A tutorial review is provided of forward and inverse radiative transfer in coupled atmosphere-snow/ice-water systems. The coupled system is assumed to consist of two adjacent horizontal slabs separated by an interface across which the refractive index changes abruptly from its value in air to that in ice/water. A comprehensive review is provided of the inherent optical properties of air and water (including snow and ice). The radiative transfer equation for unpolarized as well as polarized radiation is described and solutions are outlined. Several examples of how to formulate and solve inverse problems encountered in environmental optics involving coupled atmosphere-water systems are discussed in some detail to illustrate how the solutions to the radiative transfer equation can be used as a forward model to solve practical inverse problems.

In this work, some sea viewing wide field‐of‐view sensor (SeaWiFS) images over the Santa Barbara Channel (SBC) are analysed. Pixel‐by‐pixel measurements of radiances at eight SeaWiFS channels and analytic Jacobians are simulated using a coupled atmosphere–ocean radiative transfer model. The inverse algorithm is based on optimal estimation with loosely constrained a priori data. The five‐element state vector has two aerosol (optical depth at 865 nm, bimodal fraction of particles) and three marine (chlorophyll concentration, detrital/dissolved‐matter absorption at 443 nm, and backscattering coefficient at 443 nm) parameters. The retrieval is stable and well posed; the results are smoother and show less spread than those derived from the standard SeaDAS v4.8 algorithm. For a 28 February 2003 SeaWiFS image, the average radiance residual is less than 1% for seven SeaWiFS channels, and less than 2% for the 765 nm channel. For a series of SBC SeaWiFS match‐up cases over a 4‐year period, estimated water‐leaving radiances agree well with field measurements.

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 ($R_{\mathrm{rs}}$ estimates), aerosol optical depths, and inherent optical properties. This paper expands the capability of OC-SMART by quantifying uncertainties in ocean color retrievals. Bayesian inversion is used to relate measured top of atmosphere radiances and a priori data to estimate posterior probability density functions and associated uncertainties. A framework of the methodology and implementation strategy is presented and uncertainty estimates for $R_{\mathrm{rs}}$ retrievals are provided to demonstrate the approach by applying it to MODIS, OLCI Sentinel-3, and VIIRS sensor data.

We have shown that solutions to the radiative transfer equation for a homogeneous slab yield a zenith radiance reflectance that for collimated beam incidence in the nadir direction can be expressed in terms of the lidar ratio, defined as the extinction coefficient divided by the 180 $$^\circ $$∘ backscattering coefficient. The recently developed QlblC method, which allows one to quantify layer-by-layer contributions to radiances emerging from a slab illuminated with a collimated beam of radiation, was used to show explicitly that in the single-scattering approximation the attenuated backscatter coefficient estimated by the new QlblC method gives the same result as the lidar equation. Originally developed for the continuous wave (CW) lidar problem, we have extended the new QlblC method to apply to the pulsed lidar problem. A specific example is provided to illustrate the challenge encountered for ocean property retrievals from space observations due to the fact that a very significant fraction of the signal is due to aerosol scattering/absorption; typically only about 10% (or less) comes from the ocean. Graphical

Snow parameters have traditionally been retrieved using discontinuous, multi-band sensors; however, continuous hyperspectral sensors are now being developed as an alternative. In this paper, we investigate the performance of various sensor configurations using machine learning neural networks trained on a simulated dataset. Our results show improvements in the accuracy of retrievals of snow grain size and impurity concentration for continuous hyperspectral channel configurations. Retrieval accuracy of snow albedo was found to be similar for all channel configurations.

The Ocean Color - Simultaneous Marine and Aerosol Retrieval Tool (OC-SMART) is a robust data processing platform that supports a large array of multi-spectral and hyper-spectral sensors. It provides accurate aerosol optical depths and remote sensing reflectances (Rrs estimates) that can be used to generate products such as absorption coefficients due to phytoplankton and detritus/Gelbstoff as well as backscattering coefficients due to particulate matter. The OC-SMART platform yields improved performance in complex environments by utilizing scientific machine learning (SciML) in conjunction with comprehensive radiative transfer computations. This paper expands the capability of OC-SMART by quantifying uncertainties in ocean color retrievals. Bayesian inversion is used to relate measured top of atmosphere radiances and a priori data to estimate posterior probability density functions and associated uncertainties. A framework of the methodology and implementation strategy is presented and uncertainty estimates for Rrs retrievals are provided to demonstrate the approach by applying it to MODIS, OLCI Sentinel-3, and VIIRS sensor data.