Three-dimensional Radiative Transfer Model Research Articles

A Corona Australis cloud filament seen in NIR scattered light

With recent Herschel observations, the northern filament of the Corona Australis cloud has now been mapped in a number of bands from 1.2um to 870um. The data set provides a good starting point for the study of the cloud over several orders of magnitude in density. We wish to examine the differences of the column density distributions derived from dust extinction, scattering, and emission, and to determine to what extent the observations are consistent with the standard dust models. From Herschel data, we calculate the column density distribution that is compared to the corresponding data derived in the near-infrared regime from the reddening of the background stars, and from the surface brightness attributed to light scattering. We construct three-dimensional radiative transfer models to describe the emission and the scattering. The scattered light traces low column densities of A_V~1mag better than the dust emission, remaining useful to A_V ~ 10-15 mag. Based on the models, the extinction and the level of dust emission are surprisingly consistent with a sub-millimetre dust emissivity typical of diffuse medium. However, the intensity of the scattered light is very low at the centre of the densest clump and this cannot be explained without a very low grain albedo. Both the scattered light and dust emission indicate an anisotropic radiation field. The modelling of the dust emission suggests that the radiation field intensity is at least three times the value of the normal interstellar radiation field. The inter-comparison between the extinction, light scattering, and dust emission provides very stringent constraints on the cloud structure, the illuminating radiation field, and the grain properties.

THE THREE-DIMENSIONAL DISTRIBUTION OF DUST IN NGC 891

We produce three-dimensional Monte-Carlo radiative transfer models of the edge-on spiral galaxy NGC 891, a fast-rotating galaxy thought to be an analogue to the Milky Way. The models contain realistic spiral arms and a fractal distribution of clumpy dust. We fit our models to Hubble Space Telescope images corresponding to the B and I bands, using shapelet analysis and a genetic algorithm to generate 30 statistically best-fitting models. These models have a strong preference for spirality and clumpiness, with average face-on attenuation decreasing from 0.24(0.16) to 0.03(0.03) mag in the B(I) band between 0.5 and 2 radial scale-lengths. Most of the attenuation comes from small high-density clumps with low (<10%) filling factors. The fraction of dust in clumps is broadly consistent with results from fitting NGC 891's spectral energy distribution. Because of scattering effects and the intermixed nature of the dust and starlight, attenuation is smaller and less wavelength-dependent than the integrated dust column-density. Our clumpy models typically have higher attenuation at low inclinations than previous radiative transfer models using smooth distributions of stars and dust, but similar attenuation at inclinations above 70 degrees. At all inclinations most clumpy models have less attenuation than expected from previous estimates based on minimizing scatter in the Tully-Fisher relation. Mass-to-light ratios are higher and the intrinsic scatter in the Tully-Fisher relation is larger than previously expected for galaxies similar to NGC 891. The attenuation curve changes as a function of inclination, with R_(B,B-I)=A_(B)/E(B-I) increasing by ~0.75 from face-on to near-edge-on orientations.

A Systematic Study of Longwave Radiative Heating and Cooling within Valleys and Basins Using a Three-Dimensional Radiative Transfer Model

AbstractThe Monte Carlo code for the physically correct tracing of photons in cloudy atmospheres (MYSTIC) three-dimensional radiative transfer model was used in a parametric study to determine the strength of longwave radiative heating and cooling in atmospheres enclosed in idealized valleys and basins. The parameters investigated included valley or basin shape, width, and near-surface temperature contrasts. These parameters were varied for three different representative atmospheric temperature profiles for different times of day. As a result of counterradiation from surrounding terrain, nighttime longwave radiative cooling in topographic depressions was generally weaker than over flat terrain. In the center of basins or valleys with widths exceeding 2 km, cooling rates quickly approached those over flat terrain, whereas the cooling averaged over the entire depression volume was still greatly reduced. Valley or basin shape had less influence on cooling rates than did valley width. Strong temperature gradients near the surface associated with nighttime inversion and daytime superadiabatic layers over the slopes significantly increased longwave radiative cooling and heating rates. Local rates of longwave radiative heating ranged between −30 (i.e., cooling) and 90 K day−1. The effects of the near-surface temperature gradients extended tens of meters into the overlying atmospheres. In small basins, the strong influence of nocturnal near-surface temperature inversions could lead to cooling rates exceeding those over flat plains. To investigate the relative role of longwave radiative cooling on total nighttime cooling in a basin, simulations were conducted for Arizona’s Meteor Crater using observed atmospheric profiles and realistic topography. Longwave radiative cooling accounted for nearly 30% of the total nighttime cooling observed in the Meteor Crater during a calm October night.

LAI RETRIEVAL BASED ON THE NEW AIRBORNE MULTI-ANGLE SENSOR AMTIS

Leaf area index (LAI) is an important biophysical parameter, and remote sensing provides the probability for the LAI retrieval. LAI inversion based on the model is the main orientation of the LAI retrieval, and the multi-angle data are important parameters in the model-based inversion. The new airborne multi-angle sensor AMTIS can obtain the simultaneous multi-angle and high-resolution data. Using the AMTIS data based on the three-dimensional radiative transfer model, an inversion experiment on a wheat field in Shunyi was carried out on the basis of the AMTIS multi-angle data and the prior information. And the result was verified with the measured LAI data. The inversion precision and rate were improved by adjusting the soil classification and the matching table. The main errors in the process of inversion are also analyzed in this paper. 

DETERMINING THE MAGNETIZATION OF THE QUIET SUN PHOTOSPHERE FROM THE HANLE EFFECT AND SURFACE DYNAMO SIMULATIONS

The bulk of the quiet solar photosphere is thought to be significantly magnetized, due to the ubiquitous presence of a tangled magnetic field at subresolution scales with an average strength <B> ~ 100 G. This conclusion was reached through detailed three-dimensional (3D) radiative transfer modeling of the Hanle effect in the Sr I 4607 line, using the microturbulent field approximation and assuming that the shape of the probability density function of the magnetic field strength is exponential. Here we relax both approximations by modeling the observed scattering polarization in terms of the Hanle effect produced by the magnetic field of a 3D photospheric model resulting from a (state-of-the-art) magneto-convection simulation with surface dynamo action. We show that the scattering polarization amplitudes observed in the Sr I 4607 line can be explained only after enhancing the magnetic strength of the photospheric model by a sizable scaling factor, F=10, which implies <B> = 130 G in the upper photosphere. We argue also that in order to explain both the Hanle depolarization of the Sr I 4607 line and the Zeeman signals observed in Fe I lines we need to introduce a height-dependent scaling factor, such that the ensuing <B> = 160 G in the low photosphere and <B> = 130 G in the upper photosphere.

Structure of evolved cluster-forming regions

Context. An approach towards understanding the formation of massive stars and star clusters is to study the structure of their hot core phase, an evolutionary stage where dust has been heated, but molecules have not yet been destroyed by ultraviolet radiation. These hot molecular cores are very line-rich, but the interpretation of line surveys is also hampered by poor knowledge of the physical and chemical structure.Aims. To constrain the radial structure of high-mass star-forming regions containing hot cores, we attempt to reproduce by radiative transfer modeling both the intensity and shape of a variety of molecular lines. Methods. We observed 12 hot cores with the Atacama Pathfinder EXperiment (APEX) in lines of HCN, HCO+ , CO, and their isotopologues, including high-J lines and vibrationally excited HCN. We investigate how well the sources can be modeled as centrally heated spheres with a power-law density gradient, making use of the radiative transfer code RATRAN and the radial profile of the submm continuum emission, taken from the APEX Telescope Large Area Survey of the GALaxy (ATLASGAL).Results. Most of the observed lines have complicated shapes that incorporate self-absorption, asymmetries, and line wings. Vibrationally excited HCN is detected in all sources, and vibrationally excited H13 CN in half of the sources. We are able to successfully model most features seen in the APEX data, such as the ratio of the isotopologue lines (very high optical depths), self-absorption (temperature gradient), blue asymmetries (moderate infall), vibrationally excited HCN (high inner temperatures), and H13 CN (high HCN abundance under dense and hot conditions). Other features could not be reproduced, such as an occasional lack of self-absorption, the emission from high-J lines in the outer pixels of the CHAMP+ receiver (15′′−20′′ from the center), the outflow wings, and the red asymmetric profiles.Conclusions. The amount of molecular gas, in particular of HCN, at very high temperatures is larger than previously thought. A complex interplay between infall and outflow motions is present. Our basic model assumptions of pure central heating and a power-law radial density distribution can serve as approximations for most sources, but are too simple to explain all observed lines. In particular, taking into account clumpiness, multiplicity of heating sources and a more complex velocity field seems to be necessary to more closely match model calculations to observations. This would require three-dimensional radiative transfer modeling of high-resolution interferometric data.

Validating the MYSTIC three-dimensional radiative transfer model with observations from the complex topography of Arizona's Meteor Crater

Abstract. The MYSTIC three-dimensional Monte-Carlo radiative transfer model has been extended to simulate solar and thermal irradiances with a rigorous consideration of topography. Forward as well as backward Monte Carlo simulations are possible for arbitrarily oriented surfaces and we demonstrate that the backward Monte Carlo technique is superior to the forward method for applications involving topography, by greatly reducing the computational demands. MYSTIC is used to simulate the short- and longwave radiation fields during a clear day and night in and around Arizona's Meteor Crater, a bowl-shaped, 165-m-deep basin with a diameter of 1200 m. The simulations are made over a 4 by 4 km2 domain using a 10-m horizontal resolution digital elevation model and meteorological input data collected during the METCRAX (Meteor Crater Experiment) field experiment in 2006. Irradiance (or radiative flux) measurements at multiple locations inside the crater are then used to evaluate the simulations. MYSTIC is shown to realistically model the complex interactions between topography and the radiative field, resolving the effects of terrain shading, terrain exposure, and longwave surface emissions. The effects of surface temperature variations and of temperature stratification within the crater atmosphere on the near-surface longwave irradiance are then evaluated with additional simulations.

Three-Dimensional Transient Radiative Transfer Modeling Using Discontinuous Spectral Element Method

Three-Dimensional Transient Radiative Transfer Modeling Using Discontinuous Spectral Element Method

Study of an Optical Non-Contact Measurement Technique of the Solidification Rate for Latent Heat-Storage Materials

A new technique is developed for the measurement of the solidification rate for a latent-heat storage material that consisted of spherical n-paraffin particles and water (emulsion slurry). This method utilizes the correlation between the optical characteristics of the slurry and the solidification rate of the paraffin particles. From experiment, it was shown that the increase in the solidification rate of the particles causes the rise in the transimissivity and the drop in the reflectivity of the slurry. Each paraffin particles has a conical crater on the surface when it solidifies. Based on these observations, a new radiative transfer model has been developed for a transparent particle with a conical crater and a three-dimensional radiative transfer model for a particulate medium by the Monte Carlo method. The analytical results for the slurry using the model well agreed with the experimental ones. From the analysis, it was shown that the crater on the particle surface makes the forward scattering weak and scattering in the backward and the lateral direction strong. Therefore, it was concluded that the rise in the transmissivity and decrease in the reflectivity of the slurry by the increase in its solidification rate is caused by the craters on the particle surfaces due to their phase-change.

A three-dimensional radiative transfer model for shallow water environments

A geometric optical model for three-dimensional radiative transfer capable of handling arbitrary arrangements of surfaces within anisotropic scattering media is described. The model operates by discretizing surfaces and volumes into patches and voxels and establishing the radiative transfer relationship between every pair of elements. In a plane-parallel configuration results for directional radiance agree closely with the numerical integration invariant imbedded method. Model accuracy for two examples incorporating surface water waves and complex benthic structures were assessed by conservation of energy, errors were less than 1%. Potential applications in remote sensing or photobiological studies of structurally complex benthos in shallow water environments are illustrated.

Influence of clouds on the spectral actinic flux density in the lower troposphere (INSPECTRO): overview of the field campaigns

Abstract. Ultraviolet radiation is the key factor driving tropospheric photochemistry. It is strongly modulated by clouds and aerosols. A quantitative understanding of the radiation field and its effect on photochemistry is thus only possible with a detailed knowledge of the interaction between clouds and radiation. The overall objective of the project INSPECTRO was the characterization of the three-dimensional actinic radiation field under cloudy conditions. This was achieved during two measurement campaigns in Norfolk (East Anglia, UK) and Lower Bavaria (Germany) combining space-based, aircraft and ground-based measurements as well as simulations with the one-dimensional radiation transfer model UVSPEC and the three-dimensional radiation transfer model MYSTIC. During both campaigns the spectral actinic flux density was measured at several locations at ground level and in the air by up to four different aircraft. This allows the comparison of measured and simulated actinic radiation profiles. In addition satellite data were used to complete the information of the three dimensional input data set for the simulation. A three-dimensional simulation of actinic flux density data under cloudy sky conditions requires a realistic simulation of the cloud field to be used as an input for the 3-D radiation transfer model calculations. Two different approaches were applied, to derive high- and low-resolution data sets, with a grid resolution of about 100 m and 1 km, respectively. The results of the measured and simulated radiation profiles as well as the results of the ground based measurements are presented in terms of photolysis rate profiles for ozone and nitrogen dioxide. During both campaigns all spectroradiometer systems agreed within ±10% if mandatory corrections e.g. stray light correction were applied. Stability changes of the systems were below 5% over the 4 week campaign periods and negligible over a few days. The J(O1D) data of the single monochromator systems can be evaluated for zenith angles less than 70°, which was satisfied by nearly all airborne measurements during both campaigns. The comparison of the airborne measurements with corresponding simulations is presented for the total, downward and upward flux during selected clear sky periods of both campaigns. The compliance between the measured (from three aircraft) and simulated downward and total flux profiles lies in the range of ±15%.

Three-dimensional radiative transfer models of clumpy tori in Seyfert galaxies

Context. Tori of Active Galactic Nuclei (AGN) are made up of a mixture of hot and cold gas, as well as dust. In order to protect the dust grains from destruction by the surrounding hot gas as well as by the energetic (UV/optical) radiation from the accretion disk, the dust is often assumed to be distributed in clouds. Aims. A new three-dimensional model of AGN dust tori is extensively investigated. The torus is modelled as a wedge-shaped disk within which dusty clouds are randomly distributed throughout the volume, by taking the dust density distribution of the corresponding continuous model into account. We especially concentrate on the differences between clumpy and continuous models in terms of the temperature distributions, the surface brightness distributions and interferometric visibilities, as well as spectral energy distributions. Methods. Radiative transfer calculations with the help of the three-dimensional Monte Carlo radiative transfer code MC3D are used in order to simulate spectral energy distributions as well as surface brightness distributions at various wavelengths. In a second step, interferometric visibilities for various inclination as well as position angles and baselines are calculated, which can be used to directly compare our models to interferometric observations with the MIDI instrument. Results. We find that the radial temperature distributions of clumpy models possess significantly enhanced scatter compared to the continuous cases. Even at large distances, clouds can be heated directly by the central accretion disk. The existence of the silicate 10 µm-feature in absorption or in emission depends sensitively on the distribution, the size and optical depth of clouds in the innermost part of the dust distribution. With this explanation, failure and success of previous modelling efforts of clumpy tori can be understood. The main reason for this outcome are shadowing effects of clouds within the central region. We underline this result with the help of several parameter variations. After adapting the parameters of our clumpy standard model to the circumstances of the Seyfert 2 Circinus galaxy, it can qualitatively explain recent mid-infrared interferometric observations performed with MIDI, as well as high resolution spectral data.

Simulation of solar radiation during a total eclipse: a challenge for radiative transfer

Abstract. A solar eclipse is a rare but spectacular natural phenomenon and furthermore it is a challenge for radiative transfer modelling. Whereas a simple one-dimensional radiative transfer model with reduced solar irradiance at the top of the atmosphere can be used to calculate the brightness during partial eclipses a much more sophisticated model is required to calculate the brightness (i.e. the diffuse radiation) during the total eclipse. The reason is that radiation reaching a detector in the shadow gets there exclusively by horizontal transport of photons in a spherical shell atmosphere, which requires a three-dimensional radiative transfer model. In this study the first fully three-dimensional simulations for a solar eclipse are presented exemplified by the solar eclipse at 29 March 2006. Using a backward Monte Carlo model we calculated the diffuse radiation in the umbra and simulated the changing colours of the sky. Radiance and irradiance are decreased by 3 to 4 orders of magnitude, depending on wavelength. We found that aerosol has a comparatively small impact on the radiation in the umbra. We also estimated the contribution of the solar corona to the radiation under the umbra and found that it is negligible compared to the diffuse solar radiation in the wavelength region from 310 to 500 nm.

The Keck Aperture‐masking Experiment: Near‐Infrared Sizes of Dusty Wolf‐Rayet Stars

We report the results of a high angular resolution near-infrared survey of dusty Wolf-Rayet stars using the Keck I Telescope, including new multiwavelength images of the pinwheel nebulae WR 98a, WR 104, and WR 112. Angular sizes were measured for an additional eight dusty Wolf-Rayet stars using aperture-masking interferometry, allowing us to probe characteristic sizes down to � 20 mas (� 40 AU for typical sources). With angular sizes and specific fluxes, we can directly measure the wavelength-dependent surface brightness and size relations for our sample. We discovered tight correlations of these properties within our sample that could not be explained by simple spherically symmetric dust shells or even the more realistic ‘‘pinwheel nebula’’ (three-dimensional) radiative transfer model, when using Zubko’s optical constants. While the tightly correlated surface brightness relations we uncovered offer compelling indirect evidence of a shared and distinctive dust shell geometry among our sample, long-baseline interferometers should target the marginally resolved objects in our sample in order to conclusively establish the presence or absence of the putative underlying colliding-wind binaries thought to produce the dust shells around WC WolfRayet stars. Subject headingg binaries: general — circumstellar matter — instrumentation: interferometers —

Three-dimensional radiative transfer modeling using the control volume finite element method

In the present study, a three-dimensional algorithm for the treatment of radiative heat transfer in emitting, absorbing and scattering media is developed. The approach is based on the utilization of control volume finite element method (CVFEM) which, to the knowledge of the authors, is applied at the first time to 3D radiative heat transfer in participating media. The accuracy of the present algorithm is tested by comparing its predictions to other published works. Comparisons show that CVFEM produces good results. Moreover, this approach permits compatibility with other numerical methods used for computational fluids mechanics problems.

Cloud model evaluation using radiometric measurements from the airborne multiangle imaging spectroradiometer (AirMISR)

Detailed information on cloud properties is needed to rigorously test retrieval algorithms for satellite and ground-based remote sensors. The inherent complexity of clouds makes this information difficult to obtain from observations alone and cloud resolving models (CRMs) are often used to generate synthetic datasets that can be used as proxies for real data. We test the ability of a CRM to reproduce the observed structure of low-level clouds detected by the Earth Observing System (EOS) validation program in north central Oklahoma on March 3, 2000. A three-dimensional radiative transfer model is applied to high-resolution cloud fields generated by the CRM in order to simulate the top of atmosphere radiances. These synthetic radiances are then statistically compared with observations from the airborne Multiangle Imaging SpectroRadiometer (AirMISR), flown on the NASA ER-2 high-altitude aircraft. Simulations match well the blue channel radiance distributions at oblique view angles but overestimate the minimum in reflectance at near-nadir viewing angles. The model reproduces correctly the angular change in the width of radiance distribution, as measured by the standard deviation but the change in skewness of these distributions is captured only qualitatively. The model biases are suggestive of the simulated cloud boundaries being too sharp and the distribution of the vertical liquid water path being too narrow. A power spectrum analysis shows a close agreement between simulations and observations including a break in the scaling properties of the radiance fields around 400 m. The scaling properties of the 1D power spectrum of simulated radiance at smaller scales exhibit directional dependence not seen in corresponding observations.

Modeling the observed angular anisotropy of land surface temperature in a Savanna

Several recent studies have found that retrievals of land surface temperature (LST) from remote sensing measurements depend upon the angle of observation. To understand, predict, and ultimately correct this sensitivity, simple but physically based models of LST angular anisotropy are needed. In this study, we describe and evaluate the modified geometric projection (MGP) model, a highly parameterized model of scene thermal infrared (TIR) radiance applicable to both homogeneous and discontinuous canopy environments. Based on geometric optics modeling, MPG assumes that the angular anisotropy of TIR radiance over discontinuous canopies is due strictly to the different proportions of scene endmembers (e.g., sunlit tree crowns, background shadows) visible to a sensor at different sun-view geometries. We tested MGP against DART, a rigorous three-dimensional radiative transfer model, and against field-measured data from a southern Africa savanna. For a prescribed set of canopy conditions, MGPs estimates of observable endmember fractions and scene temperatures in the solar principal plane compared well with estimates from DART. We also parameterized MGP with field-measured endmember data for an acacia/combretum savanna near Skukuza, South Africa. We angularly integrated the MGP-predicted radiances and compared the results with measurements of scene hemispherical exitance from a tower-based pyrgeometer. The modeled exitances exhibited the normal diurnal behavior. Model predictions generally agreed with the pyrgeometer measurements; however, model accuracy decreased as the difference in endmember temperatures increased. These tests suggest that the assumptions inherent in the MGP model do not seriously impact the accuracy of the simulated radiances. We conclude that the MGP model accurately captures the predominate thermal emission directionality resulting from discontinuous canopy structure, and could therefore be applied at continental and global scales.

Inversion of a Lidar Waveform Model for Forest Biophysical Parameter Estimation

Due to its measurement principle, light detection and ranging (lidar) is particularly suited to estimate the horizontal as well as vertical distribution of forest structure. Quantification and characterization of forest structure is important for the understanding of the forest ecosystem functioning and, moreover, will help to assess carbon sequestration within forests. The relationship between the signal recorded by a lidar system and the canopy structure of a forest can be accurately characterized by physically based radiative transfer models (RTMs). A three-dimensional RTM is capable of representing the complex forest canopy structure as well as the involved physical processes of the lidar pulse interactions with the vegetation. Consequently, the inversion of such an RTM presents a novel concept to retrieve biophysical forest parameters that exploits the full lidar signal and underlying physical processes. A synthetic dataset and data acquired in the Swiss National Park (SNP) successfully demonstrated the feasibility and the potential of RTM inversion to retrieve forest structure from large-footprint lidar waveform data. The SNP lidar data consist of waveforms generated from the aggregation of small-footprint lidar returns. Derived forest biophysical parameters, such as fractional cover, leaf area index, maximum tree height, and the vertical crown extension, were able to describe the horizontal and vertical forest canopy structure.

Three‐dimensional Models of Embedded High‐Mass Stars: Effects of a Clumpy Circumstellar Medium

We use three-dimensional radiative transfer models to show the effects of clumpy circumstellar material on the observed infrared colors of high-mass stars embedded in molecular clouds. We highlight differences between three-dimensional clumpy and one-dimensional smooth models that can affect the interpretation of data. We discuss several important properties of the emergent spectral energy distribution (SED). More near-infrared light (scattered and direct from the central source) can escape than in smooth one-dimensional models. The near- and mid-infrared SED of the same object can vary significantly with viewing angle, depending on the clump geometry along the sight line. Even the wavelength-integrated flux can vary with angle by more than a factor of 2. Objects with the same average circumstellar dust distribution can have very different near- and mid-IR SEDs, depending on the clump geometry and the proximity of the most massive clump to the central source. Although clumpiness can cause similar objects to have very different SEDs, there are some observable trends. Near- and mid-infrared colors are sensitive to the weighted average distance of clumps from the central source and to the magnitude of clumpy density variations (smooth-to-clumpy ratio). Far-infrared emission remains a robust measure of the total dust mass. We present simulated SEDs, colors, and images for 2MASS and Spitzer filters. We compare them to observations of some ultracompact H II regions and find that three-dimensional clumpy models fit better than smooth models. In particular, clumpy models with fractal dimensions in the range 2.3-2.8, smooth-to-clumpy ratios of ≲50%, and density distributions with shallow average radial density profiles fit the SEDs best (⟨ρ⟩ ∝ rα, - 1.0 < α < 0.0).

Constraining the structure of the non-spherical pre-protostellar core L1544

We present a study of the pre-protostellar core L1544. A series of self-consistent, three-dimensional continuum radiative transfer models is constructed. The outputs of these models are convolved with appropriate telescope beam responses, and compared with existing SCUBA data. The resulting comparison allows us to constrain the structure of L1544. We find that the source is well-fitted by a prolate spheroid, having an ellipsoidal power-law density distribution of index m ∼ 2(1.75 < m < 2.25) in to at least r ∼ 1600 au. For r < 1600 au, the data are consistent with either an extension of the power law to smaller radii, or a flattened (Bonner-Ebert-like) density distribution. Furthermore, we find an optical depth along the short axis at 1300 μm of τ 1300,short = 5 x 10 -3 (2 x 10 -3 < τ 1300,short < 8 x 10 -3 ), a central luminosity L* =0(<10 -3 L ○. ), a long-axis diameter D = 0.1 pc [0.08 < D(pc) < 0.16; 16000 < D(au) < 32 000], an axis ratio q = 2 (1.7 < q < 2.5), and an external interstellar radiation field (ISRF) defined by Mathis et al. to within 50 per cent. The outer diameter and axis ratio may each be somewhat larger due to potential on-source chopping in the observations, and the projection of the long axis on to the plane of the sky. While these results are similar to those inferred directly from observations or spherical modelling due to the source transparency at submillimetre wavelengths, we infer a smaller size, lower mass, and higher optical depth/column density, exposed to a stronger external radiation field than previously assumed. Finally, we find that both the spectral energy distribution (SED) and surface brightness distribution are necessary to constrain the source properties in this way, and even a modest variation in X 2 can significantly alter the fit quality.