Sensitivity of radiative transfer to small-angle scattering in the ocean: Quantitative assessment

Monitoring Water Transparency in Shallow and Eutrophic Lake Waters Based on GOCI Observations

Water transparency represented by the Secchi disk depth (Zsd) plays an important role in understanding water ecology environment variations, especially for optically complex and shallow lake waters. In this study, using in situ measured remote sensing reflectance (Rrs), diffuse attenuation coefficient (Kd), and Zsd data collected in Lake Taihu (China), a regional algorithm for estimating Kd from Rrs was designed, and the semi-analytical model proposed by Lee et al. (2015) (hereafter called Lee_2015 model) was refined using a linear scaling correction for remote sensing of Zsd. The results showed that a good agreement between the derived Kd and in situ measured data (mean absolute percentage error (MAPE) = 26% for Kd(490); MAPE < 5% for Kd at 443, 555, and 660 nm). The in situ Rrs-derived Zsd results using the refined Lee_2015 model compared well with the in situ measured Zsd (R2 = 0.72 and MAPE = 36%), which was an obvious improvement over the Lee_2015 model in our study region. Subsequently, the refined Lee_2015 model was applied to the geostationary ocean color imager (GOCI) observations between 2012 and 2018 to yield the spatial and temporal variations of water transparency in the Lake Taihu waters. The long-term mean distribution of Zsd revealed that water transparency values in the northeastern Lake Taihu were generally higher than those in the southwest part. Monthly climatological Zsd patterns suggested that the Zsd distributions had large temporal variability, and distinct monthly patterns of Zsd existed in different subregions of Lake Taihu. The significant interannual variations of Zsd in Lake Taihu are probably affected by a combination of the water column stability mainly caused by wind, water temperature, human activity, and riverine discharge. The present study can provide a new approach for quantifying water visibility and serve for water-color remote sensing of optically complex and highly turbid waters.

Ocean Color Analytical Model Explicitly Dependent on the Volume Scattering Function

An analytical radiative transfer (RT) model for remote sensing reflectance that includes the bidirectional reflectance distribution function (BRDF) is described. The model, called ZTT (Zaneveld-Twardowski-Tonizzo), is based on the restatement of the RT equation by Zaneveld (1995) in terms of light field shape factors. Besides remote sensing geometry considerations (solar zenith angle, viewing angle, and relative azimuth), the inputs are Inherent Optical Properties (IOPs) absorption a and backscattering bb coefficients, the shape of the particulate volume scattering function (VSF) in the backward direction, and the particulate backscattering ratio. Model performance (absolute error) is equivalent to full RT simulations for available high quality validation data sets, indicating almost all residual errors are inherent to the data sets themselves, i.e., from the measurements of IOPs and radiometry used as model input and in match up assessments, respectively. Best performance was observed when a constant backward phase function shape based on the findings of Sullivan and Twardowski (2009) was assumed in the model. Critically, using a constant phase function in the backward direction eliminates a key unknown, providing a path toward inversion to solve for a and bb. Performance degraded when using other phase function shapes. With available data sets, the model shows stronger performance than current state-of-the-art look-up table (LUT) based BRDF models used to normalize reflectance data, formulated on simpler first order RT approximations between rrs and bb/a or bb/(a + bb) (Morel et al., 2002; Lee et al., 2011). Stronger performance of ZTT relative to LUT-based models is attributed to using a more representative phase function shape, as well as the additional degrees of freedom achieved with several physically meaningful terms in the model. Since the model is fully described with analytical expressions, errors for terms can be individually assessed, and refinements can be readily made without carrying out the gamut of full RT computations required for LUT-based models. The ZTT model is invertible to solve for a and bb from remote sensing reflectance, and inversion approaches are being pursued in ongoing work. The focus here is with development and testing of the in-water forward model, but current ocean color remote sensing approaches to cope with an air-sea interface and atmospheric effects would appear to be transferable. In summary, this new analytical model shows good potential for future ocean color inversion with low bias, well-constrained uncertainties (including the VSF), and explicit terms that can be readily tuned. Emphasis is put on application to the future NASA Plankton, Aerosol, Cloud, and ocean Ecosystem (PACE) mission.

An overview of approaches and challenges for retrieving marine inherent optical properties from ocean color remote sensing

Ocean color measured from satellites provides daily global, synoptic views of spectral waterleaving reflectances that can be used to generate estimates of marine inherent optical properties (IOPs). These reflectances, namely the ratio of spectral upwelled radiances to spectral downwelled irradiances, describe the light exiting a water mass that defines its color. IOPs are the spectral absorption and scattering characteristics of ocean water and its dissolved and particulate constituents. Because of their dependence on the concentration and composition of marine constituents, IOPs can be used to describe the contents of the upper ocean mixed layer. This information is critical to further our scientific understanding of biogeochemical oceanic processes, such as organic carbon production and export, phytoplankton dynamics, and responses to climatic disturbances. Given their importance, the international ocean color community has invested significant effort in improving the quality of satellite-derived IOP products, both regionally and globally. Recognizing the current influx of data products into the community and the need to improve current algorithms in anticipation of new satellite instruments (e.g., the global, hyperspectral spectroradiometer of the NASA Plankton, Aerosol, Cloud, ocean Ecosystem (PACE) mission), we present a synopsis of the current state of the art in the retrieval of these core optical properties. Contemporary approaches for obtaining IOPs from satellite ocean color are reviewed and, for clarity, separated based their inversion methodology or the type of IOPs sought. Summaries of known uncertainties associated with each approach are provided, as well as common performance metrics used to evaluate them. We discuss current knowledge gaps and make recommendations for future investment for upcoming missions whose instrument characteristics diverge sufficiently from heritage and existing sensors to warrant reassessing current approaches.

Re-examining the effect of particle phase functions on the remote-sensing reflectance

Even though it is well known that both the magnitude and detailed angular shape of scattering (phase function, PF), particularly in the backward angles, affect the color of the ocean, the current remote-sensing reflectance (R_rs) models typically account for the effect of its magnitude only through the backscattering coefficient (b_b). Using 116 volume scattering function (VSF) measurements previously collected in three coastal waters around the U.S. and in the water of the North Atlantic Ocean, we re-examined the effect of particle PF on R_rs in four scenarios. In each scenario, the magnitude of particle backscattering (i.e., b_bp) is known, but the knowledge on the angular shape of particle backscattering is assumed to increase from knowing nothing about the shape of particle PFs to partially knowing the particle backscattering ratio (B_p), the exact backscattering shape as defined by β˜_p(γ≥90°) (particle VSF normalized by the particle total scattering coefficient), and the exact backscattering shape as defined by the χ_p factor (particle VSF normalized by the particle backscattering coefficient). At sun zenith angle=30°, the nadir-viewed R_rs would vary up to 65%, 35%, 20%, and 10%, respectively, as the constraints on the shape of particle backscattering become increasingly stringent from scenarios 1 to 4. In all four scenarios, the R_rs variations increase with both viewing and sun angles and are most prominent in the direction opposite the sun. Our results show a greater impact of the measured particle PFs on R_rs than previously found, mainly because our VSF data show a much greater variability in B_p, β˜_p(γ≥90°), and χ_p than previously known. Among the uncertainties in R_rs due to the particle PFs, about 97% can be explained by χ_p, 90% by β˜_p(γ≥90°), and 27% by B_p. The results indicate that the uncertainty in ocean color remote sensing can be significantly constrained by accounting for χ_p of the VSFs.

Optical closure in marine waters from in situ inherent optical property measurements

Optical closure using radiative transfer simulations can be used to determine the consistency of in situ measurements of inherent optical properties (IOPs) and radiometry. Three scattering corrections are applied to in situ absorption and attenuation profile data for a range of coastal and oceanic waters, but are found to have only very limited impact on subsequent closure attempts for these stations. Best-fit regressions on log-transformed measured and modelled downwards irradiance, Ed, and upwards radiance, Lu, profiles have median slopes between 0.92 - 1.24, revealing a tendency to underestimate Ed and Lu with depth. This is only partly explained by non-inclusion of fluorescence emission from CDOM and chlorophyll in the simulations. There are several stations where multiple volume scattering function related data processing steps perform poorly which suggests the potential existence of unresolved features in the modelling of the angular distribution of scattered photons. General optical closure therefore remains problematic, even though there are many cases in the data set where the match between measured and modelled radiometric data is within 25% RMS%E. These results are significant for applications that rely on optical closure e.g. assimilating ocean colour data into coupled physical-ecosystem models.

Detailed validation of the bidirectional effect in various Case I and Case II waters

Simulated bidirectional reflectance distribution functions (BRDF) were compared with measurements made just beneath the water's surface. In Case I water, the set of simulations that varied the particle scattering phase function depending on chlorophyll concentration agreed more closely with the data than other models. In Case II water, however, the simulations using fixed phase functions agreed well with the data and were nearly indistinguishable from each other, on average. The results suggest that BRDF corrections in Case II water are feasible using single, average, particle scattering phase functions, but that the existing approach using variable particle scattering phase functions is still warranted in Case I water.

Relationships between water attenuation coefficients derived from active and passive remote sensing: a case study from two coastal environments

Relationships between the satellite-derived diffuse attenuation coefficient of downwelling irradiance (K(d)) and airborne-based vertical attenuation of lidar volume backscattering (α) were examined in two coastal environments. At 1.1 km resolution and a wavelength of 532 nm, we found a greater connection between α and K(d) when α was computed below 2 m depth (Spearman rank correlation coefficient up to 0.96), and a larger contribution of K(d) to α with respect to the beam attenuation coefficient as estimated from lidar measurements and K(d) models. Our results suggest that concurrent passive and active optical measurements can be used to estimate total scattering coefficient and backscattering efficiency in waters without optical vertical structure.

Light scattering by coccoliths detached from Emiliania huxleyi

We used in situ radiance/irradiance profiles to retrieve profiles of the spectral backscattering coefficient for all particles in an E. huxleyi coccolithophore bloom off the coast of Plymouth, UK. At high detached coccolith concentrations the spectra of backscattering all showed a minimum near approximately 550 to 600 nm. Using flow cytometry estimates of the detached coccolith concentration, and assuming all of the backscattering (over and above the backscattering by the water itself) was due to detached coccoliths, we determined the upper limit of the backscattering cross section (sigma(b)) of individual coccoliths to be 0.123+/-0.039 microm(2)/coccolith at 500 nm. Physical models of detached coccoliths were then developed and the discrete dipole approximation was used to compute their average backscattering cross section in random orientation. The result was 0.092 microm(2) at 500 nm, with the computed sigma(b) displaying a spectral shape similar to the measurements, but with less apparent increase in backscattering toward the red. When sigma(b) is computed on a per mole of calcite, rather than a per coccolith basis, it agreed reasonably well with that determined for acid-labile backscattering at 632 nm averaged over several species of cultured calcifying algae. Intact coccolithophore cells were taken into account by arguing that coccoliths attached to coccolithophore cells (forming a "coccosphere") backscatter in a manner similar to free coccoliths in random orientation. Estimating the number of coccoliths per coccosphere and using the observed number of coccolithophore cells resulted is an apparent backscattering cross section at 500 nm of 0.114+/-0.013 microm(2)/coccolith, in satisfactory agreement with the measured backscattering.

Spectra of particulate backscattering in natural waters

Hyperspectral profiles of downwelling irradiance and upwelling radiance in natural waters (oligotrophic and mesotrophic) are combined with inverse radiative transfer to obtain high resolution spectra of the absorption coefficient (a) and the backscattering coefficient (b(b)) of the water and its constituents. The absorption coefficient at the mesotrophic station clearly shows spectral absorption features attributable to several phytoplankton pigments (Chlorophyll a, b, c, and Carotenoids). The backscattering shows only weak spectral features and can be well represented by a power-law variation with wavelength (lambda): b(b) approximately lambda(-n), where n is a constant between 0.4 and 1.0. However, the weak spectral features in b(b)b suggest that it is depressed in spectral regions of strong particle absorption. The applicability of the present inverse radiative transfer algorithm, which omits the influence of Raman scattering, is limited to lambda < 490 nm in oligotrophic waters and lambda < 575 nm in mesotrophic waters.

Optical influence of ship wakes

The optical variations observed within ship wakes are largely due to the generation of copious amounts of air bubbles in the upper ocean, a fraction of which accumulate as foam at the surface, where they release scavenged surfactants. Field experiments were conducted to test previous theoretical predictions of the variations in optical properties that result from bubble injection in the surface ocean. Variations in remote-sensing reflectance and size distribution of bubbles within the ship-wake zone were determined in three different optical water types: the clear equatorial Pacific Ocean, moderately turbid coastal waters, and very turbid coastal waters, the latter two of which were offshore of New Jersey. Bubbles introduced by moving vessels increased the backscattering in all cases, which in turn enhanced the reflectance over the entire visible and infrared wave bands. The elevated reflectance had different spectral characteristics in the three locations. The color of ship wakes appears greener in the open ocean, whereas little change in color was observed in near-coastal turbid waters, consistent with predictions. Colorless themselves, bubbles increase the reflected radiance and change the color of the ocean in a way that depends on the spectral backscattering and absorption of the undisturbed background waters. For remote observation from aircraft or satellite, the foam and added surfactants further enhance the reflectance to a degree dependent on the illumination and the viewing geometry.

Phase function effects on oceanic light fields

Numerical simulations show that underwater radiances, irradiances, and reflectances are sensitive to the shape of the scattering phase function at intermediate and large scattering angles, although the exact shape of the phase function in the backscatter directions (for a given backscatter fraction) is not critical if errors of the order of 10% are acceptable. We present an algorithm for generating depth- and wavelength-dependent Fournier-Forand phase functions having any desired backscatter fraction. Modeling of a comprehensive data set of measured inherent optical properties and radiometric variables shows that use of phase functions with the correct backscatter fraction and overall shape is crucial to achieve model-data closure.

Irradiance inversion algorithm for estimating the absorption and backscattering coefficients of natural waters: Raman-scattering effects

We modify an algorithm for retrieving the absorption (a) and backscattering (b(b)) coefficient profiles in natural waters by inverting profiles of downwelling and upwelling irradiance so as to include the presence of Raman scattering. For a given wavelength of interest, lambda, the light field at the appropriate Raman excitation wavelength lambda(e) is first inverted to obtain the Raman source function at lambda. Starting from estimates of the inherent optical properties at lambda, the contribution to the irradiances at lambda from Raman scattering is then estimated and subtracted from the total irradiances to obtain the elastically scattered irradiances. We then inverted the elastically scattered irradiances to find new estimates of a and b(b) using our original method [Appl. Opt. 37, 3886 (1998)]. The algorithm then operates iteratively: The new estimates are used with the Raman source function to derive a new estimate of the Raman contribution, etc. Sample results are provided that demonstrate the working of the algorithm and show that the absorption and scattering coefficients can be retrieved with accuracies similar to those in the absence of Raman scattering down to depths at which the light field is significantly perturbed by it, e.g., with approximately 90% of the upwelling light field originating from Raman scattering.

Estimation of the inherent optical properties of natural waters from the irradiance attenuation coefficient and reflectance in the presence of Raman scattering

By means of radiative transfer simulations we developed a model for estimating the absorption a, the scattering b, and the backscattering b(b) coefficients in the upper ocean from irradiance reflectance just beneath the sea surface, R(0-), and the average attenuation coefficient for downwelling irradiance, <K(d)>1, between the surface and the first attenuation depth. The model accounts for Raman scattering by water, and it does not require any assumption about the spectral shapes of a, b, and b(b). The best estimations are obtained for a and b(b) in the blue and green spectral regions, where errors of a few percent to <10% are expected over a broad range of chlorophyll concentration in water. The model is useful for satellite ocean color applications because the model input, R(0-) and <K(d)>1, can be retrieved from remote sensing and the model output, a and b(b), is the major determinant of remote-sensing reflectance.

Transient radiative transfer equation applied to oceanographic lidar

We estimate the optical signal for an oceanographic lidar from the one-dimensional transient (time-dependent) radiative transfer equation using the discrete ordinates method. An oceanographic lidar directs a pulsed blue or green laser into the ocean and measures the time-dependent backscattered light. A large number of parameters affect the performance of such a system. Here the optical signal that is available to the receiver is calculated, rather than the receiver output, to reduce the number of parameters. The effects of albedo of a uniform water column are investigated. The effects of a school of fish in the water are also investigated for various school depths, thicknesses, and densities. The attenuation of a lidar signal is found to be greater than the diffuse attenuation coefficient at low albedo and close to it at higher albedo. The presence of fish in the water is found to have a significant effect on the signal at low to moderate albedo, but not at high albedo.

Radiance-irradiance inversion algorithm for estimating the absorption and backscattering coefficients of natural waters: vertically stratified water bodies

A full multiple-scattering algorithm for inverting profiles of the upwelling and downwelling irradiances to yield profiles of the absorption and backscattering coefficients in a vertically stratified water body is described and tested with simulated data. The algorithm does not require knowledge of the scattering phase function of the medium. The results are better the closer the phase function assumed in the retrievals is to the true phase function, although excellent retrievals of the absorption coefficient can still be obtained with an inaccurate phase function. Simulations show that the algorithm is capable of determining the vertical structure of a stratified water body and usually provides the absorption coefficient profile with an error ?2% and the backscattering coefficient profile with an error ?10%, as long as the spacing between pseudodata samples is sufficiently small that the necessary derivatives of the irradiances can be accurately computed. The performance is only slightly degraded when the upwelling radiance (nadir viewing) is substituted for the upwelling irradiance.

Radiance-irradiance inversion algorithm for estimating the absorption and backscattering coefficients of natural waters: homogeneous waters

A full multiple-scattering algorithm for inverting upwelling radiance (L(u)) or irradiance (E(u)) and downwelling irradiance (E(d)) profiles in homogeneous natural waters to obtain the absorption (a) and backscattering (b(b)) coefficients is described and tested with simulated data. An attractive feature of the algorithm is that it does not require precise knowledge of the scattering phase function of the medium. For the E(u)-E(d) algorithm, tests suggest that the error in the retrieved a should usually be ?1%, and the error in b(b)?10-20%. The performance of the L(u)-E(d) algorithm is not as good because it is more sensitive to the scattering phase function employed in the inversions; however, the error in a is usually still small, i.e., ?3%. When the algorithm is extended to accommodate the presence of a Lambertian-reflecting bottom, the retrievals of a are still excellent, even when the presence of the bottom significantly influences the upwelling light field; however, the error in b(b) can be large.