Accurate estimation of the diffuse attenuation coefficient is important for our understanding the availability of light to underwater communities, which provide critical information for the China seas ecosystem. However, algorithm developments and validations of the diffuse attenuation coefficient in the China seas have been seldom performed before and therefore our knowledge on the quality of retrieval of the diffuse attenuate coefficient is poor. In this paper optical data at 306 sites collected in coastal waters of the China seas between July 2000 and February 2004 are used to evaluate three typical existing Kd(490) models. The in situ Kd(490) varied greatly among different sites from 0.029 m−1 to 10.3 m−1, with a mean of 0.92 ± 1.59 m−1. Results show that the empirical model and the semi-analytical model significantly underestimate the Kd(490) value, with estimated mean values of 0.24 m−1 and 0.5 m−1, respectively. The combined model also shows significant differences when the in situ Kd(490) range from 0.2 m−1 to 1 m−1. Thus, the present study proposes that the three algorithms cannot be directly used to appropriately estimate Kd(490) in the turbid coastal waters of the China seas without a fine tuning for regional applications. In this paper, new Kd(490) algorithms are developed based on the semi-analytical retrieval of the absorption coefficient a(m−1) and the backscattering coefficient bb(m−1) from the reflectance at two wavelengths, 488 and 667 nm for the Moderate Resolution Imaging Spectroradiometer (MODIS) and 490 and 705 nm for the Medium Resolution Imaging Spectrometer (MERIS) applications, respectively. With the new approaches, the mean ratio and the relative percentage difference are 1.05 and 4.6%, respectively, based on an independent in situ data set. Furthermore, the estimates are reliable within a factor of 1.9 (95% confidence interval). Comparisons also show that the Kd(490) derived with the new algorithms are well correlated with the in situ measurements. Our results showed a good improvement in the estimation for Kd(490) using the new approaches, contrasting with existing empirical, semi-analytical and combined models. Therefore, we propose the new approaches for accurate retrieval of Kd(490) in the China seas.
©2013 Optical Society of America
The diffuse attenuation coefficient is a common quantity used in optical oceanography for describing the attenuation of light in the water [1–4]. This parameter allows prediction of the availability of light at various depths which impacts on physical processes such as heat transfer, photochemical reactions such as photo oxidation, and biological processes such as phytoplankton photosynthesis in the euphotic zone. Accurate estimation of the diffuse attenuation coefficient is also critical to understanding underwater ecologic health.
Therefore, the diffuse attenuation coefficient has been an important bio-optical product for satellite sensors, such as the Sea-viewing Wide field-of-view Sensor (SeaWiFS, 1997-2010), the Moderate Resolution Imaging Spectroradiometer (MODIS Terra, 1999-present; MODIS Aqua, 2002-present), and the Medium Resolution Imaging Spectrometer (MERIS, 2002-2012). Satellite observations provide synoptic views of the diffuse attenuation coefficient over coastal waters and open ocean at high spatial and temporal resolutions.
The common parameter in use is the diffuse attenuation coefficient at 490 nm, Kd(490). Three types of models are mainly used to estimate Kd(490) from satellite sensors (Table 1). First, empirical relationships between Kd(490) and spectra or chlorophyll a concentrations are derived through regression analyses [1, 5–7]. Usually the spectra are a single wavelength, or different wavelength ratios of the normalized water-leaving radiance (or remote sensing reflectance). Second, semi-analytical approaches based on radiative transfer models and some empirical coefficients are proposed for accurate estimation of Kd(490) in coastal waters [2, 3, 8]. Third, combinations of empirical models and semi-analytical approaches are used to estimate Kd(490) .
Empirical models are generally applicable to clear, open ocean waters or slightly turbid coastal waters. In turbid coastal waters, the uncertainties in the retrieval of Kd(490) significantly increase with Kd(490)>0.25 m−1 . The reason is that turbid waters are often characterized by the presence of inorganic particles and dissolved organic materials showing little correlation with the blue-green ratio.
The semi-analytical model has been shown to address limitations of empirical methods [2, 8]. In order to improve the performance of their method in turbid waters, Lee et al.  applied a wavelength in the red part of the spectrum. By using a validation data set with Kd(490) in the range of 0.04 to 4.0 m–1, they showed that their algorithm has wider applicability for both oceanic and coastal waters than empirical models.
The combined algorithm has been developed to estimate Kd(490) for both open ocean and coastal turbid waters, with the semi-analytical approach for the turbid waters and the existing standard models for the clear open ocean . Furthermore, considerably improved accuracy has been shown in applications of the combined model in the Chesapeake Bay and other turbid coastal waters .
Although satellite sensors now routinely provide synoptic and frequent measurements of Kd, our knowledge on the quality of the products is poor, especially for the China seas. The high variety of water constituents in the China seas gives rise to very optically complicated waters . Compared to other clear ocean or slight turbid waters, it is a challenge to accurately estimate Kd in such areas. Previously, algorithm development and validation of Kd in the China seas have seldom been performed. To our knowledge, no applicable algorithms have been developed and validated to accurately derive Kd products in the China seas. Furthermore, no validation for the existing models (such as those listed in Table 1) with in situ observations in the China seas has been published. The existing models might not be applicable to the China seas, although they were successfully developed and used in other waters.
The Kd products are ecologically-important indices that allow estimation of the availability of light to underwater communities, which provide critical information for the China seas ecosystem. Considering the importance of Kd products, we focus this study on the existing models validation and new approaches for obtaining Kd in the China seas, by using a data set consisting of 13 surveys in the China seas between July 2000 and February 2004.
2 Materials and methods
2.1 Field data collection and processing
A total of 13 oceanographic surveys were conducted in the turbid coastal waters of the China seas between July 2000 and February 2004 (Table 2). Sampling stations were primarily located in two areas: the Pearl River Estuary and adjacent waters (PRE) with longitude 113°E-115 °E latitude 21 °N −23 °N, and in the Yangtze River Estuary and the East China Sea (ECS) with longitude 118 °E-126 °E latitude 28 °N-36 °N (Fig. 1). Waters in these two areas are optically complex with the values of the water constituents varying in a wide range (in 2-3 orders). Observations in the surveys showed that the concentration of chlorophyll a was in the range of 0.01µgl−1-62.9 µgl−1, and the concentrations of the total suspended sediments (TSS) were in the range of 0.6 mgl−1-1762.13 mgl−1. These two areas contain extremely turbid coastal waters in the estuary regions of the Yangtze River and the Pearl River, which are the first and second largest rivers in China. The regions are among the most turbid regions in the global oceans .
Optical data were collected at selected stations using a PRR800 optical profiler (Biospherical Instruments Inc.). Here we briefly introduce the operation of the instrument. The PRR800 instrument measures downwelling irradiance (Ed) and upwelling radiance (Lu) in 18 spectral channels centered at 340, 380, 395, 412, 443, 465, 490, 510, 520, 532, 555, 565, 625, 665, 683, 694, 710 and 765 nm. We deployed the instrument at 306 stations, with 108 located in the PRE and 198 in the ECS (Fig. 1). At each station, we firstly stabilized the instrument in the water for about 5 min to equilibrate the sensor temperature and the sea water temperature. This also allows the instrument to drift further away from the ship (~10 m) to avoid potential ship-reflected light. And then we lowered the instrument at the sun-side of the ship to avoid ship shadow. Dark offset measurements were recorded at the beginning of each profile. With the hand-controlled cable, we lowered the instrument in a free-falling mode at a steady downward speed of about 0.5 ms−1. We recorded both downcast and upcast data. Each cast was repeated several times for quality control and to obtain a mean measurement profile. During the upcast, we paid extra caution to assure the sensor was not tilted when the cable was pulled. Data with tilt angles > 10 were discarded during post processing.
After correction of the measurement profile with the appropriate dark offset, Kd was derived using a non-linear fit between Ed and depth (z):
Here the downwelling irradiance Ed(λ, 0-) is defined just beneath the water-air interface. The derivation of Kd is depth interval dependent . In this study, visual examination of the Ed profile was used to chosen an upper bound that would have minimal surface wave-focusing effects. The depth corresponding to the first optical depth was chosen as the lower bound according to the method introduced in .
After correction of the Lu signal for instrument self-shading (the method is introduced in  and references therein), remote sensing reflectance (Rrs) is derived from the PRR800 measurements. The Lu vertical profile is used to derive the radiance just beneath the water-air interface Lu(λ, 0-) following . Spectral reflectance (rrs) just beneath the water-air interface is computed as following:
Finally Rrs is derived from rrs following :
2.2 Algorithm to estimate Kd(490)
Expanding on an idea presented in the work of [3, 4], we develop a new Kd(490) algorithm using satellite-measured reflectance at two wavelengths. Each step of the algorithm development is detailed in this section.
The relationship between Kd for downwelling irradiance and a, bb, and the solar zenith angle has recently been extensively studied [2–4]. We recall here their Eq. (11) in  that we use to estimate Kd(490).
Here θs is the solar zenith angle and given the value of 45° as in the work of . The method to retrieve a(490) and bb(490) are presented below.
The spectral reflectance just beneath the sea surface can be expressed as :
Here g0 and g1 are empirical coefficients and given the values of 0.0895 and 0.1247, respectively . And the variable of u(λ) is expressed as following:
On the basis of the study of , it is assumed that:
Only a small spectral variation in the scattering coefficient of marine particles in the visible wave bands was observed in . The study of  also showed very weak spectral variations in the backscattering to scattering ratio between 490 and 710nm. So it is therefore assumed that:
Here C is a constant with the value of 1.13 .
From Eq. (10) we can estimate the value of the absorption coefficient at 490nm:
Here values of θs, C, g0 and g1 are given in the previous text. If aw(710), bw(710) and bw(490) are known, Kd(490) can be derived by Eq. (16). In this paper, the value of aw(710) is interpolated from the aw spectrum measured by . The values of bw(710) and bw(490) are interpolated from the spectrum of bw measured by , divided by 2 to account for the backscattering-to-scattering ratio of molecular scattering.
Specifically, for the MODIS applications, we derive Kd(490) data using the central wavelength values of remote sensing reflectance Rrs measured in the MODIS spectral bands (channel 10: 488nm and channel 13: 667nm). Hereafter we represent it as MODIS-Approach.
Furthermore, for the Medium Resolution Imaging Spectrometer (MERIS) applications, we also derive Kd(490) product data using the central wavelength values of remote sensing reflectance Rrs measured in the MERIS spectral bands (channel 3: 490nm and channel 9: 705nm). Hereafter we represent it as MERIS-Approach.
The parameters at specific wavelengths in Eq. (16) are chosen accordingly to fit the wavelengths used in MODIS-Approach and MERIS-Approach. It is noted that the satellite-sensor spectral bands do not exactly match the PRR800 spectral channels. Therefore, we interpolate the data at the closest wavelengths to fit the satellite-sensor spectral bands.
2.3 Data analysis
To understand the applicability of our Kd(490) models, we use the data set of all 306 samples as validation data. It is noted that the data set is independent from our Kd(490) models. The in situ PRR800-measured Kd(490) values range from 0.029 m−1 to 10.3 m−1, with a mean of 0.92 ± 1.59 m−1. Algorithm evaluations for the existing Kd(490) models are also performed by comparing the models’ values with in situ observations.
Statistical analysis (mean value, linear and non-linear fitting) are performed with MATLAB software. The performances of the retrievals are evaluated by the correlation coefficient (R2), the relative percentage difference (RPD) and the mean ratio (MR).
Furthermore, the physical quantities of Kd(490) considered here span over or more than two orders of magnitude. The measurements and the algorithm outputs are affected by measurement errors . Here we consider a Type II linear regression in log space. The error associated with the retrievals by our algorithms is quantified using the 95% confidence interval around the 1:1 line of the relationships between estimated and measured values. We use the same formation to define the 95% confidence interval as Doron et al.  did:
Here SDlog10 is the arithmetic standard deviation calculated on log transformed residuals. This error metric is also applied to the retrieval of Kd(490).
3.1 Spectral Kd(λ) in the turbid coastal waters of the China seas
Figure 2 shows the spectral shape of Kd(λ) as a function of the wavelength from the in situ data collected in the turbid coastal waters of the China seas.
The mean values of Kd(λ) decreases as a function of the wavelength from the blue to green band, and then gradually increases with wavelength to the red, and finally ends with the maximum at the infrared band. The downslope (from the blue to green band) is generally steeper than the upslope (from the green to red band) and flatter than the upslope (from the red to infrared band).
We also plot two sample spectral shapes to represent Kd(λ) in two water types, clear waters and turbid waters, respectively. In the clear waters, Kd(λ) is very low in the blue and green bands, whereas Kd(λ) increases to the red and infrared bands due to water absorption. On the other hand, Kd(λ) in the turbid waters has a shape similar to the mean spectral shape of our data set. Spectral Kd(λ) in other stations show large variations between these two sample types.
3.2 Evaluation results from existing Kd(490) models
To investigate the performance of some existing Kd(490) models in turbid coastal waters of the China seas, we apply these models to the in situ data set to derive Kd(490). Here three typical algorithms are chosen, the empirical model derived from clear waters (the Mueller algorithm) , the semi-analytical model for slight turbid waters (the Lee algorithm)  and the combined model for both clear and turbid ocean waters (the Wang algorithm) .
Comparisons of the measured and estimated Kd(490) using the three typical algorithms are shown in Fig. 3. All three models work well for Kd(490)<0.2 m−1, an upper limit for empirical algorithms . For higher values, the Mueller algorithm considerably underestimates Kd(490) by a factor of ~3-5, compared with the in situ Kd(490) data. For Kd(490)>1 m−1, the data points of Kd(490) derived from the Lee algorithm largely scatter around the 1:1 line. In contrast, the Wang algorithm shows much improved performance in the turbid waters for Kd(490)>1 m−1. However, some scatter is also observed when the in situ Kd(490) ranged from 0.2m−1 to 1 m−1.
Statistical results listed in Table 3 also show significant differences between the measured Kd(490) and the estimated Kd(490) from the Mueller and Lee algorithms, with R2, RPD, 95% Confidence Interval and the mean ratio of 0.52, −37.5%, 4.96 and 0.63 for the Mueller algorithm, and 0.59, −5.8%, 3.34 and 0.94 for the Lee algorithm, respectively. The Wang algorithm performs better than the other two algorithms, with R2, RPD, 95% Confidence Interval and the mean ratio of 0.91, 26.4%, 2.37 and 1.26, respectively.
3.3 Validations of Kd(490) model for turbid coastal waters in the China seas
Figure 4 shows the performance of the two algorithms (MODIS-Approach and MERIS-Approach) when the in situ rrs data (collected from the PRR800 measurements) are used as the algorithm inputs, with statistical results in Table 3.
Both MODIS-Approach and MERIS-Approach algorithms work well for the data set. Although there is some scatter, the data points are rather well distributed around the 1:1 line. For MODIS-Approach, the correlation coefficient (R2) is high at 0.92, and the estimates are 95% reliable within a factor of 1.90. RPD and the mean ratios (model over in situ data) are 4.6% and 1.05, respectively. Similar performances are found with MERIS-Approach where R2, RPD, 95% confidence interval and the mean ratio are 0.95, 4.6%, 1.93 and 1.05, respectively. Given that Kd(490) varies over more than two orders of magnitude, this result can certainly be considered as satisfactory.
4. Discussion and conclusions
4.1 Variation of Kd(λ) in the turbid coastal waters of the China seas
The measured Kd(490) values ranging from 0.029 m−1 to 10.3 m−1 reflects the high variation of turbidity in the turbid coastal waters of the China seas. The ECS receives approximately 486 million tons of sediments annually from the Yangtze River and other rivers. And the Pearl River is the second largest river in China. As a result, large amounts of sediment as well as other particulate matter have accumulated on the seabed. Winds, tides, ocean currents, ocean waves and other forces can easily resuspend fine particles from the bottom to the surface. In the coastal areas of the ECS and the PRE, the concentration of total suspended matter (TSM) can be very high with values over 4000 gm−3 in some regions. In contrast, TSM concentrations are very low in the eastern part of the ECS, less than 0.1 gm−3 . The water turbidity consequently varies from high in coastal areas to low over the outer shelf.
4.2 Assessment of existing Kd(490) models in the China seas
The present study evaluated the performances of the existing Kd(490) models by using the in situ Kd(490) measured in the ECS and the PRE as validation data. The comparisons between the measured Kd(490) and the estimated Kd(490) from the three typical algorithms have been shown in section 3.3. Results show that the typical three methods are not appropriate to derive Kd(490) in the turbid coastal waters of the China seas according to comparisons with the in situ observations.
Results for the turbid coastal waters of the China seas from Lee et al.  semi-analytical model are similar to those from the Mueller model. The mean Kd(490) from the Lee model is 0.5 m−1 and approximate twofold lower compared with the mean value of in situ Kd(490). The Lee algorithm is based on a number of empirical relationships obtained using various regional data sets . Although the empirical relationships used by Lee et al.  proved to be robust, it is necessary to reestablish these relationships for a specific region such as the turbid waters of the China seas. The present study shows that the Lee algorithm cannot be used to appropriately estimate Kd(490) in the research areas before a fine tuning of their algorithm.
Although the Wang algorithm shows much improved performance in the turbid waters for Kd(490)>1 m−1 compared to the other two algorithms, some significant scatter is also observed when the in situ Kd(490) ranged from 0.2 m−1 to 1 m−1. The Wang algorithm is a combination model with considerations of the clear open ocean oceans and the coastal turbid waters. Similar to the Lee model, the Wang algorithm uses empirical relationships obtained using various regional data sets. For applications in other regions such as the turbid waters of the China seas, a fine tuning is necessary.
4.3 Assessment and application of MODIS-Approach and MERIS-Approach to derive Kd(490)
Comparisons of the estimation precision of MODIS-Approach and MERIS-Approach with that of the three typical models are shown in Table 3, Fig. 3 and Fig. 4. Both MODIS-Approach and MERIS-Approach appear much improved performance than the three models. It is noted that the well performance of the new approaches is validated by using independent in situ data sets, because the data sets have not been used for the model development.
The design of the new approaches presented in this paper is different from the Lee model, although they are all semi-analytical algorithms. As previous noted, the Lee model is based on a number of empirical relationships obtained using various regional data sets. In contrast, our new approaches are based on simpler assumptions by using the near infrared wavelength. Only a few parameters and one empirical relationship between the IOPs are needed to recourse. The present study proposes that the parameterization and the empirical relationship prove to be robust, as assessed by the excellent retrieval using independent in situ data sets. An important aspect of these algorithms is that most parameters are described as measurable quantities (such as, the backscattering to scattering ratio between 490 and 710 nm) and/or can be derived from radiative transfer calculations (for example, the factors of g0 and g1). It is not necessary to establish empirical coefficients regionally or measuring simultaneously the IOPs and reflectances. If needed, a fine regional tuning of the algorithms using frequently measured optical properties is sufficient.
Due to the in situ Kd(490) validation data are measured in the optically complex waters with the TSS ranged from 0.6 mgl−1-1762.13 mgl−1, the proposed algorithms are valid in both clear waters and turbid waters and are largely insensitive to regional variability in optical properties.
The algorithms presented here use remote sensing reflectance at only two wavelengths, 488 nm and 667 nm for the MODIS-Approach, and 490 nm and 705 nm for the MERIS-Approach, respectively. In fact, the remote sensing reflectance ratio is well correlated to Kd(490) from our in situ data sets. Figure 5 shows that remote sensing reflectance ratio value between bands 667 and 488 nm, Rrs(667)/Rrs(488), is strongly correlated to Kd(490) with a correlation coefficient R2 = 0.92. High correlation (R2 = 0.90) is also observed between Rrs(705)/Rrs(490) and Kd(490).
The successful application of our Kd(490) algorithms will allow the possibility of Kd(490) distributions study in the China seas over spatial and temporal scales. Furthermore, the Kd(490) algorithms will facilitate the estimation of Kd(PAR) and euphotic depth, which are important quality indexes of an ecosystem.
This study was jointly supported by the Public Science and Technology Research Funds Projects of Ocean (201005030), the National Natural Science Foundation of China (41276186), and the Fund from NUIST (S8111005001). We thank W. J. Jian for providing the optical data. We are also thankful to two anonymous reviewers who provided substantial comments and suggestions that led to the improvement of this manuscript.
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