Environ Monit Assess (2014) 186:2297–2311 DOI 10.1007/s10661-013-3538-z

Noise tolerance of algorithms for estimating chlorophyll a concentration in turbid waters Jun Chen

Received: 21 May 2013 / Accepted: 12 November 2013 / Published online: 18 December 2013 # Springer Science+Business Media Dordrecht 2013

Abstract The accuracy and noise tolerance of 13 global models and 5 Case II chlorophyll a (chl a) retrieval models were evaluated using three dataset. It was found that if 5 % input noise related to atmospheric correction is considered, then the uncertainty associated with noise tolerance varied from 5.5 % to 55.6 %, and these uncertainties generally accounts for 15.63 % to 24.75 % of the total uncertainty. This observation suggests that an optimal algorithm not only should have a strong chl a concentration prediction ability but also should possess high insensitivity to the noise of remote-sensing imagery. The accuracy evaluations of chl a models were based on comparisons of chl a predicted models with chl a concentration measured analytically for field measurements. The results indicate that none of the selected chl a estimation algorithms provide accurate retrievals of chl a in turbid waters. This may be attributed to the strong optical influence of organic and inorganic matter at the blue green range, and the non-negligible of nonorganic matter absorption at the red and near-infrared ranges. In order to solve this problem, the chl a concentration retrieval models must be further optimized. After being optimized using the empirical optimized method constructed in this paper, a single parameterized NDCI (normalized difference chl a index) model produces

J. Chen School of Ocean Sciences, China University of Geosciences, Beijing 100083, China J. Chen (*) The Key Laboratory of Marine Hydrocarbon Resources and Environmental Geology, Qingdao Institute of Marine Geology, Qingdao 266071, China e-mail: [email protected]

accurate retrievals in the Yellow River Estuary, Taihu Lake and Chesapeake Bay. If 5 % input noise associated with residual uncertainty 0of atmospheric correction is taken into account, the model produces only 29.96 % uncertainty for the remote sensing of chl a concentration in these three turbid waters. Keywords Remote sensing . Chlorophyll a concentration . Noise tolerance . Turbid waters

Introduction In recent years, many coastal waters have been enriched with excessive nutrients, leading to an increase in chlorophyll a (chl a) concentration (George 1997). As an important water quality indicator of eutrophication, chl a concentration has attracted the attention of a large number of researchers, due to its significant contribution to the biogeochemical cycling of carbon and nitrogen. Despite their accuracy for monitoring chl a concentration, traditional approaches are costly and timeconsuming, often involving sample collection and direct contact with the water body. Recent advances in optical sensor technology have opened new opportunities to study biogeochemical processes in aquatic environments at spatial and temporal scales (Clavano et al. 2007). These advances have allowed scientists to utilize ocean color satellite images to synoptically investigate the large-scale surface features of the world's oceans (Chang and Gould 2006). According to the optical classification proposed by Morel and Prieur (1977), the natural waters of the world may be divided into two different types, namely, Case I

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and Case II waters. Case I waters are characterized by having only one variable component (chlorophyll and covarying pigments) influencing their optical properties, while Case II waters are influenced by chlorophyll a pigments, total suspended materials (TSM), and colored dissolved organic matters (CDOM). Several ocean color algorithms have been developed for Case I environments. In typical Case I conditions, the resulting chl a maps may be applied to oceanographic research with greater confidence (Gordon and Voss 1999; Hu et al. 2001). However, as the uncertainty level is quite high in turbid coastal waters, Moore et al. (2009) suggested that the average relative error of the eight optical water types ranged from 16 % to 123 %, in which the distributions of the eight optical water types are identified by the color in the statistical relationship, as defined by the Ocean Chl a Version 3 Model (OC3M). Among the eight optical water types, only one type (Case I waters) meets the National Aeronautics and Space Administration (NASA) criterion of 35 % relative accuracy (Carder et al. 2003). Furthermore, the algorithms used to derive chl a from satellite radiometry have been parameterized using the NASA Bio-optical Marine Algorithm Dataset (NOMAD). Szeto et al. (2011) revealed that when the dataset is analyzed as a whole, the OC4 algorithm used for processing SeaWiFS data has an uncertainty greater than 50 %. However, instead of the errors being random, they exhibit systematic trends when the data are sorted in terms of the Atlantic, Pacific, Southern, and Indian Oceans. The algorithm underestimates chl a for stations from the Pacific, Indian, and Southern Oceans by 15 %, 17 %, and 50 %, respectively, and overestimates chl a for the Atlantic Ocean stations by 14 %. Furthermore, Szeto et al. (2011) suggested that the algorithm underestimated chl a at Pacific stations owing to the large and highly packaged cells of phytoplankton located there. By contrast, the algorithm overestimated chl a at Atlantic stations, due to the small and low packaged cells of phytoplankton. To quantify chl a in productive coastal waters, a variety of algorithms have been developed, all of which were based on the properties of the reflectance peak near 675 nm (Gitelson 1992). These include the ratio of the reflectance peak at near-infrared (NIR) to the reflectance at 670 nm. Gons et al. (1999) used the reflectance ratio at 704 and 672 nm, as well as absorption and backscattering coefficients at these wavelengths to assess chl a concentrations ranging from 3 to 185 mg/m3. Ruddick et al. (2001) analyzed how errors in reflectance

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measurements affect chl a retrievals for an NIR to red reflectance ratio algorithm with a general choice of wavelengths. They found that the effects on chl a retrieval depended strongly on the choice of the NIR wavelength if the error is spectrally neutral, suggesting a new type of algorithm, where the NIR wavelength used for retrieval is chosen dynamically for each spectrum to be processed. These approaches rely on a specific spectral feature to biophysical measurements using statistical regression. This type of model is simple and easy to implement (Matthews 2011), but lacks physical foundation, and the relationships are quite geographically specific, rendering them not applicable for use in other areas. Recently, Gitelson et al. (2008) outlined and described a three-band semi-analytical algorithm for estimating chl a concentration in turbid coastal waters, analyzed the influence factors of the algorithm, and suggested a method to optimize the band positions. This model relates chl a concentration to remote-sensing reflectance in three spectral bands, so that the model is independent of the accurate information of the inherent optical properties, which is generally difficult to obtain in remote-sensing applications. By comparison, most of these chl a concentration retrieval models generally perform calibration and validation using the bio-optical dataset collected in situ, which is considered accurate enough provided that it follows the standards for NASA's bio-optical experiments in situ (Mueller et al. 2003; Mueller and Fargion 2002). However, typical top-of-atmosphere reflectance is contaminated by scattering and absorbing atmospheric aerosol particles and molecular clusters. Due to a lack of research regarding the influence of data uncertainty on the performance of such remote-sensing algorithms, it is still difficult to determine the applicability of these chl a retrieval models in practical remote-sensing applications, as there remains a residual uncertainty of approximately 5–9 %, even though the accuracy atmospheric correction is carried out (Hu et al. 2001). With a ±5 % maximum threshold for residual uncertainty in the atmospheric correction of water-leaving reflectance (Gordon and Voss 1999), the algorithm was only capable of achieving a 35 % uncertainty in chl a estimation in Case I waters (Carder et al. 2003), due to the seven times magnification of residual uncertainty by the chl a prediction model. Chen et al. (2010b) also reported that the residual uncertainty in atmospheric correction could be magnified by a remote-sensing algorithm, negatively affecting its performance, and suggested that an optimal

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algorithm not only should have a strong chl a concentration prediction ability but also should have an excellent insensitivity to the noise of remote-sensing imagery. Hence, it is significant to perform research regarding the noise tolerance of chl a estimation models to input error. Noise tolerance is not a new concept or not specific to the field of ocean optics. Noise tolerance generally refers to the sensitivity of models to a small noise in an input. Over the past 30 years, a large number of noise tolerance evaluation methods have been developed for evaluating the noise tolerance ability of ocean biooptical models. For example, a normalized sensitivity coefficient was provided by Leathers and McCormick (1997) to discuss the sensitivity of single scattering albedo retrievals to a small error in an input. The results revealed that a 10 % uncertainty in the scattering asymmetry factor of Henyey–Greenstein phase function may result in an uncertainty in single-scattering albedo of approximately 18 %, which would be unacceptably large. An error amplification factor which may be used by Chen et al. (2010a) to evaluate the noise tolerance of chl a retrieval model in Taihu Lake, indicating that the band ratio model shows poor noise tolerance to input noise. In order to determine how the quasi-analytical algorithm (QAA) was used for retrieving the absorption and backscattering from remote-sensing reflectance of optically deep waters for erroneous data, Lee et al. (2002) suggested that a ±10 % random noise be added to the remote-sensing reflectance at each wavelength, to simulate the model's sensitivity to the input parameters; the results of the study indicated that although the remote-sensing reflectance was perturbed, the QAA still returned total absorption estimates which were quite accurate. By varying one parameter and keeping the others fixed at the default value, Smyth et al. (2006) used this approach to evaluate the noise tolerance of a semi-analytical algorithm (SAA) for derivation of ocean color inherent optical properties to input parameters, indicating that the SAA model is relatively insensitive to changes in the spectral slope of backscattering, although it is increasingly sensitive at high values of absorption. Although research concerning noise tolerance in the field of ocean remote sensing has a long developmental history, it still lacks systematic comparisons between chl a concentration estimation models, which would be beneficial for the construction and development of more accurate chl a concentration estimation models.

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In this study, a systematic study on noise tolerance of chl a concentration estimation models is performed. The specific goals of this study are as follows: (1) to construct an analytical model for the description of the noise tolerance of algorithms which estimate the chl a concentration; (2) to review the noise tolerance of 13 global algorithms and five Case II algorithms for chl a estimation; (3) to assess the performance of these 18 algorithms in turbid waters, with the input noise taken into account; and (4) to construct an accurate chl a concentration retrieval model for improving the performance of the 18 selected models in highly turbid waters.

Materials and methods Data collections In this study, three independent bio-optical datasets consisting of spectral upwelling radiance measurements and chl a concentrations were collected. The first dataset (consisting of 32 samples) was collected from the Yellow River Estuary (Shandong Province, China) during three independent cruises on September 1, 4, and 10, 2009, respectively; the second dataset (consisting of 21 samples) was collected from Taihu Lake (Jiangsu Province, China) during two independent cruises on October 27 and 28, 2003, respectively; and the third dataset (consisting of 30 samples) was collected from Chesapeake Bay (Columbia State, USA) during five independent cruises on October 13, 14, 19, 21 and 22, 2009, respectively (Achieved from SeaWiFS Bio-optical Archive and Storage System, SeaBASS, http://seabass. gsfc.nasa.gov). The spectral upwelling radiance (Fig. 1) was measured from aboard a boat. The reflectance was measured with a FieldSpec® 3 Hi-Res with 5° fiber-optic, covering the spectral range of 350– 2,500 nm (manufactured by Analytical Spectral Devices, Colorado, USA). Although data were collected in the range of 350–2,500 nm, with a spectral resolution of 3 nm (full-width-at-half-maximum, FWHM) and a 1. 4 nm sampling interval for the 350–1,050 nm spectral range (ASD 1999), the data mainly used in this study were those in the range of 400–900 nm, which is the wavelength generally used for water color remote sensing. According to the ocean optics protocols for satellite ocean color sensor validation (Mueller et al. 2003), various measurements were repeated at each station in order to estimate the uncertainty associated with each

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Fig. 1 Spectral curves measured from the Yellow River Estuary, Taihu Lake, and Chesapeake Bay

0.08 0.07

-1

R rs (sr )

0.06 0.05 0.04 0.03 0.02 0.01 0 400

measurement, and those with uncertainty < 5 % would be selected for model calibration and validation. Immediately after field measurement, water samples were collected and stored in a nitrogen canister. Laboratory analysis of chl a concentration was performed using the water samples within 24 h of collection. The chl a content was extracted and measured using 90 % acetone, in accordance with the Ocean Optical Protocols of NASA (Gilpin and Tett 2001; Mueller and Fargion 2002). Brief descriptions of selected chl a estimation algorithms for case I waters

500

600 700 Wavelength (nm)

800

900

three-band is a multiple regression equation derived using Rrs(490)/Rrs(555) and Rrs(510)/Rrs(555) band ratios, whereas the CalCOFI four-band equation was derived using Rrs(443)/Rrs(555) and Rrs(412)/Rrs(510). The Morel-1 equation presented at the Ocean Optics XII conference relates chl a concentration to Rrs(443)/ Rrs(555) via a power equation (O’Reilly et al. 1998). Similar to Morel-1, Morel-2 was derived using Rrs(490)/ Rrs(555). Morel-3 and 4 are cubic polynomials derived from in situ measurements using Rrs(443)/Rrs(555) and Rrs(490)/Rrs(555), respectively, forming an updated version of the Morel semi-analytical model. More details are provided in the research of O’Reilly et al. (1998).

SeaWiFS global algorithms for chl a estimation MODIS global algorithms for chl a estimation The Sea-viewing Wide Field-of-view Sensor (SeaWiFS) on board the OrbView-2 spacecraft was specifically designed to estimate the phytoplankton pigment concentration in the oceans in the range of 0.0164 mg/m3 to within 35 %. It has been operational since September 1994 and has provided global estimates of oceanic chl a concentration, thus contributing to understanding of the temporal variability of marine ecosystems and the function of oceanic photosynthesis and primary productivity in the earth's carbon budget and climate changes (Hyde et al. 2007). Most SeaWiFS chl a estimates have been performed using the global processing switching algorithm, with Rrs(443)/Rrs(555) at concentrations < 1.5 μg/l switched to R rs(510)/Rrs (555) at concentrations > 1.5 μg/l (Table 1; Carder et al. 2003). The California Cooperative Oceanic Fisheries Investigations (CalCOFI) algorithms were derived from CalCOFI data (O’Reilly et al. 1998). The CalCOFI two-band relates chl a concentration to Rrs(490)/Rrs(555) via a power equation, and the CalCOFI two-band cubic is a third-order polynomial equation derived using Rrs(490)/Rrs(555). The CalCOFI

The Moderate Resolution Imaging Spectroradiometer (MODIS) is a 36-band spectrometer, which observes the land, atmosphere, and oceans of the earth between 412 to 14,385 nm. The first images from MODIS Terra were obtained on February 24, 2000, and a major reprocessing of ocean data was completed in September 2002 (Carder et al. 2004). MODIS is typically two to three times more sensitive than SeaWiFS, and the chl a concentration may be derived from the radiance ratio of the MODIS sensor with an uncertainty of approximately 20 % (currently the most accurate Case I study in an open ocean; Gordon and Voss 1999). It is worth noting that the ocean biology processing group has recently completed a series of calibration and algorithm modifications and evaluations in preparation for the first complete reprocessing of ocean products derived from the MODIS/Aqua mission (http:// oceancolor.gsfc.nasa.gov). The evaluations have included a variety of alternate instrument calibrations which were developed incollaboration with the MODIS calibration support team, and the most algorithms. Other

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Table 1 SeaWiFS global chl a estimation algorithm Algorithm

Functional form

POLDER (O'Reilly et al. 1998)

C ¼ 10ða0 þa1 Rþa2 R

CalCOFI-1 (O'Reilly et al. 1998)

CalCOFI-2 (O'Reilly et al. 1998)

CalCOFI-3 (O'Reilly et al. 1998)

CalCOFI-4 (O'Reilly et al. 1998)

Morel-1 (O'Reilly et al. 1998)

Morel-2 (O'Reilly et al. 1998)

Morel-3 (O'Reilly et al. 1998)

Morel-4 (O'Reilly et al. 1998)

OC4v4 (Marrari et al. 2006)


 Rrs ð443Þ R ¼ log Rrs ð555Þ a¼ ½0:438; −2:114; 0:916; −0:851Š
 3 Rrs ð490Þ C ¼ 10ða0 þa1 R Þ ; R ¼ log Rrs ð555Þ a ¼ ½0:444; −2:431Š
 2 3 Rrs ð490Þ C ¼ 10ða0 þa1 Rþa2 R þa3 R Þ ; R ¼ log Rrs ð555Þ a¼ ½0:450; −2:860; 0:996; −0:3674Š
 Rrs ð490Þ C ¼ expða0 þ a1 R1 þ a2 R2 Þ; R1 ¼ ln Rrs ð555Þ
 ; Rrs ð510Þ ; a ¼ ½1:025; −1:622; −1:238Š R2 ¼ ln Rrs ð555Þ
 Rrs ð443Þ C ¼ expða0 þ a1 R1 þ a2 R2 Þ; R1 ¼ ln Rrs ð555Þ
 ; Rrs ð412Þ ; a ¼ ½0:753; −2:583; 1:389Š R2 ¼ ln Rrs ð510Þ
 Rrs ð443Þ ða0 þa1 RÞ C ¼ 10 ; R ¼ log Rrs ð555Þ a ¼ ½0:2492; −1:768Š
 Rrs ð490Þ C ¼ expða0 þa1 RÞ ; R ¼ ln Rrs ð555Þ a ¼ ½1:078; −2:543Š
 2 3 Rrs ð443Þ C ¼ 10ða0 þa1 Rþa2 R þa3 R Þ ; R ¼ log Rrs ð555Þ a ¼ ½0:208; −1:829; 0:759; −0:740Š
 2 3 Rrs ð490Þ C ¼ 10ða0 þa1 Rþa2 R þa3 R Þ ; R ¼ log Rrs ð555Þ a ¼ ½1:031; −2:401; 0:322; −0:291Š   2 3 4 Rrs443 Rrs490 Rrs510 > > C ¼ 10ða0 þa1 Rþa2 R þa3 R þa4 R Þ ; R ¼ log Rrs555 Rrs555 Rrs555 a ¼ ½0:366; −3:067; 1:930; 0:649; −1:532Š

recommended changes include updates to the atmospheric tables and minor enhancements to the atmospheric algorithm, as well as modifications to the definition of normalized water leaving radiance. The MODIS has become a powerful tool for oceanographers in the investigation of a wide variety of fundamental topics including ocean primary productivity, bio-geochemistry, coastal upwelling, harmful algal blooms, and eutrophication (Chen and Quan 2013). The modular data acquisition and processing system (MODAPS) was developed to produce a wide range of products based on MODIS radiometric data. MODIS data were processed by NASA using a modified version of the SeaWiFS ocean chl a 4 algorithm (OC4v4) with

2

þa3 R3 Þ

;

slightly different spectral bands. MODAPS produced three chl-a products (Table 2): (1) “chlor_a_2”, which was produced using the modified OC4v4 algorithm– ocean chl a model (OC3M; Carder et al. 2004); (2) “chlor_MODIS”, which was produced using a twoband algorithm (Aiken et al. 2007); and (3) “chlor_a_3”, which was produced using a semi-analytical model (Carder et al. 2004). A concentration estimation models for turbid case II waters In typical Case II waters, the traditional satellite-derived chl a models and semi-analytical models based on the

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Table 2 MODIS global chl a estimation algorithm Algorithm

Functional form

OC3M (Carder et al. 2004)

C ¼ 10ða0 þa1 Rþa2 R

Aiken (2007)

Carder et al. (2004)

  max½Rrs ð443Þ; Rrs ð488ފ ; R ¼ log Rrs ð551Þ a ¼ ½0:283; −2:753; 1:457; 0:659; −1:403Š   2 3 Rrs ð488Þ C ¼ 10ða0 þa1 Rþa2 R þa3 R Þ R ¼ log Rrs ð551Þ a ¼ ½0:282; −2:783; 1:863; −2:387Š h i  P 2 2 C ¼ P0 aph ð675Þ 1 ; aph ð675Þ ¼ 0:328 10ð−0:919þ1:037R1 −0:407R1 −3:531R2 þ1:702R2 Þ −0:008

 Rrs ð443Þ Rrs ð488Þ P0 ¼ 56:8; P1 ¼ 1:03; R1 ¼ log ; R2 ¼ log Rrs ð555Þ Rrs ð555Þ

ratio between the reflectance of blue and green light reflected by the surface waters cannot be used for an accurate retrieval of chl a (Spyrakos et al. 2011). However, chl a models which use green to red and NIR band ratios have shown strong performance in inland and coastal waters (Gilerson et al. 2010) (Table 3): Moses et al. (2009) presented a two-band model using red and NIR bands to quantify chl a in turbid productive waters with Medium Resolution Imaging Spectrometer (MERIS) spectral bands. They applied this model on MERIS imageries over the Azov Sea, Russia and reported the high accuracy potential of the model in estimating chl a in turbid productive waters. Similarly, Tzortziou et al. (2007) collected an extensive biooptical dataset to examine the relationship between inherent and apparent optical properties in the central area of Chesapeake Bay, USA. They observed a stronger relationship between remote-sensing reflectance ration at 665 and 559 nm and the chl a concentration in Chesapeake Bay, compared to blue green spectral band ratios. Dall’Olmo and Gitelson (2005) provided evidence that a three-band reflectance model, originally developed for estimating pigment contents in terrestrial vegetation, could also be used to assess chl a in turbid waters. They reported that the three-band algorithm was successful in providing accurate estimations of chl a in turbid productive water bodies with a wide range of optical complexity. Gons et al. (2008) presented a semi-analytical model for chl a retrieval using MERIS data. This model uses the relationship between inherent optical properties and the remote-sensing reflectance at three wavelengths, solves for chl a absorption at 665 nm, and estimates chl a by dividing absorption by chl a at 665 nm with the specific absorption coefficient

2

þa3 R3 þa4 R4 Þ

of chl a. Gons et al. (2008) indicated that this model successfully retrieved chl a concentration in the Laurentian Great Lakes, producing residuals lower than 35 % of the measured values. Recently, Mishra and Mishra (2012) proposed a normalized difference chlorophyll index (NDCI) to predict chl a concentration from remote-sensing data in estuarine and coastal turbid productive waters. The results indicate that the newly developed algorithm was successful in predicting chl a concentration in Chesapeake Bay, Delaware Bay, Mobile Bay, and the Mississippi River delta region in the northern Gulf of Mexico, USA, with an overall bias of approximately 12 %. Definition of normalized noise tolerance It is generally considered reasonable to ignore the residual uncertainty of field measurements, provided that the bio-optical measurements strictly follow the standards of bio-optical experiments (Mueller et al. 2003; Mueller and Fargion 2002). However, the final goal of oceanic remote sensing is not only to calibrate and validate optimal estimation algorithms from field measurements but also to accurately estimate the chl a concentration from satellite imageries. In general, the satellite imageries are contaminated by atmospheric path scattering and absorption, resulting in a residual uncertainty of 5–9 % even with an accurate atmospheric correction (Hu et al. 2001). Therefore, it is necessary to consider the noise tolerance of remote-sensing algorithms when comparing their performances in predicting chl a concentration. An optimal algorithm not only should provide an accurate prediction of chl a concentration for calibration

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Table 3 MERIS chl a estimation models in Case II waters, where a0 and a1 are empirical coefficients, which can be o using local bio-optical information Algorithm

Functional form

T07 (Tzortziou et al. 2007)

C=a0R+a1,R=R−1 rs (559)×Rrs(665)

M09 (Moses et al. 2009)

C=a0R+a1,R=R−1 rs (665)×Rrs(708) Þ Rrs ð753Þ C ¼ a0 ðR1 −R2 Þ þ a1 ; R1 ¼ RRrsrs ðð753 665Þ; R2 ¼ Rrs ð708Þ   1:61Rrs ð775Þ Þ C ¼ Rð0:7 þ bb Þ−0:4−bb1:06 =0:016; bb ¼ 0:082−0:6R ; R ¼ RRrsrs ðð708 665Þ rs ð775Þ

D05 (Dall'Olmo and Gitelson 2005) G08 (Gons et al. 2008)

708Þ−Rrs ð665Þ Rrs ð708Þ C ¼ a0 RRrsrsðð708 ÞþRrs ð665Þ þ a1 ; R ¼ Rrs ð665Þ

NDCI (Mishra and Mishra 2012)

and validation datasets but also should have an excellent noise tolerance to decrease the influence of residual atmospheric correction uncertainty of remote-sensing imagery on the prediction of chl a concentration. Here, the differential function of the chl a retrieval model is expressed as follows: d ½chlaŠ ¼

n X ∂½chlaŠ dRrs ðλi Þ ∂Rrs ðλi Þ i¼1

ð1Þ

where dRrs(λi) is the infinitesimal element of remotesensing reflectance at λi; [chl a] is the chl a retrieval model; d[chl a] is the differential function of [chl a]; and n is the number of independent variables in the chl a estimation model (e.g., n=2 for two-band algorithm and n=3 for three-band algorithm). A small input noise is generally defined as the ratio of the measurement uncertainty to the measurement value. For the sake of simplicity, it is assumed that the remote-sensing reflectance at all bands contains the same residual uncertainty, e.g., the 5 % residual uncertainty in the respective atmospheric corrections of MODIS, SeaWiFS, and MERIS data on NASA's mission. This assumption may be unrealistic, but it aids in avoiding controversy concerning the exact definition of uncertainty in remote-sensing reflectance at each band and its measuring method. According to Leathers and McCormick (1997) and Chen et al. (2010b), the uncertainty caused by a small input noise may be presented as follows: sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi n h i2 X ∂½chlaŠ ∂Rrs ðλi Þ Rrs ðλi Þ Δ½chlaŠD ¼ k

i¼1

½chlaŠ

ð2Þ

where k is a small noise defined in this study, and △[chl a]D represents the uncertainty in chl a retrievals caused

by the small input noise of k, such as uncertainty due to atmospheric correction. In order to compare different models more conveniently, △[chl a]D was normalized by k in practical remote-sensing application, as follows: sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi n h i2 X ∂½chlaŠ ∂Rrs ðλi Þ Rrs ðλi Þ Δ½chlaŠN ¼

i¼1

½chlaŠ

 100%

ð3Þ

where △[chl a]N refers to the normalized noise tolerance, that is, the noise tolerance defined as the uncertainty in ch a estimation caused by a 1 % residual uncertainty in atmospheric correction. Total uncertainty in chl a prediction Chen et al. (2010b) have previously shown that total uncertainty in chl a prediction may be categorized as either model prediction uncertainty or data-introduced uncertainty. The former is associated with the inaccuracy of chl a prediction algorithms due to a lack of algorithms without uncertainties, whereas the latter is introduced by the inaccuracy of satellite data due to the residual atmospheric correction uncertainty. It is worth noting that sensor noise is one of the most significant uncertainties in satellite data, next only to atmospheric correction. Moreover, there are also other sources of uncertainty, such as radiometric calibration issues, spectral smear, stray light interference, and so on, which are very difficult to estimate. Traditionally, the atmospheric correction is deemed as the extension of sensor calibration and radiance calibration, so that any uncertainty related to sensor calibration, radiance calibration, etc., may be treated as one part of the atmospheric correction uncertainty.

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A number of studies have focused on how to improve model prediction uncertainty. In this study, mainly dataintroduced uncertainty is discussed. In practical terms, the residual uncertainty of satellite imageries will inevitably be introduced into chl a products regardless of the algorithms used for the prediction of chl a concentration (Chen et al. 2010b). However, whether the residual uncertainty is magnified or reduced depends on the selection of different prediction algorithms, and the property associated with magnifying or reducing the residual data uncertainty is known as noise tolerance. Therefore, total uncertainty in chl a products is presented as follows (Chen et al. 2003): Δ½chlaŠ ¼

qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Δ½chlaŠ2M þ Δ½chlaŠ2D

ð4Þ

where △[chl a] is the total uncertainty of chl a products, and △[chl a]M is the corresponding model prediction uncertainty. The△[chl a]M can be evaluated based on the comparison of the chl a concentration predicted by chl a retrieval model with chl a concentration measured analytically, while△[chl a]D can be calculated by inserting field measured bio-optical information into Eq. 2. In practical terms, especially in model construction procedures, only model prediction uncertainty is considered as the criterion for assessing the performance of an algorithm for chl a estimation. As a result, valid ocean color data were obtained from the earth's oceans with an uncertainty of 5 % in retrieved water-leaving signatures, with a 35 % prediction accuracy of chl a concentrations in Case I waters (Hu et al. 2001), despite the strong performance of chl a estimation models during the calibration procedures (Chen and Quan 2013; Tilstone et al. 2011). Statistical criteria To evaluate the algorithm performance, this study used the statistical measure of root-mean-square (RMS) based on the ratio of RMS error to measured values (O’Reilly et al. 1998), described as follows:

RMS ¼

vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ! u m uX ½chlaŠobs;i −½chlaŠmod;i t ½chlaŠobs;i i¼1

Results Chl a concentrations Three bio-optical datasets consisting of spectral upwelling radiance measurements and chl a concentrations are used to evaluate △[chl a]M and △[chl a]D of algorithms for chl a estimation models. The descriptive information concerning the three datasets is as follows (Table 4): (1) the first dataset, consisting of 32 samples, was collected during three independent cruises in the Yellow River Estuary, China, on September 1, 4, and 10, 2009, respectively; the chl a concentrations ranged from 1.57 to 12.64 mg/m3, and the corresponding average value was 5.51 mg/m3; (2) the second dataset, consisting of 30 samples, was collected during five independent cruises in Chesapeake Bay, USA, on October 13, 14, 19, 21 and 22, 2009, respectively; the chl a concentrations ranged from 3.17 to 36.94 mg/m3, and the corresponding mean value was 11.22 mg/m3; and (3) the third dataset, consisting of 25 samples, was collected during two independent cruises in Taihu Lake, China, on October 27 and 28, 2003, respectively; the chl a concentrations ranged from 2.2 to 47.46 mg/m3, and the corresponding average value was 20.40 mg/m3. △[Chl a]M of algorithms for chl a estimation SeaWiFS, MODIS, and MERIS algorithms for estimating chl a concentrations were validated by the biooptical datasets as shown in Fig. 1, and the △[chl a]M was estimated from the bias between field measurements and modeling prediction shown in Eq. 5. Fig. 2 shows the respective △[chl a]M of MODIS, SeaWiFS, and MERIS chl a estimation algorithms in the turbid waters of the Yellow River Estuary, Taihu Lake, and Chesapeake Bay, indicating that the global chl a Table 4 Descriptive statistics of the chl a concentration measured from calibration datasets (mg/m3) Sample Max counts

 100% ð5Þ

m−1 where [chl a]mod,i is the modeled value of the ith element, [chl a]obs,i is the observed value (or that measured in situ) of the ith element, and m is the number of elements.

Chesapeake 30 Bay Yellow 32 River Estuary Taihu Lake 25

Min Median Average STDEV

36.94 3.17 9.71

11.22

7.14

12.64 1.57 5.46

5.51

2.57

47.46 2.2

20.40

12.28

17.86

Environ Monit Assess (2014) 186:2297–2311

2305

log10([chla ]M) (%)

4

Taihu Lake Yellow River Estuary Chesapeake

3 2 1 0

a

b

c

d

e

f

g

h

i j k Model name

l

m

n

o

p

q

r

Fig. 2 △[chl a]M of MODIS, SeaWiFS, and MERIS chl a estimation algorithm in the Yellow river Estuary, Chesapeake Bay, and Taihu Lake, respectively. a POLDER, b CalCOFI-1, c CalCOFI-2,

d CalCOFI-3, e CalCOFI-4, f Morel-1, g Morel-2, h Morel-3, i Morel-4, j OC4v4, k OC3M, l Aiken, m Carder, n T07, o M09, p D05, q G08, and r NDCI

estimation algorithms provide poor performances in estimating chl a from the three turbid waters used in this study, with RMS values > 51 %. These findings indicate that neither SeaWiFS nor MODIS global algorithms showed strong performance in predicting chl a concentration in turbid waters, and this observation is consistent with the findings reported in several previous studies (Chen et al. 2010b; Hu et al. 2001; Leathers and McCormick 1997; Moore et al. 2009; Mueller and Fargion 2002). All chl a models selected for use in this study failed in the accurate remote sensing of chl a concentration in both the Yellow River Estuary and Taihu Lake, with a retrieval uncertainty larger than 39 %. Regarding different study sites, both global and Case II models showed superior performances in Chesapeake Bay in comparison to the Yellow River Estuary and Taihu Lake. The NDCI model may be particularly successful in predicting chl a concentration, with approximately 16.9 % in Chesapeake Bay. This finding implies that, provided that an atmospheric correction scheme for the red and NIR bands of MERIS imagery is available, the NDCI model could be used for the quantitative monitoring of chl a in Chesapeake Bay.

collected from the Yellow River Estuary, Taihu Lake, and Chesapeake Bay. As shown in Table 8, the△[chl a]N of SeaWiFS and MODIS algorithms varied from 1.09 % to 11.11 %. The T07 model had the smallest △[chl a]N values, and the G08 model had the largest △[chl a]N values. This means that the G08 model was the most sensitive to input noise among all the selected models, and the T07 model was the most insensitive to residual uncertainty contained in input data. However, the △[chl a]M of T07 model is 147.45 %, which is 100.41 % larger than the NDCI model, the △[chl a]N value of which is 3.04 %. Hence, the NDCI model is more accurate than T07 in practical remote-sensing application, provided that the atmospheric correction accuracy is greater than 33 %. This observation indicates that an excellent algorithm not only should be quite insensitive to the noise of Table 5 Normalized noise tolerance of SeaWiFS global chl a estimation algorithm calculated using Eq. 3 Algorithm POLDER CalCOFI-1 CalCOFI-2 CalCOFI-3

△[Chl a]N of algorithms for chl a estimation By substituting the algorithms in Tables 1, 2 and 3 into Eq. 3, the analytical △[chl a]N estimating formulas of MODIS, SeaWiFS, and MERIS algorithms for chl a concentrations retrievals were obtained (Tables 5, 6 and 7). The analytical formulas of △[chl a]N were then further tested using the bio-optical datasets respectively

CalCOFI-4 Morel-1 Morel-2 Morel-3 Morel-4 OC4v4

△[chl a]N

pffiffiffi

2 a1 þ 2a2 R þ 3a3 R2 pffiffiffi 3 2a1 R2 pffiffiffi

2 a1 þ 2a2 R þ 3a3 R2 pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2a21 þ 2a22 pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2a21 þ 2a22 pffiffiffi 2a1 pffiffiffi 2a1 pffiffiffi

2 a1 þ 2a2 R þ 3a3 R2 pffiffiffi

2 a1 þ 2a2 R þ 3a3 R2 pffiffiffi

2 a1 þ 2a2 R þ 3a3 R2 þ 4a4 R3

2306

Environ Monit Assess (2014) 186:2297–2311

Table 6 Normalized noise of MODIS global chl a estimation algorithm calculated using Eq. 3 Algorithm

△[chl a]N

OC3M

pffiffiffi

2 a1 þ 2a2 R þ 3a3 R2 þ 4a4 R3

Aiken

2(a1 +2a2R+3a3R2)

Carder

1.03[aph(675)]−1[aph(675)+0.008]X rhffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffii X ¼ ð1:037−0:814R1 Þ2 þ ð−3:531 þ 3:404R2 Þ2 þ ð2:4930:814R1 −3:404R2 Þ2

remote-sensing imagery but also should possess strong chl a concentration prediction ability. △[Chl a] of algorithms for chl a estimation: simulated for 5 % input noise Several studies have shown that an uncertainty of approximately 5–9 % remains in water-leaving signatures even if an accurate atmospheric correction is performed (Gordon and Franz 2008; Hu et al. 2001). Hence, it is reasonable to assume that there is a 5 % uncertainty included in input satellite imagery after accurate atmospheric correction. In this section, the atmospheric correction uncertainty was assumed to be 5 %, which is similar to the estimation accuracy of water-leaving reflectance on NASA's mission (Gordon and Voss 1999; Hu et al. 2001). Then, the △[chl a]D was estimated according to Eq. 2 and △[chl a]D was calculated by comparison of modeled values with in situ data measured in the Yellow River Estuary, Chesapeake Bay, and Taihu Lake. Fig. 3 shows the △[chl a]D, △[chl a]M, and △[chl a] for predicting chl a in turbid waters (considering the three selected regions as a whole). It was found that the Table 7 Normalized noise tolerance of MERIS chl a estimation algorithm Algorithm

△[chl a]N

T07

a0 R 1þR2 a0 Rþa1

M09

a0 R 1þR2 a0 Rþa1

D05

a0

G08

qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 ½1:32 − 0:97Rrs ð775ފ2 ð0:7þbb Þ2 ðR2 þR4 ÞþðR−1:06b0:06 b Þ ½0:86 − 0:6Rrs ð775ފ4

pffiffiffiffiffiffiffiffi pffiffiffiffiffiffiffiffi

pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 2 4 4 R1 þR2 þR1 þR2 a0 ðR1 −R2 Þþa1

Rð0:7þbb Þ − 0:4 − bb1:06

NDCI

pffiffiffiffiffiffiffiffiffiffi 2

4

2a0 R þR a0 ðR2 −1Þþa1 ð1þRÞ

NDCI model was the most ideal chl a prediction model for remote sensing of chl a concentration from these selected regions, in which △[chl a] = 49.44 %. This accuracy level was 1.5-fold that of NASA's goal, i.e., an uncertainty of 35 % in chl a estimation in Case I waters. As the uncertainty in atmospheric correction was usually greater than 5 % in Case II waters(Chen et al. 2011a), the associated △[chl a] may be much greater than 49.44 %. Fig. 4 shows the ratio of △[chl a]D to △[chl a]M, indicating that the residual uncertainty in atmospheric correction accounted for 1.15–55.55 % of the total uncertainty. When ignoring outliers with △[chl a]M > 100 %, the chl a concentration retrieval uncertainty related to 5 % uncertainty of atmospheric correction accounted for 15.63–24.75 % of the total uncertainty. Thus, the uncertainty caused by input noise was an important source of total uncertainty. This required that an optimal algorithm for chl a estimation must be a small model prediction uncertainty and a reasonable image-introduced uncertainty.

Optimized NDCI model Taihu Lake, the Yellow River Estuary, and Chesapeake Bay represent three different water types, namely, higheutrophic, SSC-dominated, and high-productive waters, respectively. Due to the optical complexity of these Case II waters, a single parameterized empirical or SAA is able to account for the variability in the concentrations of chl a for local waters, but is not capable of producing accurate chl a estimations while the bio-optical conditions are different from those used for model development. As a result, all of the selected models produce poor performance in estimating chl a concentration from Taihu Lake, the Yellow River Estuary, and Chesapeake Bay, and an accurate semi-analytic model is still under development. In this study, in order to accurately retrieve chl a concentration from turbid Case II waters, the

Environ Monit Assess (2014) 186:2297–2311

2307

Table 8 △[chl a]N of MODIS global chl a estimation algorithm, where STD represents standard deviation Algorithm

Min

Max

Median

Mean

Fig. 5a shows the optimal optimized NDCI model regressed from the calibration dataset, indicating that the chl a concentration may be accurately estimated in the Yellow River Estuary, Taihu Lake, and Chesapeake Bay using a single parameterized model, the correlated coefficient of which is 0.9132. The stability and accuracy evaluations were based on the comparison of chl a concentration predicted by the optimized NDCI model with chl a concentration measured analytically for the independent validation dataset. A comparison of the measured and predicted estimates of chl a concentration is presented in Fig. 5b. For the range of chl a concentration from 1.68 to 38.92 mg/m3, the RMS error of chl a concentration prediction was below 5.71 mg/m3 and the corresponding RMS value was 25.82 %. If 5 % input noise was associated with residual uncertainty of atmospheric correction, the RMS value was 29.96 % for the optimized NDCI model (based on 25.82 % △[chl a]M and 15.20 % △[chl a]D by solving Eq. 4). By comparison, the optimized NDCI model produces a performance which is superior to that of the MODIS, SeaWiFS, and MERIS models selected for use in this study. Using the optimized NDCI model decreases >19.47 % RMS from MODIS, SeaWiFS, and MERIS models, e.g., 29.96 % RMS for the optimized NDCI model versus 49.44 % RMS for the best MODIS, SeaWiFS, and MERIS models. This improvement is quite significant.

STD

POLDER

3.51

6.36

4.05

4.12

0.46

CalCOFI-1

3.44

3.44

3.44

3.44

0.00

CalCOFI-2

4.24

6.05

4.49

4.54

0.29

CalCOFI-3

3.51

3.51

3.51

3.51

0.00

CalCOFI-4

4.94

4.94

4.94

4.94

0.00

Morel-1

2.50

2.50

2.50

2.50

0.00

Morel-2

3.60

3.60

3.60

3.60

0.00

Morel-3

3.03

5.45

3.48

3.54

0.39

Morel-4

3.46

4.26

3.55

3.58

0.13

OC4v4

4.48

5.53

4.85

4.85

0.19

OC3M

4.07

4.63

4.40

4.40

0.10

Aiken

4.37

9.70

4.92

5.09

0.87

Carder

4.72

5.79

4.92

4.95

0.18

T07

0.95

1.35

1.08

1.09

0.11

M09

2.67

7.74

3.81

4.18

1.43

D05

0.96

8.74

3.81

4.07

1.44

G08

3.37

52.71

6.23

11.11

10.71

NDCI

2.41

6.94

2.83

3.04

1.35

NDCI model is further optimized. An empirical optimized method is suggested for improving the performance of the NDCI model in Case II waters, which classified NDCI into three different groups, as shown in Table 9. To calibrate and validate the accuracy and stability of the optimized NDCI model, the dataset as shown in Fig. 1, was divided into two independent smaller datasets, referred to here as the calibration dataset (n=59) and validation dataset (n=28) .

Discussion The performances of 13 MODIS and SeaWiFS global chl a estimation models including modeling prediction

log10(

[chla ]i) (%)

4

[chla]M [chla]N

3

[chla]

2 1 0

a

b

c

d

e

f

g

h

i

j

k

l

m

n

o

p

q

r

Model name Fig. 3 △[chl a]N, △[chl a]M, and △[chl a] of MODIS, SeaWiFS, and MERIS chl a estimation algorithm in turbid waters, where subscript “i” represents the “N” and “N”, respectively

Environ Monit Assess (2014) 186:2297–2311

Δ [chla]m/ Δ [chla]m (%)

2308

50 40 30 20 10 0

a

b

c

d

e

f

g

h i j k Model name

l

m

n

o

p

q

r

Fig. 4 Ratio of △[chl a]D to △[chl a]M

accuracy and noise tolerance are evaluated by the respective bio-optical datasets collected from three turbid waters, namely, the Yellow River Estuary, Taihu Lake, and Chesapeake Bay,. The results indicate that all of these single parameterized models produce poor chl a estimation in these three selected regions. This is due to the fact that at high concentrations of chl a, all global models are based on empirical relationships between chl a concentration and blue green wavelength remote-sensing reflectance ratios which do not account for the typically strong blue wavelength absorption by non-covarying, dissolved and non-algal particulate components (Tzortziou et al. 2007). Additionally, five MERIS Case II models are also tested in this study. By comparison, although the MERIS Case II models produce a superior performance in chl a concentration estimation in comparison to MODIS and SeaWiFS global chl a estimation models, the best RMS value of MERIS retrieval models is 49.44 %, which is still too large for use in remote sensing of chl a concentration. An accurate chl a prediction model for Case II waters is still under development. Taihu Lake is a typical highly turbid and eutrophic body of water, the optical properties of which are codetermined by CDOM, SSC, and chl a (Wang et al. 2011). Due to the optical complexity and significant variability of the water in Taihu Lake (Chen et al. Table 9 Optimized NDCI model, where R = [Rrs(708)-Rrs(665)]/ [Rrs(708)-Rrs(665)] Empirical optimized method

Optimized parameter

(R + 0.27)/[chl a] < 0.0078

(R + 0.27) × 1.88

0.0078 ≤ (R + 0.27)/[chl a] ≤ 0.0153

(R + 0.27)

(R + 0.27)/[chl a] > 0.0153

(R + 0.27)÷2.12

2011b, 2012), all selected models, even the MERIS Case II models, failed to provide accurate remote sensing of chl a concentration in this region, with a retrieval uncertainty larger than 72 %. The Yellow River Estuary is a typical SSC-dominated water (Chen and Quan 2013). Tzortziou et al. (2006) showed that the absorption of particulate matter in the 51 %. This is due to the fact that the remote-sensing reflectance at the blue green range is very inappropriate due to the strong optical influences of organic and inorganic matter. Although MERIS Case II models produce a superior performance in comparison to MODIS and SeaWiFS global models, the improvement was not significant: 47 % in the best MERIS Case II models versus 51 % in the best models of both MODIS and SeaWiFS. This is due to the fact that the absorption by nonnegligible of non-organic matters at the red and NIR ranges is non-negligible. Hence, it is difficult to accurately estimate chl a concentration from turbid waters with widely varying bio-optical properties using a single parameterized model. In this study, in order to accurately retrieve chl a concentration from the three selected regions, an empirical optimized method is suggested for further optimizing the NDCI model by classifying the NDCI into three different groups. The results show that the range of chl a concentration from 1.68–38.92 mg/m3 root mean square error of chl a concentration prediction was below 5.71 mg/m3, and the corresponding RMS value was 25.82 %. If 5 % input noise associated with residual uncertainty of atmospheric correction, the RMS value was only 29.96 %, accurate enough for estimating the chl a concentration in the study area, where has a widely ranging level of biooptical properties. It is concluded that the optimized NIDC model should be used for estimating chl a concentration in highly turbid Case II waters, although it will be essential to reinitialize the model’s remote-sensing parameters when using local biooptical information.

Acknowledgements This study is supported by the China State Major Basic Research Project (2013CB429701), Projects of International Cooperation and Exchanges of National Natural Science Foundation of China (41210005), Science Foundation for 100 Excellent Youth Geological Scholars of China Geological Survey, Serial Maps of Geology and Geophysics on China Seas and Land on the Scale of 1:1000000 (200311000001), and the Public Science and Technology Research Funds Projects of Ocean (201005030). We would like to just express our gratitude to two anonymous reviewers for their useful comments and suggestions.

Environ Monit Assess (2014) 186:2297–2311

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