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
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 . 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 .
Models to estimate chla 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 . However, it lacks a physical foundation and the relationships are more geographically specific and cannot be applied other areas . The semi-analytical model containing the spectral optimization approach is based on solutions to the radiative transfer equation . These algorithms can be applied to different water types, and estimation accuracy is often much better than that of empirical algorithms . 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 chla concentrations . Thus, an accurate semi-analytic model is still under development.
Recently, Gitelson et al.  outlined a three-band semi-analytical algorithm for estimating chla 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 chla 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 : (1) the absorption by chla at λ1 is very different from that at λ2, but absorption by suspended solids and gelbstoff at λ1 is close to that at λ2; (2) reflectance at λ3 is minimally affected by the absorption of water quality constituents and the total absorption at λ3 is a measure of the absorption by water; and (3) the total backscattering coefficients of the three bands are approximately equal. The algorithm for chla 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  found that the variability in the quantum yield chla fluorescence and the chla specific absorption coefficient, among other factors, considerably affect the accuracy of three-band algorithm in chla prediction. Instead of re-initialization of the models for water bodies with specific optical properties, Dall'Olmo and Gitelson  suggested tuning the spectral band positions in order to minimize these effects. Recently, Chen et al.  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 chla absorption is still not perfectly isolated by three-band algorithm. It may produce an unacceptable uncertainty while using three-band algorithm to retrieve chla 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 chla concentration in coastal waters; (4) to evaluate the accuracy of the variation three-band algorithm to accurately estimate chla concentration in coastal waters; and (5) to compare the accuracy of the three-band, modified three-band, and variation three-band algorithm in estimating chla 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 . 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 . 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 .
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 chla concentration, two independent data sets containing the spectral optical properties, inherent optical properties, and chla 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. Chla concentration was extracted and measured with 90% acetone in accordance with the Ocean Optical Protocols of NASA , a generally accepted method of quantifying Chla concentration in chemical and biological fields [20, 21].The data for ap(λ) and ag(λ) were measured according to Tassan and Ferrari  and the data for CDOM according to the SeaWiFS protocols .
2.2 Accuracy assessment
The Root-Mean-Square (RMS) of the ratio of modeled-to-measured values was used to assess the accuracy of chla concentration estimation in this study. This statistic is described by:
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 Rrs(λ) to below-surface spectral rrs(λ). For the Rrs(λ) to rrs(λ) conversion [23, 24],25]. As Rrs(λ) is small for most oceanic and coastal waters, the variation of the Q value has little effect on the conversion between Rrs(λ) and rrs(λ) . Based on calculated HYDROLIGHT Rrs(λ) and rrs(λ) values, T≈0.52 and κQ≈1.7 for optically deep waters .
Remote sensing of water quality constituent’s concentration is based on the relationship between rrs(λ) and the inherent optical properties, namely, the total absorption a(λ) and the total backscattering coefficients bb(λ) :24, 25, 27]. The total absorption and scattering coefficients may be expanded as follows:28], so the ad(λ) term is combined operationally with ac(λ), and both detritus and CDOM absorption are represented by gelbstoff absorption ag(λ). the total absorption coefficient can be expressed as:
Gitelson et al.  suggested that reciprocal reflectance in the first spectral band r−1rs(λ1) should be maximally sensitive to ap(λ1); However, in addition to absorption by chla, r−1rs(λ1) 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−1rs(λ2) is minimally sensitive to absorption by chla and absorption of gelbstoff and inorganic particles at λ2 is quite close to that in band λ1. Thus, the difference r−1rs(λ1)-r−1rs(λ2) must meet the follow requirements:
Unfortunately, the difference r−1rs(λ1)-r−1rs(λ2) is still affected by bb(λ1), i.e., if backscattering varies between samples, the model output would be different for the same chla concentration. To account for this, a third spectral band λ3 is adopted, where reflectance is minimally affected by absorption of water quality constituents, i.e., a(λ3)~aw(λ3) and a(λ3)>>bb(λ3). This means that λ3 has to be restricted within the NIR regions . 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 , when they developed a reflectance model, γ with a mean value of 0.33. As shown in Morel and Gentili , the coefficient γ is not constant and varies consistently with the water optical properties. Thus, it is much more challenging to separate ap(λ1) from the remote sensing reflectance using three-band algorithm provided by Gitelson et al.  due to the poor approximation of Eq. (3). Gordon  carried out extensive computations of rrs(λ) as a function of the optical properties of the water and solar zenith angle θ0 and concluded that for θ0≥20°, rrs(λ) can be directly related to the inherent optical properties of the water through:24] found that l0≈0.0949 and l1≈0.0794 for Case I waters, while Lee et al.  suggested that l0 of 0.084 and l1 of 0.17 work better for higher scattering coastal waters. Actually the values of l0 and l1 may vary with particle phase function , which is not known remotely. Without local bio-optical information or models to predetermine the values of l0 and l1 in an semi-analytical algorithm, the Gordon et al.  suggested values are used in Case I waters, while Lee et al.  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 λ1 and λ2 and the water optical properties dependent γ in Eq. (3), the three-band should be written as,12] by replacing rrs(λ) in the three-band algorithm by s(λ). It is expressed as
Compared to three-band algorithm suggested by Gitelson et al. , 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 as33]. 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 λ3, e.g., Tzortziou et al.  showed that the absorption of particulate matter in the 700-730nm region cannot be neglected in the Chesapeake Bay, while Binding et al.  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  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 chla concentration is low enough (in most of the entire ocean), while Lee et al.  show that the water molecular backscattering ranged from negligible to generally significant for natural assemblages of global waters. Doxaran et al.  suggested that bbw(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 bbp(λ) can be modeled as15, 28], the bbw(λ) term cannot be combined operationally with bbp(λ), so the ratio of bb(λ3) to bb(λ1) 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 chla 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 λ1 and λ2 can be denoted by using:37] can be used to determine the total absorption due to water quality constituents. Starting from a general wavelength pair λ1 and λ2: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 . For Case II situations, to solve for absorption by chla, the a(λ) value of at least two or more bands are required. Similar to the deriving procedures of a(λ2), total absorption at the third band λ3 can be denoted as follow:7, 23, 38] that the absorption related to chla 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 ap(λ) and ag(λ) from total absorption, because ap(λ)<< a(λ) and ag(λ)<< a(λ), i.e., a small bias in a(λ) estimation may result in a large bias in ap(λ) and ag(λ) retrieval. To overcome this limitation, an empirical spectral decomposed method (ESDM) was used to retrieve ap(λ) from a(λ) in this study. The ESDM method is expressed by:6].
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, chla concentrations in surface waters vary from 2 to 30mg/m3, but chla concentrations during non-bloom periods are <1mg/m3 . 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 ap(440) plotted against ag(440) in the West Florida Shelf, indicating that the water optical properties in the West Florida Shelf are not only determined by chla and covarying pigments, but are also determined by other water quality constituents such non-covarying CDOM and non-algal particle, even though ap(440) and ag(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-chla, 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 , indicating that some West Florida Shelf waters are typical low-chla, 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 . 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 chla concentrations at all sites. Figure 4 shows a chla absorption peak around 440nm, so there must be a reflectance minimum near 440nm in spectral curves, but it was distinct only when the chla concentration was above 150mg/m3 . Near 490nm another trough on reflectance curve is shown due to largely carotenoids absorption . 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 chla absorption maximum in spectral curves. However, it was indistinct in West Florida Shelf water due to the low chla 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.  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  is used to determine the optimal bands for those conceptual models. It is noteworthy that the samples with low chla concentration (<0.2 mg m−3) were ignored during model calibration and validation, due to the weak absorption by chla in these sample , which would result in poor accuracy for chla retrievals.
3.3.1 Three-band algorithm calibration
In order to find the optimal positions of λ1, λ2, and λ3, 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. , the first band should be maximally sensitive to chla absorption. Figure 5(a) shows results of RMS for rrs(λ) linearly relating to ap(λ). By comparison, ap(λ) at bands ranges from 550 to 694nm is more sensitive to rrs(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  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. . The second one is minimally sensitive to absorption by chla but absorption of gelbstoff and inorganic particles at λ2 is quite close to that in band λ1. 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 λ1 suggested by Gitelson et al. . The third one should be minimally sensitive to absorption both by chla and gelbstoff. Figure 5(b) shows the ratio of [ap(λ) + ag(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−1rs(λ1)-R−1rs(λ2)] Rrs(λ3) 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 λ1 = 620nm, λ2 = 712nm and λ3 = 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 ap(λ). This means that λ1 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(λ1) affected by ag(λ1) can be easily removed by the second band using a simple linear model such as Xs(λ2). According to the study results carried out by Gitelson et al. , λ2 has to be restricted within band ranges from 710 to 750nm, where s(λ2) is minimum sensitive to absorption by chla. However, our previous research suggested that ap(λ1)-Xap(λ2) can be related to chla concentration as long as ap(λ1) is linearly related to but not equal to Xap(λ2). This means that λ2 can also be set to 580 to 694nm. Thus, for the modified three-band algorithm, λ2 should be between 580 and 750nm. The third one should be minimally sensitive to absorption both by chla and gelbstoff, so λ3 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 . 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 (λ1)-Xs−1(λ2)]s(λ3) versus [chla]. The results (Fig. 6(b)) indicates that the modified three-band algorithm has the optimal accuracy in case of [s−1(600)-0.2363s−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 bbp(λ) at s(λ2)a(λ2) and s(λ3)a(λ3) can be semi-analytically minimized by s(λ1)a(λ1) using Eq. (15). To determine the a(λ2) and a(λ3) using measurements of s(λ1), s(λ2) and s(λ3), four empirical spectral relationships should be known: a(λ1) versus a(λ2), a(λ1) versus a(λ3), bbp(λ1) versus bbp(λ2), and bbp(λ1) versus bbp(λ3), respectively. However, there is no field-measured backscattering coefficient here, so the spectral relationship of s(λ1)a(λ1) versus s(λ2)a(λ2) and s(λ1)a(λ1) versus s(λ3)a(λ3) 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 λ1, λ2, and λ3 are, respectively, turning from 400 to 750nm, e.g., for each wavelengths combination of λ1, λ2, and λ3, the constant coefficients of κ12, κ13, ζ12, ζ13, ξ12 and ξ13 as shown in Eq. (15)-(18) can be determined using inputting data set of s(λ) and a(λ) at corresponding wavelengths. Then, the π0, π1, and π2 as shown Eq. (19) can be determined by the non-linear iterative method proposed by Chen and Quan . 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 λ1 = 488, λ2 = 600, and λ3 = 610nm. Figure 7 shows the empirical spectral relationships between the optimal bands of variation three-band model, indicating that both a(λ) and bb(λ) at 600 and 610nm are strongly related to a(λ) and bb(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), ap(610), and chla 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 chla concentrations predicted by these models with chla concentration measured analytically for independent validation data set (Table 1b). Figure 9 shows the relationship between chla modeled from the three-band, modified three-band, and variation three-band models, and measured chla 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 chla 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 chla concentration was presented to demonstrate the ability of these three algorithms in estimating chla (Fig. 9). We found that the RE decreases with increasing chla 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 chla 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 chla 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.
As mentioned in previous, the samples with low chla 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 chla. Figure 10(a) shows the lab-measured chla concentration plotted against field measured absorption by chla at 610nm, indicating that the cha concentration is weakly depended on ap(610) while the chla concentration is too low. Due to the low value of ap(610) (<0.002 m−1), the noise of ap(610) was significant. That might be one of the reasons for the poor performance of chla estimation in these low concentration levels. Figure 10(b) shows the ratio of absorption by chla to total absorption (CTR) at 610nm, indicating that the ap(610) is a very small part of a(610) for samples with low chla concentration, whose CTR<0.7%. This is to say, 0.7% retrieval uncertainty in a(610) would result in 100% uncertainty in ap(610) retrievals, which would lead to much larger uncertainty in remote sensing of chla 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 chla 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 , 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 , 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 chla 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, chla concentration in surface waters varies from 2 to 30mg/m3, but is <1mg/m3 during non-bloom periods . When concentrations of chla and suspended matters are low enough, water molecular backscattering becomes non-negligible comparing to backscattering by particle. Figure 11 shows the chla 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 chla concentration is larger than 2 mg m−3, and the largest one is 60% whose chla 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 chla 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 [bbw(λ1) + bbw(λ1)]/ [bbw(λ3) + bbw(λ3)] are related either to water molecular backscattering or backscattering by particulate matters. Due to the difference in spectral shape [15, 28], the bbw(λ) term cannot be combined operationally with bbp(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 λ3 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 chla concentration retrievals algorithm than the latter two limitations in deriving chla concentration from turbid coastal waters.
Different limitations have different influence on chla 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 chla concentration from coastal and inland waters. For example, Li et al.  suggested a semi-analytical algorithm combining both three band indices and a baseline algorithm to estimate chla 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 chla concentration range from 1.4 to 146.1mg/m3. An improved OC4v4 algorithm was suggested by Chen and Quan  for estimating chla concentration from Yellow River Estuary. That improved OC4v4 algorithm produces ~32.7% RMS in estimating chla concentration in that regions. Moses et al.  constructed a three-band algorithm for retrieving chla concentration from Azov Sea and Taganrog Bay, Russia, and determined that the three-band algorithm gave consistently highly accurate estimates of chla 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 chla 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 λ1 = 488, λ2 = 600nm, and λ3 = 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 chla 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 , 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.  indicated that the specific scattering coefficient depends on the nature of the scattering particles: their size, shape, refractive index and density. Suzuki et al.  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.
In this study, three semi-analytical models for remote sensing of chla concentration were constructed by specifying the optimal bands. The three-band model has the optimal wavelengths of λ1 = 620nm, λ2 = 712nm and λ3 = 730nm; the modified three-band algorithm has optimal accuracy when [s−1(600)-0.2363s−1(580)]s(692); and the specification of the wavelength in the variation three-band model is λ1 = 488, λ2 = 600nm, and λ3 = 610nm. Evaluated using two independently collected data sets in West Florida Shelf, USA, all modes are found to have an acceptable accuracy in estimating chla 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 chla concentration levels (<1 mg m−3). Using the variation three-band algorithm to retrieve chla 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 chla 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.
In order to determine the optimal bands for three-band algorithm, the band turning method is used by Gitelson et al. . To find the optimal position of λ2, initial position for λ1 was set to λ1,A and the initial position for λ3 was set to λ3,A. As λ2 was turned from λ2,I to λ2,T, the RMS2 of [R−1rs(λ1,A)-R−1rs(λ2)] Rrs(λ3,A) versus [chla] was calculated. RMS2 varies with wavelength λ2, its minimum occurs at λ2,B. Therefore, λ2,B was selected for λ2. To determine the optimal position of λ1, λ2=λ2,B and λ3=λ3,A was used, and λ1 turned from λ1,I to λ1,T. the RMS2 of [R−1rs(λ1)-R−1rs(λ2,B)] Rrs(λ3,A) versus [chla] was again computed for each λ1. Results indicates that minimum RMSE exits at λ1,C. Thus, λ1,C was selected for λ1. The optimal λ3 was determined by setting λ1=λ1,C and λ2=λ2,B, and the minimum RMSE occurs at λ3,D. Therefore, the optimal three-band algorithm calibrated by bands turning method suggested by Gitelson et al.  is [R−1rs(λ1,C)-R−1rs(λ2,B)] Rrs(λ3,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 L2, and finds point B has minimum RMS2; (2) reinitializing the band conditions using point B, and computes RMS2 for very point in L1, and finds point C has minimum RMS2; and (3) reinitializing the band conditions using point C, and computes RMS2 for very point in L3, 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.
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.
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