Retrieving composition and sizes of oceanic particle subpopulations from the volume scattering function

Particle size distribution inversion using the Weibull-distribution adaptive-parameters cuckoo search algorithm

A Weibull-distribution adaptive-parameters cuckoo search (WACS) algorithm is proposed, which can converge quickly and prevent falling into local optimal values, and thus improve the global search performance of a cuckoo search (CS) algorithm. In simulations, particle size inversions were performed using the proposed algorithm for unimodal and bimodal particle systems obeying Johnson's SB, Rosin-Rammler, and normal distribution, and the results were compared to the original CS algorithm, Weibull-distribution CS algorithm, and adaptive-parameters CS algorithm. Among them, the WACS algorithm has the best accuracy. The relative root mean squared error (RRMSE) was three to four orders of magnitude lower than the CS algorithm. The noise immunity of the algorithm was verified by comparing the particle size inversion error. Random noise [1%, 10%] was added to the scattered light energy of the target function, in 1% noise increments. The WACS algorithm prevailed, and the advantage became more obvious as the noise increased. A small-angle forward scattering experimental platform was built, and ferric tetroxide particles were selected as the measured particles. Experimental measurements were carried out on a unimodal particle system (50 µm) and bimodal particle system (50 and 100 µm), while the WACS algorithm was used on particle size distribution inversion. Compared to the CS algorithm, the RRMSE of the WACS algorithm was approximately 51% lower on unimodal and 66% lower on bimodal particle population inversions.

Forward volume scattering function (0.03°-60°) measured using an oblique-incidence particle sizer

The forward volume scattering function (VSF) is an inherent optical property important in ocean lidar and underwater imaging and communication. The scattered power within 60° contains >90% of total scattered power, making it essential for determining the asymmetry parameter g. Thus, the new oblique-incidence-design Bettersize BT-3000 particle sizer was utilized to measure forward VSF (0.03°-60°) synchronously. A double-exponential model was then used to construct the full-angle-range VSF (0°-180°). The g value calculated therefrom had an uncertainty of <1%. Calibration was implemented using 11-µm beads alone, and the BT-3000's performance was validated.

Measurements of Aquatic Particle Volume Scattering Function up to 178.5° in the East China Sea

Particulate volume scattering function (VSF), especially at angles larger than 170°, is of particular importance for interpreting ocean optical remote sensing signals and underwater imagery. In this study, a laboratory-based VSF instrument (VSFlab) adopting the periscopic optical system was developed to obtain VSF measurements from 1°–178.5°. In the VSFlab, a new prism design that simply combines a single prism and a neutral density filter was proposed to more efficiently reduce the stray light in the backward direction, while a detailed calibration procedure was given. A full validation based on standard beads of various sizes and a comparison with the results from LISST-VSF and POLVSM indicated that the VSFlab can provide reliable results from 1° to 178.5°. VSFlab measurements in the East China Sea (ECS) exhibited a moderate increase (not more than 5 times) in VSF from 170° to 178.5° rather than a sharp increase of more than one order of magnitude presented in other instrument results measured in other coastal regions. The estimates of the particulate backscattering coefficient using single angle scattering measurements near 120° or 140° and suitable χp were justified. Two types of the VSFs with different size distribution and shape parameters in the ECS can be distinguished based on the variability of χp after 155°. The measured VSF could provide a basis for the parameterization of VSF in the radiative transfer model and the variability of χp in the backward direction had the potential to be used to characterize the particles in the coastal region of the ECS.

Characterization of suspended particulate matter in contrasting coastal marine environments with angle-resolved polarized light scattering measurements

Optical proxies based on light scattering measurements have potential to improve the study and monitoring of aquatic environments. In this study, we evaluated several optical proxies for characterization of particle mass concentration, composition, and size distribution of suspended particulate matter from two contrasting coastal marine environments. We expanded upon our previous study of Southern California coastal waters, which generally contained high proportions of organic particles, by conducting angle-resolved polarized light scattering measurements in predominantly turbid and inorganic-particle dominated Arctic coastal waters near Prudhoe Bay, Alaska. We observed that the particulate backscattering coefficient b_bp was the most effective proxy for the mass concentration of suspended particulate matter (SPM) when compared with particulate scattering and attenuation coefficients b_p and c_p. Improvements were seen with b_bp as a proxy for the concentration of particulate organic carbon (POC), although only if particulate assemblages were previously classified in terms of particle composition. We found that the ratio of polarized-light scattering measurements at 110º and 18º was superior in performance as a proxy for the composition parameter POC/SPM in comparison to the particulate backscattering ratio b_bp/b_p. The maximum value of the degree of linear polarization DoLP_p,max observed within the range of scattering angles 89°-106° was found to provide a reasonably good proxy for a particle size parameter (i.e., 90th percentile of particle volume distribution) which characterizes the proportions of small- and large-sized particles. These findings can inform the development of polarized light scattering sensors to enhance the capabilities of autonomous platforms.

Variability in Oceanic Particle Size Distributions and Estimation of Size Class Contributions Using a Non-parametric Approach

A dataset of nearly 400 measurements of the particle size distribution (PSD) compiled from the Pacific, Atlantic, and Arctic Oceans is used to examine variability in the magnitude and shape of the PSD, and to characterize the partitioning of particle number, cross-sectional area, and volume concentration among defined size intervals. The results indicate that the relative contributions of three size classes based upon the pico-, nano-, and microplankton size range exhibit substantial changes among measures of particle size and between oceanic environments. The single-slope power law model commonly employed to characterize the PSD in aquatic studies is demonstrated to have significant limitations in capturing the complexity of PSD shapes observed for natural particle assemblages, and in consequence poorly predicts the relative contributions of these different size intervals. We show that specific percentile diameters derived from the cumulative distributions of particle size are strongly correlated with the contributions of these three size classes, and that these non-parametric descriptors of the cumulative distribution provide superior performance for estimating their contributions while requiring no assumption of underlying PSD shape. A comparison of these predictive relationships with independent field measurements suggests that this approach is generally robust for particle assemblages representing a wide diversity of marine environments.

In situ measurements of the volume scattering function with LISST-VSF and LISST-200X in extreme environments: evaluation of instrument calibration and validity

The LISST-VSF and LISST-200X are commercial instruments made available in recent years, enabling underwater measurements of the volume scattering function, which has not been routinely measured in situ due to lack of instrumentation and difficulty of measurement. Bench-top and in situ measurements have enabled absolute calibration of the instruments and evaluation of instrument validity ranges, even at environmental extremes such as the clear waters at the North Pole and turbid glacial meltwaters. Key considerations for instrument validity ranges are ring detector noise levels and multiple scattering. In addition, Schlieren effects can be significant in stratified waters.

Particle Size Parameters of Particulate Matter Suspended in Coastal Waters and Their Use as Indicators of Typhoon Influence

The power law particle size distribution (PSD) slope parameter is commonly used to characterize sediment fluxes, resuspension, aggregates, and settling rates in coastal and estuarine waters. However, particle size distribution metrics are also very useful for understanding sediment source and dynamic processes. In this study, a method was proposed to employ the particle size parameters commonly used in sedimentary geology (average particle size (ø), sorting, skewness, and kurtosis) as indicators of changes in sediment dynamic processes, and MODIS images were used to estimate these parameters. The particle size parameters were estimated using a Mie scattering model, Quasi-Analytical Algorithm (QAA) analysis algorithm, and least squares QR decomposition (LSQR) solution method based on the relationship between the power law distribution of the suspended particles and their optical scattering properties. The estimates were verified by field measurements in the Yellow Sea and Bohai Sea regions of China. This method provided good estimates of the average particle size (ø), sorting, and kurtosis. A greater number of wavebands (39) was associated with more accurate particle size distribution curves. Furthermore, the method was used to monitor changes in suspended particulate matter in the vicinity of the Heini Bay of China before and after the passage of a strong storm in August 2011. The particle size parameters represented the influence of a strong typhoon on the distribution of the near-shore sediment and, together with the PSD slope, comprehensively reflected the changes in the near-shore suspended particulate matter. This method not only established the relationship between remote sensing monitoring and the historical sediment record, it also extends the power law model to the application of sediment source and dynamic processes in coastal waters.

Variability of relationship between the volume scattering function at 180° and the backscattering coefficient for aquatic particles

Properly interpreting lidar (light detection and ranging) signal for characterizing particle distribution relies on a key parameter, χ_p(π), which relates the particulate volume scattering function (VSF) at 180° (β_p(π)) that a lidar measures to the particulate backscattering coefficient (b_bp). However, χ_p(π) has been seldom studied due to challenges in accurately measuring β_p(π) and b_bp concurrently in the field. In this study, χ_p(π), as well as its spectral dependence, was re-examined using the VSFs measured in situ at high angular resolution in a wide range of waters. β_p(π), while not measured directly, was inferred using a physically sound, well-validated VSF-inversion method. The effects of particle shape and internal structure on the inversion were tested using three inversion kernels consisting of phase functions computed for particles that are assumed as homogenous sphere, homogenous asymmetric hexahedra, or coated sphere. The reconstructed VSFs using any of the three kernels agreed well with the measured VSFs with a mean percentage difference <5% at scattering angles <170^∘. At angles immediately near or equal to 180°, the reconstructed β_p(π) depends strongly on the inversion kernel. χ_p(π) derived with the sphere kernels was smaller than those derived with the hexahedra kernel but consistent with χ_p(π) estimated directly from high-spectral-resolution lidar and in situ backscattering sensor. The possible explanation was that the sphere kernels are able to capture the backscattering enhancement feature near 180° that has been observed for marine particles. χ_p(π) derived using the coated sphere kernel was generally lower than those derived with the homogenous sphere kernel. Our result suggests that χ_p(π) is sensitive to the shape and internal structure of particles and significant error could be induced if a fixed value of χ_p(π) is to be used to interpret lidar signal collected in different waters. On the other hand, χ_p(π) showed little spectral dependence.

The open-ocean missing backscattering is in the structural complexity of particles

Marine microscopic particles profoundly impact global biogeochemical cycles, but our understanding of their dynamics is hindered by lack of observations. To fill this gap, optical backscattering measured by satellite sensors and in-situ autonomous platforms can be exploited. Unfortunately, these observations remain critically limited by an incomplete mechanistic understanding of what particles generate the backscattering signal. To achieve this understanding, optical models are employed. The simplest of these models—the homogeneous sphere—severely underestimates the measured backscattering and the missing signal has been attributed to submicron particles. This issue is known as the missing backscattering enigma. Here we show that a slightly more complex optical model—the coated sphere—can predict the measured backscattering and suggests that most of the signal comes from particles >1 µm. These findings were confirmed by independent size-fractionation experiments. Our results demonstrate that the structural complexity of particles is critical to understand open-ocean backscattering and contribute to solving the enigma.

Particulate optical backscattering is key to studying the oceanic carbon pump though it remains unclear what particles are detected. Here the authors show that complex particles larger than 1 µm help reproduce all the measured backscattering across the Atlantic Ocean and explain the majority of the signal.

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.

Sizing submicron particles from optical scattering data collected with oblique incidence illumination

As submicron particles play an important role in a variety of ecosystems that include aqueous, terrestrial, and atmospheric, a measurement system to quantify them is highly desirable. In pursuit of formulating and fabricating a system to size them using visible light, a system that collects multi-directional scattered light from individual particles is proposed. A prototype of the system was simulated, built, and tested via calibration with a set of polystyrene spheres in water with known sizes. Results indicate that the system can accurately resolve the size of these particles in the 0.1 to 0.8 μm range. The system incorporates a design that uses oblique illumination to collect scattered light over a large range of both forward and backward scatter angles. This is then followed by the calculation of a ratio of forward to backscattered light, integrated over a suitably defined range. The monotonic dependence of this ratio upon particle size leads to an accurate estimate of particle size. The method was explored first, using simulations, and followed with a working version. The sensitivity of the method to a range of relative refractive index was tested using simulations. The results indicate that the technique is relatively insensitive to this parameter and thus of potential use in the analysis of particles from a variety of ecosystems. The paper concludes with a discussion of a variety of pragmatic issues, including the required dynamic range as well as further research needed with environmentally relevant specimens to create a pragmatic instrument.

Laboratory experiments for inter-comparison of three volume scattering meters to measure angular scattering properties of hydrosols

Measurements of the volume scattering function (VSF) of hydrosols is of primary importance to investigate the interaction of light with hydrosols and to further interpret in situ and remote sensing data of ocean color. In this paper, a laboratory inter-comparison experiment of three recently developed VSF meters that are able to measure the scattered light for a wide range of scattering angle at 515 nm wavelength is performed using phytoplankton cultures and mineral-like hydrosols. A rigorous measurement protocol was employed to ensure good quality data. In particular, the protocol enabled removing the influence of bacteria on the hydrosols within the sample. The differences in the VSF measurements between the instruments vary from 10 to 25% depending on the composition of the hydrosols. The analysis of the angular features of the VSF revealed a sharp increase of the VSF beyond the scattering angle of 150° for some phytoplankton species. Such behavior is observed for two of the three VSF meters, thus suggesting that it is not due to instrumental artifacts but more likely to phytoplankton optical properties themselves. Moreover, comparisons with currently used theoretical phase functions show that the models are not able to reproduce satisfactorily the directional patterns in the backscattering region. This study suggests that a better modelling of the VSF shape of phytoplankton at high scattering angles is required to correctly represent the angular shape of the VSF in the backscattering hemisphere. Tabulated values of the measured phase functions are provided for scattering angles from 0.1 to 175°.

Accurate estimation of the backscattering coefficient by light scattering at two backward angles

Backscattering coefficients are frequently estimated from light scattering at one backward angle multiplied by a conversion factor. We determined that the shapes of the volume scattering functions (VSFs), particularly for scattering angles larger than 170°, cause significant variations in the conversion factor at 120°. Our approach uses the ratio of scattering at 170° and at 120°, which is a good indicator of the shape differences of the VSFs for most oceanic waters and wavelengths in the visible range. The proposed method provides significant accuracy improvement in the determination of the backscattering coefficients with a prediction error of 3% of the mean.

Spectral attenuation and backscattering as indicators of average particle size

Measurements of the particulate beam attenuation coefficient at multiple wavelengths in the ocean typically exhibit a power law dependence on wavelength, and the slope of that power law has been related to the slope of the particle size distribution (PSD), when assumed to be a power law function of particle size. Recently, spectral backscattering coefficient measurements have been made using sensors deployed at moored observatories, on autonomous underwater vehicles, and even retrieved from space-based measurements of remote sensing reflectance. It has been suggested that these backscattering measurements may also be used to obtain information about the shape of the PSD. In this work, we directly compared field-measured PSD with multispectral beam attenuation and backscattering coefficients in a coastal bottom boundary later. The results of this comparison demonstrated that (1) the beam attenuation spectral slope correlates with the average particle size as suggested by theory for idealized particles and PSD; and (2) measurements of spectral backscattering also contain information reflective of the average particle size in spite of large deviations of the PSD from a spectral power law shape.

Inversion of spectral absorption coefficients to infer phytoplankton size classes, chlorophyll concentration, and detrital matter

Measured spectral absorption coefficients were inverted to infer phytoplankton concentration in three size classes (picoplankton, nanoplankton, and microplankton), chlorophyll concentration [Chl], and both magnitude and spectral shape of absorption by colored detrital matter (CDM). Our algorithm allowed us to solve for the nonlinear factor of CDM absorption slope separately from the other linear factors, thus fully utilizing the additive characteristic inherent in absorption coefficients. We validated the inversion with three datasets: two spatially distributed global datasets, the Laboratoire d'Océanographie de Villefranche dataset and the NASA bio-Optical Marine Algorithm Dataset, and a time series coastal dataset, the Martha's Vineyard Coastal Observatory dataset. Comparison with high performance liquid chromatography analyses showed that the phytoplankton size classes can be retrieved with correlation coefficients (r)>0.7, root mean square errors of 0.2, and median relative errors of 20% in oceanic waters and with similar performance in coastal waters. Much improved agreement was found for the entire phytoplankton population, with r>0.90 for [Chl] and absorption coefficients (a_ph) for all three datasets. The inferred a_CDM(400) and CDM spectral slope agree within ±4% of measurements in both oceanic and coastal waters. The results indicate that the chlorophyll-a specific absorption spectra used as an inversion kernel represent well the global mean states for each of the three phytoplankton size classes. The method can be applied to either bulk or particulate absorption data and is spectrally flexible.

Significance of scattering by oceanic particles at angles around 120 degree

Field observations and theoretical studies have shown that shapes of the volume scattering functions (VSFs) of oceanic particles in the backward directions, i.e., VSFs normalized by the total backscattering coefficient, exhibit a surprisingly low variability at angles near 120 degree, which is also confirmed by measurements of VSFs in coastal waters around the US. To investigate what this minimum variability angle (θ*) represents, we estimated mean values of the VSFs in the backward angles using four mean value theorems: mean value for integral, weighted mean value for integral, classic mean value for differentiation and Cauchy's mean value. We also estimated the angles corresponding to the minimum values of the VSFs. We found θ* to be very close to the angles representing the classic mean values for differentiation of the VSFs. The low variability is due to the fact that the classic mean values vary little with the composition and sizes of particles.

Comparison of optically derived particle size distributions: scattering over the full angular range versus diffraction at near forward angles

The volume scattering function (VSF) of particles in water depends on the particles' size distribution and composition as well as their shape and internal structure. Inversion of the VSF thus provides information about the particle population. The commercially available LISST instrument measures the scattering at near forward angles to estimate the bulk size distribution of particles larger than about 1 μm. By using scattering over the full angular range (0°-180°), the recently improved VSF-inversion method [X. Zhang, M. Twardowski, and M. Lewis, Appl. Opt. 50, 1240 (2011).] can characterize particles in terms of particle subpopulations, which are described by their unique size distribution and composition. Concurrent deployments of the Multispectral Volume Scattering Meter and the LISST in three coastal waters (i.e., Chesapeake Bay, Mobile Bay, and Monterey Bay) allowed us to compare the size distributions derived from these two different methods. We also obtained indirect validation of the results for submicrometer particles and for the composition of particles provided by the VSF-inversion method. For particle sizes ranging from 1 to 100 μm, the concentration was shown to vary over 10 orders of magnitude, and excellent agreement was found between the two methods with a mean relative difference less than 10% for the total size distributions. The inversion results also reproduced spectral variations in the shape of the VSF, although these spectral variations were not frequently observed in our study. The increased backscattering towards the shorter wavelengths was explained by the stronger influence of submicrometer particles affecting the backscattering. Based on published measurements of cell sizes and intracellular chlorophyll-a [Chl] concentrations over a wide range of phytoplankton species and strains, [Chl] was estimated for the inverted subpopulations that were identified as phytoplankton based on their refractive index and mean sizes. The estimated [Chl] agreed well with the fluorescence-based estimates in both magnitude and trend, thus reproducing a bloom event observed at a time series station.

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.

Plankton and particle size and packaging: from determining optical properties to driving the biological pump

Understanding pelagic ecology and quantifying energy fluxes through the trophic web and from the surface to the deep ocean requires the ability to detect and identify all organisms and particles in situ and in a synoptic manner. An idealized sensor should observe both the very small living or dead particles such as picoplankton and detritus, respectively, and the large particles such as aggregates and meso- to macroplankton. Such an instrument would reveal an astonishing amount and diversity of living and nonliving particles present in a parcel of water. Unfortunately such sensors do not exist. However, complex interactions constrain the space, temporal, and size distributions of these objects in such ways that general rules can be inferred from the measurement of their optical properties. Recent technological developments allow for the in situ measurement of the optical properties and size distributions of particles and plankton in a way such that synoptic surveys are possible. This review deals with particle and plankton size distributions (PSDs) as well as how particles' geometry and nature affect their optical properties. Finally, we propose the integration of the PSD into size-structured mathematical models of biogeochemical fluxes.