Retrieval of elements of the columnar aerosol scattering phase matrix from polarized sky radiance over the ocean: simulations

We have extended the Wang-Gordon [Appl. Opt. 32, 4598-4609 (1993)] and Gordon-Zhang [Appl. Opt.34, 5552-5555 (1995)] algorithms for retrieval of omega(0)P(?, where omega(0) is the aerosol single-scattering albedo and P(?) is the aerosol phase function for scattering through an angle ?, from measurement of the radiances exiting the top and the bottom of the atmosphere over the ocean, to include polarization. This permits derivation of the P(11)(?) and P(12)(?) elements of the Mueller scattering phase matrix P(?) from measurement of the linear polarization portion of the Stokes vectors associated with the radiance exiting the top and the bottom of the atmosphere. Simulations show that good retrievals are possible for aerosol optical thicknesses as large as 2; however, the atmosphere is required to be horizontally homogeneous. We study the influence of the elements of P(?) that cannot be determined in this manner. It is shown that including surface measurements of the linear polarization of the sky radiance improves the estimation of the radiance simultaneously exiting the top of the atmosphere (TOA) and also allows reasonably accurate estimates of the TOA polarization. This is important for in-orbit calibration of ocean-color sensors.     

Retrieval of the Columnar Aerosol Phase Function and Single-Scattering Albedo from Sky Radiance over Land: Simulations

We present a retrieval scheme that can be used to derive the aerosol phase function and single-scattering albedo from the sky radiance over land. The retrieval algorithm iteratively corrects the aerosol volume scattering function, the product of the single-scattering albedo and the phase function, based on the difference between the measured sky radiance and the radiance calculated by solving the radiative transfer equation. It is tested first under ideal conditions, i.e., the approximations made in the retrieval algorithm totally agree with actual conditions assumed in creating the pseudodata for sky radiance. It is then tested under more realistic conditions to assess its susceptibility to measurement errors and effects of conditions not recognized in the retrieval algorithm, e.g., surface horizontal inhomogeneity, departures of the surface from Lambertian, and aerosol horizontal inhomogeneity. These simulations show that, in most cases, this scheme can retrieve the aerosol single-scattering albedo with high accuracy (within 1%) and can therefore be used to identify strongly absorbing aerosols. It can also produce meaningful retrievals of most aerosol phase functions: less than 5% error at 865 nm and less than 10% at 443 nm in most cases. Typically, the error in the volume scattering function is small for scattering angles ?90 degrees , then increases for larger angles. Disappointing results in both the single-scattering albedo and the scattering phase function occur at 443 nm, either when there are large calibration errors in the radiometer used to measure the sky radiance or when the land reflection properties are significantly inhomogeneous.     

Remote sensing of ocean color: a methodology for dealing with broad spectral bands and significant out-of-band response

A methodology for delineating the influence of finite spectral bandwidths and significant out-of-band response of sensors for remote sensing of ocean color is developed and applied to the Sea-viewing Wide-Field-of-view Sensor (SeaWiFS). The basis of the method is the application of the sensor's spectral-response functions to the individual components of the top-of-the-atmosphere (TOA) radiance rather than the TOA radiance itself. For engineering purposes, this approach allows one to assess easily (and quantitatively) the potential of a particular sensor design for meeting the system-sensor plus algorithms-performance requirements. In the case of the SeaWiFS, two significant conclusions are reached. First, it is found that the out-of-band effects on the water-leaving radiance component of the TOA radiance are of the order of a few percent compared with a sensor with narrow spectral response. This implies that verification that the SeaWiFS system-sensor plus algorithms-meets the goal of providing the water-leaving radiance in the blue in clear ocean water to within 5% will require measurements of the water-leaving radiance over the entire visible spectrum as opposed to just narrow-band (10-20-nm) measurements in the blue. Second, it is found that the atmospheric correction of the SeaWiFS can be degraded by the influence of water-vapor absorption in the shoulders of the atmospheric-correction bands in the near infrared. This absorption causes an apparent spectral variation of the aerosol component between these two bands that will be uncharacteristic of the actual aerosol present, leading to an error in correction. This effect is dependent on the water-vapor content of the atmosphere. At typical water-vapor concentrations the error is larger for aerosols with a weak spectral variation in reflectance than for those that display a strong spectral variation. If the water-vapor content is known, a simple procedure is provided to remove the degradation of the atmospheric correction. Uncertainty in the water-vapor content will limit the accuracy of the SeaWiFS correction algorithm.     

How well can radiance reflected from the ocean-atmosphere system be predicted from measurements at the sea surface?

There is interest in the prediction of the top-of-the-atmosphere (TOA) reflectance of the ocean-atmosphere system for in-orbit calibration of ocean color sensors. With the use of simulations, we examine the accuracy one could expect in estimating the reflectance ρ(T) of the ocean-atmosphere system based on a measurement suite carried out at the sea surface, i.e., a measurement of the normalized sky radiance ρ(B) and the aerosol optical thickness (τ(a)), under ideal conditions-a cloud-free, horizontally homogeneous atmosphere. Briefly, ρ(B) and τ(a) are inserted into a multiple-scattering inversion algorithm to retrieve the aerosol optical properties-the single-scattering albedo and the scattering phase function. These retrieved quantities are then inserted into the radiative transfer equation to predict ρ(T). Most of the simulations were carried out in the near infrared (865 nm), where a larger fraction of ρ(T) is contributed by aerosol scattering compared with molecular scattering, than in the visible, and where the water-leaving radiance can be neglected. The simulations suggest that ρ(T) can be predicted with an uncertainty typically Θ1% when the ρ(B) and τ(a) measurements are error free. We investigated the influence of the simplifying assumptions that were made in the inversion-prediction process, such as modeling the atmosphere as a plane-parallel medium, using a smooth sea surface in the inversion algorithm, using the scalar radiative transfer theory, and assuming that the aerosol was confined to a thin layer just above the sea surface. In most cases, these assumptions did not increase the error beyond ±1%. An exception was the use of the scalar radiative transfer theory, for which the error grew to as much as ~2.5%, suggesting that the use of ρ(B) inversion and ρ(T) prediction codes that include polarization would be more appropriate. However, their use would necessitate measurement of the polarization associated with ρ(B). We also investigated the uncertainty introduced by an unknown aerosol vertical structure and found it to be negligible if the aerosols were nonabsorbing or weakly absorbing. An extension of the analysis to the blue, which requires measurement of the water-leaving radiance, showed significantly better predictions of ρ(T) because the major portion of ρ(T) is the result of molecular scattering, which is known precisely. We also simulated the influence of calibration errors in both the Sun photometer and the ρ(B) radiometer. The results suggest that the relative error in the predicted ρ(T) is similar in magnitude to that in ρ(B) (actually it was somewhat less). However, the relative error in ρ(T) induced by error in τ(a) is usually much less than the relative error in τ(a). Currently, it appears that radiometers can be calibrated with an uncertainty of ~±2.5%, therefore it is reasonable to conclude that, at present, the most important error source in the prediction of ρ(T) from ρ(B) is likely to be error in the ρ(B) measurement.     

Radiometric calibration of SeaWiFS in the near infrared

The radiometric calibration of the Sea-Viewing Wide-Field-of-View Sensor (SeaWiFS) in the near infrared (band 8, centered on 865 nm) is evaluated by use of ground-based radiometer measurements of solar extinction and sky radiance in the Sun's principal plane at two sites, one located 13 km off Venice, Italy, and the other on the west coast of Lanai Island, Hawaii. The aerosol optical thickness determined from solar extinction is used in an iterative scheme to retrieve the pseudo aerosol phase function, i.e., the product of single-scattering albedo and phase function, in which sky radiance is corrected for multiple scattering effects. No assumption about the aerosol model is required. The aerosol parameters are the inputs into a radiation-transfer code used to compute the SeaWiFS radiance. The calibration method has a theoretical inaccuracy of plus or minus 2.0-3.6%, depending on the solar zenith angle and the SeaWiFS geometry. The major source of error is in the calibration of the ground-based radiometer operated in radiance mode, assumed to be accurate to +/- 2%. The establishment of strict criteria for atmospheric stability, angular geometry, and surface conditions resulted in selection of only 26 days for the analysis during 1999-2000 (Venice site) and 1998-2001 (Lanai site). For these days the measured level-1B radiance from the SeaWiFS Project Office was generally lower than the corresponding simulated radiance in band 8 by 7.0% on average, +/- 2.8%.     

Columnar aerosol properties over oceans by combining surface and aircraft measurements: simulations

We report an algorithm that can be used to invert the radiance exiting the top and bottom of the atmosphere to yield the columnar optical properties of atmospheric aerosol under clear sky conditions over the oceans. The method is an augmentation of a similar algorithm presented by Wang and Gordon [Appl. Opt. 32, 4598 (1993)] that used only sky radiance, and therefore was incapable of retrieving the aerosol phase function at the large scattering angles that are of critical importance in remote sensing of oceanic and atmospheric properties with satellites. Well-known aerosol models were combined with radiative transfer theory to simulate pseudodata for testing of the algorithm. The tests suggest that it should be possible to retrieve the aerosol phase function and the aerosol single-scattering albedo accurately over the visible spectrum at aerosol optical thicknesses as large as 2.0. The algorithm is capable of retrievals with such large optical thicknesses because all significant orders of multiple scattering are included. We believe that combining an algorithm of this type with surface-based and high-altitude aircraft-based radiance measurements could be useful for studying aerosol columnar optical properties over oceans and large lakes. The use of the retrieval method is possible over the ocean because, unlike the land surface, the albedo of the ocean is low and spatially uniform.     

Estimation of the total uncertainty of sky-radiance measurements in field experimental conditions: implications for the aerosol single-scattering albedo

We compare the spectral sky radiance measured by three ground-based optical radiometers during the second Aerosol Characterization Experiment (ACE-2) to estimate the total uncertainty of the radiance in field experimental conditions. The propagation of this uncertainty on the column-integrated aerosol single-scattering albedo omega0 at 868 nm is investigated. The radiance measurements are affected by a systematic gain uncertainty of less than 2% in the visible spectral region and within 6% in the near-IR region. Correcting the measured radiance by a systematic uncertainty reduces the dispersion of the omega0 from 0.07 to 0.03. Besides, the total relative uncertainty of the radiance measurements in field experimental conditions is within 4% at any wavelength. The corresponding uncertainty delta omega0 is 4% for an aerosol optical thickness of 0.2.     

Estimation of aerosol columnar size distribution and optical thickness from the angular distribution of radiance exiting the atmosphere: simulations

We report the results of simulations in which an algorithm developed for estimation of aerosol optical properties from the angular distribution of radiance exiting the top of the atmosphere over the oceans [Appl. Opt. 33, 4042 (1994)] is combined with a technique for carrying out radiative transfer computations by synthesis of the radiance produced by individual components of the aerosol-size distribution [Appl. Opt. 33, 7088 (1994)], to estimate the aerosol-size distribution by retrieval of the total aerosol optical thickness and the mixing ratios for a set of candidate component aerosol-size distributions. The simulations suggest that in situations in which the true size-refractive-index distribution can actually be synthesized from a combination of the candidate components, excellent retrievals of the aerosol optical thickness and the component mixing ratios are possible. An exception is the presence of strongly absorbing aerosols. The angular distribution of radiance in a single spectral band does not appear to contain sufficient information to separate weakly from strongly absorbing aerosols. However, when two spectral bands are used in the algorithm, retrievals in the case of strongly absorbing aerosols are improved. When pseudodata were simulated with an aerosol-size distribution that differed in functional form from the candidate components, excellent retrievals were still obtained as long as the refractive indices of the actual aerosol model and the candidate components were similar. This underscores the importance of component candidates having realistic indices of refraction in the various size ranges for application of the method. The examples presented all focus on the multiangle imaging spectroradiometer; however, the results should be as valid for data obtained by the use of high-altitude airborne sensors.     

Retrieval of the scattering and microphysical properties of aerosols from ground-based optical measurements including polarization. I. Method

A method has been developed for retrieving the scattering and microphysical properties of atmospheric aerosol from measurements of solar transmission, aureole, and angular distribution of the scattered and polarized sky light in the solar principal plane. Numerical simulations of measurements have been used to investigate the feasibility of the method and to test the algorithm's performance. It is shown that the absorption and scattering properties of an aerosol, i.e., the single-scattering albedo, the phase function, and the polarization for single scattering of incident unpolarized light, can be obtained by use of radiative transfer calculations to correct the values of scattered radiance and polarized radiance for multiple scattering, Rayleigh scattering, and the influence of ground. The method requires only measurement of the aerosol's optical thickness and an estimate of the ground's reflectance and does not need any specific assumption about properties of the aerosol. The accuracy of the retrieved phase function and polarization of the aerosols is examined at near-infrared wavelengths (e.g., 0.870 mum). The aerosol's microphysical properties (size distribution and complex refractive index) are derived in a second step. The real part of the refractive index is a strong function of the polarization, whereas the imaginary part is strongly dependent on the sky's radiance and the retrieved single-scattering albedo. It is demonstrated that inclusion of polarization data yields the real part of the refractive index.     

Island perturbation to the sky radiance over the ocean: simulations

Sky-radiance measurements at the sea surface can be used to estimate radiative properties of aerosols over water. We demonstrate, through Monte Carlo simulations, that significant perturbations to sky radiance over the ocean can occur when measurements are carried out with radiometers located on islands. In particular, we present examples of the influence of the physical and optical thicknesses of an aerosol layer, the azimuth of observation relative to the Sun, the size of the island, the location of the radiometer on the island, and the albedo of the island on the magnitude of the perturbation for a circular island of uniform albedo. Relative errors in sky radiance of as high as 39% were found in the blue. Simulated (perturbed) sky radiances were combined with an algorithm for retrieving the aerosol phase function P(θ), where θ is the scattering angle, and with the single-scattering albedo ω(0), to demonstrate how the perturbation can influence the retrieved values. It was found that the fractional error in the retrieved values of the product ω(0)P(θ) can be significantly greater than the fractional error in the sky radiance, because of the effects of multiple scattering. This underscores the importance of removing the island perturbation before an inversion algorithm is used. A first-order procedure for removing the island perturbation based on the values of ω(0)P(θ) retrieved from the perturbed sky radiance is proposed and is found to be effective if the island perturbation is not too large. A simplified Monte Carlo procedure that is applicable to an island of arbitrary shape and albedo distribution is presented. The procedure could be used to assess the suitability of a given island as a measurement site, and to provide a first-order correction to actual experimental measurements.     

Influence of the angular shape of the volume-scattering function and multiple scattering on remote sensing reflectance

Scattering phase functions derived from measured (volume-scattering meter, VSM) volume-scattering functions (VSFs) from Crimean coastal waters were found to have systematic differences in angular structure from Fournier-Forand (FF) functions with equivalent backscattering ratios. Hydrolight simulations demonstrated that differences in the angular structure of the VSF could result in variations in modeled subsurface radiance reflectances of up to +/-20%. Furthermore, differences between VSM and FF simulated reflectances were found to be nonlinear as a function of scattering and could not be explained with the single-scattering approximation. Additional radiance transfer modeling demonstrated that the contribution of multiple scattering to radiance reflectance increased exponentially from a minimum of 16% for pure water to a maximum of approximately 94% for turbid waters. Monte Carlo simulations demonstrated that multiple forward-scattering events were the dominant contributors to the generation of radiance reflectance signals for turbid waters and that angular structures in the shape of the VSF at forward angles could have a significant influence in determining reflectance signals for turbid waters.     

Four-stream solution for atmospheric radiative transfer over a non-Lambertian surface

An analytical model characterizing the atmospheric radiance field over a non-Lambertian surface divides the radiation field into three components: unscattered radiance, single-scattering radiance, and multiple-scattering radiance. The first two components are calculated exactly. A δ-four-stream approximation is extended to calculate the azimuth-independent multiple-scattering radiance over a non-Lambertian surface, which is modeled by a statistical bidirectional reflectance distribution function (BRDF). Accuracy is assessed with respect to the exact results computed from a Gauss-Seidel iterative algorithm. Experiments comparing the results obtained with Lambertian and non-Lambertian surfaces show that incorporating the BRDF into the four-stream approximation significantly improves the accuracy in calculating radiance as well as radiative flux.     

Estimating aerosol optical properties over the oceans with the multiangle imaging spectroadiometer: some preliminary studies

The multiangle imaging spectroradiometer (MISR) scheduled to be flown on the first platform of the Earth Observing System in 1998 provides an opportunity to enhance considerably the accuracy with which aerosol properties over the ocean can be retrieved through passive sensing from Earth orbit. As opposed to most radiometers in space that scan the earth in a plane normal to the subsatellite path, the MISR will scan the earth simultaneously in nine planes and thus provide the radiance exiting the atmosphere over a given pixel in nine different directions and at four wavelengths. We examine the problem of extracting the aerosol optical thickness (τ(a)) over the oceans from MISR data, and we produce two algorithms, a single-band algorithm and a spectral or two-band algorithm, for deriving τ(a). The algorithms are based on the use of realistic aerosol models as candidates on which to base an estimation of the aerosol optical properties. They take into account all orders of multiple scattering. Simulations suggest that for nonabsorbing or mildly absorbing aerosol (single-scattering albedo ω(a) > 0.90) the error in the recovered τ(a) is ? 10%, as long as the candidate models adequately cover the size refractive index distribution range of the expected aerosols. In the special case of a strongly absorbing aerosol (ω(a) ? 0.75), the error in τ(a) becomes large; however, the combination ω(a)τ(a) (the scattering optical thickness) can still be recovered with an error of ? 20%, although it is always underestimated. The reason for this decrease in accuracy is that multiple-scattering effects are a strong function of ω(a). A simple extension of the two-band algorithm permits the retrieval of the aerosol scattering phase function with surprising accuracy.     

Analysis of the influence of O(2) A-band absorption on atmospheric correction of ocean-color imagery

Two satellite-borne ocean-color sensors scheduled for launch in the mid 1990's each have a spectral band (nominally 745-785 nm) that completely encompasses the O(2) A band at 762 nm. These spectral bands are to be used in atmospheric correction of the color imagery by assessment of the aerosol contribution to the total radiance at the sensor. The effect of the O(2) band on the radiance measured at the satellite is studied with a line-by-line backward Monte Carlo radiative transfer code. As expected, if the O(2) absorption is ignored, unacceptably large errors in the atmospheric correction result. The effects of the absorption depend on the vertical profile of the aerosol. By assuming an aerosol profile-the base profile-we show that it is possible to remove most of the O(2)-absorption effects from atmospheric correction in a simple manner. We also investigate the sensitivity of the results to the details of the assumed base profile and find that, with the exception of situations in which there are significant quantities of aerosol in the stratosphere, e.g., following volcanic eruptions or in the presence of thin cirrus clouds, the quality of the atmospheric correction depends only weakly on the base profile. Situations with high concentrations of stratospheric aerosol require additional information regarding vertical structure for this spectral band to be used in atmospheric correction; however, it should be possible to infer the presence of such aerosol by a failure of the atmospheric correction to produce acceptable water-leaving radiance in the red. An important feature of our method for removal of the O(2)-absorption effects is that it permits the use of lookup tables that can be prepared in the absence of O(2) absorption by the use of more efficient radiative transfer codes.     

Columnar aerosol properties over oceans by combining surface and aircraft measurements: sensitivity analysis

We report a sensitivity analysis for the algorithm presented by Gordon and Zhang [Appl. Opt. 34, 5552 (1995)] for inverting the radiance exiting the top and bottom of the atmosphere to yield the aerosol-scattering phase function [P(?)] and single-scattering albedo (omega(0)). The study of the algorithm's sensitivity to radiometric calibration errors, mean-zero instrument noise, sea-surface roughness, the curvature of the Earth's atmosphere, the polarization of the light field, and incorrect assumptions regarding the vertical structure of the atmosphere, indicates that the retrieved omega(0) has excellent stability even for very large values (~2) of the aerosol optical thickness; however, the error in the retrieved P(?) strongly depends on the measurement error and on the assumptions made in the retrieval algorithm. The retrieved phase functions in the blue are usually poor compared with those in the near infrared.     

Assessment of the Moderate-Resolution Imaging Spectroradiometer algorithm for retrieval of aerosol parameters over the ocean

The Moderate Resolution Imaging Spectroradiometer aerosol algorithm over the ocean derives spectral aerosol optical depth and aerosol size parameters from satellite measured radiances at the top of the atmosphere (TOA). It is based on the adding of apparent optical properties (AOPs): TOA reflectance is approximated as a linear combination of reflectances resulting from a small particle mode and a large particle mode. The weighting parameter eta is defined as the fraction of the optical depth at 550 nm due to the small mode. The AOP approach is correct only in the single scattering limit. For a physically correct TOA reflectance simulation, we create linear combinations of the inherent optical properties (IOPs) of small and large particle modes, in which the weighting parameter f is defined as the fraction of the number density attributed to the small particle mode. We use these IOPs as inputs to an accurate multiple scattering radiative transfer model. We find that reflectance errors incurred with the AOP method are as high as 30% for an aerosol optical depth of 2 at 550 nm. The retrieved optical depth has a relative error of up to 8%, and the retrieved fraction eta has an absolute error of approximately 6%. We show that the use of accurate radiative transfer simulations and a bimodal fraction f yields accurate values for the retrieved optical depth and the fraction f.     

Atmospheric correction for NO2 absorption in retrieving water-leaving reflectances from the SeaWiFS and MODIS measurements

The absorption by atmospheric nitrogen dioxide (NO2) gas in the visible has been traditionally neglected in the retrieval of oceanic parameters from satellite measurements. Recent measurements of NO2 from spaceborne sensors show that over the Eastern United States the NO2 column amount often exceeds 1 Dobson Unit (approximately 2.69x10(16) molecules/cm2). Our radiative transfer sensitivity calculations show that under high NO2 conditions (approximately 1x10(16) molecules/cm2) the error in top-of-atmosphere (TOA) reflectance in the blue channels of the sea-viewing wide field-of-view sensor (SeaWiFS) and moderate-resolution imaging spectroradiometer (MODIS) sensors is approximately 1%. This translates into approximately 10% error in water-leaving radiance for clear waters and to higher values (>20%) in the coastal areas. We have developed an atmospheric-correction algorithm that allows an accurate retrieval of normalized water-leaving radiances (nLws) in the presence of NO2 in the atmosphere. The application of the algorithm to 52 MODIS scenes over the Chesapeake Bay area show a decrease in the frequency of negative nLw estimates in the 412 nm band and an increase in the value of nLws in the same band. For the particular scene reported in this paper, the mean value of nLws in the 412 nm band increased by 17%, which is significant, because for the MODIS sensor the error in nLws attributable to the digitization error in the observed TOA reflectance over case 2 waters is approximately 2.5%.     

Validity of the diffusion approximation in bio-optical imaging

Accurate numerical simulations based on rigorous radiative transfer theory are used to assess the validity of the diffusion approximation that is frequently used in bio-optical imaging. These simulations show that the error is large for a non-index-matched boundary between air and tissue. This weakness of the diffusion approximation underscores the need to understand how diffusion theory can be used to extract accurate values of tissue optical properties. A validity criterion for the diffusion approximation is established on the basis of the single-scattering albedo a and the asymmetry factor g for a slab with index-matched boundaries.     

Comparison of electromagnetic theory and various approximations for computing the absorption efficiency and single-scattering albedo of hexagonal columns

The applicability of various approximations for computing the absorption efficiency and single-scattering albedo of a randomly oriented hexagonal column is tested versus electromagnetic theory. To calculate the absorption efficiency and single-scattering albedo of the hexagonal column from electromagnetic theory we used a generalization to the separation-of-variables method, which enables continuous calculation of optical properties up to size parameters of 86. We found that the asymptotic absorption efficiency is independent of particle shape, and that, as the size parameter increases, the hexagonal column tends to its asymptotic absorption value more quickly than Mie theory. The asymptotic absorption limit of the hexagonal column is calculated accurately (to within 1%) and rapidly by use of the complex-angular-momentum approximation, indicating that this approximation could be used to calculate the absorption limit of nonspherical particles. The equal-volume sphere best approximates the hexagonal column single-scattering albedo at a strongly absorbing wavelength (e.g., 11.9 mum for an ice particle). However, in the resonance region (e.g., 80 mum for an ice particle) Mie theory fails to approximate the single-scattering albedo of the hexagonal column, but as the size parameter exceeds 10 the error in the sphere approximation reduces to within 2%. At 80-mum wavelength there is a characteristic ripple structure superimposed on the hexagonal column absorption efficiency solutions between size parameters from approximately 1 to 4. The ripple structure is indicative of surface-wave interference and is similar to the sphere but less pronounced on the hexagonal column. We investigated the applicability of ray tracing for calculating the single-scattering albedo at absorbing wavelengths relevant to remote sensing of ice particles in the atmosphere and found it to be within 4% for size parameters between 3 and 42 at 3.7-mum wavelength. At mid-infrared wavelengths (e.g., 8.5 and 11.9 mum) ray tracing is within 5% of electromagnetic theory for size parameters exceeding 10. We also tested the Bryant and Latimer absorption approximation to anomalous diffraction theory by using the separation-of-variables method.     

Influence of oceanic whitecaps on atmospheric correction of ocean-color sensors

The effects of oceanic whitecaps on ocean-color imagery are simulated and inserted into the proposed Sea-Viewing Wide-Field-of-View Sensor (SeaWiFS) atmospheric-correction algorithm to understand its tolerance to error in the estimated whitecap contribution. The results suggest that for wind speeds ? 10-12 m/s, present models that relate whitecap reflectance to wind speed are sufficiently accurate to meet the SeaWiFS accuracy goal for retrieval of the water-leaving radiance in the blue, when the aerosol scattering is weakly dependent on wavelength. In contrast, when the aerosol scattering has a strong spectral signature, the retrievals will meet the goal only when the whitecap reflectance is underestimated.