Visible and near infrared reflectances measured from laboratory ice clouds

We present laboratory results of the 0.68 microm visible (VIS) and 1.617 microm near infrared (NIR) reflectances typically used for inferring optical depth and ice crystal size from satellite radiometers, from ice clouds generated in a temperature controlled column cloud chamber. Two types of ice crystals were produced in this experiment: small columns and dendrites with mean maximum dimensions of about 17 and 35 microm. Within experimental uncertainty, the measured reflectances from ice clouds at both wavelengths agree reasonably well with the theoretical results computed from the plane-parallel adding-doubling method for radiative transfer using the measured ice particle morphology. We demonstrate that laboratory scattering and reflectance data for thin ice clouds with optical depths less than 0.4 can be used for validation of the thin cirrus optical depth and ice crystal size that have been routinely retrieved from the satellite VIS-NIR two channel pair.     

Retrieval of total ozone abundances from the ultraviolet region of spectra recorded with an ultraviolet-visible spectrometer

A method is described for deriving total ozone abundances from zenith-sky intensities measured by an UV-visible spectrometer, known as the System of Analysis of Observations at Zenith (SAOZ). Total ozone abundances are determined by comparison of intensity ratios measured at two wavelengths in the UV region with ratios computed with a radiative transfer model. The wavelength pair 320-307 nm was used in this study. Spectra recorded by the SAOZ spectrometer in Oslo (60 degrees N) from the beginning of May 1995 to the end of August 1995 were analyzed, and the results were compared with total ozone measured with a Brewer instrument. The relative difference in derived ozone abundances for the whole period, including days with thin and medium-thick cloud covers, is -0.18 +/- 1.46%. We study the effects of clouds and varying ground albedo on the derived total ozone. Clouds result in an overestimation of the derived total ozone. The error increases with the optical depth tau of the cloud from approximately 2% for an optically thin cloud (tau = 0.5) to approximately 10% for a thick cloud (tau = 50). The ratio between measured intensities at 550 and 350 nm, the so-called color index, can be used as a measure of the cloud optical depth for thin and medium-thick clouds. The effects of thin and medium-thick clouds on the derived ozone abundances can be compensated for by use of an empirical relationship found between the measured color index and the error in the inferred ozone abundances caused by cloud scattering. We also study the influence of changes in the ground albedo and in the ozone profiles on derived total ozone values.     

Optical properties of contrail-induced cirrus: discussion of unusual halo phenomena

Photographs of a 120 degrees parhelion and a 22 degrees parhelion within persistent contrails are presented. These phenomena result from hexagonal plate-shaped ice crystals oriented horizontally with diameters between 300 mum and 2 mm. From our observations and reinvestigation of previous reports, we conclude that a subset of the population in persistent contrails can consist of highly regular, oriented, hexagonal plates or columns comparable to the most regular crystals in natural cirrus clouds. This is explained by measured ambient humidities below the formation conditions of natural cirrus. The resulting strong azimuthal variability of the scattering phase function impacts the radiative transfer through persistent contrails.     

Comparative analysis of selected radiative transfer approaches for aquatic environments

A comparative analysis is presented of simple approaches to radiative transfer in plane-parallel layers, such as the self-consistent Haltrin approach, the Chandrasekhar-Klier exact solution for isotropic scatters, an extended version of two-flux radiative Kubelka-Munk theory, the neutron-diffuse Gate-Brinkworth theory, and different versions of the delta-Eddington theory. It is shown that the Haltrin approach is preferable to others and can be used for the solution of an inverse optical problem of the estimation of absorption and backscattering coefficients of aquatic environments from measured apparent optical properties. Two different methods of transformation from measured irradiance reflectance at combined illumination to irradiance reflectance induced by diffuse illumination only are developed. An analysis of the use of the different models for estimation of the effect of the bottom albedo is also presented.     

Radiative transfer model: matrix operator method

A radiative transfer model, the matrix operator method, is discussed here. The matrix operator method is applied to a plane-parallel atmosphere within three spectral ranges: the visible, the infrared, and the microwave. For a homogeneous layer with spherical scattering, the radiative transfer equation can be solved analytically. The vertically inhomogeneous atmosphere can be subdivided into a set of homogeneous layers. The solution of the radiative transfer equation for the vertically inhomogeneous atmosphere is obtained recurrently from the analytical solutions for the subdivided layers. As an example for the application of the matrix operator method, the effects of the cirrus and the stratocumulus clouds on the net radiation at the surface and at the top of the atmosphere are investigated. The relationship between the polarization in the microwave range and the rain rates is also studied. Copies of the FORTRAN program and the documentation of the FORTRAN program on a diskette are available.     

Experimental and theoretical spectral reflection properties of ice clouds generated in a laboratory chamber

In a preliminary experimental program, the measured bidirectional reflection properties between 1.0 and 3.5 mum from a grating spectrometer with a resolution of approximately 0.1 mum for ice crystal clouds generated in a cold chamber are compared with theoretical results computed from a line-by-line equivalent solar radiative transfer model. The theoretical calculations are based on the measured habits, concentrations, and sizes of the ice particles from replicas of the ice crystals that show a mean maximum size of approximately 7 mum. The experimental design was first tested with transmission measurements in a pure water-vapor environment that compare closely with theoretical expectations. Within the uncertainties and in consideration of the assumptions necessitated by the preliminary nature of this program, there is a close comparison between the experimental and theoretical results.     

Multiple-scattering effects on differential absorption for the transmission of a plane-parallel beam in a homogeneous medium

The transmission, including all scattering orders, of a plane-parallel beam in a homogeneous scattering medium containing aerosols (e.g., water cloud) mixed with an absorbing gas (e.g., ozone) is computed with a two-stream radiative transfer model. From differential transmission the concentration of the gas is deduced. The effect of multiple-scattering on the deduced concentration is shown for conservative scattering aerosols for which the multiple scattering by the aerosols is differentially absorbed by the gas and for nonconservative scattering aerosols for which the multiple scattering is differentially absorbed by the aerosols as well as differentially absorbed by the gas. The two-stream analytical model (with no dependence on the field of view) shows good qualitative agreement (especially for a small field of view) with a numerical radiative transfer model in which the trace gas concentration is computed for the different detector's field of view.     

Atmospheric correction of ocean-color sensors: effects of the Earth's curvature

We investigate the influence of the curvature of the Earth on a proposed atmospheric-correction scheme for the Sea-Viewing Wide-Field-of-View Sensor (SeaWiFS) by simulating the radiance exiting the top of a spherical-shell atmosphere and inserting the result into the proposed correction algorithm. The error in the derived water-leaving reflectance suggests that the effects of the curvature are negligible for solar zenith angles (θ(0)) ≤ 70°. Furthermore, for θ(0) > 70° the error in atmospheric correction can usually be reduced if the molecular-scattering component of the top of the atmosphere reflectance (ρ(r)) is computed with a spherical-shell atmosphere radiative transfer code. Also, for θ(0) > 70° the error in atmospheric correction in a spherical-shell atmosphere, when ρ(r) is computed with a spherical-shell model, can be predicted reasonably well from computations made with plane-parallel atmosphere radiative transfer codes. This implies that studies aimed at improving atmospheric correction can be made assuming plane-parallel geometry and that the investigator can be confident when θ(0)> 70° that any improvements will still be valid for a spherical-shell atmosphere as long as ρ(r) is computed in spherical-shell geometry. Finally, a scheme for computing ρ(r) in a spherical-shell atmosphere in a relatively simple manner is developed.     

Comparison of radiative transfer Monte Carlo and volume integral equation methods of studying the clustering of small scatterers

The effect of clustering of small scatterers on optical properties was studied by creation of a Poisson distributed plane-parallel geometry and slow cooling of the particle system in the sense of simulated annealing in an attempt to minimize the assumed total potential energy and sample the spatial distribution during the process. The optical properties were calculated by the volume integral equation method (VIEM). The scattering results for unclustered structures with different size parameters and packing densities were also compared with those given by Monte Carlo simulation for radiative transfer. In particular, measuring the intensity distribution of the VIEM is well suited to the classic radiative transfer approach.     

Multiple-scattering transmission and an effective average photon path length of a plane-parallel beam in a homogeneous medium

A two-stream radiative transfer model is used to derive expressions for the multiple-scattered transmitted flux (including single-scattering contributions) and the total effective average photon path length on transmission of a normally incident plane-parallel beam on a homogeneous layer characterized by the optical depth, the single-scattering albedo, and the asymmetry parameter of the scatterers. The results are simple analytical expressions that are useful for modifying the Beer-Lambert transmission law for a thick scattering medium in which the multiple-scattering contribution to the transmission is not negligible.     

Method for correcting the wavelength misalignment in measured ultraviolet spectra

A new method for correcting the wavelength misalignment in measured UV spectra is presented. It is based on a comparison between measured irradiances and irradiances computed from a radiative transfer code for a set of given atmospheric and solar conditions (250 < Dobson units < 450, 30 degrees < solar zenith angle < 75 degrees ). Results of tests run with spectra recorded on a clear-sky day by two spectroradiometers in a French UV spectral network station are analyzed. Applying the method once reduces shift to less than 0.05 nm. The smoothing included in the method enables detection of aberrant irradiance values and then completion of an initial quality control of measured spectra. A technique for assessing the instruments' slit function is also presented. The key algorithms needed to build a computer code based on this method are given.     

Efficient vector radiative transfer calculations in vertically inhomogeneous cloudy atmospheres

Accurate radiative transfer calculations in cloudy atmospheres are generally time consuming, limiting their practical use in satellite remote sensing applications. We present a model to efficiently calculate the radiative transfer of polarized light in atmospheres that contain homogeneous cloud layers. This model combines the Gauss-Seidel method, which is efficient for inhomogeneous cloudless atmospheres, with the doubling method, which is efficient for homogeneous cloud layers. Additionally to reduce the computational effort for radiative transfer calculations in absorption bands, the cloud reflection and transmission matrices are interpolated over the absorption and scattering optical thicknesses within the cloud layer. We demonstrate that the proposed radiative transfer model in combination with this interpolation technique is efficient for the simulation of satellite measurements for inhomogeneous atmospheres containing one homogeneous cloud layer. For example, the Scanning Imaging Absorption Spectrometer for Atmospheric Cartography (SCIAMACHY) measurements in the oxygen A band (758-773 nm) and the Hartley-Huggins ozone band (295-335 nm) with a spectral resolution of 0.4 nm can be simulated for these atmospheres within 1 min on a 2.8 GHz PC with an accuracy better than 0.1%.     

Generalized Eddington analytical model for azimuthally dependent radiance simulation in stratified media

A fast analytical radiative transfer model to account for propagation of unpolarized monochromatic radiation in random media with a plane-parallel geometry is presented. The model employs an Eddington-like approach combined with the delta phase-function transformation technique. The Eddington approximation is extended in a form that allows us to unfold the azimuthal dependence of the radiance field. A first-order scattering correction to the azimuth-dependent Eddington radiative model solution is also performed to improve the model accuracy for low-scattering media and flexibility with respect to use of explicit arbitrary phase functions. The first-order scattering-corrected solution, called the generalized Eddington radiative model (GERM), is systematically tested against a numerical multistream discrete ordinate model for backscattered radiance at the top of the medium. The typical mean accuracy of the GERM solution is generally better than 10% with a standard deviation of 20% for radiance calculations over a wide range of independent input optical parameters and observation angles. GERM errors are shown to be comparable with the errors due to an input parameter uncertainty of precise numerical models. The proposed model can be applied in a quite arbitrary random medium, and the results are appealing in all cases where speed, accuracy, and/or closed-form solutions are requested. Its potentials, limitations, and further extensions are discussed.     

Measurement and Modeling of the Bidirectional Reflectance of SiO2 Coated Si Surfaces

An understanding of the variation of directional radiative properties of rough surfaces with dielectric coatings is important for temperature measurements and heat transfer analysis in many industrial processes. An experimental study has been conducted to investigate the effect of coating thickness on the bidirectional reflectance distribution function (BRDF) of rough silicon surfaces.Silicon dioxide films with thicknesses of 107.2, 216.5, and 324.6 nm were deposited using plasma-enhanced chemical vapor deposition onto the rough side of two Si wafers. The wafer surfaces exhibit distinct anisotropic characteristics as a result of chemical etching during the manufacturing process. A laser scatterometer measures the BRDF at a wavelength of 635 nm, after improvement of the signal-to-noise ratio. The slope distribution function obtained from the measured BRDF of uncoated Si surfaces was used in an analytical model based on geometric optics for rough surface scattering and thin-film optics for microfacet reflectance. The predicted BRDFs are in reasonable agreement with experimental results for a large range of coating thicknesses. The limitations of the geometric optics for modeling the BRDF of coated anisotropic rough surfaces in the specular direction are demonstrated. The results may benefit future radiative transfer analysis involving complicated surface microstructures with thin-film coatings.     

Radiative properties of snow for clear sky solar radiation

Spectral and integrated radiative properties (reflection, transmission, and the rate of heating) of finegrained wind-packed snow typical of subpolar regions are studied through a model taking into account surface reflection and volumetric multiple scattering. The surface reflection is modeled by a bidirectional reflectance distribution function applicable to powdered dielectric material. For the volumetric multiple scattering, the radiative transfer equation designed for strongly asymmetric scattering is solved. All multiple scattering parameters (single scattering albedo, various moments of the scattering phase function, and optical depth) are related to measurable physical characteristics (density, grain size, and the absorption coefficient of pure ice).Parameterized atmospheric spectral transmission coefficients for scattering and absorption by aerosols and gases are used to obtain the direct and diffuse components of solar flux, incident on the snow-cover. Calculated values of spectral and integrated visible and near infrared reflection and flux attenuation coefficients of snow are compared with observations. The rate of radiative heating at different depths within the snowcover is calculated from the net flux divergence. It is shown that the conventional method of calculating this rate using measured bulk extinction coefficients grossly underestimates the amount of heating within the top few millimeters. This study provides a better overall understanding of the radiative properties of snow under clear sky conditions in terms of the physical characteristics of the snowcover.     

Sensitivity and information content of aerosol retrievals from the Advanced Very High Resolution Radiometer: radiometric factors

The sensitivity of aerosol optical depths tau1 and tau2 derived from the Advanced Very High Resolution Radiometer (AVHRR) channels 1 and 2, centered at lambda1 = 0.63 and lambda2 = 0.83 microm, respectively, and of an effective Angstrom exponent alpha, derived therefrom as alpha = -ln(tau1/tau2)/ln(lambda1/lambda2), to calibration uncertainties, radiometric noise, and digitization is estimated. Analyses are made both empirically (by introduction of perturbations into the measured radiances and estimation of the respective partial derivatives) and theoretically (by use of a decoupled form of the single-scattering approximation of the radiative transfer equation). The two results are in close agreement. The errors, deltataui and deltaalphai, are parameterized empirically as functions of taui, radiometric errors, and Sun and view geometry. In particular, the alpha errors change in approximately inverse proportion to tau and are comparable with, or even exceed, typical alpha signals over oceans when tau < 0.25. Their detrimental effect on the information content of the AVHRR-derived size parameter gradually weakens as tau increases.     

Near-field radiative cooling of nanostructures

We measure near-field radiative cooling of a thermally isolated nanostructure up to a few degrees and show that in principle this process can efficiently cool down localized hotspots by tens of degrees at submicrometer gaps. This process of cooling is achieved without any physical contact, in contrast to heat transfer through conduction, thus enabling novel cooling capabilities. We show that the measured trend of radiative cooling agrees well theoretical predictions and is limited mainly by the geometry of the probe used here as well as the minimum separation that could be achieved in our setup. These results also pave the way for realizing other new effects based on resonant heat transfer, like thermal rectification and negative thermal conductance.     

Discrete-ordinated finite-element method for atmospheric radiative transfer and remote sensing

Advantages and disadvantages of modern discrete-ordinates finite-element methods for the solution of radiative transfer problems in meteorology, climatology, and remote sensing applications are evaluated. After the common basis of the formulation of radiative transfer problems in the fields of neutron transport and atmospheric optics is established, the essential features of the discrete-ordinates finite-element method are described including the limitations of the method and their remedies. Numerical results are presented for 1-D and 2-D atmospheric radiative transfer problems where integral as well as angular dependent quantities are compared with published results from other calculations and with measured data. These comparisons provide a verification of the discrete-ordinates results for a wide spectrum of cases with varying degrees of absorption, scattering, and anisotropic phase functions. Accuracy and computational speed are also discussed. Since practically all discrete-ordinates codes offer a builtin adjoint capability, the general concept of the adjoint method is described and illustrated by sample problems. Our general conclusion is that the strengths of the discrete-ordinates finite-element method outweight its weaknesses. We demonstrate that existing general-purpose discrete-ordinates codes can provide a powerful tool to analyze radiative transfer problems through the atmosphere, especially when 2-D geometries must be considered.     

Enhanced solar irradiance across the atmosphere-sea ice interface: a quantitative numerical study

A radiative transfer model for the coupled atmosphere-sea ice system is used to study the change in downward irradiance across the air-ice interface. Computations demonstrate that the downward solar irradiance can be significantly enhanced across the air-ice interface. The enhancement is mainly due to light in the ice that is scattered upward and then totally reflected by the air-ice interface. It depends primarily on the change in the index of refraction across this interface and the optical properties of the sea ice, but also on the direct solar and sky illumination of the interface.     

Monte Carlo radiative transfer in the microwave and in the visible: biasing techniques

Two Monte Carlo methods for atmospheric radiative transfer are presented. One is a backward three-dimensional code suitable for the visible region of the electromagnetic spectrum in which the source is considered to be a parallel flux incident on the upper boundary. The second is a forward plane-parallel code for the microwave region in which radiation is given by thermal emission. The biasing techniques used to reduce the computational time and keep the statistical oscillations relatively small are described. The results are tested by comparison with the results of equivalent codes, when available, and the speed of convergence is analyzed.