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.     

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.     

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.     

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%.     

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.     

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.     

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.     

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.     

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.     

Sensitivity metric approach for retrieval of aerosol properties from multiangular and multispectral polarized radiances

Linearly polarized radiation is sensitive to the microphysical properties of aerosols, namely, to the particle-size distribution and refractive index. The discriminating power of polarized radiation increases strongly with the increasing range of scattering angles and the addition of multiple wavelengths. The polarization and directionality of the Earth's reflectances (POLDER) missions demonstrate that some aerosol properties can be successfully derived from spaceborne polarimetric, multiangular measurements at two visible wavelengths. We extend the concept to analyze the retrieval capabilities of a spaceborne instrument with six polarimetric channels at 412, 445, 555, 865, 1250, and 2250 nm, measuring approximately 100 scattering angles covering a range between 50 and 150 deg. Our focus is development of an analysis methodology that can help quantify the benefits of such multiangular and multispectral polarimetric measurements. To that goal we employ a sensitivity metric approach in a framework of the principal-component analysis. The radiances and noise used to construct the sensitivity metric are calculated with the realistic solar flux for representative orbital viewing geometries, accounting for surface reflection from the ground, and statistical and calibration errors of a notional instrument. Spherical aerosol particles covering a range of representative microphysical properties (effective radius, effective variance, real and imaginary parts of the refractive index, single-scattering albedo) are considered in the calculations. We find that there is a limiting threshold for the effective size (approximately 0.7 microm), below which the weak scattering intensity results in a decreased signal-to-noise ratio and minimal polarization sensitivity, precluding reliable aerosol retrievals. For such small particles, close to the Rayleigh scattering limit, the total intensity provides a much stronger aerosol signature than the linear polarization, inspiring retrieval when the combined signals of intensities and the polarization fraction are used. We also find a strong correlation between aerosol parameters, in particular between the effective size and the variance, which forces one to simultaneously retrieve at least these two parameters.     

Radiance reflected from the ocean-atmosphere system: synthesis from individual components of the aerosol size distribution

We describe a method by which the aerosol component of the radiance at the top of the atmosphere (TOA) can be synthesized from the radiances generated by individual components of the aerosol size-refractive-index distribution. The method is exact in the single-scattering approximation. For regimes in which the single-scattering approximation is not valid, the method usually reproduces the aerosol contribution with an error ?2-3% (and only rarely >3-4%) for Sun and viewing angles as large as 80° and 70°, respectively, and for aerosol optical thicknesses as large as 0.50. In the blue, where molecular scattering makes a dominant contribution to the TOA radiance, the percent error in the synthesized total radiance is significantly less than in the synthesized aerosol component and typically will be less than the radiometric calibration uncertainties of Earth-orbiting sensors. When the aerosol is strongly absorbing, the method can fail; however, the potential for failure is easy to anticipate a priori. An obvious application of our technique is to provide a basis for the estimation of aerosol properties with Earth-orbiting sensors, e.g., the Multiangle Imaging Spectroradiometer.     

Ocean optics estimation for absorption,backscattering, and phase function parameters

We propose and test an inverse ocean optics procedure with numerically simulated data for the determination of inherent optical properties using in-water radiance measurements. If data are available at only one depth within a deep homogeneous water layer, then the single-scattering albedo and the single parameter that characterizes the Henyey-Greenstein phase function can be estimated. If data are available at two depths, then these two parameters can be determined along with the optical thickness so that the absorption and scattering coefficients, and also the backscattering coefficient, can be estimated. With a knowledge of these parameters, the albedo and Lambertian fraction of reflected radiance of the bottom can be determined if measurements are made close to the bottom. A simplified method for determining the optical properties of the water also is developed for only three irradiance-type measurements if the radiance is approximately in the asymptotic regime.     

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.     

Use of sky brightness measurements from ground for remote sensing of particulate polydispersions

The software code SKYEAD.pack for retrieval of aerosol size distribution and optical thickness from data of direct and diffuse solar radiation is described; measurements are carried out with sky radiometers in the wavelength range 0.369-1.048 μm. The treatment of the radiative transfer problem concerning the optical quantities is mainly based on the IMS (improved multiple and single scattering) method, which uses the delta-M approximation for the truncation of the aerosol phase function and corrects the solution for the first- and second-order scattering. Both linear and nonlinear inversion methods can be used for retrieving the size distribution. Improved calibration methods for both direct and diffuse radiation, the data-analysis procedure, the results from the proposed code, and several connected problems are discussed. The results can be summarized as follows: (a) the SKYRAD.pack code can retrieve the columnar aerosol features with accuracy and efficiency in several environmental situations, provided the input parameters are correctly given; (b) when data of both direct and diffuse solar radiation are used, the detectable radius interval for aerosol particles is approximately from 0.03 to 10 μm; (c) besides the retrieval of the aerosol features, the data-analysis procedure also permits the determination of average values for three input parameters (real and imaginary aerosol refractive index, ground albedo) from the optical data; (d) absolute calibrations for the sky radiometer are not needed, and calibrations for direct and diffuse radiation can be carried out with field data; (e) the nonlinear inversion gives satisfactory results in a larger radius interval, without the unrealistic humps that occur with the linear inversion, but the results strongly depend on the first-guess spectrum; (f) aerosol features retrieved from simulated data showed a better agreement with the given data for the linear inversion than for the nonlinear inversion.     

Remote sensing of aerosol plumes: a semianalytical model

A semianalytical model, named APOM (aerosol plume optical model) and predicting the radiative effects of aerosol plumes in the spectral range [0.4,2.5 microm], is presented in the case of nadir viewing. It is devoted to the analysis of plumes arising from single strong emission events (high optical depths) such as fires or industrial discharges. The scene is represented by a standard atmosphere (molecules and natural aerosols) on which a plume layer is added at the bottom. The estimated at-sensor reflectance depends on the atmosphere without plume, the solar zenith angle, the plume optical properties (optical depth, single-scattering albedo, and asymmetry parameter), the ground reflectance, and the wavelength. Its mathematical expression as well as its numerical coefficients are derived from MODTRAN4 radiative transfer simulations. The DISORT option is used with 16 fluxes to provide a sufficiently accurate calculation of multiple scattering effects that are important for dense smokes. Model accuracy is assessed by using a set of simulations performed in the case of biomass burning and industrial plumes. APOM proves to be accurate and robust for solar zenith angles between 0 degrees and 60 degrees whatever the sensor altitude, the standard atmosphere, for plume phase functions defined from urban and rural models, and for plume locations that extend from the ground to a height below 3 km. The modeling errors in the at-sensor reflectance are on average below 0.002. They can reach values of 0.01 but correspond to low relative errors then (below 3% on average). This model can be used for forward modeling (quick simulations of multi/hyperspectral images and help in sensor design) as well as for the retrieval of the plume optical properties from remotely sensed images.     

Improving atmospheric correction for highly productive coastal waters using the short wave infrared retrieval algorithm with water-leaving reflectance constraints at 412 nm

The recently developed short wave infrared (SWIR) atmospheric correction algorithm for ocean color retrieval uses long wavelength channels to retrieve atmospheric parameters to avoid bright pixel contamination. However, this retrieval is highly sensitive to errors in the aerosol model, which is magnified by the higher variability of aerosols observed over urban coastal areas. While adding extra regional aerosol models into the retrieval lookup tables would tend to increase retrieval error since these models are hard to distinguish in the IR, we explore the possibility that for highly productive waters with high colored dissolved organic matter, an estimate of the 412 nm channel water-leaving reflectance can be used to constrain the aerosol model retrieval and improve the water-leaving reflectance retrieval. Simulations show that this constraint is particularly useful where aerosol diversity is significant. To assess this algorithm we compare our retrievals with the operational SeaWiFS Data Analysis System (SeaDAS) SWIR and near infrared retrievals using in situ validation data in the Chesapeake Bay and show that, especially for absorbing aerosols, significant improvement is obtained. Further insight is also obtained by the intercomparison of retrieved remote sensing reflectance images at 443 and 551 nm, which demonstrates the removal of anomalous artifacts in the operational SeaDAS retrieval.     

Bandpass-resampling effects for the retrieval of surface emissivity

The retrieval of surface emissivity in the 8-14-microm region from remotely sensed thermal imagery requires channel-averaged values of atmospheric transmittance, path radiance, and downwelling sky flux. Band-pass resampling introduces inherent retrieval errors that depend on atmospheric conditions, spectral region, bandwidth, flight altitude, and surface temperature. This simulation study is performed for clear sky conditions and moderate atmospheric water vapor contents. It shows that relative emissivity retrieval errors can reach as much as 3% for broadband sensors (1-2-microm bandwidth) and 0.8% for narrowband instruments (0.15 microm), even for constant surface emissivity. For spectrally varying surface emissivities the relative retrieval error increases for the broadband instrument by approximately 2% in channels with strong emissivity changes of 0.05-0.1. The corresponding retrieval errors for narrowband sensors increase by approximately 3-4%. The channels in the atmospheric window regions with lower transmittance, i.e., 8-8.5 and 12.5-14 microm, are most sensitive to retrieval errors.     

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.     

Sun and aureole spectrometer for airborne measurements to derive aerosol optical properties

We have designed an airborne spectrometer system for the simultaneous measurement of the direct Sun irradiance and aureole radiance. The instrument is based on diffraction grating spectrometers with linear image sensors. It is robust, lightweight, compact, and reliable, characteristics that are important for airborne applications. The multispectral radiation measurements are used to derive optical properties of tropospheric aerosols. We extract the altitude dependence of the aerosol volume scattering function and of the aerosol optical depth by using flight patterns with descents and ascents ranging from the surface level to the top of the boundary layer. The extinction coefficient and the product of single scattering albedo and phase function of separate layers can be derived from the airborne measurements.     

Influence of crystal tilt on solar irradiance of cirrus clouds

The single and multiple scattering and absorption properties of hexagonal ice columns with different degrees of particle orientation are modeled in the solar spectral range by means of a ray-tracing single-scattering code and a Monte Carlo radiative-transfer code. The scattering properties are most sensitive to particle orientation for the solar zenith angles of 50 degrees (asymmetry parameter) and 90 degrees (single-scattering albedo). Provided that the ice columns are horizontally oriented, the usual assumption of random orientation leads to an overestimation (underestimation) of the reflected (transmitted) solar broadband radiation at high Sun elevation and to an underestimation (overestimation) at medium solar zenith angles. The orientation effect is more (less) pronounced in scattering and transmission (absorption) for smaller ice crystals.