# Retrieval of diffuse attenuation coefficient in the Chesapeake Bay and turbid ocean regions for satellite ocean color applications

## Abstract

[1] There are several empirical and semianalytical models for the satellite-based estimation of the diffuse attenuation coefficient for the downwelling spectral irradiance at the wavelength 490 nm, *K*_{d}(490), or the diffuse attenuation coefficient for the downwelling photosynthetically available radiation (PAR), *K*_{d}(PAR). An empirical algorithm has been used to routinely produce NASA standard *K*_{d}(490) product from the Moderate Resolution Imaging Spectroradiometer (MODIS). However, these models are generally applicable for clear open ocean waters. Our results show that for the Chesapeake Bay, *K*_{d}(490) data from the existing models are significantly underestimated by a factor of ∼2–3 compared with the in situ data. In this paper, new *K*_{d}(490) models for the Chesapeake Bay and coastal turbid waters are derived using a relationship relating the backscattering coefficient at the wavelength 490 nm, *b*_{b}(490), to the irradiance reflectance just beneath the surface at the red wavelengths. For coastal turbid ocean waters, *b*_{b}(490) can be more accurately correlated to the irradiance reflectance at the red bands. Using the in-situ-derived *b*_{b}(490) relationship in the Chesapeake Bay, *K*_{d}(490) models are formulated using the semianalytical approach. Specifically, two *K*_{d}(490) models using the MODIS-derived normalized water-leaving radiances at wavelengths 488 and 667 nm and 488 and 645 nm are proposed and tested over the Chesapeake Bay and other coastal ocean regions. Match-up comparisons between the MODIS-derived and in-situ-measured *K*_{d}(490) and *K*_{d}(PAR) products in the Chesapeake Bay show that the satellite-derived data using the proposed models are well correlated with the in situ measurements. However, the new models are mostly suitable for turbid waters, whereas existing empirical and semianalytical models provide better results in clear open ocean waters. Therefore, we propose to use a combination of the standard (for clear oceans) and turbid *K*_{d}(490) models for more accurate retrieval of *K*_{d}(490) (or *K*_{d}(PAR)) products for both clear and turbid ocean waters.

## 1. Introduction

[2] The diffuse attenuation coefficient is an important water property related to light penetration and availability in aquatic systems. Accurate estimation of the diffuse attenuation coefficient is critical to understand not only physical processes such as the heat transfer in the upper layer of the ocean [*Lewis et al.*, 1990; *Morel and Antoine*, 1994; *Sathyendranath et al.*, 1991; *Wu et al.*, 2007], but also biological processes such as phytoplankton photosynthesis in the ocean euphotic zone [*Platt et al.*, 1988; *Sathyendranath et al.*, 1989]. Satellite observations of the diffuse attenuation coefficient at the wavelength 490 nm, *K*_{d}(490), is the only effective method to provide large-scale maps of *K*_{d}(490) over basin and global scales for ocean waters at high spatial and temporal resolutions. Several empirical and semianalytical models of *K*_{d}(490) are commonly in use to derive the *K*_{d}(490) maps from ocean color satellite sensors such as the Sea-viewing Wide Field-of-view Sensor (SeaWiFS) [*McClain et al.*, 2004], and the Moderate Resolution Imaging Spectroradiometer (MODIS) [*Esaias et al.*, 1998]. First, an empirical relationship between the blue-green normalized water-leaving radiance ratio and *K*_{d}(490) is used to estimate *K*_{d}(490) [*Mueller*, 2000]. The second model is derived empirically through regression analyses using the relationship of *K*_{d}(490) and chlorophyll-a concentration [*Morel*, 1988; *Morel et al.*, 2007]. To provide improved accuracy for *K*_{d}(490) in coastal waters, semianalytical approaches based on radiative transfer models have been proposed [*Lee et al.*, 2002, 2005a, 2005b, 2007].

[3] However, these models are generally applicable to clear open ocean waters, e.g., NASA standard *K*_{d}(490) product data derived using *Mueller* [2000] from SeaWiFS and MODIS measurements are generally accurate for clear open ocean waters. Although the semianalytical model [*Lee et al.*, 2002] has been developed to address limitations of empirical methods [*Morel*, 1988; *Mueller*, 2000], there are still large uncertainties in estimating *K*_{d}(490) for turbid coastal waters where there are significant ocean contributions at the near-infrared (NIR) bands, e.g., waters with abundant suspended sediment and/or colored dissolved organic matter (CDOM). It has been reported that the SeaWiFS standard *K*_{d}(490) product was not applicable for optically complex waters [*Son et al.*, 2005]. In fact, *Son et al.* [2005] derived *K*_{d}(490) data from a relationship between Secchi depth and the SeaWiFS normalized water-leaving radiance at the wavelength 555 nm for applications in the Yellow Sea. In a study using a semianalytical model of spectral diffuse attenuations for a turbid estuary [*Gallegos et al.*, 1990], empirical relationships for regional water absorption and scattering coefficients with water optical and biological parameters, such as chlorophyll-a, dissolved organic matter (DOM), and suspended sediment, as well as tabulated values of specific absorption, were used to derive diffuse attenuation coefficients. Recently, an algorithm using the water-leaving reflectance measured at wavelengths 490 and 709 nm to derive *K*_{d}(490) data has been proposed [*Doron et al.*, 2007]. Using the ground-based measurements, *Doron et al.* [2007] demonstrated that the proposed algorithm gave improved estimates of *K*_{d}(490) for various turbid coastal waters.

[4] In this paper, we briefly describe the *Mueller* [2000] and *Lee et al.* [2002] models for deriving a *K*_{d}(490) product, and examine the performance of models for the turbid coastal waters. Expanding on an idea presented in the work of *Doron et al.* [2007], we develop a new *K*_{d}(490) algorithms using MODIS-measured reflectances at wavelengths 488 and 667 nm and 488 and 645 nm applicable to turbid coastal waters, in particular, in the Chesapeake Bay. Since new models are mostly applicable to turbid coastal waters, we propose a merging algorithm that combines the *K*_{d}(490) models applicable to the open ocean and turbid coastal waters to derive a satellite *K*_{d}(490) product. The in situ bio-optical data provided by the NASA SeaWiFS Bio-optical Archive and Storage System (SeaBASS) are used for the algorithm development. SeaBASS in situ data have been frequently used in support of the satellite ocean color product validation and algorithm evaluations [e.g., *Bailey and Werdell*, 2006; *Wang et al.*, 2005]. The proposed new diffuse attenuation coefficient models, as well as models from *Mueller* [2000] and *Lee et al.* [2002], are assessed using both SeaBASS data (for the Chesapeake Bay and global oceans) and a separate in situ data set from the Chesapeake Bay Program. Finally, using the new *K*_{d}(490) models, we provide the MODIS-derived *K*_{d}(490) product images for the Chesapeake Bay and three other extremely turbid coastal regions, as well as for the global ocean.

## 2. Diffuse Attenuation Coefficient Models

[5] There are commonly two types of models for estimation of the diffuse attenuation coefficient at the wavelength 490 nm, *K*_{d}(490), using the satellite measurements, i.e., the empirical model derived from in situ water optical and bio-optical data [*Austin and Petzold*, 1986; *Morel*, 1988; *Morel et al.*, 2007; *Mueller*, 2000], and the semianalytical approach based on in situ data and radiative transfer modeling [*Lee et al.*, 2002]. We briefly describe these models, which have been used for producing *K*_{d}(490) product data from SeaWiFS/MODIS measurements.

*Mueller*[2000] proposed an empirical model based on the ratio of normalized water-leaving radiances

*nL*

_{w}(

*λ*) at wavelengths 490 and 555 nm, i.e.,

*K*

_{w}(490),

*A*, and

*B*are coefficients to best fit the formula from in situ measurements. The original fitting coefficient values [

*Mueller*, 2000] of

*K*

_{w}(490),

*A*, and

*B*, have been revised to

*K*

_{w}(490) = 0,

*A*= 0.1853, and

*B*= −1.349 to improve algorithm performance for the clearest ocean waters (J. Werdell, Ocean color K490 algorithm evaluation, 2005, available online at http://oceancolor.gsfc.nasa.gov/REPROCESSING/SeaWiFS/R5.1/k490_update.html). The revised algorithm [

*Mueller*, 2000] has been implemented in the NASA standard SeaWiFS and MODIS ocean color data processing to generate global ocean

*K*

_{d}(490) products. For the rest of the paper, we refer to the

*Mueller*[2000] model as the

*Mueller*[2000] with revised coefficients from Werdell (online reference, 2005). Similarly, an empirical

*K*

_{d}(490) model based on chlorophyll-a concentration has been proposed [

*Morel*, 1988]. This model has recently been revised [

*Morel et al.*, 2007] using in situ measurements from the NASA Bio-Optical Marine Algorithm Data (NOMAD) set [

*Werdell and Bailey*, 2005], and the revised formula is given as

^{3}. It is noted that both empirical algorithms [

*Morel et al.*, 2007;

*Mueller*, 2000] are only suitable for nonturbid ocean waters with

*K*

_{d}(490) values up to ∼0.3 m

^{−1}.

*Lee et al.*[2002] proposed a semianalytical approach for deriving

*K*

_{d}(

*λ*) based on radiative transfer modeling [

*Lee et al.*, 2005a]. The model has been revised recently and can be written as [

*Lee et al.*, 2002, 2005a, 2007]

_{0}is the solar zenith angle in the air [

*Lee et al.*, 2005b]. Specifically, at

*λ*= 490 nm,

*K*

_{d}(490) can be derived from equation (3) with inputs of the absorption and backscattering coefficients at the wavelength 490 nm,

*a*(490) and

*b*

_{b}(490), which are calculated using the normalized water-leaving reflectances at wavelengths 443, 490, 555, and 670 nm [

*Lee et al.*, 2002, 2005a, 2007]. Compared with results from empirical model,

*Lee et al.*[2005a] show that with the semianalytical approach the

*K*

_{d}(490) product can be improved for coastal ocean waters.

## 3. Algorithm Evaluations for the Existing *K*_{d}(490) Models

### 3.1. In Situ Data

[8] In situ radiometric data including the diffuse attenuation coefficient for the Chesapeake Bay were obtained from the SeaBASS (http://seabass.gsfc.nasa.gov/) to derive a regional diffuse attenuation model and to evaluate existing models for turbid Chesapeake Bay waters (Figure 1). For this study, the SeaBASS data in the main stem of the Chesapeake Bay were used. Those data were collected using two optical instruments, MER2040/2041 profiling spectroradiometer (Biospherical Instruments Inc., http://www.biospherical.com/) and Satlantic MicroPro multispectral profiling radiometer (http://www.satlantic.com/), and provide spectral in-water upward radiance profile data (*L*_{u}(*λ*, *z*)) and spectral downwelling irradiance profile (*E*_{d}(*λ*, *z*)) data. Spectral diffuse attenuation coefficients (*K*_{d}(*λ*)) were computed as the slopes from linear regressions of data from in situ spectral irradiance profiles (*E*_{d}(*λ*, *z*)) on water depth using natural logarithmic transformed *E*_{d}(*λ*, *z*), and *K*_{d}(*λ*) data. These profiles were obtained from 1996 to 2003 and at various wavelengths from 412 to 700 nm for the MER instrument and from 400 to 700 nm using the MicroPro radiometer. Normalized water-leaving radiances (*nL*_{w}(*λ*)) [*Gordon*, 2005; *Gordon and Wang*, 1994; *Wang*, 2006] are calculated using the following equation: *nL*_{w}(*λ*) = *F*_{0}(*λ*)*L*_{w}(*λ*)/*E*_{s}(*λ*), where *F*_{0}(*λ*) and *E*_{s}(*λ*) are the extraterrestrial solar irradiance and the downward surface irradiance at the wavelength *λ* (total number of the measurements is 350), respectively. Since the wavelengths for the radiances in SeaBASS are not exactly matched with those of satellite measurements, we used the nearest wavelength values of water-leaving radiances at wavelengths 443, 490, 531, 555, and 670 nm to apply the existing standard algorithms for the diffuse attenuation coefficient computation. Because the MicroPro casts were usually performed up to three times at each station, we computed average values from multiple measurements. Additionally, the radiometric data measured by the MER2040/2041 and *K*_{d}(*λ*) data derived from in situ radiometric measurements for three cruises were excluded because the values were significantly different (e.g., about 1–2 orders lower in magnitude for both radiometric and *K*_{d}(*λ*) data) compared with values measured using the MicroPro on the same cruises.

[9] In addition, a long-term Chesapeake Bay Program Water Quality Database that began in 1984, including diffuse attenuation coefficients for the downwelling photosynthetically available radiation (PAR), *K*_{d}(PAR), and downwelling irradiance PAR data at various depth *z*, PAR(z), has been maintained by the Chesapeake Bay Program (http://www.chesapeakebay.net/wquality.htm) and these data are readily available for this study. The PAR(z) data (from 400 to 700 nm) have been measured using the LI-192SA Underwater Quantum Sensor (http://www.licor.com/) at various water depths. In the Chesapeake Bay Program Water Quality Database, however, there are no in situ spectral water-leaving radiance data. Thus, we used in situ downwelling irradiance PAR(z) and diffuse attenuation coefficient data (Figure 1) for validation and evaluation of the satellite algorithms in deriving the *K*_{d}(PAR) product.

[10] Furthermore, to evaluate the existing and new proposed models of *K*_{d}(490) for the global ocean, the NASA SeaBASS in situ data set excluding all the Chesapeake Bay data was also used (data from open oceans and some coastal waters). Remote sensing reflectance (*R*_{rs}) data were converted to the normalized water-leaving radiances as *nL*_{w}(*λ*) = *F*_{0}(*λ*)*R*_{rs}(*λ*).

[11] In summary, the following three groups of the in situ data sets are used for the study: (1) the SeaBASS Chesapeake Bay data set, (2) the global SeaBASS data set with excluding the Chesapeake Bay data, and (3) the data set from the Chesapeake Bay Program Water Quality Database.

### 3.2. Spectral *K*_{d}(*λ*) in the Chesapeake Bay

[12] The spectral shape of the diffuse attenuation coefficient *K*_{d}(*λ*) as a function of the wavelength from the SeaBASS data in the Chesapeake Bay waters is plotted in Figure 2. Figure 2 shows that *K*_{d}(*λ*) decreases as a function of the wavelength to the green band with the maximum at the blue band, and then gradually increases as increase of the wavelength to the red. However, the downslope (from the blue to green band) is generally steeper than the upslope (from the green to red band). The high diffuse attenuation coefficients in the blue and green bands are most likely due to the high concentrations of yellow substances (i.e., CDOM) and suspended sediments. Two sample spectral shapes of diffuse attenuation coefficients from waters in the Bermuda Island (dotted line) and the Strait of Dover (dash line) are also plotted in the same Figure 2. In the clear open ocean (near Bermuda), the diffuse attenuation coefficient is very low in the blue and green bands (unlike the spectral shapes for Chesapeake Bay waters), whereas the diffuse attenuation coefficient increases to the red bands due to water absorption. On the other hand, *K*_{d}(*λ*) data obtained around the Dover Strait, where waters are typically turbid, are similar to those from the Chesapeake Bay region.

### 3.3. Ocean Color Satellite Data From MODIS-Aqua

[13] Because the Chesapeake Bay is generally turbid [*Shi and Wang*, 2007b; *Wang and Shi*, 2005], MODIS level 2 ocean color products were generated from the MODIS-Aqua level 1B data using recently developed shortwave infrared (SWIR) and NIR-SWIR combined atmospheric correction algorithms [*Wang*, 2007; *Wang and Shi*, 2005, 2007]. It has been demonstrated that the SWIR-based algorithm improves satellite-derived ocean color products for turbid coastal waters [*Wang et al.*, 2009, 2007], and SWIR-derived data product can have various important applications [*Nezlin et al.*, 2008; *Shi and Wang*, 2007a, 2008, 2009a]. The level 2 product data were remapped and processed to generate composite images. We used a similar method as presented by *Bailey and Werdell* [2006] and *Wang et al.* [2009] for satellite and in situ ocean color data match-up analyses. The match-up method is briefly described here. For comparison with the in situ measurements, we extracted pixels from a 5 × 5 box centered at the location of the in situ measurement from the MODIS level 2 product after applying a set of masks such as land, cloud/ice, and sun glint, as well as two flags (high solar zenith and sensor zenith angles). Mean values were computed for a match-up box where at least 50% valid pixels occurred. To remove highly biased satellite data, data with their values within the range of one standard deviation are selected to derive a revised mean. In addition, the match-up analyses are performed only for the data where the time difference between MODIS and in situ measurements are within 8 (i.e., ±8) hours.

### 3.4. Evaluation Results From Existing *K*_{d}(490) Models

[14] To investigate the performance of some existing *K*_{d}(490) models [e.g., *Mueller*, 2000; *Lee et al.*, 2002] in Chesapeake Bay waters, we applied these models to the SeaBASS data set to derive *K*_{d}(490) data (Figure 3). Figure 3 shows that the model derived *K*_{d}(490) values are all considerably underestimated by a factor of ∼2–3, compared with the in situ *K*_{d}(490) data, although results from the semianalytical model [*Lee et al.*, 2002] are slightly better than empirical models. The mean ratio values (model versus in situ) for *Mueller* [2000] (Figure 3a) and *Lee et al.* [2002] (Figure 3b) are 0.42 and 0.57, respectively. It is noted that these comparisons are all with in situ data, i.e., *K*_{d}(490) data were derived from the in situ water-leaving radiance data.

[15] Histograms of the in situ *K*_{d}(490) in the main stem of the Chesapeake Bay, as well as that of *K*_{d}(490) derived from the *Mueller* [2000] model using the same in situ data, have also been analyzed (results not shown). The in situ *K*_{d}(490) values range from 0.35 to 6.6 m^{−1} and the distribution is different from that of the model *K*_{d}(490) data. The mean value (1.27 m^{−1}) of in situ *K*_{d}(490) in the Chesapeake Bay region is more than twofold higher compared with the mean *K*_{d}(490) (0.51 m^{−1}) from the *Mueller* [2000] model. The apparent underestimation of the model *K*_{d}(490) results is because those models are derived for the clear open ocean. The empirical model from the blue-green radiance ratio has large uncertainties in the waters where *K*_{d}(490) is greater than 0.25 m^{−1} [*Mueller*, 2000]. Results for Chesapeake Bay waters from the chlorophyll-based empirical algorithm [*Morel*, 1988; *Morel et al.*, 2007] and *Lee et al.* [2002] semianalytical model are similar to those from the *Mueller* [2000] model.

## 4. Development of *K*_{d}(490) Model for Turbid Coastal Waters

### 4.1. Expression of the Backscattering Coefficient at the Wavelength 490 nm

*b*

_{b}(

*λ*) can generally be expressed as a function of the spectral irradiance reflectance just beneath the sea surface

*R*(

*λ*) and the absorption coefficient

*a*(

*λ*) [

*Gordon et al.*, 1988].

*Doron et al.*[2007] show that the backscattering coefficient at the wavelength 490 nm,

*b*

_{b}(490), can be linearly related to the irradiance reflectance just beneath the surface at the wavelength 709 nm,

*R*(709) [

*Doron et al.*, 2007]. Following this idea, we relate

*b*

_{b}(490) to the irradiance reflectance just beneath the surface at the wavelength 670 nm,

*R*(670), as

*C*

_{0}and

*C*

_{1}are taken as constants related to water optical and bio-optical properties. In fact,

*C*

_{0}and

*C*

_{1}can be expressed as [

*Doron et al.*, 2007]

*b*

_{bw}(

*λ*) and

*b*

_{bp}(

*λ*) are the backscattering coefficients at a given wavelength for pure seawater and particles, respectively. The parameter

*a*(

*λ*) is the total absorption coefficient, and

*f*(

*λ*) is the coefficient that relates ocean upwelling irradiance reflectance to the ocean inherent optical properties (IOPs). On the other hand, the absorption coefficient at the wavelength 490 nm,

*a*(490), can be related to the irradiance reflectance at the wavelength 490 nm,

*R*(490), and the backscattering coefficient at the wavelength 490 nm,

*b*

_{b}(490), i.e.,

*f*(490) can be approximated as a constant [

*Gordon et al.*, 1975;

*Morel and Prieur*, 1977], which can be set to 0.335 [

*Loisel and Morel*, 2001]. Figure 4a shows results of

*b*

_{b}(490) as a function of

*R*(670) for the Chesapeake Bay region. The

*b*

_{b}(490) data were derived by solving equations (3) and (7) using the in-situ-measured

*K*

_{d}(490) and the reflectance at the wavelength 490 nm data,

*R*(490), from the SeaBASS data set, while

*R*(670) data are also in situ measurements from the Chesapeake Bay region. To clearly show the relationship between

*b*

_{b}(490) and

*R*(670), particularly for low

*b*

_{b}(490) and

*R*(670) values, log scales for both

*x*and

*y*axis are used. In Figure 4a, a linear fit is plotted, indicating an intercept of 0.0007 and a slope of 2.7135 with a correlation coefficient of 0.974. Thus, in the Chesapeake Bay, the backscattering coefficient at the wavelength 490 nm,

*b*

_{b}(490), can be accurately calculated from measurements of the upwelling irradiance reflectance just beneath the sea surface

*R*(670) as

[17] It is noted that, however, in deriving equation (8) we have assumed that *C*_{1} in equation (6) is a constant. In effect, we have assumed that *a*(670)/*f*(670) is a constant for the region because the variation of *b*_{bp}(490)/*b*_{bp}(670) is generally small [*Barnard et al.*, 1998]. The variation in *a*(670) is mostly from the variation of absorption by phytoplankton for the Chesapeake Bay region. From the SeaBASS Chesapeake Bay data set, it is found that the mean values of absorption coefficients for phytoplankton *a*_{ph}(670), suspended sediment *a*_{s}(670), and yellow substance *a*_{y}(670) are 0.259, 0.0264, and 0.0104 m^{−1}, respectively, with the corresponding standard deviation values of 0.141, 0.0245, and 0.005 m^{−1}, respectively. However, it has been shown that *f*(670) actually increases (or decreases) with increase (or decrease) of *a*_{ph}(670) (i.e., chlorophyll-a) [*Morel and Mueller*, 2002]. Results shown in Figure 4a confirmed that, as an approximation, *b*_{b}(490) can be linearly related to *R*(670) in the Chesapeake Bay.

### 4.2. *K*_{d}(490) Model Using MODIS-Derived *nL*_{w}(488) and *nL*_{w}(667) Data

*K*

_{d}(490) for the Chesapeake Bay and turbid ocean waters can be derived. Specifically, for the MODIS applications, we derive

*K*

_{d}(490) product data using the MODIS-measured normalized water-leaving radiances

*nL*

_{w}(

*λ*) at wavelengths 488 and 667 nm (assuming θ

_{0}of 30° in equation (3) [

*Lee et al.*, 2005b]), i.e.,

*R*(

*λ*) can be computed from the MODIS-derived

*nL*

_{w}(

*λ*) as [

*Gordon et al.*, 1988;

*Lee et al.*, 2002;

*Mobley*, 1994] (with assuming the

*Q*factor of 4 for Case 2 waters following

*Loisel and Morel*[2001])

*F*

_{0}(

*λ*) is the extraterrestrial solar irradiance at a given wavelength

*λ*. Thus,

*K*

_{d}(490) data can be derived from satellite-measured

*nL*

_{w}(

*λ*) at wavelengths 488 and 667 nm through equations (9) and (10). It is noted that

*K*

_{d}(490) in equation (9) is essentially a function of the MODIS-derived reflectance ratio between wavelengths at 667 and 488 nm,

*R*(667)/

*R*(488). We will show later that for the turbid coastal waters there is a strong correlation between

*K*

_{d}(490) and

*R*(667)/

*R*(488).

[19] Figure 4b shows *K*_{d}(490) comparison results of the new model-derived values using equation (9) and in-situ-measured data. Note that the model *K*_{d}(490) data were derived using equation (9) with the in-situ-measured reflectance data from SeaBASS data set. In Figure 4b, two sets of the in situ *K*_{d}(490) data (all from SeaBASS), one from the Chesapeake Bay region and another from global non-Chesapeake Bay data, are used. The Chesapeake Bay *K*_{d}(490) data have generally high values ranging from ∼0.4–5 m^{−1}, while the non-Chesapeake Bay in situ data have *K*_{d}(490) values ranging from ∼0.02–3.7 m^{−1} covering deep clear oceans (e.g., oligotrophic waters) to some coastal turbid waters. Results in Figure 4b verified the new algorithm performance for the Chesapeake Bay region because equation (9) is essentially obtained using the same Chesapeake Bay in situ data. It is important to note that the new algorithm (equation (9)) worked well in other coastal ocean regions with *K*_{d}(490) values >∼0.3 m^{−1}, indicating that the new *K*_{d}(490) algorithm is also applicable for global turbid ocean waters. However, compared with the non-Chesapeake Bay in situ measurements, for *K*_{d}(490) values of ∼0.1–0.3 m^{−1} the new algorithm obtained *K*_{d}(490) data were biased high (Figure 4b). Thus, the new model may not be applicable to clear ocean waters.

### 4.3. *K*_{d}(490) Model Using MODIS *nL*_{w}(488) and *nL*_{w}(645) Data

*K*

_{d}(490) product using the MODIS-measured

*nL*

_{w}(

*λ*) data at the wavelengths 488 and 645 nm. MODIS-measured high spatial radiance data (0.25 km) at wavelength 645 nm is particularly useful for retrieval of

*K*

_{d}(490) product in coastal regions due to high spatial variation in the regional water optical and bio-optical properties. In addition, for extremely turbid waters, MODIS band 667 nm is often saturated and cannot be used. Thus, MODIS radiance measured at the wavelength 645 nm needs to be substituted in this case. Using the MODIS-measured

*K*

_{d}(490) (from equation (9)) and

*nL*

_{w}(

*λ*) data at wavelengths 488, 645, and 667 nm, and the same procedure outlined in section 4.1,

*b*

_{b}(490) as a function of the irradiance reflectance at the wavelength 645 nm,

*R*(645), can be derived as

*K*

_{d}(490) using the MODIS

*R*(488) and

*R*(645) data can be written as

*R*(

*λ*) given by equation (10).

### 4.4. *K*_{d}(490) Model for Both Open Oceans and Coastal Turbid Waters

[21] It has been demonstrated that for open ocean waters both empirical [*Morel*, 1988; *Mueller*, 2000] and semianalytical [*Lee et al.*, 2002] models can derive accurate *K*_{d}(490) product data. For the Chesapeake Bay region, however, both models significantly underestimated *K*_{d}(490) values (Figure 3), although the semianalytical model produced slightly better results compared with the data from *Mueller* [2000] empirical model. The empirical models use information on the normalized water-leaving reflectance ratio derived from wavelengths at the blue and green bands (either use reflectance ratio directly or through derived chlorophyll-a from reflectance ratio) to infer the *K*_{d}(490) product. Figure 5a provides *K*_{d}(490) as a function of the remote-sensing reflectance ratio between bands 555 and 490 nm, *R*_{rs}(555)/*R*_{rs}(490), from the SeaBASS in situ data set (all data). Results in Figure 5a show that, for low *K*_{d}(490) values, i.e., <∼0.3 m^{−1}, the reflectance ratio between bands 555 and 490 nm is strongly correlated to *K*_{d}(490), while for *K*_{d}(490) > ∼0.3 m^{−1} the relationship of *K*_{d}(490) versus the ratio of *R*_{rs}(555)/*R*_{rs}(490) is quite noisy. Conversely, Figure 5b shows that reflectance ratio value between bands 670 and 490 nm, *R*_{rs}(670)/*R*_{rs}(490), is strongly correlated to *K*_{d}(490) when its values are high, e.g., >∼0.3 m^{−1}, whereas for *K*_{d}(490) < ∼0.3 m^{−1} the *K*_{d}(490) versus *R*_{rs}(670)/*R*_{rs}(490) relationship is quite noisy. In particular, when *K*_{d}(490) < ∼0.3 m^{−1}, the reflectance ratio value in *R*_{rs}(670)/*R*_{rs}(490) is very low and thereby difficult to use for accurately deriving the *K*_{d}(490) product from satellite measurements, due to noisiness (errors) of the derived water-leaving reflectance product, e.g., errors from atmospheric correction algorithm.

*K*

_{d}(490) product data using equation (9) and/or equation (10) for turbid coastal waters, while for open oceans the

*Mueller*[2000] and

*Morel*[1988] or

*Lee et al.*[2002] models can be used. These two algorithms (for open oceans and turbid coastal waters) need to be combined to produce smooth

*K*

_{d}(490) data for clear ocean and turbid waters, as well as waters of intermediate transparency. Figure 6 provides

*K*

_{d}(490) versus the reflectance ratio

*R*

_{rs}(670)/

*R*

_{rs}(490), demonstrating a method for merging two algorithms. In Figure 6, a linear fitting between

*K*

_{d}(490) values of 0.3 and 0.6 m

^{−1}is derived using

*K*

_{d}(490) data from

*Lee et al.*[2002] (for low values), the new model (equation (9)) (for high values), and in situ data, i.e.,

*R*

_{rs}(670)/

*R*

_{rs}(490) = 0.2604 and 0.4821,

*K*

_{d}(490) = 0.3 and 0.6 m

^{−1}, respectively. The weighting function for bridging two types of

*K*

_{d}(490) models can be obtained by normalizing equation (13), i.e.,

*K*

_{d}(490) model can thus be expressed as

*W*is computed from equation (14) with

*W*= 0 for

*W*≤ 0 and

*W*= 1 for

*W*≥ 1. In the above equation,

*K*

_{d}

^{Clear}(490) is the model for open oceans [e.g., from

*Mueller*, 2000;

*Morel et al.*, 2007;

*Lee et al.*, 2002], and

*K*

_{d}

^{Turbid}(490) is the model developed in this study for turbid coastal waters (equation (9) or equation (12)). Thus, for values of

*K*

_{d}(490) ≤ 0.3 m

^{−1},

*K*

_{d}

^{Comb}(490) in equation (15) produces diffuse attenuation coefficient using the

*K*

_{d}

^{Clear}(490) model, while for values of

*K*

_{d}(490) ≥ 0.6 m

^{−1}the

*K*

_{d}

^{Turbid}(490) model is used in equation (15). For values of

*K*

_{d}(490) between 0.3 and 0.6 m

^{−1}, a weight according to equation (14) is used to combine values produced from models of

*K*

_{d}

^{Clear}(490) and

*K*

_{d}

^{Turbid}(490). It is noted that for MODIS measurements, the reflectance ratio of

*R*

_{rs}(667)/

*R*

_{rs}(488) is used in equations (13)–(15).

## 5. MODIS-Aqua Results From the New *K*_{d}(490) Model

[23] The new proposed *K*_{d}^{Comb}(490) model (equation (15)) is used to derive the MODIS-Aqua *K*_{d}(490) data in the Chesapeake Bay and other turbid and open ocean regions. The *nL*_{w}(*λ*) spectra data, which are inputs for the proposed *K*_{d}^{Comb}(490) model, are derived using the SWIR and NIR-SWIR combined atmospheric correction algorithms. The satellite-derived *K*_{d}(490) data are compared with the in situ measurements. These comparison results are provided and discussed in sections 5.1–5.3.

### 5.1. MODIS-Measured *K*_{d}(490) Data in the Chesapeake Bay

[24] MODIS-Aqua-derived *K*_{d}(490) values in the Chesapeake Bay are compared with the SeaBASS in situ data. There are only eight MODIS-in-situ *K*_{d}(490) match-up data points from the SeaBASS data set for the Chesapeake Bay (Figure 7). In Figure 7, four satellite algorithms (with MODIS-Aqua measurements) are evaluated using the Chesapeake Bay in situ data. Similar to the results in Figure 3, the MODIS-Aqua *K*_{d}(490) values derived from the *Mueller* [2000] and *Lee et al.* [2002] models are underestimated compared with the in situ *K*_{d}(490) data, although results from the semianalytical model [*Lee et al.*, 2002] are slightly better than those from the empirical model. The mean ratio values (model versus in situ) for *Mueller* [2000] and *Lee et al.* [2002] in Figure 7 are 0.31 and 0.43, respectively. Meanwhile, the MODIS *K*_{d}(490) values derived using the proposed algorithm *K*_{d}^{Comb}(490) (equation (15)) are well correlated with the in situ data (Figure 7). Since in situ *K*_{d}(490) data for the Chesapeake Bay are all >0.6 m^{−1}, the MODIS *K*_{d}(490) data derived with the new algorithm *K*_{d}^{Comb}(490) (equation (15)) are in fact *K*_{d}^{Turbid}(490) values (i.e., *W* = 1 in equation (15)), which were obtained effectively using equation (9) (with MODIS *nL*_{w}(488) and *nL*_{w}(667) data) and equation (12) (with MODIS *nL*_{w}(488) and *nL*_{w}(645) data). In Figure 7, the mean ratios (model versus in situ) for the proposed algorithms using MODIS *nL*_{w}(488) and *nL*_{w}(667) data (equation (9)) and *nL*_{w}(488) and *nL*_{w}(645) data (equation (12)) are 0.96 and 0.92, respectively.

### 5.2. MODIS-Measured *K*_{d}(PAR) Data in the Chesapeake Bay

*K*

_{d}(PAR), which provides information of underwater light field and the euphotic depth, is an important parameter for satellite-derived primary productivity estimates within the water column. The

*K*

_{d}(PAR) can be defined and related to

*K*

_{d}(

*λ*) through the following equation [

*Baker and Frouin*, 1987;

*Morel and Smith*, 1974]:

^{−2}) at depths of

*z*= 0 (just beneath the surface) and

*z*, respectively, and

*E*

_{d}(

*λ*,

*z*= 0) is the spectral downwelling irradiance for a given wavelength

*λ*and at the depth z = 0. The integration limits

*λ*

_{1}and

*λ*

_{2}are 400 and 700 nm, respectively. It is noted that

*K*

_{d}(PAR) is usually not a constant vertically [

*Lee*, 2009;

*Zaneveld et al.*, 1993], but this variation is less serious in the upper layer for turbid Chesapeake Bay waters. In general,

*K*

_{d}(490) is a common indicator of water turbidity and can be used as a surrogate for

*K*

_{d}(PAR). Studies have shown that

*K*

_{d}(490) is robustly correlated to

*K*

_{d}(PAR), but the relationship has quite wide regional variations [

*Barnard et al.*, 1999;

*Morel et al.*, 2007;

*Pierson et al.*, 2008;

*Zaneveld et al.*, 1993]. In addition, those relationships were generally derived from relatively clear waters. Using the SeaBASS Chesapeake Bay in situ data set, the relationships of

*K*

_{d}(490) and

*K*

_{d}(PAR) for the Chesapeake Bay region were derived using equation (16), i.e.,

*K*

_{d}(490) for the Chesapeake Bay region can be readily converted to

*K*

_{d}(PAR) data using equation (17).

[26] The Chesapeake Bay Program maintains long-term in situ measurements from the Chesapeake Bay Program Water Quality Database (1984 to present), including data on underwater optical properties. In particular, in situ PAR(z) data at various depth *z* for the Chesapeake Bay are available. We used the in situ PAR(z) data in the main stem of the Chesapeake Bay (gray squares in Figure 1) from 2002 to 2008 to derive *K*_{d}(PAR) for match-up comparisons with MODIS measurements. The discrete PAR(z) data were measured from just beneath the surface (∼0.1–0.5 m) to deeper depths. For computations of *K*_{d}(PAR), we use only upper layer PAR(z) values (mostly <2 m) and extrapolate PAR(z) to PAR(z = 0) to derive *K*_{d}(PAR) data. There are total of 291 in situ *K*_{d}(PAR) data in the Chesapeake Bay main stem (Figure 1) for the MODIS match-up analyses.

[27] MODIS SWIR-based *K*_{d}(PAR) data were derived for the Chesapeake Bay using equation (17) to convert MODIS-derived *K*_{d}(490) data from various models [i.e., *Mueller*, 2000; *Lee et al.*, 2002], and the proposed new model *K*_{d}^{Comb}(490) (equation (15)). Comparisons between the MODIS-derived and the in-situ-measured *K*_{d}(PAR) data are shown in Figure 8. *K*_{d}(PAR) data obtained from the Chesapeake Bay Program for the main stem of the Chesapeake Bay were used for match-up analyses with the MODIS SWIR-based *K*_{d}(PAR) data. Figures 8a–8d are comparisons for *K*_{d}(PAR) data derived using models of the *Mueller* [2000], *Lee et al.* [2002], and new models *K*_{d}^{Comb}(490) (equation (15) with *K*_{d}^{Clear}(490) from *Mueller* [2000]) with *R*(488) and *R*(667) and with *R*(488) and *R*(645) data, respectively. Similar to the results for comparisons of *K*_{d}(490) products, *K*_{d}(PAR) data using some existing models are considerably underestimated. Mean ratios of the MODIS-Aqua model-derived to the in-situ-measured *K*_{d}(PAR) data are 0.394 and 0.515 for the models of *Mueller* [2000] and *Lee et al.* [2002], respectively. The MODIS *K*_{d}(PAR) data using the proposed models are much improved with the mean ratios of model versus in situ data as 0.951 and 0.958 using MODIS *R*(667) (equation (9)) and *R*(645) (equation (12)) data, respectively.

### 5.3. MODIS-Measured *K*_{d}(490) Data in Other Clear and Turbid Ocean Regions

[28] To investigate whether the new models of *K*_{d}(490), developed for turbid Chesapeake Bay waters, perform well in the global ocean, the SeaBASS non-Chesapeake Bay in situ data [*Werdell and Bailey*, 2005] are used for algorithm evaluations (Figure 9). Figure 9a shows comparisons of *K*_{d}(490) using the proposed approach *K*_{d}^{Comb}(490) (equation (15)) with *Mueller* [2000] for *K*_{d}^{Clear}(490) model, while Figure 9b provides results for which the *Lee et al.* [2002] model was used for *K*_{d}^{Clear}(490) computation in equation (15). These results are for cases where MODIS-derived water reflectance at the wavelength 667 nm, *R*(667), was used. Similar results were obtained using the MODIS-derived reflectance at the wavelength 645 nm for *K*_{d}^{Turbid}(490) computations (equation (12)). The in situ *K*_{d}(490) data cover a quite large data range, from ∼0.02 to ∼3.7 m^{−1}. Indeed, for *K*_{d}(490) < ∼0.3 m^{−1}, both the *Mueller* [2000] and *Lee et al.* [2002] models perform quite well, although the *Lee et al.* [2002] model has slight overestimations for very low *K*_{d}(490) data (the clearest ocean waters). For large *K*_{d}(490) data (>∼0.6 m^{−1}), the new *K*_{d}^{Turbid}(490) model also produced reasonably accurate *K*_{d}(490) data for turbid coastal waters (other than the Chesapeake Bay). Quantitatively, the mean ratios (model over in situ data) for Figures 9a and 9b are 1.037 and 1.055, respectively. For cases using MODIS-measured *R*(645) to derive *K*_{d}(490) data (results not shown), the corresponding mean ratio values are 1.020 and 1.039, respectively. Therefore, the proposed *K*_{d}^{Turbid}(490) model is also applicable to other turbid coastal waters for computing diffuse attenuation coefficients.

## 6. Regional and Global Satellite *K*_{d}(490) Composite Images

### 6.1. Along the United States East Coastal Region

[29] Climatology *K*_{d}(490) images from July 2003 to December 2007 for the MODIS-Aqua NIR-SWIR-based data processing algorithm [*Wang and Shi*, 2007; *Wang et al.*, 2009] are derived for the United States east coastal region using various *K*_{d}(490) models. Figure 10 provides examples of *K*_{d}(490) composite images for comparisons. Figure 10a is a *K*_{d}(490) image derived using the *Mueller* [2000] model (MODIS standard model), compared with images in Figures 10b and 10c that were obtained using the new model *K*_{d}^{Comb}(490) (equation (15)) with MODIS-derived water reflectances of *R*(667) and *R*(645) for *K*_{d}^{Turbid}(490) and the *Mueller* [2000] model for *K*_{d}^{Clear}(490), respectively. Similarly, Figure 10d is a *K*_{d}(490) image from the *Lee et al.* [2002] model, compared with the corresponding images of Figures 10e and 10f from the new models with *K*_{d}^{Clear}(490) from the *Lee et al.* [2002] model. As expected, the new models (Figures 10b, 10c, 10e, and 10f) show the same *K*_{d}(490) results in the open oceans as their corresponding *K*_{d}^{Clear}(490) models, i.e., either *Mueller* [2000] (Figures 10a–10c) or *Lee et al.* [2002] (Figures 10d–10f). However, in coastal waters, e.g., the Chesapeake Bay, Outer Banks, Delaware Bay, there are significant differences in the MODIS-derived *K*_{d}(490) data between the proposed new models (equations (9) and (12)) and models from *Mueller* [2000] or *Lee et al.* [2002] (both *K*_{d}(490) values are considerably biased low). It is noted that, as also shown in section 5.3, for the clear open ocean waters the *Mueller* [2000] model produced slightly lower *K*_{d}(490) values than those from the *Lee et al.* [2002] model, whereas for turbid coastal waters, the *Lee et al.* [2002] model performed better than the *Mueller* [2000] model with higher *K*_{d}(490) data.

### 6.2. In the Global Ocean

[30] The proposed new *K*_{d}(490) algorithm has been further evaluated for producing MODIS-Aqua global ocean *K*_{d}(490) product data. Figure 11 provides color images for global composite distributions of the MODIS-Aqua *K*_{d}(490) for the months of January and July 2005 derived using the NIR-SWIR-combined atmospheric correction algorithm for the MODIS-Aqua data processing. Figures 11a and 11c are color images of *K*_{d}(490) derived from the *Mueller* [2000] model for month of January and July 2005, respectively, and Figures 11b and 11d are global *K*_{d}(490) images obtained using the new proposed algorithm *K*_{d}^{Comb}(490) with the *Mueller* [2000] model for the corresponding *K*_{d}^{Clear}(490) computations. Results in Figure 11 show that for the open oceans both the new model and the *Mueller* [2000] model produced the same *K*_{d}(490) data (as designed), whereas for coastal regions the new algorithm produced significantly higher *K*_{d}(490) values than the *Mueller* [2000] model. Therefore, using the proposed new approach to derive a *K*_{d}(490) product, *K*_{d}(490) product data in turbid coastal waters can be improved while excellent *K*_{d}(490) results are still generated for open ocean regions.

### 6.3. Over Various Extremely Turbid Coastal Regions

[31] To clearly see the differences in the MODIS-derived *K*_{d}(490) images for various extremely turbid coastal regions, the MODIS-Aqua 1 km resolution data are used to derive the monthly (January and July 2005) *K*_{d}(490) composite images for coastal regions of (1) the China east coastal region, (2) the Amazon River Estuary, and (3) the La Plata River Estuary (locations shown in Boxes A, B, and C, respectively, in Figure 11a). These three regions are among the most turbid regions in the global oceans [*Shi and Wang*, 2009b]. Figure 12 provides comparisons of *K*_{d}(490) results for these three regions derived using the NIR-SWIR-combined atmospheric correction algorithm for the MODIS-Aqua data processing. Figures 12a–12d are *K*_{d}(490) imageries for the China east coastal region, Figures 12e–12h are *K*_{d}(490) results for the Amazon River Estuary, and Figures 12i–12l are comparisons for the La Plata River Estuary. *K*_{d}(490) results in Figures 12a, 12c, 12e, 12g, 12i, and 12k are derived using the *Mueller* [2000] model, while Figures 12b, 12d, 12f, 12h, 12j, and 12l are obtained using the proposed new algorithm with the *Mueller* [2000] model for the corresponding *K*_{d}^{Clear}(490) computations in equation (15). It is noted that the scale for the *K*_{d}(490) results in Figure 12 is increased to 8 m^{−1} due to significantly large *K*_{d}(490) values derived in these regions from the new algorithm. Results in Figure 12 show that, for these extremely turbid waters, the *Mueller* [2000] model again very considerably underestimated the *K*_{d}(490) values, compared with results from the new method. There are also clearly seasonal variations in *K*_{d}(490) for these coastal regions. For example, along the China east coastal region, waters are more turbid in the boreal winter (Figure 12b) than in the boreal summer (Figure 12d), while for the La Plata Estuary waters are more turbid in the austral winter (Figure 12l) as compared with the austral summer (Figure 12j).

## 7. Discussion

[32] The new *K*_{d}(490) algorithm was developed based on in situ data obtained from the Chesapeake Bay region where water properties are highly influenced by phytoplankton, suspended sediments, and to some extent yellow substance or CDOM. In fact, in the Chesapeake Bay region, the absorption coefficients for phytoplankton *a*_{ph}(*λ*), suspended sediment *a*_{s}(*λ*), and yellow substance *a*_{y}(*λ*) at the wavelength 490 nm range around from 0.070 to 1.249, from 0.012 to 0.706, and from 0.037 to 0.483 m^{−1}, respectively, with the corresponding mean values (standard deviations) of 0.416 (0.216), 0.184 (0.128), and 0.183 (0.066) m^{−1}, respectively. At the wavelength 670 nm, the data ranges for *a*_{ph}(*λ*), *a*_{s}(*λ*), and *a*_{y}(*λ*) are 0.038–0.841, 0.0–0.131, and 0.0–0.026 m^{−1}, respectively. Thus, Chesapeake Bay waters are probably more influenced by the phytoplankton and suspended sediment. For CDOM-dominated waters, e.g., Baltic Sea, the new algorithm may produce some uncertainties. We have compared MODIS-derived *K*_{d}(490) data using the new algorithm in July 2005 for the Baltic Sea region at 14°E–20°E and 53°N–56°N with the range of in situ *K*_{d}(490) from a previous study [*Darecki and Stramski*, 2004]. *Darecki and Stramski* [2004] found that the in situ *K*_{d}(490) data at the Baltic Sea range about from 0.1 to 3.0 m^{−1} with most of the data between 0.1 and 1.0 m^{−1}. MODIS-derived *K*_{d}(490) data using the new algorithm for the Baltic Sea range from 0.143 to 2.839 m^{−1} with a mean value of 0.484 m^{−1}, similar to the in situ measurements.

## 8. Conclusions

[33] There are several empirical and semianalytical models for computing the diffuse attenuation coefficients. However, there is a compelling need to have a diffuse attenuation model for turbid coastal waters since the existing models are essentially for clear open ocean waters. We examined three existing *K*_{d}(490) models (two empirical and one semianalytical) for the Chesapeake Bay waters. Results using the in situ measurements obtained from the main stem of the Chesapeake Bay waters showed that the *K*_{d}(490) values (ranging from 0.35 to 6.6 m^{−1} with the mean of 1.27 m^{−1}) using the standard models are significantly underestimated by a factor of ∼2–3 compared with the in situ measurements. The new *K*_{d}(490) algorithms for the Chesapeake Bay are developed based on a relationship relating the backscattering coefficient at the wavelength 490 nm to the irradiance reflectance at the red wavelengths. For turbid coastal waters, the backscattering coefficient can be more accurately correlated to irradiance reflectance at the red bands than the blue and green bands. With the *b*_{b}(490) relationship derived from the Chesapeake Bay in situ measurements, *K*_{d}(490) models for the turbid waters are formulated using the semianalytical approach. Particularly, two algorithms using the MODIS-derived normalized water-leaving radiances at wavelengths 488 and 667 nm and 488 and 645 nm are proposed. The new models, however, are mostly applicable for turbid waters, whereas the existing standard models provide excellent results for the clear open ocean. Thus, a merged algorithm combining *K*_{d}(490) models for clear oceans and turbid coastal waters is proposed. Match-up comparisons between MODIS-derived and in-situ-measured *K*_{d}(490) and *K*_{d}(PAR) products for the Chesapeake Bay show that the satellite-derived data using the proposed models are significantly improved. The new algorithm has also been used to derive *K*_{d}(490) data in other turbid coastal waters and shows considerably improved accuracy in MODIS-retrieved *K*_{d}(490) products compared with in situ measurements. With the new approach (merged algorithm), accurate *K*_{d}(490) product data for both open oceans and coastal turbid waters can be generated.

## Acknowledgments

[34] This research was supported by the NASA and NOAA funding and grants. The authors are grateful to the Chesapeake Bay Program for providing the water quality in situ data set and Mike Mallonee for prompt responses regarding some details about the Chesapeake Bay Water Quality Database. We thank all scientists who have contributed valuable data to SeaBASS database, the NASA/GSFC Ocean Biology Processing Group for maintaining and distributing the SeaBASS database, Wei Shi for help in processing MODIS data, and Zhong-Ping Lee for help in implementing the semianalytical model. We thank two anonymous reviewers for their valuable comments that significantly improved the manuscript. The MODIS L1B data were obtained from the NASA/GSFC MODAPS Service website. The views, opinions, and findings contained in this paper is those of the authors and should not be construed as an official NOAA or the United States' Government position, policy, or decision.