Particle Size Distribution Slope Research Articles

Particle Size Distribution Slope Changes along the Yellow River Delta Observed from Sentinel 3A/B OLCI Images

Quantitative estimates of particle size in estuaries and shelf areas are important to understand ocean ecology and biogeochemistry. Particle size can be characterized qualitatively from satellite observations of ocean color. As a typical marginal sea, the Yellow River Delta (YRD) with the Bohai Sea experiences a complex hydrodynamic environment. Here, we attempt to quantify the particle size distribution (PSD) slope (ξ) based on its relationship with the particle backscattering exponent from Sentinel-3A/B OLCI. The PSD slope, ξ displays temporal and spatial variability in the YRD with the Bohai Sea. Its value varies between 3 and 4, and typically exceeds 5 in offshore areas. The lowest value of ξ occurs in the winter, indicating the presence of fine inorganic particles in the water, while high values are attained in the spring, when phytoplankton blooms increase the particle size. ξ decreases near the river mouth because of the large sediment-laden discharge debouching into the sea. We detected a slight increase in ξ when turbid waters were present in the period 2016–2022. Environmental factors, such as sea surface temperature, sea surface wave height, and wind, may control particle size and ξ in the long term. Inorganic suspended particle matter is derived along the YRD using the magnitude of ξ. The mean inorganic suspended particle matter area in winter approaches 23,900 km2 when ξ < 4.6. This study thoroughly characterizes variations in ξ in the YRD with the Bohai Sea and clarifies the contributions of driving factors from human activities and climate change.

Particle size distribution at Ocean Station Papa from nanometers to millimeters constrained with intercomparison of seven methods

Particle size distribution (PSD) is a fundamental property that affects almost every aspect of the marine ecosystem, including ecological trophic interactions and transport of organic matter and trace elements. We measured PSDs using a suite of seven instruments in waters near Ocean Station Papa in the Northeast Pacific Ocean. These instruments and their sizing ranges are: Laser In-Situ Scattering and Transmissometer (LISST)-Volume Scattering Function meter (VSF) and Multispectral Volume Scattering Meter (MVSM), both sizing particles from 0.02 µm to 2000 µm; the LISST-100X, from 3 µm to 180 µm; the ViewSizer, from 0.3 µm to 2 µm; the Coulter Counter, from 2 µm to 40 µm; the Imaging Flow CytoBot (IFCB), from 5 µm to 100 μm; and the underwater vision profiler (UVP), from 100 µm to 2000 µm. Together, they cover an unprecedented size range spanning 5 orders of magnitude from 20 nm to 2 mm. The differences in size definition for the different instruments cause biases in comparing PSDs. The absolute differences in PSDs, after correcting for mean biases, were less than a factor of 3 among all the instruments, and within 50% among LISST-100X, LISST+MVSM, Coulter Counter and IFCB. We also found that particles of sizes <50 µm were not very porous; however, porosity must be considered for particles >50 µm. The merged PSDs, ranging from 0.02 µm to 2000 µm, showed little variation in the PSD slope in the upper 75 m of the water column even though the total number of particles decreased with depth. While submicrometer particles are numerically dominant, particles of sizes 1 µm to 100 µm account for 70–90% of the solid volume of particles. We expect that the results of this study will lead to improved estimates of mass and carbon flux in the study area.

Variability of Marine Particle Size Distributions and the Correlations with Inherent Optical Properties in the Coastal Waters of the Northern South China Sea

Particle size distribution (PSD), which is an important characteristic of marine suspended particles, plays a role in how light transfers in the ocean and impacts the ocean’s inherent optical properties (IOPs). However, PSD properties and the correlations with IOPs are rarely reported in coastal waters with complex optical properties. This study investigated the PSD variabilities both for the surface water and the water in vertical planes, and the correlations between PSD and the backscattering coefficient (bbp), scattering coefficient (bp), and attenuation coefficient (cp), based on in situ PSD observations (within a size range of 2.05–297 μm) and IOPs in the coastal northern South China Sea. The results show a large variety of PSDs, with a range of 41.06–263.02 μm for the median particle diameter (Dv50) and a range of 2.61–3.74 for the PSD slope. In addition, the predominance of small particles is most likely to appear in the nearshore shallow water and estuaries with a large amount of sediment discharge, and vice versa. For the variabilities of IOPs, the particle concentration in a cross-sectional area (AC) is the first driving factor of the variations of bbp, bp, and cp, and the product of the mean particle diameter (DA) and the apparent density (ρa) can explain most variations of the mass-specific bbp (bbp/SPM), bp (bp/SPM), and cp (cp/SPM). In this study, we found that particle size is strongly correlated with volume-specific bbp (bbp/VC), bp (bp/VC), and cp (cp/VC), and the 10th percentile diameter of the accumulated volume concentration (Dv10) can better explain the variations of bbp/VC. These findings suggest a potential PSD retrieval method utilizing the bbp or bp, which may be determined by remote sensing observations.

Optical Properties and Biochemical Indices of Marine Particles in the Open Mediterranean Sea: The R/V Maria S. Merian Cruise, March 2018

A rich data set on particulate matter optical properties and parameters (beam attenuation coefficient, volume concentration, particle size and PSD slope), accompanied by measurements of biochemical indices (particulate organic carbon, particulate nitrogen and their stable isotopic composition) was obtained from the surface to deep waters across the Mediterranean Sea, in March-April 2018. A decrease of beam attenuation coefficients, total particle volume concentrations, particulate organic carbon and nitrogen concentrations was noted towards the eastern Mediterranean Sea (EMed) in comparison to the western Mediterranean Sea (WMed). LISST-derived optical properties were significantly correlated with water mass characteristics. Overall, the most turbid water mass identified in the Mediterranean Sea was the Surface Atlantic water (AW), and the most transparent was the Transitional Mediterranean Water (TMW) in the Cretan Sea, whereas a general decrease in particulate matter concentration is observed from the WMed towards the EMed. Relatively depleted δ13C-POC values in the particle pool of the open Mediterranean Sea can be attributed to contribution from terrestrial inputs, mainly via atmospheric deposition. Throughout the entire water column, a significant positive correlation between particle beam attenuation coefficient and particulate organic carbon concentration is observed in the open Mediterranean Sea. Such relationship suggests the predominance of organic particles with biogenic origin. POC concentration and particle median diameter D50 are significantly and negatively correlated both in the WMed and the EMed Sea, confirming that small particles are POC-rich. At depth, a prominent decrease of most measured parameters was observed, with the exception of particle median diameter that increased substantially in the EMed towards the deep sea, suggesting potentially enhanced aggregation processes. The low particle size distribution slope ξ observed in the EMed, corresponding to larger particle populations, supports the above notion. Basin-wide Rayleigh-type isotopic fractionation in vertical profiles of δ15N-PN across the Mediterranean Sea, underlines the differences in the trophic characters of the two sub-basins and highlights the role of circulation changes on biogeochemical parameters and the redistribution of particulate matter as a source of nutrients in the water column.

What millimeter-wavelength radar reflectivity reveals about snowfall: an information-centric analysis

Abstract. The ability of single-frequency, millimeter-wavelength radar reflectivity observations to provide useful constraints for retrieval of snow particle size distribution (PSD) parameters, snowfall rates, and snowfall accumulations is examined. An optimal estimation snowfall retrieval that allows analyses of retrieval uncertainties and information content is applied to observations of near-surface W-band reflectivities from multiple snowfall events during the 2006–2007 winter season in southern Ontario. Retrieved instantaneous snowfall rates generally have uncertainties greater than 100 %, but single-event and seasonal snow accumulations from the retrieval results match well with collocated measurements of accumulations. Absolute fractional differences are mainly below 30 % for individual events that have more substantial accumulations and, for the season, 12.6 %. Uncertainties in retrieved snowfall rates are driven mainly by uncertainties in the retrieved PSD parameters, followed by uncertainties in particle model parameters and, to a lesser extent, the uncertainties in the fall-speed model. Uncertainties attributable to assuming an exponential distribution are negligible. The results indicate that improvements to PSD and particle model a priori constraints provide the most impactful path forward for reducing uncertainties in retrieved snowfall rates. Information content analyses reveal that PSD slope is well-constrained by the retrieval. Given the sensitivity of PSD slope to microphysical transformations, the results show that such retrievals, when applied to radar reflectivity profiles, could provide information about microphysical transformations in the snowing column. The PSD intercept is less well-constrained by the retrieval. While applied to near-surface radar observations in this study, the retrieval is applicable as well to radar observations aloft, such as those provided by profiling ground-based, airborne, and satellite-borne radars under lighter snowfall conditions when attenuation and multiple scattering can be neglected.

A semi-analytical algorithm for deriving the particle size distribution slope of turbid inland water based on OLCI data: A case study in Lake Hongze.

The particle size distribution (PSD) slope (ξ) can indicate the predominant particle size, material composition, and inherent optical properties (IOPs) of inland waters. However, few semi-analytical methods have been proposed for deriving ξ from the surface remote sensing reflectance due to the variable optical state of inland waters. A semi-analytical algorithm was developed for inland waters having a wide range of turbidity and ξ in this study. Application of the proposed model to Ocean and Land Color Instrument (OLCI) imagery of the water body resulted in several important observations: (1) the proposed algorithm (754nm and 779nm combination) was capable of retrieving ξ with R2 being 0.72 (p<0.01, n=60), and MAPE and RMSE being 4.37% and 0.22 (n=30) respectively; (2) the ξ in HZL was lower in summer than other seasons during the period considered, this variation was driven by the phenological cycle of algae and the runoff caused by rainfall; (3) the band optimization proposed in this study is important for calculating the particle backscattering slope (η) and deriving ξ because it is feasible for both algae dominant and sediment governed turbid inland lakes. These observations help improve our understanding of the relationship between IOPs and ξ, which are affected by different bio-optic processes and algal phenology in the lake environment.

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.

Remote Monitoring of PSD Slope Under the Influence of Sand Dredging Activities in Lake Hongze Based on Landsat-8/OLI Data and VIIRS/DNB Night-Time Light Composite Data

Particle size distribution (PSD) is an important characterization parameter of the particle size structure of suspended particles, which is vulnerable to human activities such as sand dredging. In this study, sand dredging numbers were evaluated by the accumulated radiance algorithm using the night-time light composite data of the visible infrared imaging radiometer suite, and the PSD slope was derived by band ratio algorithm of Landsat-8/operational land imager (OLI) imagery. Then, the influence of sand mining on PSD slope was analyzed. We draw several crucial findings. First, the ratio of ${\boldsymbol{R}_{{{\bf rs}}({{{\bf Red}}})}}$ to ${\boldsymbol{R}_{{{\bf rs}}({{{\bf Green}}})}}$ based on OLI imagery was capable of retrieving PSD slope with good robustness ( R 2 = 0.71, p n = 41) and verified acceptance (mean absolute percentage error = 4.29%, root mean square error = 0.19, n = 20), and the PSD slope in HZL was lower in summer than in the other seasons from 2014 to 2017. Second, The night active vessels extracted from the night-time images show that sand dredging activities began at the outlet of Chengzi Lake (CZL) in April 2012, spread to the whole lake between 2014 and 2016, and then stopped in the northeast region in March 2017 due to the strict control of the local government. Third, the PSD slope is strongly influenced by sand mining, which is positively correlated with the number of sand dredgers ( R 2 = 0.92), i.e., the PSD slope increases 0.21 per 100 working sand dredgers in CZL.

Variability of particle size distribution with respect to inherent optical properties in Poyang Lake, China.

Suspended particulate matter plays a significant role in the studies of sediment fluxes, phytoplankton dynamics, and water optical properties. This study focuses on the relationships between particle size distribution (PSD), water's inherent optical properties (IOPs), and water constituents. We investigated the complex waters of Poyang Lake, the largest freshwater lake in China, in wet and dry seasons during 2008-2011. Because of the distinct temporal-spatial variation of Poyang Lake, these parameters and relationships also demonstrate seasonal and regional variability. The variation range of the concentration of suspended particulate matter is 0.32-69.08 mg/l, with a mean value of 22.21 mg/l. The median particle size in the dry season is much larger than that of the wet season. The Junge distribution fits the PSD of Poyang Lake very well in the scope of 6.21-331 μm. Furthermore, the slopes of the PSD range from 3.54 to 4.69, with a mean value of 4.11, with the steepest slopes (>4.5) occurring in the waters around Songmen Mountain Island and the northern waterway. A negative correlation was found between median particle size (Dv50) and the mass-specific absorption coefficient at 443 nm [apm(443)] for both wet and dry seasons. Identical to analogous waters, the spectral slopes of the PSD correlate well with the spectral slopes of the attenuation coefficient, but with different fitted formulas. In the dry season, the particle size can better explain the variability of the scattering coefficient, while the mass-specific scattering coefficient is better explained by the apparent density. However, no similar results were found for the wet season. In addition, the spectral slopes of the backscattering coefficient correlated well with the PSD slope, and the bulk refractive index calculated from the backscattering ratio and PSD slope can indicate the particle composition of Poyang Lake. Overall, the knowledge on the PSD and IOPs gained in this study broadens our understanding of water optics in highly turbid water columns.

Semi-analytical modeling and parameterization of particulates-in-water phase function for forward angles

A model based on Mie theory is described for predicting scattering phase functions at forward angles (0.1°-90°) with particle size distribution (PSD) slope and bulk refractive index as input parameters. The PSD slope 'ξ ' is calculated from the hyperbolic slope of the particle attenuation spectrum measured in different waters. The bulk refractive index 'n' is evaluated by an inversion model, using measured backscattering ratio (Bp) and PSD slope values. For predicting the desired phase function in a certain water type, in situ measurements of the coefficients of particulate backscattering, scattering and beam attenuation are needed. These parameters are easily measurable using commercially available instruments which provide data with high sampling rates. Thus numerical calculation of the volume scattering function is carried out extensively by varying the optical characteristics of particulates in water. The entire range of forward scattering angles (0.1°-90°) is divided into two subsets, i.e., 0.1° to 5° and 5° to 90°. The particulates-in-water phase function is then modeled for both the ranges. Results of the present model are evaluated based on the well-established Petzold average particle phase function and by comparison with those predicted by other phase function models. For validation, the backscattering ratio is modeled as a function of the bulk refractive index and PSD slope, which is subsequently inverted to give a methodology to estimate the bulk refractive index from easily measurable optical parameters. The new phase function model which is based on the exact numerical solution obtained through Mie theory is mathematically less complex and predicts forward scattering phase functions within the desired accuracy.

High frequency variability of particle size distribution and its dependency on turbulence over the sea bottom during re-suspension processes

The impact of tidal current, waves and turbulence on particles re-suspension over the sea bottom is studied through Eulerian high frequency measurements of velocity and particle size distribution (PSD) during 5 tidal cycles (65h) in a coastal environment of the eastern English Channel. High frequency variability of PSD is observed along with the velocity fluctuations. Power spectral analysis shows that turbulent velocity and PSD parameters have similarities in their spectral behaviour over the whole range of examined temporal scales. The low frequency variability of particles is controlled by turbulence (β≃−5/3) and the high frequency is partly driven by dynamical processes impacted by the sea bottom interactions with turbulence (wall turbulence). Stokes number (St), rarely measured in situ, exhibits very low values, emphasizing that these particles can be considered as passive tracers. The effect of tide and waves on turbidity and PSD is highlighted. During slack tide, when the current reaches its minimum value, we observe a higher proportion of small particles compared to larger ones. To a lower extent, high significant wave heights are also associated with a greater concentration of suspended sediments and the presence of larger particles (larger Sauter׳s diameter DA, and lower PSD slope ξ).

Anomalous diffraction approach to the visible spectra of absorption by marine particles with power-law size distributions

The spectral shape of the light absorption by marine particles with power-law size distribution was analyzed. The anomalous diffraction approximation (ADA) in its conventional form for optically “soft” homogenous particles was used to model the absorption cross section. Based on this theory, particular formulas describing the spectral shape of absorption of an assemblage of particles were derived. Exemplary calculations were performed for particles of selected shapes (spheres, thin cylinders and disks). The results suggest that relative absorption spectra of marine particles in many cases can be approximated by a simple formula, i.e. a power function of the ratio of their imaginary part of the refractive index and the light wavelength. As long as the ADA is considered, the value of the exponent varies between 0 and 1 and depends on the particle size distribution slope, the range of particles’ sizes, their shapes, and the magnitude of the refractive index. These factors also influence the accuracy of this approximation.

A regional comparison of particle size distributions and the power law approximation in oceanic and estuarine surface waters

The particle size distribution (PSD) is commonly used in studies of sediment fluxes, phytoplankton dynamics, and optical scattering from particulates, but little is known about the spatial and temporal variability of this parameter. Here, we analyze in situ laser diffraction measurements of the PSD from a variety of estuarine and open ocean systems. The power law or “Junge‐type” distribution provided a good fit to surface ocean particle size distributions measured from 6 to 250μm. PSD slopes ranged from 2.7 to 4.7 with a mean of 3.63. Consistent with theory, high particle slopes (3.78) and low particle concentrations characterized the open ocean waters of the Atlantic and the Southern Ocean. Lower PSD slopes (3.63) and high concentrations were characteristic of estuarine waters. River plumes consistently showed the lowest PSD slopes (3.30) and highest particle concentrations characteristic of larger bloom‐forming phytoplankton and production of particle aggregates. In the North Atlantic, an inverse relationship was found between PSD slope and chlorophyll concentration. Such results follow the biological paradigm that larger phytoplankton are prevalent in bloom conditions and smaller phytoplankton dominate in oligotrophic water. Large temporal variability in PSD was observed in near coastal regions prone to sediment resuspension from storms and tidal flow. Dense sea grass beds consistently had lower particle concentrations compared to surrounding waters due to reductions in current flow and sediment resuspension. Simple power law approximations of particle size distributions can be successfully used to describe and assess particle distributions in a wide array of oceanic and estuarine water types.

Retrieval of the particle size distribution from satellite ocean color observations

The particle size distribution (PSD) provides important information about pelagic ocean ecosystem structure and function. Knowledge of the PSD and its changes in time can be used to assess the contributions made by phytoplankton functional groups to primary production, particle sinking, and carbon sequestration by the ocean. However, few field measurements of the PSD have been made in the pelagic ocean, and little is known about its space‐time variation. Here, a novel bio‐optical algorithm is introduced to retrieve the parameters of a power law particle size spectrum from satellite ocean color observations. First, the particle backscattering coefficient spectrum, bbp(λ), is retrieved from monthly Sea‐viewing Wide Field‐of‐view Sensor (SeaWiFS) normalized water‐leaving radiance observations following Loisel et al. (2006). Mie modeling is then used to estimate the parameters of a power law PSD (the PSD slope and the particle differential number concentration for a given reference diameter) as a function of the particulate backscattering spectrum. Algorithm uncertainties are greater when bbp(λ) slopes are low, which occurs in high‐productivity areas. Satellite‐based retrievals of PSD parameters are reasonably consistent with available field observations. As an example, the algorithm was applied to monthly SeaWiFS global imagery from August 2007. Global spatial distributions show subtropical oligotrophic gyres characterized by higher PSD slopes and smaller particle number concentrations, as compared with coastal and other high‐productivity areas. Partitioning particle number and volume concentrations into picophytoplankton‐, nanophytoplankton‐, and microphytoplankton‐sized classes indicates that the abundance of picoplankton‐sized particles is roughly constant spatially and that they dominate the particle volume concentrations in oligotrophic regions. On the other hand, abundances of microplankton‐sized particles vary over many orders of magnitude, and they contribute to volume concentration only in the highest‐productivity areas. These results are consistent with current understanding of particle dynamics of pelagic ecosystems and provide new tools for biogeochemical modeling and assessment of the global ocean ecosystem.

Light scattering properties and their relation to the biogeochemical composition of turbid productive waters: a case study of Lake Taihu

Light scattering properties in such a highly turbid productive lake as Lake Taihu in China were examined through 118 samples collected during three cruises in November 2006, March 2007, and November 2007. The particulate scattering and backscattering coefficients were observed using WETLabs AC-S and ECO-BB9. A power model with a spectral exponent of -0.729 was used to simulate the particulate scattering coefficient (b(p)) spectra. It has a better performance than the linear model. Scattering parameters are more closely related to inorganic suspended matter (ISM) concentration than to other water components, such as total suspended matter (TSM), organic suspended matter (OSM), and chlorophyll a (Chla). This indicates that ISM dominates the scattering signal in the lake. Three discrepancies with oceanic/coastal waters are observed: (a) the backscattering ratio (b (bp)) decreases with an increase in the ISM concentration because of a highly strong contribution by ISM to b(p); (b) the mass-specific scattering coefficient (b(p) (m)) exhibits a wider range of variability than that reported in previous studies, which can be attributed to considerable variation in the OSM and ISM distributions; (c) the particle size distribution slope (xi) is mostly larger than 4.0 in Lake Taihu, whereas it is usually within 3.5-4.0 for marine particles. In addition, the bulk refractive index (n (p)) calculated according to the Twardowski et al. model [J. Geophys. Res. 106, 14129 (2001)JGREA20148-0227] indicates that some stations (n (p)<1.07) can be regarded as organic-particle dominant. Other stations with high ISM concentrations have a very small n (p) value mostly within 1.10-1.17. Overall, the knowledge on the scattering properties gained in this study broadens our understanding of water optics in highly turbid productive water columns.

Modelling particle size distribution dynamics in marine waters

Numerical simulations were carried out to determine the particle size distribution (PSD) in marine waters by accounting for particle influx, coagulation, sedimentation and breakage. Instead of the conventional rectilinear model and Euclidean geometry, a curvilinear collision model and fractal scaling mathematics were used in the models. A steady-state PSD can be achieved after a period of simulation regardless of the initial conditions. The cumulative PSD in the steady state follows a power-law function, which has three linear regions after log–log transformation, with different slopes corresponding to the three collision mechanisms, Brownian motion, fluid shear and differential sedimentation. The PSD slope varies from −3.5 to −1.2 as a function of the size range and the fractal dimension of the particles concerned. The environmental conditions do not significantly alter the PSD slope, although they may change the position of the PSD and related particle concentrations. The simulation demonstrates a generality in the shape of the steady-state PSD in the ocean, which is in agreement with many field observations. Breakage does not affect the size distribution of small particles, while a strong shear may cause a notable change in the PSD for larger and fractal particles only. The simplified approach of previous works using dimensional analysis still offers valuable approximations for the PSD slopes, although the previous solutions do not always agree with the simulation results. The variation in the PSD slope observed in field investigations can be reproduced numerically. It is argued that non-steady-state conditions in natural waters could be the main reason for the deviation of PSD slopes. A change in the nature of the particles, such as stickiness, and environmental variables, such as particle input and shear intensity, could force the PSD to shift from one steady state to another. During such a transition, the PSD slope may vary to some extent with the particle population dynamics.

Shape of the particulate beam attenuation spectrum and its inversion to obtain the shape of the particulate size distribution

The link between the spectral shape of the beam attenuation spectrum and the shape of the particle size distribution (PSD) of oceanic particles is revisited to evaluate the extent to which one can be predicted from the other. Assuming a hyperbolic (power-law) PSD, N(D) ? D(-xi), past studies have found for an infinite distribution of nonabsorbing spheres with a constant index of refraction that the attenuation spectrum is hyperbolic and that the attenuation spectral slope gamma is related to the PSD slope xi by xi = gamma + 3. Here we add a correction to this model because of the finite size of the biggest particle in the population. This inversion model is given by xi = gamma + 3 - 0.5 exp(-6gamma). In most oceanic observations xi > 3, and the deviation between these two models is negligible. To test the robustness of this inversion, we perturbed its assumptions by allowing for populations of particles that are nonspherical, or absorbing, or with an index of refraction that changes with wavelength. We found the model to provide a good fit for the range of parameters most often encountered in the ocean. In addition, we found that the particulate attenuation spectrum, c(p)(lambda), is well described by a hyperbolic relation to the wavelength c(p) ? lambda(-gamma) throughout the range of the investigated parameters, even when the inversion model does not apply. This implies that knowledge of the particulate attenuation at two visible wavelengths could provide, to a high degree of accuracy, the particulate attenuation at other wavelengths in the visible spectrum.

A model for estimating bulk refractive index from the optical backscattering ratio and the implications for understanding particle composition in case I and case II waters

A model based on Mie theory is described that estimates bulk participate refractive index from in situ optical measurements alone. Bulk refractive index is described in terms of the backscattering ratio and the hyperbolic slope of the particle size distribution (PSD). The PSD slope ξ is estimated from the hyperbolic slope of the particulate attenuation spectrum γ according to the relationship γ ≈ ξ − 3, verified with Mie theory. Thus the required in situ measurements are the particulate backscattering coefficient, the total particulate scattering coefficient, and the particulate attenuation coefficient. These parameters can be measured with commercially available instrumentation with rapid sampling rates and real‐time data return. Application of the model to data from the Gulf of California yielded results that agreed with expectations, e.g., predicted was 1.04–1.05 in the chlorophyll maximum and 1.14–1.18 near sediments. Below the chlorophyll maximum in case I type waters, predicted values were between 1.10 and 1.12, suggesting the presence of a significant inorganic mineral component in the background or detrital organic particles with low water content.

Theoretical study of the cloud physics of Mei‐Yu

The paper theoretically explains some of the microphysical phenomena observed in Mei‐Yu. In the melting layer the theory shows that most of the changes from the top to the bottom of the melting layer in the particle number density and the particle size distribution slope can be explained by assuming a constant precipitation rate and increasing particle fall speed due to melting. However, the theory implies that some aggregation is going on during melting. In the warm‐rain region, binary interaction of coalescence and breakup are the prominent microphysical processes. In general, coalescence dominates over breakup. But in these cases the two processes will approximately arrive at equilibrium when the precipitation reaches the Earth's surface.