A Neural Network-Based Four-Band Model for Estimating the Total. Absorption Coefficients from the Global Oceanic and Coastal waters

Transcription

1 Research Article Journal of Geophysical Research: Oceans DOI /2014JC A Neural Network-Based Four-Band Model for Estimating the Total Absorption Coefficients from the Global Oceanic and Coastal waters Jun Chen 1,2* Tingwei Cui 3, Wenting Quan 4 1. School of Ocean Sciences, China University of Geosciences (Beijing), , China 2. Qingdao Institute of Marine Geology, Qingdao , China 3. First Institute of Oceanography, State Oceanic Administration, Qingdao, , China 4. Shanxi Agricultural Remote Sensing Information, , China *corresponding author: cjun@cgs.cn Abstract: In this study, a neural network-based four-band model (NNFM) for the global oceanic and coastal waters has been developed in order to retrieve the total absorption coefficients a(λ). The applicability of the quasi-analytical algorithm (QAA) and NNFM models is evaluated by five independent datasets. Based on the comparison of a(λ) predicted by these two models with the field measurements taken from the global oceanic and coastal waters, it was found that both the QAA and NNFM models had good performances in deriving a(λ), but that the NNFM model works better than the QAA model. The results of the QAA model-derived a(λ), especially in highly turbid waters with strong backscattering properties of optical activity, was found to be lower than the field measurements. The QAA and NNFM models-derived a(λ) could be obtained from the MODIS data after atmospheric corrections. When compared with the field measurements, the NNFM model decreased by a 0.86 to 24.15% uncertainty (root mean square relative error) of the estimation from the QAA model in deriving a(λ) from the Bohai, Yellow, and East China seas. Finally, the NNFM model was applied to map the global climatological seasonal mean a(443) for This article has been accepted for publication and undergone full peer review but has not been through the copyediting, typesetting, pagination and proofreading process which may lead to differences between this version and the Version of Record. Please cite this article as doi: /2014JC American Geophysical Union Received: Sep 19, 2014; Revised: Nov 21, 2014; Accepted: Dec 01, 2014

2 the time range of July, 2002 to May, As expected, the a(443) value around the coastal regions was always larger than the open ocean around the equator. Viewed on a global scale, the oceans at a high latitude exhibited higher a(443) values than those at a low latitude. Keywords: remote sensing; inherent optical property; global oceanic and coastal waters; neural network; optical activity constituents 1. Introduction Covering 71% of the Earth s surface, the ocean generates nearly 50% of the primary planetary production (Field et al., 1998), which nurtures life on our blue planet and continues to play a dominating role in regulating its global climate changes (Hoegh-Guldberg and Bruno, 2010). Fortunately, the recent advances in oceanic color remote sensing have opened new opportunities for learning regarding the biogeochemical and physical processes in oceans on both basin and global scales. Initially, the oceanic color remote sensing focused primarily on the estimation of chlorophyll-a concentration in the global oceans. However, in recent research studies attention has been paid to the importance of understanding the spatial variations of the total absorption coefficient a(λ) in global and coastal waters, using remote sensing technology (IOCCG, 2006). This is due to an accurate estimation of the absorbing characteristics in the visible wavelengths possibly providing insight into the spatial and temporal variations of the suspended sediment matters (SSM), colored dissolved organic matter (CDOM), and phytoplankton found in the oceans upper layers (Shi et al., 2014; Zhang et al., 2014). These achievements may help us to improve our knowledge regarding the material recycling processes, and also the heat balance of the global and coastal aquatic systems. 2

3 Models for accurately deriving the total absorption coefficients in oceanic and coastal waters have been under investigation for several decades. Also, methods ranging from empirical to physical have been developed (Chen et al., 2014b; Doerffer and Schiller, 2007; Garver and Siegel, 1997; IOCCG, 2006; Lee et al., 2009; Loisel D and Stramski, 2000; Loisel et al., 2001; Smyth et al., 2006). The empirical models are based on the simple or multiple regressions to the desired a(λ), and the ratios of the apparent optical properties (AOPs), such as remote sensing reflectance (Kirk, 1984; Leathers and McCormick, 1997; Lee et al., 1998). Such models do not require a full understanding of the relationship between a(λ) and AOPs. Therefore, these models are simple and easy to implement for practical oceanic color remote sensing. However, due to the natural characteristics of the empirical models, such approaches can only be used in the areas where the bio-optical properties are similar to the dataset used for the model development. The physical models use radiative transfer equations to link the spectrum of the AOPs at the top-of-atmosphere with the different bio-optical and atmospheric conditions (Gordon and Clark, 1981; Mobley, 1994). Such models require the accurate bio-optical information from the waters and atmospheres, which is not always available for the general application of oceanic color remote sensing. As a result, even though the a(λ) can be accurately retrieved in theory using the physical models, such models are not commonly used in practical oceanic color remote sensing. Based on the physical linking between the AOPs and a(λ), along with some empirical relationships, the semi-analytical models are promising techniques for the estimation of a(λ). Although considerable attention has been given to the subject of accurate remote sensing of a(λ) using semi-analytical models, at present there is still compelling need for an accurate model for both oceanic and coastal waters, since the existing models are essentially applicable only for open 3

4 oceans (Garver and Siegel, 1997; IOCCG, 2006; Kirk, 1984; Leathers and McCormick, 1997; Lee et al., 2002) or regional coastal zones (Gould and Arnone, 1997; Richard et al., 1997; Tzortziou et al., 2007). For example, the widely used quasi-analytical algorithm (QAA) was originally developed for oceanic waters, and therefore may be ineffective in optically complex coastal waters with high concentrations of SSM (Chen et al., 2014b; Zhang et al., 2010). As a result, a large amount of models can be used in order to process satellite imagery effectively (Chen et al., 2014b; IOCCG, 2006; Li et al., 2013). However, some problems are encountered when they are used to derive a(λ) from the optically complex coastal waters such as the Bohai, Yellow, and East China Seas (YCE). As of yet, no operational a(λ) retrieval model has been developed that has been proven universally robust across waters of varying geophysical characteristics. Improved a(λ) models are still needed in order to accurately estimate a(λ) from both oceanic and coastal waters,. The neural network models are good candidates for retrieving absorption coefficient from remote sensing reflectance if they are properly parameterized (Chen et al., 2014b; Doerffer and Schiller, 2007; Ioannou et al., 2013). For example, Doerffer and Schiller, 2008, suggested that a(λ) could be accurately retrieved using a neural network model from inland lakes if the MERIS remote sensing reflectance at visible bands are used as the inputs. However, from a statistical perspective, the increasing variable numbers of inversion function would lead to increases of the degree-freedom of the retrieval model (Chen et al., 2003), which in turn may result in the instability of the model for a(λ) predictions. Even though the neural network model proposed by Chen et al., 2014b, works well in the estimations of a(λ) in a great mass of oceanic and coastal waters, when it was applied in the Bohai Sea, some negative a(λ) was observed for our dataset collected in that sea. As expected, an effective neural network model is still desired. The 4

5 objectives of this study are to validate the performance of the QAA model, and to further develop a neural network-based four-band model (NNFM) for applications in both oceanic and coastal waters. The specific goals are as follows: (1) To evaluate the QAA model for accurately estimating a(λ) in the oceanic and coastal waters; (2) To develop and evaluate a NNFM model for predicting the absorption coefficients from oceanic and coastal waters; (3) To compare the accuracy of the QAA and NNFM models in estimating a(λ) in the highly turbid Bohai and YCE Seas; and (4) To discuss the spatial variations of a(443) in the global oceanic and coastal waters. 2. Data and methods 2.1 Dataset In the model calibration and validation, we are frequently limited by the availability of adequate datasets. These datasets are important for the initial development, but usually lack dynamic range and thereby make it difficult to evaluate a models performance on broader scales. In order to fill this gap and to have a common ground for the model evaluations, five independent datasets were compiled. One of these datasets (IOCCG dataset) was simulated using the widely accepted numerical code of Hydrolight, with input bio-optical conditions generated which were based on extensive measurements made in the field (IOCCG, 2006). The second dataset was compiled from global field measurements, which were conducted by the National Aeronautics and Space Administration (NASA) SeaWiFS Project, known as the NASA Optical Marine Algorithm Dataset (NOMAD dataset) (Werdell and Bailey, 2002). The third dataset was compiled from the West Florida Shelf, USA, during a period between 1999 and 2002, known as the Sea-viewing Wide Field-of-View Sensor Bio-optical Archive and Storage System (WFS dataset). The NOMAD and WFS datasets were collected by various research teams using various instruments throughout 5

6 the United States and Europe. All the measurements closely followed rigorous, community-defined deployment and data processing protocols (Werdel and Bailey, 2005; Werdell and Bailey, 2002). The fourth dataset was compiled from turbid coastal waters collected from YCE Seas during 2003 (YCE dataset), and the fifth dataset was compiled from the turbid waters of the Bohai Sea, which is an inland sea, during 2005 (Bohai dataset) (Chen et al., 2014b). The description of the measurements of these datasets has been introduced in detail in various references (Cannizzaro et al., 2008; IOCCG, 2006; Werdel and Bailey, 2005; Werdell and Bailey, 2002). The datasets were divided into two groups, whereas the IOCCG and NOMAD datasets were used for model initialization, while the WFS, YCE, and Bohai datasets were used for the evaluations of the model. 2.2 Construction of NNFM In regards to unproductive waters, the Raman-scattering was one of the important contributors to remote sensing reflectance for wavelengths longer than 550 nm (Hu and Voss, 1997; Mobley, 1994). As a result, if the Raman-scattering effect-uncorrected remote sensing reflectance in the green and red regions was utilized for a(λ) retrievals, an uncertainty would be propagated into the desired model-derived physical variables. Therefore, in order to accurately achieve the satellite-observed a(λ) in oligotrophic waters, a correction to the Raman-scattering effect should be carried out. In this study, the approach proposed by Lee et al. (2013) was used to remove the Raman-scattering effects from the field-measured or satellite-derived remote sensing reflectance: R rs ( ) ( λ ) T R λ = (1) 1 + RF where R T (λ) referred to the Raman-scattering effect-uncorrected remote sensing reflectance, while 6

7 R rs (λ) represented the Raman effect corrected remote sensing reflectance; and RF was the ratio of the Raman-scattering induced remote sensing reflectance to the remote sensing reflectance without Raman-scattering effects correcting. The corresponding value could be calculated using the method proposed by Lee et al. (2013). Due to the fact that satellites and many other sensors measured remote sensing reflectance above the water surface, it became necessary to convert the above-surface remote sensing reflectance spectral R rs (λ) into a below-surface spectral r rs (λ) (Lee et al., 2002; Mobley, 1994): r rs ( λ ) Rrs = ( λ ) R ( λ ) rs (2) The remote sensing of a(λ) was based on the physical relationship between r rs (λ) and inherent optical properties: ( λ ) ( λ ) log b b = h η ( λ ) a (3) where η(λ) is referred to as the logarithmic value of r rs (λ), and h was a function linking the inherent optical properties to η(λ). Fig. 1 shows the empirical relationships between the inherent optical properties regressed from the IOCCG and NOMAD datasets. As expected, for the MODIS 443, 488, 555, and 667 nm, the logarithmic values of a(488), and/or b b (555), could be denoted as a linear combinations of the logarithmic values of a(λ), and/or b b (λ), at the other three bands. ( ) ( ) ( ) ( ) γ 488 = 0.684γ γ γ (4) ( ) ( ) ( ) ( ) 0.354χ 555 = χ χ χ (5) where γ(λ) and χ(λ) are denoted as the logarithmic values of a(λ) and b b (λ), respectively. By substituting Eq. (3) and Eq. (4) into Eq. (5) yielded: ( ) h ( ) h ( ) h ( ) h ( ) γ 555 = η η η η (6) 7

8 In a similar way with γ(555), the γ(443), γ(488), and γ(667) could also be denoted as the function of η(λ) at 443, 488, 555, and 667 nm, respectively. Therefore, for simplicity, the mathematical relationship between a(λ) and η(λ) could be denoted using an abstract function, f, as shown below: a ( λ) f η( 443 ), η( 488 ), η( 555 ), η( 667) = (7) Therefore, since the direct use of a purely radiative transfer method was hindered by complexity and lack of underlying physical models, it was concluded that empirical data driven models were still considered to be good candidates if the physical characteristics of photonic activity in waters could be assimilated into the models. Also, neural networks were good candidates used for the developing of inverse functions in geophysical and oceanic remote sensing applications (Brajard et al., 2012; Ceyhun and Yalçın, 2010; González Vilas et al., 2011; Gross et al., 1999; Ioannou et al., 2013; Jamet et al., 2012; Wang et al., 2008). In this study, in order to accurately simulate the internal association of a(λ) to η(λ), the neural network approach was proposed. Generally speaking, the neural network with no hidden layers was used to simulate the linear relationships. Meanwhile, a single hidden layer with adequate nodes allowed the approximation of any function which contained a continuous mapping from one finite space to another (Merwe et al., 2007). Two hidden layers were only used for some particularly complicated cases. However, there was absolutely no theoretical reason to use more than two hidden layers, because more hidden layers would make the neural networks more prone to over-fitting the data. Therefore, in this study, the neural network with one hidden layer as shown in Fig. 2 was proposed for deriving a(λ) from the AOPs. 8

9 2.3 Accuracy assessment In this study, the root-mean-square of the ratio of the modeled-to-measured values was used to assess the accuracy of the atmospheric correction. This statistic was described by the following equation (Carder et al., 2003; O Reilly et al., 1998): ARE x x mod, i obs, i = (8) x obs, i 100% n 1 n i= 1 MRE = ARE (9) 2 i n 1 RMSE = log ( x ) ( ) 2 mod, i log x obs, i (10) n i= 1 where ARE referred to absolute relative error; MRE represented the mean root square relative error; RMSE was root-mean-square of the ratio of the logarithm modeled-to-logarithm measured values; x mod,i was the modeled value of the i th element; x obs,i was the observed value of the i th element; and n was the number of elements. 3. Results and discussion 3.1 Bio-optical characteristics The datasets used for the model initialization and evaluation encompassed widely varying optical conditions, as shown in Table 1. In the NOMAD, IOCCG, and WFS datasets, the values of a(443) varied over two orders of magnitude, while the values of a(488) and a(555) varied over more than one order of magnitude. In the YCE seas, the values of a(443) and a(555) varied over more than three orders of magnitude, while a(488) changed over two orders of magnitude. In the Bohai sea, the a(443) varied more than nine-fold, while a(488) and a(555) spanned more than five-fold. By comparison, the bio-optical characteristics of the YCE dataset were much wider than these of the NOMAD, IOCCG, WFS, and Bohai datasets. 9

10 3.2 NNFM model initialization and evaluation NNFM model training Therefore, since there were no available a(667) data in the YCE and Bohai datasets, the training dataset only included R T (443), R T (488), R T (555), and R T (667), as well as a(443), a(488), and a(555), from each field or synthetic dataset. The weight values of the NNFM model were determined by a supervised learning technique, using a priori information regarding the actual output which corresponded to a set of input data provided by the NOMAD and IOCCG datasets. A back propagation learning procedure was used to find the optimal weight for the NNFM model. The activation function for the hidden layers was a nonlinear hyperbolic tangent function, while the output node was only applied with a bias transfer function. The two types of architecture were tested for 0 or 1 hidden layers with the number of nodes varying from 1 to 50. The performance of the NNFM model was evaluated by comparing the field-measured results with the model-derived absorption coefficients. The training procedures would be terminated if the increased one node into the architecture of neural network would not significantly improve the MRE values (<1%). Finally, the optimal architecture was therefore found to be composed of one hidden layer with 11 neurons. We then evaluated the NNFM model estimations by computing the determination coefficients, slopes, and biases of the model-derived and field-measured a(λ) relationships. Based on the 1,713 samples, the models shown in Fig. 3 were proposed as the optimal NNFM models for quantifying a(443), a(488), and a(555) from the IOCCG and NOMAD datasets. It was found that the NNFM model was an effective predictor for deriving a(λ) at MODIS 443, 488, and 555 nm bands in the global oceanic and coastal waters, when the determination coefficients were larger than 0.98 and 10

11 the slopes ranged from 0.98 to Therefore, using the NNFM model could account for >98% of the variations of a(443), a(488), and a(555) in the IOCCG and NOMAD datasets. These findings implied that the neural network approach was a good candidate for deriving the absorption coefficients from the remote sensing reflectance in the global oceanic and coastal waters NNFM model evaluation The evaluation was based on the comparison of the a(λ) predicted by the NNFM model with a(λ) measured analytically in three independent datasets as shown in Table 1. Due to the fact that the neural network model was a poor extrapolator, the weights of the NNFM model would be different for a(λ) prediction at different bands. Fig. 4 and Table 2 show the relationship between the NNFM model-derived and field-measured a(443), a(488), and a(555) in the West Florida Shelf, Bohai Sea, and YCE Seas. For a(λ) ranging from m -1 among the datasets, the MRE values of predictions did not exceed 35.47%. The slopes of the linear relationships between the model-derived and field-measured a(λ) varied among the datasets from 0.70 to Meanwhile, the corresponding determination coefficients varied from 0.64 to In clarification, except for a(488) in the Bohai Sea, uses of the NNFM model can account for >85% of the variations of a(443), a(488), and a(555) in the West Florida Shelf, Bohai Sea and YCE Seas. By comparison, the performance of the NNFM model in the Bohai Sea was slightly better than in the YCE Seas, but was significantly worse than in the West Florida Shelf. Table 1 shows that the average and SD values of a(λ) in the Bohai Sea was higher than in the West Florida Shelf, but lower than the YCE Seas. It seemed that the stability and accuracy of the NNFM strongly depended on the optical complexity of the bodies of water. 11

12 The relationships between the ARE values and a(λ) were also presented to highlight the ability of the NNFM model to derive a(λ) from turbid coastal waters. Fig. 5 showed a plot of the field-measured a(λ) versus ARE values of the NNFM model provided by five independent datasets. These results indicated that for a(λ) ranging from to m -1, the ARE values ranged from 0.07% to 167%, with an average bias between 9.79% and 33.05%. The ARE values decreased with the increasing a(λ), but there was no statistically significant relationship between them. The a(λ) values <0.3 m -1 contributed greatly to the MRE values of the NNFM model. When the NNFM model was applied to five independent datasets together, the model predicted a(443), a(488), and a(555) to have the relative random uncertainties of 21.33%, 18.44%, and 13.27%, respectively. These findings imply that the NNFM model was an effective predictor for deriving a(λ) from optical complex coastal waters without further retraining the site-specific weight values of the neural network. 3.3 QAA model evaluation and comparison The QAA model considering the Raman-scattering effects has been described in detail in various references (Lee et al., 2013; Lee et al., 2009). The QAA model was a global algorithm that has been initialized using global datasets, including the NOMAD and IOCCG datasets (Lee et al., 2013; Lee, 2009). Since IOCCG (2006), Lee et al. (2013) and Chen et al. (2014b) have proven that the QAA model was robust for most global oceanic waters and some turbid coastal waters, the coefficients of the QAA model were not adjusted according to the bio-optical datasets collected in this study. Fig. 6 and Table 3 showed the comparisons of the QAA model-derived and field-measured a(λ) for the IOCCG, NOMAD, WFS, YCE, and Bohai datasets. For a(443), a(488), and a(555), respectively, ranging from to m -1, to m -1, and to 12

13 m -1 among the five independent datasets, the MRE values of a(443), a(488), and a(555) estimations did not exceed 37.79%. The slopes of the linear relationships between the model-derived and field-measured a(λ) varied among the datasets from 0.05 to Meanwhile, the corresponding determination coefficients varied from 0.34 to The best performance was found in the West Florida Shelf (10% < MRE < 19.9%), while the worst was found in the YCE Seas (26.87% < MRE < 37.79%). The a(λ) values were significantly underestimated by the QAA model in high levels (>1 m -1 ). By comparison, the performance of the QAA model was comparable to the NNFM model in the West Florida Shelf, but the former had significantly worse results than the later in the Bohai and YCE Seas. Therefore, using the NNFM model could decrease 1.03 to 12.42% of the MRE values from the QAA model for deriving a(λ) from the Bohai and YCE Seas. To further illuminate the performance of the NNFM model, we presented the relationships between the ARE values of the QAA model and field-measured a(λ) in this study. Fig. 7 shows the ARE values of the QAA model plotted against the field-measured a(λ). It was found that the ARE values of the QAA model increased with the increasing a(λ), but there was no statistically significant relationship between these two variables. The a(λ) above m -1 contributed greatly to the MRE values in Table 3. To clarify, the QAA model produced a superior performance in the low a(λ) levels than in the high a(λ) levels. When comparing the results of the NNFM model to that of the QAA model, indications were evident that the NNFM model considerably reduced the ARE value and it outperformed the QAA model at higher a(λ) levels. When the QAA model was applied to the five independent datasets, it predicted a(443), a(488), and a(555) with a relative random uncertainty of 32.19%, 27.29%, and 20.82%, respectively. Therefore, based on these five 13

14 datasets (2,171 samples), it was found that using the NNFM model, respectively decreased 10.86%, 8.85%, and 7.55% of the MRE values from the QAA model when deriving a(443), a(488), and a(555) from the global oceanic and coastal waters. Many studies (Chen et al., 2014b; IOCCG, 2006; Lee et al., 2013) have shown that the QAA model was effective in deriving a(λ) from the global oceanic waters, as well as some coastal waters. It was well known that the performance of the QAA model strongly depended on the retrieval accuracy of a(555) (Lee et al., 2013; Lee et al., 2002). However, the a(555) values were empirically derived using the QAA model. This empirical approach was able to suppress most of the effects of b b (λ), rather than eradicating it completely. As a result, the strong backscattering of suspended particles in turbid coastal waters inevitably exerted a residual effect on the estimation accuracy, which could potentially lead to a violation of the QAA model in these waters. Fig. 8 shows the comparison between the retrieval uncertainty (ARE value) of the QAA model-derived a(443) and the synchronized field-measured b b (488), indicating that there were two pronounced characteristics found in that relationship: (1) For b b (488) within the range varying from to m -1, the retrieval uncertainty decreased with the increasing b b (488), but there was no statistically significant relationship between them (R 2 =0.13, p<0.05); (2) For b b (488)>0.119, the retrieval uncertainty increased with the increasing b b (488), and the determination coefficient of the estimation uncertainty of the QAA model-derived a(443) versus the field-measured b b (488) was Moreover, Fig. 8 also revealed that using the QAA model, the a(443) was significantly overestimated below m -1, while was significantly underestimated above m -1. Fortunately, the NNFM model was an effective predictor in eliminating the effects of b b (λ) on a(λ) estimation in the global oceanic and coastal waters as illustrated in Fig

15 Since there was no simplifying assumption which could be made that was valid for all the special cases existing in the global oceanic and coastal waters, a semi-analytical model such as the QAA may prove to be robust for deriving a(λ) from most of the global oceanic, as well as some coastal waters (IOCCG, 2006; Lee et al., 2013), but may be ineffective in some highly turbid waters. Given the same inputs for the semi-analytical and neural network models, the latter may work better than the former, due to the fact that the neural network with one hidden layer could be used to approximate any function that contained a continuous mapping from one finite space to another, although the physical foundation of the neural network approaches were found to be weaker than the semi-analytical approaches. This could possibly be the reason why the neural network approach was found to be a promising technique for optical information estimation. 3.4 Accuracy of satellite-derived products The QAA and NNFM models-derived a(443), a(488), and a(555) values were estimated from the MODIS images after atmospheric corrections using an approach proposed by Chen et al. (2013a). The accuracy of the satellite-derived a(λ) was assessed using a comparison between the satellite-derived and field-observed a(λ). The procedure provided by Bailey and Werdell (2006) introduced in the previous section, was proposed for generating the satellite-derived a(λ) for the data match-analysis. Fig. 9 shows the satellite-predicted versus field-measured a(443), a(488), and a(555) within a ±3 hour period, when the satellite was over the region where the in situ measurements were carried out. The maximum coefficient of variation of the satellite pixels did not exceed Although 252 samples were taken from the Bohai and YCE Seas, only 43 samples could be used for the math-ups analysis. This was because other samples were outside the ±3 hour time window, or that the synchronized MODIS data was polluted by heavy cloud cover. 15

16 As shown in Fig. 9, it was found that both the QAA and NNFM models performed strongly in deriving a(λ) from the Bohai and YCE Seas, but the NNFM model (20.66% < MRE < 25.81%) produced a superior performance when compared to the QAA model (22.83% < MRE < 49.96%). By comparison, using the NNFM model for deriving a(443), a(488), and a(555) in the Bohai and YCE Seas, decreased the MRE values of estimation by 24.15%, 0.86%, and 9.26% from the QAA model, respectively. These findings implied that both the QAA and NNFM models were acceptable for accurate retrieval of a(443), a(488), and a(555) from turbid coastal waters, but the NNFM model may be more effective than the QAA model. It should be noted that the accuracy of satellite-observed R rs (λ)-based prediction was found to be comparable to the field-measured R rs (λ)-based results. In actuality, the MODIS data as the band at 667 nm were consistently saturated in highly turbid coastal waters, so therefore the samples from highly and extremely turbid waters were not always available for the match-up analysis. These limitations of the MODIS sensor would be disadvantages for the complete evaluation of the performance of the NNFM model in turbid coastal waters. 3.5 Global view of a(443) values The QAA and NNFM models were used in order to derive a climatological seasonal mean a(443) for the global oceanic and coastal waters, from the seasonal mean MODIS remote sensing reflectance, for the time ranging from July, 2002 to May, 2014 ( There were many factors which contributed to the absorption characteristics at 443 nm, which were primarily representative of absorption by CDOM, SSM, and phytoplankton (Mobley, 1994). Fig. 10 indicated that higher values of a(443) (>0.08 m -1 ) were found in the coastal zones around Asia and Europe, while lower values of <0.02 m -1 were found in the in the sub-tropical gyres. 16

17 Miliman and Meade (1983) determined that the rivers in Asia contributed to a large amount of the sediment load to the global oceans each year. This land-discharged SSM contributed greatly to the total absorbing values at 443 nm in the coastal regions. Moreover, the suspended matter played a significant role in the transport and cycling of nutrients in coastal waters. This was due to the fine-grained particles being an important carrier of phytoplankton growth requiring nutrients, such as phosphorus and nitrogen elements. Near the coastal zones (eastern and southern coastal zones of China, where the sea depth was less than 200 m), the surface waters were mixed to depths of 200 m due to the strong winds (Dasgupta et al., 2009), which in turn increased the nutrient supply to the phytoplankton in already stratified tropical waters, and therefore benefited the growth of phytoplankton within the mixed layer depths (Boyce et al., 2014). Due to the re-suspended and river-discharged sediments, the chlorophyll-a concentration was found to be higher near the coastal zones when compared to the open ocean (Dasgupta et al., 2009). In fact, Carder et al. (2003), Gitelson et al. (2008), and Chen et al. (2013b) indicated that the absorption by chlorophyll-a featured strong absorbing characteristics in the blue bands, and also that a distinct absorption peak was usually found around 443 nm. Therefore, the significant distribution of a(443) was found to be associated with the proximity to land, the depth of the ocean, and the ocean currents. For example, the a(443) values in the southern Asian coastal zones were much higher than in other regions. In viewing from a global scale, the lowest a(443) values occurred at the low-latitude regions, while the higher values were found at the high-latitude regions. In the low-latitude regions (within 45 N-45 E), a(443) values were low and the seasonal changes were not significant. Within 45 N to 45 E of the equatorial zones a(443) values were relatively high, since the effects of the north 17

18 east trade winds in the northern hemisphere and south east trade winds in the southern hemisphere gave rise to upwelling. Above 45 N, the a(443) values increased and reached a maximum at approximately 65 N. In high-latitude regions (>65 N) in the northern hemisphere, a(443) values were higher and the seasonal changes were pronounced. For example, the pixels with a(443)>0.4 m -1 in spring and summer, were much more numerous than in autumn and winter. There were many factors which contributed to the spatial distribution characteristics of a(443) at the high-latitude zones. On one hand, intense primary productivity occurred in the marginal ice zones, due to the melt water from the sea ice providing enough vertical stability in the water column for phytoplankton to grow with high-light and high-nutrient conditions in the high-latitudes (Smith and Nelson, 1986). On the other hand, the adjacent effects occurring along the sea ice margins would potentially lead to large errors in the retrieval of the remote sensing reflectance, which in turn could result in overestimations of the total absorption coefficients (Bélanger et al., 2007). Fig. 10 indicates several importantly clear differences between a(443) derived from the NNFM model, and that derived from the QAA model. For example, the former was much higher than the latter, and this phenomenon was especially pronounced around the coastal regions, where a(443) derived by the NNFM model was more than 0.1 m -1 larger than that produced by the QAA model. It seemed that the NNFM model produced a broad histogram of a(443) values in comparison to those derived by the QAA model. The reason was found to be that the QAA model produced underestimations of a(443) in the high values as illustrated in Fig. 6 and Fig. 9. Therefore, in judging the data quality by histogram, it appeared that the NNFM model produced a superior performance in comparison to the QAA model in deriving a(443) from the MODIS data. 18

19 4. Summary The accurate estimation of a(λ) in the global oceanic and coastal waters by means of remote sensing is a challenging task, as the existing models are only essentially applicable for most oceanic waters, as well as some coastal waters. Therefore, an accurate a(λ) assessment model for the global oceanic and coastal waters is still undeveloped. In this study, a neural network model has been proposed in order to monitor a(λ) from space in the global oceanic and coastal waters. The inputs of this neural network model are determined by a semi-analytical approach. The major characteristics of this study are that the neural network approach be used to directly predict a(λ) from the high temporal and spatial coverage of the logarithmic values of the remote sensing reflectance after removing the Raman-scattering effects provided by the MODIS sensor. When initialized and evaluated using five independently simulated and field-measured datasets in the global oceanic and coastal waters, the NNFM model was found to have an acceptable performance for estimating a(λ) in the global oceanic and coastal waters. The accuracy and stability of the NNFM model was compared with the QAA model for deriving a(λ) from the global oceanic and coastal waters. When the QAA and NNFM models were applied to the five independent datasets, the NNFM model used in deriving a(443), a(488), and a(555) from the global oceanic and coastal waters, decreased the MRE values by 10.86%, 8.85%, and 7.55%, respectively, compared to the QAA model. Due to the effects of the backscattering characteristics of the optical activity constituents, using the results of the QAA model for a(443) values were overestimated when b b (488) < m -1, but were underestimated when b b (488) > m -1. Fortunately, the limitation of the QAA model s sensitivity to the backscattering properties of the water bodies could be minimized by the NNFM model. The study results 19

20 indicated that both the QAA and NNFM models were effective predictors for deriving a(λ) from the global oceanic and coastal waters, but the NNFM model is more effective than the QAA model, especially in the water bodies with strong backscattering properties. The a(443), a(488), and a(555) were quantified from the MODIS images after atmospheric corrections using the QAA and NNFM models. By comparison with the field measurements, the NNFM model produced to 25.81% MRE values in deriving a(λ) from the MODIS data in the Bohai and YCE Seas, which was 0.86 to 24.15% better than the results of the QAA model. Our models were also used to produce the global climatological seasonal mean a(443) for the time range of July, 2002 to May, Our results indicate that the highest a(443) value is generally found near the coastal regions, while the lowest is usually found in the open oceans near the equator. When viewing this from a global scale, the oceans at low-latitude exhibit lower a(443) values, while the high-latitude oceans exhibit higher a(443) values. The land-discharged particles, climate characteristics, depth of the ocean, and ocean currents are the main factors leading to the special distribution characteristics of a(443) in the global oceans. Acknowledgements This study is supported by the National Natural Science Foundation of China (No ; No ); the China Scholarship Council Funding (No ); the China State Major Basic Research Project (2013CB429701); Science Foundation for 100 Excellent Youth Geological Scholars of China Geological Survey; and Serial Maps of Geology and Geophysics on China Seas and Land on the Scale of 1: ( ). We thank NASA ( and IOCCG ( for their assistance with respect to providing the NOMAD and IOCCG datasets. 20

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27 Table 1. Descriptive statistics of the measured a(λ) in NOMAD, IOCCG, YCE, Bohai, and WFS datasets: SD, standard deviation Dataset a(λ) Min Max Median Average SD NOMAD dataset n=713 a(443) a(488) a(555) IOCCG dataset n=1000 a(443) a(488) a(555) WFS dataset n=206 a(443) a(488) a(555) YCE dataset n=145 a(443) a(488) a(555) Bohai dataset n=107 a(443) a(488) a(555) Table 2. Determination coefficients, slopes, biases, MRE, and RMSE values of NNFM model for WFS, YCE, and Bohai datasets Dataset a(λ) R 2 slope bias RMSE MRE (%) 27

28 WFS dataset n=206 a(443) a(488) a(555) YCE dataset n=145 a(443) a(488) a(555) Bohai dataset n=107 a(443) a(488) a(555) Table 3. Determination coefficients, slopes, biases, MRE, and RMSE values of QAA model for IOCCG, NOMAD, WFS, YCE, and Bohai datasets Dataset a(λ) R 2 slope bias RMSE MRE (%) NOMAD dataset n=713 a(443) a(488) a(555) IOCCG dataset n=1000 a(443) a(488) a(555) WFS dataset n=206 a(443) a(488) a(555)

29 YCE dataset n=145 a(443) a(488) a(555) Bohai dataset n=107 a(443) a(488) a(555)

30 Fig. 1 Empirical relationship between inherent optical properties: (a) empirical relationship among absorption coefficients at 443, 488, 555, and 667 nm; and (b) empirical relationship among backscattering coefficients at 443, 488, 555, and 667 nm. 30

31 η ( 443) η ( 488) ( ) a λ η ( 555) η ( 667) inputs 1 st hidden output Fig. 2 Basic architecture of NNFM 31

32 Fig. 3 NNFM model-predicted plotting against field-measured a(443), a(488), and a(555) in IOCCG and NOMAD dataset, 1713 samples, where NNFM model was composed of one hidden layer with 11 neurons (Fig. 2). 32

33 Fig. 4 Accuracy and stability of NNFM model in deriving a(λ) from WFS, YCE, and Bohai datasets Fig. 5 The relationship between ARE of NNFM model and field-measured a(λ): 713 samples from 33

34 NOMAD dataset; 1000 samples from IOCCG dataset; 206 samples from WFS dataset; 145 samples from YCE dataset; and 107 samples from the Bohai dataset Fig. 6 Performance of the QAA model in deriving a(443), a(488), and a(555) from remote sensing reflectance provided by YCE, NOMAD, IOCCG, Bohai, and WFS datasets. 34

35 Fig. 7 The relationship between ARE of QAA model and field-measured: 713 samples from NOMAD dataset; 1000 samples from IOCCG dataset; 206 samples from WFS dataset; 145 samples from YCE dataset; and 107 samples from the Bohai dataset Fig. 8 The relationship between estimation uncertainty of QAA and NNFM models-derived a(443) and b b (488) 35

36 Fig. 9 Satellite-derived plotting against field-measured a(λ) in Bohai and YCE seas, 43 samples 36

37 Fig. 10 Spatial and seasonal variations of a(443) in the global oceanic and coastal waters 37