Atmospheric Correction of Ocean Color Imagery: Test of the Spectral Optimization Algorithm with the Sea-Viewing Wide Field-of-View Sensor.

We implemented the spectral optimization algorithm [SOA; Appl. Opt. 37, 5560 (1998)] in an image-processing environment and tested it with Sea-viewing Wide Field-of-View Sensor (SeaWiFS) imagery from the Middle Atlantic Bight and the Sargasso Sea. We compared the SOA and the standard SeaWiFS algorithm on two days that had significantly different atmospheric turbidities but, because of the location and time of the year, nearly the same water properties. The SOA-derived pigment concentration showed excellent continuity over the two days, with the relative difference in pigments exceeding 10% only in regions that are characteristic of high advection. The continuity in the derived water-leaving radiances at 443 and 555 nm was also within ~10%. There was no obvious correlation between the relative differences in pigments and the aerosol concentration. In contrast, standard processing showed poor continuity in derived pigments over the two days, with the relative differences correlating strongly with atmospheric turbidity. SOA-derived atmospheric parameters suggested that the retrieved ocean and atmospheric reflectances were decoupled on the more turbid day. On the clearer day, for which the aerosol concentration was so low that relatively large changes in aerosol properties resulted in only small changes in aerosol reflectance, water patterns were evident in the aerosol properties. This result implies that SOA-derived atmospheric parameters cannot be accurate in extremely clear atmospheres.

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 approximately 90% of the upwelling light field originating from Raman scattering.

Contribution of Raman scattering to water-leaving radiance: a reexamination.

We have reexamined the contribution of Raman scattering to the water-leaving radiance in case 1 waters by carrying out radiative transfer simulations that combine the latest reported measurements of the absorption coefficient of pure water with direct measurements of the spectral variation of the Raman-scattering coefficient. The resulting contribution of Raman scattering is then compared with experimental measurements of the water-leaving radiance, and the fractional contribution of radiance produced by Raman scattering to the total radiance measured at a given wavelength is determined. The results show that (1) the contribution of Raman scattering to the water-leaving radiance in an ocean of pure seawater is as much as 50-100% larger than earlier predictions, and (2) the Raman contribution does not decay as rapidly with increasing concentrations of chlorophyllouslike pigments C as predicted earlier. In fact, the Raman fraction for C 8% at wavelengths of interest in ocean color remote sensing and therefore cannot be ignored in ocean color modeling.

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.

Radiance-irradiance inversion algorithm for estimating the absorption and backscattering coefficients of natural waters: vertically stratified water bodies.

A full multiple-scattering algorithm for inverting profiles of the upwelling and downwelling irradiances to yield profiles of the absorption and backscattering coefficients in a vertically stratified water body is described and tested with simulated data. The algorithm does not require knowledge of the scattering phase function of the medium. The results are better the closer the phase function assumed in the retrievals is to the true phase function, although excellent retrievals of the absorption coefficient can still be obtained with an inaccurate phase function. Simulations show that the algorithm is capable of determining the vertical structure of a stratified water body and usually provides the absorption coefficient profile with an error ?2% and the backscattering coefficient profile with an error ?10%, as long as the spacing between pseudodata samples is sufficiently small that the necessary derivatives of the irradiances can be accurately computed. The performance is only slightly degraded when the upwelling radiance (nadir viewing) is substituted for the upwelling irradiance.

Atmospheric correction of ocean color imagery: use of the junge power-law aerosol size distribution with variable refractive index to handle aerosol absorption.

When strongly absorbing aerosols are present in the atmosphere, the usual two-step procedure of processing ocean color data-(1) atmospheric correction to provide the water-leaving reflectance (rho(w)), followed by (2) relating rho(w) to the water constituents-fails and simultaneous estimation of the ocean and aerosol optical properties is necessary. We explore the efficacy of using a simple model of the aerosol-a Junge power-law size distribution consisting of homogeneous spheres with arbitrary refractive index-in a nonlinear optimization procedure for estimating the relevant oceanic and atmospheric parameters for case 1 waters. Using simulated test data generated from more realistic aerosol size distributions (sums of log-normally distributed components with different compositions), we show that the ocean's pigment concentration (C) can be retrieved with good accuracy in the presence of weakly or strongly absorbing aerosols. However, because of significant differences in the scattering phase functions for the test and power-law distributions, large error is possible in the estimate of the aerosol optical thickness. The positive result for C suggests that the detailed shape of the aerosol-scattering phase function is not relevant to the atmospheric correction of ocean color sensors. The relevant parameters are the aerosol single-scattering albedo and the spectral variation of the aerosol optical depth. We argue that the assumption of aerosol sphericity should not restrict the validity of the algorithm and suggest an avenue for including colored aerosols, e.g., wind-blown dust, in the procedure. A significant advantage of the new approach is that realistic multicomponent aerosol models are not required for the retrieval of C.

Radiance-irradiance inversion algorithm for estimating the absorption and backscattering coefficients of natural waters: homogeneous waters.

A full multiple-scattering algorithm for inverting upwelling radiance (L(u)) or irradiance (E(u)) and downwelling irradiance (E(d)) profiles in homogeneous natural waters to obtain the absorption (a) and backscattering (b(b)) coefficients is described and tested with simulated data. An attractive feature of the algorithm is that it does not require precise knowledge of the scattering phase function of the medium. For the E(u)-E(d) algorithm, tests suggest that the error in the retrieved a should usually be ?1%, and the error in b(b)?10-20%. The performance of the L(u)-E(d) algorithm is not as good because it is more sensitive to the scattering phase function employed in the inversions; however, the error in a is usually still small, i.e., ?3%. When the algorithm is extended to accommodate the presence of a Lambertian-reflecting bottom, the retrievals of a are still excellent, even when the presence of the bottom significantly influences the upwelling light field; however, the error in b(b) can be large.

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.

Effects of stratospheric aerosols and thin cirrus clouds on the atmospheric correction of ocean color imagery: simulations.

Using simulations, we determine the influence of stratospheric aerosol and thin cirrus clouds on the performance of the proposed atmospheric correction algorithm for the moderate resolution imaging spectroradiometer (MODIS) data over the oceans. Further, we investigate the possibility of using the radiance exiting the top of the atmosphere in the 1.38-microm water vapor absorption band to remove their effects prior to application of the algorithm. The computations suggest that for moderate optical thicknesses in the stratosphere, i.e., tau(s) < or approximately 0.15, the stratospheric aerosol-cirrus cloud contamination does not seriously degrade the MODIS except for the combination of large (approximately 60 degrees) solar zenith angles and large (approximately 45 degrees) viewing angles, for which multiple-scattering effects can be expected to be particularly severe. The performance of a hierarchy of stratospheric aerosol/cirrus cloud removal procedures for employing the 1.38-microm water vapor absorption band to correct for stratospheric aerosol/cirrus clouds, ranging from simply subtracting the reflectance at 1.38 microm from that in the visible bands, to assuming that their optical properties are known and carrying out multiple-scattering computations of their effect by the use of the 1.38-microm reflectance-derived concentration, are studied for stratospheric aerosol optical thicknesses at 865 nm as large as 0.15 and for cirrus cloud optical thicknesses at 865 nm as large as 1.0. Typically, those procedures requiring the most knowledge concerning the aerosol optical properties (and also the most complex) performed the best; however, for tau(s) < or approximately 0.15, their performance is usually not significantly better than that found by applying the simplest correction procedure. A semiempirical algorithm is presented that permits accurate correction for thin cirrus clouds with tau(s) as large as unity when an accurate estimate of the cirrus cloud scattering phase function is provided, and as large as 0.5 when a coarse approximation to the phase function is used. Given estimates of the stratospheric aerosol optical properties, the implementation of the algorithm by using a set of lookup tables appears to be straightforward.

Atmospheric correction of ocean color sensors: analysis of the effects of residual instrument polarization sensitivity.

We provide an analysis of the influence of instrument polarization sensitivity on the radiance measured by spaceborne ocean color sensors. Simulated examples demonstrate the influence of polarization sensitivity on the retrieval of the water-leaving reflectance rho(w). A simple method for partially correcting for polarization sensitivity--replacing the linear polarization properties of the top-of-atmosphere reflectance with those from a Rayleigh-scattering atmosphere--is provided and its efficacy is evaluated. It is shown that this scheme improves rho(w) retrievals as long as the polarization sensitivity of the instrument does not vary strongly from band to band. Of course, a complete polarization-sensitivity characterization of the ocean color sensor is required to implement the correction.

Remote sensing of ocean color: assessment of water-leaving radiance bidirectional effects on atmospheric diffuse transmittance.

Two factors influence the diffuse transmittance (t) of water-leaving radiance (L(w)) to the top of the atmosphere: the angular distribution of upwelling radiance beneath the sea surface (L(u)) and the concentration and optical properties of aerosols in the atmosphere. We examine these factors and (1) show that the error in L(w) that is induced by assuming L(u) is uniform (i.e., in treating the subsurface reflectance by the water body as Lambertian) is significant in comparison with the other errors expected in L(w) only at low phytoplankton concentration and then only in the blue region of the spectrum; (2) show that when radiance ratios are used in biophysical algorithms the effect of the uniform- L (u) approximation is even smaller; and (3) provide an avenue for introducing accurate computation of the uniform L(u) diffuse transmittance into atmospheric correction algorithms. In an Appendix the reciprocity principle is derived for a medium in which the refractive index is a continuous function of position.

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.

Remote sensing of ocean color and aerosol properties: resolving the issue of aerosol absorption.

Current atmospheric correction and aerosol retrieval algorithms for ocean color sensors use measurements of the top-of-the-atmosphere reflectance in the near infrared, where the contribution from the ocean is known for case 1 waters, to assess the aerosol optical properties. Such measurements are incapable of distinguishing between weakly and strongly absorbing aerosols, and the atmospheric correction and aerosol retrieval algorithms fail if the incorrect absorption properties of the aerosol are assumed. We present an algorithm that appears promising for the retrieval of in-water biophysical properties and aerosol optical properties in atmospheres containing both weakly and strongly absorbing aerosols. By using the entire spectrum available to most ocean color instruments (412-865 nm), we simultaneously recover the ocean's bio-optical properties and a set of aerosol models that best describes the aerosol optical properties. The algorithm is applied to simulated situations that are likely to occur off the U.S. East Coast in summer when the aerosols could be of the locally generated weakly absorbing Maritime type or of the pollution-generated strongly absorbing urban-type transported over the ocean by the winds. The simulations show that the algorithm behaves well in an atmosphere with either weakly or strongly absorbing aerosol. The algorithm successfully identifies absorbing aerosols and provides close values for the aerosol optical thickness. It also provides excellent retrievals of the ocean bio-optical properties. The algorithm uses a bio-optical model of case 1 waters and a set of aerosol models for its operation. The relevant parameters of both the ocean and atmosphere are systematically varied to find the best (in a rms sense) fit to the measured top-of-the-atmosphere spectral reflectance. Examples are provided that show the algorithm's performance in the presence of errors, e.g., error in the contribution from whitecaps and error in radiometric calibration.

Marine asymptotic daylight field: effects of inelastic processes.

The governing equations are developed for the marine asymptotic daylight field in the scalar approximation, including the effects of inelastic processes-Raman scattering and chromophoric dissolved organic matter fluorescence. The governing equations are solved numerically and compared with Monte Carlo simulations. It is found that these solutions are the actual radiance distributions approached by the asymptotic field in the Monte Carlo simulations. Sample solutions are provided to show the sensitivity of the light field to the various parameters of the medium. For certain values of the parameters, inclusion of inelastic processes can drastically alter the radiance distribution, e.g., from a near-Dirac delta function in the absence of inelastic processes to a near-isotropic distribution in their presence. The results suggest that in a real ocean, the asymptotic (and near-asymptotic) radiance distribution will tend to become more uniform as the wavelength increases beyond ~500 nm. Finally, it is shown that even for depths far from the asymptotic regime, the radiance distribution of the inelastic component of the light field can be well approximated by the asymptotic theory developed here for inelastic processes. Two exact analytical solutions to the governing equations are also provided.

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.

Obstetrical judgments of viability and perinatal survival of extremely low birthweight infants.

OBJECTIVES: The purpose of the study was to determine whether the obstetrical judgment of viability makes a difference to fetal and neonatal survival of extremely low birthweight infants (500-749 g). METHODS: We assessed the effect of the antenatal judgment of viability in a group of 66 infants born weighing from 500 to 749 g. These infants were alive at maternal hospital admission and were subsequently live-born or stillborn between January 1, 1984, and December 31, 1985. We related the antepartum assessment of viability and other factors recorded in the medical record to fetal survival and to postneonatal survival to hospital discharge. RESULTS: The obstetrical judgement of viability was strongly associated with outcome. After birthweight and gestational age were controlled, fetuses considered viable were 18 times more likely to survive (95% confidence interval = 2, 175) than those considered nonviable. CONCLUSIONS: The effects of obstetrical practices on perinatal mortality must be taken into consideration in estimating the survival potential of very small fetuses and in evaluating the relationship between survival and disability.

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: 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 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.

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.