1. Introduction

A. Ocean-Color Retrievals in the Coastal Areas

Ocean-color retrieval is a challenge in coastal areas, but it is a powerful tool for coastal surveys. Sea-surface reflection, including sunglint and whitecap, cause significant errors in ocean-color estimation [1–3]. Sea-surface reflection can be estimated from a statistic scheme, such as that presented by Cox and Munk [4], using low-resolution wind-speed data from a microwave radiometer, a scatterometer, or objective analysis data [5,6]. The correction based on the wind-speed data is problematic in coastal areas, however, because of fine variations in the distribution of surface reflection due to variable winds, fetch length, and air-sea stability caused by the fine structure of the coastal geography. Several studies have investigated high–spatial resolution sunglint correction using hyperspectral bands or small-scale glint variations [7,8]. Murakami and Frouin [9] demonstrated the possibility of sunglint (${\rho }_g$) correction by using 500 m resolution near infrared (NIR) and shortwave infrared (SWIR) bands of moderate resolution imaging spectroradiometer (MODIS). Higher (10–30 m) spatial resolution sensors are expected to capture higher resolution spatial structures of ocean-color phenomena, especially in the coastal areas. They, however, have a limited number of spectral bands generally (e.g., without SWIR bands), which prevents the precise estimation of aerosol properties and the distinction between aerosol and sea-surface reflection.

In addition to these sensor limitations, coastal areas present difficulties for ocean-color retrievals (i.e., high NIR reflectance by suspended matter), complex inherent optical properties (IOPs) due to various material inputs from the land, and bottom reflectance in the shallow areas. This explains why the blue–green ratio of remote sensing reflectance ($R_{rs}$), which traditionally is used in the empirical estimation of chlorophyll-a concentration (Chla), does not allow to calculate Chla in most cases of the coastal area (see Table 1 for symbol definitions and units).

Table 1. Symbols and Definitions

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B. New Caledonia Lagoon

The New Caledonia lagoon is a large, almost continuous lagoon ($22177{\mathrm{km}}^2$) lying in the southwestern tropical Pacific from 20°S to 22°S and 166°E to 167°E (Fig. 1). Its heterogeneous bathymetry (25 m as a mean depth) is due to a complex geomorphology with the presence of sedimentary plains and a high proportion of shallow waters and numerous small sand islands [10–12]. It is largely connected to the open ocean along its southern side, but only by narrow passes in its southwestern side. It is an example of a coral reef lagoon system, which are sensitive to anthropogenic (nutrients, mining) perturbations [10,11] as well as to interannual changes linked to the balance between dry El Niño and wet La Niña episodes [13,14], which are amplified in lagoons [12]. The central lagoon is characterized by oligotrophic to mesotrophic waters (yearly average Chla of $0.25\pm 0.01\mathrm{mg}{\mathrm{m}}^{-3}$) [15,16] and exhibits a strong seasonal cycle with higher values in austral winter (July) or austral summer (February) during nitrogen-fixing Trichodesmium blooms [17–20]. Upwelling at the barrier reefs [21] as well as internal waves in the southern part of the lagoon are two major mechanisms of exchange with the sea, which can modify the phytoplanktonic assemblage [22].

 

Fig. 1. New Caledonia lagoon and in situ observation stations used in this study (B50, B03, B08, GD10, Ile aux Canards, M33, G003, and OC1). The background image is the RGB image of $R_{rs}$ at 652, 560, and 463 nm derived from this study.

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Rain also can induce large chlorophyll enrichments in the lagoon [23]. With relatively low river inputs and a low turbidity range ($0.20–16\mathrm{g}{\mathrm{m}}^{-3}$), its trophic state is linked to spatial variations in flushing times [12,16,24]. Similar to “optically complex” Case 2 European waters [25] or coastal bays [26], reflectance in the New Caledonia lagoon can be highly variable [27] as in other tropical environments [28], in the Australian Great Barrier Reef [29], and in tropical estuaries [30] with a high influence of mineral particles from river discharge in bays [31] or colored dissolved organic matter (CDOM) [32]. Additionally, bottom reflectance, which represents a strong component in clear tropical shallow waters, may influence $R_{rs}$ [33–36].

To improve the challenge of remote sensing in coastal environments [37], surface-water IOPs (absorption and backscattering) were measured during several observation campaigns (e.g., coastal stations of Diapalis in 2003, Bissecote, Echolag, Valhybio, and the Valhybio Monthly Survey cruises from 2008 to 2011) in the lagoon and at different seasons [27,38,39]. The bathymetry of the Southern New Caledonia lagoon was compiled [12].

C. ALOS AVNIR-2

Advanced Land Observation Satellite (ALOS) was operated by JAXA from 24 January 2006 to 12 May 2011, and carried the Advanced Visible and Near Infrared Radiometer type 2 (AVNIR-2). AVNIR-2 has four spectral bands (centered at 463, 560, 652, and 821 nm) with a 10 m spatial resolution, a 70 km field of view, and a mechanical pointing function (by moving mirror) along the cross-track direction ($\pm 44\mathrm{deg}$) for effective global land observation. To achieve the ALOS mission objectives (cartography, regional observation, disaster monitoring, resources survey, and technology development) and to expand to quantitative applications, such as determination of vegetation density, coastal water color, and time dependencies, it is important to evaluate, improve, and maintain the radiometric calibration accuracy of AVNIR-2 (the predefined target is absolute error less than 10% [40]). The cross calibration with MODIS indicated that the difference in top of atmosphere (TOA) radiance is less than 3% in the visible bands, and the temporal stability of the radiance is less than 2% per 1000 days [41].

D. Scope of Study

Atmospheric and sea-surface correction and IOP estimation were conducted using the four bands of 30 m images averaged from AVNIR-2 10 m resolution images (see Section 2.A). The linear matrix inversion (LMI) of IOPs [42–44] and atmospheric plus surface reflection correction was simplified to allow the four-band and high–spatial resolution AVNIR-2 retrievals. Influence of the bottom reflectance was reduced by using bathymetry data with a unique spectrum of bottom reflectance. We compared the IOP estimates by different candidate IOP spectra (observed particles plus CDOM absorption [$a_{pg}$] and particle backscattering [$b_{bp}$] spectra) in the LMI scheme. Chla was estimated by two ways, from a statistical relationship with $a_{pg}$, or from the blue–green ratio of $R_{rs}$. For the series of AVNIR2 images available over the New Caledonia lagoon, we validated the derived IOPs ($a_{pg}$ and $b_{bp}$) and Chla using in situ measurements around the AVNIR-2 observation dates.

2. Data and Methods

A. AVNIR-2 Images and Radiance Correction

AVNIR-2 data have 10 m spatial resolution but only 8 bit digital resolution with relatively low gain designed for the land-surface observations. We averaged AVNIR-2 TOA radiance images to a 30 m (0.0003 deg equal latitude–longitude) grid to reduce the sensor noise before the atmospheric correction because the ocean-color signal is much lower than the atmospheric signal in the visible wavelengths.

The AVNIR-2 in-orbit radiometric performance was evaluated through a comparison with Aqua MODIS by the cross-calibration scheme [41]. This scheme uses the TOA reflectance functions of the satellite zenith angle estimated by Aqua MODIS observations within $\pm 16$ days from the AVNIR-2 observation over temporally and spatially stable ground areas. The cross calibration with the Aqua MODIS over the Antarctic snow fields allow us to correct AVNIR-2 bands 1–4 by the correction coefficients shown in Table 2. We calculated the TOA reflectance of standard gas absorption conditions ($\text{column}\text{ozone}=343.8\mathrm{DU}$, $\text{water vapor}=14.19\mathrm{mm}$, and $\text{pressure}=1013.25\mathrm{hPa}$) from the AVNIR-2 radiance observation as shown in Appendix A.

Table 2. AVNIR-2 Bands, Cross-Cal Coefficients, and Gas Abruption Coefficients

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Seventeen clear AVNIR-2 scenes were captured around the target area in the ALOS mission period. The dates were 10 and 27 September in 2006; 12 February, 3 March, 15 May, and 31 July in 2007; 31 October and 17 November in 2008; 3 September and 20 November in 2009; 5 January, 3 February, 21 March, 8 August, and 22 December in 2010; and 24 March and 10 April in 2011. Some scenes (27 September 2006, 12 February 2007, 31 October and 17 November 2008, 20 November 2009, and 5 January 2010) were covered by the sunglint. Match-ups with in situ measurements were obtained (total 15 points) on 3 September 2009 (time difference from the AVNIR-2 observation $\mathrm{\Delta }D=5$ days), 17–18 November 2009 ($\mathrm{\Delta }D=2$ days), and 11 January 2010 ($\mathrm{\Delta }D=6$ days).

B. Simplification of the Atmospheric and Surface Corrections

At each solar and sensor geometry condition, the TOA reflectance ${\rho }_t$, for which gaseous absorption is normalized by standard atmosphere condition, can be described as follows:

The Rayleigh scattering of ${\rho }_r$ and $T$ (at ${\tau }_a=0$) can be estimated by atmospheric radiative transfer simulation. To achieve this, we used Pstar2b [45], which takes into account atmospheric polarization, provided by the National Institute for Environmental Studies (NIES) GOSAT project and the OpenCLASTR project [46–48]. We prepared look-up tables of ${\rho }_r({\lambda }_b)$ (including sea-surface reflection with $\text{wind speed}=0$) and $T$ at each geometric condition.

The Rayleigh-scattering subtracted reflectance (${\rho }_{agw}$) can be described by the following Eq. (2):

The spectral shape of ${\rho }_{ag}$ was improved by a correction factor, $c_{wl}$ ($=0.99$ at band 3 [652 nm] and 1.0 at other bands), which was derived from the atmospheric radiative transfer simulation (the root mean square error of ${\rho }_{ag}$ is 0.004 at 463 nm for the tropospheric, oceanic, and their mixed aerosols in the case of $\text{aerosol optical thickness}=0.3$ and air mass $pl<4$). The $\alpha$ ranged from $-0.5$ to $+0.3$ for the oceanic aerosols and from $-1.8$ to $-1.2$ for the tropospheric aerosols.

The variables about the aerosol and surface reflection, $\alpha$ and ${\rho }_{ag}$(821 nm), could be estimated using the AVNIR-2 data through an iteration with the IOP retrieval described in Section 2.C. The approximation of Eq. (3) enabled quick processing, including the iteration scheme.

C. IOP and Water-Leaving Reflectance Estimation

Most of the IOP algorithms [50] are based on the equation of remote-sensing reflectance below the surface ($r_{rs}$), the total absorption coefficient ($a$), and the backscattering coefficient ($b_b$) proposed by Gordon et al. [51]:

The water-leaving reflectance ${\rho }_w$ in Eq. (1) is simply calculated from the $R_{rs}$:

We used the LMI scheme [42–44] to estimate IOPs. The scheme requires $a_w$, $b_{bw}$, and model spectra, $a_{ph}^{\prime }$, $a_{dg}^{\prime }$ ($\text{absorption of detritus}+\text{CDOM}$), and $b_{bp}^{\prime }$, which is normalized at a specific wavelength (442 nm was used in this study). We used $a_w$ and $b_{bw}$ values from [53,54] weighted by the AVNIR-2 spectral response (shown in Table 3). Wavelength functions of $a_{dg}$ and $b_{bp}$ were as follows:

Table 3. Spectra of ${\mathsf{a}}_{\mathsf{w}}$, ${\mathsf{b}}_{\mathsf{b}\mathsf{w}}$, and ${\mathsf{a}}_{\mathsf{p}\mathsf{h}}$^a

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The inversion process was simplified to use only two IOP parameters, $a_{pg}(\equiv a_p+a_g\equiv a_{ph}+a_{dg})$ and $b_{bp}$, and two AVNIR-2 bands, band 1 (463 nm) and band 2 (560 nm). We set the $a_{pg}^{\prime }$ as follows:

If we have an initial value of $a_{pg0}$ and $b_{bp0}$, ${\rho }_w$ can be calculated by Eqs. (4)–(14). Using the ${\rho }_w$, ${\rho }_{ag}$ at 652 and 821 nm can be calculated using molecular scattering corrected reflectance derived from satellite observation (${\rho }_{agw}$) as follows:

Then, ${\rho }_w$ at 463 and 560 nm are calculated by Eqs. (3) and (15). Using the ${\rho }_w$ at the two visible bands, $a_{pg0}$ and $b_{bp0}$ can be calculated by the LMI [42–44].

The iteration process to derive the final value of $a_{pg0}$ and $b_{bp0}$ is shown in Fig. 2. The first process (a) aims to estimate $\alpha$ except for shallow areas ($\text{bathymetry}<20\mathrm{m}$) where the bottom reflectance can influence $r_{rs}$. The iteration was repeated to find optimal values of $a_{pg0}$ and $b_{bp0}$ by minimizing the difference between $b_{bp0}$ preset in Eq. (11) and $b_{bp0}$ calculated by the inversion matrix. The initial value of $a_{pg0}^{\prime }$ was set to 0.01, which does not affect the final $a_{pg0}$ estimates because $a_{pg}$ is relatively small in the total $a$ in red and NIR wavelengths. The subprocess is repeated until $|a_{pg0}-a_{pg0}^{\prime }|<0.0001$ (practically less than four times in most pixels) with revision of $a_{pg0}$ and the search range of $b_{bp0}(b_{bp0}^{(\max )})$, which is set by ${\rho }_{ag}$ at 821 nm and the extremely high $a_{pg0}=20{\mathrm{m}}^{-1}$. After completing the first process, we smoothed $\alpha$ for each $0.1\mathrm{deg}\times 0.1\mathrm{deg}$ area to reduce the AVNIR-2 sensor noise and extrapolate to the shallow ($<20\mathrm{m}$) areas where we did not estimate $\alpha$ in the first process. The second process (b) derives ${\rho }_{ag}$ $a_{pg}$, $b_{bp}$, and $R_{rs}$ for every 30 m grid using the same equations. We can derive IOPs and $R_{rs}$ at any wavelengths (AVNIR-2 bands at 463 and 560 nm and the wavelengths of the in situ measurements at 442 and 555 nm) using the IOP spectra $a_{pg}{(\lambda )}^{\prime }$ and $b_{bp}{(\lambda )}^{\prime }$ (see Section 2.D).

 

Fig. 2. Processing flow of the IOP and aerosol correction. The operation starts from the asterisk. (a) First flow produces the $\alpha$, which is used in (b) the second flow. After $a_{pg0}$ is converted ($|a_{pg0}-a_{pg0}^{\prime }|<0.0001$, (c) the sea-floor correction is applied.

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D. Chlorophyll-a Estimation

Chla was estimated by regression of $a_{pg}$ (442 nm) and the empirical blue–green ratio was calculated as follows:

The relationship between Chla and $a_{pg}(443\mathrm{nm})$ was derived from $a_{pg}$ and the fluorometric Chla data included in the NASA bio-Optical Marine Algorithm Data set (NOMAD) [55] (Fig. 3). The MODIS OC2M-HI equation developed by the NASA Ocean Biology Processing Group (OBPG) using the NOMAD database [6] was used for the two-channel equation because AVNIR-2 has only two channels in blue and green wavelengths.

 

Fig. 3. Relation between Chla and $a_{pg}$ or blue–green $R_{rs}$ ratio (${\log }_{10}$ base) based on NOMAD [55]. $N$, RMSD, and $r$ indicate sample number, root mean square error of the regression (${\log }_{10}$ scale), and the correlation. a0 and a1 are coefficients of the linear regression, that is, ${\log }_{10}(Chla)=0.9706+1.1835{\log }_{10}(a_{pg})$.

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E. In Situ Bio-Optical Measurements

Field measurements of the two IOPs, the absorption coefficient, $a$, and the backscattering coefficient, $b_b$, were obtained at stations in the southwest part of the lagoon (Fig. 1) during various seasons from 2006 to 2010. The $b_b$ was measured with a Hydroscat-6 profiler (H6: HobiLabs, wavebands ($\lambda$) centered at 442, 488, 510, 550, 620, and 670 nm with a bandwidth of 10 nm for the 442–550 nm bands and 20 nm for the 620 and 670 nm bands) [19,27]. The particulate backscattering coefficient, $b_{bp}(\lambda )$, was calculated by subtracting from $b_b(\lambda )$ the theoretical “pure water spectrum,” $b_{bw}(\lambda )$ (calculated as $b_{bw}(\lambda )=0.5\times b_w(\lambda )$) [51]. The particulate absorption coefficient, $a_p(\lambda )$, was measured with the filter-pad technique [56], using water samples filtered onto $25\mathrm{mm}\mathrm{GF}/\mathrm{F}$ Whatman filters. For pigments, the filters were dipped in 5.4 ml 100% acetone (final concentration 90% acetone taking into account water retention by the filter, e.g., $0.621\pm 0.034\mathrm{ml}$) and ground with the freshly broken end of a glass rod for chlorophyll and phaeopigment extraction [57]. For comparison with the satellite-estimated Chla, we used the sum of Chla and divinyl chlorophyll-a, Chla (in mg ${\mathrm{m}}^{-3}$), as measured by spectrofluorometry, and well correlated with fluorometry in the Caledonian lagoon [15,27].

For the LMI, we prepared the model spectra of $a_{pg}$ and $b_{bp}$ optimized for the New Caledonia in situ samples (six samples of $a_{ph}$ and $a_{dg}$ in 2003, and 112 samples of $b_{bp}$ in 2006–2010). The samples of $a_{ph}$ and $a_{dg}$ were distributed around the lagoon of the southeast New Caledonia but not near bays of the mainland. The spectral shape $a_{dg}^{\prime }$ and $b_{bp}^{\prime }$ (relative values from $\lambda =442\mathrm{nm}$) were modeled by Eqs. (12) and (13), respectively. The model spectra from the averages of the New Caledonia measurements were used as the standard in sensitivity tests.

We tested the sensitivity of different sets of model spectra: (A) $a_{pg}^{\prime }$ and $b_{bp}^{\prime }$ from the New Caledonia measurements (e.g., same as the above); (B) same as (A) but $a_{ph}^{\prime }$ from a picoplankton spectra [58]; (c) same as (A) except for $a_{ph}^{\prime }$ from a microplankton spectra [58]; (D) same as (A) except for $a_{dg}^{\prime }$ with $S=-0.018$; (E) same as (A) except for $b_{bp}^{\prime }$ with $Y=0.0$; and (F) same as (A) except for $b_{bp}^{\prime }$ with $Y=-2.0$ (Fig. 4). These $a_{ph}^{\prime }$ spectra are listed in Table 3.

 

Fig. 4. Model spectra of $a_{pg}$ and $b_{bp}$ used in this study. Models of $a_{pg}$ (A) and $b_{bp}$ ($Y=-1.4$) were set from the New Caledonia measurements. $S$ was defined as $a_{dg}=\exp (S\times (\lambda -442))$ as in Eq. (12), and $Y$ was defined as $b_{bp}={(\lambda /442)}^Y$ in Eq. (13). The spectra for picoplankton (B) and microplankton (C) from [58] were used for comparison. Curves are indicated for different $Y$ slopes for $b_{bp}$ ($Y=0$ and $Y=-2$, see also Table 4). Bars show standard deviation of the in situ measurements.

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F. Correction of Seafloor Reflection

The $R_{rs}$ and IOP estimation might be influenced by bottom reflectance especially in low absorption and shallow areas, such as site G003 near the barrier reef (11 m depth, bottom composed of white sands). In shallow areas, $r_{rs}$ was approximated by the following equation (from Lee et al. [59]):

Because ${\rho }_b$ is unknown at each image grid in this study, we used a ${\rho }_b$ spectrum of coral sand shown by Fig. 6 of [60] (${\rho }_b=0.33$ and 0.47 at 442 and 555 nm, respectively). The similar ${\rho }_b$ spectra of the sandy sea bottom were reported around the coral reef system by [61,62]. We use $H$ compiled in Ouillon et al. [12] (Fig. 5). Attenuation coefficient, $\kappa (\lambda )$, is iteratively calculated through the IOP estimation described in Section 2.C by changing $H$ from enough deep depth (1000 m) to the actual sea-floor depth gradually. Such an approach has been used to retrieve bathymetry [36].

 

Fig. 5. Bathymetry in the target area [12]. Deep areas ($>60\mathrm{m}$) are filled by black.

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G. MODIS Ocean-Color Products

NASA OBPG Aqua MODIS products, $R_{rs}$ at 443 nm, $R_{rs}$ at 555 nm, and Chla (processing version 2009.1) [6], were used to compare our results. The global accuracies of the MODIS data set, reported as the median absolute percent differences of normalized water-leaving radiance ($L_{wn}$) at 443 nm, $L_{wn}$ at 555 nm, and Chla from global in situ observations, are 18%, 17%, and 37%, respectively [6,63]. We selected clear MODIS scenes $\pm 1$ day from AVNIR-2 observations or between the AVNIR-2 and in situ observation dates.

3. Results

A. ${\mathsf{R}}_{\mathsf{r}\mathsf{s}}$ and ${\mathsf{\rho }}_{\mathsf{a}\mathsf{g}}$

Figure 6 shows results of the ${\rho }_{agw}$ (463 nm), ${\rho }_{ag}$ (463 nm), $\alpha$, ${\rho }_w$ (463 nm) without bottom correction, and ${\rho }_w$ (463 nm) with bottom correction on 17 November 2008 and 3 September 2009. On 17 November 2008, the area was covered by sunglint [brighter on the right side in Figs. 6(a) and 6(b)]. In Fig. 6(b), ${\rho }_{ag}$ showed small-scale structures of the surface reflection caused by the winds and geographical features. In Figs. 6(c) and 6(h), $\alpha$ was smoothed in each $0.1\mathrm{deg}\times 0.1\mathrm{deg}$ grid after the first process [Fig. 2(a)]. The estimated ${\rho }_w$ [Fig. 6(d)] was smooth offshore and showed fine structures inside the lagoon. On 3 September 2009, aerosol with small clouds extended northwest to southeast over the area [Fig. 6(g)]. The aerosol pattern was removed effectively in the ${\rho }_w$ image [Fig. 6(i)] by subtracting ${\rho }_{ag}$ [Fig. 6(g)] from ${\rho }_{agw}$ [Fig. 6(f)]. High reflectance areas remained inside the lagoon with a dark area along the outside of the barrier reef.

 

Fig. 6. Examples of AVNIR-2-derived ${\rho }_{agw}$, ${\rho }_{ag}$, $\alpha$, ${\rho }_w$ without bottom correction, and ${\rho }_w$ at 463 nm with bottom correction (a)–(e) for 17 November 2008 and (f)–(j) for 3 September 2009 [using model (A) in Table 4]. The field measurement sites are shown in each panel.

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The comparison between AVNIR $R_{rs}$ and MODIS $R_{rs}$ at 442 (or 443 nm) and 555 nm is shown in Fig. 7. AVNIR-2 $R_{rs}$ at 555 nm appears slightly higher, but the results are closely correlated (0.77 and 0.54 at 442 and 555 nm, respectively, and the root mean square difference [RMSD] was about 40% and 63% of the average $R_{rs}$ for AVNIR-2 and MODIS, respectively) except for some samples at the shallow stations (e.g., B50 and B03). An outlier at station G003 in Fig. 7(a) (AVNIR-2 $R_{rs}$ at 442 nm is about 0.03) seemed to be influenced by the cloud edge in the AVNIR-2 image on 31 July 2007.

 

Fig. 7. Comparison between AVNIR-2 $Rrs$ at 442 nm and MODIS $Rrs$ at (a) 443 nm and (b) 555 nm for 44 samples. The markers distinguish between the different observation stations. The horizontal bars show the standard deviation of the multiple MODIS scenes.

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Figures 6(e) and 6(j) show the AVNIR-2 ${\rho }_w$ at 463 nm with the correction of bottom reflectance. The correction decreases ${\rho }_w$ inside of the lagoon (e.g., at stations M33 and G003) and reduces the pattern of the bathymetry (Fig. 5) in most areas in the ${\rho }_w$ images. It seems, however, to cause overcorrection in some areas (e.g., around the islands and the barrier reef).

B. ${\mathsf{a}}_{\mathsf{p}\mathsf{g}}$ and ${\mathsf{b}}_{\mathsf{b}\mathsf{p}}$

Figures 8(a) and 8(b) shows $a_{pg}$ at 442 nm and $b_{bp}$ at 555 nm without the bottom correction (using model spectra (A) in Table 4). $a_{pg}$ was high along the coast and in bays near the main land. On the other hand, $b_{bp}$ was high inside the lagoon especially at shallow bottom areas (e.g., G003). Scatter plots between the in situ ($a_p\times 1.52$) and the AVNIR-2 $a_{pg}$ and $b_{bp}$ estimates are shown in Figs. 9(a) and 9(b). They show that AVNIR-2 $a_{pg}$ is well correlated with in situ values for $a_{pg}$ [$r=0.91$ in Fig. 9(a)] even though the factor 1.52 may vary with changing proportions of $a_p$ or $a_g$ in $a_{pg}=a_p+a_g$. AVNIR-2 $b_{bp}$ showed a high correlation coefficient (about 0.94 at 555 nm), but some values of $b_{bp}$ were higher than the in situ $b_{bp}$. The overestimated samples were found in shallow areas (3.6, 6, 5, and 11 m at stations B50, B03, Ile aux Canards, and G003, respectively).

 

Fig. 8. AVNIR-2 estimation of (a) $a_{pg}$ at 442 nm and (b) $b_{bp}$ at 555 nm on 3 September 2009 [using model spectra (A) in Table 4 and no correction of the bottom reflection]. (c) and (d) are same as (a) and (b) except applying the correction of the bottom reflection. Markers show in situ observation stations.

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Fig. 9. Scatter diagrams of (a) AVNIR-2 $a_{pg}$ and in situ $a_p$ ($\times 1.52$) at 442 nm, (b) $b_{bp}$ at 555 nm from model (A) in Table 4. (c) and (d) are same as (a) and (b) except applying the correction of the bottom reflection. $N$, sample number; $r$, correlation coefficient; bias, bias of AVNIR-2 from in situ; RMSD, root mean square difference; xavg, the average of in situ data (in ${\mathrm{m}}^{-1}$). (e)–(h) are same as (a)–(d) except they are derived from model (D).

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Table 4. Comparison between in situ and AVNIR-2 IOP Estimates Using Different Sets of IOP Spectra^a

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Figures 8(c) and 8(d) show $a_{pg}$ and $b_{bp}$ with the bottom reflectance correction on 3 September 2009. The correction decreased $a_{pg}$ and $b_{bp}$ in the lagoon areas. The comparison to the in situ observations [Figs. 9(c) and 9(d)] showed that the correction improved the agreement especially at stations M33, Ile aux Canards, and G003, where the bottom depth is shallow and $a_{pg}$ is relatively low. The AVNIR-2 $a_{pg}$ was still higher than the in situ $a_{pg}$ at stations B50 and B03 around the Boulari Bay. Bias of $a_{pg}(b_{bp})$ were improved from 0.188 to 0.118 (from 0.023 to 0.015), and RMSD of $a_{pg}(b_{bp})$ from 0.489 to 0.290 (from 0.042 to 0.025) by the bottom correction.

Table 4 shows the results for the 15 match-ups by using different spectra of $a_{pg}$ and $b_{bp}$. Superscripts $-$ and $+$ show results with smaller or larger bias or RMSD (statistically significance level of 95%) than ones by the model spectrum (A). The results depended on the model spectra significantly, and the model (D) brought the smallest RMSD of both $a_{pg}$ and $b_{bp}$ with the bottom reflectance correction. The microplankton for $a_{ph}$ [58] gives larger RMSD than those measured around New Caledonia. Similarly, a slope of $Y=-2$ is too different from those measured and would not allow a proper retrieval of IOPs from AVNIR-2. Figures 9(e)–9(h) show the scatter plots by the model spectrum (D). RMSDs of $a_{pg}$ and $b_{bp}$ are significantly decreased (especially stations B50 and B03) by the optimal model spectrum.

C. Chlorophyll-a Concentration

Figures 10 and 11 show the comparison among Chla estimated from $a_{pg}$ [by the optimal model (D)], Chla calculated by OC2M-HI (using $R_{rs}$ by AVNIR-2), and the MODIS standard (OC3M) 1 km Chla. Chla estimated from $a_{pg}$ [Figs. 10(a) and 11(a)] was slightly smaller than Chla determined by other algorithms in the lagoon areas (e.g., sites B08 and Ile aux Canards in Figs. 10 and 11). The AVNIR-2 OC2M-HI Chla was larger than indicated by the in situ data and similar to the MODIS standard value in the lagoon [see around sites M33 and G003 in Figs. 10(b) and 10(e) and Figs. 11(b) and 11(e)]. The scatter plots show that Chla from $a_{pg}$ provides the best agreement among the three methods in the lagoon [$\mathrm{RMSD}=0.47$, 0.61, and 0.60 in Figs. 10(a), 10(b), and 10(e)]. The MODIS data at stations M33 and GD10 were scattered because they were too near the coast or the lagoon islands compared with the 1 km resolution products.

 

Fig. 10. Scatter diagrams of in situ Chla and (a) Chla from AVNIR-2 $a_{pg}$, (b) Chla from AVNIR-2 OC2M-HI, (c) and (d) are same as (a) and (b) except applying the bottom correction, (e) Chla from the MODIS standard OC3M (1 km), and (f) the scatter plot between AVNIR-2 $a_{pg}$ Chla and the MODIS OC3M Chla. Bars show the standard deviation of the multiple MODIS scenes around the AVNIR-2 observation dates or the standard deviation of $3\times 3$ pixels of AVNIR-2 data. $N$, show sample number; $r$, correlation coefficient; bias, bias; RMSD, root mean square difference; xvag, average of $x$ axis variables in ${\log }_{10}$ scale.

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Fig. 11. (a), (b), and (e) are Chla from $a_{pg}$, Chla from OC2M-HI (3 September 2009) and the MODIS standard Chla(average from 3–9 September 2009). (c) and (d) are the same as (a) and (b) except applying the bottom correction. Markers show the in situ observation stations on 9 September 2009.

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Figures 11(c) and 11(d) show results with the bottom correction. OC2M-HI Chla [Fig. 11(d)] was calculated by $R_{rs}$ from $r_{rs}^{dp}$ [Eq. (8)]. Usual high biases of $a_{pg}$ and $b_{bp}$ in the shallow areas (B50, B03, and Ile aux Canards) around lagoon islands were decreased by the correction [Figs. 8(c) and 8(d)]. It reduced the overestimation of Chla by both $a_{pg}$ and OC2 schemes, and it improved the agreement with the in situ match-ups inside the lagoon [Figs. 10(c) and 10(d)].

4. Discussion

A. ${\mathsf{a}}_{\mathsf{p}\mathsf{g}}$ and ${\mathsf{b}}_{\mathsf{b}\mathsf{p}}$ Estimates and Spectral Models

Agreement with in situ data was dependent on spectra of $a_{pg}$ and $b_{bp}$ (Table 4). For example, the $a_{ph}$ spectrum of microplankton [58] (model C) and $b_{bp}$ spectrum of $Y=-2.0$ (F) caused worse results than the spectrum modeled from New Caledonia in situ measurements (A) (Table 4). The agreement may be improved further if we optimize the spectra to more specific water types (e.g., bays near the main land, middle-lagoon waters, and waters outside of the barrier reef, such as open ocean). For example, modification of the spectral slope of $a_{dg}$ improved the IOP estimate especially around the Boulari Bay [model (D) in Fig. (9)].

The correlation coefficients of $a_{pg}$ at 442 nm and $b_{bp}$ at 555 nm by the model (D) were $r=0.91$ and $r=0.75$ [Figs. 9(g) and 9(h)], respectively. They were better than ones calculated by the quasi-analytical algorithm (QAA) [52,64] by using the 1 km Aqua-MODIS R_rs products ($r=0.84$ and 0.72 for $a_{pg}$ 443 nm and $b_{bp}$ 555 nm, respectively). The QAA needs two blue bands and can not apply to the limited AVNIR-2 bands (figures of the QAA results are not shown here).

Such an optimization with the best-candidate spectra can be a useful way to obtain locally optimized environmental monitoring from satellite observations with a theoretical understanding of the local optical environment. This study cannot determine spectral models, such as the ratio between $a_p$ and $a_g$ (or $a_{ph}$ and $a_{dg}$), because AVNIR-2 has only two channels in the blue and green wavelengths. More bands at 250–300 m of spatial resolution from sensors, such as Second-Generation Global Imager (SGLI) and Ocean and Land Color Imager (OLCI) may be able to improve the discrimination of the IOPs.

The IOP retrieval schemes have been developed for observations by narrow (about 10–20 nm) bandwidth sensors, and estimates of absorption coefficients by the wide band can cause errors reaching about 20% [65] by the QAA [52,64] through the integration of the IOP spectra in the band wavelengths. Our estimates rely on relatively wide bands (about 90 nm) of AVNIR-2. We confirmed that our $a_{pg}$ retrievals by the LMI can be influenced about 20% (mostly overestimated) because of the bandwidth using simulated $R_{rs}$ from our in-situ $a_{pg}$ and $b_{bp}$. The error is still much smaller than the error due to differences of the model IOP spectra; however, it will need to be considered for more precise estimate in the future.

B. Aerosol and Sea-Surface Reflection Estimation

Most of the iteration schemes for the atmospheric correction use the relationship between NIR $R_{rs}$ and Chla. This study uses the relationships among $a_{pg}$, $b_{bp}$, ${\rho }_{ag}$, and $\alpha$ based on the convergence of $b_{bp}$. This scheme can avoid negative IOPs by tuning the aerosol parameters $\alpha$ and ${\rho }_{ag}$ in the iteration process. Another merit of this aerosol estimation is the fast processing time (2–3 min for our study area ($2001\times 1334$ pixels) by a wide-use Linux machine) because it does not require time to access the aerosol look-up table that is used in the standard ocean-color atmospheric correction algorithms.

The New Caledonia lagoon area has a relatively clear atmosphere compared with coasts in the northern hemisphere, such as the Asian coasts. This scheme does not consider absorptive aerosols that cannot be described by the simple Eq. (3). For more complex atmosphere (aerosol) conditions, more bands may be necessary than the two that were used for the aerosol characterization (this study used 652 and 821 nm). If the sensor has lower noise and SWIR bands (e.g., MODIS 500 m bands and SGLI 250 m band), we may be able to estimate $\alpha$ at each pixel and obtain more realistic measurements of $\alpha$ and ${\rho }_{ag}$. The absorptive aerosol correction, however, may still be difficult using the simple Eq. (3).

C. Bottom Effect

AVNIR-2 $b_{bp}$ seemed to be influenced by the bottom reflectance. Bottom sands can be seen from satellite if bathymetry is shallow. For example, the bottom depth of the station G003 is 11 m with a relatively low $a_{pg}$. Agreement between AVNIR-2 IOPs and in situ IOPs were improved by considering the bottom reflectance generally, but they seemed to be overcorrected in some areas around the islands and along the barrier reef [Fig. 6(j)]. They are supposed to be influenced by coverage of live corals or sediment from the land, which may cause a different spectrum of the bottom reflectance from the coral sand reflectance [60–62]. This indicates that our IOP estimation could be improved if the precise bottom depth and real bottom reflectance are used [36].

D. Cloud Shadow and Adjacent Scattering

For the 10 m resolution data, it is important to consider cloud shadow and sea-surface reflection of scattered light from the cloud bottom. Identification of clouds around the coast (including over the land) and geometric calculation considering the cloud height are required. In addition, the clouds and land area can influence the coastal ocean-color estimation, which is known as the adjacent effect [66]. The influence of the cloud shadow seemed to affect $b_{bp}$, but not $a_{pg}$ as observed in the southeastern part of Fig. 8. Further study is needed to determine $b_{bp}$ in the absence of the influence of the cloud effects.

5. Conclusion

This study investigated the correction of atmospheric scattering and sea-surface reflection in the southwest region of the New Caledonia lagoon using AVNIR-2 images, which have four bands from visible to NIR wavelengths with 10 m resolution. Our processing was conducted after averaging for 30 m ($3\times 3$) grids. We applied corrections for gas absorption, molecule scattering, and ${\rho }_a+{\rho }_g$ using the iteration scheme for converging $b_{bp}$ through IOPs from visible bands. This scheme was able to correct fine structure patterns of the ${\rho }_a+{\rho }_g$ successfully. The AVNIR-2-estimated $R_{rs}$ agreed well with the MODIS $R_{rs}$ (RMSD/average of $R_{rs}$ at $443\mathrm{nm}=40\%$). Future projects, for example, the Global Change Observation Mission, using the Second-Generation Global Imager (SGLI) and the Sentinel-3 Ocean and Land Color Imager (OLCI), will have finer (250–300 m) spatial resolution aiming for coastal monitoring with a swath of more than 1150 km. These missions will require a correction of the surface reflection with high spatial resolution and a reduction of masked areas to increase the observation frequency in the coastal areas.

With the bottom correction, the AVNIR-2-estimated IOPs agreed well with in situ IOP measurements (correlation coefficients were more than 0.9). Overcorrection appeared in the muddy bays and along the barrier reef, and it suggested that a constant bottom reflectance was not applicable in these areas.

This study showed that the AVNIR-2-estimated Chla from the $a_{pg}$ regression scheme in the lagoon area improved the overestimation observed with the blue–green $R_{rs}$ ratio. This also confirms that the relationship between Chla and $a_{pg}$ in the lagoon area is not different from the $a_{pg}$—Chla relationship of the NOMAD database as already shown in Dupouy et al. [27]. The NOMAD relationship cannot be used in bays (e.g., B50), where the $a_{pg}$—Chla relationship is disturbed by absorbing mineral particles and irregular $a_g$ due to river discharge.

Our atmospheric correction and IOP estimation scheme, which requires only four bands in the visible and NIR wavelengths, can be applied to other satellite sensors, such as the MODIS 500 m bands, and other multiband sensors, such as SGLI 250 m bands. The performance depends on the candidate spectra of IOPs and aerosols based on in situ measurements in the target areas. This reinforces the need to construct databases of the various spectra of IOPs and aerosols in various regions through international collaboration to develop globally applicable approaches. The target of this study is not to make a fixed algorithm but rather to demonstrate the method to make local optimal estimate of the IOPs and Chla. So, the algorithm should not be applied elsewhere without a similar effort (i.e., preparation of the candidate spectra for the target areas).