Impact of spectral resolution of in situ ocean color radiometric data in satellite matchups analyses

The spectral resolution requirements for in situ remote sensing reflectance RS R measurements aiming at supporting satellite ocean color validation and System Vicarious Calibration (SVC) were investigated. The study, conducted using sample hyperspectral RS R from different water types, focused on the visible spectral bands of the Ocean Land Color Imager (OLCI) and of the Plankton, Aerosol, Cloud, ocean Ecosystem (PACE) satellite sensors. Allowing for a ±0.5% maximum difference between in situ and satellite derived RS R solely due to the spectral band characteristics of the in situ radiometer, a spectral resolution of 1 nm for SVC of PACE is needed in oligotrophic waters. Requirements decrease to 3 nm for SVC of OLCI. In the case of validation activities, which exhibit less stringent uncertainty requirements with respect to SVC, a maximum difference of ±1% between in situ and satellite derived data indicates the need for a spectral resolution of 3 nm for both OLCI and PACE in oligotrophic waters. Conversely, spectral resolutions of 6 nm for PACE and 9 nm for OLCI appear to satisfy validation activities in optically complex waters. © 2017 Optical Society of America OCIS codes: (280.0280) Remote sensing and sensors; (120.0120) Instrumentation, measurement, and metrology. References and links 1. World Meteorological Organization (WMO), The Global Observing System for Climate: Implementation needs. Report GCOS – 200 (2016) (available at http://unfccc.int/files/science/workstreams/systematic_observation/application/pdf/gcos_ip_10oct2016.pdf). 2. H. R. Gordon, “Calibration requirements and methodology for remote sensors viewing the ocean in the visible,” Remote Sens. Environ. 22(1), 103–126 (1987). 3. G. Zibordi, J.-F. Berthon, F. Mélin, D. D’Alimonte, and S. Kaitala, “Validation of satellite ocean color primary products at optically complex coastal sites: Northern Adriatic Sea, Northern Baltic Proper and Gulf of Finland,” Remote Sens. Environ. 113(12), 2574–2591 (2009). 4. F. Mélin and G. Sclep, “Band shifting for ocean color multi-spectral reflectance data,” Opt. Express 23(3), 2262– 2279 (2015). 5. M. R. Wernand, S. J. Shimwell, and J. C. De Munck, “A simple method of full spectrum reconstruction by a fiveband approach for ocean colour applications,” Int. J. Remote Sens. 18(9), 1977–1986 (1997). 6. Z. Lee, S. Shang, C. Hu, and G. Zibordi, “Spectral interdependence of remote-sensing reflectance and its implications on the design of ocean color satellite sensors,” Appl. Opt. 53(15), 3301–3310 (2014). 7. B. C. Johnson, S. Flora, S. Brown, D. Clark, M. Yarbrough, and K. Voss, “Spectral resolution requirements for vicarious calibration of ocean color satellites”. Presented at the Ocean Color Research Team Meeting, Seattle (2007), available at http://oceancolor.gsfc.nasa.gov/cms/DOCS/ScienceTeam/OCRT_Apr2007/Posters/. 8. D. K. Clark, H. R. Gordon, K. J. Voss, Y. Ge, W. Broenkow, and C. Trees, “Validation of atmospheric correction over the oceans,” J. Geophys. Res. 102(17), 209–217 (1997). 9. S. W. Brown, S. J. Flora, M. E. Feinholz, M. A. Yarbrough, T. Houlihan, D. Peters, K. Y. S. Kim, J. L. Mueller, B. C. Johnson, and D. K. Clark, “The Marine Optical BuoY (MOBY) radiometric calibration and uncertainty budget for ocean color satellite sensor vicarious calibration,” in SPIE Conference Proceedings Remote Sensing, pp. 67441M–67441M. International Society for Optics and Photonics (2007). 10. G. Zibordi, J.-F. Berthon, F. Mélin, and D. D’Alimonte, “Cross-site consistent in situ measurements for satellite ocean color applications: The BiOMaP radiometric dataset,” Remote Sens. Environ. 115(8), 2104–2115 (2011). 11. A. Tonizzo, M. Twardowski, S. McLean, K. Voss, M. Lewis, and C. Trees, “C. and Trees, “Closure and uncertainty assessment for ocean color reflectance using measured volume scattering functions and reflective tube absorption coefficients with novel correction for scattering,” Appl. Opt. 56(1), 130–146 (2017). #290731 https://doi.org/10.1364/OE.25.00A798 Journal © 2017 Received 15 Mar 2017; revised 29 May 2017; accepted 30 May 2017; published 21 Jul 2017 Vol. 25, No. 16 | 7 Aug 2017 | OPTICS EXPRESS A798


Introduction
Satellite ocean color radiometric products, such as the water-leaving radiance, W L , or the related remote sensing-reflectance, RS R , are the fundamental quantities used to generate geophysical data products (e.g., chlorophyll concentration, Chla).Accuracy requirements set for these derived products [1,2] bound uncertainty requirements for satellite radiometric data.
Presently, post-launch system vicarious calibration (SVC) [2] is the only viable approach allowing satellite radiometric data to meet the level of uncertainty that satisfies requirements for ocean color products.The SVC process implies the use of highly accurate in situ radiometric measurements.In situ radiometric data are also frequently applied to investigate uncertainties affecting satellite products through validation exercises.
Markedly, both validation and SVC applications rely on matchups (i.e., time and space coincident) of in situ and satellite ocean color radiometric data.This implies a comprehensive assessment of the various sources of uncertainty affecting the in situ measurements, which include radiometric, methodological and environmental factors.A source of uncertainty, which causes systematic differences between in situ and satellite radiometric data, but is controllable by instrument design, is the diversity of spectral characteristics of in situ and satellite ocean color sensors due to the different widths, shapes and center-wavelengths of corresponding spectral bands.This uncertainty can be minimized through the application of corrections (i.e., band-shifting) obtained by modeling the spectral dependence of radiometric quantities such as RS R [3,4].This solution, however, may still be subject to substantial uncertainties due to the lack of accurate information on seawater optical properties and additionally by incomplete information on the spectral response functions of in situ sensors.An alternative solution is given by the statistical reconstruction of RS R from discrete values measured in various spectral bands [5,6].In this case, the uncertainties affecting the determination of RS R spectra depend on the number of spectral bands, their location and width.As the portion of the uncertainties that are driven by environmental factors and the radiometric calibration process, when combined, can be a large fraction of the desired maximum limit, it is critical that those factors that can be controlled by instrument design be minimized and do not add significantly to the combined uncertainty budget for the in situ data.
The problem of spectral differences can be reduced with in situ hyperspectral data (i.e., data collected with a relatively large number of narrow spectral bands distributed continuously over the spectrum).In fact, compared to multispectral measurements, in situ hyperspectral data allow the determination of RS R in the spectral bands of the satellite sensor with an accuracy increasing with the spectral resolution (defined by the sensor bandwidth Δλ B determined by the full width at half maximum spectral response) and the spectral sampling interval (i.e., the distance between center-wavelengths of adjacent bands Δλ C ) of the in situ sensor.
Thus, hyperspectral in situ radiometric data can be the optimum solution for SVC data due to the need to minimize this source of uncertainty in the accurate determination of mission specific gain-factors (i.e., g-factors) for satellite radiometric data.Specifically, as an extreme case, the accessibility of sub-nanometer radiometric spectra would allow accurate RS R values to be determined for any multispectral or hyperspectral space sensor.In fact, assuming the satellite sensor is comprehensively characterized, in situ sub-nanometer spectra would allow the satellite spectral response functions and out-of-band or stray light perturbations to be fully accounted for.However, the technological complexity, and cost, intrinsic in sub-nanometer radiometer systems suggests that there may be a tradeoff between spectral resolution and allowable uncertainty.
The overall objective of this work, which expands on a previous assessment [7], is to investigate the impact of the spectral resolution of in situ radiometric data on the determination of RS R at bands representative of current and forthcoming ocean color sensors.The analysis aims at estimating the sole contribution of spectral resolution to the uncertainty budget affecting the comparison of in situ and satellite RS R .It specifically focuses on the visible spectral bands of the Ocean Land Color Imager (OLCI) from the European Space Agency (ESA) operating onboard Sentinel-3 since 2016, and of the Plankton, Aerosol, Cloud, ocean Ecosystem (PACE) of the National Aeronautics and Space Administration (NASA) planned for launch in 2022.

Data and methods
The study relies on sample RS R spectra from marine waters characterized by varying concentrations of optically significant constituents.These spectra are applied to investigate differences between in situ and satellite data solely due to dissimilar spectral bands.Recalling that the analysis is restricted to satellite bands representative of current multispectral and future hyperspectral ocean color systems, the final objective of the work is the definition of requirements for in situ hyperspectral sensors supporting validation and SVC applications.It is emphasized that the study is focused on the impact of spectral resolution on in situ radiometric measurements and excludes any other source of uncertainty that may affect matchup analysis, or correction schemes that may minimize spectral differences between sensors.

Data
The study is performed using samples of in situ hyperspectral radiometric data representative of various water types.The fundamental quantities are the RS R spectra displayed in Fig. 1 and determined from the ratio of water leaving radiance W L to downward irradiance S E .One sample RS R spectra was obtained with the Marine Optical System (MOS) from fixed-depth measurements performed in ultra-oligotrophic waters at the Marine Optical Buoy (MOBY) site with spectral resolution Δλ B of 1 nm and a spectral sampling interval Δλ C of approximately 0.6 nm [8,9].Additional sample data are RS R spectra from above-water radiometric measurements performed with RAMSES hyperspectral radiometers in various European seas.These embrace oligotrophic waters in the Western Mediterranean Sea, and optically complex waters in the Western Black and northern Adriatic Seas.RAMSES radiometers, manufactured by TriOS (Rastede, Germany), have a spectral resolution of approximately 10 nm and a nominal spectral sampling interval of 3.3 nm.Clearly, while MOS spectra are suitable to address investigations up to approximately 1 nm spectral resolution, RAMSES data may not fully satisfy requirements to assess RS R spectral matching at resolutions lower than several nanometers.The uncertainties associated with this limitation, are addressed in the discussion section.It is however anticipated that, while MOS spectra are mostly applied to address both the validation and highly demanding SVC requirements in oligotrophic waters, RAMSES data are only used to draw general conclusions on the less stringent requirements for the validation of satellite products in optically complex waters.
The analysis is restricted to the spectral region between 380 nm and 700 nm for which the considered in situ radiometric data exhibit reliable values (i.e., not largely affected by reduced sensitivity of the radiometers or an input signal that is too small), and additionally represent the spectral region of utmost interest for both validation and SVC activities.With respect to this, there are some peculiar features near 400 nm in the spectrum representing ultraoligotrophic waters as displayed in Fig. 1.These can be explained by slight differences on the order of 0.1 nm in S E and W L spectral calibrations in a region characterized by Fraunhofer lines in the solar irradiance.Because of this, results related to such a narrow spectral region need to be considered with some caution.
Details of water bio-optical quantities related to the RS R spectra included in the analysis are summarized in Table 1.These include Chla, concentration of total suspended matter, TSM, and the absorption coefficient, a, and backscattering coefficient, b b , at 490 nm of optically significant water constituents.Their values fully support the diversity of cases represented by the RS R spectra considered.[11], here increased by the pure seawater contribution.

Spectral bands of satellite sensors
As already mentioned, this study is centered on OLCI [12], representative of current global satellite ocean color sensors, and additionally on PACE [13], which is assumed to be representative of future advanced hyperspectral earth observing systems.While OLCI relies on spectral bands commonly exhibiting 10 nm bandwidth in the visible spectral region (15 nm at 400 nm), PACE will have a large number of bands with 5 nm bandwidth from the ultraviolet to the near-infrared.Consequently, PACE-like bands have been designed by assuming 5 nm bandwidth, an ideal Gaussian spectral response function, and 5 nm spectral sampling interval.It is recognized that this solution produces a sampling of RS R spectra that may differ slightly from actual capabilities of the future space sensor.
The relative spectral response functions for OLCI and PACE-like bands are illustrated in Fig. 2.

Band spectral matching
The spectral matching scheme introduced in this section has been devised to investigate differences between RS where the generic variable ℜ indicates r ℜ and S designates the relative spectral response functions s S of the satellite sensor, with l wavelength index for the 0.1 nm increment.As opposed to ( ) RS s R k , the determination of ' ( ) RS s R k requires multiple steps.In agreement with the process illustrated by the light-gray path in Fig. 3, first r ℜ spectra are applied to model in situ measurements at different spectral resolution i ℜ (i.e., W i L and S i E ) as acquired from ideal hyperspectral radiometers exhibiting Gaussian spectral response functions i S at spectral bands i k .This step is again performed through Eq. ( 1) where the generic variable ℜ indicates r ℜ and S designates the relative spectral response functions i S of the in situ sensor.The derived i ℜ spectra are then deconvolved to reconstruct the ' r ℜ spectra at 0.1 nm through: where i S is the The deriv satellite senso compute ' (

Results
The comparis presented for where ℑ indica   In contrast to oligotrophic waters, RS R representing optically complex cases generally exhibit values of ε within ±1% regardless of Δλ B and Δλ C .
Because of the higher resolution of the satellite sensor bands, the same analysis performed for PACE-like bands exhibits larger values of ε than those determined for OLCI in the spectral regions with large changes in the slope of RS R .Specifically, in Fig. 5 the ε values determined with Δλ B = 9 nm and Δλ C = 3 nm exceed 4% for oligotrophic waters (e.g., at around 515 nm for NP, and, near 605 nm and 665 nm for both NP and WM).With Δλ B = 2 nm and Δλ C = 2 nm the value of ε is generally within ±0.5% in oligotrophic waters and within ±0.1% in optically complex waters.

Discussion
The discussion will show how representative the hyperspectral RS R for NP is for that site, the alternative use of W L instead of RS R for SVC, the uncertainties associated with values of ε determined using RAMSES RS R spectra, and finally the relevance of spectral sampling intervals versus spectral resolution.Accounting for the results from the analyses presented in the previous section and of findings from the discussion topics included in this section, spectral resolution and sampling interval requirements for in situ hyperspectral data supporting satellite ocean color validation and SVC applications are summarized assuming strict uncertainty thresholds.

Stability of RS R for the NP site
This study relies on a few hyperspectral RS R spectra representative of various water types.While it is impossible in one study to include every different water type, it is still expected that these results are useful in outlining the general spectral resolution requirements for in situ RS R supporting SVC and validation activities.
Since the NP site has been used extensively for SVC [14], it is important to consider how well the specific hyperspectral RS R spectrum used in this analysis represents the MOBY site.This has been addressed with a statistically significant number (i.e., 103) of MOS spectra collected from 15 May to 28 August 2015 using the same in situ sensor applied for producing the spectrum included in this analysis.Using the one spectrum for the NP case is fully supported by the mean μ and standard deviation σ of the ε values displayed in Fig. 6.Specifically, the values of ε shown in Fig. 5(a) appear equivalent to the mean values μ(ε) displayed in Fig. 6 for the 103 independent spectra from the same site.Additionally, the related standard deviations σ(ε) exhibit values that, excluding the spectral region nearby 600 nm, do not exceed 0.4% regardless of the spectral resolution considered for the determination of ε.

Accuracy of ε values
The relatively low spectral resolution of RAMSES data for WB, NA, and WM may lead to a misestimate of ε in spectral regions characterized by significant nanometer scaled features.This underestimate has been evaluated with the NP data, which benefit from a higher spectral resolution with respect to the other cases and additionally exhibit more pronounced spectral gradients providing added challenging conditions.
For this analysis, the MOS W L and S E data linearly resampled at 0.1 nm were degraded using Eq. ( 1) to match the RAMSES spectral resolution (i.e., Δλ B = 9 nm and Δλ C = 3 nm).Then, in agreement with the scheme outlined in Fig. 3, both full resolution and degraded MOS data were applied to calculate RS s R ′ spectra.The values of ε displayed in Fig. 7 identify the spectral regions for which RS R from the NP site is most affected by a reduction of spectral resolution (e.g., see regions near 385 nm, 510 nm, 600 nm and 660 nm in Fig. 7(b), which exhibit values of ε larger than ±2% for Δλ B = 9 nm and Δλ C = 3 nm).
The difference Δε between ε generated with Eq. ( 3) using the RS R data that went through the RAMSES spectral response and those obtained without spectral degradation, are displayed in Fig. 8.In particular, Fig. 8(a) shows that in the case of OLCI the most pronounced misestimates of ε as a function of spectral resolution and sampling interval are observed at the 510 nm band, with differences that may reach -0.6%.These differences are explained by the high gradient in seawater reflectance near this wavelength.In summary, in the case of OLCI bands it can be assumed that 0.6% is a tentative estimate of the maximum uncertainty that would affect the previous analysis performed with RS R data from NP, if collected with a spectral resolution of 9 nm and sampling interval of 3 nm (i.e., close to the spectral features of RAMSES data).
In the case of PACE-like bands, the values of Δε in Fig. 8(b) exceed ±1% near a few center-wavelengths (i.e., 510 nm, 600 nm, 660 nm and, with some caution, 495 nm) for the lowest spectral resolution and sampling interval (i.e., 9 nm and 3 nm, respectively).
Overall, the previous results confirm misestimates of ε for the analyses performed with RAMSES spectra.It is expected, however, that for optically complex waters (i.e., NA and WB), misestimates will be lower than those quantified through RS R from NP due to RS R naturally exhibiting less pronounced spectral features in these other locations.Thus, it can be assumed that results from the analyses of RAMSES spectra can be applied with some confidence to draw general conclusions in optically complex waters, even though it probably leads to an underestimate of requirements.Nevertheless, the case of the WM oligotrophic waters is more affected by the reduced spectral resolution of RAMSES sensors and these results should only be considered in combination with those determined from RS R related to NP.It is emphasized that the relatively low impact of spectral degradation resulting from the previous analysis is largely explained by the "smoothness" of the RS R spectrum obtained through the normalization of W L to S E .In fact, this process removes the high spectral resolution features due to the solar spectrum and atmospheric absorption that affect W L .Consequently, the same conclusions achieved for RS R do not likely apply to RAMSES W L spectra.

R
The overall analysis has been based on RS R data that are the target quantity for most ocean color applications.However, SVC is often performed using W L data [14,15].This alternative solution avoids dealing with uncertainties of computed or measured downward irradiance S E , but increases the spectral resolution requirements for in situ radiometry due to the higher spectral complexity of the W L compared with the RS R spectra.This is shown in Fig. 9 by the percent differences ε computed using Eq. ( 3) with ℑ indicating W s L ′ and r ℑ the reference quantity W s L from NP spectra (the same analysis is not presented for RAMSES data due to their relatively low spectral resolution).These ε values, when compared to those displayed in Fig. 4(a), do not show a significant of the use of W L or RS R on spectral resolution requirements for multispectral satellite sensors such as OLCI when excluding the bands in the blue spectral region.Similarly, the values of ε determined for the PACE-like bands exhibit a marked increase in the blue spectral region near 395 nm, 400 nm and 430 nm, when compared to those shown in Fig. 5(a).This is fully explained by the pronounced spectral features of W L in the blue spectral region.The comparison of Fig. 10 with Fig. 7, which display full resolution and spectrally degraded data for both W L and RS R together with the related values of ε, shows the higher spectral complexity of W L and the importance of using higher resolutions in situ sensors for applications requiring W L with respect to RS R .

Spectral sampling interval versus resolution
Spectral resolutions Δλ B and sampling intervals Δλ C considered in the previous analysis are limited to a few cases guided by the specifications of existing spectrometers.When looking at results presented in Figs. 4 and 5, the configuration defined by Δλ B = 2 nm and Δλ C = 2 nm exhibits a slightly better performance than that given by Δλ B = 3 nm and Δλ C = 1 nm.This spectral resolution (i.e., Δλ C ≤ Δλ B /2), results from Figs. 4-5 lead to the subsequent requirements solely based on RS R data.For SVC activities, which are commonly performed in oligotrophic waters [15] and consequently by solely considering findings from the analysis of RS R from ultra-oligotrophic waters, the following general conclusions can be drawn with ε within ±0.5% in the blue-green spectral region: -A spectral resolution better than 3 nm is required for in situ hyperspectral sensors in the case of satellite multispectral sensors (as shown for OLCI bands in Fig. 4(a)); -Conversely, a spectral resolution better than 1 nm is recommended for in situ sensors in the case of satellite hyperspectral sensors (as shown for PACE-like bands in Fig. 5(a)).The previous requirement can be relaxed to 2 nm when excluding spectral regions near 510 nm, 600 nm and, with caution, at 395 nm.
For validation activities performed with RS R setting ε within ±1% in the blue-green spectral region: -The spectral resolution of in situ hyperspectral sensors should be better than 3 nm in oligotrophic waters in the case of satellite multispectral sensors.The requirements can be relaxed to a spectral resolution better than approximately 9 nm for optically complex waters (as shown for OLCI bands in Fig. 4).
-The spectral resolution of in situ hyperspectral sensors should also be better than 3 nm in oligotrophic waters in the alternative case of satellite hyperspectral sensors.Excluding bands near 600 nm, spectral resolution better than 6 nm may satisfy requirements for optically complex waters (as shown for PACE-like bands in Fig. 5).It is important to remember, however, that the previous spectral resolution requirements defined for optically complex waters may be somewhat underestimated having been determined using in situ hyperspectral data with relatively low spectral resolution.Obviously, a different target ε would imply more or less stringent requirements.Additionally, the use of W L instead of RS R , would increase requirements ultimately indicating the need for subnanometer resolution in the blue spectral region for hyperspectral sensors such as PACE.

Summary and conclusions
An estimate of the uncertainties (actually biases) affecting comparisons of in situ and satellite radiometric matchups has been derived as a function of spectral band characteristics of in situ sensors.This analysis, that has relevance for SVC applications and satellite ocean color validation relying on the use of in situ RS R data, has been developed using in situ hyperspectral radiometric data representative of different water types: oligotrophic and optically complex.These spectra have been used to construct hyperspectral data characterized by different spectral resolution and sampling intervals, successively applied to quantify differences between in situ and satellite RS R values.Results obtained for the OLCI visible bands, indicate that differences may reach several percent in oligotrophic waters with spectral resolution and sampling intervals of 9 nm and 3 nm, respectively.Considering the same resolution and sampling interval, differences are always within ±1% in optically complex waters.
In the case of PACE-like visible bands defined by 5 nm width, Gaussian spectral response and 5 nm sampling interval, differences may also exhibit values exceeding several percent as a function of the water type and spectral resolution of the in situ sensor.

Fig. 1 .
Fig. 1.Sample RS R spectra used in this study.NP (a) and WM (b) refer to the North Pacific Gyre and the Western Mediterranean Sea oligotrophic waters, while WB (c) and NA (d) refer to the Western Black Sea and northern Adriatic optically complex waters.Insets in panels a-c display RS R with scales expanded in the 600-700 nm interval to better visualize spectral features.

Table 1 .
Bio-optical quantities(a) related to the RS R spectra used in this study: Chla and TSM indicate the concentration of chlorophyll-a and of total suspended matter, while a and b b indicate the absorption and backscattering coefficients at 490 nm of optically significant constituents, respectively.

R
obtained with OLCI or PACE-like sensors, and RS R values reconstructed with in situ hyperspectral data having various spectral resolutions and sampling intervals.These differences introduce uncertainties in the SVC process, and are also relevant for the application of in situ data to the validation of satellite radiometric products requiring the comparison of satellite and in situ RS R values.It is emphasized that regardless of the focus on RS R , W L and S E are processed separately before computing RS R (i.e., account for the independence of W L and S E measurements from different radiometers.The flow diagram in Fig. 3 summarizes the matching scheme.The different radiometric quantities identified in the diagram and applied in the following analysis (i.e., W L , S E or RS R ) are hereafter indicated using the generic variable ℜ .Specifically, n ℜ : sample W L and S E values from MOS or RAMSES hyperspectral sensors; r ℜ : reference W L and S E hyperspectral values determined from the resampling at higher spectral resolution (i.e., 0.1 nm) through linear interpolation of the n ℜ sample spectra; s ℜ : satellite-exact radiometric values determined from r ℜ accounting for the spectral response functions of the space sensor s S ; i ℜ : modeled in situ hyperspectral values determined from r ℜ accounting for the spectral response functions of the in situ sensor i S defined using Gaussian functions, and varying the bandwidth and center-wavelength of the hypothetical in situ instrument; ' r ℜ : reconstructed W L and S E spectra at 0.1 nm resolution using i ℜ ; ' s ℜ : satellite-equivalent radiometric values determined from ' r ℜ (i.e., from hyperspectral data generated using simulated in situ reduced resolution spectra).Briefly, with reference to the dark-gray path in Fig.3, satellite-exact ( ) RS s R k spectra are computed for each spectral band k by relying on sub-nanometer (i.e., 0.1 nm resolution) r ℜ spectra (i.e., determined through spectral convolution from: Fig. 3 satelli compr

Fig. 4 .R
Fig. 4. Percent differences ε between RS s R ′ and RS s R determined for OLCI bands.Data in different panels refer to the NP (a), WM (b), WB (c) and NA (d) spectra, and are presented at the OLCI center-wavelengths for different bandwidths Δλ B and spectral sampling intervals Δλ C of the in situ hyperspectral sensor.

Fig. 5 .R
Fig. 5. Percent differences ε between RS s R ′ and RS s R determined for PACE-like bands.Data in different panels refer to NP (a), WM (b), WB (c) and NA (d) spectra, and are presented at the considered PACE-like center-wavelengths for different bandwidths Δλ B and spectral sampling intervals Δλ C of the in situ hyperspectral sensor.

Fig. 6 .
Fig. 6.Mean μ (a) and standard deviation σ (b) values of percent differences ε between RS s R ′ and

Fig. 7 .
Fig. 7. Original (grey line) and spectrally degraded NP RS R data (black line) determined with Δλ C = 3 nm and Δλ B = 9 nm (a), and percent differences ε between degraded and the original high resolution spectra (b).

Fig. 8 .
Fig. 8. Differences Δε between values of ε determined from RS s R ′ and RS s R for the OLCI (a) or PACE-like (b) bands, with reduced resolution (i.e., Δλ B = 9 nm and Δλ C = 3 nm) and full resolution NP spectra.

Fig. 9 .L
Fig. 9. Percent differences ε between W s L ′ and W s L determined with NP spectra for OLCI (a) or PACE-like (b) bands.Data are presented at the considered OLCI or PACE-like centerwavelengths for different simulated bandwidths Δλ B and spectral sampling intervals Δλ C of the in situ hyperspectral sensor.

Fig. 10 .
Fig. 10.Original (grey line) and spectrally degraded NP W L data (black line) determined with Δλ C = 3 nm and Δλ B = 9 nm (a), and percent differences ε between degraded and the original high resolution spectra (b).