Remote Sensing a Spectral Decomposition Algorithm for Estimating Chlorophyll-a Concentrations in Lake Taihu, China

The complex interactions among optically active substances in Case II waters make it difficult to associate the variability in spectral radiance (or reflectance) to any single component. In the present study, we developed a four end-member spectral decomposition model to estimate chlorophyll-a concentrations in a eutrophic shallow lake—Lake Taihu. The new model was constructed by simulated spectral data from Hydrolight and was successfully validated using both of simulated reflectance and in situ reflectance data. Using MEdium Resolution Imaging Spectrometer (MERIS) images, the accuracy of the new model was estimated and compared with other published models. According to the MERIS retrieved results, the spatial distribution of chlorophyll-a concentrations and its relationship with environment factors were analyzed. The application of the new model and its limits to estimate water surface chlorophyll-a concentrations in turbid lakes is also discussed.


Introduction
Phytoplankton biomass is one of the three main components influencing the optical properties of natural waters.The concentration of chlorophyll-a (Chla, μg•L −1 ) has been used as a marker for phytoplankton biomass and in calculations of bio-production of many waters [1].According to the bipartite classification scheme [2][3][4], oceanic (or fresh) waters are classified into one of two types: Case I or Case II.Case I waters are considered to encompass over 90% of the world oceans, and Case II waters include many coastal and inland waters of which economic, social, and ecological significance is significant.Phytoplankton biomass is the principal agent responsible for variations in the optical properties of Case I waters.Case II waters are influenced, not only by phytoplankton and related particles, but also by other optically active substances that vary independently of phytoplankton, notably suspended inorganic particles and dissolved organic matter [5].Thus, it is generally recognized that Case II waters are more complex than Case I waters in their composition and optical properties.Case I waters can be typically treated as a single-variable problem, while Case II waters must be addressed in a non-linear, multivariate manner [5].As a result, the application of algorithms from Case I waters (such as the ratio of the near-infrared (NIR) peak reflectance to the reflectance near 675 nm, fluorescence line height and first derivative of reflectance algorithm) does not provide acceptable results for Case II waters [6][7][8].In general, the estimation of Chla in Case II waters requires more than simple adjustments to the Case I algorithms.
In recent studies, a three-band semi-analytical algorithm has been successfully used to assess Chla distributions in turbid waters without re-parameterization [8][9][10].However, the assumptions for the three-band semi-analytical algorithm may be violated in highly turbid waters, as particle absorption and backscattering vary with the type of suspended particles [11,12].Four-band semi-analytical algorithms and enhanced three-band semi-analytical algorithms provide robust alternatives [12][13][14], but require further development.
In terrestrial studies, the consideration of a given pixel as a linear combination of individual components has been widely applied.This approach has also been used in aquatic studies [15][16][17].According to this model, the observed reflectance spectra can be disaggregated into the sum of the spectra of several optically active components.Each spectrum is weighted by the relative proportion of each optically active component.In general, this is achieved by: identifying optically active components (end-members) and their spectra; constructing the relationship between decomposition coefficients and corresponding optically active components.Svab [18], Novo [19], Tyler [17] and Oyama [20][21][22] measured the reflectance spectra of end-members by laboratory determination.Others used satellite image-derived reflectance spectra of end-members [23][24][25].However, in the former case, the reflection from interior walls of the mesocosm (or tank) was found to influence the accuracy of the end-members' spectra.In the latter case, differences in the signal to noise and atmospheric correction processes for different images were found to reduce the accuracy of end-members' spectra [26].Pilorz and Davis (1990) suggested the use of libraries of absorption and scattering coefficients to model upwelling reflectance [27].Radiative transfer numerical models, such as HYDROLIGHT, estimate spectral radiance distributions, based on the absorbing and scattering properties of the water body, the sky radiance incident onto the water surface, the wind speed, and the bottom reflectance [28,29].These models help to simulate reflectance under different environment conditions, especially extreme conditions.
Based on spectrally unique end-members, Svab [18] and Tyle [17] used principal component analysis (PCA) to characterize the spectra of shallow lakes, and combined multivariate regression and a spectral linear mixture modeling approach to retrieve Chla.Oyama [20][21][22] developed the spectral decomposition algorithm (SDA) to estimate Chla in Lake Kasumigaura of Japan, which considered the mixed reflectance spectrum of a given pixel as a linear combination of three dominant components (water, non-phytoplankton suspended sediment (NPSS), and phytoplankton).However, the use of these methods in other water bodies, in particular in the hyper-eutrophic and spatially heterogeneous inland water bodies where dissolved organic matter contribute to overall optical conditions has not been explored.Lake Taihu, based on the in situ measurements during the period of 2008-2011, was found to have a seasonal and spatial distribution of dominant optical components.The absorption of non-pigment containing particles and colored dissolved organic matter absorption was found to dominate in autumn, while the absorption of phytoplankton pigment, non-pigment containing particles, and colored dissolved organic matter (CDOM) was most important in the summer [30].
Considering the optical challenges of these waters, the present study used data from Lake Taihu (China) to focus on: (1) simulating the spectra of end-members of the dominant optical components in this eutrophic shallow lake; (2) developing a four end-members spectral decomposition model (water, NPSS, phytoplankton, and CDOM); (3) validating the developed model with in situ data and MERIS data; (4) analyzing the Chla distribution and its environmental impact, and discussing the application and limits of the new model in eutrophic and turbid lakes.

Study Area
Lake Taihu is located in the center of China's Yangtze River Delta (Figure 1).With a surface area of 2428 km 2 and an average depth of 2 m (maximum depth of 3 m) [31], it is the third largest lake in China after Lake Poyang and Lake Dongting.With the recent rapid economic development of the region, Lake Taihu has become eutrophic with more frequent and more severe cyanobacteria blooms [31][32][33].In recent decades, algal bloom events have jeopardized the supply of drinking water to millions of people in the surrounding cities [34,35].

Simulated Dataset
A simulated dataset was generated using the Hydrolight radiative transfer model [28].This dataset consisted of: the end-member simulated spectra of the concentration of each single end-member (i.e., NPSS, phytoplankton, CDOM, water), the model-construction dataset and the model-validation dataset.The latter two datasets include 248 combinations of these end-members, which were divided randomly into a construction dataset (204 combinations) and a validation dataset (44 combinations).
The input parameters for the radiative transfer model were:  Inherent optical property (IOP) specification model: CASE2;  Pure water IOP [39];  IOP specifications for Chla, NPSS and CDOM including a concentration profile, specific absorption and specific scattering spectra [26];  Internal Source and Inelastic Scatter Selection linked to Chlorophyll Fluorescence, CDOM Fluorescence and Raman Scattering;  Wind speed of 3.5 m/s (average of wind speed in Lake Taihu) and solar zenith angle of 30°;  Parameters of air-water surface boundary conditions, sky conditions and bottom boundary condition were set to their default values.

Field Measurements
Two data collection campaigns (60 samples) were performed in March and September 2011 in Lake Taihu (Table 1 and Figure 2).At each station, water samples were collected from the surface to a depth of 30 cm for measurement in the laboratory and GPS coordinates (0.3-3 m accuracy) were recorded.Chla was determined by the standard spectrophotometric methods following extraction using 90% ethanol [12].Above-surface remote sensing reflectance spectra between 350 and 1050 nm (1 nm resolution) were measured with a FieldSpec Pro Dual VNIR (ASD, USA) following NASA protocols [40].Field measurements were performed from 09:30 to 14:30 local time in sunny conditions with low wind speed (<3.5 m/s).The Chla data and water surface reflectance were used to validate the new model.
Another four data collection campaigns (52 samples) were performed in April 2008 October 2008 (two campaigns) and May 2011 (Table 1 and Figure 2).Only water samples with GPS coordinates and coincident MERIS images were used to analyze the Chla distribution.

MERIS Images
Four Medium Resolution Imaging Spectrometer (MERIS) FR images were used to coincide with field campaigns on 24 April, 13 October, and 16 October 2008 and 1 May 2011.MERIS data have a spatial resolution (300 × 300 m at nadir) and spectral properties (15 narrow bands in the visible and near-infrared) that is appropriate for the optical analysis of larger inland waters [41][42][43][44].Frequent cloud cover over Lake Taihu prevented more match-ups between satellite overpasses and the field measurements.The time span between field and the MERIS observation was approximately 2 h, short enough for comparison of the spectral reflectance measurements.The atmospheric correction algorithms were based on the Basic ERS and ENVISAT (A)ATSR and MERIS Toolbox (BEAM) with the Lake/Eutrophic option [45].

The Spectral Decomposition Algorithm for Lake Taihu
Lake Taihu is characterized by an elevated CDOM.Accordingly, water, phytoplankton biomass, NPSS and CDOM were included as end members in the new algorithm.The spectral decomposition algorithm for Lake Taihu considered the mixed reflectance spectra R(λ) as a linear combination (Equation ( 1)): where C p , C n , C c , and C w are the decomposition coefficients of phytoplankton, NPSS, CDOM and water, respectively, directly related to their relative masses (e.g., concentrations).R p (λ), R n (λ), R c (λ), and R w (λ) are the standard reflectance spectra for each component [20,21].Four decomposition coefficients were calculated (i.e., C p , C n , C c , and C w ) by selecting four MERIS bands (Equation ( 2)).
Each decomposition coefficient C p was then used as an independent variable in the Chla retrieval model.The algorithm had two component parts based on: information about the individual masses of the optically active components and information about spectral properties.Therefore, the estimation model of Chla can be expressed by Equation (3): where C Chla and C p are the decomposition coefficients for Chla and phytoplankton respectively.As there are many functional expressions between C Chla and C p , the final expression was determined by the regression analysis.

The Spectral Properties of End-Members
An end member's standard spectra should include only the spectral information of the end member without the influence of the other end members.As it is very difficult to achieve these spectra by field-measured reflectance in the lake, two approaches have been used in the past: lab-experiment and the radiative transfer modeling.For the former, recent studies indicate that reflectance from tank walls and bottom can compromise the determination of individual spectra [20].Another difficulty is related to the separation of CDOM from the lake water without modification of its optical properties.Ideally, a radiative transfer model is preferable in the determination of the standard spectra of each end member.
The link between reflectance and end-member concentration at each wavelength was based on the simulated spectra of each end-member (NPSS, phytoplankton, CDOM, and water).For each end member, an increase in concentration brings the reflectance spectra closer to saturation, and accordingly, the reflectance differentiation would decrease.We used the ratio of reflectance differentiation to maximum reflectance differentiation of each end-member (Equation ( 4)) to determine the concentration and the standard reflectance spectrum.
where D(λ) and D max was defined as dR(c,λ)/dc and maximum of D(λ), respectively; λ was the wavelength of the reflectance spectra; c was the concentration (or absorption) of phytoplankton, NPSS, or CDOM.When the phytoplankton reflectance ratio was lower than 3%, slight variations in the spectra were found.Reflectance ratio thresholds of NPSS and CDOM for the standard spectra were determined in the same way.For the present study, the ratios of 3%, 2%, and 1% were used for phytoplankton, NPSS and CDOM standard spectra (Figure 3), corresponding concentrations (or absorption) of 150 μg•L −1 , 100 mg•L −1 , and 3.5 m −1 , respectively.These results support those reported by Lu [26].

Results
The mixed reflectance and standard reflectance at the same wavelength could complete one of the four equations.Four equations (Equation ( 2)) at four different wavelengths were used to determine C p , C n , C c , and C w .The MERIS bands considered most sensitive to Chla were tested with the simulated data set (n = 204) (Table 2).Model M7, including MERIS bands 3 (490 nm), 5 (560 nm), 8 (681.25 nm), and 9 (708.75nm), provided the best correlation (R 2 = 0.82, Figure 4) with Chla.For Case II waters, Chla NPSS Water CDOM low reflectance at wavelengths less than 500 nm has been associated to absorption by both algal pigments (e.g., Chla) and dissolved organic matter [46].Likewise, an increase in reflectance at wavelengths 510-620 nm has been associated to low absorption by phytoplankton pigments coupled with increased backscattering due to high particle concentration [47].A peak of reflectance at 685-715 nm was due to chlorophyll-a fluorescence [48].
The relationship between the decomposition coefficient and Chla was determined by regression analysis as (Equation ( 5) and Figure 4): C Chla = 18.219 × e 1.149Cp  (5)

Validation
The RMSE (Root Mean Square Error) and RE (Relative Error) between measured and retrieved values were calculated as:   (7) where C m and C r are the measured and retrieved Chla, respectively, and N is the number of data points.The model-validation dataset of 44 combinations of the end-members showed that the performance of the model was good, with RMSE 15.9 μg•L −1 and RE 34.4% (Figure 5).We then used the model and the in situ water surface reflectance in March and September of 2011 to estimate Chla, which were below 100 μg•L −1 (Table 3).The new model showed good results in retrieving Chla, with a total RMSE of 7.50 μg•L −1 and a RE of 30.4%.Two samples in the range of 40-50 μg•L −1 had unusually high RMSE and RE.

Accuracy Estimation Using MERIS Data
To further assess the accuracies of the algorithms, data from the 52 stations (Table 1, Figure 2) were collected on the same day as MERIS image acquisition.Our new model was compared to six models developed by Li [14], a model by Moses [49], a model by Mishra [50], and a model by Zhou [51] (Table 4).The new model provided a similar RE with respect to the other models and a smaller RMSE.As expected, the model results using with MERIS data were less accurate than those obtained using in situ data.The sources of these errors related to field measurement procedures, model assumptions, and atmospheric correction.Field measurements of the above-surface remote sensing reflectance were made several minutes prior to water sampling, leading to a delay between optical and chemical measurements.The model was built using a construction dataset of simulated results of Hydrolight.Although the input parameters of Hydrolight for Chla, NPSS, and CDOM were specific for Lake Taihu, it spatial and temporal differences in IOPs are expected [52].For example, the Chla specific absorption parameter is expected to vary for species and cell size, in relation to differences in pigment concentrations and packaging effects [52].In addition, the standard environment parameters used (e.g., solar zenith angle, water depth, and wind speed) did not capture the variability of actual conditions.Variations in the solar zenith angle influence apparent optical properties [48,53].While the importance of solar zenith angle is less evident in turbid water with respect to Case I waters [54,55], some errors can be associated to the use of these standard parameters.Additional errors associated to the actual wind field and lake topography also occur.Therefore, temporal and geographical differences in real and model IOPs is expected to occur.
The atmospheric correction of MERIS data was another source of error.It would have been possible to check the accuracy of the BEAM atmospheric correction using the field-measured spectra.The above-water reflectance spectra were not measured for the data sets of 24 April, 13 and 16 October 2008 and on 1 May 2011.It was possible to check the BEAM atmospheric correction with in-situ measured reflectance spectra measured on 11 June 2007 (Figure 6).This analysis indicated that the mean deviations of reflectance derived from boreal and eutrophic lakes of BEAM ranged from 10% to 90% [44].We concluded that none of the available MERIS processors provides a good separation of the atmospheric and water-leaving radiance over Lake Taihu.

Application of the Spectral Decomposition Algorithm to Study Chla Spatial Distributions
We applied the new spectral decomposition model to estimate Chla, after having to first remove areas of algal blooms, using Li [14].The spatial distribution of Chla in the non-bloom areas was determined using four MERIS images (Table 5 and Figure 7).The lake area with Chla less than 30 μg•L −1 was 79.14%, 63.92%, 80.04%, and 49.64%, respectively.
In Lake Taihu, the spatial distribution of floating cyanobacteria (e.g., Microcystis) is sensitive to wind and lake hydrology [55].Using the new model in non-bloom areas, Chla was found to be higher in the downwind area, indicating that wind is also an important factor for the Chla distribution in non-bloom areas.At wind speeds below 3.1 m/s, cyanobacteria tend to float to the water surface, favoring the creations of algal blooms [56].Floating algal blooms were present in the west part of the lake and in Meiliang Bay, a common area for algal blooms [35,57] and may be associated the low average wind speeds measured prior to the measurements; 2.1 and 1.0 m/s on 24 April and 13 October 2008.Compared to conventional Chla retrieval models, the spectral decomposition model should be less sensitive to geographic and temporal variability.The spatial distribution of Chla was significantly different in the two images separated by only three days, 13 October and 16 October 2008 (Figure 6).While this is surprising, it is not unusual in Lake Taihu, as the vertical distribution of the dominant cyanobacteria is highly variable and depends on conditions of wind and rain [58].

The Spectral Decomposition Model Application to Other Satellite Data
If the standard reflectance spectra of the basic components remain consistent and the spectral sensitivity is similar, this model could also be applied with other satellite data.A spectral decomposition model was utilized with Landsat TM data for Chla and NPSS estimates by Oyama [20][21][22].Compared with the TM, MERIS provides additional and more appropriate wavebands to estimate Chla [59,60], but this approach is easily transferred to multispectral data from other satellite systems.

Conclusions
A novel four end-member spectral decomposition model (including water, phytoplankton biomass, NPSS, and CDOM) was developed to estimate chlorophyll-a concentrations in the complex optical The model was applied to four MERIS datasets for Lake Taihu to estimate chlorophyll-a concentrations in areas where surface blooms were not present.The analysis showed that the spatial distribution of chlorophyll-a concentrations was strongly influenced by wind conditions, with the higher concentrations in the downwind area.The two spring and two fall analyses indicated that there was an extensive part of the lake with elevated chlorophyll-a concentrations, greater than 30 μg•L −1 .These areas ranged between 20% and 50% in these four measurement periods.
The complex optical conditions of many internal waters present challenges to the study of their temporal and spatial dynamics by remote sensing.The spectral decomposition approach developed in the present study is an important new tool to improve our understanding of these aquatic ecosystems.It proved to be more robust estimates using MERIS data than the other eight models explored.Its main limitations are those associated to most models, including errors related to field measurement procedures, radiative transfer model assumptions, and atmospheric correction.
Further research should be performed to explore the use of the spectral decomposition approach to estimate the spatial distribution of the other major optical components, both particulate and dissolved.These developments would require additional research that includes the simultaneous measurement of all major optical components, combining in situ and remote data acquisition.

Figure 2 .
Figure 2. Distribution of sample stations in Lake Taihu.

Figure 4 .
Figure 4.The relationship between the decomposition coefficients of phytoplankton (C p ) and Chla based on Hydrolight simulated data.

Figure 5 .
Figure 5.The comparison of in situ Chla and retrieved Chla using the spectral decomposition model.

Figure 6 .
Figure 6.Comparison of the BEAM atmospheric correction and in situ measured reflectance spectra measured on 11 June 2007.The lines represent the reflectance spectra by measurements.The marks represent the atmospheric corrections by BEAM.

Figure 7 .
Figure 7.The estimated distribution of Chla using the spectral decomposition model with MERIS images for 24 April, 13 October and 16 October 2008 and 1 May 2011.

Table 2 .
Accuracy evaluation of different spectral decomposition models using MERIS band-combinations of the simulated model-construction dataset.

Table 3 .
Validation of the spectral decomposition model with in situ data.

Table 4 .
Comparison of nine models with MERIS data.

Table 5 .
Coverage percentage of Chla in MERIS images for Lake Taihu.