Evaluation of chlorophyll-a retrieval algorithms based on MERIS bands for optically varying eutrophic inland lakes

Science of the Total Environment 530–531 (2015) 373–382

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Science of the Total Environment journal homepage: www.elsevier.com/locate/scitotenv

Evaluation of chlorophyll-a retrieval algorithms based on MERIS bands for optically varying eutrophic inland lakes Heng Lyu a,b,⁎, Xiaojun Li c, Yannan Wang a, Qi Jin a, Kai Cao d, Qiao Wang e, Yunmei Li a,b a

Key Laboratory of Virtual Geographic Environment, Ministry of Education, College of Geographic Science, Nanjing Normal University, Nanjing 210023, China Jiangsu Center for Collaborative Innovation in Geographical Information Resource Development and Application, Nanjing 210023, China Chongqing Institute of Surveying and Planning for Land Resources and Housing, Chongqing 400020, China d National University of Singapore, Department of Geography, Singapore 117570, Singapore e Satellite Environment Application Center, Ministry of Environmental Protection, Beijing 100029, China b c

H I G H L I G H T S • • • • •

Inland waters can be classified automatically into three types based on spectrum. We evaluated four algorithms for three water types based on MERIS bands. For two water types, the three-band algorithm had the best performance. The four-band algorithm had the highest retrieval accuracy for one water type. The three-band algorithm is preferable to the two-band algorithm for inland waters.

a r t i c l e

i n f o

Article history: Received 28 January 2015 Received in revised form 9 May 2015 Accepted 25 May 2015 Available online xxxx Editor: D. Barcelo Keywords: Chlorophyll-a concentration Retrieval algorithms MERIS bands Optical clustering Accuracy evaluation

a b s t r a c t Fourteen field campaigns were conducted in five inland lakes during different seasons between 2006 and 2013, and a total of 398 water samples with varying optical characteristics were collected. The characteristics were analyzed based on remote sensing reflectance, and an automatic cluster two-step method was applied for water classification. The inland waters could be clustered into three types, which we labeled water types I, II and III. From water types I to III, the effect of the phytoplankton on the optical characteristics gradually decreased. Four chlorophyll-a retrieval algorithms for Case II water, a two-band, three-band, four-band and SCI (Synthetic Chlorophyll Index) algorithm were evaluated for three water types based on the MERIS bands. Different MERIS bands were used for the three water types in each of the four algorithms. The four algorithms had different levels of retrieval accuracy for each water type, and no single algorithm could be successfully applied to all water types. For water types I and III, the three-band algorithm performed the best, while the four-band algorithm had the highest retrieval accuracy for water type II. However, the three-band algorithm is preferable to the two-band algorithm for turbid eutrophic inland waters. The SCI algorithm is recommended for highly turbid water with a higher concentration of total suspended solids. Our research indicates that the chlorophyll-a concentration retrieval by remote sensing for optically contrasted inland water requires a specific algorithm that is based on the optical characteristics of inland water bodies to obtain higher estimation accuracy. © 2015 Elsevier B.V. All rights reserved.

1. Introduction Chlorophyll-a (Chl-a), a photosynthetically active pigment in water, can be used to determine the water quality, biophysical status and eutrophication level of a body of water (Falkowski et al., 2000; Gons et al., 2008; Honeywill et al., 2002; Schalles et al., 1998; Simisa et al., 2007). With varying the optical properties, remote sensing is an effective and essential method for monitoring its spatial and temporal ⁎ Corresponding author. E-mail address: [email protected] (H. Lyu).

http://dx.doi.org/10.1016/j.scitotenv.2015.05.115 0048-9697/© 2015 Elsevier B.V. All rights reserved.

variations in water. In the open ocean, algorithms using reflectance in the blue and green regions have been successfully applied to estimate the Chl-a concentration (Carder et al., 2004; Darecki et al., 2005; Hu et al., 2012; O'Reilly et al., 1998). Algorithms for regularly monitoring Chl-a using satellite ocean color sensor data (e.g., the Sea-viewing Wide Field-of-view Sensor [SeaWiFS], Moderate Resolution Imaging Spectroradiometer [MODIS] and Medium Resolution Imaging Spectrometer [MERIS]) are also well-established (Dasgupta et al., 2009; IOCCG, 2006). However, these algorithms do not work well in turbid trophic waters because of the absorption of chromophoric dissolved organic matter (CDOM) and total suspended solids (TSS) (Cannizzaro and

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Carder, 2006; IOOCG, 2000). A variety of algorithms has been developed for Case II waters and has yielded relatively satisfactory Chl-a estimations in regional waters. A band ratio using reflectance in the red and the near-infrared spectral regions, instead of in the blue and green regions, has been proposed to estimate the Chl-a concentration in coastal and inland waters. The ratio was successfully used to estimate the Chl-a concentration when Chl-a was above 3 to 5 mg/m3, and the reflectance peak approximately 700 nm is quite pronounced (Dall'Olmo and Gitelson, 2005; Dekker, 1993; Gitelson et al., 2008; Jiao et al., 2006; Pierson and Strömbeck, 2000; Pulliainen et al., 2001; Ruddick et al., 2001; Stumpf and Tyler, 1988). This type of algorithm can partially remove the atmospheric effect and diminish the disturbance caused by the rough water that results from the wave, increasing the estimation accuracy. Dall'Olmo et al. (2003) and Gitelson et al. (2008) developed a semi-analytical Chl-a retrieval algorithm based on a bio-optical theory for eutrophic inland turbid waters, which established the relationship between the Chl-a concentration and the reflectance of three bands. This algorithm weakened the impact of the CDOM and inorganic suspended matter and yielded the best results for reserving the optical information of Chl-a. The algorithm has been successfully used in different lakes and reservoirs with different optical characteristics (Gitelson et al., 2009; Moses et al., 2009; Zimba and Gitelson, 2006). However, for a three-band algorithm, certain assumptions might be violated in turbid waters. For example, the absorption of Chl-a at a near-infrared region was far from zero. Furthermore, it is not fully correct to assume that the absorption of water is much greater than backscattering for highly turbid waters. Le et al. (2009) proposed a four-band, semi-analytical model for estimating Chl-a in highly turbid lakes based on the threeband algorithm, which added another near-infrared band for diminishing the effect of absorption of pure water and inorganic particles. Shen et al. (2010) built a synthetic chlorophyll index (SCI) to weaken the interference from the scattering of total suspended matter for highly turbid water, which was derived from the reflectance shape of Chl-a and inorganic particles. The SCI algorithm was successfully applied in the Changjiang (Yangtze) Estuary using MERIS bands at 560, 620, 665 and 681 nm. Gurlin et al. (2011) calibrated three NIR-red models using the in-site data with Chl-a concentrations ranging from 0 to 100 mg m−3 and recommended that the simple two-band NIR-red algorithm was suited for estimating Chl-a. The results from an evaluation of Chl-a estimation algorithms using on-site data from Lake Kinneret indicated that MERISbased NIR-red algorithms are suitable for a low-to-moderate Chl-a concentration; however, their universal applicability for inland and coastal waters has yet to be validated globally (Yacobi et al., 2011). Le et al. (2013) tested Chl-a algorithms for a CDOM-dominated estuary and found that the two-band algorithm performed the best. However, the optical characteristics of trophic inland waters were more complicated than in the open ocean. Furthermore, the optical features of inland waters vary in different regions because the ecological environment varies. Additionally, the optical features of one body of water often vary with time because water constituents in different seasons change markedly (Le et al., 2011; Shi et al., 2013). This finding explains why some algorithms can yield accurate estimations of Chl-a in specific local inland waters. Several algorithms were built based on the on-site data from specific waters, and the application criteria were not clearly identified (Le et al., 2013), making it unclear whether the results reported by Gurlin, Yacobi and Le can be applied to eutrophic inland waters or whether there might be a single algorithm that can reliably be used for turbid inland waters with varying optical features. Furthermore, for optically complex water, optical classification was suggested for estimating water constituents (Lubac and Loisel, 2007). Moore et al. (2001) developed a fuzzy logic classification scheme to the satellite-derived water leaving radiance data, and class-specific algorithms were applied to each pixel. Feng et al. (2005) adopted an unsupervised classification to classify the hyper-spectral space of reflectance collected at 45 stations near Tokyo Bay between 1982 and 1984,

leading to three spectrally distinct optical water types. The model accuracy of classified waters in the forward direction was significantly improved over that of non-classified waters, but no significant improvement was achieved in the retrieval accuracy (inverse direction). An unsupervised hierarchical cluster analysis that is applied to the Rrs spectra collected in the eastern English Channel and southern North Sea results in five spectrally distinct classes (Lubac and Loisel, 2007). Cannizzaro and Carder (2006) classified data collected from the west Florida shelf and Bahamian waters as optically shallow, optically deep, or transitional based on criteria developed from Rrs data at only three wavebands (412, 555, and 670 nm). Le et al. (2011) used reflectance at three bands, Rrs(Green), Rrs(650) and Rrs(NIR), to classify the water types, resulting in three classes. Based on the observation of the spectral shapes of data sets, Li et al. (2012) applied the decision tree comparing the Rrs spectra of MERIS bands to classify the inland water, and four water types were finally obtained. Shi et al. (2013) adopted an unsupervised classification technique to cluster optically inland lakes; then, the optical criteria were defined by comparing the in situ Rrs spectra of the MERIS bands of each water type. However, which algorithm should we select for mapping large regional Chl-a concentrations while including all types of lakes that are located in different environments? Which algorithm should we select for mapping the long-term Chl-a concentration in a lake with varying optical features? This study evaluates the performance of retrieval algorithms for Chl-a concentrations based on MERIS spectral bands in an optically contrasted aquatic environment that is characterized by a wide range of Chl-a concentrations that are typical of mesotrophic to eutrophic inland waters. In this paper, we (1) propose a classification method for trophic inland waters based on optical characteristics using statistical technology, (2) complete an assessment of four Chl-a retrieval algorithms applied in different optical classes of water and (3) recommend an optimal Chl-a retrieval algorithm for each water class with specific optical characteristics. 2. Data and methods The data used in this study were collected in different seasons in five lakes (Dongting Lake, Taihu Lake, Chaohu Lake, Dianchi Lake and the Three Gorges Reservoir) located in different basins in China. Dongting Lake, the second largest freshwater lake in China, is located at 28°40′– 29°50′N and 11°50′–113°10′E, in the middle reaches of the Yangtze River Basin, which connects to the Yangtze River through four rivers and can regulate its water levels. Dongting Lake has the notable feature that it can expand to 2691 km2 during the annual flood season and shrink to 709.9 km2 in the annual dry season (Huang, 1999). Taihu Lake is located at 30°55′–31°33′N, 119°51′–120°36′E in the lower reaches of the Yangtze River Basin and it is the third largest freshwater lake in China, with an area of approximately 2238 km2 and a mean depth of 1.9 m. Chaohu Lake, one of the five largest freshwater lakes in China, is located at 30°25′–31°43′N, 117°16′–117°51′E. It is a typical large eutrophic lake that covers an area of 780 km2 and has a mean water depth of 2.69 m. Dianchi Lake is a typical plateau lake at an altitude of 1886 m. It is the sixth largest freshwater lake in China, with an area of 306 km2 and a mean depth of 2.9 m, and it is located in the upper-middle reaches of the Yangtze River Basin, with a geographic location of 24°40′–25°02′N, 102°36′–102°47′E. A manmade lake, Three Gorges Reservoir, has an area of 1084 km2 and is located in the upper reaches of the Yangtze River, with a reservoir capacity of up to 393 million m3 and a normal storage level of 175 m. Detailed information on the field sampling campaigns is listed in Table 1. The location of the five lakes is shown in Fig. 1. Each field campaign was conducted independently, and the location of sampling sites of each field campaign for the same lake was different. A large data set was collected for the five lakes, yielding data from different geographic locations with varying ecological environments and from one lake that contained highly variable bio-physical and bio-optical features in different seasons.

H. Lyu et al. / Science of the Total Environment 530–531 (2015) 373–382 Table 1 The detailed information for 14 sampling campaigns. Sampling date

Sampling lake

Sites

August 2006 November 2006 November 2008 April 2009 June 2009 August 2009 September 2009 December 2009 May 2010 August 2010 August 2011 October 2012 May 2013 August 2013

Taihu Lake Taihu Lake Taihu Lake Taihu Lake Chaohu Lake Three Gores Reservoir Dianchi Lake Dianchi Lake Taihu Lake Taihu Lake Taihu Lake Taihu Lake Taihu Lake Dongting Lake

8 32 54 48 19 21 16 7 28 33 29 24 30 49

Therefore, these data are ideal for studying optical classifications of water and evaluating the Chl-a retrieval algorithms for turbid waters. 2.1. Field measurements Remote sensing reflectance was measured at each site with an ASD FieldSpec Pro using the above-water measurement method protocol (Mueller et al., 2003). The viewing geometry with an azimuth of 135° and zenith of 40°, as recommended by Mobley (1999), was adopted to avoid water surface reflection from direct sun. Surface water was collected at a depth of 0.5 m below the surface and stored in a dark, cool container for subsequent filtration. The water samples were used for laboratory analysis of the Chl-a concentrations; total suspended solids;

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inorganic suspended solids and the absorption of total particulates, non-algal particulates, phytoplankton and CDOM. At every site, the radiance of water-viewing (Lt), radiance of skyviewing (Lsky) and radiance reflected by a standard gray board (Lp) were measured, and such measurements were repeated ten times. The spectral remote sensing reflectance was calculated as in Eq. (1).

 Rrs ðλÞ ¼ ρp Lt ðλÞ−rLsky ðλÞ = πLp

ð1Þ

where, ρp is the reflectance of the gray board and r is the air–water interface reflectance with a value of 0.022 (Mobley, 1999; Tang et al., 2004). 2.2. Laboratory measurements The chlorophyll-a concentration was extracted in 90% hot ethanol at 80 °C (Parsons et al., 1984). The resulting extract was acidified with 1% dilute hydrochloric acid, and the absorbance at wavelengths of 665 and 750 nm was measured through a UV2550 spectrophotometer. The Chl-a concentration was calculated using absorbance at 665 nm and 750 nm (Chen et al., 2006; Lorenzen, 1964). The concentration of total suspended solids (TSS) and inorganic suspended solids (ISS) was determined using Standard Methods (American Public Health Association, 1998). The absorption coefficients of the total suspended solids, phytoplankton and non-algal particulates were measured with the quantitative filter technique (QFT) (Mitchell, 1990; Mitchell et al., 2000). Measurements of the optical density (OD) of the total particles retained on the filters were made shortly after the filtration of water samples using Whatman GF/F glass fiber filters with a 47-mm diameter by the

Fig. 1. The locations of five lakes and their sampling sites in China.

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SHIMADZU UV-2550 Spectrophotometer. The signal from a reference filter was also measured. The absorption of total suspended solids (ap) was calculated using the following Eq. (2):

where Chl-ameasured and Chl-aretrieved are the measured and retrieved Chl-a concentrations, respectively. 3. Results and discussion

s ap ¼ 2:303   ODs ðλÞ v

ð2Þ

where ODs(λ) is the adjusted OD of TSS, v is the volume of water samples, and s is the effective area of TSS on the filter. The effects of the absorption by algae pigments were removed after soaking for approximately 15 min in 90% sodium hypochlorite solution; then, the spectral absorption of non-algae particulates ad(λ) was measured by SHIMADZU UV-2550 again. The absorption of algae particulates aph(λ) was calculated using the absorption of TSS minus the absorption of non-algae particulates in Eq. (3): aph ðλÞ ¼ ap ðλÞ−ad ðλÞ:

ð3Þ

The absorption of Chromophoric Dissolved Organic Matter (CDOM) was obtained by measuring the OD of filtrate after two filtrations. Water samples were first filtered with a GF/F filter; then, the filtrate was filtered again using Millipore filters with a pore size of 0.22 μm. The absorption of CDOM was calculated using Eqs. (4) and (5) (Bricaud et al., 1981).

aCDOM ðλÞ0 ¼ 2:303ODðλÞ=r

ð4Þ

aCDOM ðλÞ ¼ aCDOM ðλÞ0 −aCDOM ð750Þ0 λ=750

ð5Þ

where OD(λ) is the OD at wavelength λ, r is the optical path (unit: m), aCDOM(λ)′ is the unadjusted absorption of CDOM at wavelength λ, and aCDOM(λ)′ is the absorption of CDOM at wavelength λ (unit: m−1). 2.3. Classification method for eutrophic water based on remote sensing reflectance An automatic cluster method, called a two-step clustering method (SPSS, 2001, 2004), was adopted. This method can be applied to either continuous or discrete variables. Furthermore, the cluster numbers can be automatically suggested based on certain statistical criteria. This automatic clustering method was completed using SPSS software for Version 11.5 or later. Either Akaike Information Criterion (AIC) (Akaike, 1973) or Bayesian Criterion (BIC) (Schwarz, 1978) was used to automatically determine the optimal number of clusters. For maintaining spectral shape information, each remote sensing reflectance was first normalized by its integral and computed over the entire spectrum before classification (Lubac and Loisel, 2007). In this clustering, BIC was selected as the criterion for determining the number of classes, and the clustering procedure was completed in SPSS V20.

3.1. Optical features of different water types Waters in all measurement sites were automatically clustered into three types based on their remote sensing reflectance. Type II had the largest number of spectra (201). Thirty-nine spectra belonged to type I, while type III had 158 spectra. The water quality and some optical parameters of the three water types are listed in Table 2. Their remote sensing reflectance is shown in Fig. 2. Table 2 shows that the average Chl-a concentration and aph(675) of type I were the highest among the three water types, and the TSS concentration and ratio of Chla:TSS were the highest. The marked reflectance peaks at 700 nm and the reflectance valley at 675 nm, which were due to the strong absorption at 675 nm and strong reflection at 700 nm of Chl-a, can be clearly observed in the water type I reflectance spectrum (Fig. 2). This indicates that the optical characteristics of type I were dominated by phytoplankton. However, for water type III, the average Chl-a concentration and aph(675) were far lower than for type I, and it was the lowest among the three water types. Furthermore, the ratio of Chl-a:TSS was the smallest. The peak at 700 nm and the valley at 67 5 nm were hardly recognized for the water type III reflectance spectrum. The optical characteristics of type III thus were primarily influenced by inorganic suspended matter. From Table 2, it can be observed that the water quality parameters of water type II were in a range between type I and type III. The reflectance valleys or peaks of water type II at 560 nm, 670 nm, and 700 nm were less clear than for water type I. The optical characteristics of water type II indicated the combined characteristics of water types I and III, demonstrating that the reflectance of water type II was influenced by both the Chl-a and inorganic suspended matter. 3.2. Calibration of four algorithms The four models were calibrated for the spectral bands of the MERIS satellite sensor. The coefficients and band combinations that were used in the models were then recalibrated using the validation dataset that we collected. All data were lumped and then classified into three

Table 2 Descriptive statistics of the water quality and optical parameters of the three water types. Water type

Water quality and optical parameters

Max.

Min.

Mean

Median

S.D.

Type I

aph(675) (m−1) ad(440) (m−1) aCDOM(440) (m−1) Chl-a (μg/L) TSS (mg/L) ISS (mg/L) Chl-a:TSS (*1000) aph(675) (m−1) ad(440) (m−1) aCDOM(440) (m−1) Chl-a (μg/L) TSS (mg/L) ISS (mg/L) Chl-a:TSS (*1000) aph(675) (m−1) ad(440) (m−1) aCDOM(440) (m−1) Chl-a (μg/L) TSS (mg/L) ISS (mg/L) Chl-a:TSS (*1000)

7.64 18.54 1.83 156.70 253 226 4.77 8.83 14.43 1.81 103.40 183.27 166.07 8.18 5.22 7.98 1.24 62.87 83.53 69.50 4.53

0.01 0.01 0.05 0.08 17.1 0.00 0 0.01 0.16 0.01 0.04 6.27 0.2 0 0.01 0.01 0.00 1.25 3.4 0.01 0.02

1.50 3.09 0.77 64.84 72.31 47.29 1.55 0.97 2.34 0.46 28.31 57.15 44.96 0.81 0.43 1.03 0.37 11.23 27.40 20.62 0.59

1.20 2.48 0.67 58.42 46.4 18.93 1.42 0.61 1.62 0.43 23.66 48.00 36.33 0.45 0.28 0.65 0.38 8.02 26 18.86 0.36

1.40 3.28 0.51 49.16 67.01 66.40 1.28 1.19 2.43 0.41 23.08 33.58 33 1.04 0.66 1.24 0.23 9.13 15.35 13.83 0.67

2.4. Accuracy assessment method for Chl-a retrieval algorithms To assess the performance of Chl-a retrieval algorithms, the root mean square error (RMSE), defined by Eq. (6), and the mean absolute percentage error (MAPE), defined by Eq. (7), were adopted.

RMSE ¼

MAPE ¼

vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi uX n
2 u u Chl‐ameasured;i −Chl‐aretrieved;i t i¼1

n  n  X  Chl‐ameasured;i −Chl‐aretrieved;i    Chl‐a i¼1

measured;i

n

 100%

Type II

Type III

ð6Þ

ð7Þ

S.D.: standard deviation.

H. Lyu et al. / Science of the Total Environment 530–531 (2015) 373–382

377

Fig. 2. (a) Reflectance spectra of type I; (b) reflectance spectra of type II; (c) reflectance spectra of type III; and (d) average reflectance spectra of three types. (Red rectangles indicate the MERIS band location.) (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

types. In each water type, the sites were sorted in ascending order based on the Chl-a concentration; then, one site was left out for testing the algorithm for every two sites. As a result, the data were subdivided into two parts for each water type. Note that the remote sensing reflectance in the MERIS bands we used were extracted from hyper-spectral reflectance acquired through ASD FieldSpec Pro, which was chosen for its ability to ignore the effect of atmospheric correction errors and obtain more synchronous validation data. The optimal band determination was completed using the band iteration and correlation optimization. At first, we predetermined λ2 = 709 nm and λ3 = 754 nm; next, we iterated the λ1 band locations. The optimal λ1 band corresponded to a maximum R2 between the [1/Rrs(λ1) − 1/Rrs (709)]*Rrs(754) predicted Chl-a and measured Chl-a. After the λ1 location was determined, we still predetermined λ3 = 754 nm and then obtained an optimal λ2 location based on λ1 and λ3 using the iteration method. Finally, λ3 was iterated based on the λ1 and λ2 locations. For the 4-band approaches, the wavelength positions were determined in the same way in an iterative manner. The four calibrated algorithms are listed in Table 3. Table 3 shows the different bands used in the three-band algorithms for different water types; the 7, 9 and 12 bands were selected for water types I and III, while the 7, 9 and 10 bands were applied to water type II. However, the 7, 9 and 13 bands were used for type I, while the 8, 9 and 10 bands were employed for water types II and III for the four-band algorithm.

3.3. Accuracy assessment of four algorithms for different water types MAPE and RMSE were calculated using Eqs. (6) and (7) for four algorithms applied to different water types, shown in Table 4. Table 4 shows that for water type I, the performance of the three-band algorithm was much better than the other three algorithms; the three-band algorithm had the lowest MAPE and RMSE. The retrieval accuracy of the two-band algorithm was acceptable, which had a relatively lower MAPE and RMSE. At the same time, the four-band and SCI algorithms do not work well for water type I. However, the four-band algorithm has the lowest MAPE among the four models when applied to water type II, and the three-band algorithm also performs well with a relatively low MAPE and the lowest RMSE. The two-band and SCI algorithms have poor estimation accuracy for water type II. By comparing the MAPE and RMSE of the four algorithms for water type III, the three-band algorithm has the best estimation accuracy, the two-band algorithm performs second best, and the four-band and SCI algorithms perform similarly. The measured and estimated Chl-a concentration using four algorithms are plotted in Fig. 3. As seen in Fig. 3(a), the four-band algorithm and SCI perform poorly, especially for higher Chl-a concentration sites. Their MAPE values for sites with a Chl-a concentration greater than 80 μg/L were 54.6% and 76.8%, respectively, which has an important impact on the overall estimation accuracy. The MAPEs for two-band, three-band, four-band and

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Table 3 The four calibrated algorithms for different water types. Algorithms

Type I

Two-band

Type II

Type III

Variable X

Equation

Variable X

Equation

Variable X

Equation

R709/R665

Chla = −80.11X2 + 364.1X − 265.72

R709/R665

Chla = −68.37X2 + 279.2X − 184.38

R709/R665

Chla = 242.31X2 − 344.71X + 127.29

Regression coefficient R2 = 0.86 Three-band [1/R665 − 1/R709]*R779

Chla = −151.94X2 + 331.72X + 16.55

Regression coefficient R2 = 0.89 Chla = 319.99X2 + Four-band [1/R665 − 1/R709]/ [1/R865 − 1/R709] 134.1X + 20.02 Regression coefficient R2 = 0.74 SCI Chla = 4031.30X + 12.95

R2 = 0.86 [1/R665 − 1/R709]*R754 R2 = 0.89 [1/R681 − 1/R709]/ [1/R754 − 1/R709] R2 = 0.88 Chla = 55297X2 + 2391X + 16.70 X = 1.2336 M8-0.7377 M6 − M7 + 0.5041 M5 R2 = 0.83

Regression coefficient R2 = 0.64

Chla = −177.45X2 + 287.95X + 26.26 Chla = −42.549X2 + 118.54X + 20.27

R2 = 0.83 [1/R665 − 1/R709]*R779 Chla = 1445.4X2 + 351.77X + 25.32 R2 = 0.84 Chla = 121.04X2 + [1/R681 − 1/R709]/ [1/R754 − 1/R709] 104.2X + 16.36 R2 = 0.79 Chla = 148831X2 + 1866X + 9.12

R2 = 0.63

Chla: The concentration of chlorophyll-a.

SCI algorithms for all water type II sites with a Chl-a concentration less than 20 μg/L were 86.1%, 65.9%, 47.8% and 78.1%, respectively, indicating that the four-band algorithm has the highest level of estimation accuracy, while the two-band algorithm, with the highest MAPE, loses its prediction capacity at lower Chl-a concentrations. The estimation accuracy of the SCI algorithm applied to water type III is significantly improved compared with the two other water types, although the RMSE of the SCI are the highest among the four algorithms and the MAPE is only slightly lower than four-band algorithm. This is because the SCI algorithm was exclusively developed for estuary water with high total suspended-solid concentrations. In addition, the optical characteristics of water type III were primarily affected by the inorganic suspended matter; as a result, the SCI performed better in water type III than in water types I and II. In general, in water types I and III, the three-band algorithms perform best among the four algorithms, and the two-band algorithms also have relatively low MAPE and RMSE. However, in water type II, four-band algorithms have the highest estimation accuracy, while two-band algorithms have the weakest estimation ability. Therefore, three-band and four-band algorithms are recommended for optically contrasted trophic inland waters. Gurlin et al. (2011) and Le et al. (2013) note that the two-band algorithm is recommended for remote estimation of Chl-a concentration in Case II waters. Based on our results, however, the two-band algorithm was not suitable for all inland trophic waters, particularly when the water had optical characteristics dominated by both Chl-a and inorganic suspended matter. 3.4. Applicability of the four algorithms for different water types 3.4.1. Two-band algorithm using NIR-red bands The two-band algorithm using an NIR-red band was specifically developed for inland and coastal waters, but there are two requirements for its application. First, the absorption of the red band is primarily caused by phytoplankton and the absorption of inorganic suspended matter and CDOM can be negligible. Second, the absorption at the NIR band is primarily attributed to pure water, and the absorption of

Table 4 The MAPE and RMSE of four algorithms for three water types. Algorithms

Two-band Three-band Four-band SCI

Type I

Type II

Type III

MAPE

RMSE(μg/L)

MAPE

RMSE(μg/L)

MAPE

RMSE(μg/L)

29.8% 24.5% 42.1% 55.7%

17.87 15.67 24.23 28.46

47.3% 38.4% 31.3% 45.5%

8.48 7.60 7.88 9.52

35.1% 32.5% 39.1% 38.1%

3.40 3.21 4.03 4.89

Bold entries indicates the best performance.

phytoplankton, total suspended solids and CDOM was negligible compared to the absorption of pure water (Dall′Olmo and Gitelson, 2005; Dall'Olmo et al., 2003; Dekker, 1993; Gitelson, 1992; Gons, 1999; Gons et al., 2008; Ruddick et al., 2001). The absorption spectra of pure water (aw), phytoplankton (aph), non-algal particulates (ad) and CDOM (aCDOM) were thus analyzed and are presented in Fig. 4, which shows that the ad is so high it cannot be neglected. For water types II and III, the absorption of non-algal particulates at wavelength 650 nm is particularly comparable to the absorption of phytoplankton. However, for water type I, because the aph is markedly higher than ad, the effect of ad is minimal. The absorption of CDOM for the three water types was also so minimal that it does not need to be considered. Based on this analysis, water type I meets the first requirement of the two-band algorithm and water types II and III are not eligible. At the same time, although the absorption of pure water at the NIR band (wavelength 709 nm) is the highest, with a value of 0.79 among all water constituents, the absorption of water constituents for water types I and II needs to be considered because of their relatively high total absorption of 0.56. The total absorption coefficient of water constituents at 709 nm is 0.28 for water type III. Compared to pure water absorption, the absorption at this band was primarily due to pure water. As a result, water type III is close to meeting the second set of requirements of the two-band algorithm. Table 5 shows the general eligibility status of the three water types in meeting the requirements of the two-band algorithm. It can be observed in Table 5 that water type I meets the first requirement and water type III partially meets the second requirement; therefore, the two-band algorithm performs relatively well for water types I and III, and it has the relatively lower MAPEs of 29.8% and 35.1%, respectively. However, water type II did not satisfy either requirement, indicating that it has the worst fit for the two-band algorithm. 3.4.2. Three-band algorithm Dall'Olmo and Gitelson (2005) and Dall'Olmo et al. (2003) developed the three-band algorithm specifically for turbid productive waters. The application of this algorithm is based on two fundamental assumptions. First, the absorption of CDOM and non-algal particulates at the first band (λ1) are close to the second band (λ2). Here, λ1 and λ2 are at 665 nm and 709 nm for all three water types. Second, the remote sensing reflectance at the third band (λ3) is minimally sensitive to absorption by constituents in the water and the total absorption is approximately equal to the absorption by pure water. The third band is at 779 nm for water types I and III and 754 nm for water type II. Fig. 4 shows that the absorptions of CDOM at 665 nm and 709 nm were minimal and the variation in the absorption at these two bands cannot be distinguished. The absorption of non-algae particulates at 665 nm is close to the value at 709 nm for all three water types, but the difference

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Fig. 3. (a)/(b)/(c) The scatter plot of the measured Chl-a concentration versus retrieved Chl-a concentration using four algorithms for water types I, II and III. The dotted lines with different colors indicate trendlines for each algorithm. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

between the two bands of water type II is the greatest because the slope of the type II ad spectrum is steeper than for the other two water types. As a result, we can infer that water types I and III both partially meet the first requirement of the three-band algorithm, while water type II does not meet the requirement. With respect to the second requirement, for water types I and III, the third band is at 779 nm, where the absorption of non-algal particulates, phytoplankton and CDOM were minimal compared to pure water absorption (2.7101 m−1, not shown in Fig. 4). The ratios of the water constituent absorption to pure water absorption for water types I and III were 6.4% and 3.4%, respectively. However, for water type II, the third band was at 754 nm, where the absorption of pure water was 2.8666 m− 1, and the ratio of the total absorption of

Table 5 The eligibility status of three water types for the requirements of the two-band algorithm.

Fig. 4. The average absorption of inorganic suspended matter, phytoplankton and CDOM of three water types in a wavelength range of between 650 nm and 800 nm. ad is the absorption of non-algal particulates, aph is the absorption of phytoplankton, aCDOM is the absorption of colored dissolved organic matter and aw is the absorption of pure water (Pope and Fry, 1997).

Water type

The total absorption at λ1 is dominated by phytoplankton absorption

The total absorption at λ2 is dominated by pure water absorption

MAPE

Type I Type II Type III

+ − −

− − +−

29.8% 47.3% 35.1%

+: indicates that they meet the requirement. −: indicates that they violate the requirement; +−: indicates that they partially meet the requirement.

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water constituents to pure water was 9.1%. Therefore, water type III adequately meets the second requirement. The general eligibility statuses of the three water types in meeting the requirements of the three-band algorithm are listed in Table 6. Because water type II did not satisfy the second requirement, the three-band algorithm had the worst estimation performance for water type II. However, because water types I and III met both requirements, the three-band algorithm performed notably well for them. Specifically, for water types I and III, the three-band algorithm has the highest estimation accuracy among the four Chl-a estimation algorithms. 3.4.3. Four-band algorithm Le et al. (2009) developed the four-band algorithm based on the three-band algorithm, and a fourth band at the NIR region is added to decrease the effect of pure water and non-algal particulates on Chl-a estimations. In Table 4, we can clearly see that the four-band algorithm performed the best of the four algorithms for water type II. For water type I, the bands at 665 nm, 709 nm and 865 nm were used, while the bands at 681 nm, 709 nm and 754 nm were applied for water types II and III in the four-band algorithm. However, the use of the four-band algorithm also has the requirement that the absorption of CDOM and non-algae particulates at the first band (λ1) are near those at the second band (λ2). From Fig. 4, it can be observed that, for all water types, the variation in the absorption coefficients for CDOM after 665 nm was minimal; however, for water type I, the absorption of non-algae particulates at 665 nm was close to the value at 709 nm. As a result, water type I partially meets this requirement. At the same time, for water types II and III, the absorption coefficient of non-algae particulates at 681 nm was near the coefficient at 709 nm. Thus, water types II and III partially satisfy this requirement. Another requirement is that the absorption of CDOM and non-algae particulates at the third band (λ3) is also close to the absorption at the fourth band (λ4). From the absorption spectral trend of nonalgae particulates for water type I, shown in Fig. 4, it can be observed that the ad(865) (not shown in Fig. 4) was smaller than at 800 nm. This absorption spectrum indicates that the ad(800) is significantly lower than at 700 nm. As a result, the ad(865) is clearly smaller than at 709 nm. Therefore, water type I did not satisfy the second requirement. Based on the non-algae particulate absorption spectrum for water types II and III, we can see that the difference between 754 nm and 709 nm was small and that water types II and III partially meet the second requirement. Based on Table 7, water types II and III both partially meet the two requirements, but the MAPE of water type III is relatively high, which is possibly because the average Chl-a concentration for this water type is lower. Water type I cannot fully meet the two requirements, resulting in the highest MAPE. The four-band algorithm had the best retrieval performance for water type II. 3.4.4. SCI algorithm Shen et al. (2010) developed SCI algorithm exclusively for the estuaries with very high TSS concentrations that do not require a recalibration of the band location. Table 4 shows that the SCI algorithm had poor performance for all three water types. This may be because the TSS concentration in inland lakes was not sufficiently high compared with the Table 6 The eligibility status of three water types for the requirements of the three-band algorithm. Water type

CDOM and detrital absorption at λ2 are close to λ1

Rrs(λ3) is minimally sensitive to absorption by constituents in the water

MAPE

Type I Type II Type III

+− − +−

+ − +

24.5% 38.4% 32.5%

+: indicates that they meet the requirement.−: indicates that they violate the requirement; +−: indicates that they partially meet the requirement.

Table 7 The eligibility status of three water types for the requirements of the four-band algorithm. Water type

CDOM and detrital absorption at λ2 are close to λ1

CDOM and detrital absorption at λ3 are close to λ4

MAPE

Type I Type II Type III

+− +− +−

− +− +−

42.1% 31.3% 39.1%

+: indicates that they meet the requirement. −: indicates that they violate the requirement; +−: indicates that they partially meet the requirement.

estuary. However, from water types I to III, as the effect of non-algal particulates on the optical characteristics of the water became increasingly evident, the MAPE of the SCI algorithm gradually decreased. This also confirms that the SCI algorithm is a good fit for highly turbid water. 3.5. The determination method of the water type based on the MERIS image In Fig. 2(d), it can be observed that the reflectance spectrum shape of water type I is clearly different from water types II and III. Although the reflectance spectrum shape of water type II is similar to water type III, there is a marked spectral distance between the two water types. Therefore, in this research, the two parameters of Spectral Angle Mapper (SAM) (Kruse et al. 1993) and Euclidean Distance (ED) were both applied to determine the pixel class based on reflectance at MERIS 15 bands. SAM is used to discriminate a pixel from others that have distinct spectral shapes. However, it does not work for differentiating water types II and III because of their similar spectral shapes. As a result, a comprehensive parameter, G (An et al., 2005; Lyu et al., 2015), which combines the SAM and Euclidean Distance, was adopted to determine the water type of MERIS image pixels, as given in Eq. (8): 1 0 n X vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi xi yi u n C B uX C B i¼1 C s ffiffiffiffiffiffiffiffiffiffiffiffi ffi s ffiffiffiffiffiffiffiffiffiffiffiffi ffi 1− ðxi −yi Þ2 B G¼t C B n n X X A @ i¼1 x2i y2i i¼1

ð8Þ

i¼1

where xi is the reflectance spectrum of MERIS pixel and yi is the standard reflectance spectrum for water type i, as determined by the SPSS sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi n

software during the reflectance classification.

∑ ðxi −yi Þ2 is the ED i¼1

between the pixel reflectance spectrum and standard reflectance specn

∑ xi yi i¼1 sffiffiffiffiffiffiffiffiffiffiffiffiffi trum of water type i and 1− sffiffiffiffiffiffiffiffiffiffiffiffiffi is the SAM for the pixel ren

∑ xi 2 i¼1

n

∑ yi 2 i¼1

flectance and standard reflectance spectrum of the water type. Then, each pixel of MERIS image will acquire three G values, indicating the similarity to three water types through Eq. (8). The water type will finally be determined based on the minimal G value. For example, if the G value calculated based on the water type, n, was the lowest of the three G values, the pixel was classified to water type n. One MERIS image of Taihu Lake with 250 m spatial resolution that was acquired on the 16th of December, 2012 was selected to demonstrate the water type determination and Chl-a estimation. The image was first atmospherically corrected using the 6S model. Then, all pixels were classified to water type I, II or III using the G-value criterion. According to each pixel's water type, the three-band algorithms listed in Table 3 were applied to water types I and III, and the four-band algorithm was used for water type II. Fig. 5(a) shows the distribution of the three water types in the Taihu Lake. Fig. 5(b) shows the corresponding Chl-a concentration map.

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Fig. 5. (a) Map of the water types and (b) distribution of Chl-a concentration in Taihu Lake, China, based on the MERIS image acquired on the 16th od December, 2012. (Note that the masked region is optically a shallow area and the reflectance is seriously influenced by the bottom of the lake and aquatic plant.)

4. Conclusions A total of 398 water samples were collected from five inland lakes in different seasons, which contain varying bio-optical features. An automatic cluster method was subsequently applied based on the optical characteristics. The results suggest that inland waters can be classified into three types. Four algorithms, a two-band, three-band, four-band and SCI algorithm, were evaluated for three water types, and they performed differently in different water types. Additionally, no single algorithm can be successfully applied to all water types. For water types I and III, the three-band algorithm performed the best, while the fourband algorithm had the highest retrieval accuracy for water type II. We conclude that the two-band algorithm is not the optimal choice for inland eutrophic turbid waters because it does not satisfy one or two requirements of the two-band algorithm. We recommend the SCI algorithm for highly turbid water with higher TSS concentrations. Generally, in water type II, the retrieval accuracy of the three-band algorithm was second only to the four-band algorithm. Furthermore, the three-band algorithm was best for water types I and III. The threeband algorithm can thus be considered the preferred choice over the two-band algorithm for turbid eutrophic inland water. Acknowledgments This research was supported by the National Natural Science Foundation of China grant (No. 41471282, 41171269) and the Priority Academic Program Development of Jiangsu Higher Education Institutions (PAPD). Thanks to the remote sensing application graduate students from Nanjing Normal University, China, for their aid with field work and lab analyses. We also thank the anonymous reviewers for their extensive comments and suggestions. References Akaike, H., 1973. Information theory and an extension of the maximum likelihood principle. In: Petrov, B.N., Csaki, F. (Eds.), 2nd International Symposium on Information Theory. Akademiai Kiado, Budapest, pp. 267–281. American Public Health Association, 1998. American Water Works Association, Water Environment Federation. Standard Methods for the Examination of Water and Wastewater. American Public Health Association, Washington, D.C.

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