1. Introduction

Remotely sensed observations from satellites, airborne and UAV platforms have become a powerful source of information for monitoring the biogeochemical constituents (including phytoplankton, suspended sediments and colored dissolved organic matter CDOM), biological patterns/processes (including harmful algal blooms), outflowing river-runoff plumes, and climate-induced external forcing and mixing processes. Satellite remote sensing has advantages because of its synoptic coverage (from local to global scales), consistent measurements, frequent temporal revisits, and capability to resolve time and length scales of geophysical and biological features in coastal and open oceanic waters. For example, multispectral water color data provided by the SeaWiFS (Sea-viewing Wide Field-of-view Sensor), MODIS-Aqua (Moderate Resolution Imaging Spectroradiometer), MERIS (MEdium Resolution Imaging Spectrometer), OCM-2 (Ocean Colour Monitor - 2) and VIIRS (Visible Infrared Imager Radiometer Suite) were extensively utilized for monitoring and forecasting water quality, sediment plume dynamics, oil spill, harmful algal blooms, phytoplankton physiology and phenology, primary productivity, seagrass ecosystem, global carbon budget, coral bleaching, acidification, shallow-water bathymetry, climate-change and its influence on biogeochemical cycle [1–9]. Similarly, water color observations provided by other satellite/space-borne sensors such as Sentinel-3 OLCI (Ocean and Land Colour Instrument), GOCI (Geostationary Ocean Color Imager), Landsat OLI (Operational Land Imager), Hyperion, and HICO (Hyperspectral Imager for the Coastal Ocean) have provided unique capabilities for certain specific needs and applications within coastal and inland environments. To utilize these space-borne data for qualitative and quantitative applications on local, regional and global scales, the normalized water-leaving radiance ${L_{wn}}$(λ) or the equivalent remote-sensing reflectance ${R_{rs}}(\mathrm{\lambda } )$ (with the difference factor of F₀(λ)) must be retrieved through the atmospheric correction process [10–14]. Atmospheric correction is one of the most challenging problems in remote sensing of coastal and inland waters because of the excessive contributions of phytoplankton and suspended sediments in the near-infrared wavelengths, which are critical for implementing the atmospheric correction algorithms. The global/standard atmospheric correction algorithms usually rely on the typical assumptions about the spectral shape and extrapolation of aerosol reflectance from the NIR or SWIR to the visible wavelengths as well as the IOP models. The IOP model is critical in the atmospheric correction process as it estimates the enhanced backscattering contributions of suspended sediments and phytoplankton in the NIR and SWIR wavelengths [15–17]. Despite such modifications done to the original atmospheric correction algorithm (which assumes the negligible water-leaving radiance at NIR), water color products derived from the standard algorithm are subject to large uncertainties in coastal and inland waters, due to the inaccurate estimation of the water contributions in the NIR and SWIR wavelengths and scarcity of NIR measurements to refine and validate the IOP models [18,19].

Satellite and other spaceborne radiometers record the top-of-atmosphere (TOA) radiance from the water–atmosphere system over a number of visible (discrete and narrow) and near-infrared (NIR) wavelengths. A major portion of the observed radiance (80–90%) arises from the atmosphere due to Rayleigh scattering by air molecules and Mie scattering by aerosol particles and a small portion of TOA radiance emerges from the water column [6,7]. The atmospheric correction procedure is applied to estimate and remove the atmospheric contributions (essentially the path radiance due to Rayleigh and aerosol scattering) from the TOA radiance in order to retrieve the normalized water-leaving radiance (or remote sensing reflectance) which is commonly used for water color remote sensing applications [20–24]. In the past decades, several atmospheric algorithms were developed, tested and validated using matchup data from the coincident in-situ and satellite measurements. The standard atmospheric correction algorithm (i.e., NASA standard atmospheric correction, STD-AC) was often used for many operational applications and it typically worked on the basis of black pixel assumption (i.e., zero water-leaving radiance in the NIR) combined with the pre-defined lookup tables (LUTs) of 12 aerosol models for calculating the aerosol radiance and retrieving the water-leaving radiance for all visible wavelengths. The assumption of the negligible water-leaving radiance in the NIR is invalid in coastal and inland waters due to the strong backscattering contribution of phytoplankton and suspended sediments. Later, the black-pixel approach was replaced by NIR and NIR-SWIR (shortwave infrared) methods to improve the water color products in turbid coastal waters [25–27]. The NIR-SWIR-based atmospheric correction worked fairly well for turbid coastal waters, but became ineffective because of its retrievals of negative and spectrally distorted water-leaving radiances from satellite data in phytoplankton-dominated (algal blooms) waters within coastal and inland environments. The SWIR-based correction often resulted the noise water color products due to the low signal-to-noise ratios (SNR) in the SWIR bands [28–30]. Alternatively, the POLYnomial-based method was developed and applied to MERIS data in the presence of aerosols and sunglint. It made a significant improvement in water color data recovery under sun glint condition and proved successful when tested on other sensor data (e.g., Sentinel-2 MSI and Sentinel-3 OCLI [9,31–35]).

The POLYMER algorithm estimates aerosol and sun glint reflectances as the polynomial function of wavelength instead of using explicit aerosol modelling approaches to calculate the atmospheric radiance contributions. Consequently, it retrieves highly inconsistent water-leaving reflectances (at 667 nm and 869 nm) in turbid coastal waters [9,36–42]. The atmospheric and sunglint radiances extrapolated above 700 nm by using the similarity spectrum and compensated by the difference of spectral-matching at the shorter wavelengths (due to the lack of CDOM and non-algal absorption data) also caused the reduced performance at red and NIR wavelengths [35,43–45]. The major source of error with the POLYMER algorithm comes from the inaccurate estimation of aerosol radiance in coastal and inland waters. The unphysical negative water-leaving radiances retrieved by both standard and POLYMER algorithms are typical of severe aerosol path radiance reduction due to the profound influence of suspended sediments and phytoplankton concentrations in coastal and inland waters [22,23,25,46–50].

Other approaches employed the POLYMER algorithm to correct the atmospheric contributions in the presence of absorbing aerosols, sediments and Sargassum [36,51–55]. Correcting for absorbing aerosols is a significant challenge in ocean color remote sensing research. Zhang et al. [51] introduced an enhanced POLYMER algorithm originally designed to mitigate sun glint effects in the absence of specific aerosol information (such as aerosol type, optical thickness, and vertical distribution). This refined algorithm demonstrated its effectiveness in partially correcting for the impact of absorbing aerosols, resulting in improved retrievals of remote sensing reflectance (${R_{rs}}(\mathrm{\lambda } )$) in the blue wavelengths. Furthermore, the POLYMER algorithm, which assumes a water reflectance model, is at present not very suitable for processing the imagery over turbid Belgian coastal waters, where the atmospheric correction problem is still significant in 665 and 709 nm bands and hence yields erroneous chlorophyll-a and turbidity retrievals. This may be caused by their internal model and/or training dataset not being well adapted to the waters encountered in the Belgian Coastal Zone (BCZ) [53].

Extracting the information about the presence and abundance of Sargassum from satellite ocean color data necessitates initial atmospheric correction. Note that the standard atmospheric correction procedure employed for oceanic waters needs adjustments when dealing with the Sargassum occurrences. This is essential because the non-zero water reflectance in the near-infrared band, caused by the optical signature of Sargassum, may result in the misidentification of Sargassum as aerosols. Notably, the current extension of the POLYMER algorithm is not entirely suitable for Sargassum-dominated waters due to the presence of negative values in NIR regions [54]. For instance, the POLYMER algorithm was employed on data acquired from the Hyperspectral Imager for the Coastal Ocean (HICO) and validated against in situ multispectral measurements (AERONET-OC). The match-up analysis showed the excellent performance of POLYMER in the green spectral region [55]. Abdelillah Mograne et al. [36] conducted a validation of OLCI water-leaving reflectance products in two distinct French coastal waters using five different atmospheric correction algorithms. However, across all atmospheric correction methods, the performance was notably less robust at 400 and 443 nm. These atmospheric correction methods demonstrated improved performance in the spectral range of 490 to 560 nm. In individual match-up exercises, C2R-CCAltNets emerged as the most accurate atmospheric correction algorithm, while in common match-ups, POLYMER proved to be the most efficient algorithm. However, in turbid and productive waters, these algorithms are not entirely sufficient in addressing the increased water-leaving radiance (or reflectance) in the NIR bands, which arises from the elevated concentrations of suspended sediments and phytoplankton, challenging the accurate estimation of NIR contributions in such sediment-laden and algal bloom waters.

This study presents an enhanced POLYMER algorithm (mPOLYMER) to accurately estimate aerosol radiances and retrieve normalized water-leaving radiance from hyperspectral/multispectral remote sensing data in inland and coastal zones. The enhanced POLYMER algorithm takes into account the NIR radiance contributions (by suspended sediments and phytoplankton) to determine accurate polynomial functions for estimating the aerosol contributions with a combination of UV and Visible-NIR bands. The performance of mPOLYMER was assessed by comparison of the satellite-retrieved ${L_{wn}}$(λ) products (from the HICO, MSI and MODIS-Aqua sensors) with AERONET-OC and OOIL-regional in-situ data. Its robustness and reliability were demonstrated using many MODIS-Aqua and HICO images from highly turbid and productive (algal bloom dominated) waters in Muttukadu Lagoon, Lake Erie, Yangtze River Estuary, Baltic Sea and Arabian Sea.

2. Datasets

To evaluate the performance of mPOLYMER algorithm, in-situ and satellite matchup data were collected from a wide range of waters within the inland, coastal and open-ocean regions. The in-situ data consist of radiometric measurements obtained from the AERONET-OC sites (Aerosol Robotic Network – Ocean Color, [56]) in different coastal regions and other turbid and productive waters in Muttukadu Lagoon (south-eastern part of India), highly productive waters in Lake Erie (North America) and extremely turbid waters in Yangtze River Estuary (East China Sea). The in-situ data coincident with HICO, Sentinel-2 MSI and MODIS-Aqua observations were used to assess the performance of mPOLYMER and POLYMER algorithms.

Briefly, the HICO sensor (Hyperspectral Imager for the Coastal Ocean) was exclusively designed for characterization of the coastal ocean environments from the space station. After its installation onto the International Space Station (ISS) on September 24, 2009, it provided full spectral coverage data (most sensitive channels from 352 to 1079 nm at 5.7 nm interval) with high signal-to-noise ratios with a spatial resolution of 90 m and a swath of 50 × 200 km. These data are relevant for the assessment of enviornmentally important biogeochemical quantities and geophysical features in coastal oceans, estuaries, rivers and other shallow and inland waters. For this study, several HICO L1B data for the period 2009-2014 were downloaded from the NASA's Ocean Color website, which is maintained by Ocean Biology Processing Group (OBPG) at the NASA's Goddard Space Flight Centre [57] [34,35,42,48].

The Sentinel-2 is a constellation of two identical sun-synchronous polar-orbiting satellites (Sentinel 2A and 2B) and carries the enhanced broad swath high-resolution multispectral instrument (MSI). The MSI has 13 spectral bands in the visible-SWIR region with different spatial resolutions of 10-60 nm, a swath width of 290 km, and a revisit time of about 5 days, continuously delivering the exceptionally useful information for coastal and inland environments at a regional scale. These data were downloaded from the Copernicus Open Access Hub [58] managed by the European Space Agency (ESA) [43].

The MODIS–Aqua Level 1A data, with a 1 km pixel resolution at nadir, were obtained from the NASA Goddard Space Flight Centre [59]. To ensure the accuracy and reliability, these data underwent a comprehensive calibration process involving radiometric and geometric adjustments. Following this meticulous calibration, the data were further scaled to Level 1C products, which represent the top-of-atmosphere total radiances/reflectances.The calibration and scaling procedures were integral for refining the accuracy of the data, laying a foundation for the reliable subsequent analysis The processed satellite/space-borne data, now in Level 1C format, were subsequently converted to Level 2 using the default POLYMER and mPOLYMER algorithms. These algorithms are essential for the retrieval of the desired products for further scientific investigations [36–38].

The performance of mPOLYMER algorithm was assessed by comparison of its retrieved normalized water-leaving radiances (${L_{wn}}$) from HICO data with AERONET-OC data [60] and POLYMER results. The HICO L1B scenes corresponding to the AERONET-OC measurements and Muttukadu Lagoon in-situ data were processed using POLYMER and mPOLYMER algorithms. The ${L_{wn}}$ match-ups of four different field campaigns in productive Muttukadu Lagoon waters provided important results on the disparity between POLYMER and mPOLYMER algorithms. These results were further substantiated by multispectral MSI ${L_{wn}}$ data from Baltic Sea waters and MODIS-Aqua ${L_{wn}}$ from Arabian Sea waters. Figure 1 shows a location map of in-situ measurements at the AERONET-OC and other regional sites and satellite/space-borne observations provided by the HICO, MSI and MODIS-Aqua sensors [38].

 

Fig. 1. Geographical locations of the global and regional in-situ datasets: AERONET-OC and Muttukadu Lagoon/Coastal waters on the coast of the Bay of Bengal.

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3. Methodology

The original POLYMER atmospheric correction algorithm operates on the basis of i) a spectral matching method that models spectral reflectance of the atmosphere and sun glint through the polynomial functions and ii) an in-water model that estimates water-leaving reflectance from the top-of-atmospheric signal [9]. It begins converting the top-of-atmospheric radiance (${L_{TOA}}$) to the reflectance (${\rho _{TOA}}$) as follows,

Further, ${\rho _{TOA}}(\mathrm{\lambda } )$ can be decomposed into several components as

The goal of atmospheric correction is to accurately estimate ${\rho _{wn}}(\mathrm{\lambda } )$ from ${\rho _{TOA}}(\mathrm{\lambda } )$ (Eq. (4)), which necessitates the accurate estimations of the atmospheric and ocean surface components. In this process, the ozone optical thickness ${t_{oz}}(\mathrm{\lambda } )$ is calculated from

The sun glint reflectance is expressed as

Now, the expression in Eq. (4) can be re-written as

Replacing the first three terms. (right side) in Eq. (7) with ${\rho _{atm}}$ gives

Unlike the traditional atmospheric correction algorithms that use LUTs to estimate the aerosol contributions, the POLYMER algorithm simplifies the characterization of atmospheric contributions through the polynomial function of wavelength using

Substituting the polynomial function Eq. (10) in Eq. (8) gives

These five parameters (i.e., ${c_0}$, ${c_1}$, ${c_2}$, Chl, and b_bNC) in Eq. (12) were generated with the best spectral fit functions based on spectral matching optimization using a simplex approach [38].

Consequently, ${\rho _{wn}}$ was calculated from the recovered parameters (${c_0}$, ${c_1}$, ${c_2}$) using

The parameter x. in Eq. (9) was set to -1 in the original POLYMER algorithm, but this value often less accurately estimates the aerosol contribution. Moreover, the POLYMER algorithm uses the pre-determine.ynomial function to model the bulk contribution of the atmosphere (determined by the multiple terms of ${\rho _{atm}}(\mathrm{\lambda } )$ specified in Eq. (10), instead of estimating the individual component of glint, aerosols and Rayleigh-aerosol coupling terms. Finally, a least square fitting of the observations was used to determine the polynomial coefficients ${c_0}$, ${c_1}$ and ${c_2}$.

Since the original POLYMER aorithm does not account for significant NIR contributions in optically complex coastal and inland water bodies (which pose a major challenge in the atmospheric correction process), it was necessary to calculate aerosol reflectance using a practical approach. For the mPOLYMER algorithm, we used a combination of two approaches - UVNIR-ex and SSP (Fig. 2) to estimate the aerosol contribution from hyperspectral and multispectral data (Singh and Shanmugam, 2014 and 2019).

 

Fig. 2. Flowchart of the atmospheric correction scheme (Singh et al., 2019) used to estimate the aerosol reflectance. The specific bands used in this scheme are denoted by: V – Violet (415 nm), B – Blue (490 nm), G – Green (536 nm), R – Red (667 nm), F – Fluorescence (684 nm) and N – Near-infrared (747 nm).

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The aerosol radiance was estimated by assessing the UV, visible and NIR water contributions in coastal and inland waters using the dimensionless spectral shape parameter k derived from the Rayleigh-corrected radiance ratios and an independent extrapolation method (Singh and Shanmugam, 2014 and 2019). According their work, the aerosol reflectance is expressed as

Thus, the expressions in Eqs. (12) and (13) can be re-written as

Utilizing the simplex method [62], the optimal values for the five parameters (${c_0}$, ${c_1}$, ${c_2}$ and $Chl,{b_{bNC}}$) can be determined by achieving the best spectral fit of ${\rho ^{\prime}_t}(\mathrm{\lambda } )$ through a spectral matching optimization.

The ${\rho _{wn}}(\mathrm{\lambda } )$ product is then obtained from

From the retrieved parameters (${c_0}$, ${c_1}$, ${c_2}$) and (${\rho _a}$, ${\rho _r}$), ${L_{wn}}(\mathrm{\lambda } )$ is calculated as

The retrieved ${\rho _w}(\mathrm{\lambda } )$ are normized to the nominal wavelength and bidirectional effects (BRDF) (for water-leaving reflectance (${\rho _{wn}}(\mathrm{\lambda } )$) to obtain the fully normalized water-leaving reflectance (Fig. 3). This quantity is corrected for the BRDF effects. Finally, the normalized water-leaving radiance are derived from the POLYMER and mPOLYMER normalized water reflectance using the Sun-Earth disn corrected extra-terrestrial solar irradiance (${F_0}(\mathrm{\lambda } )$) and $\pi $ value. This calculation transforms the reflectance into the radiance, considering solar energy and geometry.

 

Fig. 3. Flowchart of the spectral matching scheme used in the mPOLYMER algorithm.

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4. Performance assessment

To quantitatively assess the performance of POLIMER and mPOLYMER algorithms, we used the global statistical matrices such as Mean Relative Error (MRE), Root Mean Square Error (RMSE), Bias, Correlation Coefficient (R²), Slope and Intercept. These matrices were calculated from the in-situ (${X_{meas}}$) a satellite-retrieved (${X_{sat}}$ ) water color data products. The MRE, RMSE, and Bias are defined as follows,

5. Results and discussion

The current methodology is built on the same underlying principle of the POLYMER atmospheric correction algorithm toetrieve the normalized water-leaving radiance (${L_{wn}}$) from satellite data in sun-glint contaminated regions. This section presents the application and validation of mPOLYMER algorithm using HICO, MODIS and MSI data and in-situ data (AERONET-OC and other regional data) in optically complex coastal and inland waters (including dense algal blooms). In addition, the mPOLYMER-retrieved ${L_{wn}}$ products are compared with the POLYMER ${L_{wn}}$ products using in-situ data. Several satellite images of extremely turbid and productive waters within coastal and inland environments are also processed to report the relative performance of these algorithms and examine the applicability of mPOLYMER algorithm under various atmospheric and water conditions.

To assess the performance of mPOLYMER algorithm, the matchup data were generated from the HICO scenes and the coincident AERONET-OC measurements in turbid and phytoplankton-dominated waters (at stations MVCO (41°N, 70°W), LISCO (43°N, 70°W), WaveCIS_site_CSI_6 (28°N, 90°W), Gloria (44°N, 29°E) and Venice (45°N, 12°E). Despite a relatively small number of samples used for this validation (N = 49), these in-situ measurements represent clear to turbid waters. The validation was conducted over the shorter wavelengths (412, 443, 490, 555, 660 and 680 nm, which are closer to the HICO bands) due to the noise issues at the longer wavelengths.

The results showed that the POLYMER algorithm retrieved inaccurate ${L_{wn}}$ values due to the underestimated or overestimated ${L_{atm}}$ values (Figs. 4 and 5). The deviation between the satellite-retrieved and in-situ measured ${L_{wn}}$ values is more pronounced in the blue-green wavelengths, which are used to estimate phytoplankton pigment concentrations. In contrast, the mPOLYMER algorithm retrieved ${L_{atm}}$ more accurately, resulting the spectrally comparable results (in terms of shape and magnitude) with in-situ ${L_{wn}}$ data in diverse turbid waters under different atmospheric conditions. The scatterplots also show good agreement between the HICO-retrieved ${L_{wn}}$ and in-situ ${L_{wn}}$ spectra for the mPOLYMER algorithm (Fig. 4(d) and (e)). The large deviation of ${L_{wn}}$ for the original POLYMER algorithm indicates that the water color products generated from these inaccurate ${L_{wn}}$ data would be severally biased in coastal and inland waters and that would affect water color work and water management programs.

 

Fig. 4. Spectral plots of the ${L_{wn}}$ obtained from the in-situ measurements (AERONET-OC) (a), original POLYMER (b), and mPOLYMER (c) algorithms. (d and e) Comparison of the retrieved ${L_{wn}}$ from the original POLYMER and mPOLYMER algorithms with AERONET-OC data from several coastal and ocean sites such as Gloria (4 points), Lucinda (3 points), LISCO (5 points), MVCO (4 points) and Venice (33 points). The black line represents the 1:1 line. Number of observations, N = 49.

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Fig. 5. Comparison of the HICO ${L_{wn}}$. spectra derived from the POLYMER and mPOLYMER algorithms with AERONET-OC in-situ data at the representative AERONET-OC sites.

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Table 1 shows the validation results of HICO-retrieved ${L_{wn}}$ at 412, 443, 490, 555, 660, and 680 nm from the POLYMER and mPOLYMER algorithms. Because the POLYMER algorithm yielded the inaccurate ${L_{wn}}$ retrieval, the statistical analysis showed high errors and low slope and correlation coefficient values for the HICO-AERONET-OC matchup data (MRE 72%, 59%, 43%, 44.5% and 49% at 412, 440, 553, 668 and 709 nm respectively; other values are given in Table 2). These MRE values are notably reduced to 58%, 45%, 34%, 27.6% and 24% at 412, 440, 553, 668 and 709 nm respectively for the mPOLYMER algorithm. The averaged bias, RMSE, R², slope and intercept values are better for the mPOLYMER algorithm than for the original POLYMER algorithm. The lower performance of the original POLYMER algorithm may be by its inaccurate estimates of bulk atmospheric contribution instead of the separate aerosol component.

Table 1. Statistical results obtained from HICO-AERONET-OC matchup data for the POLYMER and mPOLYMER algorithms (denoted as P and mP, respectively).

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Table 2. Statistical results derived for the HICO-In-situ ${{\boldsymbol L}_{{\boldsymbol{wn}}}}$ products in Muttukadu Lagoon waters using POLYMER and mPOLYMER algorithms.

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In highly productive inland/lagoon waters, the POLYMER algorithm overestimated the atmospheric effects at red and NIR wavelengths and underestimated the atmospheric effects at blue wavelengths (Fig. 6). For these cases, the ratio of the water-leaving radiance to the top-of-atmosphere radiance was found to be low at blue wavelengths due to the increased Rayleigh scattering effects and the aerosol correlation was more uncertain at the red and NIR bands because of the increased water absorption and particle backscattering. Consequently, the POLYMER-retrieved ${L_{wn}}$ were low and increasingly distorted (in shape and magnitude) at longer wavelengths. High spectral distortions and high errors in the retrieved ${L_{wn}}$ are caused by an inaccurate depiction of non-algal/sediment particle backscattering and the lack of consideration of water absorption, fluorescence, CDOM, and non-algal particles over the red and NIR wavelengths.

 

Fig. 6. Spectral plots of the HICO retrieved ${L_{wn}}{\; }$spectra compared with in-situ ${L_{wn}}{\; }$ spectra (left panel) and the corresponding ${L_{atm}}{\; }$spectra (right panel) retrieved from the HICO image of 14 April 2014y POLYMER and mPOLYMER algorithms in Muttukadu Lagoon water.

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5.1 Satellite validation in turbid productive waters

To assess the performance of mPOLYMER algorithm under different water and atmospheric conditions, four HICO images were acquired over the Muttukadu Lagoon during 22 November 2013, 16 December 2013, 22 March 2014, and 14 April 2014 (Figs. 6 and 7). The Muttukadu Lagoon (bounded by latitude and longitude 12.77° N, 80.30° E) is a shallow water lagoon (extending up to several kilometers along the channel and varying from 100 m to 1050 m across the channel). In winter, the Muttukadu Lagoon is greatly influenced by tidal water, northeast monsoon effects on the coastal circulation, and erosion of sandbank at its mouth. Significant tidal incursions in the lagoon alters the surface salinity during this period. Accumulation of municipal waste and surface runoff materials are the main factors causing dense algal blooms (cyanobacterial Microcystis), which make atmospheric correction of satellite data difficult and eventually cause negative or highly underestimated water-leaving radiances across the visible wavelengths, particularly in the red-NIR wavelengths in case of the POLYMER algorithm (e.g., when Chl = 150–600 mg m^-3, TSS = 5–10 g m^-3, a_CDOM (412) = 3–10 m^-1).

 

Fig. 7. Spectral plots of the in-situ ${L_{wn}}$ values (a) and retrieved ${L_{wn}}$ values (b and c) from the HICO images on 22 November 2013, 16 December 2013, 22 March 2014 and 14 April 2014. (d and e) Scatterplots of the HICO retrieved ${L_{wn}}$ values by POLYMER and mPOLYMER algorithms versus the in-situ measurements from Muttukadu Lagoon water. Number of observations, N = 17.

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Figure 8 displays the true color composite image and satellite derived ${L_{atm}}$ and ${L_{wn}}$ products from HICO data in Muttukadu Lagoon waters on 14 April 2014. Notice the significant optical variability across the lagoon, with bright features in the southern part of the catchment characterized by relatively strong backscattering (suspended sediments) in the green wavelengths and dark green features in northern channels characterized by strong backscattering in the red and NIR wavelengths (algal blooms).

 

Fig. 8. The HICO RGB true color image composites generated from the total radiances and normalized water-leaving radiances using R-G-B = 645 nm – 553 nm – 467 nm for the Muttukadu Lagoon on 14 April 2014. Right panels: Spectral plots of ${L_{wn}}$ and ${L_{atm}}$ for the POLYMER and mPOLYMER algorithms.

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The performance of the POLYMER and mPOLYMER algorithms was further assessed by comparing the HICO retrieved ${L_{atm}}$ and ${L_{wn}}$ spectra at different sampling stations affected by dense algal blooms (Figs. 6 –9). Consistent with our in-situ measurement data, these turbid productive waters lowered the ${L_{wn}}$ signal in the blue bands due to the increased absorption by chlorophyll and other constituents and increased the ${L_{wn}}$ signal in the green bands due to high backscattering by the water constituents. The ${L_{wn}}$ spectra exhibit a trough at 620 nm and 675 nm due to the absorption by phycocyanin and chlorophyll pigments, a sharp peak around 680-685 nm due to the chlorophyll fluorescence and the combined action of pigment backscattering and pure water absorption as well as the increased pigment absorption at the red wavelengths (which caused the red-edge position of the radiance peak shifting to the longer wavelengths). The spectral plots of ${L_{atm}}$ and ${L_{wn}}$ from HICO data of 14 April 2014, clearly showed the overestimation of ${L_{wn}}$ in the blue wavelengths, underestimation of ${L_{wn}}$ in the green wavelengths, and improbable negative ${L_{wn}}$ values in the NIR wavelengths due to the higher amounts of algal bloom (150–600 mg m^-3). Such large deviations could be attributed to the inaccurate estimates of ${L_{atm}}$ by the POLYMER algorithm. The erroneous ${L_{atm}}$ spectra clearly indicate the inability of the POLYMER algorithm to account for the NIR water contributions caused by dense algal blooms in productive inland and coastal waters.

 

Fig. 9. The true color composite and corresponding products of ${L_{atm}}$(only shown at 443 nm for brevity), ${L_{wn}}$ (410, 553, 668, and 748 nm) and chlorophyll concentration derived from HICO data (9 September 2013) for the Yangtze River Estuary using the POLYMER and mPOLYMER algorithms.

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The negative ${L_{wn}}$ retrievals are caused by the errors in estimating the aerosol contribution and extrapolating it to the shorter wavelengths and by the adjacency effects in some cases. The statistical results demonstrate that the visible band-averaged MRE = 0.41, RMSE = 0.45 and R²= 0.836 and NIR MRE = 0.24, RMSE = 0.60 and R²= 0.839 for the mPOLYMER algorithm and MRE = 0.54, RMSE = 0.77 and R²= 0.450 and NIR MRE = 0.49, RMSE = 1.38 and R²= 0.628 for the POLYMER algorithm (Table 2). In the presence of dense algal blooms, the ${L_{wn}}$ features are more well pronounced and much higher at the NIR wavelengths. Because of the lack of practical approaches to account for such high NIR features, the original POLYMER algorithm performed very poorly in estimating ${L_{atm}}$. In contrast, the mPOLYMER algorithm proved its efficiency over the POLYMER algorithm in terms of estimating ${L_{atm}}$ algorithm accurately retrieved ${L_{wn}}$ based on our in-situ data. In comparison to the traditional water color sensors, HICO's high spatial resolution allowed for a better delineation of the spatial distribution of the algal blooms in Muttukadu Lagoon waters.

The relative performance these two algorithms was further assessed in turbid waters of the East China Sea (31.15° N, 122. 55° E, which covers both open-ocean and river-influenced waters) using HICO imagery on 6 July 2010. Due to the high suspended sediment inputs from the Yangtze River, the HICO imagery exhibited great spatial variability in the observed water-leaving radiances (brown and bright features represent the sediment-laden waters due to strong radiance in the green-NIR bands and weak radiance in the blue bands).

To understand the influence of these waters on the total and retrieved radiances as well as on the algorithms’ performance, spectral and spatial products of the ${L_{atm}}$ and POLYMER/ mPOLYMER retrieved ${L_{wn}}$ are shown in Fig. 9 (spectra were extracted from the pixels on a transect line running from highly turbid to low turbid waters). It is evident that the POLYMER algorithm underestimated ${L_{wn}}$ across the entire visible bands, with large discrepancies in the red/NIR and blue bands due to high suspended sediment concentrations. In contrast, the mPOLYMER retrieved ${L_{wn}}$ spectra are more realistic and closely consistent with the previously reported in-situ data in high turbid Yangtze River estuarine waters. The underestimated ${L_{wn}}$ by POLYMER algorithm is the result of the overestimated atmospheric radiances due to the inaccurate estimates of the bulk atmospheric contributions.

The mPOLYMER algorithm was also extended and tested on a number of HICO scenes from the various regions. Figure 10 depicts similar hyperspectral results for the Lake Erie (42.2° N, -81.2° W), which included a toxic bright green cyanobacteria Microcystis bloom (similar to the one reported in the Muttukadu Lagoon) across its western basin on September 3, 2011. The toxic cyanobacterial cells formed patches due to runoff pollution within a period of two-three weeks. Due to the increasing concentration of pigments, the POLYMER algorithm retrieved high ${L_{wn}}$ values in blue bands and low ${L_{wn}}$ values (including negative radiance) in red-NIR bands. In contrast, the mPOLYMER algorithm was robust in terms of producing ${L_{wn}}$ having the same shape and magnitude reported in the previous studies [35].

 

Fig. 10. The HICO-derived images at three key wavelengths from the POLYMER and mPOLYMER algorithms for the Lake Erie on 3 September 2011. Right panels: Spectral plots of ${L_{wn}}$ and atmospheric radiance (${L_{atm}}$) from the POLYMER and mPOLYMER algorithms.

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5.2 mPOLYMER performance analysis using multispectral data

The applicability of mPOLYMER algorithm was examined using multispectral sensor (MODIS-Aqua and MSI) data from two regional seas with dense algal-blooms (i.e., Baltic Sea and Arabian Sea). On 7 August 2015, the MSI sensor observed the spatially intense cyanobacteria bloom in Baltic Sea waters (56.27° N, 20.19° E). This intracontinental complex marginal sea ecosystem is strongly influenced by human activities, drainage waters and terrestrial substances with high amounts of nitrogen and phosphorus wastes from the border countries. In the midst of summer, the observed area experienced a wide spread and potentially hazardous cyanobacterial bloom in coastal and open sea waters which exhibited high Chl concentrations as shown in Fig. 11 (mPOLYMER-based ABI-Chl image product). The mPOLYMER-${L_{wn}}$ products captured streaks, eddies and whirls of the bloom features. In this case of blooms, the ${L_{wn}}$ spectra of lower and higher density blooms retrieved by POLYMER and mPOLYMER algorithms were compared in the context of their detection, characterization, and quantification using the spectral shape algorithms.

 

Fig. 11. The true color composite and corresponding products of the ${L_{atm}}$(only shown at 560 nm for brevity), ${L_{wn}}$ (443, 560, 665, and 740 nm) and chlorophyll concentration derived from Sentinel MSI data (7 August 2015) for the Baltic Sea using POLYMER and mPOLYMER algorithms.

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The mPOLYMER-retrieved ${L_{wn}}$ spectra clearly show the amplitude variation of the fluorescence peak around 682 nm backscattered radiance variation at the longer wavelengths due to the lower and higher density blooms (right panels in Fig. 11), while exhibiting strong signals in the green bands and weak signals in the blue bands consistent with the earlier measurement data from Baltic Sea. The POLYMER-retrieved ${L_{wn}}$ spectra are suppressed over the visible and NIR bands and show physically improbable negative values at the red and NIR bands with increasing bloom concentrations. Such data must be discorded for any water color work on the spectral characterization and quantification of algal blooms. Thus, the mPOLYMER algorithm proved its ability to produce accurate ${L_{wn}}$ retrievals under different water types and atmospheric conditions.

The Arabian Sea is a similar case of intense algal blooms, as previously reported by Gomes et al. (2008) and Singh and Shanmugam (2014) and as seen in the MODIS-Aqua products on 18 February 2010 (Fig. 12). The colour composite image generated from the TOA radiances (and chlorophyll image) show strong sun glints, aerosols and intricate patterns of Noctiluca scintillans blooms in coastal and offshore waters in the northern Arabian sea (Fig. 12). The observed aerosols were mineral dust particles blown up by wind and transported across the Arabian Sea during this period. The dense algal blooms were caused by nutrient-rich upwelled waters along the western coast of the Arabian Sea and transported and concentrated into the northern Arabian Sea by eddies and surface currents. Similar to land vegetation and inland-water blooms, Noctiluca scintillans blooms are characterized by weaker radiances in blue bands and stronger radiances in green and NIR bands, which pose a major challenge for the retrieval of ${L_{wn}}$ from satellite data using the standard atmospheric correction algorithms (Singh and Shanmugam, 2014). The POLYMER-retrieved ${L_{wn}}$ were also noticeably affected by sediment-laden waters in the Gulfs of Kutch and Cambay on the eastern coast of the Arabian Sea and seriously reduced in the red and NIR bands due to dense algal blooms in the northern/central Arabian Sea (Fig. 12, right panels). In contrast, the mPOLYMER algorithm yielded more accurate ${L_{wn}}$ retrievals in sediment-laden waters in the Gulfs of Kutch and Cambay and produced ${L_{wn}}$ spectral forms (shape and magnitude) comparable to those reported in earlier studies (Singh and Shanmugam, 2014). Overall, the POLYMER algorithm suffers from its inability to appropriately treat these complex waters (algal blooms and suspended sediments) and extreme atmospheric/sea surface conditions (mineral aerosols, cloud-aerosol interactions, cloud-induced glints and sun glint) to retrieve the ${L_{wn}}$ products from MODIS-Aqua data.

 

Fig. 12. The MODIS–Aqua glint affected image of the Arabian Sea on 18 February 2010 and the corresponding chlorophyll-a and ${L_{wn}}$ products generated using the POLYMER and mPOLYMER algorithm (${L_{wn}}$ spectra are shown for sediment-laden waters in the Gulf of Kutch and algal blooms in the northern Arabian Sea).

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6. Summary and conclusion

The atmospheric constituents that are unrelated to the water components contribute around 80-90% of the total radiance recorded by the satellite sensors. Thus, atmospheric correction is critical as it has a significant impact on the precision and accuracy of the retrieved water color products. The atmospheric correction scheme for Case-1 waters was well established in the past decades, but that remains unsatisfactory for Case-2 waters usually found in coastal and inland environments (mainly productive waters with algal blooms and turbid coastal/inland waters with large inputs of suspended sediments). The treatment of Rayleigh, aerosol and sun glint radiances in the atmospheric correction scheme is commonly attributed to the main sources of error in the retrieved water-leaving radiances in such optically complex waters. An alternative approach to STD-AC is based on the assumptions of aerosol spectral shape and in-water bio-optical constraints (i.e., POLYMER). The POLYMER algorithm was originally designed for MERIS to retrieve ${L_{wn}}$ under both optimal and non-optimal (i.e., sun glint, thin clouds) conditions. It performs atmospheric correction in sun-glint affected regions and retrieves the water-leaving radiance products based on the idea that a flexible atmospheric model could incorporate the sun glint signal, despite the fact that it is highly strong and unpredictable signal. This algorithm was used in the absence of aerosol information (i.e., aerosol type, optical thickness and vertical distribution). It uses the polynomial functions to estimate the atmospherically contributed radiance instead of using an explicit aerosol modelling approach to calculate the atmospheric path signal. As a result, the POLYMER products showed discrepancies at red (667 nm) and NIR (869 nm) for Case 2 waters, due to the (backscattering) contribution of inorganic particles, which was not well represented in the POLYMER algorithm. Other factors for the degradation of ${L_{wn}}$ products include the compensation of differences by the spectral-matching scheme at the shorter wavelengths caused by the lack of CDOM and non-algal absorption and ${L_{wn}}$ extrapolation above 700 nm using the similarity spectrum.

The proposed mPOLYMER algorithm estimates the atmospherically-contributed radiances using the new aerosol estimation scheme and retrieves consistent ${L_{wn}}$ products from satellite data. The resultant mPOLYMER ${L_{wn}}$ products were compared with concurrent in-situ ${L_{wn}}$ measurements and POLYMER ${L_{wn}}$ products. In general, our results showed that the performance of POLYMER algorithm was deteriorating with the increasing radiance contribution of algal blooms and sediment plumes in the NIR bands. Multiple tests were also conducted using hyperspectral (HICO) and multispectral (MODIS-Aqua and MSI) data obtained across different coastal and inland water zones to provide a quantitative assessment of the applied algorithms. For this analysis, several satellite scenes were obtained corresponding to the in-situ measurements (AERONET-OC) from different coastal waters with sediment plumes and algal blooms. Several satellite scenes were also obtained under diverse atmospheric conditions. The validion analysis based on the satellite-retrieved ${L_{wn}}$ by POLYMER and mPOLYMER algorithms and in situ measurement data showed that the relative errors (MRE and RMSE) in the retrieved ${L_{wn}}$ products varied marginally for the visible bands and drastically for the NIR bands for these algorithms. Overall, the mPOLYMER yielded the lowest errors and highest slope and correlation coefficients for the matchup data. The errors associated with the POLYMER algorithm were increased several folds at the longer wavelength bands, which could be attributed to the insufficient bio-optical model or incorrect estimation of atmospherically-contributed radiances due to the aerosols in the POLYMER algorithm.

In turbid productive waters (Muttukadu Lagoon), the mPOLYMER algorithm was more robust in reproducing the normalized water-leaving radiances (in terms of spectral shape and magnitude) and chlorophyll concentration. The POLYMER algorithm produced negative or low ${L_{wn}}$ in the Red-NIR bands due to high chlorophyll concentration and poor atmospheric correction (aerosol radiance). The results (based on our in-situ ${L_{wn}}$ and satellite-derived ${L_{wn}}$ data products) revealed that the relative errors (MRE and RMSE) in ${L_{wn}}$ retrievals were minimal in the visible bands but increased drastically in the NIR bands. When testing the applicability and consistency of the POLYMER and mPOLYMER algorithms on two HICO scenes from highly turbid (sediment-laden) locations in the Yangtze River Estuary (YRE) and algal bloom waters in Lake Erie, it was found that the POLYMER algorithm produced highly degraded/lower and negative (for some cases) ${L_{wn}}$ retrievals in the Red-NIR bands for the Yangtze River Estuary (sediment-laden) and Lake Erie (algal bloom) waters. For these sediment-laden and bloom waters, the mPOLYMER algorithm proved its excellent performance in reproducing the consistent ${L_{wn}}$ products.

Finally, the mPOLYMER algorithm was applied to several MSI and MODIS-Aqua images acquired under different atmospheric conditions and water types. In bloom-dominated waters of Lake Erie and Baltic Sea, the mPOLYMER algorithm retrieved ${L_{wn}}$ more accurately than the POLYMER algorithm. The accurate calculation of aerosol radiance enabled us to estimate the atmospheric radiances and retrieve the water leaving radiances (${L_{wn}}$), as corroborated by the quantitative and qualitative results presented in this study. The satellite derived mPOLYMER-${L_{wn}}$ products acrately captured all minor and major absorption and fluorescence features in the visible bands as well as the backscattering features in the NIR bands caused by algal blooms (in-water and floating) and suspended sediments in inland and coastal waters. To further test the algorithm's performance, the MODIS-Aqua image of the Arabian Sea taken on 18 February 2010 showed the spatially broad and intense Noctilica blooms in the Gulf of Oman and central/northern Arabian Sea. The mPOLYMER algorithm produced good results of ${L_{wn}}$ and chlorophyll products in different complex water column conditions (such as dense floating blooms, high turbidity and high sun glint) than the POLYMER algorithm.

The validation datasets utilized this study covered coastal, inland, and open ocean waters, and revealed a considerable overestimation or underestimation of atmospheric radiances as the wavelengths got shorter and longer. This resulted in erroneous or even negative/negligible ${L_{wn}}$ in the red and NIR bands. In conclusion, the mPOLYMER algorithm is an important tool for estimating atmospheric radiances and normalized water-leaving radiances in complex coastal and inland waters.