Volume Backscatter Coefficient Research Articles

Atmospheric Temperature Profile Measurements Using Mobile High Spectral Resolution Lidar

The High Spectral Resolution Lidar (HSRL) designed at the University of Wisconsin-Madison discriminates between Mie and Rayleigh backscattering [1]. It exploits the Doppler effect caused by thermal motion of molecules, which broadens the spectrum of the transmitted laser light. That allows for absolute calibration of the lidar and measurements of the aerosol volume backscatter coefficient. Two iodine absorption filters with different absorption line widths (a regular iodine vapor filter and Argon buffered iodine filter) allow for atmospheric temperature profile measurements. The sensitivity of the measured signal-to-air temperature ratio is around 0.14%/K. The instrument uses a shared telescope transmitter-receiver design and operates in eyesafe mode (the product of laser average power and telescope aperture equals 0.1 W m 2 at 532 nm).

Equations describing finite-amplitude effects in acoustic fish abundance estimation

Species identification of fish and abundance estimation of zooplankton employ frequencies typically in the range of 20–400 kHz. Estimates are based on measurement of (a) the single-target backscattering cross section, σbs, used in echo sounder calibration and fish target strength measurements; and (b) the volume backscattering coefficient, sv, used in oceanic surveying. The power budget equations used today for σbs and sv pre-assume small-amplitude signals (i.e., linear sound propagation). For operating frequencies about 100 kHz and higher, finite-amplitude (nonlinear) sound propagation effects in seawater may cause measurements errors at accessible echo sounder transmit power levels. In the present work, power budget equations are derived for σbs and sv that account for finite-amplitude sound propagation effects. The expressions derived can be used to establish upper limits for echo sounder transmit power levels, in order to reduce finite-amplitude errors in calibration and surveying. They can alternatively be used to develop correction factors for calibration and/or survey data already subjected to finite-amplitude errors. The expressions derived are fully consistent with the small-signal expressions used in fisheries acoustics today.

Laboratory measurements of acoustic backscattering from polystyrene pseudo-ice particles as a basis for quantitative characterization of frazil ice

Measurements of volume backscattering coefficients in brine suspensions of neutrally buoyant, uniformly-sized, polystyrene spheres and disks were used to quantify size, shape and concentration dependences expected in equivalent measurements on freshwater suspensions of frazil ice. The results confirmed expectations of qualified compatibility with existing scattering theory. Specifically, the measured logarithmic backscattering coefficients were expressible, to within 1–2dB, as products of particle concentration and individual cross sections as calculated from the modal expansion of Faran (1951) applied to spheres with radii equal to either their actual values or (for hexagonal disks) to “effective” spherical radii. The limitations on the applicability of the theory were closely linked to: acoustic frequency, target-volume-determined effective radii; the linear dimensions of the faces of the individual target disks; and to particle concentrations. For combinations of particle dimensions, acoustic frequencies and concentrations outside of a well-defined Rayleigh Linear (RL) concentration dependence range, the relationships between measured volume backscattering coefficients and particle properties were complex and not amenable to a simple interpretation: reflecting, it is believed, polystyrene-specific scattering features. The features of the observed extensive Anomalous Linear (AL) and Non-Linear (NL) concentration dependence regimes were documented in terms of both their parameter dependences and the forms and parameters associated with their deviations from RL regime dependences. Analyses focused on identifying the boundaries of the latter regimes which currently provide the only measurement environments compatible with accurate extraction of particle concentration and size parameters. These identifications, made on the basis of polystyrene in brine data, were used, after insertion of frazil and freshwater material parameters, to identify equivalent RL boundaries for ABS (Acoustic Backscattering Sonar) frazil measurements. In practical terms, this framework led to estimates of upper and lower limits for usable ABS acoustic frequencies and established upper limits on the concentrations of larger frazil particles contributing significantly to backscattering signal returns. These results formed the basis for a measurement framework for obtaining validated frazil characterizations. This framework was tested on mixtures of differently-sized pseudo-frazil species to show compatibility between mixture data and equivalent backscattering coefficients calculated for each mixture on the basis of its composition and measured single species coefficients. Applications of this framework to actual frazil field data are essential for both further testing of effectiveness and to allow refinements of imposed, intentionally conservative, restrictions. Results of such applications are described and interpreted in a second publication.

Backscattering Properties of Gold Nanoshells: Quantitative Analysis and Optimization for Biological Imaging

In this article, we investigate the dependence of the backscattering properties of gold nanoshells on the core material, core radius, and shell thickness by using Mie theory of a coated sphere. The size-dependent and dispersive dielectric function of metal nanoparticles permits to consider the localized surface plasmon resonance of gold nanoshells with the classical Mie theory. Our results show that gold nanoshells exhibit resonant backscattering feature due to the resonance of the free electrons in gold shells at a specific incident wavelength. The resonance peak intensity depends on the core material and the dimensions of core and shell, and the resonance wavelength can be tuned to the near-infrared region where biological tissues possess high transmissivity. We obtain the maximum backscattering and the corresponding optimal core radii and shell thicknesses of gold nanoshells at four typical wavelengths (830, 840, 900, and 1310nm) frequently-used in biological imaging. It is found that silica core-gold nanoshells have maximum volume backscattering coefficient (7.01μm-1) at wavelength of 830nm when the core radius is 54.2nm and the shell thickness is 10.1nm. For longer wavelength, the optimal core radius is larger while the optimal shell thickness is thinner, and the maximum volume backscattering coefficient become small. If the core material is changed from silica to vacuum, the gold nanoshells have bigger maximum volume backscattering coefficient with larger core radius and thinner shell thickness. The optimized gold nanoshells can be used as the ideal contrast agents for biological imaging.

Multifrequency analyses of 2011–2012 Peace River SWIPS frazil backscattering data

A four-frequency SWIPS (Shallow Water Ice Profiling Sonar) instrument was deployed in the Peace River during the November 2011–May 2012 period near the Town of Peace River. The deployment site was previously used for deployments of one- and two-frequency SWIPS instruments. Acoustic volume backscattering coefficient and ice thickness data were collected at frequencies 125kHz, 235kHz, 455kHz and 774kHz. The data, acquired as a function of height in the water column, were processed to test particle size, concentration and acoustic frequency restrictions identified in a closely-related laboratory study of backscattering in pseudo-frazil suspensions (Marko & Topham, 2015) prior to applying optimal processing strategies on the 2011–2012 frazil data. Although one of the transducers (235kHz) displayed anomalous returns under certain environmental conditions, simultaneous measurements at 125kHz, 455kHz and 774kHz were found to yield consistent measures of particle concentration, size distribution and fractional volume with accuracies limited, primarily, only by the 1dB transducer calibration uncertainties. Fractional volumes were found to vary by less than an order of magnitude from interval to interval, with maximum values being approximately 10−4 (0.01%) except within, roughly, 0.75m of the river surface where interpretations were complicated by the frequent presence of surface ice. These results confirmed the effectiveness of multifrequency acoustic backscattering sonar (ABS) technology in applications to frazil monitoring problems and expanded its range of applicability beyond that conservatively estimated in the laboratory. The obtained data also provided an unprecedented basis for evaluating current river ice modeling assumptions. Comparisons with corresponding results from CRISSP model runs appear to be indicative of massive over-prediction of suspended frazil despite good model performance for simulating surface ice quantities. The origins of the possible discrepancies are discussed and accompanied by suggested options for improving model performance.

Properties of atmospheric aerosol in smoke plumes from forest fires according to spectronephelometer measurements

A series of polarization spectronephelometer measurements of the angular aerosol scattering coefficients under conditions of extremely dense smoke haze from Siberian forest fires was performed in Tomsk in July–August, 2012. The dispersed composition of the haze comprised ultrafine (particle radii <150 nm) and medium (with the volume distribution peaking around 350 nm) particle fractions. The effective radius of particles was about 220 nm. The smoke haze was characterized by weak absorption; the imaginary part of the refractive index of ultrafine and medium particles had values of ∼0.038 and ∼0.012, respectively. The mean value of the single scattering albedo at a wavelength of 525 nm was about 0.91. In the dense smoke haze, there was a high correlation between volume backscattering and extinction coefficients, an argument in favor of the applicability of a one-parameter model for describing the optical-microphysical properties of the smoke-polluted atmosphere. When smoke haze “decays” (in peripheral zones of smoke plumes), the optical contribution of the ultrafine fraction increases, manifested in an increase in the imaginary part of the refractive index of ultrafine particles up to ∼0.5 and in reducing the albedo from 0.91 to 0.84.

Possibilities of laser location for remote monitoring of marine organisms (analytic review)

Possibilities of lidar detection of fish and plankton are overviewed on cited results of nature experiments in the sea. Volume-backscattering coefficients for the lidar with wave-length 532 nm and the acoustic sonar are compared for schools of some fish species. Examples of effective detecting of fish schools and assessment of their abundance by lidar are demonstrated for cases of sardine and anchovy at California coast, capelin and herring in the North Pacific, mullet at the west coast of Florida, juvenile mackerel in the coastal Atlantic waters of southern Europe, menhaden in the Chesapeake Bay, and others. In some experiments, the per-kilometer costs of airborne lidar surveys are estimated as 10 % or less as compared to ship-based sampling. Besides, the lidar surveys take a shorter time and their results are not distorted by avoidance behavior of fish caused by ship and sampling gear noises. Experimental surveys of thin scattering layers (probably formed by plankton) made by NOAA fish lidar are overviewed, as well, including the first tests of the system in the South California Bay in April 1997, the tests in the North-West Atlantic at Iberian coast in August-September 1998, in the Gulf of Alaska in July-September 2001 and May-August 2002, in the Norwegian Sea in July 2002, in the North-East Pacific at the coast of Oregon and Washington in July 2003, and in the Gulf of Alaska in July 2003. Some aspects of future development for improvement of school-detecting capabilities of lidar are discussed, as additional scanning for 2D-images and adding of second receiver co-polarized with the laser light for better identification of fish species and other scatterers in the sea.

Seasonal variation of surface and vertical profile of aerosol properties over a tropical urban station Hyderabad, India

One year measurement of vertical profiles of volume backscatter and extinction coefficient, aerosol optical depth (AOD), mass concentration of black carbon (BC) and composite aerosol along with thermodynamic structure of the atmosphere has been carried out over an urban tropical location of Hyderabad(17.47°N, 78.58°E), India, during April 2009 to March 2010. The mean mixing layer height (MLH) exhibits large seasonality exceeding 4 km in pre‐monsoon period whereas in winter it comes down to ~1.5 km with an annual mean value of 2.35 ± 1.02 km. Surface BC mass fraction (FBC) shows marked seasonal variation from winter (13 ± 1.9%), pre‐monsoon (8.19 ± 2.16%), monsoon (7.3 ± 1.8%) to post‐monsoon (11.8 ± 0.18%). The profiles of volume backscatter and extinction coefficients reveal presence of elevated aerosol layers from 2 to 4 km and strong oscillations during pre‐monsoon (March–May) and monsoon (June–September) seasons, respectively, while in post‐monsoon (October–November) and winter (December–February), the aerosols are well within the lower boundary layer and also exhibit a drastic decrease with increasing altitude. These elevated aerosol layers and vertical distribution appear to be closely linked to the thermodynamic structure of the atmosphere. The aerosol optical properties in conjunction with air mass back trajectory analysis indicate that the observed elevated aerosol layers during pre‐monsoon and monsoon could contain significant fraction of coarse mode particles with a mix of dust and marine aerosols. Further analysis reveals that the aerosols within atmospheric boundary layer (ABL) dominate the column aerosol loading with ABL‐AOD contributing to ~77.7 ± 17.0%, with significant seasonal variation from winter (86.2 ± 13.1%), pre‐monsoon (76.6 ± 12.8%), monsoon (54.2 ± 15.6%) to post monsoon (80.8 ± 14.8%). Seasonal variation of ABL‐AOD and BC mass fraction follows similar pattern in the ABL indicating that BC may be an important contributor to the ABL aerosol loading.

A comparison of light backscattering and particle size distribution measurements in tropical cirrus clouds

Abstract. An FSSP-100 Optical Particle Counter designed to count and size particles in the micron range and a backscattersonde that measures in-situ particle optical properties such as backscatter and depolarization ratio, are part of the payload of the high altitude research aircraft M55 Geophysica. This aircraft was deployed in tropical field campaigns in Bauru, Brasil (TROCCINOX, 2004) Darwin, Australia (SCOUT-Darwin, 2005) and Ouagadougou, Burkina Faso (SCOUT-AMMA, 2006). In those occasions, measurements of particle size distributions and optical properties within cirrus cloud were performed. Scope of the present work is to assess and discuss the consistency between the particle volume backscatter coefficient observed by the backscattersonde and the same parameter retrieved by optical scattering theory applied to particle size distributions as measured by the FSSP-100. In addition, empirical relationships linking the optical properties measured in-situ by the backscattersonde, which generally can be obtained by remote sensing techniques (LIDAR), and microphysical bulk properties like total particle number, surface and volume density will be presented and discussed.

How pulse lengths impact fish stock estimations during hydroacoustic measurements at 70 kHz

Water Framework Directive requires reliable and effective monitoring tools, and hydroacoustics has a potential to be one of them. The effect of pulse duration on in situ acoustical estimates of fish density and their size distribution was investigated. Measurements were performed in the oligo-mesotrophic Lake Hancza (Poland) using a SIMRAD EK60 split-beam echo-sounder at 70 kHz frequency. During the survey, two similar transducers pinged alternatively through the multiplexer using 4 different pulse lengths, from short to long ones. The results show that the volume backscattering coefficient (Sv) values, equivalent of the fish biomass, were not influenced by the pulse length. However, the number of the detected fish, the mean target strength (TS), and consequently the fish density, differed significantly for the long pulse duration data. This was especially noticeable in the layer above the thermocline with dense fish populations. In this upper layer, for the long pulse the Sawada index frequently exceeded value of 0.1 leading to overestimation of the mean TS and underestimation of the fish density.

Acoustic characterization of the Argentinean short-fin squid aggregations

The characterization of the acoustic recordings obtained by an echo sounder is the first step in the process of identification and classification of marine organisms. This technique is essential for abundance estimation or for detailed ecological studies using acoustic methods. This paper presents echo recordings of Argentine short-fin squid ( Illex argentinus) concentrations, collected during February in three pre-recruit bottom trawl assessment surveys (2006, 2007, and 2009) carried out by the INIDEP (National Institute for Fisheries Research and Development). The survey area was a region on the Patagonian Shelf (100–200 m depth) between 44°S and 51°S where pre recruits of I. argentinus South Patagonian Stock (16–29 cm ML) were feeding on dense aggregations of zooplankton. Advanced techniques were used for post-processing the acoustic data, including the generation of synthetic echograms and the use of recognition algorithms of geometric patterns. Data were collected at two ultrasonic frequencies: 38 and 120 kHz. Typically, squid pre-recruits aggregated in schools located on or near the bottom. Squid concentrations varied in size, shape, and volume backscattering coefficient (average S v ). Squid schools echo traces usually overlapped with those of predators such as Argentine hake ( Merluccius hubbsi) and prey such as amphipods ( Themisto gaudichaudii). Results show how the frequency response of the sound scattering can help characterize the squid concentrations and differentiate them from the other main scatterers in the area. The average differential scattering of S v ( 120 – 38 kHz ) was +5 dB for squid, while values of +18 dB and −1.6 dB corresponded to the amphipods and hake, respectively. Statistical analysis supported the validity of the differentiation method.

Quantifying suspended frazil ice using multi‐frequency underwater acoustic devices

AbstractAn intensive frazil ice field sampling campaign was undertaken at the Port of Quebec on the St. Lawrence River from February–March 2009. Two underwater acoustic instruments set at different frequencies of 420 and 1228.8 kHz were used to detect frazil ice in the water column. In this paper, frequency inversion methods are presented and subsequently applied to the observations to estimate frazil ice characteristics and concentration. Using inversion methods, most of the detected ice crystals had estimated radii of 0.06–0.18 mm. This range compares favourably to the estimated value of 0.20 mm obtained by analysing the Rouse number related to the vertical distribution of the frazil crystals. The results were in contrast to a previous study of frazil ice at another site in the St. Lawrence, which reported radii tens of times larger . The tiny crystals observed here were of similar size to those observed in laboratories (e.g. 0.09 mm), suggesting that the particles formed locally. Frequency analyses were also used to estimate the volumetric suspended frazil concentration, which appeared to be on the order of 6 ppm. Based on evidence suggested by the data and the volume backscattering coefficient at the two frequencies, this study also presents the complex sequence of processes that occurs during a typical supercooling frazil event. This paper concludes with future directions for research using acoustic instrumentation for further understanding of frazil ice dynamics. Copyright © 2010 John Wiley &amp; Sons, Ltd.

Sonar detection and measurement of ice in a freezing river II: Observations and results on frazil ice

Results from 2004–2008 BC Hydro SWIPS (Shallow Water Ice Profiling Sonar) monitoring programs on the Peace River are presented and analyzed with respect to their content of information on the properties and behaviour of frazil ice suspended in water column. Strong distinctions were made in analyses applied to data collected, respectively, prior to and following local stabilization of the seasonal ice cover. This choice is shown to reflect both the behaviour and origins of the frazil ice present in these two intervals. Pre-freeze-up frazil tends to coat submerged surfaces, grows rapidly while in suspension and is only rarely and episodically present. It shows time dependences quite different from those associated with frazil detected prior to freeze-up. Frazil under a stationary ice cover is ubiquitous, does not adhere to other materials and appears to closely associated with the ice cover undersurface. The return intensity profiles observed in pre-freeze-up frazil events increased roughly linearly with height in the water column. Profile comparisons with earlier simulation results allowed inferences on particle size distributions and their controlling processes. The bulk of data analysis efforts was devoted to clarifying the time dependences of the more abundant post-stabilization SWIPS intensity data and its underlying connections to changes in the major river, atmosphere and ice cover environmental parameters. The obtained results showed unlagged or weakly negatively-lagged, positive correlations between such intensities and both river water levels and air temperatures (or solar radiation input) on, at least, diurnal and shorter time scales. The water level parameter was the stronger of these two influences and was believed to be representative of a physical link to river flow speed. Lower frequency connections to the physical state of the ice cover were also apparent. Interpretations of these results were offered in terms of a local equilibrium between the suspended frazil population and a dynamic slush layer at the bottom of the ice cover. Initial steps were taken toward developing and testing analysis tools potentially capable of supporting combined analysis and modelling of this equilibrium. A simple interpretative approach was applied to data acquired at a single acoustic frequency based upon combined use of a Rouse Law-based Inverted sediment model of uniformly-sized spherical frazil particles and volume backscattering coefficients measured in post-freeze-up intervals. Results suggested consistency with the basic form of return intensity profiles at most but not all times. For suitable measurement periods, the approach yielded reasonable estimates of the major particle size and concentration parameters. The deficiencies of this approach are discussed and compared with expectations and results from recently successful simultaneous measurements at two acoustic frequencies. Priorities are identified for validation, and refinement of single and multifrequency approaches along with integrated study of the lower ice cover as part of a broader program to understand frazil ice growth in freezing rivers.

Lidar signature from bubbles in the sea

The lidar signature from a collection of bubbles is proportional to the volume backscatter coefficient at a scattering angle of 180 degrees . This quantity, calculated using a combination of geometric optics and diffraction, is proportional to the void fraction of the bubbles in the water for any bubble size distribution. The constant of proportionality is 233 m(-1) sr(-1)for clean bubbles, slightly less for bubbles coated with a thin layer of organic material, and as large as 1445 m(-1) sr(-1) for a thick coating of protein.

Target strength spectrum of Atlantic herring over a low‐kilohertz frequency band.

Atlantic herring (Clupea harengus) in the stock of Norwegian spring‐spawning herring were observed in their wintering area off the northwest coast of Norway in November 2009. The volume backscattering coefficient sV was measured with the Simrad EK60/38‐kHz scientific echo sounder, yielding numerical values of fish density ρ through the fundamental equation of echo integration sV = ρσ, where ρ is the mean backscattering cross section of the ensonified fish. Derived values of ρ were used to convert measurements of sV made with the Kongsberg TOPAS PS18 parametric sub‐bottom profiling sonar to infer σ, thence its logarithmic measure target strength, over the approximate difference‐frequency band 1.5–6 kHz. [Work supported by ONR Award No. N000140910482 and Norwegian Research Council Grant No. 184705.]

The relative frequency response derived from individually separated targets of northeast Arctic cod (Gadus morhua), saithe (Pollachius virens), and Norway pout (Trisopterus esmarkii)

Abstract Pedersen, G., and Korneliussen, R. J. 2009. The relative frequency response derived from individually separated targets of northeast Arctic cod (Gadus morhua), saithe (Pollachius virens), and Norway pout (Trisopterus esmarkii). – ICES Journal of Marine Science, 66: 1149–1154. The concept of relative frequency response r(f) of fish is an important feature used to characterize acoustic targets. It is defined as the volume-backscattering coefficient at a specific frequency f relative to that of a reference frequency. When based on volume backscattering, r(f) reliably distinguishes several acoustic categories if the insonified volumes are reasonably comparable between the frequencies, and that enough samples and targets are measured to constrain stochastic variations in the data within acceptable limits. Therefore, r(f) distinguishes different fish species with swimbladders poorly if they appear as single targets. Using target-strength (TS) data, the acoustic measurements are more spatially comparable, and averaging the TS over an echotrace of a single fish improves the ability to distinguish between different species. Frequency response was estimated using TS data from in situ measurements, collected using Simrad EK60 echosounders with split-beam transducers transmitting simultaneously at 18, 38, 70, 120, and 200 kHz. Selected series with nearly pure catches of northeast Arctic cod (Gadus morhua), saithe (Pollachius virens), and Norway pout (Trisopterus esmarkii) were analysed using a target-tracking algorithm. The frequency response of northeast Arctic cod and saithe did not differ significantly, but at high frequencies, the response of both northeast Arctic cod and saithe differed from that of Norway pout. However, in the latter case, northeast Arctic cod and saithe could be separated, because of their different TS magnitudes.

Range compensation function for echo integration in transducer near fields, with special reference to parametric sonar.

Range compensation functions are applied to echo signals so that the corresponding range‐compensated echo intensity equals the volume backscattering coefficient to within a multiplicative constant. For echo integration in a transducer far field, the transmit and receive pressure fields each decrease inversely with range r, and the well‐known range compensation function, applied to intensity, is r2×10αr/5, where α is the absorption coefficient. For echo integration in a transducer near field, the range compensation function is that of the far field modified by a multiplying factor. This factor is, approximately, the ratio of the square of the surface integral of the field intensity at r due to extrapolation from the far field, assuming inverse range dependence of the amplitude, to the product of the surface integrals of transmit and receive intensities at r. This general range compensation function is developed for the special case of echo integration with a parametric sonar in which scatterers are ensonif...

Reexamination of depolarization in lidar measurements

Almost all of the depolarization papers in the lidar literature employ a physically inappropriate notation and they use a definition of the depolarization ratio that is not linear in the quantity of interest. This depolarization lidar legacy is misleading and confusing. In particular, subscripts meaning parallel and perpendicular do not apply to atmospheric parameters, such as the volume backscatter coefficient, because (for linear polarization) the two components of the backscattered light are polarized in the transmitted sense and completely unpolarized; the unpolarized component is not "perpendicular." An analysis of lidar depolarization measurements with a particle scattering matrix recently provided in the literature yields algorithms for retrieving the depolarization parameter from either linear or circular depolarization lidar measurements. The analysis, notation, and definitions recommended here harmonize lidar depolarization analysis with radiative transfer theory, particle scattering theory, and standard polarization measurement techniques.

Quantifying gas ebullition with echosounder: the role of methane transport by bubbles in a medium‐sized lake

In lakes and reservoirs with variable water level, gas ebullition can play a substantial role in methane transport in the water column and to the atmosphere. However, measuring methane ebullition from sediment is difficult as releases are highly heterogeneous and intermittent on macro‐ and micro‐scales. In contrast to conventional gas traps and optical methods, hydroacoustic technology allows rapid scanning over large volumes of the water column synoptically to quantify gas bubble abundance. A 120‐kHz dual beam downward‐looking echosounder was used to measure the size distributions of bubbles that do not resonate at the sonar frequency. Data obtained with this sonar permit accurate calculation and evaluation of ebullition flux from the bottom. A robust relationship was established between gas volumes and backscattering cross‐section of individual bubbles in experimental conditions, and rise velocities of bubbles were precisely measured. The volume backscattering coefficient was shown to be a good gauge of the total volume of bubbles per cubic meter of water, allowing the use of a single‐beam sonar for measuring volumetric bubble concentrations. Data obtained from hydroacoustic surveys on Lake Kinneret, where gaseous methane is emitted from randomly dispersed sediment sources, indicated that ~90% of bubbles escaping from soft sediments ranged from 1.3 mm to 4.5 mm and ~50% ranged from 2.0 mm to 3.2 mm in equivalent radius. In summer‐fall 2001, the gaseous methane fluxes from hypolimnetic sediments was ~10 mmol m−2 d−1, accounting for one‐third of the observed methane accumulation in the hypolimnion. This relatively high ebullition rate could be attributed to the gradual decreasing of the mean water level in preceding years.

Statistical Treatment of Remote Sensing Reflectance from Coastal Ocean Water: Proportionality of Reflectance from Multiple Scattering to Source Function b/a

Abstract I treat the reflectance of light from coastal ocean water in terms of diffused volume scattering phase function P(θ) derived from successive products of the normalized volume scattering function β(θ). My results show that the wavelength dependence for backscattering in a multiple scattering process is directly proportional to the angle-independent dimensionless source function b/a, which is the ratio of the total volume scattering coefficient b and the total volume absorption coefficient a. I use this result to produce a statistical formula for remote sensing reflectance (Rrs). The statistical formula shows good agreement with experimental data, and—unlike the standard oceanographic expressions for Rrs given in terms of bb/(a + bb), where bb is the volume backscattering coefficient—the statistical relationship for Rrs accounts for the effects of photon turnaround and reduces to the expected asymptotic limits for diffuse reflectance when a → 0 but bb remains finite and when bb → 0 but a and b rema...