Abstract

The need to obtain ocean color essential climate variables (OC-ECVs) using hyperspectral technology has gained increased interest in recent years. Assessing ocean color on a large scale in high latitude environments using satellite remote sensing is constrained by polar environmental conditions. Nevertheless, on a small scale we can assess ocean color using above-water and in-water remote sensing. Unfortunately, above-water remote sensing can only determine apparent optical properties leaving the sea surface and is susceptible to near surface environmental conditions for example sky and sunglint. Consequently, we have to rely on accurate in-water remote sensing as it can provide both synoptic inherent and apparent optical properties of seawater. We use normalized water leaving radiance LWN or the equivalent remote sensing reflectance RRS from 27 stations to compare the differences in above-water and in-water OC-ECVs. Analysis of above-water and in-water RRS spectra provided very good match-ups (R2 > 0.97, MSE<1.8*10−7) for all stations. The unbiased percent differences (UPD) between above-water and in-water approaches were determined at common OC-ECVs spectral bands (410, 440, 490, 510 and 555) nm and the classic band ratio (490/555) nm. The spectral average UPD ranged (5 – 110) % and band ratio UPD ranged (0 – 12) %, the latter showing that the 5% uncertainty threshold for ocean color radiometric products is attainable. UPD analysis of these stations West of Greenland, Labrador Sea, Denmark Strait and West of Iceland also suggests that the differences observed are likely a result of environmental and instrumental perturbations.

© 2013 OSA

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    [CrossRef]

2013

T. Kutser, E. Vahtmäe, B. Paavel, and T. Kauer, “Removing glint effects from field radiometry data measured in optically complex coastal and inland waters,” Remote Sens. Environ.133, 85–89 (2013).
[CrossRef]

Z. Lee, N. Pahlevan, Y.-H. Ahn, S. Greb, and D. O’Donnell, “Robust approach to directly measuring water-leaving radiance in the field,” Appl. Opt.52(8), 1693–1701 (2013).
[CrossRef] [PubMed]

2012

S. P. Garaba, J. Schulz, M. R. Wernand, and O. Zielinski, “Sunglint detection for unmanned and automated platforms,” Sensors (Basel)12(9), 12545–12561 (2012).
[CrossRef] [PubMed]

T. Suresh, M. Talaulikar, E. Desa, S. G. Prabhu Matondkar, T. S. Kumar, and A. Lotlikar, “A simple method to minimize orientation effects in a profiling radiometer,” Mar. Geod.35(4), 441–454 (2012).
[CrossRef]

2011

A. Calbet, K. Riisgaard, E. Saiz, S. Zamora, C. Stedmon, and T. Nielsen, “Phytoplankton growth and microzooplankton grazing along a sub-Arctic fjord (Godthabsfjord, west Greenland),” Mar. Ecol. Prog. Ser.442, 11–22 (2011).
[CrossRef]

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).
[CrossRef]

2010

2007

S. Bélanger, J. K. Ehn, and M. Babin, “Impact of sea ice on the retrieval of water-leaving reflectance, chlorophyll a concentration and inherent optical properties from satellite ocean color data,” Remote Sens. Environ.111(1), 51–68 (2007).
[CrossRef]

2006

P. Kowalczuk, M. J. Durako, W. J. Cooper, D. Wells, and J. J. Souza, “Comparison of radiometric quantities measured in water, above water and derived from seaWiFS imagery in the South Atlantic Bight, North Carolina, USA,” Cont. Shelf Res.26(19), 2433–2453 (2006).
[CrossRef]

K. G. Ruddick, V. De Cauwer, Y. J. Park, and G. Moore, “Seaborne measurements of near infrared water-leaving reflectance: The similarity spectrum for turbid waters,” Limnol. Oceanogr.51(2), 1167–1179 (2006).
[CrossRef]

2005

2004

I. Reda and A. Andreas, “Solar position algorithm for solar radiation applications,” Sol. Energy76(5), 577–589 (2004).
[CrossRef]

C. D. Mobley, D. Stramski, W. P. Bissett, and E. Boss, “Optical modeling of ocean waters: Is the Case 1 - Case 2 classification still useful?” Oceanography (Wash. D.C.)17(2), 60–67 (2004).
[CrossRef]

2002

S. B. Hooker, G. Lazin, G. Zibordi, and S. McLean, “An evaluation of above- and in-water methods for determining water-leaving radiances,” J. Atmos. Ocean. Technol.19(4), 486–515 (2002).
[CrossRef]

2001

R. W. Gould, R. A. Arnone, and M. Sydor, “Absorption, scattering, and, remote-sensing reflectance relationships in coastal waters: Testing a new inversion algorithm,” J. Coast. Res.17, 328–341 (2001).

2000

H. M. Dierssen and R. C. Smith, “Bio-optical properties and remote sensing ocean color algorithms for Antarctic Peninsula waters,” J. Geophys. Res.105(C11), 26301–26312 (2000).
[CrossRef]

1999

1984

H. Neckel and D. Labs, “The solar radiation between 3300 and 12500 Å,” Sol. Phys.90(2), 205–258 (1984).
[CrossRef]

1977

A. Morel and L. Prieur, “Analysis of variations in ocean color,” Limnol. Oceanogr.22(4), 709–722 (1977).
[CrossRef]

Ahn, Y.-H.

Andreas, A.

I. Reda and A. Andreas, “Solar position algorithm for solar radiation applications,” Sol. Energy76(5), 577–589 (2004).
[CrossRef]

Arnone, R.

Arnone, R. A.

R. W. Gould, R. A. Arnone, and M. Sydor, “Absorption, scattering, and, remote-sensing reflectance relationships in coastal waters: Testing a new inversion algorithm,” J. Coast. Res.17, 328–341 (2001).

Babin, M.

S. Bélanger, J. K. Ehn, and M. Babin, “Impact of sea ice on the retrieval of water-leaving reflectance, chlorophyll a concentration and inherent optical properties from satellite ocean color data,” Remote Sens. Environ.111(1), 51–68 (2007).
[CrossRef]

Bélanger, S.

S. Bélanger, J. K. Ehn, and M. Babin, “Impact of sea ice on the retrieval of water-leaving reflectance, chlorophyll a concentration and inherent optical properties from satellite ocean color data,” Remote Sens. Environ.111(1), 51–68 (2007).
[CrossRef]

Berthon, J. F.

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).
[CrossRef]

Bissett, W. P.

C. D. Mobley, D. Stramski, W. P. Bissett, and E. Boss, “Optical modeling of ocean waters: Is the Case 1 - Case 2 classification still useful?” Oceanography (Wash. D.C.)17(2), 60–67 (2004).
[CrossRef]

Boss, E.

C. D. Mobley, D. Stramski, W. P. Bissett, and E. Boss, “Optical modeling of ocean waters: Is the Case 1 - Case 2 classification still useful?” Oceanography (Wash. D.C.)17(2), 60–67 (2004).
[CrossRef]

Calbet, A.

A. Calbet, K. Riisgaard, E. Saiz, S. Zamora, C. Stedmon, and T. Nielsen, “Phytoplankton growth and microzooplankton grazing along a sub-Arctic fjord (Godthabsfjord, west Greenland),” Mar. Ecol. Prog. Ser.442, 11–22 (2011).
[CrossRef]

Cooper, W. J.

P. Kowalczuk, M. J. Durako, W. J. Cooper, D. Wells, and J. J. Souza, “Comparison of radiometric quantities measured in water, above water and derived from seaWiFS imagery in the South Atlantic Bight, North Carolina, USA,” Cont. Shelf Res.26(19), 2433–2453 (2006).
[CrossRef]

D'Alimonte, D.

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).
[CrossRef]

De Cauwer, V.

K. G. Ruddick, V. De Cauwer, Y. J. Park, and G. Moore, “Seaborne measurements of near infrared water-leaving reflectance: The similarity spectrum for turbid waters,” Limnol. Oceanogr.51(2), 1167–1179 (2006).
[CrossRef]

Desa, E.

T. Suresh, M. Talaulikar, E. Desa, S. G. Prabhu Matondkar, T. S. Kumar, and A. Lotlikar, “A simple method to minimize orientation effects in a profiling radiometer,” Mar. Geod.35(4), 441–454 (2012).
[CrossRef]

Dierssen, H. M.

H. M. Dierssen and R. C. Smith, “Bio-optical properties and remote sensing ocean color algorithms for Antarctic Peninsula waters,” J. Geophys. Res.105(C11), 26301–26312 (2000).
[CrossRef]

Durako, M. J.

P. Kowalczuk, M. J. Durako, W. J. Cooper, D. Wells, and J. J. Souza, “Comparison of radiometric quantities measured in water, above water and derived from seaWiFS imagery in the South Atlantic Bight, North Carolina, USA,” Cont. Shelf Res.26(19), 2433–2453 (2006).
[CrossRef]

Ehn, J. K.

S. Bélanger, J. K. Ehn, and M. Babin, “Impact of sea ice on the retrieval of water-leaving reflectance, chlorophyll a concentration and inherent optical properties from satellite ocean color data,” Remote Sens. Environ.111(1), 51–68 (2007).
[CrossRef]

Garaba, S. P.

S. P. Garaba, J. Schulz, M. R. Wernand, and O. Zielinski, “Sunglint detection for unmanned and automated platforms,” Sensors (Basel)12(9), 12545–12561 (2012).
[CrossRef] [PubMed]

Gould, R. W.

R. W. Gould, R. A. Arnone, and M. Sydor, “Absorption, scattering, and, remote-sensing reflectance relationships in coastal waters: Testing a new inversion algorithm,” J. Coast. Res.17, 328–341 (2001).

Greb, S.

Hooker, S. B.

S. B. Hooker, G. Lazin, G. Zibordi, and S. McLean, “An evaluation of above- and in-water methods for determining water-leaving radiances,” J. Atmos. Ocean. Technol.19(4), 486–515 (2002).
[CrossRef]

Kauer, T.

T. Kutser, E. Vahtmäe, B. Paavel, and T. Kauer, “Removing glint effects from field radiometry data measured in optically complex coastal and inland waters,” Remote Sens. Environ.133, 85–89 (2013).
[CrossRef]

Kowalczuk, P.

P. Kowalczuk, M. J. Durako, W. J. Cooper, D. Wells, and J. J. Souza, “Comparison of radiometric quantities measured in water, above water and derived from seaWiFS imagery in the South Atlantic Bight, North Carolina, USA,” Cont. Shelf Res.26(19), 2433–2453 (2006).
[CrossRef]

Kumar, T. S.

T. Suresh, M. Talaulikar, E. Desa, S. G. Prabhu Matondkar, T. S. Kumar, and A. Lotlikar, “A simple method to minimize orientation effects in a profiling radiometer,” Mar. Geod.35(4), 441–454 (2012).
[CrossRef]

Kutser, T.

T. Kutser, E. Vahtmäe, B. Paavel, and T. Kauer, “Removing glint effects from field radiometry data measured in optically complex coastal and inland waters,” Remote Sens. Environ.133, 85–89 (2013).
[CrossRef]

Labs, D.

H. Neckel and D. Labs, “The solar radiation between 3300 and 12500 Å,” Sol. Phys.90(2), 205–258 (1984).
[CrossRef]

Lazin, G.

S. B. Hooker, G. Lazin, G. Zibordi, and S. McLean, “An evaluation of above- and in-water methods for determining water-leaving radiances,” J. Atmos. Ocean. Technol.19(4), 486–515 (2002).
[CrossRef]

Lee, Z.

Lotlikar, A.

T. Suresh, M. Talaulikar, E. Desa, S. G. Prabhu Matondkar, T. S. Kumar, and A. Lotlikar, “A simple method to minimize orientation effects in a profiling radiometer,” Mar. Geod.35(4), 441–454 (2012).
[CrossRef]

McLean, S.

S. B. Hooker, G. Lazin, G. Zibordi, and S. McLean, “An evaluation of above- and in-water methods for determining water-leaving radiances,” J. Atmos. Ocean. Technol.19(4), 486–515 (2002).
[CrossRef]

Mélin, F.

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).
[CrossRef]

Mobley, C.

Mobley, C. D.

C. D. Mobley, D. Stramski, W. P. Bissett, and E. Boss, “Optical modeling of ocean waters: Is the Case 1 - Case 2 classification still useful?” Oceanography (Wash. D.C.)17(2), 60–67 (2004).
[CrossRef]

C. D. Mobley, “Estimation of the remote-sensing reflectance from above-surface measurements,” Appl. Opt.38(36), 7442–7455 (1999).
[CrossRef] [PubMed]

Moore, G.

K. G. Ruddick, V. De Cauwer, Y. J. Park, and G. Moore, “Seaborne measurements of near infrared water-leaving reflectance: The similarity spectrum for turbid waters,” Limnol. Oceanogr.51(2), 1167–1179 (2006).
[CrossRef]

Morel, A.

A. Morel and L. Prieur, “Analysis of variations in ocean color,” Limnol. Oceanogr.22(4), 709–722 (1977).
[CrossRef]

Neckel, H.

H. Neckel and D. Labs, “The solar radiation between 3300 and 12500 Å,” Sol. Phys.90(2), 205–258 (1984).
[CrossRef]

Nielsen, T.

A. Calbet, K. Riisgaard, E. Saiz, S. Zamora, C. Stedmon, and T. Nielsen, “Phytoplankton growth and microzooplankton grazing along a sub-Arctic fjord (Godthabsfjord, west Greenland),” Mar. Ecol. Prog. Ser.442, 11–22 (2011).
[CrossRef]

O’Donnell, D.

Ouillon, S.

Paavel, B.

T. Kutser, E. Vahtmäe, B. Paavel, and T. Kauer, “Removing glint effects from field radiometry data measured in optically complex coastal and inland waters,” Remote Sens. Environ.133, 85–89 (2013).
[CrossRef]

Pahlevan, N.

Park, Y. J.

K. G. Ruddick, V. De Cauwer, Y. J. Park, and G. Moore, “Seaborne measurements of near infrared water-leaving reflectance: The similarity spectrum for turbid waters,” Limnol. Oceanogr.51(2), 1167–1179 (2006).
[CrossRef]

Petrenko, A.

Prabhu Matondkar, S. G.

T. Suresh, M. Talaulikar, E. Desa, S. G. Prabhu Matondkar, T. S. Kumar, and A. Lotlikar, “A simple method to minimize orientation effects in a profiling radiometer,” Mar. Geod.35(4), 441–454 (2012).
[CrossRef]

Prieur, L.

A. Morel and L. Prieur, “Analysis of variations in ocean color,” Limnol. Oceanogr.22(4), 709–722 (1977).
[CrossRef]

Reda, I.

I. Reda and A. Andreas, “Solar position algorithm for solar radiation applications,” Sol. Energy76(5), 577–589 (2004).
[CrossRef]

Riisgaard, K.

A. Calbet, K. Riisgaard, E. Saiz, S. Zamora, C. Stedmon, and T. Nielsen, “Phytoplankton growth and microzooplankton grazing along a sub-Arctic fjord (Godthabsfjord, west Greenland),” Mar. Ecol. Prog. Ser.442, 11–22 (2011).
[CrossRef]

Ruddick, K. G.

K. G. Ruddick, V. De Cauwer, Y. J. Park, and G. Moore, “Seaborne measurements of near infrared water-leaving reflectance: The similarity spectrum for turbid waters,” Limnol. Oceanogr.51(2), 1167–1179 (2006).
[CrossRef]

Saiz, E.

A. Calbet, K. Riisgaard, E. Saiz, S. Zamora, C. Stedmon, and T. Nielsen, “Phytoplankton growth and microzooplankton grazing along a sub-Arctic fjord (Godthabsfjord, west Greenland),” Mar. Ecol. Prog. Ser.442, 11–22 (2011).
[CrossRef]

Schulz, J.

S. P. Garaba, J. Schulz, M. R. Wernand, and O. Zielinski, “Sunglint detection for unmanned and automated platforms,” Sensors (Basel)12(9), 12545–12561 (2012).
[CrossRef] [PubMed]

Smith, R. C.

H. M. Dierssen and R. C. Smith, “Bio-optical properties and remote sensing ocean color algorithms for Antarctic Peninsula waters,” J. Geophys. Res.105(C11), 26301–26312 (2000).
[CrossRef]

Souza, J. J.

P. Kowalczuk, M. J. Durako, W. J. Cooper, D. Wells, and J. J. Souza, “Comparison of radiometric quantities measured in water, above water and derived from seaWiFS imagery in the South Atlantic Bight, North Carolina, USA,” Cont. Shelf Res.26(19), 2433–2453 (2006).
[CrossRef]

Stedmon, C.

A. Calbet, K. Riisgaard, E. Saiz, S. Zamora, C. Stedmon, and T. Nielsen, “Phytoplankton growth and microzooplankton grazing along a sub-Arctic fjord (Godthabsfjord, west Greenland),” Mar. Ecol. Prog. Ser.442, 11–22 (2011).
[CrossRef]

Stramski, D.

C. D. Mobley, D. Stramski, W. P. Bissett, and E. Boss, “Optical modeling of ocean waters: Is the Case 1 - Case 2 classification still useful?” Oceanography (Wash. D.C.)17(2), 60–67 (2004).
[CrossRef]

Suresh, T.

T. Suresh, M. Talaulikar, E. Desa, S. G. Prabhu Matondkar, T. S. Kumar, and A. Lotlikar, “A simple method to minimize orientation effects in a profiling radiometer,” Mar. Geod.35(4), 441–454 (2012).
[CrossRef]

Sydor, M.

R. W. Gould, R. A. Arnone, and M. Sydor, “Absorption, scattering, and, remote-sensing reflectance relationships in coastal waters: Testing a new inversion algorithm,” J. Coast. Res.17, 328–341 (2001).

Talaulikar, M.

T. Suresh, M. Talaulikar, E. Desa, S. G. Prabhu Matondkar, T. S. Kumar, and A. Lotlikar, “A simple method to minimize orientation effects in a profiling radiometer,” Mar. Geod.35(4), 441–454 (2012).
[CrossRef]

Vahtmäe, E.

T. Kutser, E. Vahtmäe, B. Paavel, and T. Kauer, “Removing glint effects from field radiometry data measured in optically complex coastal and inland waters,” Remote Sens. Environ.133, 85–89 (2013).
[CrossRef]

Wells, D.

P. Kowalczuk, M. J. Durako, W. J. Cooper, D. Wells, and J. J. Souza, “Comparison of radiometric quantities measured in water, above water and derived from seaWiFS imagery in the South Atlantic Bight, North Carolina, USA,” Cont. Shelf Res.26(19), 2433–2453 (2006).
[CrossRef]

Wernand, M. R.

S. P. Garaba, J. Schulz, M. R. Wernand, and O. Zielinski, “Sunglint detection for unmanned and automated platforms,” Sensors (Basel)12(9), 12545–12561 (2012).
[CrossRef] [PubMed]

Zamora, S.

A. Calbet, K. Riisgaard, E. Saiz, S. Zamora, C. Stedmon, and T. Nielsen, “Phytoplankton growth and microzooplankton grazing along a sub-Arctic fjord (Godthabsfjord, west Greenland),” Mar. Ecol. Prog. Ser.442, 11–22 (2011).
[CrossRef]

Zibordi, G.

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).
[CrossRef]

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O. Zielinski, D. Voß, D. Meier, R. Henkel, L. Holinde, S. P. Garaba, and A. Cembella, “Spectral sky radiance during Maria S. Merian cruise MSM21/3 (ARCHEMHAB)” (2013), http://doi.pangaea.de/10.1594/PANGAEA.810739 .

O. Zielinski, D. Voß, D. Meier, R. Henkel, L. Holinde, S. P. Garaba, and A. Cembella, “Downward irradiance during Maria S. Merian cruise MSM21/3 (ARCHEMHAB)” (2013), http://doi.pangaea.de/10.1594/PANGAEA.810741 .

O. Zielinski, D. Voß, D. Meier, R. Henkel, L. Holinde, S. P. Garaba, and A. Cembella, “Upward radiance radiance during Maria S. Merian cruise MSM21/3 (ARCHEMHAB)” (2013), http://doi.pangaea.de/10.1594/PANGAEA.810740 .

J. L. Mueller, C. Davis, R. Arnone, R. Frouin, K. Carder, Z. P. Lee, R. G. Steward, S. Hooker, C. D. Mobley, and S. McLean, “Above-water radiance and remote sensing reflectance measurement and analysis protocols,” in Ocean Optics Protocols for Satellite Ocean Color Sensor Validation, Revision 4, NASA/TM-2003–21621, J. L. Mueller, G. S. Fargion, and C. R. McClain eds. (2003), pp. 21–31.

O. Zielinski, D. Voß, D. Meier, R. Henkel, L. Holinde, S. P. Garaba, and A. Cembella, “Normalized water leaving radiance during Maria S. Merian cruise MSM21/3 (ARCHEMHAB)” (2013), http://doi.pangaea.de/10.1594/PANGAEA.810858 .

O. Zielinski, D. Voß, D. Meier, R. Henkel, L. Holinde, S. P. Garaba, and A. Cembella, “Water leaving radiance during Maria S. Merian cruise MSM21/3 (ARCHEMHAB)” (2013), http://doi.pangaea.de/10.1594/PANGAEA.810857 .

O. Zielinski, D. Voß, D. Meier, R. Henkel, L. Holinde, S. P. Garaba, and A. Cembella, “Remote sensing reflectance during Maria S. Merian cruise MSM21/3 (ARCHEMHAB)” (2013), http://doi.pangaea.de/10.1594/PANGAEA.810742 .

O. Zielinski, D. Voß, D. Meier, R. Henkel, L. Holinde, S. P. Garaba, and A. Cembella, “Cloud cover observations during Maria S. Merian cruise MSM21/3 (ARCHEMHAB)” (2013), http://doi.pangaea.de/10.1594/PANGAEA.810649 .

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Figures (6)

Fig. 1
Fig. 1

Above-water (red) and in-water (green) sampled stations during RV Maria S. Merian field campaign 21 leg 3 between 27 July and 08 August 2012.

Fig. 2
Fig. 2

Flowchart showing how ocean color essential climate variables (water leaving radiance – LW, normalized water leaving radiance - LWN, and remote sensing reflectance – RRS) were collected and processed for the comparison task.

Fig. 3
Fig. 3

Illustration of how above-water and in-water observation times were matched.

Fig. 4
Fig. 4

Sample plot for RRS (sr−1) of 4 in-water casts and a single above-water estimation using different sky and sun glint correction approaches used in the match-up analysis. Note that the in-water casts only reach ~610 nm as a result of high of light attenuation with depth.

Fig. 5
Fig. 5

Spectra corrected for glint using the respective correction approach.

Fig. 6
Fig. 6

All spectra above-water (red) and in-water (blue) observations used distinguish station water type into case 1 or case 2.

Tables (3)

Tables Icon

Table 1 Best statistical match-up results for above-water vs. in-water RRS. N is the number of matching wavebands for both above-water and in-water observations. MSE is the mean square error [1/N(y (i)-x (i))2]. The solar zenith was computed using the solar position algorithm [22]. Cloud cover [23] was approximated from visual inspection and absolute wind speed was obtained from ship weather station.

Tables Icon

Table 2 Summary of unbiased percent differences (UPD) between above-water and in-water measured RRS at chosen discrete wavelengths (410, 440, 490, 510, and 555) nm and their average spectral UPD with the standard deviation and the band ratio (490/555) nm UPD.

Tables Icon

Table 3 Ouillon and Petrenko [26] Case 1 and Case 2 water classification method applied to above-water and in-water observations.

Equations (5)

Equations on this page are rendered with MathJax. Learn more.

R RS = L W E S = L sfc ( ρ airsea L sky ) E S ,
L WN = R RS F 0 ,
ψ B A (λ,t)= | X i A (λ,t) X i B (λ,t) | 0.5( X i A (λ,t)+ X i B (λ,t) ) *100%,
Ψ B A (λ)= 1 N i=1 N ψ B A ( λ i ) .
φ B A ( λ c/d )= | R rs A ( λ c/d ) R rs B ( λ c/d ) | 0.5( R rs A ( λ c/d )+ R rs B ( λ c/d ) ) *100%,

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