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A new three-band algorithm for estimating chlorophyll concentrations in turbid inland lakes

A new three-band model was developed to estimate chlorophyll-a concentrations in turbid inland waters. This model makes a number of important improvements with respect to the three-band model commonly used, including lower restrictions on wavelength optimization and the use of coefficients which represent specific inherent optical properties. Results showed that the new model provides a significantly higher determination coefficient and lower root mean squared error (RMSE) with respect to the original model for upwelling data from Taihu Lake, China. The new model was tested using simulated data for the MERIS and GOCI satellite systems, showing high correlations with the former and poorer correlations with the latter, principally due to the lack of a 709 nm centered waveband. The new model provides numerous advantages, making it a suitable alternative for chlorophyll-a estimations in turbid and eutrophic waters.


Introduction
Chlorophyll-a is an important pigment in nearly all marine and freshwater algal species. The concentration of this pigment (Chla, mg m −3 ) has often been used as a marker for phytoplankton biomass and in calculations of bio-production of many water bodies. The use of satellite based sensors to estimate Chla in large ecosystems provides numerous advantages with respect to standard field measurements (Kutser 2004). However, making such estimates in turbid lakes presents a number of difficulties, largely due to the complex optical conditions. In recent years, three-band reflectance models have been used with success in systems where Chla is not the dominant optical component (Dall'Olmo et al 2003, Gitelson et al 2008, Xu et al 2009. These models are based on the following relationship between Chla and reflectance (R rs ): [Chla] ∝ [R −1 rs (λ 1 ) − R −1 rs (λ 2 )]R rs (λ 3 ) where R rs is a function of the inherent absorption (a(λ)) and scattering (b b (λ)) properties of the medium, according to the basic radiative transfer equation (Gordon et al 1988): . (2) Absorption a(λ) which can be separated into absorption related to phytoplankton biomass (a ph ), detritus (a d ), chromophoric dissolved organic matter (CDOM, a g ) and pure water (a w ), while b b (λ) is the measurement of total backscattering. The term f/Q, a function dependent on sun zenith angle (Morel and Gentili 1993), can be approximated to be 0.0945 (Gordon et al 1988), and t/n 2 = 0.54 (Clark 1981, Austin 1974. In the three-band models developed to date, the difference between the reciprocal reflectance R −1 rs (λ 1 ) and R −1 rs (λ 2 ) (equation (1)) is approximated by based on the following assumptions: (a) b b is spectrally invariant between λ 1 and λ 2 ; . In lakes where high (non-phytoplankton-related) turbidity is present, such as Lake Taihu, assumptions (b) and (c) are not always valid. If these assumptions cannot be made, the difference between the reciprocal reflectances remains in its original form: In many turbid systems, a g , a d and a w are independent of Chla, but are characteristic for the ecosystem. The sum of the wavelength differences (a g (λ 1 ) − a g (λ 2 ) + a d (λ 1 ) − a d (λ 2 ) + a w (λ1) − a w (λ 2 )) can then be treated as an ecosystem specific parameter c, making the equation In three-band models, the third spectral band, λ 3 , is included to represent the effects of backscattering (b b ) with respect to absorption by water. In most cases, λ 3 is chosen to be in the near infrared (NIR) wavelengths, where reflectance by a ph , a d and a g is minimal, i.e. a(λ 3 ) ∼ a w : Based on equations (2), (5) and (6), the original relationship now becomes (7) If the specific absorption of chlorophyll-a (a * ph , m −1 (mg m −3 ) −1 ) is considered as a ph = a * ph × [Chla] (Morel and Prieur 1977), It should be noted that the difference in the specific absorption coefficients [a * ph (λ 1 ) − a * ph (λ 2 )] will not be constant throughout the ecosystem as the pigment composition will vary temporally and spatially. Equation (8) can be further simplified by combining the ecosystem specific optical properties into two variables, ε = This new model contains two optically identifiable parameters that can be determined empirically by fitting of the measured Chla and observed reflectances. Most importantly, these parameters can be checked by comparing them with the inherent optical properties of the study waters. While the form of the equation is similar to the original three wavelength model, the proportionality constants are now associated with measurable quantities.
To compare models, we used measurements obtained in the field and simulated satellite based reflectance measurements for a large turbid lake in China. Lake Taihu (31.15 N, 120.15 E) presents a range of optical properties which are influenced by recurring phytoplankton blooms (Duan et al 2009b). MERIS is a medium spectral resolution, imaging spectrometer which has provided multispectral data for water color analysis since 2002 (Bezy et al 2000). GOCI (the Geostationary Ocean Color Imager) is the world's first geostationary ocean color multispectral system, with medium spatial resolution (500 m) and very high temporal resolution (refresh rate: 1 h). It is scheduled to be launched on 23 June 2010 by the Republic of Korea (ROK), and will include Lake Taihu in its coverage area.
In the present study, we compare the performance of the new three-band model to standard Chla models using measured spectral reflectances and in situ measurements. We examine the physical significance of the parameters used in the new three-band model. Finally, we assess the potential use of this model to estimate Chla using MERIS and GOCI reflectance data.

Data
Four data collection campaigns were performed in October 2004, June 2007, October 2008 and April-May 2010 in Lake Taihu, China (table 1). At each station GPS coordinates (0.3-3 m accuracy) were recorded and water samples were collected from the surface to a depth of 30 cm for measurement in the laboratory. Remote sensing reflectance was measured with a FieldSpec Pro Dual VNIR (ASD, USA) using NASA protocols (Mueller et al 2003). The absorption by total suspended matter, pigment, detritus and CDOM were determined using the quantitative filter technique with a Shimadzu UV2401 spectrophotometer (Shimadzu, Tokyo, Japan).
Chla concentrations were extracted using 90% ethanol and measured with a UV2401 spectrophotometer. The concentrations of total suspended solids (TSM) were determined gravimetrically.

Fitting method
In order to optimize the three band positions of equation (9), an iterative fitting algorithm with linear least squares was developed using MATLAB software. The algorithm minimizes the sum of squared residuals between the measured concentration and the value provided by a model. The root mean squared error (RMSE) is employed to assess the performance of the model as where n is the number of samples and Chla mea,i and Chla pre,i are the measured and predicted Chla values. Table 2 shows the results of both models in estimating Chla during the four measurement campaigns in Lake Taihu based on field reflectance measurements. In all campaigns, the new three-band model provided a higher determination coefficient (R 2 ) and a smaller RMSE than the original model. Considering the whole dataset, the new model predicted Chla with a R 2 of 0.78 with respect to 0.66 for the original model. For Chla ranging from 0.13 to 108.90 μg l −1 , the RMSE for the new model did not exceed 6.64 μg l −1 . In the light of these results, the new model provided better results than the older model. Another restriction with the original three-band model is related to the limits of the wavelength intervals for each spectral band λ 1 , λ 2 and λ 3 with respect to the following assumptions: (1) λ 1 should be located at the maximum phytoplankton absorption; (2) the absorption by detritus and CDOM at λ 2 should be similar to that at λ 1 , while a ph (λ 2 ) a ph (λ 1 ); (3) reflectance at λ 3 should be least affected by differences in absorption while remaining sensitive to the variability in scattering and (4) the total backscattering coefficients for λ 1 , λ 2 and λ 3 , are approximately equal. To meet the above requirements, each wavelength is restricted within certain intervals . By using the spectral reflectance measured over Lake Taihu in the 2004-2010 dataset, it is possible to identify these wavelength limits (figure 1).

Model comparison
In the visible and NIR spectral regions, reflectance was highly variable and similar to typical reflectance spectra collected in turbid waters (Gitelson et al 2006). Absorption by dissolved organic matter and detritus as well as backscattering by particulate matter combines to determine the spectral distribution of reflectance. The reflectance in the 400-500 nm interval was relatively low with respect to that between 500 and 600 nm. Reflectance above 600 nm presented several spectral features: (a) a slight reflectance reduction around 620 nm probably linked to phycocyanin absorption from cyanobacteria (Simis et al 2005); (b) a minimum reflectance around 675 nm likely to be related to chlorophyll-a absorption, although no direct correlation between Chla and R 675 was observed. The peak between 670 and 715 nm observed in most reflectance curves can be associated with high backscattering and minimum absorption by all optically active constituents in this wavelength interval (Gitelson et al 2008). The optimal wavelengths which meet the four assumptions of the original three-band model fall into the following intervals: 650-690 nm for λ 1 , 710-740 nm for λ 2 , and >750 nm for λ 3 .
The optimal positions for each wavelength of the threeband model will depend on the optical properties of the study waters. For example, in Chesapeake Bay, the optimal λ 1 , λ 2 , and λ 3 were found in the intervals between 674-676, 691-698, and 723-739 nm, respectively (Gitelson et  Shitoukoumen Reservoir and Songhua Lake, these intervals were 650-680 nm, 670-700 nm, and >700 nm (Xu et al 2009); in lakes and reservoirs of Nebraska and Iowa, they were 658-674 nm, 700-735 nm, and 733-780 nm (Gitelson et al 2008); in Lake Taihu, they were 660-690, 700-750, and 730-750 nm ; in Lake Chagan, they were 670-710 nm, 660-690 nm, and 710-750 nm (Duan et al 2009a). Therefore, the selection of wavelength intervals for each band depends on a priori knowledge of the optical conditions of the study waters. It is important to note that the selection of wavelength intervals will influence the Chla estimation. For example, using the 2007 Lake Taihu dataset, if different wavelength ranges for λ 1 , λ 2 , and λ 3 are compared, in one case 650-685 nm, 690-730 nm, and 730-780 nm, in the other 650-690 nm, 710-740 nm, and 750-900 nm, the determination coefficient between estimated and measured Chla will vary from 0.82 to 0.86, respectively. In many eutrophic and turbid lakes, the dominance of absorption related to phytoplankton pigments with respect to detritus and CDOM may not occur, negating the second assumption of the original model ( figure 2(A)). Furthermore, in such optical conditions, the difference between [a d (λ 1 ) + a g (λ 1 )] and [a d (λ 2 ) + a g (λ 2 )] may not be zero ( figure 2(B)). Finally, a ph (λ 1 ) may not always be far larger than a ph (λ 2 ), especially when λ 1 is located beyond the peak near 680 nm (figure 2(A)), going against the first assumption. The new three-band model, by including c, does not require such rigid assumptions. It has the further advantage that it does not depend on specific wavelength ranges in the estimation of the three optimal wavelengths. The new model makes fewer rigid assumptions due to the fact that the specific optical properties of the lake are included in the calibration equation. As a results, larger wavelength intervals are possible, λ 1 > 600 nm, λ 2 > 600 nm, λ 3 > 750 nm. This allows for a less subjective selection of wavelengths as well as allowing for better interlake comparison.

Applying the new model to MERIS and GOCI
MERIS was designed mainly for ocean and coastal water remote sensing and therefore has a large number of wavebands specifically selected for ocean color. GOCI provides a very high temporal resolution with a smaller number of wavebands. We investigated the potential use of the new three-band model for both of these remote imagining spectrometers using simulated reflectance data. Field spectra were resampled with respect to their center wavelengths for the MERIS spectral bands (413, 443, 490, 510, 560, 620, 665, 681, 709, 754, 761, 779, 865, 886, 900 nm) and GOCI spectral bands (412, 443, 490, 555, 660, 680, 745, 865 nm). To meet the requirements of the new model, nine bands from 665 to 900 nm were used for MERIS, but only four bands (660, 680, 745, 865 nm) were used for GOCI. The results show that the new threeband model successfully estimates Chla using the MERIS spectral bands with high determination coefficients and low RMSEs. For most datasets, the optimal wavebands selected were 681 nm (λ 1 ), 709 nm (λ 2 ) and 754 nm (λ 3 ) (table 3). Two datasets showed the best results for 865 nm (λ 3 ), but NIR bands beyond 750 nm are rarely used for aircraft and satellite based remote sensing of water . Likewise, the 681 nm band is strongly affected by variation in phytoplankton fluorescence, leading sometimes to difficulties for remote observations. To examine the use of the model for more commonly used wavebands (λ 1 at 665 nm, λ 2 at 709 nm, and λ 3 at 753 nm) a new analysis was made, showing slightly lower determination coefficients (table 4). By comparison, the highest determination coefficients were found for the hyperspectral data, followed by the optimal wavebands and finally by the most common MERIS wavebands (tables 2-4). The GOCI simulated reflectance data provided poorer estimates with respect to the MERIS sensors, even though the results from 2008 to 2010 gave an elevated determination coefficient (table 3). The loss in precision for the GOCI estimates can be associated with the lack of a reflectance waveband at 709 nm (λ 2 ).

Physical significance of ε and τ
The parameters c, ε, and τ in the new model are directly linked to specific inherent optical properties of the study waters, as ε represents , and c is the sum of (a g (λ 1 ) − a g (λ 2 ) + a d (λ 1 ) − a d (λ 2 ) + a w (λ 1 ) − a w (λ 2 )). The comparison between ε estimated from reflectance data with respect to ε determined from the inherent optical properties of Lake Taihu during different measurement campaigns shows a high 1:1 correlation (figure 3(A)). A negative correlation (r = −0.93) for τ ( figure 3(B)) occurs. This is largely due to the lack of in situ absorption data (a g and a d ) at wavelengths greater than 700 nm, where zero absorption  was assumed. As expected, these parameters showed a wide interannual variation (tables 2 and 3).
The original three-band model is parameterized using a linear regression between [R −1 rs (λ 1 ) − R −1 rs (λ 2 )]R rs (λ 3 ) and Chla concentrations, where the slope and intercept are not intended to be related to specific optical properties and provide no information to compare optically different waters. Furthermore, the model assumes that the Chla specific absorption coefficient, a * ph , remains constant, whereas this coefficient will vary in relation to differences in the phytoplankton community and physiological state. In the new three-band model, a * ph is not considered constant and is included in the parameters ε and τ , the latter also including the errors in the absorption coefficients of the major optical constituents of the water body. Making fewer assumptions and linking model parameters to the optical conditions of the water body, the new model responds better to the complex conditions of turbid and eutrophic waters.

Summary
In the present study, a new three-band model was developed to estimate Chla in eutrophic and turbid waters. Unlike the original three-band model, larger waveband intervals can be used (λ 1 > 600 nm, λ 2 > 600 nm, λ 3 > 750 nm). Furthermore, the parameters that result from the fitting procedure, ε and τ , have clear links to the inherent optical properties of the water body. The new model was shown to provide a higher precision than the original threewavelength model for the turbid and eutrophic waters of Lake Taihu. Importantly, it can be used with MERIS data, while its use with the new GOCI data is reduced due to the lack of a waveband at 709 nm. Since the dataset has a broad range of water component concentrations and shows a seasonal and interannual variability, it is very representative for Lake Taihu and other lake ecosystems. The three-wavelength model presented here offers a robust alternative to other Chla estimation approaches currently being used and can be used widely.