Abstract

The primary mission of ocean color remote sensing is to provide accurate marine bio-optical properties from satellite data. We propose a new algorithm that uses symbolic regression to estimate chlorophyll a (chl a) concentrations from remote sensing reflectance. We compared the accuracy and computational efficiency of the new algorithm to that of the explicit empirical algorithms (OC4v4 and OC4v6), and implicit algorithms based on neural networks or support vector machines (SVM). Results show that the accuracy of the symbolic regression algorithm is higher than that of the OC4 algorithms and comparable to that of implicit algorithms. The improvement is particularly important for high biomass areas (chl a3mgm3) that are often found in optically complex waters. The computational efficiency of the explicit algorithm developed by symbolic regression is comparable to that of the two versions of OC4 algorithms and better than that of implicit algorithms based on SVM. With its good precision and fast processing, the symbolic regression algorithm is a powerful tool for remote sensing of chl a that could be used advantageously in the reprocessing of large datasets.

© 2012 Optical Society of America

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References

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2010 (2)

A. Gitelson, J. Zhou, D. Gurlin, W. Moses, I. Ioannou, and S. Ahmed, Opt. Express 18, 24109 (2010).
[CrossRef]

P. Salyuk, O. Bukin, A. Alexanin, A. Pavlov, A. Mayor, K. Shmirko, D. Akmaykin, and V. Krikun, Int. J. Remote Sens. 31, 4651 (2010).
[CrossRef]

2009 (2)

P. J. Werdell, S. W. Bailey, B. A. Franz, L. W. Harding, G. C. Feldman, and C. R. McClain, Remote Sens. Environ. 113, 1319 (2009).
[CrossRef]

M. Schmidt and H. Lipson, Science 324, 81 (2009).
[CrossRef]

2008 (2)

S. Tang, C. Chen, H. Zhan, J. Zhang, and J. Yang, Int. J. Remote Sens. 29, 6217 (2008).
[CrossRef]

S. Tang, C. Chen, H. Zhan, and T. Zhang, Int. J. Remote Sens. 29, 6227 (2008).
[CrossRef]

2007 (1)

T. Zhang and F. Fell, Limnol. Oceanogr. Meth. 5, 457 (2007).
[CrossRef]

2006 (1)

G. Camps-Valls, L. Gómez-Chova, J. Muñoz-Marí, J. Vila-Francés, J. Amorós-López, and J. Calpe-Maravilla, Remote Sens. Environ. 105, 23 (2006).
[CrossRef]

2005 (1)

P. J. Werdell and S. W. Bailey, Remote Sens. Environ. 98, 122 (2005).
[CrossRef]

2004 (1)

C. R. McClain, G. C. Feldman, and S. B. Hooker, Deep-Sea Res. Part II-Top. Stud. Oceanogr. 51, 5 (2004).
[CrossRef]

2003 (1)

H. Zhan, P. Shi, and C. Chen, IEEE Trans. Geosci. Remote Sens. 41, 2947 (2003).
[CrossRef]

2002 (2)

2001 (1)

H. Zhan, P. Shi, and C. Chen, Chinese Sci. Bull. 46, 158 (2001).
[CrossRef]

1999 (2)

L. E. Keiner and C. W. Brown, Int. J. Remote Sens. 20, 189 (1999).
[CrossRef]

K. L. Carder, F. R. Chen, Z. P. Lee, S. K. Hawes, and D. Kamykowski, J. Geophys. Res. 104, 5403 (1999).
[CrossRef]

1998 (1)

J. E. O’Reilly, S. Maritorena, B. G. Mitchell, D. A. Siegel, K. L. Carder, S. A. Garver, M. Kahru, and C. J. McClain, Geophys. Res. Bull. 103, 24937 (1998).
[CrossRef]

1996 (1)

1994 (1)

R. Doerffer and J. Fischer, J. Geophys. Res. 99, 7457 (1994).
[CrossRef]

1993 (1)

1986 (1)

Ahmed, S.

Akmaykin, D.

P. Salyuk, O. Bukin, A. Alexanin, A. Pavlov, A. Mayor, K. Shmirko, D. Akmaykin, and V. Krikun, Int. J. Remote Sens. 31, 4651 (2010).
[CrossRef]

Alexanin, A.

P. Salyuk, O. Bukin, A. Alexanin, A. Pavlov, A. Mayor, K. Shmirko, D. Akmaykin, and V. Krikun, Int. J. Remote Sens. 31, 4651 (2010).
[CrossRef]

Amorós-López, J.

G. Camps-Valls, L. Gómez-Chova, J. Muñoz-Marí, J. Vila-Francés, J. Amorós-López, and J. Calpe-Maravilla, Remote Sens. Environ. 105, 23 (2006).
[CrossRef]

Arnone, R.

Bailey, S. W.

P. J. Werdell, S. W. Bailey, B. A. Franz, L. W. Harding, G. C. Feldman, and C. R. McClain, Remote Sens. Environ. 113, 1319 (2009).
[CrossRef]

P. J. Werdell and S. W. Bailey, Remote Sens. Environ. 98, 122 (2005).
[CrossRef]

Blaisdell, J. M.

J. W. Campbell, J. M. Blaisdell, and M. Darzi, in NASA Technical Memorandum, S. B. Hooker and E. R. Firestone, eds. (NASA Goddard Space Flight Center, 1995).

Brown, C. W.

L. E. Keiner and C. W. Brown, Int. J. Remote Sens. 20, 189 (1999).
[CrossRef]

Bukin, O.

P. Salyuk, O. Bukin, A. Alexanin, A. Pavlov, A. Mayor, K. Shmirko, D. Akmaykin, and V. Krikun, Int. J. Remote Sens. 31, 4651 (2010).
[CrossRef]

Calpe-Maravilla, J.

G. Camps-Valls, L. Gómez-Chova, J. Muñoz-Marí, J. Vila-Francés, J. Amorós-López, and J. Calpe-Maravilla, Remote Sens. Environ. 105, 23 (2006).
[CrossRef]

Campbell, J. W.

J. W. Campbell, J. M. Blaisdell, and M. Darzi, in NASA Technical Memorandum, S. B. Hooker and E. R. Firestone, eds. (NASA Goddard Space Flight Center, 1995).

Camps-Valls, G.

G. Camps-Valls, L. Gómez-Chova, J. Muñoz-Marí, J. Vila-Francés, J. Amorós-López, and J. Calpe-Maravilla, Remote Sens. Environ. 105, 23 (2006).
[CrossRef]

Carder, K. L.

Z. P. Lee, K. L. Carder, and R. Arnone, Appl. Opt. 41, 5755 (2002).
[CrossRef]

K. L. Carder, F. R. Chen, Z. P. Lee, S. K. Hawes, and D. Kamykowski, J. Geophys. Res. 104, 5403 (1999).
[CrossRef]

J. E. O’Reilly, S. Maritorena, B. G. Mitchell, D. A. Siegel, K. L. Carder, S. A. Garver, M. Kahru, and C. J. McClain, Geophys. Res. Bull. 103, 24937 (1998).
[CrossRef]

Chen, C.

S. Tang, C. Chen, H. Zhan, J. Zhang, and J. Yang, Int. J. Remote Sens. 29, 6217 (2008).
[CrossRef]

S. Tang, C. Chen, H. Zhan, and T. Zhang, Int. J. Remote Sens. 29, 6227 (2008).
[CrossRef]

H. Zhan, P. Shi, and C. Chen, IEEE Trans. Geosci. Remote Sens. 41, 2947 (2003).
[CrossRef]

H. Zhan, P. Shi, and C. Chen, Chinese Sci. Bull. 46, 158 (2001).
[CrossRef]

Chen, F. R.

K. L. Carder, F. R. Chen, Z. P. Lee, S. K. Hawes, and D. Kamykowski, J. Geophys. Res. 104, 5403 (1999).
[CrossRef]

Darzi, M.

J. W. Campbell, J. M. Blaisdell, and M. Darzi, in NASA Technical Memorandum, S. B. Hooker and E. R. Firestone, eds. (NASA Goddard Space Flight Center, 1995).

Doerffer, R.

R. Doerffer and J. Fischer, J. Geophys. Res. 99, 7457 (1994).
[CrossRef]

J. Fischer, R. Doerffer, and H. Grassl, Appl. Opt. 25, 448 (1986).
[CrossRef]

Feldman, G. C.

P. J. Werdell, S. W. Bailey, B. A. Franz, L. W. Harding, G. C. Feldman, and C. R. McClain, Remote Sens. Environ. 113, 1319 (2009).
[CrossRef]

C. R. McClain, G. C. Feldman, and S. B. Hooker, Deep-Sea Res. Part II-Top. Stud. Oceanogr. 51, 5 (2004).
[CrossRef]

Fell, F.

T. Zhang and F. Fell, Limnol. Oceanogr. Meth. 5, 457 (2007).
[CrossRef]

Fischer, J.

R. Doerffer and J. Fischer, J. Geophys. Res. 99, 7457 (1994).
[CrossRef]

J. Fischer, R. Doerffer, and H. Grassl, Appl. Opt. 25, 448 (1986).
[CrossRef]

Franz, B. A.

P. J. Werdell, S. W. Bailey, B. A. Franz, L. W. Harding, G. C. Feldman, and C. R. McClain, Remote Sens. Environ. 113, 1319 (2009).
[CrossRef]

Garver, S. A.

J. E. O’Reilly, S. Maritorena, B. G. Mitchell, D. A. Siegel, K. L. Carder, S. A. Garver, M. Kahru, and C. J. McClain, Geophys. Res. Bull. 103, 24937 (1998).
[CrossRef]

Gentili, B.

Gitelson, A.

Gómez-Chova, L.

G. Camps-Valls, L. Gómez-Chova, J. Muñoz-Marí, J. Vila-Francés, J. Amorós-López, and J. Calpe-Maravilla, Remote Sens. Environ. 105, 23 (2006).
[CrossRef]

Grassl, H.

Gurlin, D.

Harding, L. W.

P. J. Werdell, S. W. Bailey, B. A. Franz, L. W. Harding, G. C. Feldman, and C. R. McClain, Remote Sens. Environ. 113, 1319 (2009).
[CrossRef]

Hawes, S. K.

K. L. Carder, F. R. Chen, Z. P. Lee, S. K. Hawes, and D. Kamykowski, J. Geophys. Res. 104, 5403 (1999).
[CrossRef]

Hooker, S. B.

C. R. McClain, G. C. Feldman, and S. B. Hooker, Deep-Sea Res. Part II-Top. Stud. Oceanogr. 51, 5 (2004).
[CrossRef]

Ioannou, I.

Kahru, M.

J. E. O’Reilly, S. Maritorena, B. G. Mitchell, D. A. Siegel, K. L. Carder, S. A. Garver, M. Kahru, and C. J. McClain, Geophys. Res. Bull. 103, 24937 (1998).
[CrossRef]

Kamykowski, D.

K. L. Carder, F. R. Chen, Z. P. Lee, S. K. Hawes, and D. Kamykowski, J. Geophys. Res. 104, 5403 (1999).
[CrossRef]

Keiner, L. E.

L. E. Keiner and C. W. Brown, Int. J. Remote Sens. 20, 189 (1999).
[CrossRef]

Krikun, V.

P. Salyuk, O. Bukin, A. Alexanin, A. Pavlov, A. Mayor, K. Shmirko, D. Akmaykin, and V. Krikun, Int. J. Remote Sens. 31, 4651 (2010).
[CrossRef]

Lee, Z. P.

Z. P. Lee, K. L. Carder, and R. Arnone, Appl. Opt. 41, 5755 (2002).
[CrossRef]

K. L. Carder, F. R. Chen, Z. P. Lee, S. K. Hawes, and D. Kamykowski, J. Geophys. Res. 104, 5403 (1999).
[CrossRef]

Lipson, H.

M. Schmidt and H. Lipson, Science 324, 81 (2009).
[CrossRef]

Maritorena, S.

S. Maritorena, D. A. Siegel, and A. R. Peterson, Appl. Opt. 41, 2705 (2002).
[CrossRef]

J. E. O’Reilly, S. Maritorena, B. G. Mitchell, D. A. Siegel, K. L. Carder, S. A. Garver, M. Kahru, and C. J. McClain, Geophys. Res. Bull. 103, 24937 (1998).
[CrossRef]

Mayor, A.

P. Salyuk, O. Bukin, A. Alexanin, A. Pavlov, A. Mayor, K. Shmirko, D. Akmaykin, and V. Krikun, Int. J. Remote Sens. 31, 4651 (2010).
[CrossRef]

McClain, C. J.

J. E. O’Reilly, S. Maritorena, B. G. Mitchell, D. A. Siegel, K. L. Carder, S. A. Garver, M. Kahru, and C. J. McClain, Geophys. Res. Bull. 103, 24937 (1998).
[CrossRef]

McClain, C. R.

P. J. Werdell, S. W. Bailey, B. A. Franz, L. W. Harding, G. C. Feldman, and C. R. McClain, Remote Sens. Environ. 113, 1319 (2009).
[CrossRef]

C. R. McClain, G. C. Feldman, and S. B. Hooker, Deep-Sea Res. Part II-Top. Stud. Oceanogr. 51, 5 (2004).
[CrossRef]

Mitchell, B. G.

J. E. O’Reilly, S. Maritorena, B. G. Mitchell, D. A. Siegel, K. L. Carder, S. A. Garver, M. Kahru, and C. J. McClain, Geophys. Res. Bull. 103, 24937 (1998).
[CrossRef]

Morel, A.

Moses, W.

Muñoz-Marí, J.

G. Camps-Valls, L. Gómez-Chova, J. Muñoz-Marí, J. Vila-Francés, J. Amorós-López, and J. Calpe-Maravilla, Remote Sens. Environ. 105, 23 (2006).
[CrossRef]

O’Reilly, J. E.

J. E. O’Reilly, S. Maritorena, B. G. Mitchell, D. A. Siegel, K. L. Carder, S. A. Garver, M. Kahru, and C. J. McClain, Geophys. Res. Bull. 103, 24937 (1998).
[CrossRef]

Pavlov, A.

P. Salyuk, O. Bukin, A. Alexanin, A. Pavlov, A. Mayor, K. Shmirko, D. Akmaykin, and V. Krikun, Int. J. Remote Sens. 31, 4651 (2010).
[CrossRef]

Peterson, A. R.

Salyuk, P.

P. Salyuk, O. Bukin, A. Alexanin, A. Pavlov, A. Mayor, K. Shmirko, D. Akmaykin, and V. Krikun, Int. J. Remote Sens. 31, 4651 (2010).
[CrossRef]

Schmidt, M.

M. Schmidt and H. Lipson, Science 324, 81 (2009).
[CrossRef]

Shi, P.

H. Zhan, P. Shi, and C. Chen, IEEE Trans. Geosci. Remote Sens. 41, 2947 (2003).
[CrossRef]

H. Zhan, P. Shi, and C. Chen, Chinese Sci. Bull. 46, 158 (2001).
[CrossRef]

Shmirko, K.

P. Salyuk, O. Bukin, A. Alexanin, A. Pavlov, A. Mayor, K. Shmirko, D. Akmaykin, and V. Krikun, Int. J. Remote Sens. 31, 4651 (2010).
[CrossRef]

Siegel, D. A.

S. Maritorena, D. A. Siegel, and A. R. Peterson, Appl. Opt. 41, 2705 (2002).
[CrossRef]

J. E. O’Reilly, S. Maritorena, B. G. Mitchell, D. A. Siegel, K. L. Carder, S. A. Garver, M. Kahru, and C. J. McClain, Geophys. Res. Bull. 103, 24937 (1998).
[CrossRef]

Tang, S.

S. Tang, C. Chen, H. Zhan, J. Zhang, and J. Yang, Int. J. Remote Sens. 29, 6217 (2008).
[CrossRef]

S. Tang, C. Chen, H. Zhan, and T. Zhang, Int. J. Remote Sens. 29, 6227 (2008).
[CrossRef]

Vila-Francés, J.

G. Camps-Valls, L. Gómez-Chova, J. Muñoz-Marí, J. Vila-Francés, J. Amorós-López, and J. Calpe-Maravilla, Remote Sens. Environ. 105, 23 (2006).
[CrossRef]

Werdell, P. J.

P. J. Werdell, S. W. Bailey, B. A. Franz, L. W. Harding, G. C. Feldman, and C. R. McClain, Remote Sens. Environ. 113, 1319 (2009).
[CrossRef]

P. J. Werdell and S. W. Bailey, Remote Sens. Environ. 98, 122 (2005).
[CrossRef]

Yang, J.

S. Tang, C. Chen, H. Zhan, J. Zhang, and J. Yang, Int. J. Remote Sens. 29, 6217 (2008).
[CrossRef]

Zhan, H.

S. Tang, C. Chen, H. Zhan, J. Zhang, and J. Yang, Int. J. Remote Sens. 29, 6217 (2008).
[CrossRef]

S. Tang, C. Chen, H. Zhan, and T. Zhang, Int. J. Remote Sens. 29, 6227 (2008).
[CrossRef]

H. Zhan, P. Shi, and C. Chen, IEEE Trans. Geosci. Remote Sens. 41, 2947 (2003).
[CrossRef]

H. Zhan, P. Shi, and C. Chen, Chinese Sci. Bull. 46, 158 (2001).
[CrossRef]

Zhang, J.

S. Tang, C. Chen, H. Zhan, J. Zhang, and J. Yang, Int. J. Remote Sens. 29, 6217 (2008).
[CrossRef]

Zhang, T.

S. Tang, C. Chen, H. Zhan, and T. Zhang, Int. J. Remote Sens. 29, 6227 (2008).
[CrossRef]

T. Zhang and F. Fell, Limnol. Oceanogr. Meth. 5, 457 (2007).
[CrossRef]

Zhou, J.

Appl. Opt. (5)

Chinese Sci. Bull. (1)

H. Zhan, P. Shi, and C. Chen, Chinese Sci. Bull. 46, 158 (2001).
[CrossRef]

Deep-Sea Res. Part II-Top. Stud. Oceanogr. (1)

C. R. McClain, G. C. Feldman, and S. B. Hooker, Deep-Sea Res. Part II-Top. Stud. Oceanogr. 51, 5 (2004).
[CrossRef]

Geophys. Res. Bull. (1)

J. E. O’Reilly, S. Maritorena, B. G. Mitchell, D. A. Siegel, K. L. Carder, S. A. Garver, M. Kahru, and C. J. McClain, Geophys. Res. Bull. 103, 24937 (1998).
[CrossRef]

IEEE Trans. Geosci. Remote Sens. (1)

H. Zhan, P. Shi, and C. Chen, IEEE Trans. Geosci. Remote Sens. 41, 2947 (2003).
[CrossRef]

Int. J. Remote Sens. (4)

S. Tang, C. Chen, H. Zhan, and T. Zhang, Int. J. Remote Sens. 29, 6227 (2008).
[CrossRef]

P. Salyuk, O. Bukin, A. Alexanin, A. Pavlov, A. Mayor, K. Shmirko, D. Akmaykin, and V. Krikun, Int. J. Remote Sens. 31, 4651 (2010).
[CrossRef]

S. Tang, C. Chen, H. Zhan, J. Zhang, and J. Yang, Int. J. Remote Sens. 29, 6217 (2008).
[CrossRef]

L. E. Keiner and C. W. Brown, Int. J. Remote Sens. 20, 189 (1999).
[CrossRef]

J. Geophys. Res. (2)

K. L. Carder, F. R. Chen, Z. P. Lee, S. K. Hawes, and D. Kamykowski, J. Geophys. Res. 104, 5403 (1999).
[CrossRef]

R. Doerffer and J. Fischer, J. Geophys. Res. 99, 7457 (1994).
[CrossRef]

Limnol. Oceanogr. Meth. (1)

T. Zhang and F. Fell, Limnol. Oceanogr. Meth. 5, 457 (2007).
[CrossRef]

Opt. Express (1)

Remote Sens. Environ. (3)

P. J. Werdell, S. W. Bailey, B. A. Franz, L. W. Harding, G. C. Feldman, and C. R. McClain, Remote Sens. Environ. 113, 1319 (2009).
[CrossRef]

G. Camps-Valls, L. Gómez-Chova, J. Muñoz-Marí, J. Vila-Francés, J. Amorós-López, and J. Calpe-Maravilla, Remote Sens. Environ. 105, 23 (2006).
[CrossRef]

P. J. Werdell and S. W. Bailey, Remote Sens. Environ. 98, 122 (2005).
[CrossRef]

Science (1)

M. Schmidt and H. Lipson, Science 324, 81 (2009).
[CrossRef]

Other (1)

J. W. Campbell, J. M. Blaisdell, and M. Darzi, in NASA Technical Memorandum, S. B. Hooker and E. R. Firestone, eds. (NASA Goddard Space Flight Center, 1995).

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Figures (1)

Fig. 1.
Fig. 1.

(A) Scatter plots of retrieved versus measured chl a concentrations using the OC4v4 algorithm, (B) the OC4v6 algorithm, (C) the OC4N algorithm developed in this paper, and (D) the symbolic regression algorithm. Plus symbols represent chl a concentrations 3mgm3 (N=530). Dot symbols represent chl a concentration <3mgm3 (N=1854).

Tables (1)

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Table 1. Estimated Performances of Different Algorithms Using the NOMAD v2 Data Seta

Equations (1)

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log10(C)=3.172×r2×r3+max(0.2952+1.116×r1,0.5811+2.196×r1)r24.613×max(r1,r2,r3,0.1846),

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