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Edited by: David Antoine, Curtin University, Australia

Reviewed by: Quinten Vanhellemont, Royal Belgian Institute of Natural Sciences, Belgium; Thomas Schroeder, CSIRO Oceans and Atmosphere (O&A), Australia

This article was submitted to Atmospheric Science, a section of the journal Frontiers in Earth Science

This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.

National Aeronautics and Space Administration's (NASA's) current atmospheric correction (AC) algorithm for ocean color utilizes two bands and their ratio in the near infrared (NIR) to estimate aerosol reflectance and aerosol type. The algorithm then extrapolates the spectral dependence of aerosol reflectance to the visible wavelengths based on modeled spectral dependence of the identified aerosol type. Future advanced ocean color sensors, such as the Ocean Color Instrument (OCI) that will be carried on the Plankton, Aerosol, Cloud, and ocean Ecosystem (PACE) satellite, will be capable of measuring the hyperspectral radiance from 340 to 890 nm at 5-nm spectral resolution and at seven discrete short-wave infrared (SWIR) channels: 940, 1,038, 1,250, 1,378, 1,615, 2,130, and 2,260 nm. To optimally employ this unprecedented instrument capability, we propose an improved AC algorithm that utilizes all atmospheric-window channels in the NIR to SWIR spectral range to reduce the uncertainty in the AC process. A theoretical uncertainty analysis of this, namely, multiband AC (MBAC), indicates that the algorithm can reduce the uncertainty in remote sensing reflectance (_{rs}) retrievals of the ocean caused by sensor random noise. Furthermore, in optically complex waters, where the NIR signal is affected by contributions from highly reflective turbid waters, the MBAC algorithm can be adaptively weighted to the strongly absorbing SWIR channels to enable improved ocean color retrievals in coastal waters. We provide here a description of the algorithm and demonstrate the improved performance in ocean color retrievals, relative to the current NASA standard AC algorithm, through comparison with field measurements and assessment of propagated uncertainties in applying the MBAC algorithm to MODIS and simulated PACE OCI data.

Ocean color retrieval algorithms require an atmospheric correction (AC) process to separate the radiometric contribution of the atmosphere from the ocean, given the radiance measured at the top of atmosphere (TOA). The National Aeronautics and Space Administration (NASA) standard approach to the AC is a two-step process: the atmosphere and surface contributions are first removed using minimal assumptions about the water optical properties (Gordon and Wang, ^{−3}) where the NIR bands on MODIS-Aqua saturate at TOA radiances >2.8–3.45 mW cm^{−2} μm^{−1} sr^{−1} for 748 nm and >1.9–2.45 mW cm^{−2} μm^{−1} sr^{−1} for 869 nm and improper cloud masking (Aurin et al.,

One way for reducing the uncertainty in ocean color retrievals using the SWIR bands is to use more spectral information to reduce sensor random noise impact produced by low SNR. Gao et al. (

Cloud detection and masking in turbid waters can also be challenging. Extremely turbid waters are masked as clouds when a simple NIR threshold technique is used, as is the case for the standard NASA processing. Wang and Shi (

NASA is planning to launch the Plankton, Aerosol, Cloud, and ocean Ecosystem (PACE) satellite in 2022. The PACE satellite will host a state-of-the-art hyperspectral ocean color sensor (the Ocean Color Instrument, OCI). OCI will measure the hyperspectral radiance at the TOA from 340 to 890 nm at 5-nm spectral resolution and at seven discrete channels in the SWIR: 940, 1,038, 1,250, 1,378, 1,615, 2,130, and 2,260 nm, of which two are water vapor bands (940 and 1,378 nm) and five are window bands (i.e., no major gas absorption features). In fact, OCI will host the first instrument with a set of SWIR bands primarily designed for the ocean AC. The SWIR bands will have sufficient radiometric performance (i.e., high SNR with low systematic bias) to enable their use for AC over open oceans as well as coastal water conditions (Ibrahim and McKinna,

The heritage aerosol correction algorithm utilizes two bands either in the NIR or SWIR spectral range by calculating a band ratio of the Rayleigh (+ surface) and gas corrected reflectance, namely, epsilon, as follows:

where λ_{s} and λ_{l} correspond to the short and long wavelength either in the NIR or SWIR range (e.g., for MODIS, λ_{s} = 748 _{l} = 869 _{a}(λ) is the aerosol reflectance defined as:

_{0} is the extraterrestrial solar irradiance and μ_{0} is the cosine of the solar zenith angle. Since the aerosol radiance term is a strong function of the viewing/illumination geometry, the LUT is generated as a function of the solar and sensor zenith angle and relative azimuth angle. NASA's current approach to estimate the aerosol reflectance term is by finding the best match of the observed single scattering epsilon value to the model single scattering epsilon value. Since the LUT is calculated for a set of deterministic aerosol models based on Ahmad et al. (

The process of deriving single scattering epsilon and then converting it into multiple scattering radiance is unnecessary since currently computationally feasible multiple scattering tables can be easily generated and irreversible since there is no 1–1 relationship between multiple and single scattering when different aerosol types are mixed. Ahmad and Franz (

A graph of multiple-scattering epsilon (ε_{748} = ρ_{748}/ρ_{869}) vs. ρ_{869} for solar zenith, θ_{0} = 36°, view zenith, θ = 30°, relative azimuth angle, φ = 120°, and relative humidity (RH) = 80% from MODIS LUT (Ahmad and Franz,

In

The multiband AC (MBAC) algorithm is based on this multi-scattering epsilon approach by Ahmad and Franz (

where

For consistency with the system vicarious calibration procedure, which is performed relative to one wavelength in the NIR (e.g., 869 nm for MODIS), the optical depth is estimated at that wavelength.

For an observed aerosol reflectance, the optical depth can be calculated for each aerosol model set (

The aerosol reflectance as a function of the aerosol optical depth at 869 nm for aerosol models with relative humidity RH = 75% and 80% and for fine-mode fraction

The algorithm then calculates the aerosol optical depth and reflectance spectrally for all aerosol models as:

where ξ(λ,

The MBAC algorithm fits the aerosol reflectance in the NIR and SWIR for all models calculated in the previous step. However, since multiple solutions can exist, especially at low optical depth over the open ocean, we constrain the model selection to consider only those models with the two relative humidities bracketing the observed RH (as obtained from ancillary meteorological data). The maximum likelihood method is used to find the closest solution by minimizing the cost function:

where ρ_{obs}(λ) is the observed aerosol reflectance and ρ_{a}(λ, _{s}, to the longest band in the SWIR, λ_{l}. σ^{2}(λ) is the squared measurement uncertainty (variance assuming gaussian random noise) of the sensor, as determined from the sensor-specific noise model for a given radiance level.

_{rs}(NIR) = 0], where the AC is performed, and then the _{rs}(NIR) is estimated based on a bio-optical model that is propagated to the TOA to perform another AC and this process is repeated until the changes in the retrieved ocean reflectance is <2%. Similarly, the MBAC algorithm performs the AC at every iteration while bio-optical model parameters and the SW are tuned until the convergence criterion of 2% change in ocean reflectance is met. Thus, more iterations indicate more difficulty in fitting the bio-optical model possibly due to a higher optical complexity in turbid waters. The SW is then calculated as _{max} is the maximum number of iterations set in the Bailey algorithm (operationally _{max} = 11). Note that the actual number of iterations is reduced by 2 since the algorithm always performs at least two iterations in the AC: the first one with Rayleigh correction only (to estimate glint), and the second one for the aerosol correction. _{rs} convergence in the first few iterations where the AC is affected by the modeled NIR reflectance. After three or four iterations, the bio-optical model becomes irrelevant since the cost function will be mostly skewed toward the SWIR bands. With every iteration, a new cost function will be calculated with new aerosol models, and the NIR-SWIR ocean radiance will be estimated until the convergence criteria in Bailey et al. (

At each iteration of the AC, the following steps are performed.

Assuming a smooth unimodal shape to the cost function ^{2}(

For the sake of simplicity in the operational code implementation, the 2-d partial derivate can be converted into 1-d minimization problem by finding the minimum of the cost function for a given RH set (i.e., _{1}) from National Centers for Environmental Prediction (NCEP). However, ideally, the cost function minimization could be done for optical depth, fine-mode fraction, and relative humidity [i.e., ∇^{2}(τ, ^{2} values in the set will be:

The observed aerosol reflectance typically falls in-between the two closest aerosol reflectance, ρ_{a}(λ, _{1}, _{min 1}) and ρ_{a}(λ, _{1}, _{min 2}) from the model set, and are chosen based on the ^{2}.

where ^{2} and ends with the maximum ^{2}. However, there is no strong justification to mix all models since a mixture of all the models is not what happens in the atmosphere. A more physical description is to find the most immediate models around the observations, of which

This process is repeated for the second set of RH in the case that the ancillary RH falls between two values in the aerosol LUT to estimate ρ_{a}(λ, _{2}, _{mix}). Finally, a linear interpolation of the two estimated aerosol reflectance is calculated as follows:

The final ρ_{a}(λ, _{obs}, _{mix}) should fit through the observed aerosol reflectance in the NIR and SWIR channels, while the extrapolated reflectance to the visible channels based on the model mixtures are used for the aerosol correction.

To demonstrate how the fitting of the spectral information improves the determination of the aerosol spectral dependence, we show in ^{−3}, from The International Ocean-Color Coordinating Group (IOCCG) report 10 for MODIS bands, to the TOA and adding the Rayleigh (+ glint) and the aerosol reflectance at one geometry (solar zenith θ_{0} = 25°, view zenith, θ = 26°, relative azimuth angle, φ = 90°) (IOCCG,

Example to demonstrate the aerosol reflectance retrievals for MODISA using the 2-band (red curve) and 6-band (green curve) algorithms. The input model reflectance (black curve) is before adding noise; meanwhile, the observed reflectance (blue curve) is the noised reflectance after removing the Rayleigh + glint reflectance (i.e., the observed reflectance is the aerosol + water signal). The left panel is for aerosol with 50% fine-mode fraction and the right panel is for 10% fine-mode fraction, and in both cases for 0.2 optical depth at 869 nm. Solar zenith θ_{0} = 25°, view zenith, θ = 26°, relative azimuth angle, φ = 90°.

Since the 2-band algorithm aims to match the spectral dependence of the aerosol as a two-band ratio in the NIR, extrapolating that information to the visible (and SWIR) will depend on the radiometric quality of these two NIR bands and the linear mixing of the aerosol types in the LUT necessary for the visible correction. As can be seen from

Ocean color bands are designed to avoid detection in spectral regions contaminated by strongly absorbing gases such as water vapor, oxygen, methane, and carbon dioxide. However, due to the imperfect spectral response of the detectors (i.e., broad bandwidth and out-of-band response), the measured TOA radiance is modulated by strongly absorbing gases. AC requires a correction for strongly absorbing gases as well as broadly absorbing gases, such as ozone and nitrogen dioxide that mostly absorb in the visible. The current NASA algorithm uses the method of Gordon (

The aerosol LUT in the MBAC algorithm is pre-computed at discretized optical properties of the aerosols; thus, the interpolation step between different fine-mode fractions and relative humidity increases the uncertainty in the retrieval of the remote sensing reflectance. To assess the algorithm error, we introduce a set of aerosol optical properties that are not part of the discretized LUT. We do so by simulating the aerosol reflectance set for an RH of 77.5%, which falls between the 75% and 80% RH in the operational LUT. The aerosol properties and reflectance are then calculated using the model set of Ahmad et al. (_{w} for the normalized water-leaving radiance. We do so by assuming a reference ocean reflectance from IOCCG report 10 for case I clear waters with chlorophyll concentration, Chlor-a, 0.03 mg m^{−3} (IOCCG, _{w} at 443 nm for all view geometries in the LUT, where 0° relative azimuth is specular reflection plane, and for three solar angles, 10, 20, 30, and 60°.

_{w}, at 443 nm as a function of the viewing geometry for solar zenith angles of 10, 20, 30, and 60°, respectively. The simulations are done for all aerosol models with relative humidity RH = 77.5% at optical depth at 869 nm from 0.05 to 0.35, and the retrieval is done using models with RH = 75% and 80%.

The aerosol models encompass all aerosol types, as defined in Ahmad et al. (

The normalized density histogram of the percentage difference for the aerosol reflectance and optical depth retrievals at 443 and 869 nm, respectively, and the Angstrom coefficient for all cases of different aerosol types, optical depths, and geometries.

The mean bias in the aerosol reflectance at 443 nm is −0.04% and the standard deviation is 3.5%, while optical depth retrieval is 0.05% with a standard deviation of 1.35%, and the Angstrom coefficient retrieval shows a mean bias of −1.9% with a standard deviation of 15%. The small bias and standard deviation indicate that the algorithm can well-retrieve the optical depth; however, there is a more significant uncertainty in the Angstrom coefficient retrievals with tendency to retrieve coarser aerosol types than the input data. This could be an inherent error due to the definition of the Angstrom coefficient that assumes a power law relationship of the aerosol spectral dependence from 443 to 869 nm. Since we are including all cases of aerosol types with equal representation, the uncertainty is overestimated. In the cases at the extreme ends of the aerosol's LUT, there could be large errors in the retrievals because of the necessity to extrapolate to models that are not in the table. However, these extreme ends of the LUT are intentionally added to reduce that necessity for the extrapolation since these aerosol conditions are rarely observed based on AERONET data (Ahmad et al.,

The uncertainty in the TOA radiance measurements due to sensor random noise will impact the retrieval uncertainty of the ocean reflectance through influence on the AC process. The uncertainty propagation of the sensor noise is simulated here using the Monte Carlo method, where the sensor noise at a given SNR value is generated for 300 iterations for all aerosol model sets mentioned above. We performed the sensitivity analysis using the NIR 2-band AC (standard approach) and a 6-band MBAC (i.e., for MODIS 748, 859, 869, 1,240, 1,640, and 2,130 nm). The theoretical analysis for MODIS-Aqua is done for the six bands; however, we drop 1,640 nm in our real retrievals because of defective detectors at that band. The noise model here is based on the MODIS model with the noise-equivalent radiance of:

where _{0}(λ) and _{1}(λ) are linear fit coefficients of the noise model from Xiong et al. (

The random noise for each iteration is generated as follows:

and the Gaussian random noise is generated as:

The result of the analysis shown in _{w}, is closer to 0.0016 levels for the 6-band MBAC algorithm, while it is slightly higher near 0.0021 levels for the 2-band AC for MODIS-Aqua noise levels. The improvement in the uncertainty between the two algorithms is shown in _{w}(6 − _{w}(2 −

_{w}, at 443 nm as a function of the viewing geometry for solar zenith angles of 30°, using six bands MBAC and two NIR bands AC, respectively.

To have a complete understanding of the potential sources of uncertainty for the MBAC algorithm, we also performed an analysis to understand the impact of systematic uncertainty on the retrievals. Systematic errors in measurements are very difficult to characterize post-launch due to the lack of an accurate absolute calibration apparatus on-orbit. Typically, a solar diffuser is used as a calibration reference; however, due to the immediate degradation of the diffuser, the absolute calibration with a high degree of certainty cannot generally be achieved. Thus, the ocean color community depends on a system vicarious calibration, which aims to remove any systematic bias due to the sensor or algorithm errors. For all ocean color sensors processed by NASA GSFC, we use the vicarious calibration method by Franz et al. (_{n}, λ_{m}), of the system errors is equal to 0.1 for off-diagonal elements and 1 for diagonal ones. The correlated random bias is then calculated as follows:

The bias is generated for the number of iterations in the MC analysis for each band. _{n}, λ_{m}) is Lower Cholesky factorization of the covariance matrix such that:

_{n}, λ_{m}) is the diagonal matrix. The Cholesky matrix allows the generation of random errors with inter-bands correlation specified in the covariance matrix. The bias levels are then re-adjusted to match the level of the instrument.

In _{w}, at 443 nm is due to algorithm + random + systematic errors for the 6-band MBAC and NIR 2-band AC, respectively. The average uncertainty for the 2-band AC is 0.0036, while for the 6-band MBAC algorithm, the average uncertainty is 0.0024, with an improvement of 33% over the 2-band standard algorithm as shown in

_{w}, at 443 nm as a function of the viewing geometry for solar zenith angles of 30°, using six bands MBAC and NIR two bands AC, respectively.

Unlike MODIS or VIIRS, the SWIR detection assembly on OCI will include channels specifically tuned for good radiometric performance over the relatively dark ocean. This significant advancement will provide an opportunity to improve ocean color observations in complex water environments (i.e., coastal ocean) due to the increased sensitivity to the aerosols and less to the water signal. With the MBAC algorithm, the combined utilization of all SWIR channels (excluding water vapor bands) and NIR channels will offer an improved AC over coastal waters and open ocean by utilizing more spectral bands to reduce the effect of sensor noise and with adaptive weighting toward the bands that are less influenced by non-negligible water-leaving radiance.

_{w}, for proxy OCI wavelengths from the UV to red wavelengths for open ocean and coastal turbid waters (with high total suspended material, TSM). The open ocean reflectance was simulated with Hydrolight assuming Chlor-a = 0.03 mg/m^{3} and TSM = 0 g m^{−3} while turbid waters assume TSM = 10 g m^{−3} that has been propagated to the TOA for each atmospheric composition and geometry [more details are in Ibrahim and McKinna (_{0} = 25°, view zenith, θ = 26°, relative azimuth angle, φ = 90°). For an OCI-like instrument, the SWIR MBAC algorithm shows a slight reduction in the uncertainty as compared to the 2-band NIR AC over open ocean conditions. In contrast, over turbid waters, the non-negligible water-leaving radiance at the NIR bands shows a large uncertainty (systematic bias) in the reflectance retrievals from the 2-band NIR AC, which is substantially reduced using the SWIR MBAC algorithm. As previously discussed, the SW,

The spectral uncertainty, Δ_{w}, for a proxy OCI wavelengths from the UV to red wavelengths for open ocean and coastal turbid waters. The uncertainty is calculated at one specific geometry (i.e., solar zenith θ_{0} = 25°, view zenith, θ = 26°, relative azimuth angle, φ = 90°). The analysis assumes a 2% systematic bias at NIR and SWIR bands.

The MBAC algorithm has been implemented into NASA's L2gen processing code. L2gen (Level-2 generator) within the SeaDAS software package is the multi-sensor Level-1 to Level-2 processing code developed and maintained by NASA's Ocean Biology Processing Group (OBPG) that is capable of retrieving ocean color products from TOA radiances for a host of sensors. L2gen supports multiple AC methods and variations that can be applied to a variety of ocean color sensors (Gordon and Wang,

MODISA chlor-a retrieval of a scene over the east coast of the US using the operational 2-bands and the MBAC algorithm, the average percent difference (APD), and the NIR Spectral Weight (SW) map used in the MBAC retrievals.

We also show in

MODISA retrieval of the aerosols' Angstrom coefficient of a scene over the east coast of the US using the operational 2-band and the MBAC algorithm.

The operational algorithm shows an increased Angstrom over turbid or shallow regions near the coast that can be attributed to the failure in the NIR iterative algorithm to mitigate the non-negligible water-leaving radiance in the NIR bands. This artifact in the aerosol properties typically leads to the overcorrection of aerosol radiance and the potential retrieval of negative radiances. However, using the adaptive SW in the MBAC algorithm, it quickly damps that NIR contamination by decreasing the weight of the NIR bands in the cost function, and thus, the Angstrom coefficient is reduced to a range that agrees better with the surrounding pixels. Notice that the southwesternmost part of the scene shows an increase in the Angstrom coefficient with the MBAC algorithm, which could be a more realistic retrieval or an artifact due to a bias in the SWIR calibration. However, this could indicate that the MBAC algorithm is sensitive to fine-mode as much as coarse-mode aerosols. Better quantitative evidence is further discussed in the next section.

Using NASA's SeaBASS dataset of _{rs} measurements, we performed match-up to MODIS retrievals at eight bands in the visible spectral range near 412, 443, 488, 531, 547, 555, 667, and 678 nm, using both the 2-band operation algorithm and the MBAC algorithm for MODIS-Aqua. Many of the SeaBASS data points are coastal, however less frequent than AERONET-OC data. _{rs}(λ), ^{2}, and the mean bias in the retrievals compared to _{rs}(λ), for the 6-band MBAC algorithm is reduced as compared to the operational algorithm, especially in the green wavelengths at 531, 547, and 555 nm, where the uncertainty is reduced by 52, 55, and 29%, respectively. There is a slight increase in uncertainty at 678 nm, which could be due to the lack of high-quality

A summary of statistical indicators to match-ups of MODISA retrievals with _{rs} from the SeaBASS dataset.

_{rs}^{−1}) |
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_{rs} (^{−1}) |
^{2} |
^{−1}) |
_{rs} (^{−1}) |
^{2} |
^{−1}) |
|||

412 | 331 | 0.00078–0.01783 | 0.0020 | 0.74 | −0.00089 | 0.0020 | 0.71 | −0.000012 |

443 | 486 | 0.00126–0.02289 | 0.0014 | 0.73 | −0.00044 | 0.0014 | 0.71 | 0.000029 |

488 | 506 | 0.00146–0.02587 | 0.0013 | 0.74 | −0.00053 | 0.0011 | 0.76 | −0.00017 |

531 | 95 | 0.00137–0.02759 | 0.0021 | 0.77 | −0.00050 | 0.0011 | 0.91 | −0.00013 |

547 | 51 | 0.00102–0.02799 | 0.0029 | 0.68 | −0.00079 | 0.0013 | 0.90 | −0.00018 |

555 | 353 | 0.00002–0.01196 | 0.0014 | 0.76 | −0.00058 | 0.0010 | 0.83 | −0.00040 |

667 | 380 | 0.00013–0.00286 | 0.0005 | 0.72 | −0.00007 | 0.0003 | 0.85 | −0.00008 |

678 | 12 | 0.00078–0.01783 | 0.0004 | 0.78 | −0.00004 | 0.0005 | 0.69 | −0.00006 |

A further investigation into a proper estimation of systematic uncertainty and its spectral correlation is necessary to provide uncertainties that are similar to

The MBAC algorithm shows several potential merits over NASA's current operational Gordon and Wang (

AI performed the analysis in the manuscript for the sections Error Assessment, Application to Ocean Color Instrument, Application to MODIS Retrievals, and Validation. BF contributed to editing and guiding the manuscript discussion. ZA provided

AI was employed by Science Systems and Applications Inc. and ZA was employed by Science Application International Corp. when this manuscript was being prepared. The remaining authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

We acknowledge the MOBY team of NOAA for providing the