Abstract

Rayleigh-scattering radiance (Lr) calculations based on the standard algorithm are often associated with significant uncertainties leading to inconsistent water-leaving radiance retrievals, both spatially and temporally across latitudes and altitudes. The uncertainty could result from the use of Rayleigh lookup tables generated for the standard surface atmospheric pressure and hence the Rayleigh optical thickness (ROT) at the specific atmospheric pressure regardless of its daily and seasonal variations. This study presents a new algorithm (hereafter referred to as the refined algorithm) to compute the Rayleigh-scattering radiance that relies on accurate calculations of the ROT as a function of the composition of air (CO2 volume concentration), surface atmospheric pressure and relative air mass for given sun-sensor geometries. As CO2 is well mixed throughout the atmospheric column, the CO2 volume concentrations derived from this study agree well with measurements in different seasons across studied latitudes. Relative air mass has a significant effect on the ROT and that is calculated as a function of apparent sun-sensor zenith angles with the variations in pressure and thermal characteristics of the atmosphere. Thus, the results indicate significant variations of ROT and air mass with location on the earth’s surface and their influence on the Lr, particularly in the UV-Blue region of the spectrum. The refined algorithm for calculating the Lr is tested on several MODIS-Aqua Level 1A data and the relative errors in Rayleigh-scattering radiance and normalized water-leaving radiance (Lwn) retrievals between the refined algorithm and standard (SeaDAS) algorithm are compared using in-situ measurement data collected at MOBY (clear ocean), AERONET (turbid coastal ocean), and NOMAD (clear ocean) sites. The results indicate that the Lr calculated using the SeaDAS algorithm are mostly underestimated and show significant departures with the Lr calculated using the refined algorithm. This departure induced by the SeaDAS algorithm to Lr becomes larger with decreasing wavelength (ΔLr from −2.38% at 412 nm to 1.69% at 678 nm), which causes errors in Lwn retrievals (ΔLwn) of up to 26.48% at 412 nm and 13.34% at 678 nm. The overall improvements in the retrieved Lwn values achieved vary from 56% at 412 nm to 29% at 678nm, which yield similar improvements in Lwn retrievals with lower errors and higher slopes and correlation coefficients when compared with the in-situ Lwn data. These results indicate that the refined algorithm for computation of the Lr can yield more accurate Lwn retrievals and produce spatially and temporally consistent biogeochemical products at different latitudes and altitudes as desired by the scientific community.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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  29. H. J. Nasiha, P. Shanmugam, and R. Sundaravadivelu, “Estimation of sediment settling velocity in estuarine and coastal waters using optical remote sensing data,” Adv. Space Res. 63(11), 3473–3488 (2019).
    [Crossref]
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2019 (1)

H. J. Nasiha, P. Shanmugam, and R. Sundaravadivelu, “Estimation of sediment settling velocity in estuarine and coastal waters using optical remote sensing data,” Adv. Space Res. 63(11), 3473–3488 (2019).
[Crossref]

2018 (1)

T. Varunan and P. Shanmugam, “Use of Landsat 8 data for characterizing dynamic changes in physical and acoustical properties of coastal lagoon and estuarine waters,” Adv. Space Res. 62(9), 2393–2417 (2018).
[Crossref]

2017 (2)

T. Varunan and P. Shanmugam, “An optical tool for quantitative assessment of phycocyanin pigment concentration in cyanobacterial blooms within inland and marine environments,” J. Great Lakes Res. 43(1), 32–49 (2017).
[Crossref]

N. Pahlevan, J. R. Schott, B. A. Franz, G. Zibordi, B. Markham, S. Bailey, C. B. Schaaf, M. Ondrusek, S. Greb, and C. M. Strait, “Landsat 8 remote sensing reflectance (Rrs) products: Evaluations, intercomparisons, and enhancements,” Remote Sens. Environ. 190, 289–301 (2017).
[Crossref]

2015 (2)

J. Zhao, M. Temimi, and H. Ghedira, “Characterization of harmful algal blooms (HABs) in the Arabian Gulf and the Sea of Oman using MERIS fluorescence data,” ISPRS J. Photogramm. Remote Sens. 101, 125–136 (2015).
[Crossref]

C. Tomasi and B. H. Petkov, “Spectral calculations of Rayleigh-scattering optical depth at Arctic and Antarctic sites using a two-term algorithm,” J. Geophys. Res.: Atmos. 120(18), 9514–9538 (2015).
[Crossref]

2014 (3)

A. J. Brown, “Spectral bluing induced by small particles under the Mie and Rayleigh regimes,” Icarus 239, 85–95 (2014).
[Crossref]

R. K. Singh and P. Shanmugam, “Corrigendum to “A novel method for estimation of aerosol radiance and its extrapolation in the atmospheric correction of satellite data over optically complex oceanic waters” [Remote Sensing of Environment 142 (2014) 188–206],” Remote Sens. Environ. 148, 222–223 (2014).
[Crossref]

R. K. Singh and P. Shanmugam, “A novel method for estimation of aerosol radiance and its extrapolation in the atmospheric correction of satellite data over optically complex oceanic waters,” Remote Sens. Environ. 142, 188–206 (2014).
[Crossref]

2012 (1)

K. Ruddick, Q. Vanhellemont, J. Yan, G. Neukermans, G. Wei, and S. Shang, “Variability of suspended particulate matter in the Bohai Sea from the geostationary Ocean Color Imager (GOCI),” Ocean Sci. J. 47(3), 331–345 (2012).
[Crossref]

2011 (2)

P. Shanmugam, “A new bio-optical algorithm for the remote sensing of algal blooms in complex ocean waters,” J. Geophys. Res. 116(C4), C04016 (2011).
[Crossref]

P. Shanmugam, “New models for retrieving and partitioning the colored dissolved organic matter in the global ocean: Implications for remote sensing,” Remote Sens. Environ. 115(6), 1501–1521 (2011).
[Crossref]

2010 (2)

2009 (2)

G. Zibordi, F. Mélin, J.-F. Berthon, B. Holben, I. Slutsker, D. Giles, D. D’Alimonte, D. Vandemark, H. Feng, G. Schuster, B. E. Fabbri, S. Kaitala, and J. Seppälä, “AERONET-OC: A Network for the Validation of Ocean Color Primary Products,” J. Atmos. Ocean. Technol. 26(8), 1634–1651 (2009).
[Crossref]

M. Wang, S. Son, and W. Shi, “Evaluation of MODIS SWIR and NIR-SWIR atmospheric correction algorithms using SeaBASS data,” Remote Sens. Environ. 113(3), 635–644 (2009).
[Crossref]

2006 (2)

Y.-H. Ahn and P. Shanmugam, “Detecting the red tide algal blooms from satellite ocean color observations in optically complex Northeast-Asia Coastal waters,” Remote Sens. Environ. 103(4), 419–437 (2006).
[Crossref]

S. W. Bailey and P. J. Werdell, “A multi-sensor approach for the on-orbit validation of ocean color satellite data products,” Remote Sens. Environ. 102(1-2), 12–23 (2006).
[Crossref]

2005 (2)

M. Wang, “A refinement for the Rayleigh radiance computation with variation of the atmospheric pressure,” Int. J. Remote Sens. 26(24), 5651–5663 (2005).
[Crossref]

C. Tomasi, V. Vitale, B. Petkov, A. Lupi, and A. Cacciari, “Improved algorithm for calculations of Rayleigh-scattering optical depth in standard atmospheres,” Appl. Opt. 44(16), 3320–3341 (2005).
[Crossref]

2001 (1)

P. A. Raymond and J. E. Bauer, “Riverine export of aged terrestrial organic matter to the North Atlantic Ocean,” Nature 409(6819), 497–500 (2001).
[Crossref]

2000 (1)

C. Hu, K. L. Carder, and F. E. Muller-Karger, “Atmospheric Correction of SeaWiFS Imagery over Turbid Coastal Waters,” Remote Sens. Environ. 74(2), 195–206 (2000).
[Crossref]

1999 (1)

B. A. Bodhaine, N. B. Wood, E. G. Dutton, and J. R. Slusser, “On Rayleigh Optical Depth Calculations,” J. Atmos. Ocean. Technol. 16(11), 1854–1861 (1999).
[Crossref]

1998 (2)

H. R. Gordon, “In-Orbit Calibration Strategy for Ocean Color Sensors,” Remote Sens. Environ. 63(3), 265–278 (1998).
[Crossref]

J. E. O’Reilly, S. Maritorena, B. G. Mitchell, D. A. Siegel, K. L. Carder, S. A. Garver, M. Kahru, and C. McClain, “Ocean color chlorophyll algorithms for SeaWiFS,” J. Geophys. Res. 103(C11), 24937–24953 (1998).
[Crossref]

1997 (1)

H. R. Gordon, “Atmospheric correction of ocean color imagery in the Earth Observing System era,” J. Geophys. Res.: Atmos. 102(D14), 17081–17106 (1997).
[Crossref]

1994 (3)

1992 (2)

1990 (1)

1989 (1)

1988 (1)

1984 (2)

M. Nicolet, “On the molecular scattering in the terrestrial atmosphere : An empirical formula for its calculation in the homosphere,” Planet. Space Sci. 32(11), 1467–1468 (1984).
[Crossref]

D. R. Bates, “Rayleigh scattering by air,” Planet. Space Sci. 32(6), 785–790 (1984).
[Crossref]

1983 (1)

L. W. Thomason, B. M. Herman, and J. A. Reagan, “The Effect of Atmospheric Attenuators with Structured Vertical Distributions on Air Mass Determinations and Langley Plot Analyses,” J. Atmos. Sci. 40(7), 1851–1854 (1983).
[Crossref]

1968 (1)

R. J. List, “Smithsonian meteorological tables,” Smithsonian Miscellaneous Collections 114(1), 1–527 (1968).

1966 (1)

B. Edlén, “The Refractive Index of Air,” Metrologia 2(2), 71–80 (1966).
[Crossref]

1957 (1)

Ahn, Y.-H.

Y.-H. Ahn and P. Shanmugam, “Detecting the red tide algal blooms from satellite ocean color observations in optically complex Northeast-Asia Coastal waters,” Remote Sens. Environ. 103(4), 419–437 (2006).
[Crossref]

Antoine, D.

C. Schueler, J. Yoder, D. Antoine, C. Castillo, R. Evans, C. Mengelt, C. Mobley, J. Sarmiento, S. Sathyendranath, D. Siegel, and C. Wilson, “Assessing Requirements for Sustained Ocean Color Research and Observations,” in AIAA SPACE 2011 Conference & Exposition (American Institute of Aeronautics and Astronautics, 2011), pp. 1–7.

Bailey, S.

N. Pahlevan, J. R. Schott, B. A. Franz, G. Zibordi, B. Markham, S. Bailey, C. B. Schaaf, M. Ondrusek, S. Greb, and C. M. Strait, “Landsat 8 remote sensing reflectance (Rrs) products: Evaluations, intercomparisons, and enhancements,” Remote Sens. Environ. 190, 289–301 (2017).
[Crossref]

Bailey, S. W.

S. W. Bailey, B. A. Franz, and P. J. Werdell, “Estimation of near-infrared water-leaving reflectance for satellite ocean color data processing,” Opt. Express 18(7), 7521–7527 (2010).
[Crossref]

S. W. Bailey and P. J. Werdell, “A multi-sensor approach for the on-orbit validation of ocean color satellite data products,” Remote Sens. Environ. 102(1-2), 12–23 (2006).
[Crossref]

Bates, D. R.

D. R. Bates, “Rayleigh scattering by air,” Planet. Space Sci. 32(6), 785–790 (1984).
[Crossref]

Bauer, J. E.

P. A. Raymond and J. E. Bauer, “Riverine export of aged terrestrial organic matter to the North Atlantic Ocean,” Nature 409(6819), 497–500 (2001).
[Crossref]

Berthon, J.-F.

G. Zibordi, F. Mélin, J.-F. Berthon, B. Holben, I. Slutsker, D. Giles, D. D’Alimonte, D. Vandemark, H. Feng, G. Schuster, B. E. Fabbri, S. Kaitala, and J. Seppälä, “AERONET-OC: A Network for the Validation of Ocean Color Primary Products,” J. Atmos. Ocean. Technol. 26(8), 1634–1651 (2009).
[Crossref]

Bodhaine, B. A.

B. A. Bodhaine, N. B. Wood, E. G. Dutton, and J. R. Slusser, “On Rayleigh Optical Depth Calculations,” J. Atmos. Ocean. Technol. 16(11), 1854–1861 (1999).
[Crossref]

Boyer, Jorge A.

F. A. C. Jonathan R, Joseph N. Pennock, Jorge A. Boyer, Richard L. Herrern-Silveira, Terry E. Iverson, and Behzad Mortazavi Whitledgc, “Nutrient Behavior and Phytoplankton Production in Gulf of Mexico Estuaries,” in Biogeochemistry of Gulf of Mexico Estuaries, R. R. T. Thomas, S. Bianchi, and Jonathan R. Pennock, eds. (John Wiley & Sons, Inc., 1999), pp. 109–162.

Brown, A. J.

A. J. Brown, “Spectral bluing induced by small particles under the Mie and Rayleigh regimes,” Icarus 239, 85–95 (2014).
[Crossref]

Brown, J. W.

Cacciari, A.

Carder, K. L.

C. Hu, K. L. Carder, and F. E. Muller-Karger, “Atmospheric Correction of SeaWiFS Imagery over Turbid Coastal Waters,” Remote Sens. Environ. 74(2), 195–206 (2000).
[Crossref]

J. E. O’Reilly, S. Maritorena, B. G. Mitchell, D. A. Siegel, K. L. Carder, S. A. Garver, M. Kahru, and C. McClain, “Ocean color chlorophyll algorithms for SeaWiFS,” J. Geophys. Res. 103(C11), 24937–24953 (1998).
[Crossref]

Castillo, C.

C. Schueler, J. Yoder, D. Antoine, C. Castillo, R. Evans, C. Mengelt, C. Mobley, J. Sarmiento, S. Sathyendranath, D. Siegel, and C. Wilson, “Assessing Requirements for Sustained Ocean Color Research and Observations,” in AIAA SPACE 2011 Conference & Exposition (American Institute of Aeronautics and Astronautics, 2011), pp. 1–7.

D’Alimonte, D.

G. Zibordi, F. Mélin, J.-F. Berthon, B. Holben, I. Slutsker, D. Giles, D. D’Alimonte, D. Vandemark, H. Feng, G. Schuster, B. E. Fabbri, S. Kaitala, and J. Seppälä, “AERONET-OC: A Network for the Validation of Ocean Color Primary Products,” J. Atmos. Ocean. Technol. 26(8), 1634–1651 (2009).
[Crossref]

DeLuisi, J. J.

E. G. Dutton, P. Reddy, S. Ryan, and J. J. DeLuisi, “Features and effects of aerosol optical depth observed at Mauna Loa, Hawaii: 1982–1992,” J. Geophys. Res. 99(D4), 8295–8306 (1994).
[Crossref]

Dutton, E. G.

B. A. Bodhaine, N. B. Wood, E. G. Dutton, and J. R. Slusser, “On Rayleigh Optical Depth Calculations,” J. Atmos. Ocean. Technol. 16(11), 1854–1861 (1999).
[Crossref]

E. G. Dutton, P. Reddy, S. Ryan, and J. J. DeLuisi, “Features and effects of aerosol optical depth observed at Mauna Loa, Hawaii: 1982–1992,” J. Geophys. Res. 99(D4), 8295–8306 (1994).
[Crossref]

Edlén, B.

B. Edlén, “The Refractive Index of Air,” Metrologia 2(2), 71–80 (1966).
[Crossref]

Evans, R.

C. Schueler, J. Yoder, D. Antoine, C. Castillo, R. Evans, C. Mengelt, C. Mobley, J. Sarmiento, S. Sathyendranath, D. Siegel, and C. Wilson, “Assessing Requirements for Sustained Ocean Color Research and Observations,” in AIAA SPACE 2011 Conference & Exposition (American Institute of Aeronautics and Astronautics, 2011), pp. 1–7.

Evans, R. H.

Fabbri, B. E.

G. Zibordi, F. Mélin, J.-F. Berthon, B. Holben, I. Slutsker, D. Giles, D. D’Alimonte, D. Vandemark, H. Feng, G. Schuster, B. E. Fabbri, S. Kaitala, and J. Seppälä, “AERONET-OC: A Network for the Validation of Ocean Color Primary Products,” J. Atmos. Ocean. Technol. 26(8), 1634–1651 (2009).
[Crossref]

Feng, H.

G. Zibordi, F. Mélin, J.-F. Berthon, B. Holben, I. Slutsker, D. Giles, D. D’Alimonte, D. Vandemark, H. Feng, G. Schuster, B. E. Fabbri, S. Kaitala, and J. Seppälä, “AERONET-OC: A Network for the Validation of Ocean Color Primary Products,” J. Atmos. Ocean. Technol. 26(8), 1634–1651 (2009).
[Crossref]

Franz, B. A.

N. Pahlevan, J. R. Schott, B. A. Franz, G. Zibordi, B. Markham, S. Bailey, C. B. Schaaf, M. Ondrusek, S. Greb, and C. M. Strait, “Landsat 8 remote sensing reflectance (Rrs) products: Evaluations, intercomparisons, and enhancements,” Remote Sens. Environ. 190, 289–301 (2017).
[Crossref]

S. W. Bailey, B. A. Franz, and P. J. Werdell, “Estimation of near-infrared water-leaving reflectance for satellite ocean color data processing,” Opt. Express 18(7), 7521–7527 (2010).
[Crossref]

Garver, S. A.

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Figures (13)

Fig. 1.
Fig. 1. Map of in-situ sampling location points in coastal and open ocean waters.
Fig. 2.
Fig. 2. Flowchart depicting the implementation of refined algorithm for computing the Rayleigh-scattering radiance.
Fig. 3.
Fig. 3. Comparison of the monthly NOAA mean CO2 concentration and modelled CO2 concentration as a function of the latitude for the periods 2003 and 2004.
Fig. 4.
Fig. 4. The variation of air mass as a function of the solar and sensor zenith angles.
Fig. 5.
Fig. 5. Comparison of the MODIS-Aqua derived normalized water-leaving radiance (Lwn) spectra retrieved using the refined and SeaDAS algorithms with in-situ measurements in open ocean (MOBY) and coastal water sites (AERONET-OC sites – Thornton_C-power, WaveCIS, and Helsinki). Results from the standard schemes for calculating Rayleigh-scattering radiance and aerosol radiance (SeaDAS-INIR) are also included for clear oceanic waters (MOBY) only for comparison purposes.
Fig. 6.
Fig. 6. Comparison of the mean relative error (MRE) in the MODIS-Aqua derived normalized water-leaving radiance (Lwn) using the SeaDAS and refined algorithms for some key wavelengths (412, 443, 488, 555, and 678 nm) at the selected MOBY and AERONET sites.
Fig. 7.
Fig. 7. Comparison of histograms in mean relative error (MRE) for retrieving the normalized water-leaving radiance (Lwn) from MODIS-Aqua images using the refined and SeaDAS algorithms for some key wavelengths (412, 443, 488, 555, and 678 nm) at the sleected MOBY and AERONET sites.
Fig. 8.
Fig. 8. Comparison of the MODIS-Aqua derived normalized water-leaving radiance (Lwn) spectra retrieved using the refined and SeaDAS algorithms with in-situ measurements (NOMAD) in open ocean waters within Atlantic and Paficic Oceans.
Fig. 9.
Fig. 9. Comparison of the spatial products of Rayleigh-scattering radiance (Lr) and normalized water-leaving radiance (Lwn) derived from MODIS-Aqua data (25 October 2016) using the SeaDAS and refined algorithms in clear oceanic water at the MOBY site (Pacific Ocean near Hawaii) Figs. 9(a)–9(d). For comparison purposes, histogram representations of Lr, Lwn, ΔLr and ΔLwn products derived using the SeaDAS and refined algorithms for the entire MODIS-Aqua scene are shown in the bottom panels.
Fig. 10.
Fig. 10. Comparison of the spatial products of Rayleigh-scattering radiance (Lr) and normalized water-leaving radiance (Lwn) derived from MODIS-Aqua data (17 March 2016) using the SeaDAS and refined algorithms in coastal waters in the North Atlantic Ocean (LISCO ARONET-OC site) Figs. 10(a)–10(d). For comparison purposes, histogram representations of Lr, Lwn, ΔLr and ΔLwn products derived using the SeaDAS and refined algorithms for the entire MODIS-Aqua scene are shown in the bottom panels.
Fig. 11.
Fig. 11. Comparison of the spatial products of Rayleigh-scattering radiance (Lr) and normalized water-leaving radiance (Lwn) derived from MODIS-Aqua data (17 March 2011) using the SeaDAS and refined algorithms in coastal and open-sea waters in the Gulf of Mexico (WaveCIS AERONET-OC site) Figs. 11(a)–11(d). For comparison purposes, histogram representations of Lr, Lwn, ΔLr and ΔLwn products derived using the SeaDAS and refined algorithms for the entire MODIS-Aqua scene are shown in the bottom panels.
Fig. 12.
Fig. 12. Comparison of the spatial products of Rayleigh-scattering radiance (Lr) and normalized water-leaving radiance (Lwn) derived from MODIS-Aqua data (17 January 2019) using the SeaDAS and refined algorithms in the Southern Ocean) Figs. 12(a)–12(d). For comparison purpose, histogram representations of Lr, Lwn, ΔLr and ΔLwn products derived using the SeaDAS and refined algorithms for the entire MODIS-Aqua scene are shown in the bottom panels.
Fig. 13.
Fig. 13. Results for evaluating the effect of ROT/airmass ratios (5%, 10%, 20% And 30%) with the refined algorithm on the Lr and Lwn products in comparison with the results derived from the SeaDAS algorithm using MODIS-Aqua data from Titicaca lake waters and MODIS-Aqua and in-situ matchup data from oceanic cases (MOBY, NOMAD and AERONET-OC).

Tables (2)

Tables Icon

Table 1. The average increment per year of CO2 for each month calculated from 2000 to 2006 (NOAA Greenhouse Gas Marine Boundary Layer Reference).

Tables Icon

Table 2. Statistical comparison of the MODIS-Aqua derived normalized water-leaving radiance (Lwn) using the refined and SeaDAS algorithms and the MOBY/AERONET-OC in-situ data from mostly coastal oceanic water and NOMAD in-situ data from open oceanic waters. Results are shown only for some key wavelengths and errors indicate both standard and random errors along with the correlation coefficients derived from the analysis between the retrieved and measured in-situ Lwn data.

Equations (18)

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L T O A ( λ ) = L r ( λ ) + L a ( λ ) + L r a ( λ ) + T ( λ ) L g ( λ ) + L w c ( λ ) + t ( λ ) L w ( λ ) .
L r ( λ ) = F 0 ( λ ) τ r ( λ ) p r ( θ 0 , θ , λ ) / F 0 ( λ ) τ r ( λ ) p r ( θ 0 , θ , λ ) 4 π 4 π .
p r ( θ 0 , θ , λ ) = { P r ( θ 0 , λ ) + [ ρ ( θ 0 ) + ρ ( θ ) ] P r ( θ 0 + , λ ) } / { P r ( θ 0 , λ ) + [ ρ ( θ 0 ) + ρ ( θ ) ] P r ( θ 0 + , λ ) } cos θ 0 cos θ 0 .
cos θ ± = ± cos θ cos θ 0 sin θ sin θ 0 cos ( ϑ 0 ϑ ) .
P r ( α ) = 3 / 3 4 4 [ 1 + cos 2 α ] .
I ( λ ) I 0 ( λ ) = e ( τ ( λ ) cos θ ) .
τ 0 ( λ ) = 0.008569 λ 4 ( 1 + 0.0113 λ 2 + 0.00013 λ 4 ) .
τ R ( λ ) = τ 0 ( λ ) P P 0 .
L r [ τ r ( λ , P 0 + P ) ] L r [ τ r ( λ , P 0 ) ] = 1 exp [ τ r ( λ , P 0 + P ) / cos θ ] 1 exp [ τ r ( λ , P 0 ) / cos θ ] .
L r [ τ r ( λ , P 0 + P ) ] L r [ τ r ( λ , P 0 ) ] = 1 exp [ C ( λ , M ) τ r ( λ , P 0 + P ) M ] 1 exp [ C ( λ , M ) τ r ( λ , P 0 ) M ] .
L r ( τ r , P ) = L r ( τ 0 ( λ , P 0 ) ) ( P P 0 + C ) .
C = 0.1 × ( τ r M ) .
σ = 24 π 3 ( n s 2 1 ) 2 λ 4 N s 2 ( n s 2 + 2 ) 2 ( 6 + 3 ρ 6 7 ρ ) .
( n 300 1 ) = 8060.51 + 2480990 132.274 λ 2 + 17455.7 39.32957 λ 2 .
( n C O 2 1 ) ( n 300 1 ) = 1 + 0.54 ( C O 2 0.0003 ) .
F ( a i r , C O 2 ) = ( 78.084 × x × F ( N 2 ) + 20.946 × x × F ( O 2 ) + 0.934 × x × C C O 2 × 1.15 ) 100 .
τ ( λ , C O 2 ) = σ P A m a g .
M ( θ ) = 1 P 0 Z 0 Z α P 1 ( n 0 n z ) 2 ( z 0 z ) 2 sin 2 θ .

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