.9 3.4 3.1 3.5 4.4 13.8 18.1 u (L )/L c WN WN IOP IOP 2.8 2.5 2.1 1.7 1.9 2.8 11.9 16.0 u (L )/L WN WN IOP IOP 3.9 3.6 3.3 3.0 3.3 4.2 12.2 15.8 u (L )/L c,mj WN WN IOP u (L ) 0.034 0.037 0.034 0.028 0.022 0.014 0.007 0.005 c,mj WN correlations among the input quantities, u (L ) is expected mismatches between in situ and satellite data (Zibordi et al. c,mj WN to show higher values, even if some exceptions may occur due 2022). Even though not strictly connected with measurement to negative correlation values. This means that the choice of in- uncertainties, the temporal variability characterizing L at WN cluding only major correlations generally provides conservative various AERONET-OC sites was quantified benefitting of results with respect to the inclusion of all correlation terms. measurements from CE-318T 12-band instruments with the objective to assist future analysis of in situ and satellite match- f. Site-dependent temporal variability ups. This was accomplished by determining CVs from pairs of CE-318 9-band instruments, characterized by the capability L obtained with 1, 2, or 3 h delay, where L indicates WN WN of producing a single measurement sequence every 30 min, values of L from the average of triplets performed around WN were operated at the considered AERONET-OC sites up to local noon. The use of large time differences is not affected by fall 2017. Due to these instruments intrinsic limitations, changes in illumination being L normalized with respect to WN Gergely and Zibordi (2014) determined values of u (L )or en T the illumination conditions. u (L ) across temporal intervals of 30 min well exceeding the en i duration of a measurement sequence generally restricted to 3. Results 3 min for CE-318 instruments. Still, such a determination in- Results from the uncertainty analysis are summarized in the cluding contributions by temporal variability was shown rele- vant for the application of AERONET-OC L in the following subsections for each site by providing both absolute WN evaluation of uncertainties affecting satellite-derived L by [e.g., u(L )] and relative [e.g., u(L )/L ] combined uncer- WN WN WN WN making it possible to partially account for temporal tainties together with the related median L values. Results are WN Chla FIG.3.(left) Median L at CPL and (right) u (L )/L for selected center wavelengths for each uncertainty WN x WN WN source (see text for symbols). The black and red error bars in the left panel indicate the median absolute deviation m Chla and u (L ), respectively. c,mj WN APRIL 2023 CA ZZ A N I G A A N D ZI BO R D I 417 TABLE 5. As in Table 4, but for AAOT. l (nm) 400 412 443 490 510 560 620 667 Chla Chla 0.57 6 0.14 0.70 6 0.17 0.84 6 0.22 1.10 6 0.28 1.06 6 0.28 0.93 6 0.28 0.21 6 0.09 0.13 6 0.06 L 6 m(L ) WN WN IOP IOP 0.55 6 0.13 0.68 6 0.16 0.83 6 0.20 1.08 6 0.27 1.06 6 0.27 0.93 6 0.29 0.21 6 0.09 0.13 6 0.06 L 6 m(L ) WN WN Chla Chla 5.9 5.4 4.7 4.3 4.3 4.9 7.3 9.6 u ˜ (L )/L WN WN Chla Chla 5.3 4.9 3.9 3.2 2.9 3.1 5.1 7.2 u (L )/L c WN WN Chla Chla 5.6 5.2 4.6 4.3 4.3 4.9 7.2 9.2 u (L )/L WN WN c,mj Chla 0.032 0.037 0.04 0.047 0.045 0.045 0.015 0.012 u (L ) WN c,mj IOP IOP ˜ 5.4 5.0 4.4 4.0 4.0 4.1 5.6 6.5 u (L )/L c WN WN IOP IOP 3.7 3.3 2.6 2.1 2.1 2.3 4.0 5.2 u (L )/L c WN WN IOP IOP 5.1 4.8 4.4 4.0 4.0 4.1 5.5 6.2 u (L )/L c,mj WN WN IOP u (L ) 0.029 0.034 0.037 0.044 0.042 0.036 0.012 0.009 c,mj WN Chla IOP reported for both L and L data products. Combined un- signal close to nil. As expected, due to the assumption of WN WN Chla IOP certainties are provided by either neglecting any correlation (u ˜ ), larger uncertainties for C than for C , the computed rel- c Q Q Chla including all correlations among variables (u ), and finally only ative combined uncertainties are higher for L than for WN IOP including the major correlation between L and L (u ). Addi- i T c,mj L . Also predictable, the median values of relative com- WN tionally, the values of the L uncertainty that are obtained con- WN bined uncertainties determined accounting for all correla- Chla Chla IOP IOP sidering only a single uncertainty source at a time, are reported tions, u (L )/L and u (L )/L , exhibit values c WN WN c WN WN for each site: these are denoted as u (L )/L with x indicat- Chla Chla IOP IOP ˜ ˜ x WN WN appreciably lower than u (L )/L and u (L )/L . WN WN WN WN c c ing the uncertainty source considered. Median values of W, u , However, those lower estimates may be questioned by the and t at the 412 nm center wavelength, Chla (as determined statistical significance of some correlations often exhibiting from regional algorithms embedded in the AERONET-OC values well below 0.5. Unsurprisingly, when considering the processing), and r are shown in Table 3 for the various sites, sole major correlation between L and L , the related T i even though restricted to the time interval considered in the anal- Chla Chla median relative combined uncertainties u (L )/L and WN WN c,mj ysis. The site-dependent relative uncertainty values of various IOP IOP u (L )/L show values slightly lower than those of c,mj WN WN model input quantities are provided in appendix B for each site. Chla Chla IOP IOP ˜ ˜ u (L )/L and u (L )/L . c WN WN c WN WN Figure 3 (right panel) displays the value of u (L )/L a. CPL x WN WN for selected center wavelengths calculated for each uncer- Chla IOP Mean values of L and L for CPL, which is frequently WN WN tainty source independently (with x denoting the uncertainty representative of Case-1 waters, are provided in Table 4 and source considered in the calculation). Notably, the highest in Fig. 3 together with the computed uncertainties. With refer- contributions are those associated with r and exhibit a spec- ence to Table 4, the median values of relative combined un- Chla IOP Chla Chla IOP IOP tral dependence opposite to that of L and L .The ˜ ˜ certainties u (L )/L and u (L )/L exhibit their WN WN c WN WN c WN WN second main source of uncertainty is the environmental minima at 490 nm, whereas higher values affect the blue and red bands. Maxima are observed in the red because of the variability. FIG.4.As Fig. 3, but for AAOT. 418 J OUR N A L O F A T M O S P H E R I C A N D O C E A N I C T E C H N O L OGY VOLUME 40 FIG.5. As Fig. 3, but for (top) GLT and (bottom) ST7. b. AAOT reduce the combined uncertainty values, except in the green Chla IOP spectral region where the correlation between L and L is i T Mean values of L and L for AAOT are provided in WN WN the lowest. Comparing the uncertainty values of the various Table 5 and in Fig. 4 together with the computed uncertainty Chla sources (see appendix B) with those previously obtained by values. The L median spectrum shows much lower values WN Gergely and Zibordi (2014), notably lower values are ob- in the blue and much higher in the red (up to 4 times at served for u (L )/L and u (L )/L , now estimated consider- 667 nm) with respect to those from CPL. The combined un- en i i en T T ing a time window lower than 10 min instead of 30 min. certainties show the same spectral dependence observed for Conversely, the values of u(r)/r are larger than those deter- CPL, but the relative uncertainties exhibit much lower values Chla in the red because of the higher L . Similar results are ob- mined by Gergely and Zibordi (2014) solely using mean spec- WN Chla tained by including major correlations effects, which slightly tral values of L . WN TABLE 6. As in Table 4, but for GLT. l (nm) 400 412 443 490 510 560 620 667 Chla Chla 0.31 6 0.10 0.41 6 0.13 0.55 6 0.16 0.79 6 0.23 0.74 6 0.21 0.60 6 0.18 0.12 6 0.04 0.07 6 0.03 L 6 m(L ) WN WN IOP IOP 0.31 6 0.09 0.40 6 0.12 0.54 6 0.15 0.78 6 0.22 0.74 6 0.20 0.59 6 0.17 0.11 6 0.04 0.07 6 0.03 L 6 m(L ) WN WN Chla Chla ˜ 10.2 8.5 6.1 4.7 4.6 4.9 9.3 12.5 u (L )/L c WN WN Chla Chla 9.9 8.3 5.9 4.1 3.8 3.8 8.0 11.2 u (L )/L c WN WN Chla Chla 9.5 8.1 5.9 4.5 4.5 4.8 8.8 11.9 u (L )/L c,mj WN WN Chla 0.031 0.035 0.035 0.036 0.034 0.029 0.012 0.009 u (L ) c,mj WN IOP IOP u ˜ (L )/L 9.9 8.2 5.7 4.2 4.2 4.3 8.1 10.3 c WN WN IOP IOP 8.3 6.9 4.5 3.0 3.0 2.9 6.7 9.0 u (L )/L WN WN IOP IOP u (L )/L 9.2 7.8 5.5 4.1 4.1 4.2 7.6 9.5 c,mj WN WN IOP 0.03 0.033 0.033 0.034 0.032 0.025 0.01 0.008 u (L ) c,mj WN APRIL 2023 CA ZZ A N I G A A N D ZI BO R D I 419 TABLE 7. As in Table 4, but for ST7. l (nm) 400 412 443 490 510 560 620 667 Chla Chla 0.26 6 0.07 0.33 6 0.08 0.43 6 0.10 0.63 6 0.13 0.66 6 0.15 0.66 6 0.22 0.17 6 0.08 0.11 6 0.05 L 6 m(L ) WN WN IOP IOP 0.26 6 0.06 0.33 6 0.08 0.43 6 0.09 0.65 6 0.13 0.67 6 0.16 0.69 6 0.24 0.18 6 0.08 0.11 6 0.05 L 6 m(L ) WN WN Chla Chla 13.0 11.2 8.2 6.2 5.9 6.4 9.8 12.5 u ˜ (L )/L WN WN Chla Chla 12.7 11.0 8.0 5.8 5.4 5.5 7.9 10.8 u (L )/L c WN WN Chla Chla 12.4 10.8 8.0 6.1 5.8 6.3 9.6 12.3 u (L )/L WN WN c,mj Chla 0.035 0.039 0.036 0.039 0.04 0.044 0.017 0.013 u (L ) WN c,mj IOP IOP ˜ 12.2 10.3 7.1 5.0 4.8 4.7 6.5 7.7 u (L )/L c WN WN IOP IOP 10.1 8.5 5.6 3.8 3.5 3.3 5.2 6.7 u (L )/L WN WN IOP IOP 11.5 9.9 6.9 4.9 4.7 4.6 6.2 7.3 u (L )/L c,mj WN WN IOP u (L ) 0.033 0.036 0.033 0.033 0.033 0.033 0.013 0.01 c,mj WN c. GLT and ST7 are also slightly higher than those determined for the AAOT site. Due to the higher wind speed characterizing these Chla The GLT and ST7 Black Sea sites exhibit median L WN two Black Sea sites with respect to AAOT, u(r)/r (see spectra with maxima at 490 and 560 nm, respectively (see the appendix B) exhibits larger values than any other site [ex- left panels in Fig. 5). The relative combined uncertainties cept for ILT showing the maximum median wind speed and summarized in Tables 6 and 7 vary from 4.5% at 490 and consequently a maximum value of u(r)/r)]. However, be- 510 nm to 11.9% at 667 nm for GLT, and from 5.8% at yond 443 nm, except at the 667 nm center wavelength for 510 nm to 12.4% at 400 nm for ST7. These values are slightly Chla IOP GLT, the largest uncertainty contribution is from u(C ) lower when considering L data and further reduced when WN considering correlations. Absolute combined uncertainties (see the right panels in Fig. 5). FIG.6.As Fig. 3, but for (top) GDLT and (bottom) ILT. 420 J OUR N A L O F A T M O S P H E R I C A N D O C E A N I C T E C H N O L OGY VOLUME 40 TABLE 8. As in Table 4, but for GDLT. l (nm) 400 412 443 490 510 560 620 667 Chla Chla 0.09 6 0.04 0.12 6 0.05 0.18 6 0.05 0.31 6 0.06 0.37 6 0.07 0.46 6 0.11 0.17 6 0.04 0.11 6 0.03 L 6 m(L ) WN WN IOP IOP 0.10 6 0.04 0.13 6 0.05 0.19 6 0.05 0.32 6 0.06 0.39 6 0.07 0.49 6 0.12 0.17 6 0.04 0.11 6 0.03 L 6 m(L ) WN WN Chla Chla 27.0 20.3 12.2 7.5 6.9 7.6 9.4 11.9 u ˜ (L )/L WN WN Chla Chla 26.7 20.1 12.2 6.9 6.1 6.3 8.0 10.6 u (L )/L c WN WN Chla Chla 24.6 19.2 11.7 7.4 6.9 7.6 9.3 11.7 u (L )/L WN WN c,mj Chla 0.025 0.026 0.023 0.026 0.028 0.037 0.017 0.014 u (L ) WN c,mj IOP IOP ˜ 26.6 19.7 11.5 6.0 5.1 4.4 5.6 6.6 u (L )/L c WN WN IOP IOP 25.8 18.8 10.1 4.5 3.4 2.8 4.5 5.8 u (L )/L WN WN IOP IOP 24.0 18.5 10.9 5.9 5.0 4.4 5.5 6.5 u (L )/L c,mj WN WN IOP u (L ) 0.024 0.025 0.022 0.022 0.023 0.024 0.011 0.008 c,mj WN Chla Chla Opposite to the previous sites, the values of u (L )/L e. Temporal variability c,mj WN WN at blue bands for ST7 are lower than those obtained including all Chla Chla The temporal variability over 1, 2, or 3 h u (L )/L tv WN WN correlations among the input variables. This is due to the contri- was determined from pairs of L . The computed values WN bution of negative correlation terms exceeding in value the con- Chla Chla of u (L )/L were combined in quadrature with WN WN tv tribution from the positive ones. Chla Chla u (L )/L to estimate the expected overall uncertainty c,mj WN WN Chla Chla Chla u (L )/L affecting AERONET-OC L data applied mu WN WN WN d. GDLT and ILT for the construction of matchups, thus attempting to account Chla Figure 6 shows the median spectra of L for the GDLT for the temporal mismatch between in situ and satellite data. WN and ILT sites in the Baltic Sea. These spectra exhibit very sim- Results from this specificanalysis are summarized in Table 10. Chla Chla ilar shapes, with slightly higher values for ILT and extremely With a time difference Dt 5 1h, the increaseof u (L )/L mu WN WN Chla Chla low values in the blue for both sites. As expected, relative un- with respect to u (L )/L is generally confined to WN WN c,mj certainties are very high in correspondence of these minima 3%. It naturally increases when considering Dt 5 2and with median values exceeding 20% at 400 nm. Combined un- Dt 5 3 h. Still, the increase is small for CPL and AAOT at certainties rapidly decrease with wavelength, with minima in the blue and green center wavelengths. In particular, for Chla Chla the 510–560 nm spectral region (see Tables 8 and 9). When CPL the values u (L )/L between 412 and 510 nm mu WN WN Chla considering the absolute uncertainty values, u (L ) ex- are confined below the ideal uncertainty target of 5%. It WN c,mj hibit the maximum at 560 nm, still lower than that determined must be however considered that the number of values for other sites. As for ST7, also for these sites the values available for the analysis may appreciably vary with Dt and Chla Chla IOP IOP of u (L )/L [and additionally u (L )/L for likely affect the statistical significance of results (see ST7 c,mj WN WN c,mj WN WN GDLT only] at blue bands are lower than those obtained in- for which the values obtained with Dt 5 3 h are lower than cluding all correlations among the input variables. those obtained with Dt 5 2h). TABLE 9. As in Table 4, but for ILT. l (nm) 400 412 443 490 510 560 620 667 Chla Chla L 6 m(L ) 0.13 6 0.04 0.16 6 0.04 0.23 6 0.05 0.39 6 0.06 0.46 6 0.07 0.58 6 0.09 0.22 6 0.05 0.14 6 0.04 WN WN IOP IOP 0.13 6 0.03 0.16 6 0.04 0.23 6 0.04 0.41 6 0.06 0.48 6 0.07 0.61 6 0.09 0.22 6 0.05 0.14 6 0.03 L 6 m(L ) WN WN Chla Chla ˜ 24.0 20.1 12.4 7.5 6.9 7.4 9.2 11.7 u (L )/L c WN WN Chla Chla 22.3 19.3 12.5 7.6 6.6 6.3 7.8 10.5 u (L )/L c WN WN Chla Chla 22.8 19.3 11.9 7.3 6.8 7.4 9.1 11.5 u (L )/L c,mj WN WN Chla 0.030 0.032 0.028 0.029 0.032 0.042 0.02 0.016 u (L ) c,mj WN IOP IOP u ˜ (L )/L 23.5 19.6 11.7 6.1 5.2 4.5 6.0 7.0 c WN WN IOP IOP 20.7 17.3 10.7 5.7 4.7 3.7 5.3 6.6 u (L )/L WN WN IOP IOP u (L )/L 22.3 18.7 11.1 5.9 5.1 4.5 5.8 6.7 c,mj WN WN IOP 0.029 0.031 0.027 0.025 0.026 0.027 0.013 0.009 u (L ) c,mj WN APRIL 2023 CA ZZ A N I G A A N D ZI BO R D I 421 Chla Chla Chla Chla TABLE 12. Median relative uncertainty u (L )/L (in TABLE 10. Median relative uncertainty u (L )/L mu WN WN mu WN WN units of %) for diverse Dt, obtained from triplets satisfying (in %) for diverse time differences Dt. N is the number of pairs Chla Chla t (412) # 0.2 and u # 458. N is the number of pairs of triplets used to determine u (L )/L . a 0 tv WN WN Chla Chla used to determine u (L )/L . Results are only reported for tv WN WN l (nm) those cases exhibiting a number of pairs N exceeding 80, heuristically assumed statistically relevant. Site Dt (h) 400 412 443 490 510 560 620 667 N l (nm) CPL 1 5.0 4.6 4.2 3.8 4.4 5.7 15.4 20.1 1478 2 5.4 4.9 4.5 4.1 4.7 6.3 17.6 22.1 812 Site Dt (h) 400 412 443 490 510 560 620 667 N 3 5.5 5.0 4.5 4.2 4.9 6.4 18.7 24.5 418 CPL 1 3.5 3.3 3.0 2.8 3.0 4.1 11.3 14.4 366 AAOT 1 6.2 5.7 5.1 4.7 4.7 5.4 8.2 10.3 2558 2 3.9 3.7 3.2 3.1 3.2 4.4 12.1 15.1 188 2 6.9 6.4 5.7 5.2 5.2 6.0 9.5 11.6 1666 AAOT 1 3.9 3.7 3.3 3.1 3.2 4.1 9.9 12.5 483 3 7.3 6.7 6.2 5.6 5.8 6.8 10.8 12.9 952 2 6.3 5.6 4.9 4.7 4.7 5.6 7.9 9.0 260 GLT 1 10.8 9.1 6.7 5.1 5.1 5.2 9.9 13.4 984 3 6.4 5.9 5.2 4.8 5.4 6.2 9.3 10.0 104 2 13.1 11.2 8.4 6.2 6.2 6.2 11.5 15.2 516 GLT 1 7.4 6.3 4.8 3.8 3.8 4.0 7.0 9.4 250 3 19.6 19.1 13.2 9.7 9.1 9.3 16.2 19.3 186 ST7 1 9.3 7.9 6.3 5.0 4.7 4.9 7.1 8.7 144 ST7 1 12.5 10.9 8.1 5.7 5.6 5.5 10.4 13.3 786 GDLT 1 17.9 15.1 10.8 6.9 7.0 7.4 9.1 11.4 82 2 18.7 15.4 11.8 7.9 6.9 6.7 12.9 16.5 374 ILT 1 20.4 17.4 11.6 7.1 6.7 7.4 9.3 11.2 121 3 14.6 13.0 10.3 7.3 7.2 6.8 12.0 15.2 354 GDLT 1 27.8 21.8 13.5 8.2 7.5 8.0 10.0 12.5 316 2 31.1 24.5 14.8 9.2 8.4 8.3 11.3 13.5 224 and Zibordi (2014). These results (not shown) indicate that 3 37.4 26.7 17.1 11.3 9.5 9.4 12.2 14.4 164 the lower combined values of u applied in the current analy- ILT 1 24.9 20.9 13.2 8.0 7.3 7.8 9.7 12.1 337 ac Chla Chla 2 26.5 22.0 13.7 8.0 7.4 8.1 10.1 12.6 211 sis heavily contribute to a decrease of u (L )/L . How- c,mj WN WN 3 29.2 22.3 14.2 8.4 7.7 8.5 10.2 12.6 110 ever, 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 4. Discussion by Gergely and Zibordi (2014). This is particularly evident at a. Comparison of results from the current and previous those sites exhibiting high median wind speed, such as GDLT, Chla Chla uncertainty analyses showing a significant increase of u (L )/L . When WN WN c,mj looking at the spectral values, the increase is more marked in This work is a revisitation of the former analysis of the blue due to the larger impact of u(r)/r. AERONET-OC uncertainties carried out by Gergely and Zibordi (2014). It was suggested by a number of technological b. Data reduction and science advances. In particular the recent adoption of A major contribution to combined uncertainties comes CE-318T radiometers allows for a reevaluation of environ- from u(r) and u(C ). To investigate the possibility of mini- mental perturbations u (L ) and u (L ), and a quantifi- en T en i mizing their contributions, in agreement with Gergely and cation of the temporal variability u (L ). These latest tv WN Zibordi (2014), uncertainties have been reevaluated only radiometers are in fact capable of performing consecutive including data alternatively characterized by W # 3m s , measurement sequences (e.g., triplets) leading to the determi- Chla # 0.7 mg m , u # 458, and t (412) # 0.2. Results pro- nation of successive values of L and L a few minutes apart 0 a T i posed for the sole AAOT site are summarized in Table 11.As from each other. As expected, the new u (L ) and u (L ) en T en i expected, limiting the input data to conditions determined by exhibit much lower values with respect to those characteriz- W # 3m s leads to a substantial decrease of u(r)/r. This ing the previous analysis. decrease (not shown) is more pronounced at those sites exhi- In view of assessing the impact of the other methodological biting the highest median wind speed [e.g., with u(r)/r changes introduced in the current study, relative combined Chla Chla decreasing by 1.1% for AAOT, and up to approximately uncertainties u (L )/L were also calculated applying c,mj WN WN Chla Chla 3.5% and 4.2% for ST7 and ILT]. Consequently, the com- the values of u(r)/r, u(C )/C , and u used in Gergely ac Q Q Chla Chla bined uncertainties u (L )/L diversely decrease at c,mj WN WN Chla Chla various sites: up to 1.2% for AAOT and slightly above 12% TABLE 11. Values of u (L )/L (in %) determined by c,mj WN WN partitioning the AAOT dataset applying thresholds to the values in the blue for ILT and GDLT (not shown). of W, u , t (412), and Chla. N is the number of cases satisfying Imposing Chla # 0.7 mg m leads to a decrease of 0 a Chla Chla the thresholds. u(C )/C and consequently of the combined uncertain- Q Q ties (except in the red), mostly for the Black Sea sites. How- l (nm) ever, the lack of suitable data for ILT and GDLT prevents 400 412 443 490 510 560 620 667 N any assessment for these sites. Alarge influence on combined uncertainties is also W # 3m s 4.9 4.5 4.1 4.0 3.9 4.4 6.3 8.0 6173 brought by imposing u # 458. This has a large impact on u # 458 5.1 4.7 4.1 3.9 3.8 4.3 6.2 7.7 5931 0 Chla Chla t (412) # 0.2 5.9 5.5 4.8 4.5 4.5 5.1 6.6 8.5 4740 u(C )/C , which is halved at CPL. Nevertheless, the Q Q Chla # 0.7 mg m 4.5 4.2 3.6 3.4 3.4 3.8 7.6 10.3 3215 IOP IOP impact is negligible on u(C )/C . Q Q 422 J OUR N A L O F A T M O S P H E R I C A N D O C E A N I C T E C H N O L OGY VOLUME 40 Chla IOP FIG. 7. Scatterplot of median (left) L and (right) L values vs median absolute combined uncertainties WN WN Chla IOP u (L ) and u (L ). The diverse symbols represent the various sites, whereas their color identifies the c,mj WN c,mj WN wavelength. The black solid line indicates the linear regression. The gray dashed line indicates the regression pro- 2 Chla IOP posed by Zibordi et al. (2022). The determination coefficient (r ) is 0.62 and 0.60 for L and L , respectively WN WN (p value , 0.01). Finally, imposing t (412) # 0.2 leads to a slight reduction of the Gloria Platform (GLR; located close to ST7 and no longer u (L )/L (typically decreasing by less than 0.2%) without operated), GLT, GDLT, and Helsinki Lighthouse (HLT; in en i i any significant change in the combined uncertainty values, ex- the Baltic Sea) sites, to produce a linear relationship between cept for a reduction of approximately 2%–4% in the blue Chla Chla u (L ) and L regardless of wavelength and site. That WN WN c,mj spectral region for GDLT. statistical relationship applied to estimate absolute uncertain- The uncertainties determined for the temporal variability ap- Chla ties for each L spectral value was mostly explained by the WN pear smaller when simultaneously imposing t (412) # 0.2 and weight of uncertainty contributions linearly varying with u # 458, as shown in Table 12. Consequently, the values of Chla L , such as those resulting from the absolute radiometric WN Chla Chla u (L )/L also reduce with respect to those provided in WN WN mu calibration and corrections for bidirectional effects. Improve- Table 10. In particular, also for time differences Dt 5 2and 3 h, ments in the quantification of uncertainties introduced in this they become lower than 5% at the blue and green center wave- Chla work lead to a decreased correlation between L and WN lengths for CPL and between 443 and 560 nm for AAOT and Chla Chla Chla u (L ). The scatterplots in Fig. 7 display median L c,mj WN WN GLT. Nevertheless, only a few sites exhibit a statistically signifi- IOP (left panel) and L (right panel) values, versus the corre- WN cant number of data to allow evaluating the case with Dt . 1h. Chla IOP sponding median u (L ) and u (L ). The regression c,mj WN c,mj WN c. Uncertainty as a function of L (l) WN lines for the plotted values are displayed together with the re- Chla gression line proposed by Zibordi et al. (2022) for L , i.e., Zibordi et al. (2022) applied the median uncertainty values WN Chla Chla determined by Gergely and Zibordi (2014) for the AAOT, u (L ) 5 0:0091 1 0:0405L . c,mj WN WN Chla IOP Chla FIG. 8. Scatterplot of median (left) L and (right) L values vs the corresponding uncertainties u (L ) and WN WN c,mj WN IOP u (L ). The diverse symbols represent the various sites, whereas their color identifies the wavelength. The purple c,mj WN and red dashed lines indicate the linear regressions determined solely using the Black and Baltic Sea “blue bands” Chla and, alternatively, all the remaining data. For L , r is 0.81 and 0.50 for the red and purple lines, respectively (both WN IOP exhibiting p value , 0.01). For L , r is 0.92 and 0.50 for the red and purple lines, respectively (in this case too, both WN showing p value , 0.01). APRIL 2023 CA ZZ A N I G A A N D ZI BO R D I 423 Chla IOP Chla FIG.9.Scatterplots of median (left) L and (right) L values vs the corresponding uncertainties u (L ) WN WN c,mj WN IOP and u (L ) for data restricted to cases characterized by W # 3m s . The diverse symbols represent the various c,mj WN sites, whereas their color indicates the wavelength. The black solid line indicates the linear regression. The determina- 2 Chla IOP tion coefficient (r )is0.72 and 0.85 for L and L , respectively (both exhibiting p value , 0.01). WN WN Definitively, the data in Fig. 7 are much more scattered than for the normalized water leaving radiance L . The main ele- WN those shown by Zibordi et al. (2022). This is largely explained ments indicating the need for such a reevaluation of uncer- tainties were (i) the availability of time series produced with by a significant reduction of u and the application of values ac Chla CE-318T 12-band instruments exhibiting higher measurement of u(r) determined for each single L measurement. This WN leads to a separation of the median uncertainties at the blue frequency when compared to those performed with CE-318 center wavelengths (i.e., from 400 to 443 nm) from all other 9-band instruments, and consequently allowing a more accu- rate determination of environmental perturbations; (ii) a re- spectral values for those sites characterized by higher median cent rigorous quantification of uncertainties affecting absolute wind speed such as the Black Sea and Baltic Sea ones. By sep- radiometric calibrations; (iii) the potential for a more accurate arating these “blue-bands” data from the others, two distinct estimate of the uncertainties affecting corrections for the linear relations can be defined as displayed in Fig. 8. in-water bidirectional effects, performed with either the so- As already stated, wind speed has a major impact on uncer- called Chla-based and IOP-based approaches; and (iv) the tainties and specifically leads to their increase for the Baltic determination of uncertainties affecting the sea surface reflec- and Black Sea sites. Because of this, the relationships between Chla IOP Chla IOP tance factor on a measurement by measurement basis. u (L ) and u (L ) with median L and L ,re- c,mj WN c,mj WN WN WN Uncertainties were determined for the AERONET-OC spectively, were redetermined restricting the analysis to cases Chla IOP L and L data products generated by applying the Chla- characterized by W # 3m s . This reduced dataset appears WN WN based and IOP-based corrections for in-water bidirectional ef- less scattered, as shown in Fig. 9: a single regression line well Chla IOP fects, respectively. Uncertainties were computed following describes the relation between median L or L and the WN WN Chla IOP GUM (JCGM 2008) and proposed in relative and absolute corresponding uncertainties u (L ) and u (L ). c,mj WN c,mj WN units by (i) neglecting correlations among input quantities de- fining the measurement equation, which leads to the largest 5. Summary and conclusions uncertainties; (ii) accounting for each correlation term in the Advances in AERONET-OC suggested to revisit the un- measurement equation, which usually leads to the lowest un- certainties formerly quantified by Gergely and Zibordi (2014) certainties; and finally (iii) only including major correlation TABLE A1. Sources and related relative uncertainties (in %) contributing to absolute radiometric calibration uncertainties. l (nm) 400 412 443 490 510 560 620 667 Lamp (NPL #1333) 0.90 0.55 0.55 0.50 0.50 0.45 0.45 0.40 Lamp fit 0.30 0.30 0.20 0.20 0.20 0.20 0.20 0.20 Lamp aging (with 25 h of use) 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 Plaque 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 Shunt 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 Power supply (with a 7.5 mA bias) 0.07 0.07 0.07 0.06 0.06 0.05 0.05 0.04 Lamp–plaque distance 0.20 0.20 0.20 0.20 0.20 0.20 0.20 0.20 Lamp positioning 0.30 0.30 0.30 0.30 0.30 0.30 0.30 0.30 Plaque repositioning 0.10 0.10 0.10 0.10 0.10 0.10 0.10 0.10 Sensor alignment 0.10 0.10 0.10 0.10 0.10 0.10 0.10 0.10 424 J OUR N A L O F A T M O S P H E R I C A N D O C E A N I C T E C H N O L OGY VOLUME 40 contributions, which generally leads to uncertainty values TABLE B1. Median relative uncertainties (in %) for individual sources at different center wavelengths (l)for the various slightly lower than those determined neglecting correlations. AERONET-OC sites: CPL, AAOT, GLT, ST7, GDLT, and ILT. The following conclusions are based on the uncertainties de- termined solely accounting for the major correlations between l (nm) L and L . i T 400 412 443 490 510 560 620 667 Results were produced for AERONET-OC sites represen- tative of a variety of water types: Casablanca Platform (CPL) CPL exhibiting frequent occurrence of Case-1 waters; the Acqua u (L )/L 0.5 0.6 0.6 0.7 0.7 0.9 1.0 1.1 en i i Alta Oceanographic Tower (AAOT), the Galata Platform u (L )/L 1.2 1.2 1.1 1.2 1.2 1.6 2.7 3.2 en T T u (r)/r 3.9 3.9 3.9 3.9 3.9 3.9 3.9 3.9 (GLT), and the Section-7 Platform (ST7) characterized by dr u (r)/r 3.8 3.8 3.8 3.8 3.8 3.8 3.8 3.8 optically complex waters with varying concentrations of sedi- WS u(r)/r 5.6 5.6 5.6 5.6 5.6 5.6 5.6 5.6 ments and CDOM; finally, the Gustaf Dalen Lighthouse Tower (GDLT) and Irbe Lighthouse (ILT), characterized by AAOT very high concentrations of CDOM. u (L )/L 0.6 0.6 0.7 0.8 0.8 1.0 1.1 1.2 en i i The quantified uncertainties exhibit values varying from u (L )/L 1.3 1.3 1.2 1.1 1.1 1.2 1.8 2.1 en T T above 3% at 490 nm for CPL, and up to approximately u (r)/r 2.3 2.3 2.3 2.3 2.3 2.3 2.3 2.3 dr 25% at 400 nm in CDOM-dominated waters. Uncertainties u (r)/r 3.2 3.2 3.2 3.2 3.2 3.2 3.2 3.2 WS Chla IOP u(r)/r 4.2 4.2 4.2 4.2 4.2 4.2 4.2 4.2 are higher for L with respect to L due to the assump- WN WN tion of higher uncertainties for Chla-based corrections GLT than for the IOP-based ones applied to remove bidirec- u (L )/L 0.7 0.8 0.8 0.9 0.9 1.1 1.2 1.3 en i i tional effects. u (L )/L 1.8 1.7 1.6 1.3 1.4 1.3 2.2 2.4 en T T Chla Overall, the revisited uncertainties determined for L do WN u (r)/r 4.3 4.3 4.3 4.3 4.3 4.3 4.3 4.3 dr not significantly differ from the previous proposed by Gergely u (r)/r 3.9 3.9 3.9 3.9 3.9 3.9 3.9 3.9 WS and Zibordi (2014). This is largely explained by compensa- u(r)/r 6.3 6.3 6.3 6.3 6.3 6.3 6.3 6.3 tions enacted in their quantification by the increase or de- ST7 crease of diverse contributions. u (L )/L 0.8 0.9 0.9 0.9 1.0 1.2 1.2 1.3 en i i The largest contribution to uncertainties is the sea surface u (L )/L 2.1 2.1 1.9 1.7 1.6 1.7 2.2 2.5 en T T reflectance factor r. This finding is explained by the uncertain- u (r)/r 5.5 5.5 5.5 5.5 5.5 5.5 5.5 5.5 dr ties in wind speed estimation and in the data reduction u (r)/r 4.0 4.0 4.0 4.0 4.0 4.0 4.0 4.0 WS method leading to the determination of L . This is particu- u(r)/r 7.0 7.0 7.0 7.0 7.0 7.0 7.0 7.0 larly evident at those sites characterized by larger median values of wind speed. For the remaining sites such as CPL GDLT u (L )/L 0.5 0.5 0.5 0.6 0.7 0.7 0.8 0.8 and AAOT, a large fraction of the total uncertainty is ex- en i i u (L )/L 2.7 2.0 1.7 1.6 1.4 0.9 1.6 2.1 en T T plained by the contributions due to correction factors u (r)/r 4.4 4.4 4.4 4.4 4.4 4.4 4.4 4.4 dr for bidirectional effects determined with the Chla-based u (r)/r 3.7 3.7 3.7 3.7 3.7 3.7 3.7 3.7 WS method. u(r)/r 5.9 5.9 5.9 5.9 5.9 5.9 5.9 5.9 The study shows that restricting the uncertainty analysis to cases characterized by W # 3m s ,or u # 458, or Chla # 0 ILT 0.7 mg m , leads to a reduction of the uncertainties. u (L )/L 0.5 0.5 0.6 0.7 0.7 0.8 1.0 1.1 en i i u (L )/L 2.1 2.0 1.9 1.6 1.4 1.3 1.9 2.3 In agreement with Zibordi et al. (2022) the possibility to es- en T T Chla u (r)/r 6.0 6.0 6.0 6.0 6.0 6.0 6.0 6.0 timate absolute uncertainties as a linear function of L ,or dr WN IOP u (r)/r 4.3 4.3 4.3 4.3 4.3 4.3 4.3 4.3 WS alternatively L , was investigated. The analysis confirmed WN u(r)/r 7.6 7.6 7.6 7.6 7.6 7.6 7.6 7.6 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 ra- optically complex waters (i.e., at CPL and AAOT) in the diances and uncertainties. Nevertheless, a single linear rela- blue-green center wavelengths. Conversely, they exceed tionship is instead applicable for measurement conditions 21 5% at the other AERONET-OC sites considered in the characterized by W # 3m s , due to a reduction of the study, or for larger Dt. dispersion between median spectral radiances and related uncertainties. Acknowledgments. The authors thank the AERONET Finally, the impact of temporal variability was investi- Team for the effort to include and sustain the Ocean Color gated for the various AERONET-OC sites in view of best component in the AERONET observational network. They supporting matchup analysis between in situ and satellite also acknowledge the Centro Previsioni e Segnalazioni data by accounting for temporal mismatches. Simply con- Maree of Comune di Venezia for providing the in situ wind sidering a time difference Dt 5 1 h between satellite and in data. They finally thank the anonymous reviewers for their situ data, the combined values accounting for L uncer- WN tainties and contributions due to temporal variability are precious contribution. This work has received funding from generally confined below 5% in Case-1 and moderately the EMPIR programme (Grant 19ENV07 for METEOC-4) APRIL 2023 CA ZZ A N I G A A N D ZI BO R D I 425 Automated near-real-time quality control algorithm with cofinanced by the participating states and from the European improved cloud screening for sun photometer aerosol optical Union’s Horizon 2020 research and innovation programme. depth (AOD) measurements. Atmos. Meas. Tech., 12, 169– The support provided by DG DEFIS, i.e., the European 209, https://doi.org/10.5194/amt-12-169-2019. Commission Directorate-General for Defence, Industry and Gordon, H. R., 2005: Normalized water-leaving radiance: Revisit- Space, and the Copernicus programme is also gratefully ing the influence of surface roughness. Appl. Opt., 44, 241– acknowledged. 248, https://doi.org/10.1364/AO.44.000241. Hooker,S. B., W. E. Esaias,G. C.Feldman, W.W. Gregg,and Data availability statement. All AERONET-OC data used C. R. McClain, 1992: An overview of SeaWiFS and during this study are contributed by the International Ocean Color. NASA Tech. Memo. 104566, Vol. 1, 24 pp., AERONET Federation and available from AERONET-OC https://oceancolor.gsfc.nasa.gov/SeaWiFS/TECH_REPORTS/ archive at https://aeronet.gsfc.nasa.gov/cgi-bin/draw_map_ vol1_abs.html. display_seaprism_v3. 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Journal

Journal of Atmospheric and Oceanic TechnologyAmerican Meteorological Society

Published: May 1, 2023

References