Abstract

The equivalence of two radiometric methods relying on a single nadir-view optical sensor to determine the water-leaving radiance LW, namely the Single Depth Approach (SDA) and the Sky-Blocked Approach (SBA), was investigated applying identical hyperspectral radiometers operated on the same deployment platform. Values of LW from SDA and SBA measurements performed in the Black Sea across a variety of waters during ideal illumination conditions and with low-to-slight sea state, exhibited mean absolute differences within 0.5% in the blue-green spectral region and 2% in the red. This result, benefitting of a comprehensive parameterization of optical processes in combination with the characterization of sensors non-linearity, in-water response and reproducibility of absolute radiometric calibrations, indicated ample equivalence of the two near-surface methods in terms of performance and data reduction needs.

© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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2018 (1)

M. Talone and G. Zibordi, “Non-linear response of a class of hyper-spectral radiometers,” Metrologia 55(5), 747–758 (2018).
[Crossref]

2017 (2)

K. J. Voss and S. Flora, “Spectral Dependence of the Seawater–Air Radiance Transmission Coefficient,” J. Atmos. Ocean. Tech. 34(6), 1203–1205 (2017).
[Crossref]

Z. Shang, Z. Lee, Q. Dong, and J. Wei, “Self-shading associated with a skylight-blocked approach system for the measurement of water-leaving radiance and its correction,” Appl. Opt. 56(25), 7033–7040 (2017).
[Crossref]

2016 (5)

2015 (1)

2014 (2)

J. M. Beltrán-Abaunza, S. Kratzer, and C. Brockmann, “Evaluation of MERIS products from Baltic Sea coastal waters rich in CDOM,” Ocean Sci. 10(3), 377–396 (2014).
[Crossref]

S. C. V. Cristina, G. F. Moore, P. R. F. C. Goela, J. D. Icely, and A. Newton, “In situ validation of MERIS marine reflectance off the southwest Iberian Peninsula: assessment of vicarious adjustment and corrections for near-land adjacency,” Int. J. Rem. Sensing 35(6), 2347–2377 (2014).

2013 (2)

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]

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]

2012 (1)

G. Zibordi, K. Ruddick, I. Ansko, G. Moore, S. Kratzer, J. Icely, and A. Reinart, “In situ determination of the remote sensing reflectance: an inter-comparison,” Ocean Sci. 8(4), 567–586 (2012).
[Crossref]

2010 (1)

2009 (1)

G. Zibordi, J.-F. Berthon, and D. D’Alimonte, “An evaluation of radiometric products from fixed-depth and continuous in-water profile data from moderately complex waters,” J. Atmos. Ocean. Tech. 26(1), 91–106 (2009).
[Crossref]

2006 (3)

G. Zibordi and M. Darecki, “Immersion factors for the RAMSES series of hyper-spectral underwater radiometers,” J. Opt. A: Pure Appl. Opt. 8(3), 252–258 (2006).
[Crossref]

G. Zibordi, “Immersion factor of in-water radiance sensors: assessment for a class of radiometers,” J. Atmos. Ocean. Tech. 23(2), 302–313 (2006).
[Crossref]

A. Tanaka, H. Sasaki, and J. Ishizaka, “Alternative measuring method for water-leaving radiance using a radiance sensor with a domed cover,” Opt. Express 14(8), 3099–3105 (2006).
[Crossref]

2004 (2)

R. A. Leathers, T. V. Downes, and C. D. Mobley, “Self-shading correction for oceanographic upwelling radiometers,” Opt. Express 12(20), 4709–4718 (2004).
[Crossref]

G. Zibordi, D. D’Alimonte, and J.-F. Berthon, “An evaluation of depth resolution requirements for optical profiling in coastal waters,” J. Atmos. Ocean. Tech. 21(7), 1059–1073 (2004).
[Crossref]

2002 (1)

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. Tech. 19(4), 486–515 (2002).
[Crossref]

2001 (1)

2000 (1)

1997 (1)

1996 (1)

G. M. Ferrari, M. D. Dowell, S. Grossi, and C. Targa, “Relationship between the optical properties of chromophoric dissolved organic matter and total concentration of dissolved organic carbon in the southern Baltic Sea region,” Mar. Chem. 55(3-4), 299–316 (1996).
[Crossref]

1995 (2)

S. Tassan, S. and G, and M. Ferrari, “An alternative approach to absorption measurements of aquatic particles retained on filters,” Limnol. Oceanogr. 40(8), 1358–1368 (1995).
[Crossref]

G. Zibordi and G. M. Ferrari, “Instrument self-shading in underwater optical measurements: experimental data,” Appl. Opt. 34(15), 2750–2754 (1995).
[Crossref]

1992 (1)

H. R. Gordon and K. Ding, “Self shading of in-water optical instruments,” Limnol. Oceanogr. 37(3), 491–500 (1992).
[Crossref]

Ahn, Y. H.

and G, S.

S. Tassan, S. and G, and M. Ferrari, “An alternative approach to absorption measurements of aquatic particles retained on filters,” Limnol. Oceanogr. 40(8), 1358–1368 (1995).
[Crossref]

Ansko, I.

M. Talone, G. Zibordi, I. Ansko, A. C. Banks, and J. Kuusk, “Stray light effects in above-water remote-sensing reflectance from hyperspectral radiometers,” Appl. Opt. 55(15), 3966–3977 (2016).
[Crossref]

G. Zibordi, K. Ruddick, I. Ansko, G. Moore, S. Kratzer, J. Icely, and A. Reinart, “In situ determination of the remote sensing reflectance: an inter-comparison,” Ocean Sci. 8(4), 567–586 (2012).
[Crossref]

Armstrong, R.

Arnone, R.

Austin, R. W.

R. W. Austin, “The remote sensing of spectral radiance from below the ocean surface,” in Optical Aspects of Oceanography (Academic, 1974).

Banks, A. C.

Beltrán-Abaunza, J. M.

J. M. Beltrán-Abaunza, S. Kratzer, and C. Brockmann, “Evaluation of MERIS products from Baltic Sea coastal waters rich in CDOM,” Ocean Sci. 10(3), 377–396 (2014).
[Crossref]

Berthon, J.-F.

G. Zibordi, J.-F. Berthon, and D. D’Alimonte, “An evaluation of radiometric products from fixed-depth and continuous in-water profile data from moderately complex waters,” J. Atmos. Ocean. Tech. 26(1), 91–106 (2009).
[Crossref]

G. Zibordi, D. D’Alimonte, and J.-F. Berthon, “An evaluation of depth resolution requirements for optical profiling in coastal waters,” J. Atmos. Ocean. Tech. 21(7), 1059–1073 (2004).
[Crossref]

Brockmann, C.

J. M. Beltrán-Abaunza, S. Kratzer, and C. Brockmann, “Evaluation of MERIS products from Baltic Sea coastal waters rich in CDOM,” Ocean Sci. 10(3), 377–396 (2014).
[Crossref]

Casal, G.

T. Kutser, B. Paavel, C. Verpoorter, M. Ligi, T. Soomets, K. Toming, and G. Casal, “Remote sensing of black lakes and using 810 nm reflectance peak for retrieving water quality parameters of optically complex waters,” Remote Sens. 8(6), 497 (2016).
[Crossref]

Cone, M. T.

Cristina, S. C. V.

S. C. V. Cristina, G. F. Moore, P. R. F. C. Goela, J. D. Icely, and A. Newton, “In situ validation of MERIS marine reflectance off the southwest Iberian Peninsula: assessment of vicarious adjustment and corrections for near-land adjacency,” Int. J. Rem. Sensing 35(6), 2347–2377 (2014).

D’Alimonte, D.

G. Zibordi, J.-F. Berthon, and D. D’Alimonte, “An evaluation of radiometric products from fixed-depth and continuous in-water profile data from moderately complex waters,” J. Atmos. Ocean. Tech. 26(1), 91–106 (2009).
[Crossref]

G. Zibordi, D. D’Alimonte, and J.-F. Berthon, “An evaluation of depth resolution requirements for optical profiling in coastal waters,” J. Atmos. Ocean. Tech. 21(7), 1059–1073 (2004).
[Crossref]

Darecki, M.

G. Zibordi and M. Darecki, “Immersion factors for the RAMSES series of hyper-spectral underwater radiometers,” J. Opt. A: Pure Appl. Opt. 8(3), 252–258 (2006).
[Crossref]

Ding, K.

H. R. Gordon and K. Ding, “Self shading of in-water optical instruments,” Limnol. Oceanogr. 37(3), 491–500 (1992).
[Crossref]

Dong, Q.

Dowell, M. D.

G. M. Ferrari, M. D. Dowell, S. Grossi, and C. Targa, “Relationship between the optical properties of chromophoric dissolved organic matter and total concentration of dissolved organic carbon in the southern Baltic Sea region,” Mar. Chem. 55(3-4), 299–316 (1996).
[Crossref]

Downes, T. V.

Ferrari, G. M.

G. M. Ferrari, M. D. Dowell, S. Grossi, and C. Targa, “Relationship between the optical properties of chromophoric dissolved organic matter and total concentration of dissolved organic carbon in the southern Baltic Sea region,” Mar. Chem. 55(3-4), 299–316 (1996).
[Crossref]

G. Zibordi and G. M. Ferrari, “Instrument self-shading in underwater optical measurements: experimental data,” Appl. Opt. 34(15), 2750–2754 (1995).
[Crossref]

Ferrari, M.

S. Tassan, S. and G, and M. Ferrari, “An alternative approach to absorption measurements of aquatic particles retained on filters,” Limnol. Oceanogr. 40(8), 1358–1368 (1995).
[Crossref]

Flora, S.

K. J. Voss and S. Flora, “Spectral Dependence of the Seawater–Air Radiance Transmission Coefficient,” J. Atmos. Ocean. Tech. 34(6), 1203–1205 (2017).
[Crossref]

Fry, E. S.

Goela, P. R. F. C.

S. C. V. Cristina, G. F. Moore, P. R. F. C. Goela, J. D. Icely, and A. Newton, “In situ validation of MERIS marine reflectance off the southwest Iberian Peninsula: assessment of vicarious adjustment and corrections for near-land adjacency,” Int. J. Rem. Sensing 35(6), 2347–2377 (2014).

Gordon, H. R.

H. R. Gordon and K. Ding, “Self shading of in-water optical instruments,” Limnol. Oceanogr. 37(3), 491–500 (1992).
[Crossref]

Greb, S.

Grossi, S.

G. M. Ferrari, M. D. Dowell, S. Grossi, and C. Targa, “Relationship between the optical properties of chromophoric dissolved organic matter and total concentration of dissolved organic carbon in the southern Baltic Sea region,” Mar. Chem. 55(3-4), 299–316 (1996).
[Crossref]

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. Tech. 19(4), 486–515 (2002).
[Crossref]

Icely, J.

G. Zibordi, K. Ruddick, I. Ansko, G. Moore, S. Kratzer, J. Icely, and A. Reinart, “In situ determination of the remote sensing reflectance: an inter-comparison,” Ocean Sci. 8(4), 567–586 (2012).
[Crossref]

Icely, J. D.

S. C. V. Cristina, G. F. Moore, P. R. F. C. Goela, J. D. Icely, and A. Newton, “In situ validation of MERIS marine reflectance off the southwest Iberian Peninsula: assessment of vicarious adjustment and corrections for near-land adjacency,” Int. J. Rem. Sensing 35(6), 2347–2377 (2014).

Ishizaka, J.

Jerlov, N. G.

N. G. Jerlov, “Marine optics,” Elsevier Oceanography Series Vol. 14 (Elsevier, 1976).

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]

Kratzer, S.

J. M. Beltrán-Abaunza, S. Kratzer, and C. Brockmann, “Evaluation of MERIS products from Baltic Sea coastal waters rich in CDOM,” Ocean Sci. 10(3), 377–396 (2014).
[Crossref]

G. Zibordi, K. Ruddick, I. Ansko, G. Moore, S. Kratzer, J. Icely, and A. Reinart, “In situ determination of the remote sensing reflectance: an inter-comparison,” Ocean Sci. 8(4), 567–586 (2012).
[Crossref]

Kutser, T.

T. Kutser, B. Paavel, C. Verpoorter, M. Ligi, T. Soomets, K. Toming, and G. Casal, “Remote sensing of black lakes and using 810 nm reflectance peak for retrieving water quality parameters of optically complex waters,” Remote Sens. 8(6), 497 (2016).
[Crossref]

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]

Kuusk, J.

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. Tech. 19(4), 486–515 (2002).
[Crossref]

Leathers, R. A.

Lee, Z.

Lewis, M.

Ligi, M.

T. Kutser, B. Paavel, C. Verpoorter, M. Ligi, T. Soomets, K. Toming, and G. Casal, “Remote sensing of black lakes and using 810 nm reflectance peak for retrieving water quality parameters of optically complex waters,” Remote Sens. 8(6), 497 (2016).
[Crossref]

Mason, J. D.

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. Tech. 19(4), 486–515 (2002).
[Crossref]

Mobley, C.

Mobley, C. D.

Moore, G.

G. Zibordi, K. Ruddick, I. Ansko, G. Moore, S. Kratzer, J. Icely, and A. Reinart, “In situ determination of the remote sensing reflectance: an inter-comparison,” Ocean Sci. 8(4), 567–586 (2012).
[Crossref]

Moore, G. F.

S. C. V. Cristina, G. F. Moore, P. R. F. C. Goela, J. D. Icely, and A. Newton, “In situ validation of MERIS marine reflectance off the southwest Iberian Peninsula: assessment of vicarious adjustment and corrections for near-land adjacency,” Int. J. Rem. Sensing 35(6), 2347–2377 (2014).

Mueller, J. L.

J. L. Mueller, “In-water radiometric profile measurements and data analysis protocols," Ocean Optics protocols for satellite ocean color sensor validation, Revision 4, NASA/TM-2003-21621/Rev-Vol III, 7–20 (2003).

Newton, A.

S. C. V. Cristina, G. F. Moore, P. R. F. C. Goela, J. D. Icely, and A. Newton, “In situ validation of MERIS marine reflectance off the southwest Iberian Peninsula: assessment of vicarious adjustment and corrections for near-land adjacency,” Int. J. Rem. Sensing 35(6), 2347–2377 (2014).

O’Donnell, D.

Ondrusek, M.

Paavel, B.

T. Kutser, B. Paavel, C. Verpoorter, M. Ligi, T. Soomets, K. Toming, and G. Casal, “Remote sensing of black lakes and using 810 nm reflectance peak for retrieving water quality parameters of optically complex waters,” Remote Sens. 8(6), 497 (2016).
[Crossref]

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.

Piskozub, J.

Pope, R. M.

Reinart, A.

G. Zibordi, K. Ruddick, I. Ansko, G. Moore, S. Kratzer, J. Icely, and A. Reinart, “In situ determination of the remote sensing reflectance: an inter-comparison,” Ocean Sci. 8(4), 567–586 (2012).
[Crossref]

Robinson, I. S.

Ruddick, K.

G. Zibordi, K. Ruddick, I. Ansko, G. Moore, S. Kratzer, J. Icely, and A. Reinart, “In situ determination of the remote sensing reflectance: an inter-comparison,” Ocean Sci. 8(4), 567–586 (2012).
[Crossref]

Sasaki, H.

Schwarz, J. N.

Shang, Z.

Soomets, T.

T. Kutser, B. Paavel, C. Verpoorter, M. Ligi, T. Soomets, K. Toming, and G. Casal, “Remote sensing of black lakes and using 810 nm reflectance peak for retrieving water quality parameters of optically complex waters,” Remote Sens. 8(6), 497 (2016).
[Crossref]

Talone, M.

Tanaka, A.

Targa, C.

G. M. Ferrari, M. D. Dowell, S. Grossi, and C. Targa, “Relationship between the optical properties of chromophoric dissolved organic matter and total concentration of dissolved organic carbon in the southern Baltic Sea region,” Mar. Chem. 55(3-4), 299–316 (1996).
[Crossref]

Tassan, S.

S. Tassan, S. and G, and M. Ferrari, “An alternative approach to absorption measurements of aquatic particles retained on filters,” Limnol. Oceanogr. 40(8), 1358–1368 (1995).
[Crossref]

Toming, K.

T. Kutser, B. Paavel, C. Verpoorter, M. Ligi, T. Soomets, K. Toming, and G. Casal, “Remote sensing of black lakes and using 810 nm reflectance peak for retrieving water quality parameters of optically complex waters,” Remote Sens. 8(6), 497 (2016).
[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]

Verpoorter, C.

T. Kutser, B. Paavel, C. Verpoorter, M. Ligi, T. Soomets, K. Toming, and G. Casal, “Remote sensing of black lakes and using 810 nm reflectance peak for retrieving water quality parameters of optically complex waters,” Remote Sens. 8(6), 497 (2016).
[Crossref]

Voss, K. J.

K. J. Voss and S. Flora, “Spectral Dependence of the Seawater–Air Radiance Transmission Coefficient,” J. Atmos. Ocean. Tech. 34(6), 1203–1205 (2017).
[Crossref]

G. Zibordi and K. J. Voss, “Requirements and strategies for in situ radiometry in support of satellite ocean color,“ in Experimental Methods in the Physical Sciences Vol. 47 (Academic, 2014).

Weeks, A. R.

Wei, J.

Zibordi, G.

M. Talone and G. Zibordi, “Non-linear response of a class of hyper-spectral radiometers,” Metrologia 55(5), 747–758 (2018).
[Crossref]

G. Zibordi, “Experimental evaluation of theoretical sea surface reflectance factors relevant to above-water radiometry,” Opt. Express 24(6), A446–A459 (2016).
[Crossref]

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G. Zibordi, K. Ruddick, I. Ansko, G. Moore, S. Kratzer, J. Icely, and A. Reinart, “In situ determination of the remote sensing reflectance: an inter-comparison,” Ocean Sci. 8(4), 567–586 (2012).
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S. C. V. Cristina, G. F. Moore, P. R. F. C. Goela, J. D. Icely, and A. Newton, “In situ validation of MERIS marine reflectance off the southwest Iberian Peninsula: assessment of vicarious adjustment and corrections for near-land adjacency,” Int. J. Rem. Sensing 35(6), 2347–2377 (2014).

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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. Tech. 19(4), 486–515 (2002).
[Crossref]

G. Zibordi, D. D’Alimonte, and J.-F. Berthon, “An evaluation of depth resolution requirements for optical profiling in coastal waters,” J. Atmos. Ocean. Tech. 21(7), 1059–1073 (2004).
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G. Zibordi, “Immersion factor of in-water radiance sensors: assessment for a class of radiometers,” J. Atmos. Ocean. Tech. 23(2), 302–313 (2006).
[Crossref]

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Figures (11)

Fig. 1.
Fig. 1. Schematics of (a) the Single-Depth Approach (SDA) and of (b) the Skylight-Blocked Approach (SBA). The self-shaded volumes refer to the idealized self-shading solely due to the direct sun light interacting with the bottom components of the two optical systems (i.e., they neglect any 3-D shading contribution from radiometers and shield). The shield-shaded volume refers to the shading by the immersed portion of the shield. The symbol z0 indicates the depth of the optical window of the SDA sensor and of the bottom of the SBA shield. The symbol τs indicates the distance between the optical window for SDA or the bottom of the shield for SBA, and the ideal point at which the field-of-view leaves the self-shaded volume.
Fig. 2.
Fig. 2. Location of the measurement stations supporting the comparison of methods.
Fig. 3.
Fig. 3. Optical Floating System (OFS) equipped with THS, SDA and SBA sensors.
Fig. 4.
Fig. 4. $R_{rs}^{SBA}(\lambda )$ spectra from the 472 SBA quality checked data collected in the Western Black Sea during 25 independent measurement sequences.
Fig. 5.
Fig. 5. (a) Percent differences $\varepsilon (\lambda )$ between the 472 pairs of $L_W^{SBA}(\lambda )$ and $L_W^{SDA}(\lambda )$ spectra qualified for the comparison (the grey lines indicate individual spectra, the red dashed line indicates null differences, the blue dashed line indicates the mean values of $\varepsilon (\lambda )$ and finally the error bars indicate ± 1 σ). (b) Percent differences $\varepsilon (\lambda )$ between the 472 pairs of $L_W^{SBA}(\lambda )$ and $L_W^{SDA}(\lambda )$ samples at selected spectral bands (the colored bars present the distribution of differences while the error bars indicate ± 1 σ).
Fig. 6.
Fig. 6. Scatter plots of $L_W^{SBA}({\lambda _i})$ versus $L_W^{SDA}({\lambda _i})$ at a few bands identified by their center-wavelengths (i.e., 412, 489, 555 and 665 nm) across the visible spectral region. The regression values are represented by the dashed lines. $\bar{\Psi }$ indicates the mean of the $\varepsilon (\lambda )$ values, while $|\bar{\Psi }|$ is the mean of the absolute values of $\varepsilon (\lambda )$.
Fig. 7.
Fig. 7. Correction factors: ${C_{nl}}(\lambda )$ applied for sensor non-linearity; $C_{ss}^{SDA}(\lambda )$ and $C_{ss}^{SBA}(\lambda )$ applied for self-shading and computed accounting for the ${f^{SDA}} \simeq 0.1$ and ${f^{SBA}} \simeq 0.2$ ratios; ${C_{{K_L}}}(\lambda )$ applied for radiance propagation from the depth ${z_0}$ to ${0^ - }$; and finally ${C_{is}}(\lambda )$ applied for radiance attenuation in the shield-shaded water volume. The error bars indicate ± 1 σ with respect to the mean values represented by the continuous thick lines.
Fig. 8.
Fig. 8. Percent differences $\bar{\varepsilon }(\lambda )$ between the $\bar{L}_W^{SBA}(\lambda )$ and $\bar{L}_W^{SDA}(\lambda )$ spectra determined from the averaging of measurements from each individual sequence (the grey lines indicate mean spectra determined from the various measurement sequences, the red dashed line indicates null differences, the blue dashed line indicates the mean of the $\bar{\varepsilon }(\lambda )$ values and finally the error bars indicate ± 1 σ).
Fig. 9.
Fig. 9. Coefficients of variation CV determined for the individual values of $\bar{L}_W^{SBA}(\lambda )$ and $\bar{L}_W^{SDA}(\lambda )$ pairs from each measurement sequence. The blue dashed lines indicate the mean values.
Fig. 10.
Fig. 10. Scatter plot of $\bar{L}_W^{SDA}({\lambda _i})$ versus $L_W^{\mu P}({\lambda _i})$ and of $\bar{L}_W^{SBA}({\lambda _i})$ versus $L_W^{\mu P}({\lambda _i})$, at the µPRO center-wavelengths (i.e., 412, 443, 489, 510, 555 and 665 nm) across the visible spectral region. $\bar{\Psi }^{\prime}$ and $\bar{\Psi }^{\prime\prime}$ indicate the spectrally averaged values of the mean of the unbiased percent differences determined with $\bar{L}_W^{SDA}$ and $L_W^{\mu P}$ or, alternatively with $\bar{L}_W^{SBA}$ and $L_W^{\mu P}$, respectively. $|\bar{\Psi }^{\prime}|$ and $|\bar{\Psi }^{\prime\prime}|$ indicate the corresponding spectrally averaged values of the mean of the absolute unbiased percent differences.
Fig. 11.
Fig. 11. Spectral ratio $L_W^{SBA}(\lambda )/L_u^{SDA}({0^ - },\lambda )$ from the individual measurements qualified for the comparison. The red line indicates the theoretical value of ${t_{wa}}(\lambda )/n_w^2(\lambda )$ while the dashed blue line indicates the mean of the $L_W^{SBA}(\lambda )/L_u^{SDA}({0^ - },\lambda )$ spectral values. The error bars indicate ± 1 σ.

Tables (1)

Tables Icon

Table 1. Minimum, maximum and mean values of quantities characterizing the field radiometric measurements applied in this study. The symbol θ 0 indicates the sun zenith angle, K L ( 490 ) the diffuse attenuation coefficient of upwelling radiance at 490 nm, a ( 490 ) the seawater absorption coefficient, b b ( 490 ) the seawater back-scattering coefficient, I r ( 490 ) the diffuse-to-irradiance ratio, S the salinity and T the water temperature.

Equations (7)

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K L ( λ ) = K L ( λ i ) a ( λ i ) + b b ( λ i ) | λ [ a ( λ ) + b b ( λ ) ] ,
L W S D A ( λ ) = L u ( z 0 , λ ) C s s S D A ( λ , a , I r , θ 0 , R d , f S D A ) C K L ( λ , K L , z 0 ) t w a ( λ ) n w 2 ( λ ) ,
L W S B A ( λ ) = L W ( z 0 , λ ) C s s S B A ( λ , a , I r , R d , f S B A ) C K L ( λ , K L , z 0 ) C i s ( λ , a , b b , z 0 ) C w w ( λ ) ,
ε ( λ ) = 200 L W S B A ( λ ) L W S D A ( λ ) L W S B A ( λ ) + L W S D A ( λ ) .
L W ( λ ) = D N i w ( λ ) C f ( λ ) I f ( λ ) t w a ( λ ) n w 2 ( λ ) ,
L W ( λ ) = D N a w ( λ ) C f ( λ ) t a g ( λ ) t w g ( λ ) t w a ( λ ) .
δ ( λ ) = I f ( λ ) 1 n w 2 ( λ ) t w g ( λ ) t a g ( λ ) t w a 2 ( λ ) ,

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