Ioannis Ioannou, Alexander Gilerson, Barry Gross, Fred Moshary, and Samir Ahmed, "Neural network approach to retrieve the inherent optical properties of the ocean from observations of MODIS," Appl. Opt. 50, 3168-3186 (2011)
Retrieving the inherent optical properties of water from remote sensing multispectral reflectance measurements is difficult due to both the complex nature of the forward modeling and the inherent nonlinearity of the inverse problem. In such cases, neural network (NN) techniques have a long history in inverting complex nonlinear systems. The process we adopt utilizes two NNs in parallel. The first NN is used to relate the remote sensing reflectance at available MODIS-visible wavelengths (except the fluorescence channel) to the absorption and backscatter coefficients at (peak of chlorophyll absorption). The second NN separates algal and nonalgal absorption components, outputting the ratio of algal-to-nonalgal absorption. The resulting synthetically trained algorithm is tested using both the NASA Bio-Optical Marine Algorithm Data Set (NOMAD), as well as our own field datasets from the Chesapeake Bay and Long Island Sound, New York. Very good agreement is obtained, with values of 93.75%, 90.67%, and 86.43% for the total, algal, and nonalgal absorption, respectively, for the NOMAD. For our field data, which cover absorbing waters up to about , is 91.87% for the total measured absorption.
P. Jeremy Werdell, Bryan A. Franz, Sean W. Bailey, Gene C. Feldman, Emmanuel Boss, Vittorio E. Brando, Mark Dowell, Takafumi Hirata, Samantha J. Lavender, ZhongPing Lee, Hubert Loisel, Stéphane Maritorena, Fréderic Mélin, Timothy S. Moore, Timothy J. Smyth, David Antoine, Emmanuel Devred, Odile Hembise Fanton d’Andon, and Antoine Mangin Appl. Opt. 52(10) 2019-2037 (2013)
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Values in parentheses for and indicate our field data from the Chesapeake Bay and Long Island Sound, New York. Numbers in parentheses for and indicate the statistics after “fitting” (see text).
Table 5
Statistics of Comparison of the Three Algorithms for a
SAA
QAA-v5
NN
SAA
QAA-v5
NN
QAA-v5
NN
0.9255
0.9200
0.9402
0.9300
0.9195
0.9393
0.9242
0.9375
Slope
0.8352
0.9319
0.8890
0.8137
0.9101
0.8721
0.8222
0.8745
Intercept
0.0405
0.0248
0.1471
0.1531
0.1216
0.1744
0.1665
0.1404
0.2021
0.1638
e
0.4032
0.4226
0.3231
0.4941
0.4673
0.3815
0.5925
0.4581
N
392
392
392
590
590
590
936
936
N is the number of successful retrievals of the SAA.
Table 6
Statistics of Comparison of the Three Algorithms for a
SAA
QAA-v5
NN
SAA
QAA-v5
NN
QAA-v5
NN
0.6793
0.8033
0.8703
0.7741
0.7270
0.8725
0.8048
0.9104
Slope
0.7165
0.8587
0.9971
0.6808
0.7821
0.9863
0.8968
1.0042
Intercept
0.0020
0.0085
0.2998
0.2094
0.1627
0.3451
0.2728
0.1717
0.2577
0.1698
e
0.9944
0.6195
0.4546
1.2137
0.8740
0.4850
0.8101
0.4786
N
383
383
383
567
567
567
882
882
N is the number of successful retrievals of the SAA and QAA.
Table 7
Statistics of Comparison of the Three Algorithms for a
SAA
QAA-v5
NN
SAA
QAA-v5
NN
QAA-v5
NN
0.8939
0.8176
0.8703
0.8735
0.8115
0.8725
0.8099
0.8558
Slope
0.8010
0.8927
0.8161
0.8122
0.8886
0.7854
0.8904
0.7817
Intercept
0.0530
0.0348
0.0185
0.2029
0.2706
0.2058
0.2272
0.2853
0.2436
0.3113
0.3004
e
0.5956
0.8645
0.6061
0.6872
0.9290
0.7521
1.0479
0.9973
N
383
383
383
567
567
567
882
882
N is the number of successful retrievals of the SAA and QAA.
Table 8
Statistics of Comparison of the Three Algorithms for a
SAA
QAA-v5
NN
SAA
QAA-v5
NN
QAA-v5
NN
0.4131
0.4012
0.3441
0.5363
0.5133
0.4954
0.5913
0.6169
Slope
0.4111
0.7802
0.4042
0.4840
0.9431
0.4941
0.9956
0.5656
Intercept
0.0031
0.1730
0.1228
0.1581
0.1401
0.1200
0.1368
0.1207
0.1277
e
0.4895
0.3268
0.4391
0.3807
0.3183
0.3702
0.3205
0.3418
N
96
96
96
153
153
153
211
211
N is the number of successful retrievals of the SAA.
Table 9
Mean and Standard Deviation of the Inputs for the and Network
0.3084
0.2777
0.2430
0.3577
0.4230
0.7375
Table 10
Mean and Standard Deviation of the Inputs for the Network
0.3072
0.2789
0.2447
0.3620
0.4289
0.7389
Table 11
Mean and Standard Deviation of the Outputs in the Simulated Dataset
(0.1441)
1.6355
1.8108
1.1600 (1.5206)
Tables (11)
Table 1
Statistics of Comparison for Figs. 4, 5 without Noisea
0.9946
0.9932
0.9274 (0.9730)
0.9850 (0.9851)
Slope
1.0001
0.9973
1.0109 (1.0240)
1.0172 (1.0149)
Intercept
0.0013
(0.0005)
0.0079 ()
0.0556
0.0583
0.2267 (0.1359)
0.1068 (0.1070)
e
0.1367
0.1438
0.6854 (0.3676)
0.2788 (0.2794)
N
3965
3965
3965 (3686)
3965 (3686)
Values in parentheses indicate the results when is at least 10% of .
Table 2
Statistics of Comparison for Figs. 4, 5 When 10% Noise Is Added at Each a
0.9923
0.9913
0.9188 (0.9645)
0.9823 (0.9824)
Slope
0.9994
0.9967
1.0038 (1.0171)
1.0153 (1.0129)
Intercept
0.0005
0.0061 ()
0.0665
0.0662
0.2382 (0.1543)
0.1155 (0.1158)
e
0.1656
0.1647
0.7304 (0.4266)
0.3046 (0.3055)
N
3965
3965
3965 (3686)
3965 (3686)
Values in parentheses indicate the results when is at least 10% of .
Table 3
Statistics of Comparison for Figs. 4, 5 When 20% Noise Is Added at Each a
0.9863
0.9866
0.8956 (0.9428)
0.9750 (0.9751)
Slope
0.9963
0.9940
0.9813 (0.9966)
1.0098 (1.0076)
Intercept
0.0886
0.0823
0.2675 (0.1937)
0.1363 (0.1366)
e
0.2264
0.2086
0.8515 (0.5620)
0.3687 (0.3698)
N
3965
3965
3965 (3686)
3965 (3686)
The values in parentheses indicate the results when is at least 10% of .
Values in parentheses for and indicate our field data from the Chesapeake Bay and Long Island Sound, New York. Numbers in parentheses for and indicate the statistics after “fitting” (see text).
Table 5
Statistics of Comparison of the Three Algorithms for a
SAA
QAA-v5
NN
SAA
QAA-v5
NN
QAA-v5
NN
0.9255
0.9200
0.9402
0.9300
0.9195
0.9393
0.9242
0.9375
Slope
0.8352
0.9319
0.8890
0.8137
0.9101
0.8721
0.8222
0.8745
Intercept
0.0405
0.0248
0.1471
0.1531
0.1216
0.1744
0.1665
0.1404
0.2021
0.1638
e
0.4032
0.4226
0.3231
0.4941
0.4673
0.3815
0.5925
0.4581
N
392
392
392
590
590
590
936
936
N is the number of successful retrievals of the SAA.
Table 6
Statistics of Comparison of the Three Algorithms for a
SAA
QAA-v5
NN
SAA
QAA-v5
NN
QAA-v5
NN
0.6793
0.8033
0.8703
0.7741
0.7270
0.8725
0.8048
0.9104
Slope
0.7165
0.8587
0.9971
0.6808
0.7821
0.9863
0.8968
1.0042
Intercept
0.0020
0.0085
0.2998
0.2094
0.1627
0.3451
0.2728
0.1717
0.2577
0.1698
e
0.9944
0.6195
0.4546
1.2137
0.8740
0.4850
0.8101
0.4786
N
383
383
383
567
567
567
882
882
N is the number of successful retrievals of the SAA and QAA.
Table 7
Statistics of Comparison of the Three Algorithms for a
SAA
QAA-v5
NN
SAA
QAA-v5
NN
QAA-v5
NN
0.8939
0.8176
0.8703
0.8735
0.8115
0.8725
0.8099
0.8558
Slope
0.8010
0.8927
0.8161
0.8122
0.8886
0.7854
0.8904
0.7817
Intercept
0.0530
0.0348
0.0185
0.2029
0.2706
0.2058
0.2272
0.2853
0.2436
0.3113
0.3004
e
0.5956
0.8645
0.6061
0.6872
0.9290
0.7521
1.0479
0.9973
N
383
383
383
567
567
567
882
882
N is the number of successful retrievals of the SAA and QAA.
Table 8
Statistics of Comparison of the Three Algorithms for a
SAA
QAA-v5
NN
SAA
QAA-v5
NN
QAA-v5
NN
0.4131
0.4012
0.3441
0.5363
0.5133
0.4954
0.5913
0.6169
Slope
0.4111
0.7802
0.4042
0.4840
0.9431
0.4941
0.9956
0.5656
Intercept
0.0031
0.1730
0.1228
0.1581
0.1401
0.1200
0.1368
0.1207
0.1277
e
0.4895
0.3268
0.4391
0.3807
0.3183
0.3702
0.3205
0.3418
N
96
96
96
153
153
153
211
211
N is the number of successful retrievals of the SAA.
Table 9
Mean and Standard Deviation of the Inputs for the and Network
0.3084
0.2777
0.2430
0.3577
0.4230
0.7375
Table 10
Mean and Standard Deviation of the Inputs for the Network
0.3072
0.2789
0.2447
0.3620
0.4289
0.7389
Table 11
Mean and Standard Deviation of the Outputs in the Simulated Dataset