A new approach for the near-infrared (NIR) ocean reflectance correction in atmospheric correction for satellite ocean color data processing in coastal and inland waters is proposed, which combines the advantages of the three existing NIR ocean reflectance correction algorithms, i.e., Bailey et al. (2010) [Opt. Express 18, 7521 (2010) Appl. Opt. 39, 897 (2000) Opt. Express 20, 741 (2012)], and is named BMW. The normalized water-leaving radiance spectra nLw(λ) obtained from this new NIR-based atmospheric correction approach are evaluated against those obtained from the shortwave infrared (SWIR)-based atmospheric correction algorithm, as well as those from some existing NIR atmospheric correction algorithms based on several case studies. The scenes selected for case studies are obtained from two different satellite ocean color sensors, i.e., the Moderate Resolution Imaging Spectroradiometer (MODIS) on the satellite Aqua and the Visible Infrared Imaging Radiometer Suite (VIIRS) on the Suomi National Polar-orbiting Partnership (SNPP), with an emphasis on several turbid water regions in the world. The new approach has shown to produce nLw(λ) spectra most consistent with the SWIR results among all NIR algorithms. Furthermore, validations against the in situ measurements also show that in less turbid water regions the new approach produces reasonable and similar results comparable to the current operational algorithm. In addition, by combining the new NIR atmospheric correction with the SWIR-based approach, the new NIR-SWIR atmospheric correction can produce further improved ocean color products. The new NIR atmospheric correction can be implemented in a global operational satellite ocean color data processing system.
© 2014 Optical Society of America
To derive the normalized water-leaving radiance spectra nLw(λ) [1–4] from the top-of-atmosphere (TOA) radiances measured by satellite ocean color sensors, atmospheric correction has to be performed to remove signals contributed from the atmosphere and ocean surface [1, 5, 6], which mainly include radiance contributions from multiple scattering by air molecules (Rayleigh scattering) [7–10] and multiple scattering (and absorption) by aerosols [5, 11, 12] with the latter including the effect from Rayleigh-aerosol interactions [1, 5, 13]. In addition, there are other undesirable TOA radiances from surface-level radiance contributors such as ocean whitecaps [14–16] and sun glint [17–19]. Except for the aerosol radiance contribution, all other signals contributed to the TOA radiance can be estimated [5, 6, 11] based on the solar-sensor geometry and ancillary data inputs from surface wind speed, atmospheric pressure, column ozone, and water-vapor concentrations . Therefore, the sensor-measured TOA radiance with Rayleigh radiance, whitecaps radiance, and sun glint radiance corrected or masked, Lt(C)(λ), can be written as [1, 5, 6, 11]:1, 5, 13], with the solar-zenith angle θ0. The quantities t0(λ) and t(λ) are the atmospheric diffuse transmittances  from the sun to the surface and from the surface to the sensor, respectively. nLw(λ) is the normalized water-leaving radiance, which is the desired quantity for satellite ocean color remote sensing . The major challenge of atmospheric correction is to accurately derive nLw(λ) from Eq. (1), i.e., to accurately remove/correct aerosol radiance contribution LA(λ) from Eq. (1) .
For global open oceans, nLw(λ) at two near-infrared (NIR) wavelengths, nLw(λNIR1) and nLw(λNIR2), where λNIR1 and λNIR2 are two NIR wavelengths from sensor spectral bands, are negligible (close to zero). Thus, aerosol radiances at the two NIR bands in Eq. (1), LA(λNIR1) and LA(λNIR2), can be derived assuming zero contributions in nLw(λNIR1) and nLw(λNIR2), i.e., the NIR black pixel assumption [5, 22]. Next, LA(λ) values at all visible wavelengths can be derived from the specific aerosol models determined by LA(λNIR1) and LA(λNIR2) . Finally, nLw(λ) at all visible wavelengths are obtained from Eq. (1) with known (derived) LA(λ) [1, 5]. It is noted that the two NIR bands, λNIR1 and λNIR2, may have some slight spectral differences for different satellite ocean color sensors.
However, the method mentioned above only works for clear open ocean waters. For coastal and inland lake regions this method will often underestimate nLw(λ) in the visible due to the failure of the black pixel assumption at the NIR wavelengths [22–27]. In order to derive correct LA(λNIR1) and LA(λNIR2) for coastal regions, the non-zero values of nLw(λNIR1) and nLw(λNIR2) first need to be properly estimated and removed. The NASA ocean color data processing for the Moderate Resolution Imaging Spectroradiometer (MODIS)  estimates the NIR nLw(λNIR1) and nLw(λNIR2) using the bio-optical model described by Bailey et al. (2010)  (hereafter also referred to as the “Bailey” algorithm), which is an improved version of the NIR nLw(λ) correction algorithm over Stumpf et al. (2003) . The latter was originally developed for the Sea-viewing Wide Field-of-view Sensor (SeaWiFS)  in its fourth data reprocessing  (hereafter also referred to as the “Stumpf” algorithm). In fact, Stumpf  was also an algorithm update/replacement to Siegel et al. (2000) , which was the first study to assess the ocean NIR black pixel assumption and the proposed correction algorithm was initially implemented in the SeaWiFS ocean color data processing (the third data reprocessing). Note that MODIS has λNIR1 and λNIR2 at 748 and 869 nm, while SeaWiFS has two NIR bands at 765 and 865 nm. Both the Bailey  and Stumpf  algorithms use an iterative approach to derive nLw(λNIR1) and nLw(λNIR2) from visible nLw(λ) and derived chlorophyll-a by exploiting the relationship between non-water absorption at the red band and chlorophyll-a concentration, as well as the wavelength dependence on the non-water backscattering coefficients at red and NIR bands [24, 26].
The above algorithms, however, may not work well in some highly turbid waters or non-phytoplankton-dominated waters, such as sediment-dominated or colored dissolved organic matter (CDOM)-dominated waters. For those waters, the assumption could be in significant error (or invalid) in that the absorption coefficients at the NIR wavelengths are pure water absorptions only. Furthermore, for non-phytoplankton-dominated waters the relationship between non-water absorption for the red band and chlorophyll-a concentration could be invalid, as well as the wavelength dependence for the non-water backscattering coefficients. These are all inherent limitations of the bio-optical model used for deriving nLw(λNIR1) and nLw(λNIR2).
In an effort to deal with the highly turbid waters in China’s coastal ocean regions [31–33], Wang et al. (2012)  developed a NIR atmospheric correction algorithm for the Korean Geostationary Ocean Color Imager (GOCI) onboard the Communication, Ocean, and Meteorological Satellite (COMS) that covers a ~2500 × 2500 km2 target area centered on the Korean Peninsula . GOCI has eight spectral bands including two NIR bands at 745 and 865 nm. Based on regional empirical relationships between NIR-nLw(λNIR1) and the diffuse attenuation coefficient at the wavelength of 490 nm Kd(490)  and between nLw(λNIR1) and nLw(λNIR2), which were derived from long-term MODIS-Aqua measurements (2002–2009) using the shortwave infrared (SWIR)-based atmospheric correction algorithm , an iterative scheme with the NIR-based atmospheric correction algorithm has been developed  and used for processing GOCI data for producing ocean color products in the region [36, 37]. Therefore, in the Wang et al. (2012) algorithm , nLw(λNIR1) and nLw(λNIR2) can be estimated using an iterative method similar to the bio-optical model approaches [24, 26]. However, the derived relationship between nLw(λNIR1) and Kd(490), which effectively relates nLw(λNIR1) to nLw(λ) at visible wavelengths, is highly regional-dependent and most suitable for sediment-dominated waters. Thus, significant error can be induced when this method is applied to other types of ocean regions. On the other hand, for waters that are not extremely turbid, the derived relationship between nLw(λNIR1) and nLw(λNIR2) was found to be much more robust and applicable to other coastal regions [38, 39]. The robustness of the relationship between nLw(λ) at the two NIR bands  is due to the facts that (1) the NIR similarity spectrum  is valid for clear to moderately turbid waters, and (2) for waters that are not extremely turbid there is generally a good relationship between the two NIR nLw(λ) from sediment-dominant waters where the relationship was derived [27, 33]. Though, it should be noted that for different sources (types) of sediments there are still some differences in the two NIR nLw(λ) relationship, in particular, for extremely turbid waters . Thus, the relationship between two NIR nLw(λ) may be fine tuned for a specific region. Hereafter, Wang et al. (2012) algorithm  will be also referred as the “Wang” algorithm.
The iterative method used in Stumpf, Bailey, and Wang is generally a typical approach to estimate nLw(λNIR1) and nLw(λNIR2). On the other hand, there is also a non-iterative approach originally proposed by Ruddick et al. (2000)  and implemented in SeaWiFS atmospheric correction for ocean color data processing over coastal and inland waters. Ruddick et al. (2000) model  is also often referred to as MUMM model , with MUMM standing for the Management Unit of the North Sea Mathematical Models which is the institute the authors are affiliated. The MUMM approach does not rely on any bio-optical model, and it simultaneously solves for nLw(λ) and LA(λ) in Eq. (1) at the two NIR bands (with the assumption of uniformly distributed aerosols in a region). However, it requires a priori knowledge of the reflectance ratios both in water α(λNIR1,λNIR2) and in aerosol ε(M)(λNIR1,λNIR2) between the two NIR bands, i.e.,41]. Similarly, ρA(λ) = π⋅LA(λ)/[F0(λ)⋅cosθ0] is the corresponding aerosol reflectance with solar-zenith angle of θ0. When both α(λNIR1,λNIR2) and ε(M)(λNIR1,λNIR2) are known, Eqs. (2) and (3) can then be combined with Eq. (1) at the two NIR wavelengths to solve for nLw(λNIR1), nLw(λNIR2), LA(λNIR1), and LA(λNIR2). To obtain accurate solutions, reflectance ratios α(λNIR1,λNIR2) and ε(M)(λNIR1,λNIR2) need to be accurately estimated first. We will also refer to the Ruddick et al. (2000) approach  as the “MUMM” algorithm.
Ruddick et al. (2000)  originally proposed using a scatter plot for the entire scene to determine the ratios ε(M)(λNIR1,λNIR2), while α(λNIR1,λNIR2) was assumed to be a constant (~1.72) in practice since the parameter was believed to be relatively invariant, i.e., similarity spectrum at the NIR bands . However, it has been found that, based on the in situ data, model simulations, and satellite-measured NIR nLw(λ) data using the SWIR-based data processing, the variation of α(λNIR1,λNIR2) is quite significant, and NIR similarity spectrum can only be valid in low to moderately turbid waters [27, 33, 42]. In fact, the linear relationship between nLw(λNIR1) and nLw(λNIR2) deviates considerably when the water is extremely turbid [27, 33, 38, 42]. Additionally, it is noted that using a scatter plot to determine the aerosol reflectance ratio can be done for case studies , but is not realistic for the operational global ocean color data processing, which has to be completely automated. Furthermore, the MUMM algorithm assumes a uniform aerosol reflectance ratio ε(M)(λNIR1,λNIR2) over the entire scene, which can introduce significant errors when aerosol properties vary greatly over the entire scene.
All previously discussed existing NIR nLw(λ) estimation approaches for atmospheric correction, in particular, the Bailey, MUMM, and Wang algorithms, have advantages and disadvantages, which motivated this study. In the following sections, we propose a new approach that is based on the three methods (i.e., Bailey, MUMM, and Wang) and aims to overcome the existing disadvantages. We name the new algorithm as “BMW” to reflect the combination of the Bailey, MUMM, and Wang algorithms.
The rest of the paper is organized as following: Section 2 gives a detailed description of the BMW algorithm; Section 3 presents results from individual case studies comparing different algorithms; Section 4 shows statistics from matchup comparisons against results from the SWIR approach and in situ data; Section 5 discusses routine global ocean color data processing using the BMW algorithm; and finally Section 6 summarizes the performance of the new algorithm.
2. BMW methodology
The basic idea of this new algorithm is to use the MUMM algorithm  as the foundation for improvements to overcome its disadvantages. First, the aerosol multiple-scattering reflectance ratio ε(M)(λNIR1,λNIR2) [43, 44] needs to be estimated with reasonable accuracy without making a scatter plot. Also, it should not be assumed that ε(M)(λNIR1,λNIR2) is uniformly distributed spatially over the entire satellite image. Our solution is to first use the Bailey algorithm  to categorize each valid pixel into either clear or turbid water pixel based on its Bailey-derived nLw(λNIR2) values. “Valid pixels” are defined as pixels that are not contaminated by cloud [45, 46], stray light , or sun glint [17, 18], and are not under high solar- or sensor-zenith angles. For clear water pixels, nLw(λNIR1) and nLw(λNIR2) are assumed to be zero, and ε(M)(λNIR1,λNIR2) values can therefore be accurately estimated for those pixels based on Eq. (1). For turbid water pixels, however, ε(M)(λNIR1,λNIR2) values can be estimated from neighboring clear water pixels . Thus, ε(M)(λNIR1,λNIR2) values are locally derived and relatively accurate without the need for any human involvement, e.g., using scatter plots. Therefore, this method can be easily implemented into any operational ocean color data processing system. Second, to account for the nonlinear relationship between nLw(λNIR1) and nLw(λNIR2) in highly turbid waters, Eq. (2) in the MUMM algorithm is replaced with a quadratic relationship used in the Wang algorithm , i.e.,Eq. (4) is that the computation turns the original linear equation into a quadratic equation. Some small adjustments need to be made to deal with the situation when the final quadratic equation has no real-value solution (i.e., the discriminant “delta” is less than zero), in which case the discriminant “delta” is forced to be zero. In addition, the solutions also need be constrained so that both LA(λNIR1) and nLw(λNIR1) have non-negative values. Specifically, the BMW algorithm works as follows with its flowchart shown in Fig. 1:
- Step 2: For each turbid water pixel, assign a mean ε(M)(λNIR1,λNIR2) value, i.e., ε(M,Mean)(λNIR1,λNIR2), which is calculated from the distance-weighted mean of the ε(M)(λNIR1,λNIR2) for all clear water pixels within the 101 × 101 pixel box centered at the turbid water pixel, i.e.,
where ri is the distance between the turbid water pixel with the ith clear water pixel within the box and εi(M)(λNIR1,λNIR2) the aerosol reflectance ratio of that ith clear water pixel. If there is no clear water pixel within the box, the turbid water pixel will wait for assignment of a ε(M,Mean)(λNIR1,λNIR2) value in the next iteration;
- Step 3: For each remaining turbid water pixels not yet assigned a ε(M,Mean)(λNIR1,λNIR2) value due to missing clear water pixels in the box, a distance-weighted mean of the ε(M,Mean)(λNIR1,λNIR2) value (Eq. (5)) derived from all turbid pixels in the 101 × 101 box that were reassigned ε(M,Mean)(λNIR1,λNIR2) values from the previous iteration is used. If no pixels from the previously reassigned ε(M,Mean)(λNIR1,λNIR2) values are found in the box, this turbid water pixel remains unassigned a ε(M,Mean)(λNIR1,λNIR2) value in the current iteration;
- Step 4: Iterate on Step 3 until the number of turbid water pixels with an unassigned ε(M,Mean)(λNIR1,λNIR2) value ceases to decrease with each iteration;
- Step 5: All remaining turbid water pixels with unassigned ε(M,Mean)(λNIR1,λNIR2) values are assigned the un-weighted mean of ε(M)(λNIR1,λNIR2) of all clear water pixels in the entire scene; and
It is noted that in the BMW algorithm the scene has to be processed twice (Steps 1 and 6), which increases data processing time. Considering the preliminary atmospheric correction with the Bailey algorithm is only to classify turbid and clear water pixels, one can reduce the maximum iteration number in Step 1 to save some computational resources. On the other hand, the data processing in Step 6 (MUMM) only involves solving a quadratic equation that is non-iterative.
The new BMW ocean reflectance correction algorithm, as well as other NIR algorithms such as Stumpf, Bailey, and Wang, has been implemented in the NOAA Multi-Sensor Level-1 to Level-2 (MSL12) ocean color data processing system. MSL12 was developed as a consistent and common ocean color data processing system to produce ocean color data from multiple satellite ocean color sensors [36, 49–52]. Specifically, NOAA-MSL12 is based on the SeaWiFS Data Analysis System (SeaDAS) version 4.6, with various modifications and improvements, e.g., the SWIR-based atmospheric correction [6, 25, 53–55], Rayleigh radiance improvement and aerosol lookup tables updates [6, 10, 12, 56], cloud masking for coastal and inland waters , ice-detection algorithm , etc. In addition, the NOAA-MSL12 is also capable of deriving ocean color products from the Visible Infrared Imaging Radiometer Suite (VIIRS) onboard the Suomi National Polar-orbiting Partnership (SNPP) and has been routinely producing VIIRS global ocean color products since VIIRS launch on October 28, 2011 . In fact, MSL12 is now the official NOAA operational ocean color data processing system for VIIRS. In the following, comparison of nLw(λ) spectra results using various NIR ocean reflectance algorithms implemented in NOAA-MSL12 for some turbid and highly turbid coastal and inland waters are provided and discussed.
3. Results from case studies
3.1. Case studies in the U.S. East Coast region
Figure 2 shows some true color images from MODIS and VIIRS for various case studies in this paper. Figure 2(a) shows the true color image of a section of the U.S. East Coast (Mid Atlantic Bight), centered around (38°N, 76.0°W), which was acquired by MODIS-Aqua on April 5, 2004 at around 18:20 UTC. The area is mostly cloud-free, with slight cloud coverage only at the southeast corner of the image. The major coastal water bodies in the area include four estuaries from south to north: Pamlico Sound and Albemarle Sound in North Carolina, and the Chesapeake Bay and Delaware Bay that border the Delmarva Peninsula.
The normalized water-leaving radiances nLw(λ) for three selected bands in the blue, green, and red (443, 551, and 667 nm) are shown in Fig. 3 with results for columns 1 to 6 from the SWIR atmospheric correction algorithm, three existing NIR atmospheric correction algorithms (Stumpf, Bailey, and Wang), the new BMW NIR atmospheric correction algorithm, and the NIR-SWIR combined atmospheric correction algorithm that uses the BMW as the NIR component, respectively. Cloud pixels are shown in white and pixels with missing values due to sensor saturation or atmospheric correction failure, etc., are in black. In all cases, the SWIR-derived results are regarded as the reference to determine the performance of various NIR algorithms.
Figure 3 shows that the Stumpf algorithm produced lower nLw(λ) values in turbid regions, while the Wang algorithm produced slightly higher values for less turbid waters than those from the SWIR method throughout the image for all three bands. The Bailey algorithm does show some improvements over the Stumpf algorithm, especially in the turbid regions, but it still significantly underestimates nLw(λ) values in the Pamlico Sound compared to the SWIR results (yellow-orange versus red for nLw(λ) at 667 nm). On the other hand, the BMW results are consistent with SWIR results, including the Pamlico Sound where the Stumpf and Bailey algorithms produced much lower nLw(λ) values. The NIR bio-optical models used in the Stumpf and Bailey algorithms fail in Pamlico Sound probably due to the high concentration of suspended sediment, which dominates the water optical properties [25, 58]. In addition, the Wang algorithm overestimates nLw(λ) values probably because it uses a highly regional-dependent relationship between nLw(λNIR) and Kd(490) in highly turbid waters, which does not seem to work well in this region . The BMW algorithm, however, does not suffer from the constraint of bio-optical models and is globally applicable. Furthermore, the NIR-SWIR algorithm  that uses the BMW as the NIR component (Figs. 3(f), 3(l), and 3(r)) produces results that match both the SWIR results in highly turbid waters and BMW results in less turbid waters (as expected). It is noted that in the Pamlico Sound the NIR-SWIR-derived nLw(λ) spectra are in fact from the SWIR method, while those offshore of the Delaware Bay and the mouth of the Chesapeake Bay are from the BMW approach.
Three stations are selected for a detailed quantitative spectral analysis (marked in Fig. 2(a)), located at the Pamlico Sound at (35.4°N, 75.8°W), the Chesapeake Bay at (37.85°N, 75.9°W), and the Delaware Bay at (39.1°N, 75.0°W), which are noted as a1, a2, and a3 in Fig. 2(a), respectively. We have purposely selected the locations of highly turbid waters to make sure the NIR water reflectance correction process is triggered in various NIR atmospheric correction algorithms and to test the capabilities of different NIR atmospheric correction algorithms in dealing with highly turbid waters. For each station, nLw(λ) values of all valid pixels within a 21 × 21 pixel box centered at that location are averaged to derive nLw(λ) spectra. Valid pixels are again those not contaminated by cloud, stray light or sun glint, not under high solar- or sensor-zenith angles, and do not have a missing value due to sensor saturation or atmospheric correction failure, etc. nLw(λ) spectra for the three stations a1, a2, and a3 in Fig. 2(a) are shown in Figs. 4(a)–4(c), respectively. Overall, all of the NIR and SWIR algorithms produce similar spectral distributions for typical turbid waters with nLw(λ) peaking at the green band. The Stumpf algorithm produces the lowest nLw(λ) values (up to ~2.5 mW cm−2 µm−1 sr−1 lower than those of the SWIR method) for all three stations, and Bailey produces better values but still underestimates (up to ~2.0 mW cm−2 µm−1 sr−1) based on the SWIR results. Conversely, the BMW and Wang algorithms produce nLw(λ) spectra that are quite consistent (within ~0.2 mW cm−2 µm−1 sr−1) with those from the SWIR algorithm for all three locations. These results have confirmed our qualitative conclusion discussed previously (i.e., from Fig. 3).
To give an idea of the performance of the BMW algorithm over the entire MODIS-Aqua granule in Fig. 2(a), a scatter plot between the BMW-derived and SWIR-produced nLw(λ) values at various wavelengths for 500 randomly sampled pixels over the entire scene is shown in Fig. 4(d). It is confirmed that the features captured by the randomly sampled scatter plot reflect the complete scatter plot (not shown here) adequately well. The agreement in nLw(λ) between BMW and SWIR results is very good throughout the entire spectrum from the blue to NIR wavelengths. Obviously, nLw(λ) results from the BMW can be either underestimated or overestimated compared those from the SWIR algorithm due to the BMW algorithm performance. It is noted that the maximum nLw(859) value is ~1.0–1.5 mW cm−2 µm−1 sr−1, which is within the required limitation for the iterative bio-optical model .
Table 1 provides a more quantitative comparison of the proximity for various NIR algorithm results to the SWIR results. The ratio is defined as nLw(λ) derived from any given algorithm divided by that from the SWIR method, and the difference is the nLw(λ) of any given algorithm minus that of the SWIR approach. Median ratio values are shown instead of mean ratios because the latter is severely impacted by outliers due to low sensor signal-to-noise ratio (SNR) at the SWIR bands and noise-induced sign fluctuation from the SWIR algorithm . The difference is expressed in terms of “bias ± standard deviation (STD)”. All valid pixels in nLw(λ) from the entire granule in Fig. 2(a) are included in the statistics except for those with nLw(869) < 0.05 mW cm−2 µm−1 sr−1, because for those clear water pixels the NIR reflectance correction algorithm is not invoked. The total number of pixels included in the statistics for this case is approximately 12,000.
Results show that nLw(λ) biases between the NIR and SWIR atmospheric correction for all bands are quite small for all NIR algorithms except for the Stumpf algorithm, which has a bias of −0.3 with an STD value of ~0.87 mW cm−2 µm−1 sr−1 at 412 nm. The Bailey algorithm improves over the Stumpf algorithm with its smaller bias and reduced STD values. However, the STD values for the Bailey algorithm are still 1.5 to 2 times larger than those of the BMW and Wang algorithms. The median ratios for all NIR algorithms are generally within ~10% of unity for visible bands. It is noted that the Stumpf algorithm has produced quite good median ratios for all bands (larger than one), but with large negative biases and large STD values. BMW has insignificant bias despite of a 0.905 median ratio for nLw(412). Among all the NIR algorithms, BMW has the smallest STD and bias values. The Wang algorithm is the second with slightly larger STD and bias values. The Bailey algorithm has small bias but large STD, while Stumpf has large bias and STD values. All algorithms produced reasonable median ratio values. For all NIR algorithms, the differences in nLw(λ) with the SWIR algorithm reflected in all three statistics parameters (median ratio, bias, STD) are smaller in longer wavelengths than in shorter wavelengths since there are larger extrapolation errors in the aerosol reflectance estimation for nLw(λ) at the shorter wavelengths .
To address the performance of various atmospheric correction algorithms for different sensors, we have also selected a scene (not shown) from VIIRS, which was acquired on December 14, 2012 at 18:10 UTC for the same statistics analysis (Table 2). It is noted that VIIRS has the NIR spectral bands at 745 and 862 nm. The pixel selection criteria are the same as the MODIS granule, which includes around 9,000 pixels from the entire VIIRS granule. The BMW and Wang algorithms have positive biases and larger-than-one ratios, while the Stumpf and Bailey algorithms have negative biases and smaller-than-one ratios for almost all bands. Bailey has insignificant biases and close-to-one median ratios, but moderate STD values. BMW has the smallest STD values with small positive biases, while Stumpf has the largest STD values with negative biases. Wang has the largest and positive biases, but its STD values are quite small and only larger than those of BMW. The Bailey algorithm performed a little better than Stumpf, but the BMW has significant advantage over Bailey in STD values and thus in the total root-mean-square (RMS) error (not shown). The Wang algorithm performs moderately in this case with large biases but relatively small STD values.
3.2. Case studies at the La Plata River estuary
The La Plata River, or Río de la Plata, located near (35°S, 57°W), is an estuary on the border between Argentina and Uruguay in South America. A cloud-free true-color image of the La Plata River area acquired on March 30, 2006 at 17:35 UTC by MODIS-Aqua is shown in Fig. 2(b). In addition, another true-color image of a portion of the estuary taken on March 23, 2012 at 17:55 UTC by VIIRS is shown in Fig. 2(c) (upper right corner of Fig. 2). Both images show extremely turbid waters in the La Plata estuary .
The nLw(λ) spectra for four selected bands in the blue, green, red, and NIR (443, 555, 645, and 859 nm) are shown in Fig. 5 with results in columns 1 to 4 from the SWIR, Bailey, BMW, and NIR-SWIR algorithm, respectively. Results from the Stumpf and Wang algorithms are not shown in Fig. 5 since the comparisons are now mainly focused between the Bailey and BMW algorithms, the former being the current NASA operational algorithm and the latter being the new proposed algorithm for future operational use. In addition, the Stumpf algorithm is also excluded in the all analyses hereafter.
The most striking feature in Fig. 5 is the large region of missing values (black) in both Bailey and BMW results due to the TOA radiance saturation at 748 nm band of MODIS-Aqua in extremely turbid estuarine waters. Note that MODIS bands at 555 and 645 nm are used in this case instead of the ocean bands at 551 and 667 nm to avoid sensor saturation in those two bands. However, for the NIR band at 748 nm, there is no replacement band available, and an unusable NIR band at 748 nm makes any NIR-based atmospheric correction algorithm fail because the NIR band at 748 nm is needed together with the NIR band at 869 nm (or 859 nm as replacement in case 869 nm band saturates) to estimate aerosol properties in atmospheric correction process . In this situation, the SWIR algorithm has a great advantage because it uses the two SWIR bands (1240 and 2130 nm in this case) , which do not saturate, to perform atmospheric correction. For the NIR-SWIR approach, the current implementation in MSL12 switches to the SWIR atmospheric correction when the NIR method fails or the NIR-derived nLw(869) is above certain threshold. Therefore, the NIR-SWIR algorithm does not suffer from atmospheric correction failure due to saturation of the MODIS NIR bands. It should be mentioned again that for the NIR-SWIR approach the NIR atmospheric correction with the BMW algorithm is used for the NIR component. The Bailey and BMW algorithms produced similar values, which are slightly higher than those produced by the SWIR algorithm, especially in the estuary and for the blue band (comparing Fig. 5(a) to Figs. 5(b) and 5(c)). One difference between the Bailey and BMW algorithms is in the most southern of the two lagoons (Lagoon Mirim) near the coast east of the estuary, where the Bailey algorithm produced lower nLw(859) values than those from BMW and the latter is consistent with those from the SWIR method.
Three stations located in the northern, middle, and southern portions of the La Plata River estuary are selected for a quantitative nLw(λ) spectral analysis. For stations in the north at (34.3°S, 58.3°W) marked b1 in Fig. 2(b) and in the south at (35.3°S, 56.7°W) marked b2 in Fig. 2(b), pixels are selected from the MODIS-Aqua image (Fig. 2(b)), while for the middle station at (34.75°S, 57.7°W) marked c1 in Fig. 2(c), pixels are selected from the VIIRS image. This is because MODIS suffers from NIR saturation in the middle of the estuary, while VIIRS does not have such a saturation problem. The nLw(λ) spectra at stations b1, b2, and c1 are shown in Figs. 6(a)–6(c), respectively. Again, all atmospheric correction algorithms produced similar and typical spectral nLw(λ) shape for highly turbid waters with nLw(λ) peaking at the red band. In these three stations, the Wang algorithm performs quite well, and is very close to the BMW and SWIR results at all three stations. The three NIR algorithms produced very close nLw(λ) spectra that are slightly higher (~0.5–1.0 mW cm−2 µm−1 sr−1 at 412 nm) than the SWIR results at stations b1 and b2. At station c1, Bailey overestimates nLw(410) by ~1.5 mW cm−2 µm−1 sr−1, most likely because the water turbidity of this site (nLw(869) ~2.0 mW cm−2 µm−1 sr−1) is beyond what an iterative bio-optical model could handle . Nonetheless, the BMW and Wang approaches performed quite well with their deviation from the SWIR results within ~0.2 mW cm−2 µm−1 sr−1.
Figure 6(d) shows the scatter plot of seven-band nLw(λ) results between the BMW and SWIR from 500 randomly sampled pixels from the entire MODIS granule that includes the scene shown in Fig. 2(b). Again the agreement between BMW and SWIR is remarkably good for nLw(λ) values at all bands. It is also worth noting that values of nLw(859) actually reach ~2.0 mW cm−2 µm−1 sr−1 (extremely turbid waters), which is also reflected in the large deviation of the Bailey algorithm in Fig. 6(c).
A detailed statistics evaluation for the performance of the NIR atmospheric correction algorithms over the entire MODIS-Aqua granule described earlier is shown in Table 3 with approximately 16,000 pixels meeting the same selection criteria. The median ratios and bias values indicate consistent overestimation with the NIR algorithms over the SWIR algorithm. It is observed that the BMW has similar median ratio and bias, but better STD statistics than those of Bailey. For all five bands, the Wang algorithm has slightly larger biases but smaller STD values than those from the BMW. It is also noted that the Bailey algorithm has quite large STD values, which makes the Bailey algorithm’s performance slightly worse than the Wang algorithm in terms of RMS error. This is almost certainly because the turbid water in this case is sediment dominant, which is the water type the Wang algorithm is developed for.
3.3. Case studies at the East China Sea
The East China Sea, located near (31°N, 124°E), is a marginal sea east of China and a part of the Pacific Ocean . Figure 2(d) shows a portion of the East China Sea near the Yangtze River Delta, acquired by MODIS-Aqua on October 19, 2003 at 5:15 UTC. Major coastal and inland water bodies include the triangle-shaped Hangzhou Bay, the Yangtze River outlet to the north, and Lake Taihu, the third-largest inland lake of China, to the west , which all appear to be highly turbid. It is also noted that a sand ridge system exists at the northern part of Fig. 2(d) , and Fig. 2(e) shows a true color image taken by VIIRS on October 15, 2012 at 5:02 UTC, in which coastal waters to the north of the sand ridge are extremely turbid [32, 62].
nLw(λ) spectra images for four selected bands in the blue, green, red, and NIR (443, 555, 645, and 859 nm for MODIS and 443, 551, 671, and 862 nm for VIIRS) are shown in Fig. 7 with results from the SWIR and BMW approaches. MODIS results are shown in the two left columns and VIIRS results are presented in the two right columns, respectively.
In MODIS results (first two columns), some pixels have a “missing value” (in black color) from the BMW algorithm due to saturation of the NIR 748 nm (or 869 nm) band. It can be confirmed by comparing Fig. 7(n) with Fig. 7(m), where the pixels in black in Fig. 7(n) co-located with the pixels with high values (in red color) in Fig. 7(m). Other than the saturated pixels, BMW results agree reasonably well with the SWIR results, although with a slight overestimation in nLw(λ) at the blue band. It is also noted that at non-saturated locations, nLw(859) is less than ~1.5 mW cm−2 µm−1 sr−1. In contrast, VIIRS results (two columns in the right) show some discrepancy between those from the BMW and SWIR algorithms. The BMW significantly underestimates nLw(λ) in a region close to the coast north of the sand ridge, which is mostly apparent in Fig. 7(h). In Fig. 7(o), it is shown that VIIRS-derived nLw(862) in this region reach an extremely high value of ~3.0 mW cm−2 µm−1 sr−1. For such extremely turbid waters with nLw(862) > ~2.0 mW cm−2 µm−1 sr−1, the NIR nLw(λ) relationship used by the BMW algorithm is no longer valid [27, 33], and the SWIR atmospheric correction should be used instead . In fact, even for the SWIR 1240 nm band, SWIR nLw(λ) can have non-negligible contributions when nLw(862) > ~2.5 mW cm−2 µm−1 sr−1 [33, 63], in which case the desired band set for the SWIR atmospheric correction is 1640 and 2130 nm (1610 and 2250 nm for VIIRS) [6, 33]. However, the 1640 nm band of MODIS-Aqua has a couple of bad detectors, leaving the 1240 and 2130 nm bands as the usual choice for MODIS-Aqua SWIR atmospheric correction. For the VIIRS SWIR approach, VIIRS SWIR 1238 and 1610 nm bands are used because there are still some calibration issues for the VIIRS SWIR 2250 nm band. Still, from Fig. 7 it is found that VIIRS SWIR results are much smoother and more realistic than the BMW results. We have also checked the aerosol optical thickness and found that the SWIR method gives smooth and realistic results in the extremely turbid region (not shown here) where BMW fails.
Figures 8(a)–8(c) show nLw(λ) spectra for the three stations located at Lake Taihu (31.0°N, 120.2°E) marked d1 in Fig. 2(d), Hangzhou Bay (30.4°N, 121.8°E) marked d2 in Fig. 2(d), and near the sand ridge off Jiangsu coast (34.0°N, 121.0°E) marked e1 in Fig. 2(e). Stations d1 and d2 use pixels from the MODIS-Aqua scene (Fig. 2(c)) and Station e1 uses pixels from the VIIRS scene (Fig. 2(e)). Both the Bailey and Wang algorithms underestimate at Station d1 and overestimate at Stations d2 and e1. On the other hand, the BMW algorithm has a slight overestimation at Stations d1 and d2 and an underestimation at Station e1. It is noted that Station e1 is extremely turbid with SWIR-derived nLw(862) > 1.5 mW cm−2 µm−1 sr−1, and all algorithms produce different nLw(λ) values. As far as Stations d1 and d2 are considered, BMW produces results quite consistent with SWIR.
A scatter plot of six-band nLw(λ) spectra between the BMW and SWIR from 500 randomly sampled pixels for the entire VIIRS granule that includes the study region (Fig. 2(e)) is shown in Fig. 8(d). Most data points are concentrated on the 1:1 line, except for those from extremely turbid waters where the BMW fails and severely underestimates the results. This is consistent with the low nLw(λ) values observed in Figs. 7(d), 7(h), 7(l), and 7(p). It is important to note the shape of the nLw(862) scatter plot, and that the BMW-derived nLw(862) values get saturated near ~1.5–2.0 mW cm−2 µm−1 sr−1 and start to decrease (drop off) with increasing SWIR-derived nLw(λ) values. The SWIR-derived nLw(862) values reach as large as ~3.5 mW cm−2 µm−1 sr−1. Therefore, BMW should only be used when nLw(862) is less than ~1.5–2.0 mW cm−2 µm−1 sr−1, and when above this value the SWIR algorithm should be used . It should also be noted that the suboptimal (or even poor) performance of the all three NIR algorithms in Fig. 8(c) is due to extremely turbid waters in the region, with nLw(862) close to ~2.0 mW cm−2 µm−1 sr−1.
Similar to the first case, Tables 4 and 5 show the statistics in performance evaluation for the NIR atmospheric correction algorithms over the entire MODIS and VIIRS granules, with about 51,000 and 109,000 pixels included, respectively. For the MODIS granule (Table 4), the BMW significantly outperformed the other two algorithms in terms of all three statistics parameters: median ratio, bias, and STD values. It is also noted that the Wang algorithm outperformed the Bailey algorithm in all three parameters. For the VIIRS granule (Table 5), all NIR algorithms performed poorly with extremely large STD values, especially for BMW. Bailey seems to produce the smallest STD among the four, though still quite large, and its bias for blue bands reaches ~0.6 mW cm−2 µm−1 sr−1. The main reason for the poor performance of all three NIR reflectance correction algorithms is the presence of extremely turbid waters with the NIR nLw(λ) too large to be handled by any NIR nLw(λ) estimation approach . The performance of BMW deteriorates steeply once the water becomes extremely turbid (nLw(862) > ~2.0 mW cm−2 µm−1 sr−1), which results in the extremely large STD values in Table 5. This is caused by the normalized water-leaving reflectance ratio at two NIR bands α(λNIR1,λNIR2) (its value decreases with the increase of water turbidity [27, 33, 38]) as defined in Eq. (2) being too close to aerosol reflectance ratio ε(M)(λNIR1,λNIR2), as defined in Eq. (3), to be effectively differentiated from aerosol reflectance ratio ε(M)(λNIR1,λNIR2). This leads to large errors in nLw(λ) spectra derived from BMW algorithm, because the difference between α(λNIR1,λNIR2) and ε(M)(λNIR1,λNIR2) is the key to separate the aerosol and water signals for atmospheric correction from the corrected TOA signals defined by Eq. (1) [23, 33].
3.4. Statistics including additional cases
In order to obtain a more comprehensive and objective assessment of the performance of various NIR ocean reflectance correction algorithms in turbid water regions, we have included additional cases and calculated the overall statistics similar to Table 3, for all pixels from 30 MODIS-Aqua granules (10 for each of the 3 case study locations, including the three granules used in previous case studies). The date and time (in UTC) of the MODIS-Aqua granules included in the overall statistics are listed in Table 6 and the overall statistics are given in Table 7. The 30 granules were randomly picked after visually confirming, by browsing the MODIS-Aqua true color images, that the areas of interest were not covered by cloud or affected by sun-glint. The statistics are calculated similar to previous practices with the only exception being the ratio statistics. Due to the huge amount of pixels in the 30 satellite images, a mean ratio is used instead of a median ratio here. To remove outliers from the mean ratio calculation, only pixels with ratio values within 0.0–2.0 were included. For example, for BMW this criterion excluded ~3% at nLw(443) and ~5% at nLw(869) of all the pixels. Approximately 840,000 pixels passed the selection criteria and are included in the calculation.
The statistics obtained from 30 MODIS-Aqua granules show that overall the BMW algorithm performs better than the other two NIR algorithms in terms of both bias and STD, and the Bailey algorithm performed slightly better than Wang. Specifically, the BMW results have STD values ~1.2–1.5 times smaller than the Bailey and Wang algorithms. On the other hand, the mean ratio is very comparable between the three algorithms, with the BMW giving slightly better numbers for nLw(λ) results in two NIR bands.
4. Matchup comparisons with SeaBASS in situ measurements
The previous section has focused on the performance comparisons in turbid waters. Due to lack of reliable and available in situ data in extremely turbid water regions, we have used results from the SWIR algorithm as reference. In this section, however, we use the in situ measurements from the SeaWiFS Bio-optical Archive and Storage System (SeaBASS) data set  to evaluate the new NIR reflectance correction algorithm.
Table 8 lists the matchup statistics of MODIS-Aqua nLw(λ) products with SeaBASS in situ measurements from four different atmospheric correction algorithms: BMW, Bailey, NIR-SWIR, and SWIR. For all matchups, the satellite values are derived using the averaged value of the valid pixels within 5 × 5 pixels around the in situ measurement location in any satellite image which passed over within a ± 3 hours window of the measurement time, following Wang et al. (2009) procedure . The numbers of matchups are different for different bands because each in situ measurement may only include a subset of the bands listed here. In particular, the matchup count for nLw(λ) at 551 nm is significantly less than those in the other bands (51 for 551 nm versus thousands for other wavelengths). The ratios are calculated by dividing satellite-derived nLw(λ) by the in situ-measured nLw(λ), and both the median and mean ratio values are reported for comparison. The difference is defined as satellite-derived minus in situ-measured nLw(λ), and is expressed again in terms of “bias ± STD”.
It is noted that Bailey, BMW, and NIR-SWIR produce very similar statistics, indicating the matchups are located mostly at regions with relatively low to moderately turbid waters. The biases are generally small except for 551 nm, which is likely due to the small sample size. Furthermore, the NIR-SWIR produced slightly improved statistics overall than those of the BMW. On the other hand, SWIR results overestimated nLw(λ) at all bands with non-negligible biases and produced much larger STD values than the other three methods, especially at 667 nm band, due to small in situ-measured values and noisy from satellite derived values (low SWIR SNR values) [54, 55]. For mean/median ratios of nLw(667), results from two in situ data ranges are included to show the effect of small (near zero) nLw(667) values on the comparison ratio results. With excluding nLw(667) < 0.05 mW cm−2 µm−1 sr−1 (only 92 data left from total of 2873), ratio values for all algorithms are reasonable, with some overestimations from the SWIR method. The SWIR noise effects  on atmospheric correction are clearly shown in these comparisons. In addition, it shows that most in situ data are indeed from clear open ocean waters. Thus, these comparisons (Table 8) show that, for clear ocean waters, the Bailey, BMW, and NIR-SWIR algorithms generally have similar performance (as expected). Specifically, the current comparison indicates that BMW produces comparable results with Bailey, with respect to the SeaBASS data set. This data set includes regions with relatively low to moderately turbid waters, and by combining with the SWIR algorithm the new NIR-SWIR atmospheric correction, which uses BMW as the NIR component, produces slightly improved nLw(λ) results.
5. Global ocean color data processing using BMW
We have implemented the BMW algorithm in NOAA-MSL12 for VIIRS global ocean color data processing and have routinely produced VIIRS global ocean color data products, including global Level-3 VIIRS ocean color products for daily, 8-day, and monthly images. These VIIRS global Level-3 ocean color images as well as VIIRS calibration and validation results can be accessed from our website at (www.star.nesdis.noaa.gov/sod/mecb/color). The global images generated with BMW agree very well with those from the Bailey algorithm (not shown) as expected, with difference only in turbid coastal and inland waters. In addition, it is found that, for a normal one-day global VIIRS ocean color data processing, the BMW approach requires an average of about 25% longer CPU time than that with the Bailey algorithm. Overall, however, the BMW algorithm in MSL12 is still quite efficient with <~30 minutes for VIIRS global one-day ocean color data processing in a 144-core computer cluster system. Therefore, MSL12 with the BMW algorithm is readily available to routinely produce VIIRS global ocean color products, and the BMW algorithm can also be implemented into any other ocean color data processing systems.
6. Concluding remarks
From the case studies in the three regions including the U.S. East Coast, La Plata River estuary, and China’s east coast region, the BMW algorithm has been shown to produce the most consistent results with those from the SWIR algorithm in turbid coastal and inland waters. In less turbid waters, the BMW algorithm has produced results with the data quality comparable to the current NASA operating algorithm. From the current and earlier studies , the Bailey algorithm is shown to have some improvements over its previous algorithms and may work in turbid waters with nLw(859) up to ~1.0–1.5 mW cm−2 µm−1 sr−1. The BMW algorithm may be applicable to the waters with nLw(859) up to ~1.5–2.0 mW cm−2 µm−1 sr−1, and the SWIR algorithm with the SWIR 1240 nm band can be used in regions with nLw(859) up to ~2.0–2.5 mW cm−2 µm−1 sr−1. For extremely turbid waters with nLw(859) > ~2.5 mW cm−2 µm−1 sr−1, the SWIR atmospheric correction algorithm must be used with the combination of the atmospheric correction bands at two longer SWIR wavelengths (1640 and 2130 nm for MODIS, and 1610 and 2250 nm for VIIRS). However, it should be emphasized that the SWIR approach is generally preferred to directly derive the NIR nLw(λ) contributions instead of using modeling approach. Thus, it is required to have high performance SWIR bands for future satellite ocean color sensors .
In addition to the limitation from extremely turbid waters, the BMW algorithm also faces some constraints on the aerosol property variations over non-clear waters. Since the aerosol reflectance ratio ε(M)(λNIR1,λNIR2) over non-clear water pixels is interpolated from nearby clear water pixels, the spatial gradient of ε(M)(λNIR1,λNIR2) over that region should not be too large. If this condition is not met, there might be unacceptable error in the estimation of ε(M)(λNIR1,λNIR2) (acceptable error means <10% or <0.1 according to our experiments), as well as in the final derived nLw(λ) values. Still, the BMW algorithm has improved the accuracy greatly over the original MUMM algorithm by replacing the granule-level uniform ε(M)(λNIR1,λNIR2) approximation with a local ε(M)(λNIR1,λNIR2) generation scheme. In addition, it has been shown that the BMW algorithm can be implemented for routine global ocean color data processing for producing improved ocean color products in coastal and inland waters.
The work was supported by the Joint Polar Satellite System (JPSS) funding. The authors are grateful to all of the scientists and investigators who have contributed valuable in situ data to the SeaBASS database, and we thank the NASA Ocean Biology Processing Group for maintaining and distributing the SeaBASS database. The views, opinions, and findings contained in this paper are those of the authors and should not be construed as an official NOAA or U.S. Government position, policy, or decision.
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