Deriving ocean color products using neural networks

Remote Sensing of Environment 134 (2013) 78–91

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Deriving ocean color products using neural networks Ioannis Ioannou, Alexander Gilerson, Barry Gross, Fred Moshary, Samir Ahmed ⁎ Optical Remote Sensing Laboratory, Department of Electrical Engineering, City University of New York, New York, New York, 10031, USA

a r t i c l e

i n f o

Article history: Received 8 August 2012 Received in revised form 28 January 2013 Accepted 18 February 2013 Available online 25 March 2013 Keywords: Ocean color Neural network Inversion MODIS Absorption Chlorophyll CDOM NAP

a b s t r a c t In this paper we develop a neural network (NN) algorithm for retrieving inherent optical properties (IOP) from above water remote sensing reflectances (Rrs) at available MODIS (or similar satellite) wavelengths. In previous work we used Hydrolight5 simulations of Rrs with widely varying globally representative constituent physical parameters as a training basis to develop a neural network algorithm, which, using the Rrs at the MODIS visible wavelengths (412, 443, 488, 531, 547 and 667 nm) as input, retrieves the in-water particulate backscattering (bbp), phytoplankton (aph) and non-phytoplankton (adg) absorption coefficients at 443 nm. In this work, using the same dataset, we develop a NN which takes these same Rrs as input, and produces an output which is used to separate the non-phytoplankton absorption coefficient (adg) at 443 nm into dissolved (ag) and particulate (adm) components. We then apply this synthetically trained algorithm to the NASA bio-Optical Marine Algorithm Data set (NOMAD) Rrs to retrieve IOP at 443 nm, with the measured NOMAD and retrieved IOP values showing good agreement. These retrieved IOP along with their related Rrs values are then used to train an additional NN that produces chlorophyll concentration [Chl] as output. It is shown that these [Chl] values are retrieved more accurately when compared with ones retrieved with a similar approach which does not use IOP as input, as well as with those derived using the MODIS OC3 algorithm. © 2013 Elsevier Inc. All rights reserved.

1. Introduction Relating water leaving remote sensing reflectance (Gordon & Morel, 1983), Rrs (refer to Table 1 for abbreviation list), an apparent optical property (AOP), to inherent optical properties (IOP) (Preisendorfer, 1976; Tyler & Preisendorfer, 1962), (i.e. absorption, scattering coefficients) of interest is important for improving estimations of concentrations of chlorophyll, [Chl], color dissolved organic matter, CDOM (often referred to as gelbstoff), and concentrations of non-phytoplankton particulates, [NAP]. These constituents co-vary in case 1 (Morel & Prieur, 1977) waters and adequate retrieval of the desired properties such as [Chl] can be achieved with simple empirical algorithms (Gordon et al., 1983; Lee et al., 1998; Loisel et al., 2001; Morel & Prieur, 1977; O'Reilly et al., 1998; Sathyendranath et al., 1994; Sydor et al., 1998). In case 2 waters (Morel & Prieur, 1977), however, where constituents can vary independently, simple empirical algorithm estimates result in significantly increased uncertainty. Thus, simple empirical algorithms are generally limited to regional scales where the underlying water characteristics are more uniform, and should not be used for global retrieval (Le et al., 2013).

⁎ Corresponding author. Tel.: +1 212 650 7250. E-mail address: [email protected] (S. Ahmed). 0034-4257/$ – see front matter © 2013 Elsevier Inc. All rights reserved. http://dx.doi.org/10.1016/j.rse.2013.02.015

To address the complexity of case 2 waters, semi-analytical oceancolor inversion algorithms, SAA (Carder et al., 1999; Garver & Siegel, 1997; Hoge & Lyon, 1996; Roesler & Perry, 1995; Wang et al., 2005), are often used. These algorithms utilize approximate solutions of the radiative transfer equation, (RTE), (analytical part) together with assumptions about the spectral shapes of IOP (empirical part). Unlike purely empirical algorithms, SAA's are generally less sensitive to disparate geographical regions or water type. The performance of these algorithms, however, relies on the correct modeling of the RTE and on accurate spectral models for the absorption and scattering coefficients of each individual constituent present in the water. Because these are not in general known accurately, retrievals are not always successful. Since the direct use of a purely RTE approach is hindered by complexity and lack of underlying physical models, empirical data driven models are still a good choice if the underlying characteristics of the water properties can be assimilated into the algorithms. One possible method in this direction is the application of a multilayer perceptron neural network (MLPNN) (Bishop, 1995), which we will hereafter denote as neural network (NN). NN based algorithms are usually designed to relate the reflectance measured by an above water sensor to the desired property to be retrieved. In this context, algorithms in have been proposed for the processing of data from SeaWiFS (Dzwonkowski & Yan, 2005; Gross et al., 1999, 2000; Jamet et al., 2012; Keiner & Brown, 1999), MODIS (Ioannou et al., 2011), MERIS (Buckton et al., 1999; D'Alimonte et al., 2012; Doerffer & Schiller, 2007; Dransfeld

I. Ioannou et al. / Remote Sensing of Environment 134 (2013) 78–91 Table 1 Abbreviation list. Symbol adm

Description

Absorption coefficient due to non-phytoplankton particulates ag Absorption coefficient due to dissolved substances adg Absorption coefficient due to non-phytoplankton particulates and dissolved substances, adm + ag aph Absorption coefficient due to phytoplankton ap Absorption coefficient due to particulates, aph + adm apg Absorption coefficient due to particulates and dissolved substances aw Absorption coefficient due to water a Absorption coefficient (total), aph + ag + adm + aw AOP Apparent optical properties bbp Backscattering coefficient due to particulates bbw Backscattering coefficient due to water bb Backscattering coefficient (total), bbp + bbw [Chl] Chlorophyll concentration CDOM Color dissolved organic matter ε Uniform random noise [−1,1] e Linear percentage error Down welling irradiance Ed HPLC High-performance liquid chromatography IOP Inherent optical properties IOP NN [Chl] NN deriving [Chl] from Rrs and inverted IOP as inputs Kd Diffuse attenuation coefficient Lw Water leaving radiance MBR Maximum band ratio MLPNN Multi Layer perceptron neural network N Number of points [NAP] Non-phytoplankton particulate concentration NN Neural network NN [Chl] NN deriving [Chl] from Rrs as inputs NOMAD NASA bio-Optical Marine Algorithm Data set OC Ocean color OC3 [Chl] Chlorophyll concentration derived using MODIS algorithm (O'Reilly et al., 1998) RTE Radiative transfer equation RMSElog10 Root mean square error of the log10 of the values Rrs Above-surface remote-sensing reflectance Raadm ð443Þ Ratio of non-phytoplankton particulate to g dissolved absorption coefficient at 443 nm a ð443Þ Ratio of phytoplankton to non-phytoplankton Raph dg absorption coefficient at 443 nm SPM Suspended particulate matter SSA Semi-analytical algorithm SSD Sum square difference μ Mean value σ Standard deviation

Unit m−1 m−1 m−1 m−1 m−1 m−1 m−1 m−1

m−1 m−1 m−1 mg/m3 ppm

mW/cm2/um

m−1 mW/cm2/um/sr1

g/m3

sr−1 Dimensionless Dimensionless g/m3

et al., 2004, 2006; Schiller & Doerffer, 2005; Vilas et al., 2011) and OCTS (Tanaka et al., 2004). These NNs rely on Rrs measured at several wavelengths for estimating ocean color data products. Typical outcomes of such retrievals are backscattering and absorption coefficients which include the total absorption and its components: the phytoplankton and non-phytoplankton absorption coefficients (Ioannou et al., 2011; Lee et al., 2002). Unfortunately, further separation of the non-phytoplankton absorption coefficient, adg, into its two independent components, ag, due to dissolved matter and, adm, due to non-phytoplankton particulates is difficult because of the similar absorbing spectral characteristics of these substances. The major difference in the optical features of these two components arises from their scattering characteristics, since the dissolved component is an insignificant scatterer, whereas the non-phytoplankton particulates are, typically, significant contributors to the scattering in sea water. However the separation of these components would have significant benefits.

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For example, isolating ag should improve our ability to better estimate, at least locally (Mannino et al., 2008; Rochelle-Newall & Fisher, 2002), the dissolved organic carbon (DOC). As seen in previous studies (Babin et al., 2003b) adm is very well related to the suspended particulate matter (SPM) and a stronger relationship should be observable between adm and [NAP]. When representing inorganic particles, [NAP] can be used to delineate river plumes, and can also be used to point to regions of increased wave turbulence from natural events (Gould et al., 2002). Attempts to separate adg into ag and adm were previously reported and were based on estimating the CDOM component from the total absorption in a purely empirical manner (Gould et al., 2002). The total absorption used in the algorithm, could then either be directly measured, or retrieved remotely from Rrs. Another method for isolating the CDOM absorption is that of estimating the particulate absorption through the Rrs derived backscattering (Kempeneers et al., 2005; Lee, 1994; Zhu et al., 2011). Although empirical, these techniques exploit the main difference of these two substances - their scattering characteristics. A combination of using backscattering and total absorption in the blue wavelengths to derive ag was recently shown in a study (Dong et al., 2013). There the absorption and backscattering at the required wavelength can be measured directly or derived using Rrs and inversion algorithms. Further motivating the isolation of the different components, is that it is well understood that changes in CDOM and [NAP] will significantly impact estimation of [Chl] by the traditional band ratio algorithms (MBR) (O'Reilly et al., 1998). Thus the high variability of these parameters especially in the coastal regions needs to be taken into consideration when estimating [Chl]. In this paper we extend our recent work (Ioannou et al., 2011), where we developed 2 neural networks to retrieve bb, aph and adg at 443 nm. We now develop a new NN to separate adg into ag and adm components. In addition, [Chl] is also estimated using an additional NN. These networks are trained and tested on synthetic and field data sets that represent well the global variability of these parameters.

2. Methods 2.1. Multilayer perceptron neural network (MLPNN) The multilayer perceptron neural network (MLPNN) (Bishop, 1995) was implemented for the retrieval of all parameters in this work. An MLPNN is a feed forward network that has been used in many disciplines mainly because of its aptitude to approximate the transfer function between a given set of input and the equivalent output data. An MLPNN consists of computational elements, named neurons (often called ‘nodes’), prearranged in several layers that are interrelated in a feed forward manner, so that every neuron of a layer is simply connected to the neurons of the directly subsequent layer, and has no associations to neurons in the preceding layers. A typical MLPNN configuration consists of an input layer, intermediary or hidden layer(s) and an output layer. The first is used to distribute the input into the network, without any processing. The neurons in the hidden and output layers transform their input signal by an activation function (we used the hyperbolic tangent sigmoid transfer function). Once the MLPNN architecture, number of hidden layers and number of neurons, is decided, the association between the input and the output ultimately depends on the weight values associated with each connection. These values are established by a supervised learning technique, using a priori information about the actual output that corresponds to a set of input data. The network is adjusted, so that the optimum estimate to the actual output is achieved. The weights are iteration adjusted to minimize an error function, computed as the sum square difference (SSD) between the model and the real outputs. A back-propagation learning procedure was used: the learning occurs backwards, layer by layer in a

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looping pattern, starting with the output layer and ending with the input layer. 2.2. Optimization algorithm: Bayesian Regularization To minimize the SSD, the Levenberg–Marquardt optimization with Bayesian Regularization was used in this study (Foresee & Hagan, 1997; Levenberg, 1944; Mackay, 1992; Marquardt, 1963). The algorithm combines Levenberg–Marquardt, a combination of steepest descent and Gauss–Newton method, and regulates the network with the probabilistic approach of Bayes' rule in order to minimize the combination of squared errors and weights and determine the correct combination so as to create a network which generalizes well. Once these criteria are met, it automatically ends the training. Bayesian Regularized neural networks are more robust than standard back-propagation nets and can reduce or eliminate the need of lengthy cross validation (Livingstone, 2009). They are hard to over-train, since verification procedures provide an objective criterion for ending the training and remove the need for a separate validation set to detect the onset of over-training (Livingstone, 2009). They are also difficult to over-fit, because they compute and train only on the effective number of parameters, essentially the number of non-trivial weights in the trained neural network (Livingstone, 2009). This is considerably fewer than the number of weights in a standard fully connected back-propagation net. Bayesian networks basically integrate Occam's razor (Mackay, 1992), routinely and optimally penalize extremely complex models. Bayesian nets are also insensitive to the architecture of the network as long as the necessary minimal architecture has been provided (Livingstone, 2009). The exact algorithm, with the default parameters that were used, can be found in the NN toolbox of MATLAB 7.6.0 (2008a) and is a direct implementation of previous work (Foresee & Hagan, 1997). 2.3. Data transformation and standardization The inputs and outputs of each network were transformed into their log domain and standardized (Lawrence, 1991) by subtracting the mean and dividing by the standard deviation before the training stage. 2.4. IOP product derivation Our extended NN algorithm is based on the synthetic dataset (Ioannou et al., 2011) and is illustrated in Fig. 1. It utilizes three

NNs (previously developed NN-I, NN-II and new NN-III) working in parallel to derive, from the measured Rrs, the following: the combined particulate and dissolved absorption, apg, the particulate backscattering, bbp, at 443 nm (NN-I), the ratio of phytoplankton to a non-phytoplankton absorption at 443 nm, Raph ð443Þ (NN-II), and the dg ratio of non-phytoplankton particulate absorption to dissolved absorption at 443 nm, Raadm ð443Þ (NN-III). Using this information, we g can subsequently analytically obtain bbp, aph, adm, and ag at 443 nm. As can be seen from the order of retrievals, products can rank from level 1 to level 3, where each level depends on the previous product(s) and therefore is retrieved with higher uncertainty. The process for retrieving level 1 and level 2 data was presented in previous work (Ioannou et al., 2011). The process to derive the level 3 adm and ag from level 2 data is presented here. 2.5. Deriving chlorophyll concentration It is well understood, and can be observed in this study, that when one of the IOP dominates the water optical properties, retrieval of the additional properties becomes a predicament and it is usually erroneous. To address this issue, an additional NN is trained to derive [Chl] using the NASA bio-Optical Marine Algorithm Data set (NOMAD) (Werdell & Bailey, 2005) by combining previously derived IOP values of bbp, aph, adm, and ag at 443 nm as described in Section 2.4 with already existing Rrs measurements, and thus train a network to derive the in-situ [Chl] using the NOMAD. In this way when the aph is overestimated due to inversion limitations arising from excessive adm or ag, the network will be able to better address this issue and improve retrieval accuracy. 3. Data 3.1. Simulated data set The full description of the synthetic data set that was used in training and testing procedures was described in a previous study (Ioannou et al., 2011). It includes 9000 reflectance spectra simulated using Hydrolight5 (Mobley & Sundman, 2008) with 1 nm resolution for all observable natural water conditions. The range of parameters is: [Chl] = 0.02 ~ 70 mg/m 3, ag(412) = 10 −3 ~ 6 m −1, [NAP] = 0.02–50 g/m 3. The specific phytoplankton absorption spectral distributions were modeled as described in a previous study (Ciotti et al., 2002) and are linearly associated with [Chl] for concentrations greater 1 mg/m 3 and as [Chl] 0.626 for concentrations less than 1 mg/m 3. The range and variability of IOP used in our bio-optical modeling is well represented in the literature (Babin et al., 2003a, 2003b; Bricaud et al., 1995; Lee et al., 2002; Mobley & Sundman, 2008; Morel & Maritorena, 2001; Morel et al., 2007; Oishi et al., 2002; Stramski et al., 2001). Pure water absorption (Pope & Fry, 1997) and scattering (Morel, 1974) properties are well established. Solar input was simulated using the Gregg and Carder model for a cloud-free sky (Gregg & Carder, 1990). 3.2. Field data set (NOMAD)

Fig. 1. Algorithm description and levels of products.

As we mentioned earlier, the field data set we used in this study is NOMAD. For AOP we used the available water leaving radiance measurements, Lw, together with coincident downwelling irradiance measurements Ed at 411 nm, 443 nm, 489 nm, 531 nm, 550 nm, 555 nm, 665 nm and 670 nm (which are close to bands available on the different ocean color sensors). Normalizing Lw with Ed we obtain Rrs, the basis of most inversion algorithms. Two supplementary NNs are trained and used to relate Rrs measurements at 488 and 555 nm (available in most measurements in NOMAD) to the remote sensing reflectance measurements at 531 and 547 nm (available from a

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limited number of records) respectively, thereby implementing a robust NN based interpolation that can be used when different satellite channels are used. In this case, these additional NN components assisted in increasing the number of matchups between Rrs and water parameters, including [Chl], in the NOMAD. For a detailed description of these NNs we refer the reader to the Appendix. For the in-situ IOP, we used all available values for ap, adm and ag for which a set of Rrs was also available. With IOP being purely additive properties, aph is obtained by subtracting adm from ap. Both high-performance liquid chromatography (HPLC) and the fluorometric [Chl] values were used for available sets of Rrs measurements. For the cases when both HPLC and fluorometric [Chl] were available, both measurements were used as independent inputs; averaging them does not necessarily improve the data quality. Eliminating these points would have reduced our data set by 646 measurements. In this manner we have created a Rrs to [Chl] matchup of 3288 measurements. 3.3. Satellite data To illustrate our results on satellite data, we applied our algorithm to MODIS level 2 data of the Mid-Atlantic Bight. The image is directly downloadable from the NASA Ocean Color website (http://oceancolor.

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gsfc.nasa.gov) for March 14, 2012 (file#A2012074180000.L2_LAC). We choose this region as it represents a good example, since this region covers all the range of water types, from clear to turbid. Before analyzing the image, pixels with negative reflectance data were eliminated.

4. Deriving adm and ag at 443 nm 4.1. Training: deriving adm and ag using simulated data set The NN considered in this section (Fig. 1, NN-III), following the development of NN-I and NN-II in (Ioannou et al., 2011), is designed to generate Raadm ð443Þ from the visible Rrs spectral bands of the MODIS g sensor (412, 443, 488, 531, 547 and 667 nm). With this information and the previous estimation of adg(443), adm(443) can be analytically ð443Þ into adm ð443Þ ¼ adg ð443Þ= determined by substituting Raadm g   adm 1 þ 1=Rag ð443Þ , and ag(443) is then given by subtracting adm(443) from adg(443). This NN-III is a one layer network with 6 neurons at the hidden layer. We choose to use this simple form of network to avoid over-fitting which significantly affects the generalization capabilities of any NN algorithm. The network was trained using 35% of the simulated data set of 9000 records. Noise, ε (up to +/−30%) was

Fig. 2. Performance of the NN on the part of our simulated data set that was not used in the training stage. These figures show the inverted adm(443) m−1 (left column) and ag(443) m−1 (right column) plotted against the “known” values for these parameters from our simulated data set. Noise levels, ε, up to 30% (the top row is ε = 0%) were added at each Rrs. Gray dots indicate cases where adm(443) is less than 10% of ag(443) or vice versa. Corresponding statistics for each parameter for all noise levels are shown in Tables 2 and 3.

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Table 2 Statistics of comparison for Fig. 2 for adm(443)a. ε

0%

10%

20%

30%

R2 Slope Intercept RMSElog10 e N

0.8902 (0.9472) 1.0346(1.0134) −0.2327(−0.0685) 0.3668(0.2302) 1.3269(0.6991) 2439(1962)

0.8881(0.9454) 1.0340(1.0131) −0.2299(−0.0637) 0.3689(0.2335) 1.3381(0.7120) 2439(1962)

0.8821(0.9399) 1.0317(1.0108) −0.2378(−0.0704) 0.3770(0.2443) 1.3820(0.7553) 2439(1962)

0.8722(0.9303) 1.0147(0.9948) −0.2929(−0.1207) 0.3893(0.2625) 1.4505(0.8303) 2439(1962)

a

The values in parenthesis indicate the results when adm(443) is at least 10% of ag(443) or vice versa. The noise, ε that was added to the reflectance is indicated in the first row.

Table 3 Statistics of comparison for Fig. 2 for ag(443)a. ε

0%

10%

20%

30%

R2 Slope Intercept RMSElog10 e N

0.9215(0.9493) 1.0131(1.0269) −0.0648(−0.0406) 0.2450(0.2060) 0.7581(0.6069) 2439(1962)

0.9199(0.9472) 1.0118(1.0255) −0.0588(−0.0334) 0.2467(0.2089) 0.7649(0.6175) 2439(1962)

0.9107(0.9361) 1.0076(1.0205) −0.0692(−0.0443) 0.2602(0.2286) 0.8203(0.6926) 2439(1962)

0.8959(0.9210) 0.9821(0.9964) −0.1197(−0.0921) 0.2803(0.2522) 0.9067(0.7872) 2439(1962)

a

The values in parentheses indicate the results when adm(443) is at least 10% of ag(443) or vice versa. The noise, ε that was added to the reflectance is indicated in the first row.

added to the inputs to improve the algorithm generalization capabilities. The training data range of our simulated data set was restricted during the training so that the adm(443) is at least 10% of ag(443) or vice

versa, ensuring that sufficient signal features will occur to permit inversion. Nevertheless, when testing the algorithm in the next Section 4.2, we show the behavior of our algorithm for the omitted cases.

Fig. 3. NN derived and in-situ aph (443) (A), ag (443) (B), adm (443) (C), and ap (443) (D).

I. Ioannou et al. / Remote Sensing of Environment 134 (2013) 78–91

4.2. Testing: evaluating adm and ag on simulated data set

Table 4 Statistics of comparison for Fig. 2 for ag(443).

We evaluate the NN estimations by calculating the coefficient of determination, R 2, slope and intercept, root mean square error in the log10,  RMSElog10 ¼

1 N 2 ∑ ½ log10 ðx^i Þ− log10 ðxi Þ N i¼1

1 2

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ð1Þ

Dong et al. (2013) R2 Slope intercept RMSElog10 E N

0.7407 0.8427 −0.1791 0.3053 1.0195 949

Zhu et al. (2011) 0.7002 0.7879 −0.2691 0.3378 1.1765 949

This study 0.7712 0.7731 −0.2891 0.3100 1.0418 949

and linear percentage error, e, where e ¼ 10

RMSE log10

−1:

ð2Þ

The performance of the NN for the derivation of adm(443) and ag(443) is first evaluated on the synthetic data set that was not used during the training. Excluding all the data that were used for the training phase of NN-I and NN-II (Ioannou et al., 2011) and NN-III described

here, we have a total of 2439 total points left for testing, of which 1962 points meet the criterion of our training (the non-phytoplankton particulate absorption being equal to at least 10% of the dissolved absorption at 443 nm or vice versa). Using the output of this network together with the retrieved non-phytoplankton absorption (Ioannou et al., 2011), we retrieve the non-phytoplankton particulate and dissolved absorption

Fig. 4. Derived vs in-situ ag (443) (left column), and adm (443) (right column). Absorptions were derived using (Dong et al., 2013) (upper row), (Zhu et al., 2011) (middle row), and this study (last row). Statistics are provided in Tables 4 and 5.

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4.3. Testing: evaluating adm and ag on NOMAD

Table 5 Statistics of comparison for Fig. 2 for adm(443). Dong et al. (2013) R2 Slope intercept RMSElog10 E N

0.8705 1.1273 0.2294 0.2874 0.9382 1040

Zhu et al. (2011) 0.7621 0.7207 −0.0030 0.8576 6.2047 1040

This study 0.8733 1.0012 −0.1194 0.2985 0.9886 1040

coefficients at 443 nm with R2 of 0.89 and 0.92, RSMElog10 of 0.36 and 0.24, and the linear percentage error, e, is 1.32 and 0.75 for adm(443) and ag(443) respectively. These results are illustrated in Fig. 2 and the corresponding statistics are shown in Tables 2 and 3. The statistics improve significantly when we compare the outputs for the cases where the adm(443) is at least 10% of ag(443) or vice versa. These cases are shown in Fig. 2 as black dots. The part of the data that falls outside this criterion is illustrated in the same figure by gray dots. These parameters (when compared to the known ones) appear to be overestimated by our algorithm. As expected, the statistics in Tables 2 and 3 decay with the addition of noise, but results are still very good indicating that retrieval of these parameters is not very sensitive to noise. This decay is also, to some extent, observable in Fig. 2.

Although degraded, the retrieval of ag and adm is quite good when we apply our algorithm to the NOMAD database. Fig. 3 shows the agreement between the in-situ and the inverted parameters for aph (A), ag (B) and adm (C) as well as the total particulate absorption coefficient, ap (443), (m−1), (D) that is now obtainable and is simply the sum of aph and adm. The new products of ag and adm, shown in Fig. 3(B) and (C) respectively, agree very well with the in-situ measurements, given that they heavily depend on the previous retrievals.

4.4. Comparison with current experimental algorithms We compare our algorithm retrievals of ag (443) and adm (443) with the retrievals from recent studies (Dong et al., 2013; Zhu et al., 2011). A detailed comparison is shown in Fig. 4 and Tables 4 and 5. Although the statistics indicate that the algorithms perform similarly over the observable range of these parameters, it is quite clear that the NN algorithm derives better estimates when absorption coefficients are above 0.1 (m−1) for both parameters. These conditions usually indicate case 2 waters. All algorithms perform similarly for low absorptions, showing large deviations between the NOMAD measured and algorithm retrieved values. Further work is necessary to improve these results.

Fig. 5. Derived [Chl], (mg/m3) using the OC3 (upper), NN (middle) and IOP NN (lower) compared with the in-situ measured [Chl], (mg/m3) for the part of the data set that was used in the training (left) and testing(right). The 5:1 and 2:1 lines are shown in black and red respectively. Statistics are provided in Tables 6 and 7.

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5. Estimation of [Chl] using NOMAD dataset

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Table 7 Statistics of comparison for testing data.

5.1. OC3 algorithm It is the goal of many inversion algorithms to ultimately derive [Chl] and there are several approaches to derive this parameter from remote data. One is to use inversion algorithms to derive aph (Ioannou et al., 2011; Lee et al., 2002; Maritorena et al., 2002; Wang et al., 2005) and empirically relate aph to [Chl], as there is a well known, though slightly varying relationship, between these, at least for case 1 waters (Bricaud et al., 1995; Morel, 1991). However, the relationship between aph and [Chl] for a broad range of water conditions has also been shown to vary by almost an order of magnitude (Ciotti et al., 2002). Another approach is to use Rrs band ratios and relate these, again empirically, to [Chl]. A widely accepted and operational algorithm that derives [Chl] in such manner is OC3 (O'Reilly et al., 1998). It is used in this work with the coefficients calibrated for MODIS, mainly as a baseline, to illustrate the improvement that can be achieved by deriving [Chl] with our NN approaches. 5.2. Training: deriving [Chl] using NOMAD First, we generate a NN that derives [Chl] directly from the Rrs measurements from NOMAD. The NN inputs are the Rrs values at 412, 443, 488, 531, 547 and 667 nm and the output is [Chl]. The training procedure is similar to that of the network described in Section 4.2 and is a one layer network with 10 neurons at the hidden layer. Noise (up to +/−20%) was added to both the inputs and the outputs to improve the NN generalization capabilities. The NN was trained on 90% of the NOMAD, with the remaining 10% reserved for testing. This new network is called NN [Chl].

R2 Slope intercept RMSElog10 E N

OC3

NN

IOP NN

0.8455 0.9768 0.0316 0.2955 0.9749 319

0.9011 1.0543 0.0279 0.2387 0.7325 319

0.9116 1.0390 0.0119 0.2238 0.6744 319

[Chl] for the same data is shown in Fig. 5(C) and (D) respectively and the evaluation of IOP NN [Chl] is shown in Fig. 5(E) and (F). While it can be clearly observed that both NN algorithms perform significantly better than OC3, and an improvement is observed when including the previously derived IOP as inputs, it is also clear that these NNs cannot obtain a perfect relationship between the inputs and the desired [Chl] output. This is either due to measurement errors, insufficient available radiance measurements, or the fact that optical remote sensing alone may not be able to derive better estimates given the global variability. To sum up, significant improvement in [Chl] retrieval by the NN in comparison with OC3 algorithm is observed in R2 which increased from ~0.84 to ~0.9 as well as the linear percentage error that decreased from 0.94 to 0.65. A comparison of these and more detailed statistics can be seen in Tables 6 and 7. 5.5. Illustrating the improvement obtained by the addition of IOP To further illustrate that the improvement achievable by including retrieved IOP as additional inputs is indeed robust, we statistically compare NN [Chl] and IOP NN [Chl] over many different scenarios. Although the architecture on both NNs is identical and are both trained and tested

5.3. Training: deriving [Chl] with additional IOP inputs Here we generate a NN similar to the one described in Section 5.2 with the only difference being the addition to the input of IOP derived from the same Rrs set following the procedures described in Section 2.4. Thus the NN inputs are: the previously Rrs retrieved IOP at 443 nm (bbp, aph, adm, and ag) and Rrs values at 412, 443, 488, 531, 547 and 667 nm and the output is [Chl]. The NN was trained on the same 90% of the NOMAD used to train the network described in Section 5.2, with the same 10% reserved for testing. Because of the addition of IOP to the input this network, it is named IOP NN [Chl]. A comparison of the performance of the networks, described in Section 5.2 and this one, is discussed in Sections 5.4 and 5.5. In Section 5.5, we also discuss the method we employ to optimize the NN against random initialization noise. 5.4. Testing: evaluating [Chl] estimation We now present the performance of the NN algorithms for both the part of the NOMAD used for the training as well as the part reserved for testing in Fig. 5. For comparison the OC3 algorithm was applied to the NOMAD part that was used for training the NNs – Fig. 5(A) and on the part that was reserved for testing – Fig. 5(B). The performance of NN Table 6 Statistics of comparison for training data. OC3 2

R Slope intercept RMSElog10 E N

0.8388 0.9362 −0.0531 0.2884 0.9428 2969

NN 0.8890 1.0199 0.0057 0.2334 0.7115 2969

IOP NN 0.9038 1.0128 −0.0061 0.2172 0.6489 2969

Fig. 6. Histogram of the correlation coefficient (R2) of the IOP NN [Chl] (dotted line) and the NN [Chl] (continuous line) for all 1000 different NN coefficients derived. Clearly the addition of the IOP improves the estimation of [Chl].

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on an identical part of the NOMAD, there are still three differences between these networks:1) the IOP addition to the input, 2) the noise that is randomly added to the inputs and output before training, and 3) the initial conditions that are randomly chosen by the optimization algorithm (Foresee & Hagan, 1997) before the training. By initial conditions we mean the initialized network coefficients that are randomly selected as starting values for the weights and biases of the network. To significantly reduce and better understand the effect of the latter two (noise and initial conditions), we trained both networks 1000 times using random noise and different initial conditions, allowing us to assess the robustness of the improvement in the IOP NN [Chl] approach. The results of all training performance in terms of R2 are shown in the histograms in Fig. 6 for the training (90% NOMAD) and testing (10% NOMAD). As we can observe, IOP NN [Chl] repeatedly gives better coefficients of determination (R2) during the training (Fig. 6A) and for a significant amount of the testing (Fig. 6B). It is clear that by including these IOP estimates we robustly improve our [Chl] estimation capabilities. In choosing the best NN, we choose from the 1000 ensemble networks, the network that maximizes the sum of R2 values of the training and testing data (max(train(R2) + test(R2))) for both the NN [Chl] and IOP NN [Chl]. This network choice was then used to

derive the statistics in Tables 6 and 7 and to compare with OC3 in Section 5.4. We should also note here that the quality of these networks depends significantly on the quality of the NOMAD. 6. Satellite application 6.1. Derived [Chl] comparison The MODIS image in Fig. 7 presents the products of our algorithm of IOP NN [Chl], aph(443), ag(443) and adm(443) as well as the standard MODIS OC3 [Chl] product (O'Reilly et al., 1998). Visual inspection of Fig. 7 shows no anomalous discontinuities or graininess. Our derivation of IOP NN [Chl] is shown in Fig. 7(A) and equivalent MODIS product of OC3 [Chl] in Fig. 7(B) and they show some differences in both coastal and open ocean waters. We performed some basic comparison by calculating the percent difference between the IOP NN [Chl] and OC3 [Chl]. For most areas within the image in Fig. 7(C), both algorithms derive [Chl] values that are within ~+− 40% agreement. An increasing overestimation in the derivation of [Chl] (over 50% percent difference) using the OC3 is generally observed as we approach the east coast north of Chesapeake Bay.

Fig. 7. Processed MODIS image for the following parameters: IOP NN [Chl], mg/m3 (A), OC3[Chl], mg/m3 (B), percent difference (C), aph(443), m−1 (D), ag(443), m−1 (E) and adm(443), m−1 (F).

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On the contrary, in the open waters east of Long Island and New Jersey Shore, OC3 demonstrates a significant underestimation in deriving [Chl], always when compared to our IOP NN derivation of [Chl]. Examples of retrieved fields of aph(443), ag(443) and adm(443) are shown in Fig. 7(D), (E) and (F). The MatLab program for the NN algorithms described in this paper can be downloaded from the algorithm section of the Optical Remote Sensing Laboratory website (http://sky.ccny.cuny.edu/cw/algorithms2. php).

7. Summary We have developed a set of NNs that model different ocean color processes and can be presented together as a global retrieval algorithm that uses the Rrs measured just above water at specific wavelengths as input. In our previous work (Ioannou et al., 2011) we developed two NNs from which backscattering coefficient bb, total absorption coefficient a, absorption of the phytoplankton aph and combined absorption of gelbstoff (CDOM) and non-phytoplankton particulates adg at 443 nm were successfully retrieved. Expanding on this work we have developed here an additional NN, that when used with the previous 2 NNs, can separate this adg absorption coefficient into absorption of gelbstoff ag and absorption of non-phytoplankton particulates adm at the same 443 nm wavelength. We first successfully retrieved these additional IOP parameters based on our existing synthetic data set. The generalization capabilities of the algorithm were then validated through global matchups against the NOMAD. Good agreement was obtained with high R2 and reduced error values for the NOMAD, that were close to the values we obtained when we applied the algorithm to our simulated data. For comparison, retrievals using two recently presented algorithms (Dong et al., 2013; Zhu et al., 2011) were also evaluated using the NOMAD.

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We next developed a neural network that has uses the Rrs values at 412, 443, 488, 531, 547 and 667 nm as input, and has [Chl] as output. This network was trained and tested using the NOMAD and was found to improve the derivation of [Chl] when compared with the OC3 algorithm (O'Reilly et al., 1998). Moreover, we demonstrate that further improvement in the derivation of [Chl] can be achieved if a NN has as additional inputs the NN derived IOP values at 443 nm (bbp aph ag adm), which were previously derived from the same Rrs values. While we present some results of retrievals from satellite data, further work should be done to evaluate and compare the NN retrievals from satellite derived Rrs with in-situ matchup data. Once trained, the NN algorithms developed here and in our previous work (Ioannou et al., 2011) appear to be accurate, fast, and insensitive to reasonable noise levels. They are easy to implement and provide successful retrievals of each parameter for all reasonable Rrs input values. Furthermore, while the NN algorithm developed was originally designed for use with the MODIS sensor, it is not restricted to the exact MODIS bands used, since slightly different bands can be accommodated with an additional NN based interpolation step as described in detail in the Appendix. This step makes it possible to accommodate the same architecture for SeaWiFS as well as VIIRS.

Acknowledgments This work was partially supported by grants from ONR and NOAA. We would like to thank R. Arnone, W. Balch, F. Chavez, L. Harding, S. Hooker, G.Mitchell, R. Morrison, F. Muller-Karger, N. Nelson, D.Siegel, A. Subramaniam, R. Stumpf, and all of their co-investigators for their contribution to the NOMAD. This work wouldn't be possible without efforts of these, and the numerous other contributors. We would also like to thank Alan Weidemann and an anonymous reviewer for their valuable reviewer comments that helped improve the quality of this work.

Appendix Interpolating Rrs values The NNs described here to perform the interpolation were mainly developed to assist in improving the number of validation matchups in comparison to NOMAD. Nevertheless these can be easily adapted to the VIIRS sensor to implement the same algorithm. Both NNs described in this section accept as input the log10 of the Rrs measurements at 488 nm and 555 nm and output the log10 of the Rrs values at 531 and 547 nm respectively. These networks were trained in a similar way as the networks described in Section 4.1 using synthetic data for the training while using the independent NOMAD for validations. The exact details about the architecture and training and testing methodology can be seen in Table A1.

Table A1 Neural network training and testing information.

NN(Rrs531) NN(Rrs547)

# hidden layers

# neurons

ε (inputs)

ε (outputs)

Train data type

Size train data set

%data used training

Test data type

Size test data set

%data used testing

1 1

2 2

10% 10%

0% 0%

Synthetic Synthetic

9000 9000

100% 100%

Field Field

1259 616

100% 100%

The training accuracy is shown in Fig. A1. The Rrs values are derived with very good accuracy and are capable of providing accurate inputs to inversion algorithms. Being closer to an input parameter the Rrs(547) is clearly estimated more accurately than Rrs(531) with better derived statistics. Nevertheless the estimation of Rrs(531) is very good given that over 90% of the data are within 5%. We also compare the NN derived Rrs values at 531 and 547 nm to the NOMAD measured values at 531 and 550 nm. The 550 nm is the closest measurement that we have to compare with the NN output value of Rrs(547). As can be seen in Fig. A2 very similar behavior to the simulated data set is observed, which indicates the flexibility of these networks. The statistics of these results for NOMAD, although slightly degraded, are very similar to the statistics derived when applying the networks to the synthetic data sets. Figs. A2(C), (D) and A3(C), (D) also show the accuracy of estimating these parameters when using more conservative methods (linear interpolation between 488 and 555 nm).

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Fig. A1. NN derived Rrs (531), (sr−1)(upper left-(A)) and the NN derived Rrs(547), (sr−1) (upper right-(B)) compared with the known values for these parameters from the simulated data set. Histogram of the percent error at 531 nm (lower left-(C)), at 547 nm (lower right-(D)).

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Fig. A2. NN derived Rrs(531), (sr−1)(upper left-(A)) and the NN derived Rrs (547), (sr−1) (upper right-(B)) compared with the in-situ measurement for these parameters. The derived results using interpolation are shown for Rrs(531), (sr−1)(lower left-(C)) and Rrs (547), (sr−1) (lower right-(D)) compared with the in-situ measurement for these parameters.

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Fig. A3. Histograms of the percent error for Rrs(531), (sr−1)(upper left-(A)) and Rrs (547), (sr−1) (upper right-(B)) when comparing with the NN derived value for the same parameter. The histograms of the interpolated values are shown for Rrs(531), (sr−1)(lower left-(C)) and Rrs(547), (sr−1) (lower right-(D)).

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