Spherical Albedo Research Articles

Photometric models of disk-integrated observations of the OSIRIS-REx target Asteroid (101955) Bennu

We used ground-based photometric phase curve data of the OSIRIS-REx target Asteroid (101955) Bennu and low phase angle data from Asteroid (253) Mathilde as a proxy to fit Bennu data with Minnaert, Lommel-Seeliger, (RObotic Lunar Orbiter) ROLO, Hapke, and McEwen photometric models, which capture the global light scattering properties of the surface and subsequently allow us to calculate the geometric albedo, phase integral, spherical Bond albedo, and the average surface normal albedo for Bennu. We find that Bennu has low reflectance and geometric albedo values, such that multiple scattering is expected to be insignificant. Our photometric models relate the reflectance from Bennu’s surface to viewing geometry as functions of the incidence, emission, and phase angles. Radiance Factor functions (RADFs) are used to model the disk-resolved brightness of Bennu. The Minnaert, Lommel-Seeliger, ROLO, and Hapke photometric models work equally well in fitting the best ground-based photometric phase curve data of Bennu. The McEwen model works reasonably well at phase angles from 20° to 70°. Our calculated geometric albedo values of 0.047-0.014+0.012,0.047-0.014+0.005, and 0.048-0.022+0.012 for the Minnaert, the Lommel-Seeliger, and the ROLO models respectively are consistent with the geometric albedo of 0.045±0.015 computed by Emery et al. (Emery, J.P. et al. [2014]. Icarus 234, 17–35) and Hergenrother et al. (Hergenrother, C.W. et al. [2014]. <http://arxiv.org/abs/1409.4704>). Also, our spherical Bond albedo values of 0.016-0.004+0.005,0.015-0.001+0.003, and 0.015-0.005+0.007 for the Minnaert model, Lommel-Seeliger, and ROLO models respectively are consistent with the value of 0.017±0.002 presented by Emery et al. (Emery, J.P. et al. [2014]. Icarus 234, 17–35). On the other hand, the semi-physical models such as the Hapke model, where several assumptions and approximations were necessary, and the McEwen model are not supported by the global disk-integrated data, indicating that disk-resolved measurements will be necessary to constrain these models, as expected.

On the relationship between the scattering phase function of cirrus and the atmospheric state

Abstract. This is the first paper to investigate the relationship between the shape of the scattering phase function of cirrus and the relative humidity with respect to ice (RHi, using space-based solar radiometric angle-dependent measurements. The relationship between RHi and the complexity of ice crystals has been previously studied using data from aircraft field campaigns and laboratory cloud chambers. However, to the best of our knowledge, there have been no studies to date that explore this relationship through the use of remotely sensed space-based angle-dependent solar radiometric measurements. In this paper, one case study of semi-transparent cirrus, which occurred on 25 January 2010 off the north-east coast of Scotland, is used to explore the possibility of such a relationship. Moreover, for the first time, RHi fields predicted by a high-resolution numerical weather prediction (NWP) model are combined with satellite retrievals of ice crystal complexity. The NWP model was initialised at midnight, on 25 January 2010, and the mid-latitude RHi field was extracted from the NWP model at 13:00 UTC. At about the same time, there was a PARASOL (Polarization and Anisotropy of Reflectance for Atmospheric science coupled with Observations from a Lidar) overpass, and the PARASOL swath covered the NWP-model-predicted RHi field. The cirrus case was located over Scotland and the North Sea. From the satellite channel based at 0.865 μm, the directionally averaged and directional spherical albedos were retrieved between the scattering angles of about 80 and 130°. An ensemble model of cirrus ice crystals is used to predict phase functions that vary between phase functions that exhibit optical features (referred to as pristine) and featureless phase functions. For each of the PARASOL pixels, the phase function that best minimised differences between the spherical albedos was selected. This paper reports, for this one case study, an association between the most featureless phase function model and the highest values of NWP-predicted RHi (i.e. when RHi &gt; 1.0). For pixels associated with NWP-model-predicted RHi &lt; 1, it was impossible to generally discriminate between phase function models at the 5% significance level. It is also shown that the NWP model prediction of the vertical profile of RHi is in good agreement with dropsonde, in situ measurements and independent aircraft-based physical retrievals of RHi. Furthermore, the NWP model prediction of the cirrus cloud-top height and its vertical extent is also found to be in good agreement with aircraft-based lidar measurements.

Reconstruction of the annual average values of the Earth’s albedo

The problem of reconstruction of a many-year series of values of the Earth’s spherical albedo is considered. The model developed reconstructs the annual average values of the albedo based on the annual average surface air temperature and thermal inertia of the hydrosphere. Tolerance of the model to variations in the input data is proved and confirmed by a series from 1880. The albedo reconstruction accuracy is assessed over the interval 1984–1999.

Correction of the readings of albedo dosimeters at the MC400 LNR cyclotron with the use of the spherical albedo system and comparison with other correction methods

The results of correcting the readings of DVGN-01 albedo dosimeters behind the shielding of the MC400 cyclotron at the Laboratory of Nuclear Reactions (LNR) with the use of the spherical albedo system are presented. The formulas approximating the dependences of correction coefficients used to correct the readings on the hardness parameters of low-energy neutron spectra were obtained based on these results and the results of earlier studies. Neutron spectra were measured at three points behind the MC400 shielding, and the correction coefficients for DVGN-01 were calculated based on these spectra. It was demonstrated that these coefficients agree well with the coefficients obtained with the use of the spherical albedo system. This suggests that the obtained correction coefficient values are accurate. The recommended correction coefficient values to be used in the individual dosimetric control at LNR were specified based on the results of the present study and the data given in other papers.

Atmospheric correction of HJ-1 A/B CCD over land: Land surface reflectance calculation for geographical information product

This paper proposed a method to retrieve the land surface reflectance from the HJ-1A/B CCD data. The aerosol optical depth (AOD), the most important factor affecting the atmospheric correction of CCD images at all bands, is proposed to retrieve from the CCD imagery by the approach of dense dark vegetation (DDV) method. A look-up table in terms of the transmittances, the path radiances and the atmospheric spherical albedo as functions of the AOD was established for a variety of sun-sensor geometry and aerosol loadings. The atmospheric correction is then achieved with the look-up table and the MODIS surface reflectance output (MOD09) as the priori datasets. Based on the retrieved AOD and the look-up table of atmospheric correction coefficients, the land surface reflectance was retrieved for the HJ-1A/B data according to the atmospheric radiative transfer equation. Some in-situ measurement Data for Yanzhou of Shandong province in East China and MODIS land surface reflectance products MOD09 are used to preliminarily validate the proposed method. The results show that the proposed method can remove effectively the atmospheric contributions, and the overall accuracy of the retrieval land surface reflectance can be improved substantially.

ANALYTICAL MODELS OF EXOPLANETARY ATMOSPHERES. II. RADIATIVE TRANSFER VIA THE TWO-STREAM APPROXIMATION

We present a comprehensive analytical study of radiative transfer using the method of moments and include the effects of non-isotropic scattering in the coherent limit. Within this unified formalism, we derive the governing equations and solutions describing two-stream radiative transfer (which approximates the passage of radiation as a pair of outgoing and incoming fluxes), flux-limited diffusion (which describes radiative transfer in the deep interior) and solutions for the temperature-pressure profiles. Generally, the problem is mathematically under-determined unless a set of closures (Eddington coefficients) is specified. We demonstrate that the hemispheric (or hemi-isotropic) closure naturally derives from the radiative transfer equation if energy conservation is obeyed, while the Eddington closure produces spurious enhancements of both reflected light and thermal emission. We concoct recipes for implementing two-stream radiative transfer in stand-alone numerical calculations and general circulation models. We use our two-stream solutions to construct toy models of the runaway greenhouse effect. We present a new solution for temperature-pressure profiles with a non-constant optical opacity and elucidate the effects of non-isotropic scattering in the optical and infrared. We derive generalized expressions for the spherical and Bond albedos and the photon deposition depth. We demonstrate that the value of the optical depth corresponding to the photosphere is not always 2/3 (Milne's solution) and depends on a combination of stellar irradiation, internal heat and the properties of scattering both in optical and infrared. Finally, we derive generalized expressions for the total, net, outgoing and incoming fluxes in the convective regime.

Use of a spherical albedo system for correcting the readings of albedo dosimeters in JINR phasotron neutron radiation fields

Results of calibrating a spherical albedo system in the radiation fields of a Pu-Be radionuclide neutron source are presented. It is shown that it can be used for correcting the readings of the DVGN-01 albedo dosimeter. The results of measurements with the system in JINR phasotron neutron fields for the purpose of correcting the DVGN-01 readings in these fields are given. The values of the correction factors for DVGN-01 albedo dosimeters when used in personnel neutron dosimetry (PD) on the JINR phasotron are determined.

Comparative analysis of radiative transfer approaches for calculation of diffuse reflectance of plane-parallel light-scattering layers

We present an analysis of a number of different approximations for the diffuse reflectance (spherical and plane albedo) of a semi-infinite, unbounded, plane-parallel, and optically homogeneous layer. The maximally wide optical conditions (from full absorption to full scattering and from fully forward to fully backward scattering) at collimated, diffuse, and combined illumination conditions were considered. The approximations were analyzed from the point of view of their physical limitations and compared to the numerical radiative transfer solutions, whenever it was possible. The main factors impacting the spherical and plane albedo were revealed for the known and unknown scattering phase functions. The main criterion for inclusion of the models in analysis was the possibility of practical use, i.e., approximations were well parameterized and only included easily measured or estimated parameters. We give a detailed analysis of errors for different models. An algorithm for recalculation of results under combined (direct and diffuse) illumination also has been developed.

A self‐consistent scattering model for cirrus. II: The high and low frequencies

AbstractThe predictive quality of an ensemble model of cirrus ice crystals to model passive and active measurements of ice cloud, from the ultraviolet (UV) to the microwave, is tested. The ensemble model predicts m ∝ D2, where D is the maximum dimension of the ice crystal, and m is its mass. This predicted m‐D relationship is applied to a moment estimation parametrization of the particle size distribution (PSD), to estimate the PSD shape, given ice water content (IWC) and in‐cloud temperature. The same microphysics is applied across the electromagnetic spectrum to model UV, infrared, microwave and radar observations. The short‐wave measurements consist of airborne UV backscatter lidar (light detection and ranging) estimates of the volume extinction coefficient, total solar optical depth, and space‐based multi‐directional spherical albedo retrievals, at 0.865 µm, between the scattering angles 85° and 125°. The airborne long‐wave measurements consist of high‐resolution interferometer upwelling brightness temperatures, obtained between the wavelengths of about 3.45 µm and 4.1 µm, and 8.0 µm to 12.0 µm. The low‐frequency measurements consist of ground‐based Chilbolton 35 GHz radar reflectivity measurements and space‐based upwelling 190 GHz brightness temperature measurements. The predictive quality of the ensemble model is demonstrated to be generally within the experimental uncertainty of the lidar backscatter estimates of the volume extinction coefficient and total solar optical depth. The ensemble model prediction of the high‐resolution brightness temperature measurements is generally within ±2 K and ±1 K at solar and infrared wavelengths, respectively. The 35 GHz radar reflectivity and 190 GHz brightness temperatures are generally simulated to within ±2 dBZe, and ±2 K, respectively. The directional spherical albedo observations suggest that the scattering phase function of the most randomized ensemble model gives the best fit to the measurements (generally within ±3%). This article demonstrates that the ensemble model, assuming the same microphysics, is physically consistent across the electromagnetic spectrum.

Comparison of PARASOL Observations with Polarized Reflectances Simulated Using Different Ice Habit Mixtures

AbstractInsufficient knowledge of the habit distribution and the degree of surface roughness of ice crystals within ice clouds is a source of uncertainty in the forward light scattering and radiative transfer simulations of ice clouds used in downstream applications. The Moderate Resolution Imaging Spectroradiometer (MODIS) collection-5 ice microphysical model presumes a mixture of various ice crystal shapes with smooth facets, except for the compact aggregate of columns for which a severely rough condition is assumed. When compared with Polarization and Anisotropy of Reflectances for Atmospheric Sciences coupled with Observations from a Lidar (PARASOL) polarized reflection data, simulations of polarized reflectance using smooth particles show a poor fit to the measurements, whereas very rough-faceted particles provide an improved fit to the polarized reflectance. In this study a new microphysical model based on a mixture of nine different ice crystal habits with severely roughened facets is developed. Simulated polarized reflectance using the new ice habit distribution is calculated using a vector adding–doubling radiative transfer model, and the simulations closely agree with the polarized reflectance observed by PARASOL. The new general habit mixture is also tested using a spherical albedo differences analysis, and surface roughening is found to improve the consistency of multiangular observations. These results are consistent with previous studies that have used polarized reflection data. It is suggested that an ice model incorporating an ensemble of different habits with severely roughened surfaces would potentially be an adequate choice for global ice cloud retrievals.

Seven years of global retrieval of cloud properties using space-borne data of GOME

Abstract. We present a global and regional multi-annual (June 1996–May 2003) analysis of cloud properties (spherical cloud albedo – CA, cloud optical thickness – COT and cloud top height – CTH) of optically thick (COT &gt; 5) clouds, derived using measurements from the GOME instrument on board the ESA ERS-2 space platform. We focus on cloud top height, which is obtained from top-of-atmosphere backscattered solar light measurements in the O2 A-band using the Semi-Analytical CloUd Retrieval Algorithm SACURA. The physical framework relies on the asymptotic equations of radiative transfer. The dataset has been validated against independent ground- and satellite-based retrievals and is aimed to support trace-gases retrievals as well as to create a robust long-term climatology together with SCIAMACHY and GOME-2 ensuing retrievals. We observed the El Niño-Southern Oscillation anomaly in the 1997–1998 record through CTH values over the Pacific Ocean. The global average CTH as derived from GOME is 5.6 ± 3.2 km, for a corresponding average COT of 19.1 ± 13.9.

ANALYTIC MODELS FOR ALBEDOS, PHASE CURVES, AND POLARIZATION OF REFLECTED LIGHT FROM EXOPLANETS

New observational facilities are becoming increasingly capable of observing reflected light from transiting and directly imaged extrasolar planets. In this study, we provide an analytic framework to interpret observed phase curves, geometric albedos, and polarization of giant planet atmospheres. We compute the observables for non-conservative Rayleigh scattering in homogeneous semi-infinite atmospheres using both scalar and vector formalisms. In addition, we compute phase curves and albedos for Lambertian, isotropic, and anisotropic scattering phase functions. We provide analytic expressions for geometric albedos and spherical albedos as a function of the scattering albedo for Rayleigh scattering in semi-infinite atmospheres. Given an observed geometric albedo our prescriptions can be used to estimate the underlying scattering albedo of the atmosphere, which in turn is indicative of the scattering and absorptive properties of the atmosphere. We also study the dependence of polarization in Rayleigh scattering atmospheres on the orbital parameters of the planet-star system, particularly on the orbital inclination. We show how the orbital inclination of non-transiting exoplanets can be constrained from their observed polarization parameters. We consolidate the formalism, solution techniques, and results from analytic models available in the literature, often scattered in various sources, and present a systematic procedure to compute albedos, phase curves, and polarization of reflected light.

Retrieval of snow grain size and albedo of western Himalayan snow cover using satellite data

Abstract. In the present study we describe the retrievals of snow grain size and spectral albedo (plane and spherical albedo) for western Himalayan snow cover using Hyperion sensor data. The asymptotic radiative transfer (ART) theory was explored for the snow retrievals. To make the methodology operational only five spectral bands (440, 500, 1050, 1240 and 1650 nm) of Hyperion were used for snow parameters retrieval. The bi-spectral method (440 nm in the visible and 1050/1240 nm in the NIR region) was used to retrieve snow grain size. Spectral albedos were retrieved using satellite reflectances and estimated grain size. A good agreement was observed between retrieved snow parameters and ground observed snow-meteorological conditions. The satellite retrieved grain sizes were compared with field spectroradiometer retrieved grain sizes and close results were found for lower Himalayan snow. The wavelength 1240 nm was found to be more suitable compared to 1050 nm for grain size retrieval along the steep slopes. The methodology was able to retrieve the spatial variations in snow parameters in different parts of western Himalaya which are due to snow climatic and terrain conditions of Himalaya. This methodology is of importance for operational snow cover and glacier monitoring in Himalayan region using space-borne and air-borne sensors.

Retrieval of snow albedo and grain size using reflectance measurements in Himalayan basin

Abstract. In the present paper, spectral reflectance measurements of Himalayan seasonal snow were carried out and analysed to retrieve the snow albedo and effective grain size. The asymptotic radiative transfer (ART) theory was applied to retrieve the plane and spherical albedo. The retrieved plane albedo was compared with the measured spectral albedo and a good agreement was observed with ±10% differences. Retrieved integrated albedo was found within ±6% difference with ground observed broadband albedo. The retrieved snow grain sizes using different models based on the ART theory were compared for various snow types and it was observed that the grain size model using two channel method (one in visible and another in NIR region) can work well for the Himalayan seasonal snow and it was found consistent with temporal changes in grain size. This method can work very well for clean, dry snow as in the upper Himalaya, but sometimes, due to the low reflectances (&lt;20%) using wavelength 1.24 μm, the ART theory cannot be applied, which is common in lower and middle Himalayan old snow. This study is important for monitoring the Himalayan cryosphere using air-borne or space-borne sensors.

A global view of one‐dimensional solar radiative transfer through oceanic water clouds

Solar radiative transfer through a cloudy atmosphere is commonly computed assuming clouds to be one‐dimensional, i.e., plane‐parallel. Here we provide a global perspective on how often and with what degree oceanic water clouds may be considered plane‐parallel by fusing multi‐view‐angle and multi‐spectral satellite data. We show that the view‐angular distribution of the retrieved reflectance, spherical albedo and cloud optical thickness measured at 1 km resolution are indistinguishable from plane‐parallel clouds 24%, 25% and 79% of the time, respectively, at the 95% confidence level of our measurement method. These plane‐parallel clouds occur most frequently within regions dominated by stratiform clouds under solar zenith angles &lt;60°. For all other regions or sun‐angles, the frequency in which clouds are indistinguishable from plane‐parallel drops sharply to as low as a few percent. Our results provide a basis for interpreting space‐time variability within many satellite‐retrieved variables and reveal a need for continued efforts to handle three‐dimensional radiative transfer in environmental modeling and monitoring systems.

View‐angle consistency in reflectance, optical thickness and spherical albedo of marine water‐clouds over the northeastern Pacific through MISR‐MODIS fusion

View‐angle consistency in bidirectional reflectance factor (BRF), optical thickness and spherical albedo is examined for marine water clouds over a region of the northeastern Pacific using six years of fused Moderate Resolution Imaging Spectroradiometer (MODIS) and Multiangle Imaging SpectroRadiometer (MISR) data. Consistency is quantified by the root‐mean‐square of relative differences between MISR‐measured BRF and their plane‐parallel values and variation of plane‐parallel retrieved optical thickness and spherical albedo across multiple view‐angles. Probability distribution functions of consistency show that, for example, these clouds are angularly consistent within 5% in BRF, optical thickness and spherical albedo 72.2%, 39.0% and 81.1% of the time, respectively. We relate angular consistency to the spatial variability of nadir‐BRF, thus allowing us to potentially identify, with a prescribed confidence level, which MODIS microphysical retrievals within the MISR swath meet the plane‐parallel assumption to within any desired range in view‐angle consistency.

Spherical albedo problem for isotropic scattering

Abstract The pseudo-slab problem by using the HN method, proper neutron flux definitions and physical boundary conditions is used to study spherical albedo. The selected numerical values can be compared with data available in the literature. The sphere radius can be calculated for the secondary neutron number and for the spherical albedo.

A self‐consistent scattering model for cirrus. I: The solar region

AbstractIn this paper a self‐consistent scattering model for cirrus is presented. The model consists of an ensemble of ice crystals where the smallest ice crystal is represented by a single hexagonal ice column. As the overall ice crystal size increases, the ice crystals become progressively more complex by arbitrarily attaching other hexagonal elements until a chain‐like ice crystal is formed, this representing the largest ice crystal in the ensemble. The ensemble consists of six ice crystal members whose aspect ratios (ratios of the major‐to‐minor axes of the circumscribed ellipse) are allowed to vary between unity and 1.84 for the smallest and largest ice crystal, respectively. The ensemble model's prediction of parameters fundamental to solar radiative transfer through cirrus such as ice water content and the volume extinction coefficient is tested using in situ based data obtained from the midlatitudes and Tropics. It is found that the ensemble model is able to generally predict the ice water content and extinction measurements within a factor of two. Moreover, the ensemble model's prediction of cirrus spherical albedo and polarized reflection are tested against a space‐based instrument using one day of global measurements. The space‐based instrument is able to sample the scattering phase function between the scattering angles of approximately 60° and 180° , and a total of 37 581 satellite pixels were used in the present analysis covering latitude bands between 43.75°S and 76.58°N. It is found that the ensemble model phase function is well able to minimize significantly differences between satellite‐based measurements of spherical albedo and the ensemble model's prediction of spherical albedo. The satellite‐based measurements of polarized reflection are found to be reasonably described by more simple members of the ensemble. The ensemble model presented in this paper should find wide applicability to the remote sensing of cirrus as well as more fundamental solar radiative transfer calculations through cirrus, and improved solar optical properties for climate and Numerical Weather Prediction models. Copyright © 2007 Royal Meteorological Society

Exact results in modeling planetary atmospheres—III.: The general theory applied to the Earth's semi-gray atmosphere

We apply the semi-gray model of our previous paper to the particular case of the Earth's atmosphere, in order to illustrate quantitatively the inverse problem associated with the direct problem we dealt with before. From given climatological values of the atmosphere's spherical albedo and transmittance for visible radiation, the single-scattering albedo and the optical thickness in the visible are inferred, while the infrared optical thickness is deduced for given global average surface temperature. Eventually, temperature distributions in terms of the infrared optical depth will be shown for a terrestrial atmosphere assumed to be semi-gray and, locally, in radiative and thermodynamic equilibrium.

Retrieval of cloud spherical albedo from top-of-atmosphere reflectance measurements performed at a single observation angle

Abstract. The paper is aimed to the derivation of the simple analytical relationship between the cloud spherical albedo and the cloud reflection function in the visible. The relationship obtained can be used for the retrieval of the spherical albedo from backscattered solar light measurements performed by radiometers on geostationary and polar orbiting satellites. The example of the application of the technique to MODIS data is shown.