Radiative Transfer Simulations Research Articles

Consideration of the cloud motion for aircraft-based stereographically derived cloud geometry and cloud top heights

Abstract. Cloud geometry and in particular cloud top heights can be derived from 2-D camera measurements by applying a stereographic method to data from an overflight over a scene of clouds (see, e.g., Kölling et al., 2019). Although airplane overpasses are relatively fast, cloud motion with the wind is important and can result in errors in the cloud localization. Here, the impact of the wind is investigated using the method from Kölling et al. (2019) for measurements of the airborne hyperspectral imaging system spectrometer of the Munich Aerosol Cloud Scanner (specMACS). Further, a method for cloud motion correction using model winds from the European Centre for Medium-Range Weather Forecasts (ECMWF) is presented. It is shown that the update is important as the original algorithm without the cloud motion correction can over- or underestimate the cloud top heights by several hundred meters, depending on the wind speed and the relative wind direction. This is validated using data from the Elucidating the role of clouds–circulation coupling in climate (EUREC4A) campaign and realistic 3-D radiative transfer simulations. From the comparison of the derived cloud top heights with the expected ones from the model input, an average accuracy of the cloud top heights of less than (20±140) m (mean deviation and 1 standard deviation) is estimated for the updated method.

Quantifying the effects of the microphysical hygroscopic restructuring of soot on ensemble optical properties and satellite aerosol optical depth retrievals

Black carbon, or soot, significantly contributes to atmospheric light absorption due to its low single scattering albedo (SSA). This study investigates the impact of soot's hygroscopic restructuring on satellite remote sensing, focusing on radiative forcing, top-of-atmosphere (TOA) reflectance, and aerosol optical depth (AOD) retrievals. We characterized soot aging using relative humidity (RH) growth factor functions and modeled fresh and aging soot aggregates using a cluster-cluster aggregation algorithm. Bulk optical properties for each RH level were simulated using core-mantle generalized multi-sphere Mie-solution, weighted by the probability density function of soot monomer numbers. We incorporated soot aging models into the 6S radiative transfer model by adjusting the geometric mean radius of the soot component to match bulk SSA values at each aging degree. Extensive radiative transfer simulations were conducted, complemented by an analysis of 16 actual soot-containing cases in China from 2016 to 2019. Results showed that identical soot loads correspond to lower reflectance in dry environments and higher reflectance in humid environments. MODIS AOD retrieval errors approached zero when RH was close to 70 %, likely due to the similarity between the 6S default soot and the aging model at this humidity. Neglecting RH led to overestimations in AOD for cases with RH < 65 % and underestimations in high humidity cases (RH > 75 %). The average MODIS AOD retrieval errors for RH < 65 %, RH between 65 % and 75 %, and RH > 75 % were −33.15 %, −1.80 %, and +42.42 %, respectively. This study underscores the necessity of incorporating RH into satellite AOD retrieval algorithms to enhance accuracy and reduce uncertainties.

Structural Complexity Significantly Impacts Canopy Reflectance Simulations as Revealed from Reconstructed and Sentinel-2-Monitored Scenes in a Temperate Deciduous Forest

Detailed three-dimensional (3D) radiative transfer models (RTMs) enable a clear understanding of the interactions between light, biochemistry, and canopy structure, but they are rarely explicitly evaluated due to the availability of 3D canopy structure data, leading to a lack of knowledge on how canopy structure/leaf characteristics affect radiative transfer processes within forest ecosystems. In this study, the newly released 3D RTM Eradiate was extensively evaluated based on both virtual scenes reconstructed using the quantitative structure model (QSM) by adding leaves to point clouds generated from terrestrial laser scanning (TLS) data, and real scenes monitored by Sentinel-2 in a typical temperate deciduous forest. The effects of structural parameters on reflectance were investigated through sensitivity analysis, and the performance of the 3D model was compared with the 5-Scale and PROSAIL radiative transfer models. The results showed that the Eradiate-simulated reflectance achieved good agreement with the Sentinel-2 reflectance, especially in the visible and near-infrared spectral regions. Furthermore, the simulated reflectance, particularly in the blue and shortwave infrared spectral bands, was clearly shown to be influenced by canopy structure using the Eradiate model. This study demonstrated that the Eradiate RTM, based on the 3D explicit representation, is capable of providing accurate radiative transfer simulations in the temperate deciduous forest and hence provides a basis for understanding tree interactions and their effects on ecosystem structure and functions.

Influence of cloudy and clear-sky partitions, aerosols, and geometry on the recent variability in surface solar irradiance components in northern France

Abstract. Surface solar irradiance (SSI) is a fundamental parameter whose components (direct and diffuse) and variabilities are highly influenced by changes in atmospheric content and scene parameters. The respective importance of cloudy-sky conditions and atmospheric aerosols on SSI evolutions is region dependent and only partially quantified. Here we provide a comprehensive analysis of SSI variabilities recorded in northern France, a region with extensive variability in sky conditions and aerosol loads. Through the application of automatic filtering methods to 1 min resolution SSI ground-based measurements over Lille, sky conditions are classified as clear-sky, 11 %; clear-sun-with-cloud, 22 %; and cloudy-sun situations, 67 % from 2010 to 2022, for which we analyze the statistics and variabilities in the global horizontal irradiance (GHI), beam horizontal irradiance (BHI), and diffuse horizontal irradiance (DHI). Coincident photometric measurements of aerosol properties and radiative-transfer simulations provide the means to conduct a multivariate analysis of the SSI observed trends and year-to-year evolutions and to estimate aerosol and cloud forcings under clear-sun conditions. The analysis of the record value of all-sky GHI in spring 2020 attributes 89 % of the changes to the exceptional sunlight conditions (57 % of clear-sun situations). It highlights also for that season the importance of solar zenith-angle changes, whose positive effects on clear-sun conditions surpass those due to aerosols. Our results show all-sky GHI and BHI positive trends of around +4.0 and +4.4 Wm-2yr-1, respectively, in both spring and summer, which are explained by more than 60 % by an increase in clear-sun occurrences of +1 % yr−1. Additional significant BHI increases under clear-sun conditions are mainly explained in spring by the negative trend in aerosol optical depth (−0.011 yr−1) and partly by angular effects in summer. Moreover, we find that clear-sun-with-cloud situations are frequently marked by irradiance enhancement due to clouds, with 13 % more GHI on a monthly average and 10 % additional diffuse proportion than in clear-sky situations. Under such conditions, clouds add on average 25 W m−2 of diffuse irradiance that sets the GHI at the remarkable level of pristine (aerosol-and-cloud-free) conditions or even higher, by more than +10 W m−2 in summer and for low aerosol loads. Overall, our results highlight the dominant and complex influence of cloudy conditions on SSI, which precedes or combines with that of aerosols and geometrical effects, and leads to a remarkable global level of SSI in clear-sun-with-cloud situations.

A Mystery of the Inconsistency Between Microwave Polarimetric Observations and Radiative Transfer Simulations

AbstractA factor of 2 difference is found between microwave brightness temperature (TB) observations and simulations from vector radiative transfer models. A physical explanation of this difference is related to the calibration process. In principle, for the calibration of polarimetric instruments of a total power radiometer, the radiation should be only half of the values derived from Planck function but in the actual calibration process, a full value is used. When this full value is converted to a TB it is approximately, but not exactly, twice the TB simulated by a vector radiative transfer model. This inconsistency is verified by simulations of three conically scanning microwave imagers (WindSat, AMSR2 and MWRI) and one cross‐track scanning microwave sounder (AMSU‐A). This difference cannot be compensated simply by dividing a factor of 2 to the processed TBs, especially at high frequencies or at low physical temperatures due to the nonlinear property of Planck function.

Radiative transfer of Lyman-α photons at cosmic dawn with realistic gas physics

Abstract Lyman-α photons enable the cosmic dawn 21-cm signal through a process called the Wouthuysen-Field effect. An accurate model of the signal in this epoch hinges on the accuracy of the computation of the Lyα coupling, which requires one to calculate the specific intensity of Lyα photons emitted from the first stars. Most traditional calculations of the Lyα coupling assume a delta-function scattering cross-section, as the resonant nature of the Lyα scattering makes an accurate radiative transfer (RT) solution computationally expensive. Attempts to improve upon this traditional approach using numerical RT have recently emerged. However, some of these treatments suffer from assumptions such as a uniform gas distribution, coherent scattering in the gas frame and isotropic scattering. While others which do not account for these only do so through certain schemes along with core-skipping algorithms. We present results from a self-consistent Monte Carlo RT simulations devoid of any of the assumptions in the previous work for the first time. We find that gas bulk motion is the most important effect to account for in RT resulting in an RMS difference of 37% in the 21-cm signal and anisotropic scattering being the least important effect contributing to less than 3% RMS difference in 21-cm signal. We also evaluate the 21-cm power spectrum and compare that with the traditional results at cosmic dawn. This work points the way towards higher-accuracy models to enable better inferences from future measurements.

A public grid of radiative transfer simulations for Lyα and metal lines in idealised galactic outflows

The vast majority of star-forming galaxies are surrounded by large reservoirs of gas ejected from the interstellar medium. Ultraviolet absorption and emission lines represent powerful diagnostics to constrain the cool phase of these outflows, through resonant transitions of hydrogen and metal ions. The interpretation of these observations is often remarkably difficult as it requires detailed modelling of the propagation of the continuum and emission lines in the gas. To this aim, we present a large public grid of ≈20 000 simulated spectra that includes H I Lyα and five metal transitions associated with Mg II, C II, Si II, and Fe II which is accessible online. The spectra have been computed with the RASCAS Monte Carlo radiative transfer code for 5760 idealised spherically symmetric configurations surrounding a central point source emission, and characterised by their column density, Doppler parameter, dust opacity, wind velocity, as well as various density and velocity gradients. Designed to predict and interpret Lyα and metal line profiles, our grid exhibits a wide diversity of resonant absorption and emission features, as well as fluorescent lines. We illustrate how it can help better constrain the wind properties by performing a joint modelling of observed Lyα, C II, and Si II spectra. Using CLOUDY simulations and virial scaling relations, we also show that Lyα is expected to be a faithful tracer of the gas at T ≈ 104 − 105 K, even if the medium is highly ionised. While C II is found to probe the same range of temperatures as Lyα, other metal lines merely trace cooler phases (T ≈ 104 K). As their gas opacity strongly depends on gas temperature, incident radiation field, metallicity and dust depletion, we caution that optically thin metal lines do not necessarily originate from low H I column densities and may not accurately probe Lyman continuum leakage.

Determination of optimal solar-viewing geometry for in-flight polarization calibration using sun glint over ocean

The sun glint has been proven to be a valuable natural polarization calibration target because it is strongly polarized, and its polarization characteristics can be accurately simulated with models. It is convenient to calibrate the satellite’s in-flight polarimetry by comparing the polarization simulations with actual measurements. Meanwhile, the accuracy of polarization simulation at the top of the atmosphere (TOA) over sun glint is affected by several atmospheric and oceanic surface factors and depends on the specific solar-viewing geometry. In this paper, the sensitivity of the degree of linear polarization (DOLP) at the TOA to the uncertainties of the aerosol optical depth, aerosol model, absorption gas content (CWV, O3), sea surface instantaneous wind speed (WS), and chlorophyll concentration (Chl) under different solar-viewing geometries is analyzed via radiative transfer simulation. The error budgets indicate that aerosols and WS are the main error factors for polarization calibration, while the uncertainties of Chl and absorbing gases can be disregarded. The total DOLP error increases with the solar zenith angle and viewing zenith angle (i.e., the increase of atmospheric optical path) and the sun glint angle (SGA, the angle between the viewing and the specular directions of the sun) (i.e., the decrease of sun glint brightness). The dependence of the total DOLP error on SGA decreases with the WS (i.e., the increase of sun glint spot area and the decrease of the sun glint intensity) and increases with the wavelength (i.e., the decrease of atmospheric scattering contribution). Based on the error budgets, an optimized solar-viewing geometry screening strategy is proposed to ensure that the simulated DOLP error is limited to 0.02. The in-flight DOLP calibration result of POLDER/PARASOL shows that the proposed screening strategy obtained more calibration samples and covered a wider range of DOLP, especially for the samples with DOLP of less than 0.2, compared with the screening strategies of Toubbe et al. [IEEE Trans. Geosci. Remote Sens. 37, 513 (1999)IGRSD20196-289210.1109/36.739104]and Hagolle et al. [IEEE Trans. Geosci. Remote Sens. 42, 1472 (2004)IGRSD20196-289210.1109/TGRS.2004.826805] in previous work. The smaller standard error (SE) of the samples indicates more stable calibration results obtained for the optimized strategy. This research presents an optimized strategy for screening the solar-viewing geometry of the samples to calibrate satellite in-flight polarization measurements using the sun glint.

Cloud Collision Signatures in the Central Molecular Zone

Molecular cloud collisions are a prominent theory for the formation of stars. Observational studies into cloud collisions identify the collision via a bridging feature: a continuous strip of line emission that connects two intensity peaks that are related in position space and separated in velocity space. Currently, most observations of collisions and these bridging features take place in the Milky Way disc. They are also theorized to take place in the Central Molecular Zone (CMZ), where temperatures and densities are both significantly higher than in the disc. For studies in the Milky Way Disc, the most commonly-used tracer tends to be CO. However, for studies in the CMZ, where the density and temperature are significantly higher, CO becomes so abundant that it loses its ability to adequately highlight the bridging feature of cloud collisions. As a result, studies have begun using other tracers, whose physical and chemical behavior has not been studied under CMZ conditions. We perform combined hydrodynamical, chemical and radiative transfer simulations of cloud collisions under both disc- and CMZ-like conditions, and investigate collision signatures in a number of commonly-observed molecular lines. Under the Milky Way disc conditions ( ) has the standard bridging feature; however, the other tracers, CS, HCO +, N 2H + only emit in the intermediate-velocity bridge region, making the feature itself non-existent. In the CMZ, the higher density and temperature make the bridging feature far more indistinct for CO, but the other tracers have morphologically similar bridging features to the CO disc model, validating their use as tracers of cloud collisions under these conditions.

HAMSTER: Hyperspectral Albedo Maps dataset with high Spatial and TEmporal Resolution

Abstract. Surface albedo is an important parameter in radiative-transfer simulations of the Earth's system as it is fundamental for correctly calculating the energy budget of the planet. The Moderate Resolution Imaging Spectroradiometer (MODIS) instruments on NASA's Terra and Aqua satellites continuously monitor daily and yearly changes in reflection at the planetary surface. The MODIS Surface Reflectance Black-Sky Albedo dataset (version 6.1 of MCD43D) provides detailed albedo maps for seven spectral bands in the visible and near-infrared range. These albedo maps allow us to classify different Lambertian surface types and their seasonal and yearly variability and change, albeit only into seven spectral bands. However, a complete set of albedo maps covering the entire wavelength range is required to simulate radiance spectra and correctly retrieve atmospheric and cloud properties from remote sensing observations of the Earth. We use a principal component analysis (PCA) regression algorithm to generate hyperspectral albedo maps of the Earth. By combining different datasets containing laboratory measurements of hyperspectral reflectance for various dry soils, vegetation surfaces, and mixtures of both, we reconstruct albedo maps across the entire wavelength range from 400 to 2500 nm. The PCA method is trained with a 10-year average of MODIS data for each day of the year. We obtain hyperspectral albedo maps with a spatial resolution of 0.05° in latitude and longitude, a spectral resolution of 10 nm, and a temporal resolution of 1 d (day). Using the hyperspectral albedo maps, we estimate the spectral profiles of different land surfaces, such as forests, deserts, cities, and icy surfaces, and study their seasonal variability. These albedo maps will enable us to refine calculations of the Earth's energy budget and its seasonal variability and improve climate simulations.

The k-bin tool: Fast and flexible k-distribution algorithms written in Python

Radiative transfer simulations (RTS) still face significant challenges in accurately representing the highly complex gas absorption spectra of the Earth’s atmosphere. Line-by-line RTS achieves high accuracy by solving radiative transfer equations for narrow spectral intervals, but at a considerable computational cost. Especially in remote sensing and climate modeling, a trade-off between efficiency and accuracy must be done. k-distribution methods are widespread in the scientific community and offer a way to make this trade-off. k-distribution methods reorder the absorption spectra k for a given spectral interval and find appropriate so-called k-bins. In the k-space much less integration points can be used, while maintaining high accuracy. The way to find optimal k-bins differs from method to method and depends on the application. In this paper, we present the flexible and fast k-bin tool. The python based lightweight k-bin tool provides a variety of different k-distribution methods and configuration options. One k-distribution method is the in-house developed k-bin approach. The different setups of the tool can be easily compared, helping to decide which method and configuration is best suited for a given application. We encourage the user of the tool to continue to optimize the k-bin tool and to extend it with new approaches and functionalities.

Impact of ice growth on the physical and chemical properties of dense cloud cores

We investigated the effect of time-dependent ice growth on dust grains on the opacity and hence on the dust temperature in a collapsing molecular cloud core, with the aim of quantifying the effect of the dust temperature variations on ice abundances as well as the evolution of the collapse. To perform the simulations, we employed a one-dimensional collapse model that self-consistently and time-dependently combines hydrodynamics with chemical and radiative transfer simulations. The dust opacity was updated on the fly based on the ice growth as a function of the location in the core. The results of the fully dynamical model were compared against simulations run with different values of fixed ice thickness. We found that the ice thickness increases quickly and reaches a saturation value (as a result of a balance between adsorption and desorption) of approximately 90 monolayers in the central core (volume density ~104 cm−3), and several tens of monolayers at a volume density of ~103 cm−3, after only a few 105 yr of evolution. The results thus exclude the adoption of thin (approximately ten monolayer) ices in molecular cloud simulations except at very short timescales. However, the differences in abundances and the dust temperature between the fully dynamic simulation and those with a fixed dust opacity are small; abundances change between the solutions generally within a factor of two only. The assumptions on the dust opacity do have an effect on the collapse dynamics through the influence of the photoelectric effect on the gas temperature, and the simulations take a different time to reach a common central density. This effect is, however, small as well. In conclusion, carrying out chemical simulations using a dust temperature corresponding to a fixed opacity seems to be a good approximation. Still, although at least in the present case its effect on the overall results is limited – as long as the grains are monodisperse – ice growth should be considered to obtain the most accurate representation of the collapse dynamics. We have found in a previous work that considering a grain size distribution leads to a complicated ice composition that depends on the grain size nonlinearly. With this in mind, we will carry out a follow-up study where the influence of the grain size on the present simulation setup is investigated.

3D Radiation-hydrodynamical Simulations of Shadows on Transition Disks

Shadows are often observed in transition disks, which can result from obscuring by materials closer to the star, such as a misaligned inner disk. While shadows leave apparent darkened emission as observational signatures, they have significant dynamical impact on the disk. We carry out 3D radiation-hydrodynamical simulations to study shadows in transition disks and find that the temperature drop due to the shadow acts as an asymmetric driving force, leading to spirals in the cavity. These spirals have zero pattern speed following the fixed shadow. The pitch angle is given by tan−1(c s /v ϕ ) (6° if h/r = 0.1). These spirals transport mass through the cavity efficiently, with α ∼ 10−2 in our simulation. Besides spirals, the cavity edge can also form vortices and flocculent streamers. When present, these features could disturb the shadow-induced spirals. By carrying out Monte Carlo radiative transfer simulations, we show that these features resemble those observed in near-infrared scattered light images. In the vertical direction, the vertical gravity is no longer balanced by the pressure gradient alone. Instead, an azimuthal convective acceleration term balances the gravity–pressure difference, leading to azimuthally periodic upward and downward gas motion reaching 10% of the sound speed, which can be probed by Atacama Large Millimeter/submillimeter Array line observations.

Do Subsampling Strategies Reduce the Confounding Effect of Errors in Bispectral Retrievals on Estimates of Aerosol Cloud Interactions?

AbstractBi‐spectral retrievals of droplet effective radius and cloud optical depth are widely utilized to estimate aerosol cloud interactions (ACI) in warm clouds in the marine boundary layer. Here, we assess the effect of retrieval errors due to the neglect of 3D radiative transfer during the retrieval process on this analysis of ACI. We use an ensemble of stochastically‐modeled cloud fields and 3D radiative transfer simulations to study the retrieval errors at a solar zenith angle of 30°. Simulated retrieval biases in droplet number concentration (Nd) for all three MODIS channels vary systematically from +35% to −80% as cloud heterogeneity increases. Pixel‐level errors can be much larger. Commonly utilized subsampling strategies do not reduce the systematic variation in retrieval error. Negative error correlations between optical depth and droplet effective radius produce spuriously negative slopes between the logarithm of liquid water path and Nd (−1.0 to −0.3). Pixels at the center of (8 km)2 patches that are not overcast have a relative bias in Nd of −50%. The relative frequency of these biased pixels varies linearly with the clear fraction in MODIS data and form the basis for a simple parameterization of Nd bias that varies with cloud fraction (CF). Using this parameterization, synthetic data experiments indicate that estimates of the first indirect effect in the tropical ocean can be overestimated by up to 30%, and the effect of aerosol on CF is overestimated by 50%, due to neglecting the correlation between retrieval errors and cloud microphysics.

Publisher’s Note: “Benchmark simulations of radiative transfer in participating binary stochastic mixtures in two dimensions” [Matter Radiat. Extremes 9, 067802 (2024)

Publisher’s Note: “Benchmark simulations of radiative transfer in participating binary stochastic mixtures in two dimensions” [Matter Radiat. Extremes 9, 067802 (2024)

Efficient physics-informed transfer learning to quantify biochemical traits of winter wheat from UAV multispectral imagery

Accurate and efficient estimation of biochemical traits, including leaf index area (LAI), leaf chlorophyll content (LCC) and canopy chlorophyll content (CCC), is crucial for crop growth monitoring in agricultural management. Recent advancements in unmanned aerial vehicle (UAV) multispectral remote sensing have enabled fast and cost-effective measurements of these traits. However, traditional statistical regression models trained on specific datasets lack scalability and transferability across practical field conditions without retraining. This study proposed an efficient physics-informed transfer learning model (PITL) for winter wheat biochemical traits estimation from UAV multispectral data. The PITL integrates the strengths of physical radiative transfer simulations and deep neural network architectures through transfer learning to improve the estimation of biochemical traits from UAV multispectral data. The PITL was tested with convolutional neural network (CNN), deep neural network (DNN), and long short-term memory (LSTM) architectures. Results indicated that PITLDNN had better accuracy than PITLCNN and PITLLSTM models in predicting LAI (R2=0.94, RMSE = 0.32 m2/m2), LCC (R2=0.81, RMSE = 5.20 μg/cm2) and CCC (R2=0.928, RMSE = 0.2 g/m2). Moreover, PITLDNN demonstrated higher capability in computational efficiency, making it suitable for processing large volumes of UAV multispectral data in crop growth monitoring applications. Furthermore, PITL's integration of radiative transfer knowledge with labeled field data yielded higher predictive accuracy compared to physically-based inversion model, pure data-driven deep neural network approaches, and hybrid models. This study highlighted the performance of PITLDNN in accurately and efficiently quantifing biochemical traits from UAV multispectral data, thereby providing timely and accurate information for guiding crop growth monitoring applications.

Integrated neural network based simulation of thermo solutal radiative double-diffusive convection of ternary hybrid nanofluid flow in an inclined annulus with thermophoretic particle deposition

Numerical simulation of magnetohydrodynamic radiative double-diffusive convective heat and mass transfer of a ternary hybrid nanofluid with thermophoretic particle deposition in an inclined annulus is studied. Both sides of cylinders are preserved at uniform temperatures, while the remaining sides are thermally insulated. The coupled nonlinear partial differential equations are solved using a finite difference approach. The detailed computational results of heat and mass transfer rate, temperature, concentration and flow fields are presented and discussed for a distinct range of significant physical parameters. The results demonstrated that increasing the angle of the inclination factor increases fluid flow. In light of buoyancy, when the annular cavity is set downward, the enhanced shear velocity is transported upwards, where it reaches its optimal temperature. The higher temperature difference leads to augmented dynamic fluid motion, particularly in the radial direction, as the system seeks to balance the thermal energy through convective transfer. The Brownian motion parameter has abrupt mobility of nanoparticles in liquid, which promotes particle collisions with liquid molecules, yielding kinetic energy. Increased values of thermophoretic parameters augment the thermophoresis force. Thermophoretic particle deposition increases the concentration of nanoparticles in an annulus due to the migration of particles from hot to cold regions under the influence of temperature gradient. The heat and mass transfer characteristics of ternary hybrid nanofluid are forecasted through an artificial neural network-based Levenberg–Marquardt backpropagated algorithm. The built model shows the heat and mass transfer rate root mean squared values through the Levenberg–Marquardt algorithm as one and mean squared error values as 1e-07 and 1e-08 respectively.

Light Transfers Through a Koch Shape Cloud

AbstractModeling radiative transfer in a 3D cloudy atmosphere is critical to climate projections. A recently developed fast 3D radiation parameterization scheme gains some success in quantifying horizontal radiative transfer through cloud sides using cloud area fraction. Based on 3D Monte Carlo simulations of radiative transfer through an idealized single‐layer cloud with Koch‐shaped fractal geometry edges, here we show that radiative energy transport through cloud sides correlates more significantly with cloud area fraction than with cloud perimeter length. The results exemplify the importance of accounting for the horizontal radiative energy exchanges between cloud‐free and cloudy regions with cloud area fraction. Results from additional sensitivity simulations show that increased cloud vertical extent often enhances cloud‐side sunlight leak more significantly than cloud‐side sunlight interception. At low sun elevations, cloud‐side sunlight interception is enhanced more than cloud‐side sunlight leak does with the increase of cloud mass.

X-ray polarisation in AGN circumnuclear media

Context. Cold gas and dust reprocess the central X-ray emission of active galactic nuclei (AGN), producing characteristic spectro-polarimetric features in the X-ray band. The recent launch of IXPE allows for observations of this X-ray polarisation signal, which encodes unique information on the parsec-scale circumnuclear medium of obscured AGN. However, the models for interpreting these polarimetric data are under-explored and do not reach the same level of sophistication as the corresponding spectral models. Aims. We aim at closing the gap between the spectral and spectro-polarimetric modelling of AGN circumnuclear media in the X-ray band by providing the tools for simulating X-ray polarisation in complex geometries of cold gas alongside X-ray spectra. Methods. We lay out the framework for X-ray polarisation in 3D radiative transfer simulations and provide an implementation to the 3D radiative transfer code SKIRT, focussing on (de)polarisation due to scattering and fluorescent re-emission. As an application, we explored the spectro-polarimetric properties of a 2D toroidal reprocessor of cold gas, modelling the circumnuclear medium of AGN. Results. For the 2D torus model, we find a complex behaviour of the polarisation angle with photon energy, which we interpret as a balance between the reprocessed photon flux originating from different sky regions, with a direct link to the torus geometry. We calculated a large grid of AGN torus models and demonstrated how spatially resolved X-ray polarisation maps could form a useful tool for interpreting the geometrical information that is encoded in IXPE observations. With this work, we release high-resolution AGN torus templates that simultaneously describe X-ray spectra and spectro-polarimetry for observational data fitting with XSPEC. Conclusions. The SKIRT code can now model X-ray polarisation simultaneously with X-ray spectra and provide synthetic spectro-polarimetric observations for complex 3D circumnuclear media, with all features of the established SKIRT framework available.

Benchmark simulations of radiative transfer in participating binary stochastic mixtures in two dimensions

We study radiative transfer in participating binary stochastic mixtures in two dimensions (2D) by developing an accurate and efficient simulation tool. For two different sets of physical parameters, 2D benchmark results are presented, and it is found that the influence of the stochastic mixture on radiative transfer is clearly parameter-dependent. Our results confirm that previous multidimensional results obtained in different studies are basically consistent, which is interpreted in terms of the relationship between the photon mean free path lp and the system size L. Nonlinear effects, including those due to scattering and radiation–material coupling, are also discussed. To further understand the particle size effect, we employ a dimensionless parameter lp/L, from which a critical particle size can be derived. On the basis of further 2D simulations, we find that an inhomogeneous mix is obtained for lp/L &amp;gt; 0.1. Furthermore, 2D material temperature distributions reveal that self-shielding and particle–particle shielding of radiation occur, and are enhanced when lp/L is increased. Our work is expected to provide benchmark results to verify proposed homogenized models and/or other codes for stochastic radiative transfer in realistic physical scenarios.