An improved analytical algorithm for remote estimation of chlorophyll-a in highly turbid waters

An analytical three-band algorithm for spectrally estimating chlorophyll-a (Chl-a) has been proposed recently and the model does not need to be trained. However, the model did not consider the effects of the absorption due to colored detritus matter (CDM) and backscattering of the water column, resulting in an overestimation when Chl-a < 50 mg m − 3 and an underestimation when Chl-a ≥ 50 mg m − 3. In this letter, an improved three-band algorithm is proposed by integrating both backscattering and CDM absorption coefficients into the model. The results demonstrate that the improved three-band model resulted in more accurate estimation of Chl-a than the previously used three-band model when they were applied to water samples collected from five highly turbid water bodies with Chl-a ranging from 2.54 to 285.8 mg m − 3. The best results, after model modification, were observed in three Indiana reservoirs with R2 = 0.905 and relative root mean square error of 20.7%, respectively.


Introduction
Human activities have resulted in significant negative effects on the water quality of reservoirs, lakes and estuaries (Matthews et al 2010, Simis et al 2007 as indicated by the increasing occurrence of algal blooms, especially toxic cyanobacterial blooms (Matthews et al 2010, Simis et al 2005. Remote sensing techniques have been considered for timely efficient monitoring approach of inland waters (Becker et al 2009, Jupp et al 1994. However, the optical 4 Current address: Scripps Institution of Oceanography, Marine Physical Laboratory, University of California-San Diego, La Jolla, CA 92093-0238, USA. complexity of case 2 waters makes it difficult to spectrally retrieve chlorophyll-a (Chl-a), an index of trophic status of inland waters. This difficulty results from high concentration of non-algal particles (NAP) and colored dissolved organic matter (CDOM) in case 2 water as compared to case 1 waters (Schalles et al 2001, Schalles 2006). Among many empirical or semi-empirical algorithms, three-band algorithms have been widely used for estimation of Chl-a in inland waters because of its capability of accommodating the influence of NAP and CDOM on the estimation. The three-band spectral index shown in equation (1) is expressed as a simple algebra operation of remote sensing reflectance, RS(λ), in three spectral bands (Dall'Olmo et al 2003): RS(λ) includes both below water subsurface remote sensing reflectance r rs (λ) and above water surface remote sensing reflectance R rs (λ), and R rs (λ) = 0.54r rs (λ) (Gons et al 2005). r rs (λ) can be related to the inherent optical properties of inland waters as shown in equation (2) (Gordon et al 1988): where C(λ) is a variable depending on wavelength λ for a given sample location, a(λ) is the sum of the absorption coefficients of phytoplankton pigments, a ph (λ), colored detritus matters (CDM = CDOM + NAP), a cdm (λ), and pure water, a w (λ). While three-band algorithms performed well in many studies (Gitelson et al 2007, 2008, Hunter et al 2010, Yacobi et al 2011, it does require calibration to achieve an accurate prediction of Chl-a when applying to new dataset, which involves with optimization of spectral bands and regression coefficients. Duan et al (2010) recently decomposed the algorithm with detailed bio-optical interpretation, but calibration is still required by linear least square regression or by inputting measured inherent optical properties that are difficult to obtain (Gitelson et al 2007(Gitelson et al , 2008. Gilerson et al (2010) recently proposed a universal form for the three-band algorithm (denoted as G10), which can be directly applied to the medium resolution imaging spectrometer (MERIS) bands centered at 665, 708 and 753 nm. This universal model shown in equation (3) (equation (18) in Gilerson et al (2010)) can be derived by substituting equation (2) into equation (1) (see section 2.2 for details).
The three-band algorithm (equation (3)) performed well with synthetic data set (Gilerson et al 2007) and field data set collected in Fremont State Lakes, Nebraska, USA, 2008 , but resulted in overestimated Chl-a for the samples with Chl-a < 50 mg m −3 and underestimated for the samples with Chl-a 50 mg m −3 (refer to figure 11(b) in Gilerson et al 2010). The reason for overestimated and underestimated Chl-a in Gilerson et al (2010) originates from the assumptions: b b (753) a w (753) and a cdm (665) − a cdm (708) = 0. In fact, these two assumptions may not be valid for highly turbid waters. When waters become more turbid, we assume that errors for estimated Chl-a introduced by the assumptions for b b (753) and a cdm (λ) must be significant and should be taken into count. In this study, we propose to revise the universal three-band algorithm with the aim of minimizing the influences of backscattering and CDM absorption on the Chl-a estimation and improving the performance of the threeband algorithm for retrieving Chl-a from various spectral datasets collected in highly turbid and eutrophic waters.

Data
Field data were collected in Shitoukoumen  Boulder, CO, USA) at each station of Shitoukoumen reservoir and Lake Tai by following NASA protocols (Mueller et al 2003) with radiometer about 2 m above surface. Below water surface spectral reflectance r rs (λ) in three central Indiana reservoirs was measured with Ocean Optics USB4000 (Ocean Optics, Inc., Dunedin, FL, USA) by following the procedures recommended by Gitelson et al (2007) with radiometer dipped about 2-3 cm below surface. Chl-a was extracted using 90% acetone and its concentration was determined with a Shimadzu UV2401 spectrophotometer (Shimadzu, Inc., Tokyo, Japan). Concentrations of total suspended matters (TSM) were measured gravimetrically. Figure 1 shows the in situ measured remote sensing reflectance spectra, and the range and mean for the Chl-a and TSM concentration of the samples collected in the three study regions are shown in table 1.

Method
We propose to expand the three-band index R3 used in equation (3) into (4): With the same assumption used in previous studies, i.e. that b b (665), b b (708) and b b (753) are not significantly different (Duan et al 2010, Gilerson et al 2010, and a ph (708), a cdm (753) and a ph (753) are negligible (Gilerson et al 2010), equation (4) can be simplified as: (5) Meanwhile, a ph (665) has relationship with Chl-a as equation (6) in which the relationship a * ph (665) = 0.022Chl-a p−1 is directly cited from Gilerson et al (2010) with p as a constant.
The difference between ITA and G10 lies in that Gilerson et al (2010) assumed that b b (753) is much less than a w (753) and a cdm (708)−a cdm (665) approaches to 0, thus both variables are negligible in equation (3), but we emphasize that in highly turbid waters both b b (753) and a cdm (708) − a cdm (665) have significant impacts on the estimation of Chl-a.
To apply equation (7) for Chl-a estimation, b b (753) and a cdm (708) − a cdm (665) should be derived. We propose to use the method by Gons et al (2005) to derive b b (753) from r rs (753) (equation (8)) or from R rs (753) (equation (9)). Both equations are derived from equation (2) and based on relationship that a(λ) ≈ a w (753) and assumption that C(753) = 0.082. According to Gons et al (2005) and Simis et al (2005), C(778) = 0.082 is realistic for inland waters, although it is more complicatedly related to several factors, e.g. sun angle, viewing geometry. In this letter, it is assumed that C(753) ≈ C(778) since band 753 nm is closed to band 778 nm. However, more studies on values of C(λ) are required, if possible, in the future.
For turbid waters, it is well known that the absorption of CDM can be modeled by the following equation: Given a cdm (440) and S cdm have typical average values for most of turbid inland waters, i.e. a cdm (440) = 2 m −1 and S cdm = 0.015 nm −1 , a cdm (708) − a cdm (665) is calculated to be 0.0325 m −1 using equation (10). The prediction accuracy of Chl-a is evaluated by the coefficient of determination (R 2 ), relative error, and relative root mean square error (rRMSE) which are defined as: whereX i is the estimated value and X i is the measured value for sample i .

Model comparison
Comparison between measured and estimated Chl-a for Shitoukoumen reservoir, Lake Tai and three Indiana reservoirs is shown in figure 2 and table 2. The proposed ITA performs better than that by G10 (see figure 2 and table 2). It is apparent that ITA results in correlations between measured and estimated Chl-a closer to 1:1 line, higher R 2 and lower rRMSE than those resulting from G10. Our model shows significantly improved estimation of Chl-a for samples collected in both Lake Tai and three Indiana reservoirs. Even for samples from Shitoukoumen reservoir, the improvement of ITA over G10   is evident, i.e. R 2 increases from 0.597 to 0.710 and rRMSE decreases from 43.3% to 41.2%. The advantage of ITA can also be appreciated by examining the relative error, an indicator of bias in estimated Chl-a. Figure 3 shows that G10 results in an overestimation for samples with Chl-a < 50 mg m −3 and underestimation for samples with Chl-a 50 mg m −3 , but this estimation bias was significantly reduced and overall estimation tends to be more closed to ground measurements (figure 3) when the ITA was applied. Figure 4 exhibits that relative errors resulting from ITA distribute nearly normally, while those from G10 have a skew distribution to a positive bias.

Significance of b b (753) and a cdm (λ) for Chl-a estimation
Remote sensing reflectance spectra used in this study have similar shapes to those collected in other turbid productive waters (Duan et al 2010, Gitelson et al 2009, andreferences therein), but they do demonstrate much larger reflectance magnitudes at wavelengths longer than 750 nm than those spectra presented in Gitelson et al (2009). This indicates that the waters examined in this study are highly turbid due to abundant suspended particles that significantly contribute the RS(λ) in the near-infrared region. As shown in table 1, b b (753) can be as high as 5.82 m −1 , more than twice of a w (753), and it is not surprising that ignoring high b b (753) results in large uncertainty in estimated Chl-a as shown in figures 2 and 3.
While a cdm (665) − a cdm (708) has insignificant effect on the estimation of Chl-a when Chl-a concentration is high, failing to accommodate the effect of a cdm (665) − a cdm (708) could lead to dramatic estimation errors when Chl-a is low because a * ph (665) is also relatively small. Our modeling results (not shown here) also indicate that only correcting for the effect of b b (753) is not sufficient for samples with Chl-a 20 mg m −3 . In addition, ITA resulted in large magnitude relative errors (−0.6 ∼ −1) for some samples (Chl-a 20 mg m −3 ) from Shitoukoumen reservoir, which suggests that although a cdm (665) − a cdm (708) = 0.0325 m −1 works well for most samples used in this study, this value may not best suitable for low Chl-a samples from Shitoukoumen reservoir. To further improve the performance of the current threeband model, a robust retrieval model for modeling a cdm (λ) is required. The results for samples from Shitoukoumen reservoir also imply that it is very difficult to accurately estimate Chla in such extremely turbid water bodies, e.g. for waters with TSM up to 211.91 g m −3 . Nonetheless, the current ITA does show high performance and perform better than G10 for all study sites, especially for Lake Tai and three Indiana reservoirs where TSM is relatively low (table 1).

Conclusions
An improved three-band model is proposed and tested with the datasets of water samples collected from two China lakes, Shitoukoumen reservoir and Lake Tai, and three central Indiana reservoirs. Our results demonstrate that the model by G10 can result in significant overestimation for samples with Chl-a < 50 mg m −3 and underestimation for samples with Chl-a 50 mg m −3 . However, the correction for the effects of b b (753) and a cdm (λ) results in an improved threeband model which works well with three data sets collected over five different reservoirs and lakes with Chl-a covering from 2.54 mg m −3 to 285.8 mg m −3 and TSM from 1.51 g m −3 to 211.91 g m −3 , respectively. Therefore, it should be preferred over other three-band algorithms for estimating Chl-a from satellite image spectra such as MERIS data.