## Abstract

Abstract: The objectives of this study are to validate the applicability of a three-band algorithm in determining chlorophyll-a in eutrophic coastal waters, and to improve the model using improved three-band algorithm. Evaluated using two independent data sets collected from the West Florida Shelf, the variation three-band model was found to have a superior performance to both the three-band and modified three-band model. Using the variation three-band algorithm decreased 18% and 56% uncertainty, respectively, from the three-band and modified three-band algorithms. The significantly reduced uncertainty in chlorophyll-a estimations is attributed to effective removal of absorption of gelbstoff and suspended solids and backscattering of water molecules.

© 2013 OSA

## 1. Introduction

By comparison to the open ocean, the coastal environment is a dynamic region where events and processes operate over short temporal and spatial scales. Additionally, there are many factors that influence the optical regime, e.g., tidal currents, variable wind and current regimes due to diurnal heating and cooling, river discharge of colored dissolved organic matter (gelbstoff), and suspended sediment, resuspension of bottom material from wave action and storms events, and algal blooms from frequent, pulsed episodes of nutrient loading [1]. These processes can rapidly alter the optical properties of coastal waters and their impacts can be clearly observed by water color. The use of satellite imagery has proven beneficial for rapidly assessing the optical biophysical variables in coastal environments dominated by phytoplankton at temporal and spatial scales difficult to attain with direct field measurements [2].

Models to estimate chl*a* concentrations are commonly empirically or semi-analytically based. Empirical approaches rely on a specific spectral feature, such as a spectral ratio modeled to biophysical measurements using statistical regression. This kind of model is simple and easy to implement [3]. However, it lacks a physical foundation and the relationships are more geographically specific and cannot be applied other areas [4]. The semi-analytical model containing the spectral optimization approach is based on solutions to the radiative transfer equation [5]. These algorithms can be applied to different water types, and estimation accuracy is often much better than that of empirical algorithms [6]. Because this strategy relies on accurate spectral models for inherent optical properties of each individual constituent presented in the water, however, these kinds of algorithm are generally only appropriate to waters with characteristics similar to those used in the algorithm development. Their applicability then can be quite limited and can result in significant errors. More importantly, because of the wide variation of optical properties found for global waters, one semi-analytical function cannot fit all waters, unless the waters are restricted to Case I conditions where all optical properties co-vary with chl*a* concentrations [7]. Thus, an accurate semi-analytic model is still under development.

Recently, Gitelson et al. [8] outlined a three-band semi-analytical algorithm for estimating chl*a* concentration in turbid coastal waters, described how the algorithm works, analyzed the influence factors of the algorithm, and suggested a method to optimize the band positions. This model relates chl*a* concentration to remote sensing reflectance in three spectral bands, so the model independents the accurate information for the inherent optical properties in remote sensing applications. The model involves three assumptions [8]: (1) the absorption by chl*a* at *λ*_{1} is very different from that at *λ*_{2}, but absorption by suspended solids and gelbstoff at *λ*_{1} is close to that at *λ*_{2}; (2) reflectance at *λ*_{3} is minimally affected by the absorption of water quality constituents and the total absorption at *λ*_{3} is a measure of the absorption by water; and (3) the total backscattering coefficients of the three bands are approximately equal. The algorithm for chl*a* estimation has been well tested and evaluated using observations from lakes and reservoirs with variable optical properties in Nebraska and Iowa, and it was determined that the conceptual model may be considered as a unified approach for remote quantification of absorbing constituents in a variety of systems with Case II waters [8, 9].

Dall'Olmo and Gitelson [10] found that the variability in the quantum yield chl*a* fluorescence and the chl*a* specific absorption coefficient, among other factors, considerably affect the accuracy of three-band algorithm in chl*a* prediction. Instead of re-initialization of the models for water bodies with specific optical properties, Dall'Olmo and Gitelson [10] suggested tuning the spectral band positions in order to minimize these effects. Recently, Chen et al. [11] have demonstrated that the three assumptions for the three-band algorithm may be violated in turbid waters. The reasons can be attributed to [11, 12]: (1) the absorption curves of water quality constituents were related exponentially to the wavelength at near-infrared regions [13, 14], so it is difficult to detect two bands that meet the requirement of the “spectrally flat” assumption; (2) the aquatic particle absorption significantly varies with the type of suspended particles at near-infrared (NIR) and cannot be neglected in turbid coastal waters [5, 15], so that the second assumption may be violated in such waters; and (3) the total backscattering coefficient exponentially decrease with wavelength [15, 16], so that the third assumption may fail to completely removing the impacts of backscattering on three-band algorithm. Consequently, due to the limitations of these three assumptions, the desirable chl*a* absorption is still not perfectly isolated by three-band algorithm. It may produce an unacceptable uncertainty while using three-band algorithm to retrieve chl*a* concentration from these waters with highly turbidity or spectrally unevenness of gelbstoff at NIR regions [6,12]. More local information or improved models are required to further optimize the three-band algorithm.

The objectives of this study are to validate the performance of the three-band algorithm and further improve it for coastal waters. The specific goals are: (1) to assess the applicability of a three-band algorithm in turbid coastal waters; (2) to discuss the impacts of the limitations of the three assumptions on three-band algorithm; (3) to develop an innovative modified three-band algorithm and variation three-band algorithm for estimating chl*a* concentration in coastal waters; (4) to evaluate the accuracy of the variation three-band algorithm to accurately estimate chl*a* concentration in coastal waters; and (5) to compare the accuracy of the three-band, modified three-band, and variation three-band algorithm in estimating chl*a* concentration from coastal waters.

## 2. Data, methods and techniques

#### 2.1 Data sets used

Satellite ocean color missions require and abundance of high quality *in situ* measurements for bio-optical and atmospheric algorithm development and post-launch product validation and sensor calibration [17]. Since 1997, to facilitate the assembly of a global data set, NASA has funded the collection of ocean *in situ* data for data product validation, algorithm development, satellite data comparison and inter-calibration, and data merger studies and time series analyses [18]. The Sea-viewing Wide Field-of-View Sensor Bio-optical Archive and Storage System (SeaBASS) maintains a local repository of *in situ* ocean optical and bio-optical data to support and sustain regular scientific analyses. Specifically, the database includes *in situ* ocean optical, biological, and other related oceanographic data (see details in http://seabass.gsfc.nasa.gov). These data were collected by various researchers around United States and Europe, using various instrumentation with all measurements closely following rigorous, community-defined deployment and data processing protocols [19].

The SeaBASS *in situ* data have been continuously used to support the SeaWiFS and MODIS ocean color product validation and algorithm [17, 18]. Thus, the SeaBASS data are appropriate for the new algorithm calibration and evaluations. To evaluate the accuracy of the three-band, modified three-band, and variation three-band algorithms in predicting chl*a* concentration, two independent data sets containing the spectral optical properties, inherent optical properties, and chl*a* concentration of water column were used. These data sets (Fig. 1) were collected by the NASA SeaWiFS project as the SeaBASS data set. The first data set was used for model calibration, while the second one was used for model validation. The calibration data set containing 151 samples was collected in 2000-2001 in West Florida Shelf, USA, and the second data set including 52 samples was collected on 1999 and 2002, in West Florida Shelf, USA. The laboratory analyses were carried out within 24 h following sample collection. Chl*a* concentration was extracted and measured with 90% acetone in accordance with the Ocean Optical Protocols of NASA [19], a generally accepted method of quantifying Chl*a* concentration in chemical and biological fields [20, 21].The data for *a*_{p}(*λ*) and *a*_{g}(*λ*) were measured according to Tassan and Ferrari [22] and the data for CDOM according to the SeaWiFS protocols [19].

#### 2.2 Accuracy assessment

The Root-Mean-Square (RMS) of the ratio of modeled-to-measured values was used to assess the accuracy of chl*a* concentration estimation in this study. This statistic is described by:

*x*

_{mod,}

*is the modeled value of the*

_{i}*i*

^{th}element,

*x*

_{obs,}

*is the observed value of the*

_{i}*i*

^{th}element, and

*n*is the number of elements.

#### 2.3 Brief description of three-band algorithm

Because satellites and other sensors measure remote sensing reflectance from above the surface, it is necessary to convert above-surface remote sensing reflectance spectral *R*_{rs}(*λ*) to below-surface spectral *r*_{rs}(*λ*). For the *R*_{rs}(*λ*) to *r*_{rs}(*λ*) conversion [23, 24],

*T*=

*t*

^{u}

*t*

^{d}/

*n*

^{2}with

*t*

^{u}the radiance transmittance from below to above the surface,

*t*

^{d}is the irradiance transmittance from above to below the surface, and

*n*is the refractive index of waters.

*κ*is the water-to-air internal reflection coefficient, and

*Q*is the ratio of upwelling irradiance to upwelling radiance evaluated below the surface. For a nadir-viewing sensor and remote sensing domain,

*Q*, in general, ranges between 3 and 6 [25]. As

*R*

_{rs}(

*λ*) is small for most oceanic and coastal waters, the variation of the

*Q*value has little effect on the conversion between

*R*

_{rs}(

*λ*) and

*r*

_{rs}(

*λ*) [7]. Based on calculated HYDROLIGHT

*R*

_{rs}(

*λ*) and

*r*

_{rs}(

*λ*) values,

*T*≈0.52 and

*κQ*≈1.7 for optically deep waters [26].

Remote sensing of water quality constituent’s concentration is based on the relationship between *r*_{rs}(*λ*) and the inherent optical properties, namely, the total absorption *a*(*λ*) and the total backscattering coefficients *b _{b}*(

*λ*) [27]:

*γ*is unchanging with respect to wavelength and viewing geometric conditions [24, 25, 27]. The total absorption and scattering coefficients may be expanded as follows:

*a*, colored dissolved organic matters (CDOM) and inorganic particles, respectively. Due to the similarity in spectral shape, the

*a*

_{c}(

*λ*) and

*a*

_{d}(

*λ*) are difficult to spectrally separate with the current absorption coefficients decomposed model, expect for Case I conditions [28], so the

*a*

_{d}(

*λ*) term is combined operationally with

*a*

_{c}(

*λ*), and both detritus and CDOM absorption are represented by gelbstoff absorption

*a*

_{g}(

*λ*). the total absorption coefficient can be expressed as:

Gitelson et al. [8] suggested that reciprocal reflectance in the first spectral band *r*^{−1}_{rs}(*λ*_{1}) should be maximally sensitive to *a*_{p}(*λ*_{1}); However, in addition to absorption by chl*a*, *r*^{−1}_{rs}(*λ*_{1}) is also affected by absorption of gelbstoff, inorganic particles, and water as well as backscattering by all particulate matter. Fortunately, the effect of these factors can be minimized using a second spectral band, where *r*^{−1}_{rs}(*λ*_{2}) is minimally sensitive to absorption by chl*a* and absorption of gelbstoff and inorganic particles at *λ*_{2} is quite close to that in band *λ*_{1}. Thus, the difference *r*^{−1}_{rs}(*λ*_{1})-*r*^{−1}_{rs}(*λ*_{2}) must meet the follow requirements:

Unfortunately, the difference *r*^{−1}_{rs}(*λ*_{1})-*r*^{−1}_{rs}(*λ*_{2}) is still affected by *b*_{b}(*λ*_{1}), i.e., if backscattering varies between samples, the model output would be different for the same chl*a* concentration. To account for this, a third spectral band *λ*_{3} is adopted, where reflectance is minimally affected by absorption of water quality constituents, i.e., *a*(*λ*_{3})~*a*_{w}(*λ*_{3}) and *a*(*λ*_{3})>>*b*_{b}(*λ*_{3}). This means that *λ*_{3} has to be restricted within the NIR regions [8]. Thus, the three-band algorithm can be approximated as follow [8, 29, 30]:

#### 2.4 Modified three-band algorithm

The structure of Eq. (3) comes from Morel and Prieur [27], when they developed a reflectance model, *γ* with a mean value of 0.33. As shown in Morel and Gentili [25], the coefficient *γ* is not constant and varies consistently with the water optical properties. Thus, it is much more challenging to separate *a*_{p}(*λ*_{1}) from the remote sensing reflectance using three-band algorithm provided by Gitelson et al. [8] due to the poor approximation of Eq. (3). Gordon [31] carried out extensive computations of *r*_{rs}(*λ*) as a function of the optical properties of the water and solar zenith angle *θ*_{0} and concluded that for *θ*_{0}≥20°, *r*_{rs}(*λ*) can be directly related to the inherent optical properties of the water through:

*s*(

*λ*) is the ratio of total backscattering coefficient to total absorption coefficient. For nadir-viewed

*r*

_{rs}(

*λ*), Gordon et al. [24] found that

*l*

_{0}≈0.0949 and

*l*

_{1}≈0.0794 for Case I waters, while Lee

*et al*. [32] suggested that

*l*

_{0}of 0.084 and

*l*

_{1}of 0.17 work better for higher scattering coastal waters. Actually the values of

*l*

_{0}and

*l*

_{1}may vary with particle phase function [5], which is not known remotely. Without local bio-optical information or models to predetermine the values of

*l*

_{0}and

*l*

_{1}in an semi-analytical algorithm, the Gordon et al. [24] suggested values are used in Case I waters, while Lee

*et al*. [32] determined values work in Case II waters.

From Eq. (8),

If considering non-negligible absorption and backscattering of suspended solids at NIR regions, the violation “spectrally flat” assumption at *λ*_{1} and *λ*_{2} and the water optical properties dependent *γ* in Eq. (3), the three-band should be written as,

*a*

_{g}(

*λ*

_{1}) =

*a*

_{g}(

*λ*

_{1})-

*a*

_{g}(

*λ*

_{2}) caused by violation “spectrally flat” assumption. Recently, an improved three-band algorithm was developed by Chen and Quan [12] by replacing

*r*

_{rs}(

*λ*) in the three-band algorithm by

*s*(

*λ*). It is expressed as

Compared to three-band algorithm suggested by Gitelson et al. [8], the influences associated with *γ* and backscattering of suspended solid have been removed in the improved three-band algorithm. However, the improved three-band algorithm is still impacted by the violation of the “spectrally flat” assumption and the absorption of suspended solids. A modification of the three-band algorithm was developed by adding a linear factor to rectify the violation of the “spectrally flat” assumption in the improved three-band algorithm. It is denoted as

*X*= [

*a*

_{g}(

*λ*

_{2})/

*b*

_{b}(

*λ*

_{2})]/[

*a*

_{g}(

*λ*

_{1})/

*b*

_{b}(

*λ*

_{1})]. Note that the value of

*X*may vary based on the nature of waters under study, such as humic versus fulvic acids and abundance of detritus [33]. Local information or and improved algorithm is needed to reinitialize the

*X*value in typical remote sensing application.

#### 2.5 variation three-band algorithm

Compared to the three-band algorithm, the three limitations have been reduced by the modified three-band algorithm. These are: (1) the backscattering scattering of suspended solids over NIR region in highly turbid waters; (2) violation of the “spectrally flat” assumption in optical complicated waters; and (3) poor approximation of coefficient *γ*. However, the modified three-band algorithm may still be violated in both turbid waters and in most of the entire ocean, because this model is still limited in that: (1) non-negligible absorption of suspended solids at *λ*_{3}, e.g., Tzortziou et al. [34] showed that the absorption of particulate matter in the 700-730nm region cannot be neglected in the Chesapeake Bay, while Binding et al. [13] suggested that particle matter may be an important contributor to the total spectral absorption signals in Lake Erie waters at red and NIR regions; and (2) non-negligible water molecular backscattering at red and NIR regions (*λ*<800nm), except for highly turbid waters, e.g., Morel and Loisel [35] indicate that the influence of molecular scattering by water molecules is not negligible, leading to a gradual change in the shape of the phase function, when the chl*a* concentration is low enough (in most of the entire ocean), while Lee et al. [23] show that the water molecular backscattering ranged from negligible to generally significant for natural assemblages of global waters. Doxaran et al. [36] suggested that *b*_{bw}(*λ*) was equal to one-half of the total backscattering coefficient for the range 400-800nm and is negligible at greater wavelengths in aquatic environments with low concentration of water quality constituents.

Traditionally, the wavelength dependence of *b*_{bp}(*λ*) can be modeled as

*Y*is the exponential coefficient. Owing to the difference in spectral shape [15, 28], the

*b*

_{bw}(

*λ*) term cannot be combined operationally with

*b*

_{bp}(

*λ*), so the ratio of

*b*

_{b}(

*λ*

_{3}) to

*b*

_{b}(

*λ*

_{1}) is not constant and varies consistently with backscattering by particle matter. This limitation may cause modified three-band algorithm to be violated in slightly turbid waters. To account for this, a variation of the three-band algorithm was developed for estimating pigment concentrations both in turbid and low chl

*a*concentration waters.

Because the *s*(*λ*) is the ratio of total backscattering to total absorption, backscattering by particle matters can be isolated from product of *s*(*λ*)*a*(*λ*) as long as backscattering by water molecules is known, i.e.,

When the analytical expression of backscattering coefficients is known (Eq. (13)), the relationship of product of *s*(*λ*)*a*(*λ*) at *λ*_{1} and *λ*_{2} can be denoted by using:

*κ*

_{12}= (

*λ*

_{2}/

*λ*

_{1})

^{Y}. To determine the total absorption coefficient using measurements of

*s*(

*λ*), the spectral slope technique [37] can be used to determine the total absorption due to water quality constituents. Starting from a general wavelength pair

*λ*

_{1}and

*λ*

_{2}:where

*ζ*

_{12}and

*ξ*

_{12}are semi-analytical coefficients, which have been either related to concentration of water quality constituents or absorption at a wavelength. Substituting Eq. (16) into Eq. (15), yields:

It is impossible to partition the total absorption if the total absorption value is known only at one wavelength, expect perhaps for Case I waters [7]. For Case II situations, to solve for absorption by chl*a*, the *a*(*λ*) value of at least two or more bands are required. Similar to the deriving procedures of *a*(*λ*_{2}), total absorption at the third band *λ*_{3} can be denoted as follow:

*κ*

_{13}= (

*λ*

_{3}/

*λ*

_{1})

^{Y},

*ζ*

_{13}and

*ξ*

_{13}are semi-analytical coefficients, which have been either related to water quality constituents’ concentration or absorption at

*λ*

_{1}and

*λ*

_{3}. Several studies have reported [7, 23, 38] that the absorption related to chl

*a*and gelbstoff at blue-green ranges can be calculated using a spectral decomposed method, as long as total absorptions at two wavelengths are known. However, at red-NIR ranges, the spectral decomposed method produces poor accuracy in decomposing

*a*

_{p}(

*λ*) and

*a*

_{g}(

*λ*) from total absorption, because

*a*

_{p}(

*λ*)<<

*a*(

*λ*) and

*a*

_{g}(

*λ*)<<

*a*(

*λ*), i.e., a small bias in

*a*(

*λ*) estimation may result in a large bias in

*a*

_{p}(

*λ*) and

*a*

_{g}(

*λ*) retrieval. To overcome this limitation, an empirical spectral decomposed method (ESDM) was used to retrieve

*a*

_{p}(

*λ*) from

*a*(

*λ*) in this study. The ESDM method is expressed by:

*π*

_{0},

*π*

_{1}, and

*π*

_{2}are empirical coefficients, which are computed using non-linear robust regression method suggested by Chen and Quan [6].

## 3. Results

#### 3.1 Chla concentrations and water optical characteristics

Episodic blooms of toxic dinoflagellates have been reported as potential contributors to the total primary production in the West Florida Shelf. During dinoflagellate bloom periods, chl*a* concentrations in surface waters vary from 2 to 30mg/m^{3}, but chl*a* concentrations during non-bloom periods are <1mg/m^{3} [39]. By comparison, each of the data sets taken in West Florida Shelf from 1999 through 2002 (Table 1a and Table 1b) contained both bloom and non-bloom periods. Figure 2 shows *a*_{p}(440) plotted against *a*_{g}(440) in the West Florida Shelf, indicating that the water optical properties in the West Florida Shelf are not only determined by chl*a* and covarying pigments, but are also determined by other water quality constituents such non-covarying CDOM and non-algal particle, even though *a*_{p}(440) and *a*_{g}(440) are significantly correlated in these data set (correlation coefficient 0.6931). Thus, the West Florida Shelf water falls into Case II category.

#### 3.2 Reflectance spectra

Remote-sensing reflectance exhibits a large variability over the visible and NIR spectral regions. The magnitude and shape of the reflectance curves in two data sets (Fig. 3) are all different from each other, clearly indicating that they represent very different optical environments, ranging from low-chl*a*, blue waters to turbid coastal waters. The spectral curves with a negative slope at the blue regions are quite similar in magnitude and shape to typical reflectance in Case I waters [27], indicating that some West Florida Shelf waters are typical low-chl*a*, blue waters. In these waters, the reflectance in the blue range was shown to be very low (<0.01 sr^{−1}), was even lower at the green-red regions (<0.005 sr^{−1}), and reached its lowest point at the NIR regions (<0.0002 sr^{−1}). However, some spectral curves with positive slopes at the blue regions are quite similar to typical reflectance in Case II waters, indicating that some of the West Florida Shelf waters fall into the productive Case II water type [27]. In these waters, remote sensing reflectance in the range from 400 to ~480 nm remained below 0.01 sr^{−1}, but remote sensing reflectance in the green range was much higher, reaching 0.026 sr^{−1}, and the peak around 690 nm at many stations was quite lower than that at the green reflectance peak.

Multiple factors contribute to the reflectance patterns in aquatic environments. In the blue range (400-500nm), absorption by geblstoff and SSC, and scattering by particulate matter contributed strongly to reflectance patterns [33, 40], but reflectance did not have pronounced spectral features for the broad range of turbidity and chl*a* concentrations at all sites. Figure 4 shows a chl*a* absorption peak around 440nm, so there must be a reflectance minimum near 440nm in spectral curves, but it was distinct only when the chl*a* concentration was above 150mg/m^{3} [8]. Near 490nm another trough on reflectance curve is shown due to largely carotenoids absorption [41]. In the green spectral ranges (500-600nm), absorption by pigments was minimal and scattering by all particulate matter played the main role in reflectance, and reflectance had a prominent peak around 575nm. An absorption peak around 675nm indicated a trough around 675nm corresponds to the red chl*a* absorption maximum in spectral curves. However, it was indistinct in West Florida Shelf water due to the low chl*a* concentration. A distinct peak located around 695nm,appeared in almost all samples. This peak is the result of both high backscattering and a minimum in absorption by all water quality constituents including pure water [8, 40].

#### 3.3 Model calibration

Appendix I shows the limitations of bands turning method suggested by Gitelson et al. [8] in determining the optimal positions of three-band algorithm, indicating that although the bands turning method is simple and easy to implement, it cannot find the optimal bands within the bands searching ranges for three-band algorithm. Thus, in order to find out the optimal bands of three-band, the modified three-band and variation three-band algorithms, the non-linear recursive method suggested by Chen and Quan [6] is used to determine the optimal bands for those conceptual models. It is noteworthy that the samples with low chl*a* concentration (<0.2 mg m^{−3}) were ignored during model calibration and validation, due to the weak absorption by chl*a* in these sample [42], which would result in poor accuracy for chl*a* retrievals.

### 3.3.1 Three-band algorithm calibration

In order to find the optimal positions of *λ*_{1}, *λ*_{2}, and *λ*_{3}, we turned the model according to the optical properties of the water bodies studied. The calibration data set contained 151 samples taken in the West Florida Shelf in 2000-2001. According to Gitelson et al. [8], the first band should be maximally sensitive to chl*a* absorption. Figure 5(a) shows results of RMS for *r*_{rs}(*λ*) linearly relating to *a*_{p}(*λ*). By comparison, *a*_{p}(*λ*) at bands ranges from 550 to 694nm is more sensitive to *r*_{rs}(*λ*) than other regions, whose RMS is <47%, so the first band can be restricted within the range from 550 to 694nm. Smith and Baker [43] suggested that it is readily observed that for *λ*>~580nm, backscattering by water molecules is essentially insignificant. In order to minimize the effects of backscattering water molecules (in the denominator of Eq. (3)), it is better to set the first band within 580 to 694nm, which is wider than band ranges suggested by Gitelson et al. [8]. The second one is minimally sensitive to absorption by chl*a* but absorption of gelbstoff and inorganic particles at *λ*_{2} is quite close to that in band *λ*_{1}. This means that the second band should be set within 710 to 750nm, because the RMS at this band region (Fig. 5(a)) is much low than that within 580 to 694nm, while the absorption by gelbstoff is quite close to that in band *λ*_{1} suggested by Gitelson et al. [8]. The third one should be minimally sensitive to absorption both by chl*a* and gelbstoff. Figure 5(b) shows the ratio of [*a*_{p}(*λ*) + *a*_{g}(*λ*)] to total absorption in West Florida Shelf waters. By comparison, the absorption by particulate matter is much smaller than total absorption or absorption by water molecules at NIR band, e.g., ratio value no more than 4% at band position larger than 600nm. Thus, the third band is set within 600 to 750nm. Finally, the non-linear recursive method is used to calculate the RMS of [*R*^{−1}_{rs}(*λ*_{1})-*R*^{−1}_{rs}(*λ*_{2})] *R*_{rs}(*λ*_{3}) versus [*chla*] within the bands setting ranges given as previous. The results (Fig. 6) indicates that the three-band algorithm has the optimal accuracy in case of *λ*_{1} = 620nm, *λ*_{2} = 712nm and *λ*_{3} = 730nm, whose correlated coefficients are larger than 0.3885.

### 3.3.2 Modified three-band algorithm calibration

The underlying assumption of modified three-band algorithm requires that the *s*(*λ*) at first band should be quite sensitive to *a*_{p}(*λ*). This means that *λ*_{1} has to be restricted within a range from 580 to 694nm (Fig. 5(a)). Compared to the three-band algorithm, a linear factor *X* is used by the modified three-band algorithm to improve the potential violation of “spectrally flat” assumption of three-band algorithm. Because absorption by gelbstoff is very well fitted to the negative exponential function, *s*(*λ*_{1}) affected by *a*_{g}(*λ*_{1}) can be easily removed by the second band using a simple linear model such as *Xs*(*λ*_{2}). According to the study results carried out by Gitelson et al. [8], *λ*_{2} has to be restricted within band ranges from 710 to 750nm, where *s*(*λ*_{2}) is minimum sensitive to absorption by chl*a*. However, our previous research suggested that *a*_{p}(*λ*_{1})-*Xa*_{p}(*λ*_{2}) can be related to chl*a* concentration as long as *a*_{p}(*λ*_{1}) is linearly related to but not equal to *Xa*_{p}(*λ*_{2}). This means that *λ*_{2} can also be set to 580 to 694nm. Thus, for the modified three-band algorithm, *λ*_{2} should be between 580 and 750nm. The third one should be minimally sensitive to absorption both by chl*a* and gelbstoff, so *λ*_{3} has to be restricted 600 to 750nm, which is same with the band ranges of three-band algorithm.

Note that parameter *X* in modified three-band algorithm is usually predetermined using accurate information for the inherent optical properties. However, such local information is difficult to be accurately measured [44]. However, the *X* can be deemed as an “unknown” variable and can be robustly regressed using non-linear recursive method during procedure for determining the optimal relationship of [*s*^{−1} (*λ*_{1})-*Xs*^{−1}(*λ*_{2})]*s*(*λ*_{3}) versus [*chla*]. The results (Fig. 6(b)) indicates that the modified three-band algorithm has the optimal accuracy in case of [*s*^{−1}(600)-0.2363*s*^{−1}(580)]*s*(692), whose correlated coefficients are larger than 0.8302.

### 3.3.3 Variation three-band algorithm calibration

The backscattering by particulate matters were strongly related exponentially to the wavelength at visible and NIR regions [15, 23], so the effects of *b*_{bp}(*λ*) at *s*(*λ*_{2})*a*(*λ*_{2}) and *s*(*λ*_{3})*a*(*λ*_{3}) can be semi-analytically minimized by *s*(*λ*_{1})*a*(*λ*_{1}) using Eq. (15). To determine the *a*(*λ*_{2}) and *a*(*λ*_{3}) using measurements of *s*(*λ*_{1}), *s*(*λ*_{2}) and *s*(*λ*_{3}), four empirical spectral relationships should be known: *a*(*λ*_{1}) versus *a*(*λ*_{2}), *a*(*λ*_{1}) versus *a*(*λ*_{3}), *b _{bp}*(

*λ*

_{1}) versus

*b*(

_{bp}*λ*

_{2}), and

*b*(

_{bp}*λ*

_{1}) versus

*b*(

_{bp}*λ*

_{3}), respectively. However, there is no field-measured backscattering coefficient here, so the spectral relationship of

*s*(

*λ*

_{1})

*a*(

*λ*

_{1}) versus

*s*(

*λ*

_{2})

*a*(

*λ*

_{2}) and

*s*(

*λ*

_{1})

*a*(

*λ*

_{1}) versus

*s*(

*λ*

_{3})

*a*(

*λ*

_{3}) were used to substitute the spectral relationships of backscattering for initializing the variation three-band algorithm.

By inputting the bio-optical data including *s*(*λ*) and *a*(*λ*), the variation three-band algorithm is determined by non-linear iterative method while *λ*_{1}, *λ*_{2}, and *λ*_{3} are, respectively, turning from 400 to 750nm, e.g., for each wavelengths combination of *λ*_{1}, *λ*_{2}, and *λ*_{3}, the constant coefficients of *κ*_{12}, *κ*_{13}, *ζ*_{12}, *ζ*_{13}, *ξ*_{12} and *ξ*_{13} as shown in Eq. (15)-(18) can be determined using inputting data set of *s*(*λ*) and *a*(*λ*) at corresponding wavelengths. Then, the *π*_{0}, *π*_{1}, and *π*_{2} as shown Eq. (19) can be determined by the non-linear iterative method proposed by Chen and Quan [6]. The optimal variation three-band algorithm must be the one with smallest RMS value. The results indicate that the optimal positions of three bands of variation three-band algorithm are *λ*_{1} = 488, *λ*_{2} = 600, and *λ*_{3} = 610nm. Figure 7 shows the empirical spectral relationships between the optimal bands of variation three-band model, indicating that both *a*(*λ*) and *b*_{b}(*λ*) at 600 and 610nm are strongly related to *a*(*λ*) and *b*_{b}(*λ*) at 488nm, whose correlation coefficients are larger than 0.979. The variation three-band model can be initialized as long as spectral relationships between selected bands are known. Figure 8 shows the optimal variation three-band algorithm regressed from calibration data set taken from West Florida Shelf waters in 2000-2001, indicating that the relationships of *a*(610), *a*_{p}(610), and chl*a* concentration versus variation three-band model were found to be linear/non-linear and highly significant, whose correlation coefficients are larger than 0.9468.

#### 3.4 Evaluation of model accuracy

In this section of the paper, we present the evaluation of the performance of the three-band, modified three-band, and variation three-band models. The evaluation was based on a comparison of the chl*a* concentrations predicted by these models with chl*a* concentration measured analytically for independent validation data set (Table 1b). Figure 9 shows the relationship between chl*a* modeled from the three-band, modified three-band, and variation three-band models, and measured chl*a* in the calibration data set taken on West Florida Shelf waters. We found that the variation three-band algorithm (*RMS* = 24.43%) had a superior performance compared to both the modified three-band algorithm (*RMS* = 42.17%) and three-band algorithm (*RMS* = 80.45%) algorithms. Using the variation three-band algorithm for retrieving chl*a* concentration in the West Florida Shelf waters decreased 17.74% *RMS* from the modified three-band algorithm and 56.02% *RMS* from the three-band algorithm.

The relationship between RE (relative error) and chl*a* concentration was presented to demonstrate the ability of these three algorithms in estimating chl*a* (Fig. 9). We found that the RE decreases with increasing chl*a* concentration, but there is no statistically significant relationship between them. Comparison of the variation three-band model to that of modified three-band and three-band models indicates that the variation three-band model considerably reduces the RE value and outperforms the three-band algorithm, especially at a low chl*a* concentration level (<1 mg m^{−3}). These findings imply that the variation three-band algorithm dose not require further optimization of spectral band positions and site-specific parameterization to accurately estimate chl*a* concentration in water bodies with widely varying bio-optical characteristics taken in different seasons and years from West Florida Shelf waters, even though the optimal spectral band positions and site-specific parameterization are semi-analytically determined in the algorithm calibration procedures.

## 4. Discussion

As mentioned in previous, the samples with low chl*a* concentration level (<0.2 mg m^{−3}) were deemed as outliers and ignored in model calibration and validation procedures due to the weak absorption by chl*a*. Figure 10(a) shows the lab-measured chl*a* concentration plotted against field measured absorption by chl*a* at 610nm, indicating that the ch*a* concentration is weakly depended on *a*_{p}(610) while the chl*a* concentration is too low. Due to the low value of *a*_{p}(610) (<0.002 m^{−1}), the noise of *a*_{p}(610) was significant. That might be one of the reasons for the poor performance of chl*a* estimation in these low concentration levels. Figure 10(b) shows the ratio of absorption by chl*a* to total absorption (CTR) at 610nm, indicating that the *a*_{p}(610) is a very small part of *a*(610) for samples with low chl*a* concentration, whose CTR<0.7%. This is to say, 0.7% retrieval uncertainty in *a*(610) would result in 100% uncertainty in *a*_{p}(610) retrievals, which would lead to much larger uncertainty in remote sensing of chl*a* concentration. In fact, the uncertainty associated with *a*(610) retrievals is 1.24% derived by the variation three-band algorithm in this case study, so accurate estimation of chl*a* from remote sensing data is particularly challenging in coastal waters with low concentration level. Additionally, recent intercomparisons have demonstrated that uncertainty in remote sensing determined by approach of “radiometer measurements and data analysis protocols” to be <5% under varied cloudy and sea state conditions [45], which would strongly impact the accuracy of model construction results. In addition to this, there is ~5% uncertainty contained in satellite-derived water-leaving reflectance when a very accurate atmospheric correction method is used remove the atmospheric absorption and scattering from satellite data even in Case I waters [42], which would further influence the retrieval accuracy of *a*(610) from satellite images. These technical limitations make optical sensor technology to be unable to derive chl*a* concentration from coastal waters with low concentration level (<0.2 mg m^{−3}) Further work is required on this subject.

Episodic blooms of toxic dinoflagellates have been reported as potential contributors to the total primary production in West Florida Shelf. During dinoflagellate bloom periods, chl*a* concentration in surface waters varies from 2 to 30mg/m^{3}, but is <1mg/m^{3} during non-bloom periods [39]. When concentrations of chl*a* and suspended matters are low enough, water molecular backscattering becomes non-negligible comparing to backscattering by particle. Figure 11 shows the chl*a* concentration plotted against ratio of water backscattering to total backscattering (WTR) at 670nm. Because there is no field-measured backscattering coefficient in this study, the values determined using *s*(670)*a*(670) are used to substitute the backscattering coefficient for discussing the impacts of WTR on the performances of the variation three-band algorithm. We found that the WTR value is >10% while chl*a* concentration is larger than 2 mg m^{−3}, and the largest one is 60% whose chl*a* concentration is 0.21 mg m^{−3}. This is to say, the molecular backscattering is very significant and cannot be negligible in water samples with low chl*a* concentration (<2 mg m^{−3}). The three-band and modified three-band models are limited in that they are able to suppress the effect of water molecular backscattering instead of eradicating it completely, i.e., these two algorithms assume that [*b*_{bw}(*λ*_{1}) + *b*_{bw}(*λ*_{1})]/ [*b*_{bw}(*λ*_{3}) + *b*_{bw}(*λ*_{3})] are related either to water molecular backscattering or backscattering by particulate matters. Due to the difference in spectral shape [15, 28], the *b*_{bw}(*λ*) term cannot be combined operationally with *b*_{bp}(*λ*). Thus, the strong water molecular backscattering inevitably exerts a residual effect on the estimation accuracy in West Florida Shelf waters.

According to results shown in Fig. 9, we found that the modified three-band algorithm decreases 38.28% RMS values from the three-band algorithm, while the variation three-band algorithm decreases 17.74% RMS values from the modified three-band algorithm. The former improved performances may be attributed to the improvement in the negligible backscattering scattering of suspended solids over NIR region in highly turbid waters, violation of the“spectrally flat” assumption in optical complicated waters, and poor approximation of coefficient *γ*, while the latter is related to the improvement in negligible absorption of suspended solids at *λ*_{3} and negligible water molecular backscattering at red and NIR regions (*λ*<800nm), except for highly turbid waters. By comparison, the former three limitations more significantly impact the performances of chl*a* concentration retrievals algorithm than the latter two limitations in deriving chl*a* concentration from turbid coastal waters.

Different limitations have different influence on chl*a* concentration retrievals in different water types. For example, the limitations of the “spectrally flat” assumption and the poor approximation of coefficient *γ* may be violated in all water types because of the wavelengths-depended of inherent optical properties of water quality constituents; the assumptions of negligible absorption of suspended solids at NIR and negligible backscattering of suspended solids over NIR region may work well in blue or clear waters, but may be violated in the turbid waters with high suspended sediment concentration; on the contrary, the assumption of negligible water molecular backscattering at red and NIR regions may work well in turbid waters, but may be violated in blue or clear waters.

During past several years, many semi-analytical algorithms have been successfully used for estimating chl*a* concentration from coastal and inland waters. For example, Li et al. [46] suggested a semi-analytical algorithm combining both three band indices and a baseline algorithm to estimate chl*a* concentration, and then tested the algorithm in three eutrophic and turbid reservoirs. Their algorithm accurately estimated chla concentration with 31.4% RMS for water samples with the chl*a* concentration range from 1.4 to 146.1mg/m^{3}. An improved OC4v4 algorithm was suggested by Chen and Quan [6] for estimating chl*a* concentration from Yellow River Estuary. That improved OC4v4 algorithm produces ~32.7% RMS in estimating chl*a* concentration in that regions. Moses et al. [47] constructed a three-band algorithm for retrieving chl*a* concentration from Azov Sea and Taganrog Bay, Russia, and determined that the three-band algorithm gave consistently highly accurate estimates of chl*a* concentration, with 21.05%. In comparing the performance of variation three-band algorithm in this study with the optimal results of these algorithms, they found that the RMS of chl*a* concentration prediction was comparable: 24% RMS in variation three-band algorithm versus 21-33% RMS in these semi-analytical algorithms.

The variation three-band algorithm presented in this study may be applied to NASA HYPERION and the Compact High Resolution Imaging Spectrometer (CHRIS). As an example, the HYPERION channels at 487.87, 599.90 and 609.97nm is quite close to the position of *λ*_{1} = 488, *λ*_{2} = 600nm, and *λ*_{3} = 610nm, respectively. These findings indicate that, provided that an atmospheric correction scheme for visible and near-infrared bands is available, the variation three-band algorithm may be used for the quantitative monitoring of chlorophyll-a concentration from the HYPERION sensor in West Florida Shelf waters. However, the field data set used in this study is quite small and covers only a narrow range of natural waters, so it is insufficient to completely validate the accuracy of the variation three-band algorithm. More independent tests with field-measured data are required for the validation and improvement of variation three-band algorithm. The variation three-band algorithm should be used for estimating chl*a* in coastal waters, even though it is essential to reinitialize the model statistic parameters using local aquatic bio-optical information. We suggest calibration and validation of the algorithms based on more in situ measurements of waters with different optical properties.

There are some caveats that need to be considered when attempting to apply the variation three-band model to satellite. Since the variation three-band algorithm relies strongly on reflectance in the red region, there are specific hurdles that need to be addressed. The strong absorption by water in red band greatly reduces the magnitude of the recorded signal in the red region, reducing the signal-to-noise ratio and enhancing the effect of the inherent noise in the recorded signal [8], This may make the variation three-band algorithm sensitive to inherent noise in the measured signal. The parameters related to spectral slope in Eq. (17)-(19) may vary based on the nature of waters under study. For example, Bowers et al. [15] indicated that the specific scattering coefficient depends on the nature of the scattering particles: their size, shape, refractive index and density. Suzuki et al. [48] determined that the differences in phytoplankton pigment composition of each water mass may lead to differences in phytoplankton absorption spectral of each water mass. Therefore, local information or an improved algorithm is needed to reinitialize the parameters of variation three-band algorithm in practical remote sensing application, when the bio-optical properties are different from these used for model development in this study.

## 5. Summary

In this study, three semi-analytical models for remote sensing of chl*a* concentration were constructed by specifying the optimal bands. The three-band model has the optimal wavelengths of *λ*_{1} = 620nm, *λ*_{2} = 712nm and *λ*_{3} = 730nm; the modified three-band algorithm has optimal accuracy when [*s*^{−1}(600)-0.2363*s*^{−1}(580)]*s*(692); and the specification of the wavelength in the variation three-band model is *λ*_{1} = 488, *λ*_{2} = 600nm, and *λ*_{3} = 610nm. Evaluated using two independently collected data sets in West Florida Shelf, USA, all modes are found to have an acceptable accuracy in estimating chl*a* concentration, expect for three-band model. Comparison of the variation three-band model to the other two semi-analytical models indicates that the variation three-band model considerably reduces the uncertainty and outperforms the three-band and modified three-band algorithms, especially at a low chl*a* concentration levels (<1 mg m^{−3}). Using the variation three-band algorithm to retrieve chl*a* concentration in the West Florida Shelf waters decreased uncertainty by 18% compared to the modified three-band algorithm and 56% uncertainty from the three-band algorithm. The significantly reduced uncertainty in chl*a* estimations is due to removal of absorption effect of gelbstoff and suspended solids and the effects of water backscattering. The spectral position of variation three-band model is quite closed to the position of HYPERION sensor. These findings indicate that, provided that an atmospheric correction scheme for visible and near-infrared bands is available, the variation three-band algorithm can be used for the quantitative monitoring of chlorophyll-a concentration from the HYPERION sensor in eutrophic coastal waters such as West Florida Shelf waters, even though it may be essential to reposition the wavelength of the three bands for the given study area accordingly or reinitialize the parameters of variation three-band algorithm using local bio-optical information.

## Appendix I

In order to determine the optimal bands for three-band algorithm, the band turning method is used by Gitelson et al. [8]. To find the optimal position of *λ*_{2}, initial position for *λ*_{1} was set to *λ*_{1,A} and the initial position for *λ*_{3} was set to *λ*_{3,A}. As *λ*_{2} was turned from *λ*_{2,I} to *λ*_{2,T}, the RMS2 of [*R*^{−1}_{rs}(*λ*_{1,A})-*R*^{−1}_{rs}(*λ*_{2})] *R*_{rs}(*λ*_{3,A}) versus [*chla*] was calculated. RMS2 varies with wavelength *λ*_{2}, its minimum occurs at *λ*_{2,B}. Therefore, *λ*_{2,B} was selected for *λ*_{2}. To determine the optimal position of *λ*_{1}, *λ*_{2}=*λ*_{2,B} and *λ*_{3}=*λ*_{3,A} was used, and *λ*_{1} turned from *λ*_{1,I} to *λ*_{1,T}. the RMS2 of [*R*^{−1}_{rs}(*λ*_{1})-*R*^{−1}_{rs}(*λ*_{2,B})] *R*_{rs}(*λ*_{3,A}) versus [*chla*] was again computed for each *λ*_{1}. Results indicates that minimum RMSE exits at *λ*_{1,C}. Thus, *λ*_{1,C} was selected for *λ*_{1}. The optimal *λ*_{3} was determined by setting *λ*_{1}=*λ*_{1,C} and *λ*_{2}=*λ*_{2,B}, and the minimum RMSE occurs at *λ*_{3,D}. Therefore, the optimal three-band algorithm calibrated by bands turning method suggested by Gitelson et al. [8] is [*R*^{−1}_{rs}(*λ*_{1,C})-*R*^{−1}_{rs}(*λ*_{2,B})] *R*_{rs}(*λ*_{3,D}). Figure 12 shows the flowchart of band turning method for searching optimal band of three-band algorithm, indicating that the band turning method can be denoted to: (1) given an initial point A, calculates RMS2 at each point along line *L*_{2}, and finds point B has minimum RMS2; (2) reinitializing the band conditions using point B, and computes RMS2 for very point in *L*_{1}, and finds point C has minimum RMS2; and (3) reinitializing the band conditions using point C, and computes RMS2 for very point in *L*_{3}, and finds point D has minimum RMS2. Thus, point D is the optimal results of band turning method. In fact, the bands turning method uses the minimum RMS2 of three lines to approximate to the minimum RMS2 of the whole bands searching ranges. Thus, the optimal bands determined using bands turning method are the local optimal bands but not the global optimal bands.

## Acknowledgments

This study is supported by the Science Foundation for 100 Excellent Youth Geological Scholars of China Geological Survey, open fund of Key Laboratory of Marine Hydrocarbon Resources and Environmental Geology (MRE201109), Serial Maps of Geology and Geophysics on China Seas and Land on the Scale of 1:1000000 (200311000001), and the National Natural Science Foundation of China (No. 41106154). We would like to just express our gratitude to Prof. K. L. Carder (download from SeaBASS) for providing the bio-optical data set for this study. We would also like to express our gratitude to two anonymous reviewers for their useful comments and suggestions.

## References and links

**1. **W. Richard, J. Could, and A. A. Robert, “Remote sensing estimates of inherent optical properties in a coastal environment,” Remote Sens. Environ. **61**(2), 290–301 (1997). [CrossRef]

**2. **N. M. Komick, M. P. F. Costa, and J. Gower, “Bio-optical algorithm evaluation for MODIS for western Canada coastal waters: An exploratory approach using in situ reflectance,” Remote Sens. Environ. **113**(4), 794–804 (2009). [CrossRef]

**3. **M. W. Matthews, “A current review of empirical procedures of remote sensing in inland and near-coastal transitional waters,” Int. J. Remote Sens. **32**(21), 6855–6899 (2011). [CrossRef]

**4. **J. Chen and H. Sheng, “An empirical algorithm for hyperspectral remote sensing of chlorophyll-a in turbid waters: a case study on Hyperion sensor,” IEEE Sensor Lett., doi. [CrossRef] (2012).

**5. **Z. P. Lee and K. L. Carder, “Absorption spectrum of phytoplankton pigments derived from hyperspectral remote-sensing reflectance,” Remote Sens. Environ. **89**(3), 361–368 (2004). [CrossRef]

**6. **J. Chen and W. T. Quan, “An improved algorithm for retrieving chlorophyll-a from the Yellow River Estuary using MODIS imagery,” Environ. Monit. Assess. **185**(3), 2243–2255 (2013). [CrossRef] [PubMed]

**7. **Z. P. Lee, K. L. Carder, and R. A. Arnone, “Deriving inherent optical properties from water color: a multi-band quasi-analytical algorithm for optically deep waters,” Appl. Opt. **41**(27), 5755–5772 (2002). [CrossRef] [PubMed]

**8. **A. A. Gitelson, G. Dall'Olmo, W. Moses, D. C. Rundquist, T. Barrow, T. R. Fisher, D. Gurlin, and J. Holz, “A simple semi-analytical model for remote estimation of chlorophyll-a in turbid waters: Validation,” Remote Sens. Environ. **112**(9), 3582–3593 (2008). [CrossRef]

**9. **G. Dall'Olmo, A. A. Gitelson, D. C. Rundquist, B. Leavitt, T. Barrow, and J. C. Holz, “Assessing the potential of SeaWiFS and MODIS for estimating chlorophyll concentration in turbid productive waters using red and near-infrared bands,” Remote Sens. Environ. **96**(2), 176–187 (2005). [CrossRef]

**10. **G. Dall’Olmo and A. A. Gitelson, “Effect of bio-optical parameter variability and uncertainties in reflectance measurements on the remote estimation of chlorophyll-a concentration in turbid productive waters: modeling results,” Appl. Opt. **45**(15), 3577–3592 (2006). [CrossRef] [PubMed]

**11. **J. Chen, X. F. Hu, and W. T. Quan, “A multi-band semi-analytical algorithm for estimating chlorophyll-a concentration in the Yellow River Estuary, China,” Water Environ. Res. (2012). [CrossRef]

**12. **J. Chen, W. T. Quan, Z. H. Wen, and T. W. Cui, “An improved three-band semi-analytical algorithm in estimating chlorophyll-a concentration in high turbid Yellow River Estuary, ” Environ. Earth SCI. doi. [CrossRef] (2013).

**13. **C. E. Binging, J. H. Jerome, R. P. Bukata, and W. G. Booty, “Spectral absorption properties of dissolved and particulate matter in Lake Erie,” Remote Sens. Environ. **112**(4), 1702–1711 (2008). [CrossRef]

**14. **Y. Oyama, B. Matsushita, T. Fukushima, K. Matsushige, and A. Imai, “Application of spectral decomposition algorithm for mapping water quality in a turbid lake (Lake Kasumigaura, Japan) from Landsat TM data,” ISPRS J. Photogramm. **64**(1), 73–85 (2009). [CrossRef]

**15. **D. G. Bowers, K. M. Braithwaite, W. A. M. Nimmo-Smith, and G. W. Graham, “Light scattering by particles suspended in the sea: the role of particle size and density,” Cont. Shelf Res. **29**(14), 1748–1755 (2009). [CrossRef]

**16. **V. Volpe, S. Silvestri, and M. Marani, “Remote sensing retrieval suspended sediment concentration in shallow waters,” Remote Sens. Environ. **115**(1), 44–54 (2011). [CrossRef]

**17. **P. J. Werdell and S. W. Bailey, *The SeaWiFS bio-optical archive and storage system (SeaBASS): current architecture and implementation, Goddard Space Flight Center, Greenbelt, Maryland 20771* (2002).

**18. **M. H. Wang, S. H. Son, and W. Shi, “Evaluation of MODIS SWIR and NIR-SWIR atmospheric correction algorithms using SeaBASS data,” Remote Sens. Environ. **113**(3), 635–644 (2009). [CrossRef]

**19. **J. L. Mueller and G. S. Fargion, *Ocean optics protocols for satellite ocean color sensor validation, SeaWiFS Technical Report Series, Revision 3 Part II* (2002).

**20. **L. Gilpin and P. Tett, *A methods for analysis of Benthic chlorophyll-a pigment, in: marine biology report* (Napier University Press, 2001).

**21. **N. A. Welschmeyer, “Fluorometric analysis of chlorophyll a in the presence of chlorophyll b and pheopigments,” Limnol. Oceanogr. **39**(8), 1985–1992 (1994). [CrossRef]

**22. **S. Tassan and G. M. Ferrari, “An alternative approach to absorption measurement of aquatic particles retained on filters,” Limnol. Oceanogr. **40**(8), 1358–1368 (1995). [CrossRef]

**23. **Z. P. Lee, K. L. Carder, and K. P. Du, “Effects of molecular and particle scatterings on the model parameter for remote-sensing reflectance,” Appl. Opt. **43**(25), 4957–4964 (2004). [CrossRef] [PubMed]

**24. **H. R. Gordon, O. B. Brown, R. H. Evans, J. W. Brown, R. C. Smith, K. S. Baker, and D. K. Clark, “A semianalytic radiance model of ocean color,” J. Geophys. Res. **93**(D9), 10909–10924 (1988). [CrossRef]

**25. **A. Morel and B. Gentili, “Diffuse reflectance of oceanic waters. III. implication of bidirectionality for the remote-sensing problem,” Appl. Opt. **35**(24), 4850–4862 (1996). [CrossRef] [PubMed]

**26. **C. D. Mobley, *Hydrolight 6.0 user's guide, final report, SRI international, Menlo Park, Calif* (2012).

**27. **A. Morel and L. Prieur, “Analysis of variances in ocean color,” Limnol. Oceanogr. **22**(4), 709–722 (1977). [CrossRef]

**28. **K. L. Carder, F. R. Chen, Z. P. Lee, S. K. Hawes, and J. P. Cannizzaro, *MODIS ocean science team agorithm theoretical basis document: case 2 chlorophyll a, ATBD 19, version 7* (2003).

**29. **G. Dall’Olmo and A. A. Gitelson, “Effect of bio-optical parameter variability on the remote estimation of chlorophyll-a concentration in turbid productive waters: experimental results,” Appl. Opt. **44**(3), 412–422 (2005). [CrossRef] [PubMed]

**30. **G. Dall'Olmo, A. A. Gitelson, and D. Rundquist, “Towards a unified approach for remote estimation of chlorophyll-a in both terrestrial vegetation and turbid productive waters,” Geophys. Res. Lett. **30**(18), 1–4 (2003). [CrossRef]

**31. **H. R. Gordon, “Radiometric considerations for ocean color remote sensors,” Appl. Opt. **29**(22), 3228–3236 (1990). [CrossRef] [PubMed]

**32. **Z. P. Lee, K. L. Carder, C. D. Mobley, R. G. Steward, and J. S. Patch, “Hyperspectral remote sensing for shallow waters. 2. deriving bottom depths and water properties by optimization,” Appl. Opt. **38**(18), 3831–3843 (1999). [CrossRef] [PubMed]

**33. **C. D. Mobley, *Light and Water: Radiative Transfer in Natural Waters* (Academic Press, 1994).

**34. **M. Tzortziou, J. R. Herman, C. L. Gallegos, P. J. Neale, A. Subramanian, L. W. Harding, and Z. Ahmad, “Determination of chlorophyll contentand tropic state of lakes using field spectrometer and IRS-IC satellite data in the Mecklenburg Lake Distract, Germany,” Remote Sens. Environ. **73**, 227–235 (2006).

**35. **A. Morel and H. Loisel, “Apparent optical properties of oceanic water: dependence on the molecular scattering contribution,” Appl. Opt. **37**(21), 4765–4776 (1998). [CrossRef] [PubMed]

**36. **D. Doxaran, J.-M. Froidefond, S. Lavender, and P. Castaing, “Spectral signature of highly turbid waters,” Remote Sens. Environ. **81**(1), 149–161 (2002). [CrossRef]

**37. **T. J. Smyth, G. F. Moore, T. Hirata, and J. Aiken, “Semi-analytical model for the derivation of ocean color inherent optical properties: description, implementation, and performance assessment,” Appl. Opt. **45**(31), 8116–8131 (2006). [CrossRef] [PubMed]

**38. **T. S. Moore, J. W. Campbell, and M. D. Dowell, “A class-based approach to characterizing and mapping the uncertainty of the MODIS ocean chlorophyll product,” Remote Sens. Environ. **113**(11), 2424–2430 (2009). [CrossRef]

**39. **F. Gilbes, C. Tomas, J. J. Walsh, and F. E. Muller-Karger, “An episodic chlorophyll plume on the west florida shelf,” Cont. Shelf Res. **16**(9), 1201–1224 (1996). [CrossRef]

**40. **A. A. Gitelson, J. F. Schalles, and C. M. Hladik, “Remote chlorophyll-a retrieval in turbid, productive estuaries: Chesapeake Bay case study,” Remote Sens. Environ. **109**(4), 464–472 (2007). [CrossRef]

**41. **D. T. Yang, D. L. Pan, X. Y. Zhang, X. F. Zhang, X. Q. He, and S. J. Li, “Retrieval of chlorophyll a and suspended solid concentrations by hyperspectral remote sensing in Taihu Lake, China,” Chin. J. Limnol. Oceanogr. **24**(4), 428–434 (2006). [CrossRef]

**42. **H. R. Gordon and B. A. Franz, “Remote sensing fo ocean color: Assessment of the water-leaving radiance bidirectional effects on the atmospheric diffuse transmittance for SeaWiFS and MODIS intercomparisons,” Remote Sens. Environ. **112**(5), 2677–2685 (2008). [CrossRef]

**43. **R. C. Smith and K. S. Baker, “Optical classification of natural waters,” Limnol. Oceanogr. **23**(2), 260–267 (1978). [CrossRef]

**44. **C. D. Mobley, L. K. Sundman, and E. Boss, “Phase function effects on oceanic light fields,” Appl. Opt. **41**(6), 1035–1050 (2002). [CrossRef] [PubMed]

**45. **J. L. Mueller, C. O. Davis, R. A. Arnone, R. Frouin, K. L. Carder, Z. P. Lee, R. G. Steward, S. Hooker, C. D. Mobley, and C. R. McClain, “*Above-water radiance and remote sensing measurement and analysis protocols,” Ocean Optics Protocols for Satellite Ocean-Color Sensor Validation, vol. Revision 4, III: Radiometric Measurements and Data Analysis Protocols, pp. NASA Tech. Memo* (2003).

**46. **L. Li, L. Li, K. Shi, Z. Li, and K. Song, “A semi-analytical algorithm for remote estimation of phycocyanin in inland waters,” Sci. Total Environ. **435-436**, 141–150 (2012). [CrossRef] [PubMed]

**47. **W. J. Moses, A. A. Gitelson, S. Berdnikov, V. Saprygin, and V. Povazhnyi, “Operational MERIS-based NIR-red algorithms for estimating chlorophyll-a concentrations in coastal waters — The Azov Sea case study,” Remote Sens. Environ. **121**, 118–124 (2012). [CrossRef]

**48. **K. Suzuki, M. Kishino, K. Sasaoka, S. Saitoh, and T. Saino, “Chlorophyll-specific absorption coefficients and pigments of phytoplankton off Sanriku, Northwestern North Pacific,” J. Oceanogr. **54**(5), 517–526 (1998). [CrossRef]