Abstract

This paper proposes new inversion algorithms for the estimation of Chlorophyll-a concentration (Chla) and the ocean’s inherent optical properties (IOPs) from the measurement of remote sensing reflectance (Rrs). With in situ data from the NASA bio-optical marine algorithm data set (NOMAD), inversion algorithms were developed by the novel gene expression programming (GEP) approach, which creates, manipulates and selects the most appropriate tree-structured functions based on evolutionary computing. The limitations and validity of the proposed algorithms are evaluated by simulated Rrs spectra with respect to NOMAD, and a closure test for IOPs obtained at a single reference wavelength. The application of GEP-derived algorithms is validated against in situ, synthetic and satellite match-up data sets compiled by NASA and the International Ocean Color Coordinate Group (IOCCG). The new algorithms are able to provide Chla and IOPs retrievals to those derived by other state-of-the-art regression approaches and obtained with the semi- and quasi-analytical algorithms, respectively. In practice, there are no significant differences between GEP, support vector regression, and multilayer perceptron model in terms of the overall performance. The GEP-derived algorithms are successfully applied in processing the images taken by the Sea Wide Field-of-view Sensor (SeaWiFS), generate Chla and IOPs maps which show better details of developing algal blooms, and give more information on the distribution of water constituents between different water bodies.

© 2015 Optical Society of America

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2014 (1)

J. Chen, W. Quan, T. Cui, Q. Song, and C. Lin, “Remote sensing of absorption and scattering coefficient using neural network model: Development, validation, and application,” Remote Sens. Environ. 149, 213–226 (2014).
[Crossref]

2012 (4)

C. Jamet, H. Loisel, and D. Dessailly, “Retrieval of the spectral diffuse attenuation coefficient K-d(λ) in open and coastal ocean waters using a neural network inversion,” J. Geophys. Res.- Oceans 117(C10), C10023 (2012).
[Crossref]

S. Tang, C. Michel, and P. Larouche, “Development of an explicit algorithm for remote sensing estimation of chlorophyll a using symbolic regression,” Opt. Lett. 37(15), 3165–3167 (2012).
[Crossref] [PubMed]

D. Odermatt, A. Gitelson, V. E. Brando, and M. Schaepman, “Review of constituent retrieval in optically deep and complex waters from satellite imagery,” Remote Sens. Environ. 118, 116–126 (2012).
[Crossref]

C. Hu, Z. Lee, and B. Franz, “Chlorophyll a algorithms for oligotrophic oceans: A novel approach based on three-band reflectance difference,” J. Geophys. Res.- Oceans 117(C1), C01011 (2012).
[Crossref]

2011 (2)

M. Z. Hashmi, A. Y. Shamseldin, and B. W. Melville, “Statistical downscaling of watershed precipitation using Gene Expression Programming (GEP),” Environ. Model. Softw. 26(12), 1639–1646 (2011).
[Crossref]

I. Ioannou, A. Gilerson, B. Gross, F. Moshary, and S. Ahmed, “Neural network approach to retrieve the inherent optical properties of the ocean from observations of MODIS,” Appl. Opt. 50(19), 3168–3186 (2011).
[Crossref] [PubMed]

2010 (4)

F. Melin, “Global distribution of the random uncertainty associated with satellite-derived Chla,” IEEE Geosci. Remote Sens. 7(1), 220–224 (2010).
[Crossref]

Z. Lee, R. Arnone, C. Hu, P. J. Werdell, and B. Lubac, “Uncertainties of optical parameters and their propagations in an analytical ocean color inversion algorithm,” Appl. Opt. 49(3), 369–381 (2010).
[Crossref] [PubMed]

A. Efstratiadis and D. Koutsoyiannis, “One decade of multi-objective calibration approaches in hydrological modelling: a review,” Hydrol. Sci. J. 55(1), 58–78 (2010).
[Crossref]

M. S. Salama and F. Shen, “Stochastic inversion of ocean color data using the cross-entropy method,” Opt. Express 18(2), 479–499 (2010).
[PubMed]

2009 (2)

H. T. Shahraiyni, S. B. Shouraki, F. Fell, M. Schaale, J. Fischer, A. Tavakoli, R. Preusker, M. Tajrishy, M. Vatandoust, and H. Khodaparast, “Application of the active learning method to the retrieval of pigment from spectral remote sensing reflectance data,” Int. J. Remote Sens. 30(4), 1045–1065 (2009).
[Crossref]

T. S. Moore, J. W. Campbell, and M. D. Dowell, “A class-based approach to characterizing and mapping the uncertainty of the MODIS ocean chlorophyll product,” Remote Sens. Environ. 113(11), 2424–2430 (2009).
[Crossref]

2008 (1)

C. C. Liu and R. L. Miller, “A spectrum matching method for estimating the chlorophyll-a concentration, CDOM ratio and backscatter fraction from remote sensing of ocean color,” Can. J. Rem. Sens. 34(4), 343–355 (2008).
[Crossref]

2007 (4)

R. Doerffer and H. Schiller, “The MERIS case 2 water algorithm,” Int. J. Remote Sens. 28(3-4), 517–535 (2007).
[Crossref]

E. G. Bekele and J. W. Nicklow, “Multi-objective automatic calibration of SWAT using NSGA-II,” J. Hydrol. (Amst.) 341(3-4), 165–176 (2007).
[Crossref]

C. H. Chang, C. C. Liu, and C. G. Wen, “Integrating semianalytical and genetic algorithms to retrieve the constituents of water bodies from remote sensing of ocean color,” Opt. Express 15(2), 252–265 (2007).
[Crossref] [PubMed]

W. Shi and M. H. Wang, “Detection of turbid waters and absorbing aerosols for the MODIS ocean color data processing,” Remote Sens. Environ. 110(2), 149–161 (2007).
[Crossref]

2006 (3)

G. Zibordi, F. Melin, and J. F. Berthon, “Comparison of SeaWiFS, MODIS and MERIS radiometric products at a coastal site,” Geophys. Res. Lett. 33(6), L06617 (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]

G. Camps-Valls, L. Gomez-Chova, J. Munoz-Mari, J. Vila-Frances, J. Amoros-Lopez, and J. Calpe-Maravilla, “Retrieval of oceanic chlorophyll concentration with relevance vector machines,” Remote Sens. Environ. 105(1), 23–33 (2006).
[Crossref]

2005 (1)

P. J. Werdell and S. W. Bailey, “An improved in-situ bio-optical data set for ocean color algorithm development and satellite data product validation,” Remote Sens. Environ. 98(1), 122–140 (2005).
[Crossref]

2003 (3)

H. G. Zhan, P. Shi, and C. Q. Chen, “Retrieval of oceanic chlorophyll concentration using support vector machines,” IEEE Trans. Geosci. Remote 41(12), 2947–2951 (2003).
[Crossref]

D. D’Alimonte and G. Zibordi, “Phytoplankton determination in an optically complex coastal region using a multilayer perceptron neural network,” IEEE Trans. Geosci. Remote 41(12), 2861–2868 (2003).
[Crossref]

H. G. Zhan, Z. P. Lee, P. Shi, C. Q. Chen, and K. L. Carder, “Retrieval of water optical properties for optically deep waters using genetic algorithms,” IEEE Trans. Geosci. Remote 41(5), 1123–1128 (2003).
[Crossref]

2002 (2)

2001 (3)

P. Cipollini, G. Corsini, M. Diani, and R. Grasso, “Retrieval of sea water optically active parameters from hyperspectral data by means of generalized radial basis function neural networks,” IEEE Trans. Geosci. Remote 39(7), 1508–1524 (2001).
[Crossref]

C. Fonlupt, “Solving the ocean color problem using a genetic programming approach,” Appl. Soft Comput. 1(1), 63–72 (2001).
[Crossref]

C. Ferreira, “Gene expression programming: a new adaptive algorithm for solving problems,” Complex Syst. 13, 87–129 (2001).

2000 (1)

1999 (2)

K. L. Carder, F. R. Chen, Z. P. Lee, S. K. Hawes, and D. Kamykowski, “Semianalytic Moderate-Resolution Imaging Spectrometer algorithms for chlorophyll a and absorption with bio-optical domains based on nitrate-depletion temperatures,” J. Geophys. Res.- Oceans 104(C3), 5403–5421 (1999).
[Crossref]

A. H. Barnard, J. R. V. Zaneveld, and W. S. Pegau, “In situ determination of the remotely sensed reflectance and the absorption coefficient: closure and inversion,” Appl. Opt. 38(24), 5108–5117 (1999).
[Crossref] [PubMed]

1998 (3)

Z. P. Lee, K. L. Carder, R. G. Steward, T. G. Peacock, C. O. Davis, and J. S. Patch, “An empirical algorithm for light absorption by ocean water based on color,” J. Geophys. Res.- Oceans 103(C12), 27967–27978 (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.- Oceans 103(C11), 24937–24953 (1998).
[Crossref]

L. E. Keiner and X. H. Yan, “A neural network model for estimating sea surface chlorophyll and sediments from thematic mapper imagery,” Remote Sens. Environ. 66(2), 153–165 (1998).
[Crossref]

1997 (4)

S. A. Garver and D. A. Siegel, “Inherent optical property inversion of ocean color spectra and its biogeochemical interpretation. 1. Time series from the Sargasso Sea,” J. Geophys. Res.- Oceans 102(C8), 18607–18625 (1997).
[Crossref]

Z. P. Lee, K. L. Carder, R. G. Steward, T. G. Peacock, C. O. Davis, and J. L. Mueller, “Remote sensing reflectance and inherent optical properties of oceanic waters derived from above-water measurements,” Proc. SPIE 2963, 160–166 (1997).
[Crossref]

S. Sathyendranath and T. Platt, “Analytic model of ocean color,” Appl. Opt. 36(12), 2620–2629 (1997).
[Crossref] [PubMed]

R. M. Pope and E. S. Fry, “Absorption spectrum (380-700 nm) of pure water. II. Integrating cavity measurements,” Appl. Opt. 36(33), 8710–8723 (1997).
[Crossref] [PubMed]

1996 (1)

F. E. Hoge and P. E. Lyon, “Satellite retrieval of inherent optical properties by linear matrix inversion of oceanic radiance models: An analysis of model and radiance measurement errors,” J. Geophys. Res.- Oceans 101(C7), 16631–16648 (1996).
[Crossref]

1988 (1)

A. Morel, “Optical modeling of the upper ocean in relation to its biogenous matter content (case I waters).,” J. Geophys. Res.-Oceans 93(C9), 10749–10768 (1988).
[Crossref]

1986 (1)

T. Platt, “Primary production of the ocean water column as a function of surface light intensity: algorithms for remote sensing,” Deep Sea Res. Part I Oceanogr. Res. Pap. 33(2), 149–163 (1986).
[Crossref]

Ahmed, S.

Amoros-Lopez, J.

G. Camps-Valls, L. Gomez-Chova, J. Munoz-Mari, J. Vila-Frances, J. Amoros-Lopez, and J. Calpe-Maravilla, “Retrieval of oceanic chlorophyll concentration with relevance vector machines,” Remote Sens. Environ. 105(1), 23–33 (2006).
[Crossref]

Arnone, R.

Arnone, R. A.

Bailey, S. W.

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]

P. J. Werdell and S. W. Bailey, “An improved in-situ bio-optical data set for ocean color algorithm development and satellite data product validation,” Remote Sens. Environ. 98(1), 122–140 (2005).
[Crossref]

Barnard, A. H.

Bekele, E. G.

E. G. Bekele and J. W. Nicklow, “Multi-objective automatic calibration of SWAT using NSGA-II,” J. Hydrol. (Amst.) 341(3-4), 165–176 (2007).
[Crossref]

Berthon, J. F.

G. Zibordi, F. Melin, and J. F. Berthon, “Comparison of SeaWiFS, MODIS and MERIS radiometric products at a coastal site,” Geophys. Res. Lett. 33(6), L06617 (2006).
[Crossref]

Brando, V. E.

D. Odermatt, A. Gitelson, V. E. Brando, and M. Schaepman, “Review of constituent retrieval in optically deep and complex waters from satellite imagery,” Remote Sens. Environ. 118, 116–126 (2012).
[Crossref]

Calpe-Maravilla, J.

G. Camps-Valls, L. Gomez-Chova, J. Munoz-Mari, J. Vila-Frances, J. Amoros-Lopez, and J. Calpe-Maravilla, “Retrieval of oceanic chlorophyll concentration with relevance vector machines,” Remote Sens. Environ. 105(1), 23–33 (2006).
[Crossref]

Campbell, J. W.

T. S. Moore, J. W. Campbell, and M. D. Dowell, “A class-based approach to characterizing and mapping the uncertainty of the MODIS ocean chlorophyll product,” Remote Sens. Environ. 113(11), 2424–2430 (2009).
[Crossref]

Camps-Valls, G.

G. Camps-Valls, L. Gomez-Chova, J. Munoz-Mari, J. Vila-Frances, J. Amoros-Lopez, and J. Calpe-Maravilla, “Retrieval of oceanic chlorophyll concentration with relevance vector machines,” Remote Sens. Environ. 105(1), 23–33 (2006).
[Crossref]

Carder, K. L.

H. G. Zhan, Z. P. Lee, P. Shi, C. Q. Chen, and K. L. Carder, “Retrieval of water optical properties for optically deep waters using genetic algorithms,” IEEE Trans. Geosci. Remote 41(5), 1123–1128 (2003).
[Crossref]

Z. P. Lee, K. L. Carder, and R. A. Arnone, “Deriving inherent optical properties from water color: a multiband quasi-analytical algorithm for optically deep waters,” Appl. Opt. 41(27), 5755–5772 (2002).
[Crossref] [PubMed]

K. L. Carder, F. R. Chen, Z. P. Lee, S. K. Hawes, and D. Kamykowski, “Semianalytic Moderate-Resolution Imaging Spectrometer algorithms for chlorophyll a and absorption with bio-optical domains based on nitrate-depletion temperatures,” J. Geophys. Res.- Oceans 104(C3), 5403–5421 (1999).
[Crossref]

Z. P. Lee, K. L. Carder, R. G. Steward, T. G. Peacock, C. O. Davis, and J. S. Patch, “An empirical algorithm for light absorption by ocean water based on color,” J. Geophys. Res.- Oceans 103(C12), 27967–27978 (1998).
[Crossref]

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Figures (11)

Fig. 1
Fig. 1 The frequency distributions of six selected IOP data points from the NOMADv2a data set. The variations of coincident observed Rrs(λ) are illustrated as boxplots and labeled on sub-axes.
Fig. 2
Fig. 2 Example of different representations of an individual in GEP, (a) an example of GEP coded linear chromosome with one 13-digit gene, (b) gene expression tree (ET) of the example chromosome, and (c) the corresponding algebraic expression.
Fig. 3
Fig. 3 Example of performing different genetic operations to the genotype of individuals with GEP and the corresponding changes in the phenotype, (a) an example of GEP one = point mutation, (b) an example of genetic transposition operation, and (c) the GEP recombination operation.
Fig. 4
Fig. 4 The procedure of closure evaluation for IOPs derived from aph(443), adg(443) and bbp(555) algorithms.
Fig. 5
Fig. 5 Comparing the retrievals obtained by GEP and selected algorithms to the known Chla and IOPs data from the NOMADv2a data set. (a) GEP- and OC4v6-derived Chla, (b) GEP- and QAAv5-derived aph(443), (c) GEP- and QAAv5-derived adg(443), (d) GEP-derived ap(443), (e) GEP- and QAAv5-derived a(443), and (f) GEP- and QAAv5-derived bbp(555).
Fig. 6
Fig. 6 Comparisons between GEP derived and known IOPs for the NOMADv2a in situ data. (a) ag(443), (b) adg(443), and (c) adg(443) obtained through two different pathways of GEP algorithms.
Fig. 7
Fig. 7 Comparisons between GEP-algorithms derived and known IOPs for the IOCCG synthetic data. (a) Chla, (b) aph(443), (c) adg(443), (d) ap(443), (e) a(443) and (f) bbp(555).
Fig. 8
Fig. 8 Comparisons between GEP-algorithms derived and known IOPs for the IOCCG in situ data. (a) Chla, (b) aph(443), (c) adg(443), and (d) a(443).
Fig. 9
Fig. 9 Comparison between the input reflectance values and those simulated by the retrieved IOPs at the closure evaluated wavelengths.
Fig. 10
Fig. 10 Comparing the retrievals derived by GEP-algorithms to known SeaWiFS match-up data. (a) A combination of HPLC measured Chla and Fluorometric Chla, (b) aph(443), (c) adg(443), (d) ap(443), (e) a(443) and (f) bbp(555).
Fig. 11
Fig. 11 Applications of the GEP-derived algorithms in processing Level-2 SeaWiFS Global Area Coverage data for the Black Sea and part of the Mediterranean (May 4, 2002)” (a) true color image showing bright blooms developed in Black Sea [51], (b) Chla derived by OC4v6 algorithm (standard SeaWiFS product), (c) Chla derived by Eq. (5), (d) aph(443) derived by Eq. (6), (e) adg(443) derived by Eq. (7), and (f) ap(443) from Eq. (8).

Tables (7)

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Table 1 Statistical summary of the bio-optical data for training and validation of the GEP-derived inversion models

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Table 2 Summary of the GEP symbolic regression settings for the development of ocean-color inversion models

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Table 3 Statistical analysis results of Chla and IOPs retrievals obtained by the GEP-derived algorithms

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Table 4 Performance of the GEP-derived and other compared inversion algorithms for Chla and IOPs, using the NOMADv2a in situ data set

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Table 5 Performance of the GEP-derived and other compared inversion algorithms for IOPs, using a synthetic and an in situ data set compiled by IOCCG

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Table 6 Summary of the closure evaluation results for 240 selected Rrs spectra in the IOCCG synthetic data set

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Table 7 Performance of the GEP-derived inversion algorithms for satellite match-ups, using the NOMADv13 in situ data set

Equations (11)

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t=h(n1)+1.
Y ^ =f( d 0 , d 1 ,..., d 4 ).
logRMSE= { i=1 N [log( Y ^ i )log( Y i )] 2 N } 1/2 .
fitness=1000( 1 1+logRMSE )punish.
Chla= ( f 3 ( d 0 d 4 ,0.881 d 4 ) d 1 2 ) 2 +Abs[ f 3 ( f 3 ( d 3 , d 4 ) 0.09 +0.226, 1 f 3 ( d 3 , d 0 ) ) ] + f 2 { f 3 [ f 4 ( max( d 3 , d 1 , d 0 ), d 3 ), d 1 + d 4 ], f 3 [ f 3 ( d 4 ,0.369 ), d 2 ] },
a ph (443)= d 0 ( d 3 d 4 )+0.8423 ( d 0 d 3 ) 2 + f 3 ( max2( f 3 ( d 2 , d 0 ) 2 , d 0 2 ),0.0092 )+ [ 0.2475 ( d 3 d 2 ) 2 ] ( d 1 3 +1.3014) 2 ,
a dg (443)= f 4 ( d 3 0.9756, d 4 d 0 )( d 0 0.0798 f 2 ( d 1 , d 2 ) )+ f 3 ( f 4 ( d 4 , d 2 ) d 0 , d 4 0.0002 d 3 ) + f 3 [ d 1 + f 4 ( d 2 2 d 3 ,-1.0691 d 3 ), d 4 ],
a p (443)= d 2 + f 4 ( 0.0048 10 d 0 -0.016 , d 3 d 0 / d 2 )max3( f 2 [ f 2 (0.0236, d 4 ), f 3 ( d 4 , d 0 ) ], d 1 ,-0.2639 ) + f 3 ( 0.5034, d 4 2 )( 125+ 0.2262 d 2 2 ),
a(443)= ( 0.4344 d 4 max3( d 0 0.005,0.3757 d 4 , d 2 ) ) 2 + f 4 [ 0.0162+0.8085 d 0 , f 4 ( 2 d 3 , f 2 ( d 2 , d 0 ) ) ] and + f 4 [ f 1 ( d 4 2 d 0 ,max2( d 2 ,0.0068) ), f 2 ( d 3 , d 2 )+max3( d 4 , d 2 ,0.0071) ],
b b p (555)= d 4 f 4 [ d 1 , f 3 ( d 0 d 3 , f 3 ( d 2 , d 4 ) ) ] 2 + f 4 [ f 2 (0.0043, d 1 ), f 2 ( d 3 ,0.003) ] 2 + f 3 [ max3( d 1 , d 3 ,0.0035), 10 d 1 ]+ f 4 [ f 4 ( ln( d 4 )+2.3932,0.0021 ),-0.6994 d 4 d 0 + d 1 ].
a(λ)= a w (λ)+ a ph (λ)+ a d (λ)+ a g (λ)= a w (λ)+ a ph (λ)+ a dg (λ).

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