Approximate Radiative Transfer Research Articles

Three‐Dimensional Radiative Effects By Shallow Cumulus Clouds on Dynamic Heterogeneities Over a Vegetated Surface

AbstractOne‐dimensional radiative transfer solvers are computationally much more efficient than full three‐dimensional radiative transfer solvers but do not account for the horizontal propagation of radiation and thus produce unrealistic surface irradiance fields in models that resolve clouds. Here, we study the impact of using a 3‐D radiative transfer solver on the direct and diffuse solar irradiance beneath clouds and the subsequent effect on the surface fluxes. We couple a relatively fast 3‐D radiative transfer approximation (TenStream solver) to the Dutch Atmosphere Large‐Eddy Simulation (DALES) model and perform simulations of a convective boundary layer over grassland with either 1‐D or 3‐D radiative transfer. Based on a single case study, simulations with 3‐D radiative transfer develop larger and thicker clouds, which we attribute mainly to the displaced clouds shadows. With increasing cloud thickness, the surface fluxes decrease in cloud shadows with both radiation schemes but increase beneath clouds with 3‐D radiative transfer. We find that with 3‐D radiative transfer, the horizontal length scales dominating the spatial variability of the surface fluxes are over twice as large as with 1‐D radiative transfer. The liquid water path and vertical wind velocity in the boundary layer are also dominated by larger length scales, suggesting that 3‐D radiative transfer may lead to larger convective thermals. Our case study demonstrates that 3‐D radiative effects can significantly impact dynamic heterogeneities induced by cloud shading. This may change our view on the coupling between boundary‐layer clouds and the surface and should be further tested for generalizability in future studies.

Neighboring Column Approximation—An Improved 3D Thermal Radiative Transfer Approximation for Non‐Rectangular Grids

AbstractWe present a significantly improved version of the Neighboring Column Approximation (NCA 2.0), a fast 3D approximation for the calculation of thermal heating and cooling rates in cloudy atmospheres for large eddy simulation models. The method can now be used on non‐rectangular grids, and the heating rate bias in cloudy atmospheres is substantially reduced compared to a 1D solution and the original version of the NCA (NCA 1.0). For different cloud fields the bias is in the range of 5–30% in the 1D case and 2–7% for the NCA 2.0. The calculation of 3D radiative transfer quantities requires horizontal transport of radiation which causes difficulties in the parallelization of numerical models and is computationally expensive. The NCA overcomes this problem and can calculate 3D thermal heating rates at the expense of only a factor 1.5 to 2 higher compared to a 1D radiative transfer approximation. The method uses the fluxes calculated by a 1D radiation scheme and estimates horizontal fluxes using results from neighboring columns. For the estimation of the heating rates from the before estimated fluxes pre‐calculated lookup tables of emissivities are used. For the calculation of the heating rates we neglect scattering (independent of the fact if the incoming fluxes consider scattering or not). Inconsistencies made by assumptions for the method are corrected by a correction factor.

Multi-hp adaptive discontinuous Galerkin methods for simplified PN approximations of 3D radiative transfer in non-gray media

In this paper we present a multi-hp adaptive discontinuous Galerkin method for 3D simplified PN approximations of radiative transfer in non-gray media capable of reaching accuracies superior to most of methods in the literature. The simplified PN models are a set of differential equations derived based on asymptotic expansions for the integro-differential radiative transfer equation. In a non-gray media the optical spectrum is divided into a finite set of bands with constant absorption coefficients and the simplified PN approximations are solved for each band in the spectrum. At high temperature, boundary layers with different magnitudes occur for each wavelength in the spectrum and developing a numerical solver to accurately capture them is challenging for the conventional finite element methods. Here we propose a class of high-order adaptive discontinuous Galerkin methods using space error estimators. The proposed method is able to solve problems where 3D meshes contain finite elements of different kind with the number of equations and polynomial orders of approximation varying locally on the finite element edges, faces, and interiors. The proposed method has also the potential to perform both isotropic and anisotropic adaptation for each band in the optical spectrum. Several numerical results are presented to illustrate the performance of the proposed method for 3D radiative simulations. The computed results confirm its capability to solve 3D simplified PN approximations of radiative transfer in non-gray media.

The influence of Hinode/SOT NFI instrumental effects on the visibility of simulated prominence fine structures in Hα

Context. Models of entire prominences with their numerous fine structures distributed within the prominence magnetic field use approximate radiative transfer techniques to visualize the simulated prominences. However, to accurately compare synthetic images of prominences obtained in this way with observations and to precisely analyze the visibility of even the faintest prominence features, it is important to take into account the influence of instrumental properties on the synthetic spectra and images. Aims. In the present work, we investigate how synthetic Hα images of simulated prominences are impacted by the instrumental effects induced by the Narrowband Filter Imager (NFI) of the Solar Optical Telescope (SOT) onboard the Hinode satellite. Methods. To process the synthetic Hα images provided by 3D Whole-Prominence Fine Structure (WPFS) models into SOT-like synthetic Hα images, we take into account the effects of the integration over the theoretical narrow-band transmission profile of NFI Lyot filter, the influence of the stray-light and point spread function (PSF) of Hinode/SOT, and the observed noise level. This allows us to compare the visibility of the prominence fine structures in the SOT-like synthetic Hα images with the synthetic Hα line-center images used by the 3D models and with a pair of Hinode/SOT NFI observations of quiescent prominences. Results. The comparison between the SOT-like synthetic Hα images and the synthetic Hα line-center images shows that all large and small-scale features are very similar in both visualizations and that the same very faint prominence fine structures can be discerned in both. This demonstrates that the computationally efficient Hα line-center visualization technique can be reliably used for the purpose of visualization of complex 3D prominence models. In addition, the qualitative comparison between the SOT-like synthetic images and prominence observations shows that the 3D WPFS models can reproduce large-scale prominence features rather well. However, the distribution of the prominence fine structures is significantly more diffuse in the observations than in the models and the diffuse intensity areas surrounding the observed prominences are also not present in the synthetic images. We also found that the maximum intensities reached in the models are about twice as high as those present in the observations–an indication that the mass-loading assumed in the present 3D WPFS models might be too large.

A Neural Network Correction to the Scalar Approximation in Radiative Transfer

AbstractThe next generation of advanced high-resolution sensors in geostationary orbit will gather detailed information for studying the Earth system. There is an increasing desire to perform observing system simulation experiments (OSSEs) for new sensors during the development phase of the mission in order to better leverage information content from the new and existing sensors. Forward radiative transfer calculations that simulate the observing characteristics of a new instrument are the first step to an OSSE, and they are computationally intensive. The scalar approximation to the radiative transfer equation, a simplification of the vector representation, can save considerable computational cost, but produces errors in top of the atmosphere (TOA) radiance as large as 10% due to neglecting polarization effects. This article presents an artificial neural network technique to correct scalar TOA radiance over both land and ocean surfaces to within 1% of vector-calculated radiance. A neural network was trained on a database of scalar–vector TOA radiance differences at a large range of solar and viewing angles for several thousand realistic atmospheric vertical profiles that were sampled from a high-resolution (7 km) global atmospheric transport model. The profiles include Rayleigh scattering and aerosol scattering and absorption. Training and validation of the neural network was demonstrated for two wavelengths in the ultraviolet–visible (UV-Vis) spectral range (354 and 670 nm). The significant computational savings accrued from using a scalar approximation plus neural network correction approach to simulating TOA radiance will make feasible hyperspectral forward simulations of high-resolution sensors on geostationary satellites, such as Tropospheric Emissions: Monitoring of Pollution (TEMPO), GOES-R, Geostationary Environmental Monitoring Spectrometer (GEMS), and Sentinel-4.

Influences of Physical Processes and Parameters on Simulations of TOA Radiance at UV Wavelengths: Implications for Satellite UV Instrument Validation

Numerous factors can influence the radiative transfer simulation of hyper-spectral ultraviolet satellite observation, including the radiative transfer scheme, gaseous absorption coefficients, Rayleigh scattering scheme, surface reflectance, aerosol scattering, band center wavelength shifts of sensor, and accuracy of input profiles. In this study, a Unified Linearized Vector Radiative Transfer Model (UNL-VRTM) is used to understand the influences of various factors on the top of atmosphere (TOA) normalized radiance in the ultraviolet (UV) region. A benchmark test for Rayleigh scattering is first performed to verify the UNL-VRTM accuracy, showing that the model performances agree well with earlier peer-reviewed results. Sensitivity experiments show that a scalar radiative transfer approximation considering only ozone and a constant surface reflectance within the UV region may cause significant errors to the TOA normalized radiance. A comparison of the Ozone Mapping and Profiler Suite (OMPS) radiances between simulations and observations shows that the surface reflectance strongly influences the accuracy for the wavelengths larger than 340 nm. Thus, using the surface reflectivity at 331 nm as a proxy for simulating the whole OMPS hyperspectral ultraviolet radiances is problematic. The impact of rotational Raman scattering on TOA radiance can be simulated through using SCIATRAN, which can also reduce the difference between measurements and simulations to some extent. Overall, the differences between OMPS simulations and observations can be less than 3% for the entire wavelengths. The bias is nearly constant across the cross-track direction.

Dynamics of multiple protoplanets embedded in gas and pebble discs and its dependence on Σ and ν parameters

Protoplanets of super-Earth size may get trapped in convergence zones for planetary migration and form gas giants there. These growing planets undergo accretion heating, which triggers a hot-trail effect that can reverse migration directions, increase planetary eccentricities, and prevent resonant captures of migrating planets. In this work, we study populations of embryos that are accreting pebbles under different conditions, by changing the surface density, viscosity, pebble flux, mass, and the number of protoplanets. For modelling, we used the FARGO-THORIN two-dimensional (2D) hydrocode, which incorporates a pebble disc as a second pressure-less fluid, the coupling between the gas and pebbles, and the flux-limited diffusion approximation for radiative transfer. We find that massive embryos embedded in a disc with high surface density (Σ = 990 g cm−2 at 5.2 au) undergo numerous “unsuccessful” two-body encounters that do not lead to a merger. Only when a third protoplanet arrives in the convergence zone do three-body encounters lead to mergers. For a low-viscosity disc (ν = 5 × 1013 cm2 s−1), a massive co-orbital is a possible outcome, for which a pebble isolation develops and the co-orbital is further stabilised. For more massive protoplanets (5 M⊕), the convergence radius is located further out, in the ice-giant zone. After a series of encounters, there is an evolution driven by a dynamical torque of a tadpole region, which is systematically repeated several times until the co-orbital configuration is disrupted and planets merge. This may be a way to solve the problem that co-orbitals often form in simulations but they are not observed in nature. In contrast, the joint evolution of 120 low-mass protoplanets (0.1 M⊕) reveals completely different dynamics. The evolution is no longer smooth, but rather a random walk. This is because the spiral arms, developed in the gas disc due to Lindblad resonances, overlap with each other and affect not only a single protoplanet but several in the surrounding area. Our hydrodynamical simulations may have important implications for N-body simulations of planetary migration that use simplified torque prescriptions and are thus unable to capture protoplanet dynamics in its full glory.

Efficient radiative transfer techniques in hydrodynamic simulations

Radiative transfer is an important component of hydrodynamic simulations as it determines the thermal properties of a physical system. It is especially important in cases where heating and cooling regulate significant processes, such as in the collapse of molecular clouds, the development of gravitational instabilities in protostellar discs, disc-planet interactions, and planet migration. We compare two approximate radiative transfer methods which indirectly estimate optical depths within hydrodynamic simulations using two different metrics: (i) the gravitational potential and density of the gas (Stamatellos et al.), and (ii) the pressure scale-height (Lombardi et al.). We find that both methods are accurate for spherical configurations e.g. in collapsing molecular clouds and within clumps that form in protostellar discs. However, the pressure scale-height approach is more accurate in protostellar discs (low and high-mass discs, discs with spiral features, discs with embedded planets). We also investigate the $\beta$-cooling approximation which is commonly used when simulating protostellar discs, and in which the cooling time is proportional to the orbital period of the gas. We demonstrate that the use of a constant $\beta$ cannot capture the wide range of spatial and temporal variations of cooling in protostellar discs, which may affect the development of gravitational instabilities, planet migration, planet mass growth, and the orbital properties of planets.

Reliable anisotropic-adaptive discontinuous Galerkin method for simplified PN approximations of radiative transfer

In this paper we present the analysis for the error estimator for radiative transfer problems presented in Giani and Seaid (2016) where we showed the capabilities of the error estimator to accurately drive the adaptivity to resolve steep boundary layers, which are among the difficulties that most numerical methods fail to resolve accurately. We prove reliability for the error estimator in terms of a global upper bound of the error measured in the natural norm. We present a series of numerical experiments to test the efficiency of this approach within a fully automated h p -adaptive refinement algorithm.

Scattering and absorption effects on asymptotic light fields in seawater.

Asymptotic theory is based on the principle that the shape of the light field with depth gradually transforms from being dependent on the incident surface light field to being constant azimuthally and dependent only on the absorption and scattering properties of the water column. Properties such as the average cosine of the oceanic light field in the asymptotic regime, μ¯∞, are thus strictly inherent optical properties (IOPs). Because of the close link between asymptotic light fields and IOPs, radiative transfer approximations (RTAs) for the asymptotic regime have been adapted for use in algorithms describing surface remote sensing reflectance RRS ( = Lu/Ed) in terms of the IOPs. For such algorithms to have utility, the asymptotic average cosine needs to be parameterized in terms of IOPs useful for ocean color remote sensing. With this motivation, μ¯∞is approximated as a function of the ratio of total backscattering to total absorption, bb/a. An additional variable in assessments is the fractional water content of pure seawater in total backscattering, ηbb. A full range of representative phase functions for natural particle fields is included in the analysis using the Fournier-Forand analytical approximation. Analytical expressions for multi-order polynomial fits are provided for μ¯∞ as a function of bb/a for each ηbb assessed, for ηbb ≤ 0.49, and for the entire data set. The full range of phase function shapes were included in each fit. Percent absolute errors were a modest 3.4% for the fit for the entire data set. Additionally, a key assumption by Zaneveld that the attenuation coefficient for upwelling nadir radiance KLu in surface waters should be approximately equivalent to the attenuation coefficient in the asymptotic regime K∞ was evaluated. Results provide justification and relationships for the targeted application of asymptotic parameters in ocean color RTAs for the surface ocean.

A generalized analytical model for radiative transfer in vacuum thermal insulation of space vehicles

The previously developed spectral model for radiative transfer in vacuum thermal insulation of space vehicles is generalized to take into account possible thermal contact between a fibrous spacer and one of the neighboring aluminum foil layers. An approximate analytical solution based on slightly modified two-flux approximation for radiative transfer in a semi-transparent fibrous spacer is derived. It was shown that thermal contact between the spacer and adjacent foil may decrease significantly the quality of thermal insulation because of an increase in radiative flux to/from the opposite aluminum foil. Theoretical predictions are confirmed by comparison with new results of laboratory experiments.

PHOTOPHORETIC LEVITATION AND TRAPPING OF DUST IN THE INNER REGIONS OF PROTOPLANETARY DISKS

ABSTRACT In protoplanetary disks, the differential gravity-driven settling of dust grains with respect to gas and with respect to grains of varying sizes determines the observability of grains, and sets the conditions for grain growth and eventually planet formation. In this work, we explore the effect of photophoresis on the settling of large dust grains in the inner regions of actively accreting protoplanetary disks. Photophoretic forces on dust grains result from the collision of gas molecules with differentially heated grains. We undertake one-dimensional dust settling calculations to determine the equilibrium vertical distribution of dust grains in each column of the disk. In the process we introduce a new treatment of the photophoresis force which is consistent at all optical depths with the representation of the radiative intensity field in a two-stream radiative transfer approximation. The levitation of large dust grains creates a photophoretic dust trap several scale heights above the mid-plane in the inner regions of the disk where the dissipation of accretion energy is significant. We find that differential settling of dust grains is radically altered in these regions of the disk, with large dust grains trapped in a layer below the stellar irradiation surface, where the dust to gas mass ratio can be enhanced by a factor of a hundred for the relevant particles. The photophoretic trapping effect has a strong dependence on particle size and porosity.

Near-field radiative heat transfer between clusters of dielectric nanoparticles

In this work, we explore the near-field radiative heat transfer between two clusters of silicon carbide (SiC) nanoparticles using the many-body radiative heat transfer theory. The effects of fractal dimension of clusters, many-body interaction between nanoparticles and relative orientation of clusters on the thermal conductance are studied. Meanwhile, the applicability of the equivalent volume spheres (EVS) approximation for near-field radiative heat transfer between clusters is examined. It is observed that the thermal conductance is larger for clusters with larger fractal dimension, which is more significant in the near-field. The thermal conductance of EVS resembles that of the clusters, but EVS overestimates the conductance of clusters, especially in the near-field. Compared to the case of two nanoparticles, the conductance of nanoparticle clusters decays much slower with increasing distance in the near-field, but shares similar dependence on the distance in the far-field. The thermal conductance of SiC nanoparticle clusters is inhibited by the many-body interaction when surface phonon polariton is supported but enhanced at frequencies close to the resonance frequency. The total thermal conductance is decreased due to many-body interaction among particles in the cluster. The relative orientation between the clusters is also an important factor in the near-field, especially for clusters with lower fractal dimension.

Radiative transfer in disc galaxies – V. The accuracy of the

We investigate the accuracy of an approximate radiative transfer technique that was first proposed by Kylafis & Bahcall (hereafter the KB approximation) and has been popular in modelling dusty late-type galaxies. We compare realistic galaxy models calculated with the KB approximation with those of a three-dimensional Monte Carlo radiative transfer code SKIRT. The SKIRT code fully takes into account of the contribution of multiple scattering whereas the KB approximation calculates only single scattered intensity and multiple scattering components are approximated. We find that the KB approximation gives fairly accurate results if optically thin, face-on galaxies are considered. However, for highly inclined ($i \gtrsim 85^{\circ}$) and/or optically thick (central face-on optical depth $\gtrsim1$) galaxy models, the approximation can give rise to substantial errors, sometimes, up to $\gtrsim 40\%$. Moreover, it is also found that the KB approximation is not always physical, sometimes producing infinite intensities at lines of sight with high optical depth in edge-on galaxy models. There is no "simple recipe" to correct the errors of the KB approximation that is universally applicable to any galaxy models. Therefore, it is recommended that the full radiative transfer calculation be used, even though it's slower than the KB approximation.

Effects of aerosols on clear-sky solar radiation in the ALADIN-HIRLAM NWP system

Abstract. The direct shortwave radiative effect of aerosols under clear-sky conditions in the Aire Limitee Adaptation dynamique Developpement InterNational – High Resolution Limited Area Model (ALADIN-HIRLAM) numerical weather prediction system was investigated using three shortwave radiation schemes in diagnostic single-column experiments: the Integrated Forecast System (IFS), acraneb2 and the hlradia radiation schemes. The multi-band IFS scheme was formerly used operationally by the European Centre for Medium Range Weather Forecasts (ECMWF) whereas hlradia and acraneb2 are broadband schemes. The former is a new version of the HIRLAM radiation scheme while acraneb2 is the radiation scheme in the ALARO-1 physics package. The aim was to evaluate the strengths and weaknesses of the numerical weather prediction (NWP) system regarding aerosols and to prepare it for use of real-time aerosol information. The experiments were run with particular focus on the August 2010 Russian wildfire case. Each of the three radiation schemes accurately (within ±4 % at midday) simulates the direct shortwave aerosol effect when observed aerosol optical properties are used. When the aerosols were excluded from the simulations, errors of more than +15 % in global shortwave irradiance were found at midday, with the error reduced to +10 % when standard climatological aerosols were used. An error of −11 % was seen at midday if only observed aerosol optical depths at 550 nm, and not observation-based spectral dependence of aerosol optical depth, single scattering albedos and asymmetry factors, were included in the simulations. This demonstrates the importance of using the correct aerosol optical properties. The dependency of the direct radiative effect of aerosols on relative humidity was tested and shown to be within ±6 % in this case. By modifying the assumptions about the shape of the IFS climatological vertical aerosol profile, the inherent uncertainties associated with assuming fixed vertical profiles were investigated. The shortwave heating rates in the boundary layer changed by up to a factor of 2 in response to the aerosol vertical distribution without changing the total aerosol optical depth. Finally, we tested the radiative transfer approximations used in the three radiation schemes for typical aerosol optical properties compared to the accurate DISORT model. These approximations are found to be accurate to within ±13 % even for large aerosol loads.

Velocity variations associated with the large 2010 eruption of Merapi volcano, Java, retrieved from seismic multiplets and ambient noise cross-correlation

We present a study of the seismic velocity variations that occurred in the structure before the large 2010 eruption of Merapi volcano. For the first time to our knowledge, the technique of coda wave interferometry is applied to both families of similar events (multiplets) and to correlation functions of seismic noise. About half of the seismic events recorded at the summit stations belong to one of the ten multiplets identified, including 120 similar events that occurred in the last 20 hr preceding the eruption onset. Daily noise cross-correlation functions (NCF) were calculated for the six pairs of short-period stations available. Using the stretching method, we estimate time-series of apparent velocity variation (AVV) for each multiplet and each pair of stations. No significant velocity change is detected until September 2010. From 10 October to the beginning of the eruption on 26 October, a complex pattern of AVV is observed with amplitude of up to ±1.5 per cent. Velocity decrease is first observed from families of deep events and then from shallow earthquakes. In the same period, AVV with different signs and chronologies are estimated from NCF calculated for various station pairs. The location in the horizontal plane of the velocity perturbations related with the AVV obtained from NCF is estimated by using an approach based on the radiative transfer approximation. Although their spatial resolution is limited, the resulting maps display velocity decrease in the upper part of the edifice in the period 12–25 October. After the eruption onset, the pattern of velocity perturbations is significantly modified with respect to the previous one. We interpret these velocity variations in the framework of a scenario of magmatic intrusion that integrates most observations. The perturbation of the stress field associated with the magma migration can induce both decrease and increase of the seismic velocity of rocks. Thus the detected AVVs can be considered as precursors of volcanic eruptions in andesitic volcanoes, without taking their sign into account.

Mathematical aspects of the meteorological interpretation of satellite hyperspectral infrared measurements part I: statement of the inverse problem for estimation of the cloud absorption vertical profile

ABSTRACTSatellite high spectral resolution infrared measurements provide information for cloud vertical characterization when optically semi-transparent clouds at high altitude cover cloud layers at lower altitudes. It is an important issue because such atmospheric conditions are common and clouds are characterized by large-scale vertical development. An approximation radiative transfer model for a cloudy atmosphere is introduced. Cloud particle absorption of infrared (IR) radiation depends on the spectral frequency. So, the effective cloud parameters such as amount (absorption) and height, derived from IR spectral measurements, will be spectral functions as well. The degree of uncertainty in the determination of effective cloud parameters cannot be eliminated by increasing the number of spectral measurements. A cloud model should have extra degrees of freedom to address the spectral and spatial (vertical) variability of cloud absorption. A semi-discrete multilevel cloud model is used to describe the perturbation of the outgoing IR thermal radiation caused by cloudiness in the field of view of a satellite instrument. The model delineates cloudiness in a number of layers at fixed heights. Each layer (level) is characterized by the effective cloud absorption. An inverse problem of cloud absorption vertical profile (CAVP) estimation is described. The estimate of an effective cloud absorption profile is considered as predictor for identification of cloud presence at specific atmospheric layers. The problem is numerically examined for real satellite IR spectral measurements and solution estimates are compared with lidar measurements. Results show that the resulting estimate of CAVPs provides a realistic characterization of cloud top and cloud vertical scale.

Formula omitted]-adaptive discontinuous Galerkin methods for simplified [formula omitted] approximations of frequency-dependent radiative transfer

We investigate the performance of a class of hp-adaptive discontinuous Galerkin methods for the numerical solution of simplified PN approximations of radiative transfer in non-gray semitransparent media. By introducing an optical scale and using asymptotic expansions in the radiative transfer equation we formulate the simplified PN approximations. The optical spectrum is decomposed in frequency bands and the simplified PN equations are solved for each frequency band. As a numerical solver for the simplified PN equations we consider a high-order discontinuous Galerkin method. The solver belongs to a class of finite element methods whose approximate solutions are discontinuous across inter-element boundaries; this property renders the method ideally suited for the hp-adaptivity. An error estimator is shown to provide reliable and practically useful upper bounds for the numerical errors independent of the optical scales used in the simulations. The proposed method is simple, fast and highly accurate. The performance of the method is analyzed on several applications in frequency-dependent radiative transfer. The aim of such a method compared to the conventional finite element methods is to solve the simplified PN equations efficiently and with a high level of accuracy on unstructured meshes with different elements. The obtained results demonstrate the ability of the proposed method to capture the main radiative features.

An Emulator Toolbox to Approximate Radiative Transfer Models with Statistical Learning

Physically-based radiative transfer models (RTMs) help in understanding the processes occurring on the Earth’s surface and their interactions with vegetation and atmosphere. When it comes to studying vegetation properties, RTMs allows us to study light interception by plant canopies and are used in the retrieval of biophysical variables through model inversion. However, advanced RTMs can take a long computational time, which makes them unfeasible in many real applications. To overcome this problem, it has been proposed to substitute RTMs through so-called emulators. Emulators are statistical models that approximate the functioning of RTMs. Emulators are advantageous in real practice because of the computational efficiency and excellent accuracy and flexibility for extrapolation. We hereby present an “Emulator toolbox” that enables analysing multi-output machine learning regression algorithms (MO-MLRAs) on their ability to approximate an RTM. The toolbox is included in the free-access ARTMO’s MATLAB suite for parameter retrieval and model inversion and currently contains both linear and non-linear MO-MLRAs, namely partial least squares regression (PLSR), kernel ridge regression (KRR) and neural networks (NN). These MO-MLRAs have been evaluated on their precision and speed to approximate the soil vegetation atmosphere transfer model SCOPE (Soil Canopy Observation, Photochemistry and Energy balance). SCOPE generates, amongst others, sun-induced chlorophyll fluorescence as the output signal. KRR and NN were evaluated as capable of reconstructing fluorescence spectra with great precision. Relative errors fell below 0.5% when trained with 500 or more samples using cross-validation and principal component analysis to alleviate the underdetermination problem. Moreover, NN reconstructed fluorescence spectra about 50-times faster and KRR about 800-times faster than SCOPE. The Emulator toolbox is foreseen to open new opportunities in the use of advanced RTMs, in which both consistent physical assumptions and data-driven machine learning algorithms live together.

Fast approximate radiative transfer method for visualizing the fine structure of prominences in the hydrogen Hαline

Aims. We present a novel approximate radiative transfer method developed to visualize 3D whole-prominence models with multiple fine structures using the hydrogen Hα spectral line. Methods. This method employs a fast line-of-sight synthesis of the Hα line profiles through the whole 3D prominence volume and realistically reflects the basic properties of the Hα line formation in the cool and low-density prominence medium. The method can be applied both to prominences seen above the limb and filaments seen against the disk. Results. We provide recipes for the use of this method for visualizing the prominence or filament models that have multiple fine structures. We also perform tests of the method that demonstrate its accuracy under prominence conditions. Conclusions. We demonstrate that this fast approximate radiative transfer method provides realistic synthetic Hα intensities useful for a reliable visualization of prominences and filaments. Such synthetic high-resolution images of modeled prominences/filaments can be used for a direct comparison with high-resolution observations.