scholarly journals Analysis of Two Dimensionality Reduction Techniques for Fast Simulation of the Spectral Radiances in the Hartley-Huggins Band

Atmosphere ◽  
2019 ◽  
Vol 10 (3) ◽  
pp. 142 ◽  
Author(s):  
Ana del Águila ◽  
Dmitry Efremenko ◽  
Víctor Molina García ◽  
Jian Xu
Keyword(s):  
Optical Properties ◽  
Radiative Transfer ◽  
Dimensionality Reduction ◽  
Empirical Orthogonal Functions ◽  
Gas Absorption ◽  
Correction Function ◽  
Data Set ◽  
Acceleration Techniques ◽  
Computational Performance ◽  
Specific Subset

The new generation of atmospheric composition sensors such as TROPOMI is capable of providing spectra of high spatial and spectral resolution. To process this vast amount of spectral information, fast radiative transfer models (RTMs) are required. In this regard, we analyzed the efficiency of two acceleration techniques based on the principal component analysis (PCA) for simulating the Hartley-Huggins band spectra. In the first one, the PCA is used to map the data set of optical properties of the atmosphere to a lower-dimensional subspace, in which the correction function for an approximate but fast RTM is derived. The second technique is based on the dimensionality reduction of the data set of spectral radiances. Once the empirical orthogonal functions are found, the whole spectrum can be reconstructed by performing radiative transfer computations only for a specific subset of spectral points. We considered a clear-sky atmosphere where the optical properties are defined by Rayleigh scattering and trace gas absorption. Clouds can be integrated into the model as Lambertian reflectors. High computational performance is achieved by combining both techniques without losing accuracy. We found that for the Hartley-Huggins band, the combined use of these techniques yields an accuracy better than 0.05% while the speedup factor is about 20. This innovative combination of both PCA-based techniques can be applied in future works as an efficient approach for simulating the spectral radiances in other spectral regions.

scholarly journals Irradiance and atmospheric optical properties from photovoltaic power data: model improvements and first results

2021 ◽  
Author(s):  
James Barry ◽  
Dirk Böttcher ◽  
Johannes Grabenstein ◽  
Klaus Pfeilsticker ◽  
Anna Herman-Czezuch ◽  
...  
Keyword(s):  
Optical Properties ◽  
Radiative Transfer ◽  
Optical Depth ◽  
Reanalysis Data ◽  
Forward Model ◽  
Atmospheric Conditions ◽  
Data Set ◽  
Cloud Optical Depth ◽  
First Results ◽  
Weather Models

<p>Photovoltaic (PV) power data are a valuable but as yet under-utilised resource that could be used to characterise global irradiance with unprecedented spatio-temporal resolution. The resulting knowledge of atmospheric conditions can then be fed back into weather models and will ultimately serve to improve forecasts of PV power itself. This provides a data-driven alternative to statistical methods that use post-processing to overcome inconsistencies between ground-based irradiance measurements and the corresponding predictions of regional weather models (see for instance Frank et al., 2018). This work reports first results from an algorithm developed to infer global horizontal irradiance as well as atmospheric optical properties such as aerosol or cloud optical depth from PV power measurements.</p><p>Building on previous work (Buchmann, 2018), an improved forward model of PV power as a function of atmospheric conditions was developed. As part of the BMWi-funded project MetPVNet, PV power data from twenty systems in the Allgäu region were made available, and the corresponding irradiance, temperature and wind speed were measured during two measurement campaigns in autumn 2018 and summer 2019. System calibration was performed using all available clear sky days; the corresponding irradiance was simulated using libRadtran (Emde et al., 2016). Particular attention was paid to describing the dynamic variations in PV module temperature in order to correctly take into account the heat capacity of the solar panels.</p><p>PV power data from the calibrated systems were then used together with both the DISORT and MYSTIC radiative transfer codes (Emde et al., 2016) to infer aerosol optical depth, cloud optical depth and irradiance under all sky conditions.  The results were compared to predictions from the COSMO weather model, and the accuracy of the inverted quantities was compared using both a simple and more complex forward model. The potential of the method to extract irradiance data over a larger area as well as the increase in information from combining neighbouring PV systems will be explored in future work.</p><p><strong>References</strong><br>  <br>Buchmann, T., 2018: Potenzial von Photovoltaikanlagen zur Ableitung raum-zeitlich hoch aufgelöster Globalstrahlungsdaten. Heidelberg University, http://archiv.ub.uni-heidelberg.de/volltextserver/24687/.<br>Emde, C., and Coauthors, 2016: The libRadtran software package for radiative transfer calculations (version 2.0.1). <em>Geosci. Model Dev.</em>, 9, 1647–1672, doi:10.5194/gmd-9-1647-2016. https://www.geosci-model-dev.net/9/1647/2016/.<br>Frank, C. W., S. Wahl, J. D. Keller, B. Pospichal, A. Hense, and S. Crewell, 2018: Bias correction of a novel European reanalysis data set for solar energy applications.<em> Sol. Energy</em>, 164, 12–24, doi:10.1016/j.solener.2018.02.012. https://doi.org/10.1016/j.solener.2018.02.012.</p>

scholarly journals Fast Hyper-Spectral Radiative Transfer Model Based on the Double Cluster Low-Streams Regression Method

2021 ◽  
Vol 13 (3) ◽  
pp. 434
Author(s):  
Ana del Águila ◽  
Dmitry S. Efremenko
Keyword(s):  
Radiative Transfer ◽  
Single Scattering ◽  
Atmospheric Composition ◽  
Radiative Transfer Model ◽  
Transfer Model ◽  
Absorption Bands ◽  
Acceleration Techniques ◽  
Scattering Approximation ◽  
Fine Resolution ◽  
Single Scattering Approximation

Fast radiative transfer models (RTMs) are required to process a great amount of satellite-based atmospheric composition data. Specifically designed acceleration techniques can be incorporated in RTMs to simulate the reflected radiances with a fine spectral resolution, avoiding time-consuming computations on a fine resolution grid. In particular, in the cluster low-streams regression (CLSR) method, the computations on a fine resolution grid are performed by using the fast two-stream RTM, and then the spectra are corrected by using regression models between the two-stream and multi-stream RTMs. The performance enhancement due to such a scheme can be of about two orders of magnitude. In this paper, we consider a modification of the CLSR method (which is referred to as the double CLSR method), in which the single-scattering approximation is used for the computations on a fine resolution grid, while the two-stream spectra are computed by using the regression model between the two-stream RTM and the single-scattering approximation. Once the two-stream spectra are known, the CLSR method is applied the second time to restore the multi-stream spectra. Through a numerical analysis, it is shown that the double CLSR method yields an acceleration factor of about three orders of magnitude as compared to the reference multi-stream fine-resolution computations. The error of such an approach is below 0.05%. In addition, it is analysed how the CLSR method can be adopted for efficient computations for atmospheric scenarios containing aerosols. In particular, it is discussed how the precomputed data for clear sky conditions can be reused for computing the aerosol spectra in the framework of the CLSR method. The simulations are performed for the Hartley–Huggins, O2 A-, water vapour and CO2 weak absorption bands and five aerosol models from the optical properties of aerosols and clouds (OPAC) database.

scholarly journals Seasonal cycle and source analyses of aerosol optical properties in a semi-urban environment at Puijo station in Eastern Finland

2012 ◽  
Vol 12 (12) ◽  
pp. 5647-5659 ◽  
Author(s):  
A. Leskinen ◽  
A. Arola ◽  
M. Komppula ◽  
H. Portin ◽  
P. Tiitta ◽  
...  
Keyword(s):  
Optical Properties ◽  
Paper Mill ◽  
Single Scattering ◽  
Single Scattering Albedo ◽  
Scattering Coefficient ◽  
Traffic Density ◽  
Aerosol Optical Properties ◽  
Absorption Coefficients ◽  
Data Set ◽  
Pollutant Sources

Abstract. We introduce a four-year (in 2006–2010) continuous data set of aerosol optical properties at Puijo in Kuopio, Finland. We study the annual and diurnal variation of the aerosol scattering and absorption coefficients, hemispheric backscattering fraction, scattering Ångström exponent, and single scattering albedo, whose median values over this period were 7.2 Mm−1 (at 550 nm), 1.0 Mm−1 (at 637 nm), 0.15, 1.93 (between 450 and 550 nm), and 0.85, respectively. The scattering coefficient peaked in the spring and autumn, being 2–4 times those in the summer and winter. An exception was the summer of 2010, when the scattering coefficient was elevated to ~300 Mm−1 by plumes from forest fires in Russia. The absorption coefficient peaked in the winter when soot-containing particles derived from biomass burning were present. The higher relative absorption coefficients resulted in lower single scattering albedo in winter. The optical properties varied also with wind direction and time of the day, indicating the effect of the local pollutant sources and the age of the particles. Peak values in the single scattering albedo were observed when the wind blew from a paper mill and from the sector without local pollutant sources. These observations were linked, respectively, to the sulphate-rich aerosol from the paper mill and the oxygenated organics in the aged aerosol, which both are known to increase the scattering characteristics of aerosols. Decreases in the single scattering albedo in the morning and afternoon, distinct in the summertime, were linked to the increased traffic density at these hours. The scattering and absorption coefficients of residential and long-range transported aerosol (two separate cloud events) were found to be decreased by clouds. The effect was stronger for the scattering than absorption, indicating preferential activation of the more hygroscopic aerosol with higher scattering characteristics.

scholarly journals Sensitivity of aerosol radiative effects to different mixing assumptions in the AEROPT 1.0 submodel of the EMAC atmospheric-chemistry–climate model

2014 ◽  
Vol 7 (5) ◽  
pp. 2503-2516 ◽  
Author(s):  
K. Klingmüller ◽  
B. Steil ◽  
C. Brühl ◽  
H. Tost ◽  
J. Lelieveld
Keyword(s):  
Optical Properties ◽  
Radiative Transfer ◽  
Black Carbon ◽  
Atmospheric Chemistry ◽  
Radiative Forcing ◽  
Climate Model ◽  
Mixing Rule ◽  
Aerosol Optical Properties ◽  
Internal Mixing ◽  
Aerosol Radiative

Abstract. The modelling of aerosol radiative forcing is a major cause of uncertainty in the assessment of global and regional atmospheric energy budgets and climate change. One reason is the strong dependence of the aerosol optical properties on the mixing state of aerosol components, such as absorbing black carbon and, predominantly scattering sulfates. Using a new column version of the aerosol optical properties and radiative-transfer code of the ECHAM/MESSy atmospheric-chemistry–climate model (EMAC), we study the radiative transfer applying various mixing states. The aerosol optics code builds on the AEROPT (AERosol OPTical properties) submodel, which assumes homogeneous internal mixing utilising the volume average refractive index mixing rule. We have extended the submodel to additionally account for external mixing, partial external mixing and multilayered particles. Furthermore, we have implemented the volume average dielectric constant and Maxwell Garnett mixing rule. We performed regional case studies considering columns over China, India and Africa, corroborating much stronger absorption by internal than external mixtures. Well-mixed aerosol is a good approximation for particles with a black-carbon core, whereas particles with black carbon at the surface absorb significantly less. Based on a model simulation for the year 2005, we calculate that the global aerosol direct radiative forcing for homogeneous internal mixing differs from that for external mixing by about 0.5 W m−2.

scholarly journals Aerosol direct radiative forcing during Sahara dust intrusions in the Central Mediterranean

2010 ◽  
Vol 10 (8) ◽  
pp. 20673-20727
Author(s):  
M. R. Perrone ◽  
A. Bergamo ◽  
V. Bellantone
Keyword(s):  
Optical Properties ◽  
Radiative Transfer ◽  
Spectral Range ◽  
Mediterranean Basin ◽  
Transfer Model ◽  
Clear Sky ◽  
Fine Mode ◽  
The Mediterranean ◽  
The Mediterranean Basin ◽  
Sahara Dust

Abstract. The clear-sky, instantaneous Direct Radiative Effect (DRE) by all and anthropogenic particles is calculated during Sahara dust intrusions in the Mediterranean basin, to evaluate the role of anthropogenic particle's radiative effects and to obtain a better estimate of the DRE by desert dust. The clear-sky aerosol DRE is calculated by a two stream radiative transfer model in the solar (0.3–4 μm) and infrared (4–200 μm) spectral range, at the top of the atmosphere (ToA) and at the Earth's surface (sfc). Aerosol optical properties by AERONET sun-sky photometer measurements and aerosol vertical profiles by EARLINET lidar measurements, both performed at Lecce (40.33° N, 18.10° E) during Sahara dust intrusions occurred from 2003 to 2006 year, are used to perform radiative transfer simulations. Instantaneous values at 0.44 μm of the real (n) and imaginary (k) refractive index and of the of aerosol optical depth (AOD) vary within the 1.33–1.55, 0.0037–0.014, and 0.2–0.7 range, respectively during the analyzed dust outbreaks. Fine mode particles contribute from 34% to 85% to the AOD by all particles. The complex atmospheric chemistry of the Mediterranean basin that is also influenced by regional and long-range transported emissions from continental Europe and the dependence of dust optical properties on soil properties of source regions and transport pathways, are responsible for the high variability of n, k, and AOD values and of the fine mode particle contribution. Instantaneous all-wave (solar+infrared) DREs that are negative as a consequence of the cooling effect by aerosol particles, span the – (32–10) Wm−2 and the – (44–20) Wm−2 range at the ToA and surface, respectively. The instantaneous all-wave DRE by anthropogenic particles that is negative, varies within – (13–7) Wm−2 and – (18–11) Wm−2 at the ToA and surface, respectively. It represents from 41% up to 89% and from 32% up to 67% of the all-wave DRE by all particles at the ToA and surface, respectively during the analysed dust outbreaks. A linear relationship to calculate the DRE by natural particles in the solar and infrared spectral range is provided.

scholarly journals Variations in optical properties of aerosols on monsoon seasonal change and estimation of aerosol optical depth using ground-based meteorological and air quality data

2014 ◽  
Vol 14 (13) ◽  
pp. 19747-19789
Author(s):  
F. Tan ◽  
H. S. Lim ◽  
K. Abdullah ◽  
T. L. Yoon ◽  
B. Holben
Keyword(s):  
Optical Properties ◽  
Aerosol Optical Depth ◽  
Optical Depth ◽  
Statistical Tests ◽  
Air Pollutant ◽  
Quality Data ◽  
Supplementary Information ◽  
Northeast Monsoon ◽  
Data Set ◽  
Proposed Model

Abstract. In this study, the optical properties of aerosols in Penang, Malaysia were analyzed for four monsoonal seasons (northeast monsoon, pre-monsoon, southwest monsoon, and post-monsoon) based on data from the AErosol RObotic NETwork (AERONET) from February 2012 to November 2013. The aerosol distribution patterns in Penang for each monsoonal period were quantitatively identified according to the scattering plots of the aerosol optical depth (AOD) against the Angstrom exponent. A modified algorithm based on the prototype model of Tan et al. (2014a) was proposed to predict the AOD data. Ground-based measurements (i.e., visibility and air pollutant index) were used in the model as predictor data to retrieve the missing AOD data from AERONET because of frequent cloud formation in the equatorial region. The model coefficients were determined through multiple regression analysis using selected data set from in situ data. The predicted AOD of the model was generated based on the coefficients and compared against the measured data through standard statistical tests. The predicted AOD in the proposed model yielded a coefficient of determination R2 of 0.68. The corresponding percent mean relative error was less than 0.33% compared with the real data. The results revealed that the proposed model efficiently predicted the AOD data. Validation tests were performed on the model against selected LIDAR data and yielded good correspondence. The predicted AOD can beneficially monitor short- and long-term AOD and provide supplementary information in atmospheric corrections.

scholarly journals The Old and the New: Can Physics-Informed Deep-Learning Replace Traditional Linear Solvers?

2021 ◽  
Vol 4 ◽  
Author(s):  
Stefano Markidis
Keyword(s):  
Neural Networks ◽  
Deep Learning ◽  
High Performance ◽  
Critical Role ◽  
Low Frequency ◽  
Accurate Solution ◽  
Limiting Factor ◽  
Data Set ◽  
Linear Solvers ◽  
Computational Performance

Physics-Informed Neural Networks (PINN) are neural networks encoding the problem governing equations, such as Partial Differential Equations (PDE), as a part of the neural network. PINNs have emerged as a new essential tool to solve various challenging problems, including computing linear systems arising from PDEs, a task for which several traditional methods exist. In this work, we focus first on evaluating the potential of PINNs as linear solvers in the case of the Poisson equation, an omnipresent equation in scientific computing. We characterize PINN linear solvers in terms of accuracy and performance under different network configurations (depth, activation functions, input data set distribution). We highlight the critical role of transfer learning. Our results show that low-frequency components of the solution converge quickly as an effect of the F-principle. In contrast, an accurate solution of the high frequencies requires an exceedingly long time. To address this limitation, we propose integrating PINNs into traditional linear solvers. We show that this integration leads to the development of new solvers whose performance is on par with other high-performance solvers, such as PETSc conjugate gradient linear solvers, in terms of performance and accuracy. Overall, while the accuracy and computational performance are still a limiting factor for the direct use of PINN linear solvers, hybrid strategies combining old traditional linear solver approaches with new emerging deep-learning techniques are among the most promising methods for developing a new class of linear solvers.

scholarly journals Analysis of simultaneous aerosol and ocean glint retrieval using multi-angle observations

2020 ◽  
Author(s):  
Kirk Knobelspiesse ◽  
Amir Ibrahim ◽  
Bryan Franz ◽  
Sean Bailey ◽  
Robert Levy ◽  
...  
Keyword(s):  
Optical Properties ◽  
Wind Speed ◽  
Radiative Transfer ◽  
Size Distribution ◽  
Atmospheric Correction ◽  
Surface Wind ◽  
Ocean Surface ◽  
True Value ◽  
Aerosol State ◽  
The Impact

Abstract. Since early 2000, NASA's Multi-angle Imaging SpectroRadiometer (MISR) instrument has been performing remote sensing retrievals of aerosol optical properties from the polar orbiting Terra spacecraft. A noteworthy aspect of MISR observations over the ocean is that, for much of the Earth, some of the multi-angle views have contributions from solar reflection by the ocean surface (glint, or glitter), while others do not. Aerosol retrieval algorithms often discard these glint influenced observations because they can overwhelm the signal and are difficult to predict without knowledge of the (wind speed driven) ocean surface roughness. However, theoretical studies have shown that multi-angle observations of a location at geometries with and without reflected sun glint can be a rich source of information, sufficient to support simultaneous retrieval of both the aerosol state and the wind speed at the ocean surface. We are in the early stages of creating such an algorithm. In this manuscript, we describe our assessment of the appropriate level of parameterization for simultaneous aerosol and ocean surface property retrievals using sun glint. For this purpose, we use Generalized Nonlinear Retrieval Analysis (GENRA), an information content assessment (ICA) technique employing Bayesian inference, and simulations from the Ahmad-Fraser iterative radiative transfer code. We find that four parameters are suitable: aerosol optical depth (τ), particle size distribution (expressed as the fine mode fraction f of small particles in a bimodal size distribution), surface wind speed (w), and relative humidity (r, to define the aerosol water content and complex refractive index). None of these parameters define ocean optical properties, as we found that the aerosol state could be retrieved with the nine MISR near-infrared views alone, where the ocean body is black in the open ocean. We also found that retrieval capability varies with observation geometry, and that as τ increases so does the ability to determine aerosol intensive optical properties (r and f, while it decreases for w). Increases in wind speed decrease the ability to determine the true value of that parameter, but have minimal impact on retrieval of aerosol properties. We explored the benefit of excluding the two most extreme MISR view angles for which radiative transfer with the plane parallel approximation is less certain, but found no advantage in doing so. Finally, the impact of treating wind speed as a scalar parameter, rather than as a two parameter directional wind, was tested. While the simpler scalar model does contribute to overall aerosol uncertainty, it is not sufficiently large to justify the addition of another dimension to parameter space. An algorithm designed upon these principles is in development. It will be used to perform an atmospheric correction with MISR for coincident ocean color (OC) observations by the Moderate Resolution Imaging Spectroradiometer (MODIS) instrument, also on the NASA Terra spacecraft. Unlike MISR, MODIS is a single view angle instrument, but it has a more complete set of spectral channels ideal for determination of ocean optical properties. The atmospheric correction of MODIS OC data can therefore benefit from MISR aerosol retrievals. Furthermore, higher spatial resolution data from coincident MISR observations may also improve glint screening.

scholarly journals Influence of light-absorbing particles on snow spectral irradiance profiles

2019 ◽  
Vol 13 (8) ◽  
pp. 2169-2187 ◽  
Author(s):  
Francois Tuzet ◽  
Marie Dumont ◽  
Laurent Arnaud ◽  
Didier Voisin ◽  
Maxim Lamare ◽  
...  
Keyword(s):  
Optical Properties ◽  
Radiative Transfer ◽  
Black Carbon ◽  
Mineral Dust ◽  
Surface Energy Budget ◽  
Spectral Irradiance ◽  
Light Extinction ◽  
Attractive Alternative ◽  
Chemical Measurements ◽  
Radiative Impact

Abstract. Light-absorbing particles (LAPs) such as black carbon or mineral dust are some of the main drivers of snow radiative transfer. Small amounts of LAPs significantly increase snowpack absorption in the visible wavelengths where ice absorption is particularly weak, impacting the surface energy budget of snow-covered areas. However, linking measurements of LAP concentration in snow to their actual radiative impact is a challenging issue which is not fully resolved. In the present paper, we point out a new method based on spectral irradiance profile (SIP) measurements which makes it possible to identify the radiative impact of LAPs on visible light extinction in homogeneous layers of the snowpack. From this impact on light extinction it is possible to infer LAP concentrations present in each layer using radiative transfer theory. This study relies on a unique dataset composed of 26 spectral irradiance profile measurements in the wavelength range 350–950 nm with concomitant profile measurements of snow physical properties and LAP concentrations, collected in the Alps over two snow seasons in winter and spring conditions. For 55 homogeneous snow layers identified in our dataset, the concentrations retrieved from SIP measurements are compared to chemical measurements of LAP concentrations. A good correlation is observed for measured concentrations higher than 5 ng g−1 (r2=0.81) despite a clear positive bias. The potential causes of this bias are discussed, underlining a strong sensitivity of our method to LAP optical properties and to the relationship between snow microstructure and snow optical properties used in the theory. Additional uncertainties such as artefacts in the measurement technique for SIP and chemical contents along with LAP absorption efficiency may explain part of this bias. In addition, spectral information on LAP absorption can be retrieved from SIP measurements. We show that for layers containing a unique absorber, this absorber can be identified in some cases (e.g. mineral dust vs. black carbon). We also observe an enhancement of light absorption between 350 and 650 nm in the presence of liquid water in the snowpack, which is discussed but not fully elucidated. A single SIP acquisition lasts approximately 1 min and is hence much faster than collecting a profile of chemical measurements. With the recent advances in modelling LAP–snow interactions, our method could become an attractive alternative to estimate vertical profiles of LAP concentrations in snow.

scholarly journals Monte Carlo radiative transfer for the nebular phase of Type Ia supernovae

2019 ◽  
Vol 492 (2) ◽  
pp. 2029-2043 ◽  
Author(s):  
L J Shingles ◽  
S A Sim ◽  
M Kromer ◽  
K Maguire ◽  
M Bulla ◽  
...  
Keyword(s):  
Radiative Transfer ◽  
Atomic Data ◽  
Type Ia Supernovae ◽  
Data Set ◽  
High Ionization ◽  
Type Ia ◽  
Non Local ◽  
Ionization Balance ◽  
Ia Supernovae ◽  
Modest Effect

ABSTRACT We extend the range of validity of the artis 3D radiative transfer code up to hundreds of days after explosion, when Type Ia supernovae (SNe Ia) are in their nebular phase. To achieve this, we add a non-local thermodynamic equilibrium population and ionization solver, a new multifrequency radiation field model, and a new atomic data set with forbidden transitions. We treat collisions with non-thermal leptons resulting from nuclear decays to account for their contribution to excitation, ionization, and heating. We validate our method with a variety of tests including comparing our synthetic nebular spectra for the well-known one-dimensional W7 model with the results of other studies. As an illustrative application of the code, we present synthetic nebular spectra for the detonation of a sub-Chandrasekhar white dwarf (WD) in which the possible effects of gravitational settling of 22Ne prior to explosion have been explored. Specifically, we compare synthetic nebular spectra for a 1.06 M⊙ WD model obtained when 5.5 Gyr of very efficient settling is assumed to a similar model without settling. We find that this degree of 22Ne settling has only a modest effect on the resulting nebular spectra due to increased 58Ni abundance. Due to the high ionization in sub-Chandrasekhar models, the nebular [Ni ii] emission remains negligible, while the [Ni iii] line strengths are increased and the overall ionization balance is slightly lowered in the model with 22Ne settling. In common with previous studies of sub-Chandrasekhar models at nebular epochs, these models overproduce [Fe iii] emission relative to [Fe ii] in comparison to observations of normal SNe Ia.

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