Comparison of the ocean inherent optical properties obtained from measurements and inverse modeling

A model developed recently by Loisel and Stramski [Appl. Opt. 39, 3001-3011 (2000)] for estimating the spectral absorption a(lambda), scattering b(lambda), and backscattering b(b)(lambda) coefficients in the upper ocean from the irradiance reflectance just beneath the sea surface R(lambda, z = 0(-)) and the diffuse attenuation of downwelling irradiance within the surface layer ?K(d)(lambda)?(1) is compared with measurements. Field data for this comparison were collected in different areas including off-shore and near-shore waters off southern California and around Europe. The a(lambda) and b(b)(lambda) values predicted by the model in the blue-green spectral region show generally good agreement with measurements that covered a broad range of conditions from clear oligotrophic waters to turbid coastal waters affected by river discharge. The agreement is still good if the model estimates of a(lambda) and b(b)(lambda) are based on R(lambda, z = 0(-)) used as the only input to the model available from measurements [as opposed to both R(lambda, z = 0(-)) and ?K(d)(lambda)?(1) being measured]. This particular mode of operation of the model is relevant to ocean-color remote-sensing applications. In contrast to a(lambda) and b(b)(lambda) the comparison between the modeled and the measured b(lambda) shows large discrepancies. These discrepancies are most likely attributable to significant variations in the scattering phase function of suspended particulate matter, which were not included in the development of the model.     

Atmospheric correction of SeaWiFS imagery for turbid coastal and inland waters: comment

Ruddick et al. [Appl. Opt. 39, 897 (2000)] extended the standard SeaWiFS atmospheric-correction algorithm for use over turbid coastal and inland waters. However, Ruddick's method is based on the assumption of a spatially homogeneous constant ratio for the water-leaving reflectances normalized by the sun-sea atmospheric transmittance at 765 and 865 nm. Such first-order b(b)/a model-based assumption can result in an inaccuracy for highly turbid water. Using the first- and second-order b(b)/(a + b(b)) models as well as the second-order b(b)/a model (which, more realistically, do not assume spatial homogeneity ratio), we suggest using the modified assumption, R(8)(-1) = alpha0 R(7)(-1) + (l1Q)(-1) (1 - alpha0), instead of Ruddick's assumption, in SeaWiFS atmospheric-correction algorithms for highly turbid waters.     

Irradiance inversion theory to retrieve volume scattering function of seawater

An attempt to retrieve the volume scattering function (VSF) of source-free and no-inelastic-scattering ocean water is made from the upwelling irradiance Eu and downwelling irradiance Ed. It will be shown, from the radiative transfer equation, that the VSF of seawater can be calculated by the planar irradiances when the scattering phase function of the suspended particles in the backward direction and the molecular VSF are known. On the derivation of the hydrosol VSF, several optical properties such as the absorption coefficient a; the scattering coefficients of hydrosol, b, b(f), b(b) and those of the suspended particles, b(p), b(fp), b(bp); the beam attenuation coefficient c; the average cosines mu, mu(d), and mu(u); and the backscattering shape factor for the downwelling light stream, r(du), will also be obtained. On the derivation of those optical parameters, classical knowledge related to interrelationships between inherent optical properties and apparent optical properties and obtained with Monte Carlo numerical simulations is analytically verified. The present theory can be applied to surface waters and any wavelengths, except for waters and wavelengths with an extremely low b(b)/a ratio.     

Measured and modeled radiometric quantities in coastal waters: toward a closure

Accurate radiative transfer modeling in the coupled atmosphere-sea system is increasing in importance for the development of advanced remote-sensing applications. Aiming to quantify the uncertainties in the modeling of coastal water radiometric quantities, we performed a closure experiment to intercompare theoretical and experimental data as a function of wavelength lambda and water depth z. Specifically, the study focused on above-water downward irradiance E(d)(lambda, 0+) and in-water spectral profiles of upward nadir radiance L(u)(lambda, z), upward irradiance E(u)(lambda, z), downward irradiance E(d)(lambda, z), the E(u)(lambda, z)/L(u)(lambda, z) ratio (the nadir Q factor), and the E(u)(lambda, z)/E(d)(lambda, z) ratio (the irradiance reflectance). The theoretical data were produced with the finite-element method radiative transfer code ingesting in situ atmospheric and marine inherent optical properties. The experimental data were taken from a comprehensive coastal shallow-water data set collected in the northern Adriatic Sea. Under various measurement conditions, differences between theoretical and experimental data for the above-water E(d)(lambda, 0+) and subsurface E(d)(lambda, 0-) as well as for the in-water profiles of the nadir Q factor were generally less than 15%. In contrast, the in-water profiles of L(u)(lambda, z), E(d)(lambda, z), E(u)(lambda, z) and of the irradiance reflectance exhibited larger differences [to approximately 60% for L(u)(lambda, z) and E(u)(lambda, z), 30% for E(d)(lambda, z), and 50% for the irradiance reflectance]. These differences showed a high sensitivity to experimental uncertainties in a few input quantities used for the simulations: the seawater absorption coefficient; the hydrosol phase function backscattering probability; and, mainly for clear water, the bottom reflectance.     

Modeling the optical properties of mineral particles suspended in seawater and their influence on ocean reflectance and chlorophyll estimation from remote sensing algorithms

The optical properties of mineral particles suspended in seawater were calculated from the Mie scattering theory for different size distributions and complex refractive indices of the particles. The ratio of the spectral backscattering coefficient to the sum of the spectral absorption and backscattering coefficients of seawater, b(b)(lambda)/[a(lambda) + b(b)(lambda)], was analyzed as a proxy for ocean reflectance for varying properties and concentrations of mineral particles. Given the plausible range of variability in the particle size distribution and the refractive index, the general parameterizations of the absorption and scattering properties of mineral particles and their effects on ocean reflectance in terms of particle mass concentration alone are inadequate. The variations in the particle size distribution and the refractive index must be taken into account. The errors in chlorophyll estimation obtained from the remote sensing algorithms that are due to the presence of mineral particles can be very large. For example, when the mineral concentration is 1 g m(-3) and the chlorophyll a concentration is low (0.05 mg m(-3)), current global algorithms based on a blue-to-green reflectance ratio can produce a chlorophyll overestimation ranging from approximately 50% to as much as 20-fold.     

Irradiance inversion algorithm for absorption and backscattering profiles in natural waters: improvement for clear waters

Our iterative inversion algorithm for retrieving absorption a(z) and backscattering b(b)(z) from profiles of upwelling and downwelling irradiance, on the basis of assuming a depth-independent phase function for the medium, was found to have unsatisfactory accuracy for b(b)(z) in clear waters. We modified the algorithm here by assuming a depth-independent phase function for the particles and then performing an additional iteration over the fraction of total scattering that is due to the water itself. The modified algorithm's accuracy is considerably improved over the original in clear waters and reduces to the original in waters for which the particle contribution to b(b)(z) is dominant.     

Factor analysis of multispectral radiances over coastal and open ocean water based on radiative transfer calculations

Factor analysis is applied to multispectral (seventeen wavelengths) radiances simulated by a radiative transfer model (matrix-operator method) in and above coastal and open ocean waters. The calculated radiances were compared with measured radiances before applying factor analysis. They agree well for different sun elevations and even for turbid coastal waters. The factor analysis technique allows us to extract the characteristic signatures of phytoplankton, suspended matter, and yellow substance. The fluorescence of chlorophyll at lambda = 685 nm is found to be a clear signal for phytoplankton, also in the presence of other suspensions and yellow substance. A comparison of different algorithms for the extraction of the fluorescence peak favors the addition of chlorophyll absorption at lambda = 670 nm. The blue-green ratio is found to be useless for chlorophyll detection in coastal waters. Suspended matter and yellow substance can also clearly be seen in the factor loading for all multispectral radiances analyzed. However, suspended matter is reflected more strongly than yellow substance.     

Atmospheric correction of satellite ocean color imagery: the black pixel assumption

The assumption that values of water-leaving radiance in the near-infrared (NIR) are negligible enable aerosol radiative properties to be easily determined in the correction of satellite ocean color imagery. This is referred to as the black pixel assumption. We examine the implications of the black pixel assumption using a simple bio-optical model for the NIR water-leaving reflectance [rho(w)(lambda(NIR))](N). In productive waters [chlorophyll (Chl) concentration >2 mg m(-3)], estimates of [rho(w)(lambda(NIR))](N) are several orders of magnitude larger than those expected for pure seawater. These large values of [rho(w)(lambda(NIR))](N) result in an overcorrection of atmospheric effects for retrievals of water-leaving reflectance that are most pronounced in the violet and blue spectral region. The overcorrection increases dramatically with Chl, reducing the true water-leaving radiance by roughly 75% when Chl is equal to 5 mg m(-3). Relaxing the black pixel assumption in the correction of Sea-Viewing Wide Field-of-View Sensor (SeaWiFS) satellite ocean color imagery provides significant improvements in Chl and water-leaving reflectance retrievals when Chl values are greater than 2 mg m(-3). Improvements in the present modeling of [rho(w)(lambda(NIR))](N) are considered, particularly for turbid coastal waters. However, this research shows that the effects of nonzero NIR reflectance must be included in the correction of satellite ocean color imagery.     

Volume-consumption comparisons of free-space and guided-wave optical interconnections

We compare volume-consumption characteristics of free-space and guided-wave optical interconnections. System volume consumption is used as a fundamental measure of various point-to-point space-invariant and space-variant interconnections of two-dimensional arrays of N(1/2) x N(1/2) points. We show that, in free-space and space-invariant situations, although volume consumption for macroaperture optics is O(1)(N(3/2)), where O denotes the order, it is only O(2)(N) for microaperture optics. For free-space and space-variant operations only microaperture optics is possible without fundamental power losses. The corresponding minimum volume consumption is O(3)(N(3)). We show that single microaperture-per-channel implementations of either space-invariant or space-variant operations are, in general, more volume efficient than are their two-cascade microaperture-per-channel counterparts. We also show that, for minimizing volume consumption, the optimum relative apertures F#(opt) for space-variant optical elements are, respectively, (5N)(1/2)/4 for a single microaperture-per-channel geometry and (5N)(1/2)/2 for a two-cascade microaperture-per-channel geometry. In guided-wave or fiber interconnect cases our study shows that the volume consumption for space-invariant and space-variant operations is O(4)(N), with O(4) < O(2), and O(5)(N(3/2)), respectively. Thus an important conclusion of the study is that free-space optics is less volume efficient than is guided-wave optics in both space-invariant and space-variant interconnect applications.     

Toward closure of upwelling radiance in coastal waters

We present three methods for deriving water-leaving radiance L(w)(lambda) and remote-sensing reflectance using a hyperspectral tethered spectral radiometer buoy (HyperTSRB), profiled spectroradiometers, and Hydrolight simulations. Average agreement for 53 comparisons between HyperTSRB and spectroradiometric determinations of L(w)(lambda) was 26%, 13%, and 17% at blue, green, and red wavelengths, respectively. Comparisons of HyperTSRB (and spectroradiometric) L(w)(lambda) with Hydrolight simulations yielded percent differences of 17% (18%), 17% (18%), and 13% (20%) for blue, green, and red wavelengths, respectively. The differences can be accounted for by uncertainties in model assumptions and model input data (chlorophyll fluorescence quantum efficiency and the spectral chlorophyll-specific absorption coefficient for the red wavelengths, and scattering corrections for input ac-9 absorption data and volume scattering function measurements for blue wavelengths) as well as radiance measurement inaccuracies [largely differences in the depth of the L(u)(lambda, z) sensor on the HyperTSRB].     

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

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

Hyperspectral remote sensing for shallow waters. I. A semianalytical model

For analytical or semianalytical retrieval of shallow-water bathymetry and/or optical properties of the water column from remote sensing, the contribution to the remotely sensed signal from the water column has to be separated from that of the bottom. The mathematical separation involves three diffuse attenuation coefficients: one for the downwelling irradiance (K(d)), one for the upwelling radiance of the water column (K(u)(C)), and one for the upwelling radiance from bottom reflection (K(u)(B)). Because of the differences in photon origination and path lengths, these three coefficients in general are not equal, although their equality has been assumed in many previous studies. By use of the Hydrolight radiative-transfer numerical model with a particle phase function typical of coastal waters, the remote-sensing reflectance above (R(rs)) and below (r(rs)) the surface is calculated for various combinations of optical properties, bottom albedos, bottom depths, and solar zenith angles. A semianalytical (SA) model for r(rs) of shallow waters is then developed, in which the diffuse attenuation coefficients are explicitly expressed as functions of in-water absorption (a) and backscattering (b(b)). For remote-sensing inversion, parameters connecting R(rs) and r(rs) are also derived. It is found that r(rs) values determined by the SA model agree well with the exact values computed by Hydrolight (~3% error), even for Hydrolight r(rs) values calculated with different particle phase functions. The Hydrolight calculations included b(b)/a values as high as 1.5 to simulate high-turbidity situations that are occasionally found in coastal regions.     

Determination of mass density, dielectric, elastic, and piezoelectric constants of bulk GaN crystal

Mass density, dielectric, elastic, and piezoelectric constants of bulk GaN crystal were determined. Mass density was obtained from the measured ratio of mass to volume of a cuboid. The dielectric constants were determined from the measured capacitances of an interdigital transducer (IDT) deposited on a Z-cut plate and from a parallel plate capacitor fabricated from this plate. The elastic and piezoelectric constants were determined by comparing the measured and calculated SAW velocities and electromechanical coupling coefficients on the Z- and X-cut plates. The following new constants were obtained: mass density p = 5986 kg/m(3); relative dielectric constants (at constant strain S) ε(S)(11)/ε(0) = 8.6 and ε(S)(11)/ε(0) = 10.5, where ε(0) is a dielectric constant of free space; elastic constants (at constant electric field E) C(E)(11) = 349.7, C(E)(12) = 128.1, C(E)(13) = 129.4, C(E)(33) = 430.3, and C(E)(44) = 96.5 GPa; and piezoelectric constants e(33) = 0.84, e(31) = -0.47, and e(15) = -0.41 C/m(2).     

Mass-specific scattering coefficient for natural minerogenic particle populations: particle size distribution effect and closure analyses

The relationship between the particulate scattering coefficient (b(p)) and the concentration of suspended particulate matter (SPM), as represented by the mass-specific scattering coefficient of particulates (b(p)*=b(p)/SPM), depends on particle size distribution (PSD). This dependence is quantified for minerogenic particle populations in this paper through calculations of b(p)* for common minerals as idealized populations (monodispersed spheres); contemporaneous measurements of b(p), SPM, and light-scattering attributes of mineral particles with scanning electron microscopy interfaced with automated image and x-ray analyses (SAX), for a connected stream-reservoir system where minerogenic particles dominate b(p); and estimates of b(p) and its size dependency (through SAX results-driven Mie theory calculations), particle volume concentration, and b(p)*. Modest changes in minerogenic PSDs are shown to result in substantial variations in b(p)*. Good closure of the SAX-based estimates of b(p) and particle volume concentration with bulk measurements is demonstrated. Converging relationships between b(p)* and particle size, developed from three approaches, were well described by power law expressions.     

Ocean inherent optical property estimation from irradiances

A method is evaluated for estimating the absorption coefficient a and the backscattering coefficient b(b) from measurements of the upward and downward irradiances E(u)(z) and E(d)(z). With this method, the reflectance ratio R(z) and the downward diffuse attenuation coefficient K(d)(z) obtained from E(u)(z) and E(d)(z) are used to estimate the inherent optical properties R(infinity) and K(infinity) that are the asymptotic values of R(z) and K(d)(z), respectively. For an assumed scattering phase function beta , there are unique correlations between the values of R(infinity) and K(infinity) and those of a and b(b) that can be derived from the radiative transfer equation. Good estimates of a and the Gordon parameter G = b(b)/(a + b(b)) can be obtained from R(infinity) and K(infinity) if the true scattering phase function is not greatly different from the assumed function. The method works best in deep, homogeneous waters, but can be applied to some cases of stratified waters. To improve performance in shallow waters where bottom effects are important, the deep- and shallow-measurement reflectance models also are developed.     

Raman scattering by pure water and seawater

Measurements of the magnitude and spectral distribution of the Raman-scattering coefficients of pure water (b(rw)) and seawater (b(rs)) are presented. Two independent measurements of the spectral distribution of the Raman-scattering coefficient of pure water were made for incident wavelengths ranging from 250 to 500 nm. These measurements revealed a strong dependence of b(rw) on wavelength that could be represented by a (lambda')(-5.3+/-0.3) relationship, where lambda' is the incident wavelength, or a lambda(-4.6+/-0.3) relationship, where lambda is the Raman-scattered wavelength, when normalized to units of photons. The corresponding relationships for normalization to energy are (lambda')(-5.5+/-0.4) and lambda(-4.8+/-0.3), respectively. These relationships are found to be consistent with resonance Raman theory for an absorption wavelength of 130 nm. The absolute value of b(rw) for the 3400-cm(-1) line was found to be (2.7 +/- 0.2) x 10(-4) m(-1) for an incident wavelength of 488 nm, which is consistent with a number of earlier reports. The difference between the magnitudes of the Raman-scattering coefficients for pure water and seawater was statistically insignificant.     

Optical closure in a complex coastal environment: particle effects

An optical dataset was collected on a mooring in the Santa Barbara Channel. Radiative transfer modeling and statistical analyses were employed to investigate sources of variability of in situ remote sensing reflectance [r(rs)(lambda,4 m)] and the f/Q ratio. It was found that the variability of inherent optical properties and the slope of the particle size distribution (xi) were strongly related to the variability of r(rs)(lambda,4 m). The variability of f/Q was strongly affected by particle type characteristics. A semianalytical radiative transfer model was applied and effects of variable particle characteristics on optical closure were evaluated. Closure was best achieved in waters composed of a mixture of biogenic and minerogenic particles.     

Comparison of adsorption equilibrium models for the study of CL-, NO3- and SO4(2-) removal from aqueous solutions by an anion exchange resin

The removal of chloride, nitrate and sulfate ions from aqueous solutions by a macroporous resin is studied through the ion exchange systems OH(-)/Cl(-), OH(-)/NO(3)(-), OH(-)/SO(4)(2-), and HCO(3)(-)/Cl(-), Cl(-)/NO(3)(-), Cl(-)/SO(4)(2-). They are investigated by means of Langmuir, Freundlich, Dubinin-Radushkevitch (D-R) and Dubinin-Astakhov (D-A) single-component adsorption isotherms. The sorption parameters and the fitting of the models are determined by nonlinear regression and discussed. The Langmuir model provides a fair estimation of the sorption capacity whatever the system under study, on the contrary to Freundlich and D-R models. The adsorption energies deduced from Dubinin and Langmuir isotherms are in good agreement, and the surface parameter of the D-A isotherm appears consistent. All models agree on the order of affinity OH(-)相似文献   

Spectral parameters of inherent optical property models: method for satellite retrieval by matrix inversion of an oceanic radiance model

Inherent optical property (IOP) spectral models for the phytoplankton absorption coefficient, chromophoric dissolved organic matter (CDOM) absorption coefficient, and total constituent backscattering (TCB) coefficient are linear in the reference wavelength IOP and nonlinear in the spectral parameters. For example, the CDOM absorption coefficient IOP a(CDOM)(lambda(i)) = a(CDOM)(lambda(ref))exp[-S(lambda(i)- lambda(ref))] is linear in a(CDOM)(lambda(ref)) and nonlinear in S. Upon linearization by Taylor's series expansion, it is shown that spectral model parameters, such as S, can be concurrently accommodated within the same conventional linear matrix formalism used to retrieve the reference wavelength IOP's. Iteration is used to adjust for errors caused by truncation of the Taylor's series expansion. Employing an iterative linear matrix inversion of a water-leaving radiance model, computer simulations using synthetic data suggest that (a) no instabilities or singularities are introduced by the linearization and subsequent matrix inversion procedures, (b) convergence to the correct value can be expected only if starting values for a model parameter are within certain specific ranges, (c) accurate retrievals of the CDOM slope S (or the phytoplankton Gaussian width g) are generally reached in 3-20 iterations, (d) iterative retrieval of the exponent n of the TCB wavelength ratio spectral model is not recommended because the starting values must be within approximately +/-5% of the correct value to achieve accurate convergence, and (e) concurrent retrieval of S and g (simultaneously with the phytoplankton, CDOM, and TCB coefficient IOP's) can be accomplished in a 5 x 5 iterative matrix inversion if the starting values for S and g are carefully chosen to be slightly higher than the expected final retrieved values.