Three-dimensional Radiative Transfer Research Articles

Biases in Shortwave Three-Dimensional Radiative Transfer Calculations for High-Resolution Numerical Models

This study investigated biases of diffuse radiation in a look-up table approach, which pre-computed the sequential ray tracing to avoid heavy computation in full three-dimensional radiative transfer calculation. We introduced corrections that enhanced directionality of radiative propagation in the solar angle and horizontal direction. By comparing irradiance calculations with and without the corrections for cloudy field in an idealized atmospheric simulation, it was found that the corrections helped mitigate vertically localized false signals by diffuse irradiance. The results suggested that the two types of directionalities are important to accurately represent the three-dimensional transfer of diffuse radiation in an inhomogeneous atmosphere.

Explicitly Reconstructing RAMI-V Scenes for Accurate 3-Dimensional Radiative Transfer Simulation Using the LESS Model

Radiative transfer (RT) simulation based on reconstructed 3-dimensional (3D) vegetation scenarios can promote the validation and development of various retrieval algorithms to monitor the growing states of vegetation in large-scale, multi-angular, and multi-sensor ways. The radiation transfer model intercomparison (RAMI) has made great contributions to providing abstract and actual 3D vegetation scenarios, and to the benchmarking of RT models under developed evaluation systems. To date, RAMI has been updated to the fifth phase (RAMI-V). In this study, we try to implement explicit conversion from all the RAMI-V scenes to generic structural models in the Wavefront OBJ format. These reconstructed scenes are applied in the LESS RT model to probe the ability of its RT solvers to simulate all sorts of remote sensing observations and radiative budget, including the bidirectional reflectance factor (BRF), albedo, fraction of photosynthetically active radiation absorbed by vegetation, and threshold hemispherical photograph (THP). BRF simulations fully explain angle effects as well as variation and robustness of the normalized difference vegetation index. Energy conservation is well validated between simulated absorption and albedo. The gap fraction derived from THP is analyzed in directional and total situations. In addition, this paper guides us how to simplify basic geometries and tune the illumination resolution (0.02 is optimal) to balance the simulation accuracy and efficiency. The generic structural models and reliable simulation results can be referenced by other RT models and retrieval algorithms.

CANOPY STRUCTURAL EFFECTS ON BIDIRECTIONAL REFLECTANCE SIMULATED BY THE LESS MODEL: A CASE STUDY OF PICEA CRASSIFOLIA FORESTS

Abstract. Surface albedo is a dominant factor affecting the earth energy balance. Bidirectional reflectance distribution function (BRDF) describes the anisotropic surface reflection of solar radiation. Bidirectional effect is especially noticeable in the forest canopies with three-dimensional canopy structure. Thus, it is challenging to evaluate the canopy structural effects on BRDF using traditional radiative transfer modelling methods, where leaf in canopies is generally assumed to be homogeneous. LESS, a ray-tracing-based three-dimensional (3D) radiative transfer model can effectively simulate bidirectional reflectance factor while fully considering multi-component spectral and structural characteristics of vegetation. In this study, we applied the LESS model to evaluate the impacts of changes in leaf area index (LAI) on canopy reflectance in a Picea crassifolia forest. First, canopy structural parameters obtained from forest inventory were used to construct forest scenes and drive the LESS model. Then, we validated the simulation accuracy of the LESS model against BRDF calculated from MODIS BRDF parameter product using kernel-driven Ross-Li bi-directional reflectance function. Finally, we constructed forest scenes with different LAI to investigate the canopy structural effects on BRDF. We found that the BRDF simulated by the LESS model is in good accordance with the MODIS BRDF data in the red (R2 = 0.97, RMSE = 0.03) and NIR (R2 = 0.94, RMSE = 0.05) bands. The simulated canopy reflectance in the red band displayed ‘dome’ shape and decreased with increasing LAI. In contrast, canopy reflectance in the NIR band displayed ‘bowl’ shape and increased with increasing LAI. Our study highlighted the sensitivity of canopy BRDF to changes in canopy structure and have implications for retrieving LAI from BRDF data.

3D radiative transfer modeling of structurally complex forest canopies through a lightweight boundary-based description of leaf clusters

Three-dimensional (3D) radiative transfer simulations are critical for studying the radiometric properties of canopies. Efficient and easy-to-use 3D radiative transfer models are required by remote sensing inversion and many validation applications. Extensive efforts have been made to improve the computational efficiency, accuracy, and useability of 3D radiative transfer models. This study focuses on the abstraction of canopies for 3D radiative transfer simulations by proposing a lightweight boundary-based description of leaf clusters (B-cluster) to ease the creation of 3D scenes while keeping the simulation as accurate as possible. B-cluster partitions a tree crown into sub-crown leaf clusters and abstracts each of them into a turbid medium enclosed by a complex and tight boundary, while terrain and branches are described with precise mesh surfaces. The radiative transfer simulation within B-cluster has been developed based on an efficient Monte Carlo path-tracing algorithm and implemented in the LargE-Scale remote sensing data and image Simulation framework (LESS) model by considering the presence of both turbid medium and surface scattering. The performance of the model was assessed by comparing with original LESS version, which describes all landscape elements with mesh surfaces (here called M-surface approach), and with a uniform voxel-based approach (U-voxel) in terms of the multiangle bidirectional reflectance factor (BRF) as well as with pixel-wise images. Results show that B-cluster is highly consistent with M-surface in abstract canopies (mean normalized absolute BRF differences δ¯ < 2%) and in realistic forest stand (δ¯ < 5% at 5-m resolution) with considerably reduced requirements for computational memory. Compared with U-voxel, B-cluster is also more robust and better at describing canopy structures with different levels of detail. B-cluster enables to quickly construct accurate 3D scenes with reduced requirements of computational resources. It is also a unified and scale-adaptive approach that can describe crowns as simple as geometric primitives and as complex as explicitly described meshes. The newly proposed approach has been released in new LESS versions at http://lessrt.org/.

3D photon conserving code for time-dependent general relativistic radiative transfer: CARTOON

ABSTRACT We develop the three-dimensional general relativistic radiative transfer code: CARTOON (Calculation code of Authentic Radiative Transfer based On phOton Number conservation in curved space–time) which is improved from the two-dimensional code: ARTIST developed by Takahashi &amp; Umemura (2017). In CARTOON, the frequency-integrated general relativistic radiative transfer equation is solved in a photon number-conserving manner, and the isotropic and coherent scattering in the zero angular momentum observers (ZAMO) frame and the fluid rest frame is incorporated. By calculating the average energy of photons, energy conservation of the radiation is also guaranteed. With the test calculations in two-dimensional and three-dimensional space, we have demonstrated that the wavefront propagation in black hole space–time can be correctly solved in CARTOON conserving photon numbers. The position of the wavefront coincides with the analytical solution and the number of photons remains constant until the wavefront reaches the event horizon. We also solve the radiative transfer equation on the geodesic reaching the observer’s screen. The time variation of the intensity map on the observer’s screen can be simultaneously and consistently calculated with the time variation of the radiation field around the black hole. In addition, the black hole shadow can be reproduced in moderately optically thin situations.

Inferring properties of dust in supernovae with neural networks

Context. Determining properties of dust that formed in and around supernovae from observations remains challenging. This may be due to either incomplete coverage of data in wavelength or time, but also due to often inconspicuous signatures of dust in the observed data. Aims. Here we address this challenge using modern machine learning methods to determine the amount and temperature of dust as well as its composition from a large set of simulated data. We aim to quantify if such methods are suitable to infer quantities and properties of dust from future observations of supernovae. Methods. We developed a neural network consisting of eight fully connected layers and an output layer with specified activation functions that allowed us to predict the dust mass, temperature, and composition as well as their respective uncertainties for each single supernova of a large set of simulated supernova spectral energy distributions (SEDs). We produced the large set of supernova SEDs for a wide range of different supernovae and dust properties using the advanced, fully three-dimensional radiative transfer code MOCASSIN. We then convolved each SED with the entire suite of James Webb Space Telescope (JWST) bandpass filters to synthesise a photometric data set. We split this data set into three subsets which were used to train, validate, and test the neural network. To find out how accurately the neural network can predict the dust mass, temperature, and composition from the simulated data, we considered three different scenarios. First, we adopted a uniform distance of ~0.43 Mpc for all simulated SEDs. Next we uniformly distributed all simulated SEDs within a volume of 0.43–65 Mpc and, finally, we artificially added random noise corresponding to a photometric uncertainty of 0.1 mag. Lastly, we conducted a feature importance analysis via SHapley Additive explanations (SHAP) to find the minimum set of JWST bandpass filters required to predict the selected dust quantities with an accuracy that is comparable to standard methods in the literature. Results. We find that our neural network performs best for the scenario in which all SEDs are at the same distance and for a minimum subset of seven JWST bandpass filters within a wavelength range 3−25 µm. This results in rather small root-mean-square errors (RMSEs) of ~0.08 dex and ~42 K for the most reliable predicted dust masses and temperatures, respectively. For the scenario in which SEDs are distributed out to 65 Mpc and contain synthetic noise, the most reliable predicted dust masses and temperatures achieve an RMSE of ~0.12 dex and ~38 K, respectively. Thus, in all scenarios, both predicted dust quantities have smaller predicted uncertainties compared to those in the literature achieved with common SED fitting methods of actual observations of supernovae. Moreover, our neural network can well distinguish between the different dust species included in our work, reaching a classification accuracy of up to 95% for carbon and 99% for silicate dust. Conclusions. Although we trained, validated, and tested our neural network entirely on simulated SEDs, our analysis shows that a suite of JWST bandpass filters containing NIRCam F070W, F140M, F356W and F480M as well as MIRI F560W, F770W, F1000W, F1130W, F1500W, and F1800W filters are likely the most important filters needed to derive the quantities and determine the properties of dust that formed in and around supernovae from future observations. We tested this on selected optical to infrared data of SN 1987A at 615 days past explosion and find good agreement with dust masses and temperatures inferred with standard fitting methods in the literature.

Efficient calculation of radiative intensity in three-dimensional atmospheres based on the Pn-IMS truncation method with a backward ray tracing system

The computational efficiency of solving the radiative transfer (RT) equation is an important issue for remote sensing and the monitoring of aerosols, clouds, and radiation, all of which involve the analysis of large volumes of data. In this study, based on the Improved Multiple and Single scattering (IMS) correction method, a backward ray tracing method was developed for the three-dimensional RT calculation (3D-IMS). We extended the IMS method to the 3D-RT problem using a backward ray tracing Monte Carlo system for calculation of both upward and downward radiance fields. In the 3D-IMS method, photons are assumed to be of two orthogonal types: one has less anisotropic scattering, while the other has highly anisotropic scattering decomposed by the delta-M method of Wiscombe (1977) to truncate a spherical harmonics expansion series. In this manner, an accurate radiance field is reconstructed by two separated ray tracings in the two independent spaces (i.e., delta-M and IMS spaces). Compared to the ordinary Monte Carlo method with the original phase function, the 3D-IMS method can better reduce the total photon number for the reconstruction of radiances. The performance of the 3D-IMS method was evaluated for plane-parallel atmospheres and for the case-4 experiment datasets of the Intercomparison of 3D Radiation Codes (I3RC) project. Among solvers included in the intercomparison, in cases with both completely backward and lateral scattering regions, the 3D-IMS method belonged to the group near the I3RC consensus mean data.

Evaluation of the impact of crop residue on fractional vegetation cover estimation by vegetation indices over conservation tillage cropland: a simulation study

ABSTRACT Accurate estimation of fractional vegetation cover (FVC) is of great significance to agricultural production. Crop residue management affect crop residue cover (CRC) over croplands. Crop and crop residue on the soil surface both contribute to overall canopy reflectance. Few studies, however, have examined the effect of crop residue on vegetation indices (VIs) and estimated FVC. The present study evaluated the response of eight commonly used VIs to crop residues and FVC uncertainty caused by crop residue based on the dimidiate pixel model (DPM) by using simulated reflectance of low-tilled cropland via a three-dimensional radiative transfer model. The absolute difference (AD) was used to quantify the spectral difference between crop residues and soils in red and near infrared wavelengths. Increases in normalized difference VI (NDVI), ratio VI (RVI), transformed soil-adjusted VI (TSAVI), and normalized difference phenology index (NDPI) were observed when green crops were mixed with crop residue that had negative ADs with soils, but decreases in enhance VI (EVI), perpendicular VI (PVI), SAVI, and litter-soil-adjusted VI (L-SAVI) were observed when crop residue was present under medium and high vegetation cover. The presence of crop residue with a positive AD with soils reduced NDVI, RVI, TSAVI, and NDPI while increased the other VIs. Crop residue had the least impact on EVI- and SAVI-based DPMs, with FVC-estimated uncertainty less than 0.1, followed by the NDPI- and L-SAVI-based model, while DPMs based on NDVI- and RVI performed poorly. Each VI-based DPM’s estimated uncertainty was highly correlated with AD values. Furthermore, the majority of the VI-based models were sensitive to solar position except for the NDPI-based model. Our findings highlight the need of considering the impact of crop residue on FVC retrieval over low-tilled cropland in future research.

Transient three-dimensional radiative heat transfer analysis of a turbulent diffusion flame-with a focus on the effect of angular discretization scheme

Radiation modeling is a challenging and computational expensive task for turbulent combustion modeling of various fuels. Radiative intensity varies greatly in the angular direction due to turbulent fluctuations of temperature and species fields. A large number of rays are needed in the discrete ordinates method (DOM) or the finite volume method (FVM) to describe the angular variations. Determining the adequate number of rays is essential for the efficient modeling of radiation heat transfer. For this purpose, the effect of angular scheme on predicting the transient three-dimensional radiation heat transfer of a turbulent diffusion flame is investigated. Results show that a smaller number of rays produce strong ray effects and may generate significant errors for radiative heat flux prediction on surrounding walls, while the angular scheme has negligible influence on the radiative heat source. Transient radiative heat fluxes on different walls are also analyzed in detail, and they show completely different contours with unimodal frequency behavior. Recommendation for radiation modeling strategies is proposed for turbulent combustion modeling.

The transfer of polarized radiation in resonance lines with partial frequency redistribution, J-state interference, and arbitrary magnetic fields

Aims. We present the theoretical framework and numerical methods we have implemented to solve the problem of the generation and transfer of polarized radiation in spectral lines without assuming local thermodynamical equilibrium, while accounting for scattering polarization, partial frequency redistribution (due to both the Doppler effect and elastic collisions), J-state interference, and hyperfine structure. The resulting radiative transfer code allows one to model the impact of magnetic fields of an arbitrary strength and orientation through the Hanle, incomplete Paschen-Back, and magneto-optical effects. We also evaluate the suitability of a series of approximations for modeling the scattering polarization in the wings of strong resonance lines at a much lower computational cost, which is particularly valuable for the numerically intensive case of three-dimensional radiative transfer. Methods. We examine the suitability of the considered approximations by using our radiative transfer code to model the Stokes profiles of the Mg II h &amp; k lines and of the H I Lyman-α line in magnetized one-dimensional models of the solar atmosphere. Results. Neglecting Doppler redistribution in the scattering processes that are unperturbed by elastic collisions (i.e., treating them as coherent in the observer’s frame) produces a negligible error in the scattering polarization wings of the Mg II resonance lines and a minor one in the Lyman-α wings, although it is unsuitable to model the cores of these lines. For both lines, the scattering processes that are perturbed by elastic collisions only give a significant contribution to the intensity component of the emissivity. Neglecting collisional as well as Doppler redistribution (so that all scattering processes are coherent) represents a rough but suitable approximation for the wings of the Mg II resonance lines, but a very poor one for the Lyman-α wings. The magnetic sensitivity in the scattering polarization wings of the considered lines can be modeled by accounting for the magnetic field in only the ηI and ρV coefficients of the Stokes-vector transfer equation (i.e., using the zero-field expression for the emissivity).

Observability of forming planets and their circumplanetary discs – IV. With JWST and ELT

ABSTRACT To understand the potential for observing forming planets and their circumplanetary discs (CPDs) with James Webb Space Telescope (JWST) and Extremely Large Telescope (ELT), we created mock observations from three-dimensional radiative hydrodynamic simulations and radiative transfer post-processing for planets with 10, 5, and 1 Jupiter and 1 Saturn masses with orbital separation of 50 and 30 au in 0, 30, and 60○ inclinations. Instrumental effects were then simulated with Mirage for JWST/NIRCam and NIRISS, MIRISim for JWST/MIRI, and SimCADO and SimMETIS for ELT/MICADO and METIS. We found that the longer wavelengths (mid-infrared and beyond) are the best to detect CPDs, since they allow CPD of planet with smaller mass to be detected. MIRI on JWST and METIS on ELT offer the best possibility on these telescopes. Specifically, below 3 $\mu{\rm m}$, only 10 MJup planets with their CPDs are detectable with NIRCam and MICADO. 5 MJup planets are only detectable if at 30 au (i.e. closer) orbital separation. Planets above 5 MJup with their CPDs are detectable between 3 and 5 $\mu{\rm m}$ with NIRCam and METIS L/M band, or above 10 $\mu{\rm m}$ with MIRI and METIS N band. For ≤1 MJup planets &amp;gt;15 $\mu{\rm m}$ are needed, where MIRI uniquely offers imaging capability. We present magnitudes and spectral energy distributions for separate components of the planet + CPD + circumstellar disc (CSD) system, to differentiate the extinction rates of CPDs and CSDs and to provide predictions for observational proposals. Because the CPD turns out to be the main absorber of the planet’s emission, especially &amp;lt;10 $\mu{\rm m}$, this makes the detection of forming planets quite challenging.

Evaluation of Atmospheric Correction Algorithms over Lakes for High-Resolution Multispectral Imagery: Implications of Adjacency Effect

Atmospheric correction of satellite optical imagery over inland waters is a key remaining challenge in aquatic remote sensing. This is due to numerous confounding factors such as the complexity of water optical properties, the surface glint, the heterogeneous nature of atmospheric aerosols, and the proximity of bright land surfaces. This combination of factors makes it difficult to retrieve accurate information about the system observed. Moreover, the impact of radiance coming from adjacent land (adjacency effects) in complex geometries further adds to this challenge, especially for small lakes. In this study, ten atmospheric correction algorithms were evaluated for high-resolution multispectral imagery of Landsat-8 Operational Land Imager and Sentinel-2 MultiSpectral Instrument using in situ optical measurements from ~300 lakes across Canada. The results of the validation show that the performance of the algorithms varies by spectral band and evaluation metrics. The dark spectrum fitting algorithm had the best performance in terms of similarity angle (spectral shape), while the neural network-based models showed the lowest errors and bias per band. However, none of the tested atmospheric correction algorithms meet a 30% retrieval accuracy target across all the visible bands, likely due to uncorrected adjacency effects. To quantify this process, three-dimensional radiative transfer simulations were performed and compared to satellite observations. These simulations show that up to 60% of the top of atmosphere reflectance in the near-infrared bands over the lake was from the adjacent lands covered with green vegetation. The significance of these adjacency effects on atmospheric correction has been analyzed qualitatively, and potential efforts to improve the atmospheric correction algorithms are discussed.

An Angular Discretization Method Using Repulsive Particles for the Three-Dimensional Radiative Transfer Equation

An Angular Discretization Method Using Repulsive Particles for the Three-Dimensional Radiative Transfer Equation

Modeling the arc and ring structures in the HD 143006 disk

Rings and asymmetries in protoplanetary disks are considered as signposts of ongoing planet formation. In this work, we conduct three-dimensional radiative transfer simulations to model the intriguing disk around HD 143006 that has three dust rings and a bright arc. A complex geometric configuration, with a misaligned inner disk, is assumed to account for the asymmetric structures. The two-dimensional surface density is constructed by iteratively fitting the ALMA data. We find that the dust temperature displays a notable discontinuity at the boundary of the misalignment. The ring masses range from 0.6 to 16Mearth that are systematically lower than those inferred in the younger HL Tau disk. The arc occupies nearly 20% of the total dust mass. Such a high mass fraction of dust grains concentrated in a local region is consistent with the mechanism of dust trapping into vortices. Assuming a gas-to-dust mass ratio of 30 that is constant throughout the disk, the dense and cold arc is close to the threshold of being gravitationally unstable, with the Toomre parameter Q~1.3. Nevertheless, our estimate of Q relies on the assumption for the unknown gas-to-dust mass ratio. Adopting a lower gas-to-dust mass ratio would increase the inferred Q value. Follow-up high resolution observations of dust and gas lines are needed to clarify the origin of the substructures.

Research on Space-Based Visible Detection for Conical Space Targets

We conducted research into the visible light detection of conical space targets and proposed a method to determine the caliber of a space-based detection system. We constructed a three-dimensional conical space target radiation transfer model and analyzed the effect of the phase angle between the solar incident direction, the detector’s bore sight direction, and the conical target inclination on the radiation intensity of the space target received by the detector. Finally, we obtained the threshold caliber which can meet the detection requirements of the system with the system signal-to-noise ratio as the evaluation standard, and we took the SBV sensor as an example to verify that the caliber determination method in this paper is effective.

A CRASH simulation of the contribution of binary stars to the epoch of reionization

ABSTRACT We use a set of three-dimensional (3D) radiative transfer simulations to study the effect that a large fraction of binary stars in galaxies during the epoch of reionization has on the physical properties of the intergalactic medium (i.e. the gas temperature and the ionization state of hydrogen and helium), on the topology of the ionized bubbles and on the 21 cm power spectra. Consistently to previous literature, we find that the inclusion of binary stars can speed up the reionization process of H i and He i, while He ii reionization is still dominated by more energetic sources, especially accreting black holes. The earlier ionization attained with binary stars allows for more time for cooling and recombination so that gas fully ionized by binary stars is typically colder than gas ionized by single stars at any given redshift. With the same volume averaged ionization fraction, the inclusion of binary stars results in fewer small ionized bubbles and more large ones, with visible effects also on the large scales of the 21 cm power spectrum.

A SUBLIME 3D Model for Cometary Coma Emission: The Hypervolatile-rich Comet C/2016 R2 (PanSTARRS)

Abstract The coma of comet C/2016 R2 (PanSTARRS) is one of the most chemically peculiar ever observed, in particular due to its extremely high CO/H2O and N 2 + /H2O ratios, and unusual trace volatile abundances. However, the complex shape of its CO emission lines, as well as uncertainties in the coma structure and excitation, has lead to ambiguities in the total CO production rate. We performed high-resolution, spatially, spectrally, and temporally resolved CO observations using the James Clerk Maxwell Telescope and Submillimeter Array to elucidate the outgassing behavior of C/2016 R2. Results are analyzed using a new, time-dependent, three-dimensional radiative transfer code (SUBlimating gases in LIME; SUBLIME, based on the open-source version of the LIne Modeling Engine), incorporating for the first time, accurate state-to-state collisional rate coefficients for the CO–CO system. The total CO production rate was found to be in the range of (3.8 − 7.6) × 1028 s−1 between 2018 January 13 and February 1 (at r H = 2.8–2.9 au), with a mean value of (5.3 ± 0.6) × 1028 s−1. The emission is concentrated in a near-sunward jet, with a half-opening angle of ∼62° and an outflow velocity of 0.51 ± 0.01 km s−1, compared to 0.25 ± 0.01 km s−1 in the ambient (and nightside) coma. Evidence was also found for an extended source of CO emission, possibly due to icy grain sublimation around 1.2 × 105 km from the nucleus. Based on the coma molecular abundances, we propose that the nucleus ices of C/2016 R2 can be divided into a rapidly sublimating apolar phase, rich in CO, CO2, N2, and CH3OH, and a predominantly frozen (or less abundant), polar phase containing more H2O, CH4, H2CO, and HCN.

Novel framework for the three-dimensional NLTE inverse problem

The inversion of spectropolarimetric observations of the solar upper atmosphere is one of the most challenging goals in solar physics. If we account for all relevant ingredients of the spectral line formation process, such as the three-dimensional (3D) radiative transfer out of local thermodynamic equilibrium (NLTE), the task becomes extremely computationally expensive. Instead of generalizing 1D methods to 3D, we have developed a new approach to the inverse problem. In our meshfree method, we do not consider the requirement of 3D NLTE consistency as an obstacle, but as a natural regularization with respect to the traditional pixel-by-pixel methods. This leads to more robust and less ambiguous solutions. We solve the 3D NLTE inverse problem as an unconstrained global minimization problem that avoids repetitive evaluations of the Λ operator. Apart from the 3D NLTE consistency, the method allows us to easily include additional conditions of physical consistency such as the zero divergence of the magnetic field. Stochastic ingredients make the method less prone to ending up within the local minima of the loss function. Our method is capable of solving the inverse problem faster by several orders of magnitude than by using grid-based methods. The method can provide accurate and physically consistent results if sufficient computing time is available, along with approximate solutions in the case of very complex plasma structures or limited computing time.

Spectral and spatial characteristic behaviour of three-dimensional radiation transfer in SF6 switching arcs

The spectral and spatial characteristics of three-dimensional radiation transfer across an arc column of 0.08 m long, typical in high-voltage gas blast circuit breakers, has been studied in detail. The arc column under study corresponds to an instantaneous current of 15 kA in SF6 gas at a pressure of 10 bar. Our results show that to calculate the radiative flux divergence (as a volumetric energy source), only a segment of the arc column of 0.024 m in thickness needs to be considered to attain an accuracy of better than 90%. Photons with a frequency lower than 2 × 1015 Hz (150 nm in wavelength) can travel a considerable distance (>0.02 m) with an intensity attenuation factor of 0.2–0.8. Above 2 × 1015 Hz, only photons from the continuum spectrum can travel up to 0.015 m and line emission is absorbed within a distance of typically 0.0005 m, i.e. the arcing gas is optically thick to these photons. The gas within a cross-section of the arc column can be divided into a net emission core and a net absorption zone. The 55%–75% of the radiation emitted from the core is reabsorbed. The starting position of the net absorption zone sits within the temperature interval of 75%–80% of the maximum temperature on the axis. The quantitative information from this work is expected to serve as baseline data for developing improved approximate models for radiation transfer calculation in SF6 switching arcs.

Effects of Mixture Mode on the Canopy Bidirectional Reflectance of Coniferous–Broadleaved Mixed Plantations

One of the main initiatives for China to achieve the goal of being carbon neutral before 2060 is transforming monocultures into mixed plantations in subtropical China, because mixed forests possess a higher quality than monocultures in various ways. Very high spatial resolution (VHR) satellite imagery is very promising to precisely monitor the transformation process under the premise of clarifying the canopy reflectance anisotropy of mixed plantations. However, it is almost impossible to understand the canopy reflectance anisotropy of mixed plantations with real satellite data due to the extreme lack of multiangular VHR satellite images. In this study, the effects of the mixture mode on the canopy bidirectional reflectance factor (BRF) were comprehensively analyzed with simulated VHR images. The three-dimensional (3D) Discrete Anisotropic Radiative Transfer model (DART) was used to construct a pure coniferous scene, a pure broadleaved scene, and 27 coniferous–broadleaved mixed plantation scenes containing 3 mixture patterns (i.e., mixed by single trees, mixed by stripes, and mixed by patches) and 9 mixing proportions (i.e., from 10% to 90% with the interval of 10%), and to simulate red (R) and near-infrared (NIR) VHR images for these 3D scenes at both the solar principal plane (SPP) and perpendicular plane (PP) under different solar-viewing geometries. Negative correlations were generally found between the canopy BRF and the ratio of conifers in a mixed stand. The anisotropy of conifer dominated plantations is more prominent than broadleaf dominated plantations, especially for the single tree mixture. Although the level of anisotropy is much lower for PP than SPP, it should not be ignored, especially for the R band. Observations under large viewing zenith angles at PP are more preferred to study the effect of mixing proportions, followed by forward observations at SPP. The R band image has higher potential to distinguish mixture patterns for broadleaf-dominated situations, while the NIR band image has a higher potential for conifer-dominated situations. Furthermore, the canopy BRF generally increases with the solar zenith angle, and one meter can be considered as the optimal spatial resolution for the optical monitoring of the mixture mode. The findings of the current study add some valuable theoretical knowledge for the accurate monitoring of coniferous–broadleaved mixed plantations with VHR imagery.