Radiative transfer as a Bayesian linear regression problem

Physically-based approaches for estimating Leaf Area Index (LAI) using remote sensing data rely on radiative transfer (RT) models. Currently, many RT models are freely available, but determining the appropriate RT model for LAI retrieval is still problematic. This study aims to evaluate the necessity of RT model selection for LAI retrieval and to propose a retrieval methodology using different RT models for different vegetation types. Both actual experimental observations and RT model simulations were used to conduct the evaluation. Each of them includes needleleaf forests and croplands, which have contrasting structural attributes. The scattering from arbitrarily inclined leaves (SAIL) model and the four-scale model, which are 1D and 3D RT models, respectively, were used to simulate the synthetic test datasets. The experimental test dataset was established through two field campaigns conducted in the Heihe River Basin. The results show that the realistic representation of canopy structure in RT models is very important for LAI retrieval. If an unsuitable RT model is used, then the root mean squared error (RMSE) will increase from 0.43 to 0.60 in croplands and from 0.52 to 0.63 in forests. In addition, an RT model’s potential to retrieve LAI is limited by the availability of a priori information on RT model parameters. 3D RT models require more a priori information, which makes them have poorer generalization capability than 1D models. Therefore, physically-based retrieval algorithms should embed more than one RT model to account for the availability of a priori information and variations in structural attributes among different vegetation types.

Radiative transfer models (RTMs) are often used to retrieve biophysical parameters from earth observation data. RTMs with multi-temporal and realistic forest representations enable radiative transfer (RT) modeling for real-world dynamic processes. To achieve more realistic RT modeling for dynamic forest processes, this study presents the 3D-explicit reconstruction of a typical temperate deciduous forest in 2015 and 2022. We demonstrate for the first time the potential use of bitemporal 3D-explicit RT modeling from terrestrial laser scanning on the forward modeling and quantitative interpretation of: (1) remote sensing (RS) observations of leaf area index (LAI), fraction of absorbed photosynthetically active radiation (FAPAR), and canopy light extinction, and (2) the impact of canopy gap dynamics on light availability of explicit locations. Results showed that, compared to the 2015 scene, the hemispherical-directional reflectance factor (HDRF) of the 2022 forest scene relatively decreased by 3.8% and the leaf FAPAR relatively increased by 5.4%. At explicit locations where canopy gaps significantly changed between the 2015 scene and the 2022 scene, only under diffuse light did the branch damage and closing gap significantly impact ground light availability. This study provides the first bitemporal RT comparison based on the 3D RT modeling, which uses one of the most realistic bitemporal forest scenes as the structural input. This bitemporal 3D-explicit forest RT modeling allows spatially explicit modeling over time under fully controlled experimental conditions in one of the most realistic virtual environments, thus delivering a powerful tool for studying canopy light regimes as impacted by dynamics in forest structure and developing RS inversion schemes on forest structural changes.

A passive and active microwave-vector radiative transfer (PAM-VRT) model

Context. Radiative transfer modelling of expanding stellar envelopes is an important task in their analysis. To account for inhomogeneities and deviations from spherical symmetry, it is necessary to develop a 3 D approach to radiative transfer modelling. Aims. We present a 3 D Monte Carlo code for radiative transfer modelling, which is aimed to calculate the plasma ionisation and excitation state with the statistical equilibrium equations, moreover, to implement photon-matter coupling. As a first step, we present our Monte Carlo radiation transfer routines developed and tested from scratch. Methods. The background model atmosphere (the temperature, density, and velocity structure) can use an arbitrary grid referred to as the modGrid. The radiative transfer was solved using the Monte Carlo method in a Cartesian grid, referred to as the propGrid. This Cartesian grid was created based on the structure of the modGrid; correspondence between these two grids was set at the beginning of the calculations and then kept fixed. The propGrid can be either regular or adaptive; two modes of adaptive grids were tested. The accuracy and calculation speed for different propGrids was analysed. Photon interaction with matter was handled using the Lucy’s macroatom approach. Test calculations using our code were compared with the results obtained by a different Monte Carlo radiative transfer code. Results. Our method and the related code for the 3 D radiative transfer using the Monte Carlo and macroatom methods offer an accurate and reliable solution for the radiative transfer problem, and are especially promising for the inclusion and treatment of 3 D inhomogeneities.

A Fast All-sky Radiation Model for Solar applications (FARMS): Algorithm and performance evaluation

Snow-depth retrieval from passive microwave observations without a priori information is a highly undetermined problem. Achieving accurate snow-depth retrievals requires a priori information on the snowpack properties, such as grain size, density, physical temperature, and stratigraphy. On a practical level, however, retrieval algorithms must consider prior information, while minimizing the dependence on it, as accurate ancillary data are not globally available. In this study, we build on the previously published Bayesian Algorithm for Snow Water Equivalent Estimation (BASE) to retrieve snow depth using an airborne passive microwave data set over the tundra snow in the Eureka region. The method computes the optimal estimates of snow depth, density, grain size, and other variables, given the brightness temperature observations and prior information, using Markov chain Monte Carlo (MCMC). The airborne data set includes passive microwave brightness temperature (T <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">b</sub> ) at 18.7 and 36.5 GHz. The in situ measurements of the snow depth provide validation data for 464 sensor footprints. The microwave radiative transfer (RT) model used is the Dense Media RT-Multilayered (DMRT-ML) model. We use a two-layer wind slab and depth hoar assumption based on the local snow cover knowledge from the previous research on the study area. To improve our understanding of the results using the airborne T <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">b</sub> s, the inversion was also applied using the synthetic observations, where T <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">b</sub> s were generated from the RT model. For the case with synthetic observations, the snow-depth RMSE was 0.07 cm. When the airborne T <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">b</sub> s are used, the snow-depth RMSE was 21.8 cm. This discrepancy is due to the large spatial variability in the MagnaProbe snow-depth measurements and the fact that not all physical processes affecting the airborne T <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">b</sub> s are represented in the RT model. Our work verifies the feasibility and applicability of the proposed methodology regionally for the airborne retrievals and reinforces the tractable applicability of a physics-based RT model in the SWE retrievals.

Investigation of radiative heat transfer in fixed bed biomass furnaces

Context. Interstellar dust absorbs stellar light very efficiently, thus shaping the energy output of galaxies. Studying the impact of different stellar populations on the dust heating continues to be a challenge because it requires decoupling the relative geometry of stars and dust and also involves complex processes such as scattering and non-local dust heating. Aims. We aim to constrain the relative distribution of dust and stellar populations in the spiral galaxy M 81 and create a realistic model of the radiation field that adequately describes the observations. By investigating the dust-starlight interaction on local scales, we want to quantify the contribution of young and old stellar populations to the dust heating. We aim to standardise the setup and model selection of such inverse radiative transfer simulations so these can be used for comparable modelling of other nearby galaxies. Methods. We present a semi-automated radiative transfer modelling pipeline that implements necessary steps such as the geometric model construction and the normalisation of the components through an optimisation routine. We used the Monte Carlo radiative transfer code SKIRT to calculate a self-consistent, panchromatic model of the interstellar radiation field. By looking at different stellar populations independently, we were able to quantify to what extent different stellar age populations contribute to the heating of dust. Our method takes into account the effects of non-local heating. Results. We obtained a realistic 3D radiative transfer model of the face-on galaxy M 81. We find that only 50.2% of the dust heating can be attributed to young stellar populations (≲100 Myr). We confirm that there is a tight correlation between the specific star formation rate and the heating fraction by young stellar populations, both in sky projections and in 3D, which is also found for radiative transfer models of M 31 and M 51. Conclusions. We conclude that old stellar populations can be a major contributor to the heating of dust. In M 81, old stellar populations are the dominant heating agent in the central regions, contributing to half of the absorbed radiation. Regions of higher star formation do not correspond to the highest dust temperatures. On the contrary, it is the dominant bulge which is most efficient in heating the dust. The approach we present here can immediately be applied to other galaxies. It does contain a number of caveats, which we discuss in detail.

Radiative transfer modeling through terrestrial atmosphere and ocean accounting for inelastic processes: Software package SCIATRAN

The capability of spaceborne stereogrammetry using very high-resolution (VHR, <2 m) imagery with various environmental, experimental, and sensor configurations for characterizing forest canopy surfaces has not been completely explored. Existing archives of VHR imagery include a limited subset of potential stereo image acquisition configurations and may therefore exclude optimal configurations for capturing critical structural features of forest canopy surface. By contrast, simulated VHR imagery from 3-D radiative transfer models (RTM) can explore the full range of spatial, spectral, and sun-sensor configurations to identify factors that contribute to uncertainties in stereo-derived estimates of forest canopy structure. We developed a novel method to simulate VHR stereopairs using the discrete anisotropic radiative transfer (DART) model and then derive surface elevations from the simulated images. We reconstructed one open-canopy and one closed-canopy forest scene and created a reference digital surface model/digital terrain model (DSM/DTM) using airborne small-footprint lidar points over the study sites. The VHR simulations were configured to match three independent WorldView stereopairs. The results showed that, compared to the reference DSM, the surface elevations derived using simulated and WorldView image data were consistent, with differences of <1.6 m in vertical bias, < 1 m in root mean square error (RMSE), and < 0.07 in correlation coefficient (R). We demonstrated that realistic 3-D RTM simulations could be georeferenced with a camera model for DSM generation from simulated stereopairs. This work will support a follow-up investigation that examines stereo-derived DSM quality over a broad range of surface types and acquisition parameters to suggest optimal configurations for actual VHR stereo data acquisition of vegetation canopy surfaces.

Recent investigations using polarimetric decomposition and numerical models have helped to improve understanding of how radar signals interact with lake ice. However, further research is needed on how radar signals are impacted by varying lake ice properties. Radiative transfer models provide one method of improving this understanding. These are the first published experiments using the Snow Microwave Radiative Transfer (SMRT) model to investigate the response of different imaging SAR frequencies (L, C, and X-band) at HH and VV polarizations using various incidence angles (20&#x00B0;, 30&#x00B0;, and 40&#x00B0;) to changes in ice thickness, porosity, bubble radius, and ice-water interface roughness. This is also the first use of SMRT in combination with a thermodynamic lake ice model. Experiments were for a lake with tubular bubbles and one without tubular bubbles under difference scenarios. Analysis of the backscatter response to different properties indicate that increasing ice thickness and layer porosity have little impact on backscatter from lake ice. X-band backscatter shows increased response to surface ice layer bubble radius; however, this was limited for other frequencies except at shallower incidence angles (40&#x00B0;). All three frequencies display the largest response to increasing RMS height at the ice-water interface, which supports surface scattering at the ice-water interface as being the dominant scattering mechanism. These results demonstrate that SMRT is a valuable tool for understanding the response of SAR data to changes in freshwater lake ice properties and could be used in the development of inversion models.

Ability of remotely sensed solar-induced chlorophyll fluorescence (SIF) to serve as a vegetation productivity and stress indicator is impaired by confounding factors, such as varying crop-specific canopy structure, changing solar illumination angles, and SIF-soil optical interactions. This study investigates two normalisation approaches correcting diurnal top-of-canopy SIF observations retrieved from the O2-A absorption feature at 760 nm (F760 hereafter) of summer barley crops for these confounding effects. Nadir SIF data was acquired over nine breeding experimental plots simultaneously by an airborne imaging spectrometer (HyPlant) and a drone-based high-performance point spectrometer (AirSIF). Ancillary measurements, including leaf pigment contents retrieved from drone hyperspectral imagery, destructively sampled leaf area index (LAI), and leaf water and dry matter contents, were used to test the two normalisation methods that are based on: i) the fluorescence correction vegetation index (FCVI), and ii) three versions of the near-infrared reflectance of vegetation (NIRV). Modelling in the discrete anisotropic radiative transfer (DART) model revealed close matches for NIRv-based approaches when corrected canopy SIF was compared to simulated total chlorophyll fluorescence emitted by leaves (R2 = 0.99). Normalisation with the FCVI also performed acceptably (R2 = 0.93), however, it was sensitive to variations in LAI when compared to leaf emitted chlorophyll fluorescence efficiency. Based on the results modelled in DART, the NIRvH1 normalisation was found to have a superior performance over the other NIRv variations and the FCVI normalisation. Comparison of the SIF escape fractions suggests that the escape fraction estimated with NIRvH1 matched escape fraction extracted from DART more closely. When applied to the experimental drone and airborne nadir canopy SIF data, the agreement between NIRvH1 and FCVI produced chlorophyll fluorescence efficiency was very high (R2 = 0.93). Nevertheless, NIRvH1 showed higher uncertainties for areas with low vegetation cover indicating an unaccounted contribution of SIF-soil interactions. The diurnal courses of chlorophyll fluorescence efficiency for both approaches differed not significantly from simple normalisation by incoming and apparent photosynthetically active radiation. In conclusion, SIF normalisation with NIRvH1 more accurately compensates the effects of canopy structure on top of canopy far red SIF, but when applied to top of canopy in-situ data of spring barley, the effects of NIRvH1 and FCVI on the diurnal course of SIF had a similar influence.

Validation of the community radiative transfer model

The Hellenic Network for Solar Energy is a network dedicated to provide information regarding the availability of solar energy in Greece with the purpose of supporting solar installations. The Network comprises the use of satellite products and calculations from radiative transfer and prognostic models. The results have been validated using a ground-based network of 14 stations, located in various areas of Greece that provide surface solar irradiance measurements. Cloud data derived from the Meteosat Second Generation satellites are used, along with radiative transfer models, to calculate the available solar energy. As a result, global horizontal and direct normal irradiances are calculated with a high spatial and temporal resolution (5 km and 15 min respectively) from 2002 and onwards. Based on data from the period 2002 to 2012, a climatology of the solar energy field in Greece, has been produced. Solar maps are provided, presenting the climatological annual amounts of global horizontal and direct normal irradiances, for the whole country as well as for each geographic region in particular. The maps are freely available at: http://atmosphere-upatras.gr/en/solarmaps.

Radiative heat transfer in semitransparent solidifying slab considering space–time dependent refractive index