The Ocean Color—Simultaneous Marine and Aerosol Retrieval Tool (OC-SMART) is a robust data processing platform utilizing scientific machine learning (SciML) in conjunction with comprehensive radiative transfer computations to provide accurate remote sensing reflectances (

Remote sensing of the ocean is now routinely performed by using instruments deployed on satellite platforms [

Several AC algorithms have have been developed to estimate the water-leaving radiance and achieved reasonable results in open ocean areas where the water-leaving radiances at near-infrared (NIR) wavelengths are negligible. Significant issues remain however; in coastal waters, which are not black in the NIR, negative water-leaving radiances are frequently produced by traditional AC algorithms [

Traditional AC approaches typically do not provide uncertainty estimates, which should be included, however, to gain confidence in retrieved results. Recently, some studies have discussed uncertainty issues based on optimal estimation (Bayesian inversion) [

The Ocean Color—Simultaneous Marine and Aerosol Retrieval Tool (OC-SMART) approach utilizes scientific machine learning (SciML) in conjunction with radiative transfer computations of the coupled atmosphere–water system to perform the AC step and retrieve water products from the resulting

To garner meaningful information about water properties from satellite ocean color measurements, atmospheric and water surface effects must be accounted for. This task has historically been accomplished by taking the total radiance at the top of the atmosphere (TOA),

To overcome these problems, a new approach, focused on coastal areas, was invented [

It has been demonstrated that multilayer, feed-forward neural networks with one or more hidden layers and a non-linear activation function can approximate non-linear functions [

The performance of our MLNN algorithms was first evaluated with a synthetic dataset. We randomly selected 90% of the synthetic dataset to train the (

Currently OC-SMART supports ocean color data retrievals from 11 multi-spectral and hyper spectral sensors onboard satellites operated by the National Aeronautics and Space Administration (NASA), the National Oceanic and Atmospheric Administration (NOAA), the European Space Agency (ESA), the Japan Aerospace Exploration Agency (JAXA), the Korea Institute of Ocean Science and Technology (KIOST), and the China Meteorological Administration (CMA), which include SeaStar/SeaWiFS (NASA), MODIS/Aqua (NASA), SNPP/VIIRS (NASA/NOAA), ISS/HICO (NASA), Landsat8/OLI (NASA), DSCOVR/EPIC (NOAA), Sentinel-2/MSI (ESA), Sentinel-3/OLCI (ESA), GCOM-C/SGLI (JAXA), COMS/GOCI (NASA), and FengYun-3D/MERSI (CMA). The performance of OC-SMART was first tested using an independent synthetic testing dataset. Then the ocean color products retrieved by OC-SMART were validated against in situ measurements from MOBY [

As alluded to in

The Bayesian approach is summarized in this Section [

Experimental error is frequently described by a normal distribution [

Taking the logarithm of Equation (

Equation (

For our purposes, sensor L1B calibrated radiances and sun-satellite geometry data are processed by OC-SMART to yield the desired retrieval parameters. These L2 retrieval parameters are inserted into the forward model and used to compute simulated Rayleigh-corrected TOA radiances, as explained in some detail in

As alluded to above, sensor L1B Rayleigh-corrected radiances and sun-satellite geometry data comprise the measurement vector

It is important to note that if the goal is to make a retrieval of state parameters directly from TOA reflectance measurements, then the input parameters

On the other hand, if the goal is to use the MLNN [Equation (

In Equation (

The Jacobian matrix in Equations (

The measurement error covariance matrix

The measurement error covariance matrix

The

Verification of the remote sensing reflectance (

Let us now consider the special case of Equation (

Using MODIS Aqua L1B calibrated radiances and sun-satellite geometry data with 1 km resolution as inputs to OC-SMART, we produced L2 retrievals of

To explain this behavior, let us first examine the terms of the posterior error covariance matrix Equation (see Equation (

With this situation in mind now consider our definition of the

When looking at the Gulf of Mexico in

The RGB image in

The methodology laid out above can easily be applied to other ocean color sensors. Modifications to the experimental setup described in

The locations of interest shown for various regions and several sensors are intended to provide insight on a variety of water conditions beyond the open ocean where OC-SMART and other AC algorithms perform best. The OC-SMART approach currently uses a large ensemble of IOP realizations in order to represent open ocean water, as well as turbid coastal waters. It is designed to provide a smooth, seamless transition between clear open ocean and turbid coastal waters. Although adequate for many coastal regions, additional IOP data may be needed to obtain more accurate results in some optically complex coastal regions. To improve the performance of OC-SMART in such regions, more IOP data could be added to improve the response/output of OC-SMART. Introducing additional IOP modeling data is also expected to improve the uncertainty estimations discussed in this paper as it would allow use of more adaptive

We have successfully implemented a method based on Bayes’ theorem to estimate uncertainties associated with OC-SMART remote sensing reflectance (

This framework for uncertainty estimation could be expanded to include other OC-SMART retrievals, such as aerosol optical depth, chlorophyll concentration, absorption coefficients, and backscattering coefficients. The inclusion of uncertainty estimates for aerosol optical depths, in particular, would involve only minor changes to the methods described in this paper, namely adjustments to the APE values in the

Improvements could be made to our estimations by obtaining better information on the

All authors contributed to conception and design of methodology presented in this paper. Y.F., W.L. and K.S. formulated work involved with OC-SMART. E.P. and Y.F. performed the mathematical analysis. E.P. wrote the first draft of the manuscript and produced all figures. All authors have read and agreed to the published version of the manuscript.

Data used in this paper is available upon request, please contact the corresponding author with any inquiries. The OC-SMART platform can be accessed from

The Authors would like to acknowledge NASA’s Distributed Active Archive Centers and ESA’s Copernicus Open Access Hub for providing a platform for us to access data used in this paper.

The 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.

Consider a Gaussian distribution, which for an arbitrary vector

Framework for formulation of the uncertainty estimations applied to OC-SMART.

The difference between simulated Rayleigh-corrected TOA radiances and measured Rayleigh-corrected TOA radiances from MODIS represented as a percentage for (

(

Remote sensing reflectance data from MODIS sensor (

(

Remote sensing reflectance data from MODIS sensor (

(

Remote sensing reflectance data from MODIS sensor (

(

Remote sensing reflectance data from OLCI Sentinel-3 sensor (

(

Remote sensing reflectance data from VIIRS sensor (