Plane-parallel Atmosphere Research Articles

Physics-informed neural networks for modeling atmospheric radiative transfer

Understanding the radiative transfer processes in the Earth’s atmosphere is crucial for accurate climate modeling and climate change predictions. These processes are governed by complex physical phenomena, which can be generally modeled by the radiative transfer equation (RTE). Solutions to the RTE are obtained by various methods including numerical (standard RTE solvers), stochastic (Monte-Carlo), and data-driven (machine-learning) approaches. This paper introduces a novel numerical approach utilizing a Physics-Informed Neural Network (PINN) to solve the RTE in atmospheric scenarios, applying physics constraints in a machine-learning framework. We show that our PINN model offers a flexible and efficient solution, enabling the simulation of radiance values using plane-parallel atmosphere, and under diverse conditions, including clouds and aerosols.

Chemical composition of planetary hosts: C, N, and α-element abundances

Accurate atmospheric parameters and chemical composition of planet hosts play a major role in characterising exoplanets and understanding their formation and evolution. Our objective is to uniformly determine atmospheric parameters and chemical abundances of carbon (C), nitrogen (N), oxygen(O), and the alpha -elements, magnesium (Mg) and silicon (Si), along with C/O, N/O and Mg/Si abundance ratios for planet-hosting stars. In this analysis, we aim to investigate the potential links between stellar chemistry and the presence of planets. e tai Observatory telescope. The determination of stellar parameters was based on a standard analysis using equivalent widths and one-dimensional, plane-parallel model atmospheres calculated under the assumption of local thermodynamical equilibrium. The differential synthetic spectrum method was used to uniformly determine the carbon C(C2), nitrogen N(CN), oxygen O I magnesium Mg I, and silicon Si I elemental abundances as well as the C/O, N/O, and Mg/Si ratios. We analysed elemental abundances and ratios in dwarf and giant stars, finding that C/Fe O/Fe and Mg/Fe are lower in metal-rich dwarf hosts; whereas N/Fe is close to the Solar ratio. Giants show smaller scatter in C/Fe and O/Fe and lower than the Solar average C/Fe and C/O ratios. The (C+N+O) abundances increase with Fe/H in giant stars, with a minimal scatter. We also noted an overabundance of Mg and Si in planet-hosting stars, particularly at lower metallicities, and a lower Mg/Si ratio in stars with planets. In giants hosting high-mass planets, nitrogen shows a moderate positive relationship with planet mass. C/O and N/O ratios show moderate negative and positive slopes in giant stars, respectively. The Mg/Si ratio shows a negative correlation with planet mass across the entire stellar sample.

Jacobian-free Newton-Krylov method for multilevel nonlocal thermal equilibrium radiative transfer problems

Context. The calculation of the emerging radiation from a model atmosphere requires knowledge of the emissivity and absorption coefficients, which are proportional to the atomic level population densities of the levels involved in each transition. Due to the intricate interdependence of the radiation field and the physical state of the atoms, iterative methods are required in order to calculate the atomic level population densities. A variety of different methods have been proposed to solve this problem, which is known as the nonlocal thermodynamical equilibrium (NLTE) problem. Aims. Our goal is to develop an efficient and rapidly converging method to solve the NLTE problem under the assumption of statistical equilibrium. In particular, we explore whether the Jacobian-Free Newton-Krylov (JFNK) method can be used. This method does not require an explicit construction of the Jacobian matrix because it estimates the new correction with the Krylov-subspace method. Methods. We implemented an NLTE radiative transfer code with overlapping bound-bound and bound-free transitions. This solved the statistical equilibrium equations using a JFNK method, assuming a depth-stratified plane-parallel atmosphere. As a reference, we also implemented the Rybicki & Hummer (1992) method based on linearization and operator splitting. Results. Our tests with the Fontenla, Avrett and Loeser C model atmosphere (FAL-C) and two different six-level Ca II and H I atoms show that the JFNK method can converge faster than our reference case by up to a factor 2. This number is evaluated in terms of the total number of evaluations of the formal solution of the radiative transfer equation for all frequencies and directions. This method can also reach a lower residual error compared to the reference case. Conclusions. The JFNK method we developed poses a new alternative to solving the NLTE problem. Because it is not based on operator splitting with a local approximate operator, it can improve the convergence of the NLTE problem in highly scattering cases. One major advantage of this method is that it is expected to allow for a direct implementation of more complex problems, such as overlapping transitions from different active atoms, charge conservation, or a more efficient treatment of partial redistribution, without having to explicitly linearize the equations.

X-ray polarisation signatures in bombarded magnetar atmospheres

Abstract Magnetars are neutron stars that host huge, complex magnetic fields which require supporting currents to flow along the closed field lines. This makes magnetar atmospheres different from those of passively cooling neutron stars because of the heat deposited by backflowing charges impinging on the star surface layers. This particle bombardment is expected to imprint the spectral and, even more, the polarisation properties of the emitted thermal radiation. We present solutions for the radiative transfer problem for bombarded plane-parallel atmospheres in the high magnetic field regime. The temperature profile is assumed a priori, and selected in such a way to reflect the varying rate of energy deposition in the slab (from the impinging currents and/or from the cooling crust). We find that thermal X–ray emission powered entirely by the energy released in the atmosphere by the magnetospheric back–bombardment is linearly polarised and X-mode dominated, but its polarisation degree is significantly reduced (down to 10%–50%) when compared with that expected from a standard atmosphere heated only from the cooling crust below. By increasing the fraction of heat flowing in from the crust the polarisation degree of the emergent radiation increases, first at higher energies (∼10 keV) and then in the entire soft X-ray band. We use our models inside a ray-tracing code to derive the expected emission properties as measured by a distant observer and compare our results with recent IXPE observations of magnetar sources.

An Expanding Accretion Disk and a Warm Disk Wind as Seen in the Spectral Evolution of HBC 722

We present a comprehensive analysis of the post-outburst evolution of the FU Ori object HBC 722 in optical/near-infrared (NIR) photometry and spectroscopy. Using a modified viscous accretion disk model, we fit the outburst epoch spectral energy distribution to determine the physical parameters of the disk, including Ṁacc=10−4.0M⊙ yr−1, R inner = 3.65 R ⊙, i = 79°, and a maximum disk temperature of Tmax=5700 K. We then use a decade of optical/NIR spectra to demonstrate a changing accretion rate drives the visible-range photometric variation, while the NIR shows the outer radius of the active accretion disk expands outward as the outburst progresses. We also identify the major components of the disk system: a plane-parallel disk atmosphere in Keplerian rotation and a two-part warm disk wind that is collimated near the star and wide-angle at larger radii. The wind is traced by classic wind lines, and appears as a narrow, low-velocity, deep absorption component in several atomic lines spanning the visible spectrum and in the CO 2.29 μm band. We compare the wind lines to those computed from wind models for other FU Ori systems and rapidly accreting young stellar disks and find a 4000–6000 K wind can explain the observed line profiles. Fitting the progenitor spectrum, we find M * = 0.2 M ⊙ and Ṁprogenitor=7.8×10−8M⊙yr−1 . Finally, we discuss HBC 722 relative to V960 Mon, another FU Ori object we have previously studied in detail.

Radiation hydrodynamics in a moving plasma with Compton scattering: Frequency-dependent solutions

Abstract Radiation hydrodynamical equations with Compton scattering are generally difficult to solve analytically, and usually examined numerically, even if in the subrelativistic regime. We examine the equations available in the subrelativistic regime of kBT$/$(mec2) ≲ 0.1, hν$/$(mec2) ≲ 0.1, and v$/$c ≲ 0.1, where T is the electron temperature, ν the photon frequency, and v the fluid bulk velocity. For simplicity, we ignore the induced scattering terms. We then seek and obtain analytical solutions of frequency-dependent radiative moment equations of a hot plasma with bulk motions for several situations in the subrelativistic regime. For example, in the static case of a plane-parallel atmosphere without bulk motions, where equations involve the generalized Kompaneets equation with subrelativistic corrections, we find the Wien-type solution, which reduces to the usual Milne–Eddington solution in the nonrelativistic limit, as well as the power-law-type one, which has a form of [hν$/$(kBT)]−4. In the moving case of an accelerating one-dimensional flow with bulk motions, we also find the Wien-type and the power-law-type solutions affected by the bulk Compton effect. Particularly, in the Wien-type solutions, due to the bulk Compton effect, the radiation fields gain momentum from the hot plasma in the low-frequency regime of hν < 3kBT, while they lose it in the high-frequency regime of hν > 3kBT.

Low-frequency Internal Gravity Waves Are Pseudo-incompressible

Starting from the fully compressible fluid equations in a plane-parallel atmosphere, we demonstrate that linear internal gravity waves are naturally pseudo-incompressible in the limit that the wave frequency ω is much less than that of surface gravity waves, i.e., ω≪gkh , where g is the gravitational acceleration and k h is the horizontal wavenumber. We accomplish this by performing a formal expansion of the wave functions and the local dispersion relation in terms of a dimensionless frequency ε=ω/gkh . Further, we show that, in this same low-frequency limit, several forms of the anelastic approximation, including the Lantz–Braginsky–Roberts formulation, poorly reproduce the correct behavior of internal gravity waves. The pseudo-incompressible approximation is achieved by assuming that Eulerian fluctuations of the pressure are small in the continuity equation—whereas, in the anelastic approximation, Eulerian density fluctuations are ignored. In an adiabatic stratification, such as occurs in a convection zone, the two approximations become identical. However, in a stable stratification, the differences between the two approximations are stark and only the pseudo-incompressible approximation remains valid.

PEREGRINATIONS ON THE STUDY OF THE OPTICAL PROPERTIES OF NONSPHERICAL PARTICLES

PEREGRINATIONS ON THE STUDY OF THE OPTICAL PROPERTIES OF NONSPHERICAL PARTICLES

The True Nature of the Brightest Local Triple Stellar Candidates within 100 pc in the Galaxy

We present a study of a sample of bright (V ≤ 10 mag) and close (d ≤ 100 pc) triple–stellar system candidates in the galaxy, consisting of eight systems in total. Our aim is to determine their actual multiplicity and the physical properties of each stellar component in the systems. The sample was analyzed using a complex spectrophotometric technique by Al-Wardat that utilizes ATLAS9 line-blanketed plane-parallel model atmospheres. Based on our analysis, we found that five of the systems (HIP 109951, HIP 105947, HIP 40523, HIP 35733, and HIP 23824) are indeed triples, while the remaining three systems (HIP 9642, HIP 59426, and HIP 101227) are more consistent with being quadruples. We estimated the physical properties of the individual components using the most recent parallax measurements from the GAIA Data Release 3 catalog. We also examined the applicability of the well-established Mass–Luminosity (M–L) relation for individual components of all the stellar systems that have been analyzed by the Al-Wardat technique. We found that generally, the components are in good agreement with the established relationship. This further supports the reliability of the method in determining the physical properties of multiple stellar systems. In addition, we investigated the M–L relation for each order of stellar multiplicity (i.e., binary, triple, and quadruple) by performing linear fitting to the data. It was found that the slopes for each multiplicity are consistent with each other. The relations also seem to shift down in luminosity for a given total mass, as the order of multiplicity increases from binary to quadruple.

Radiative interaction of atmosphere and surface: Write-up with elements of code

In passive satellite remote sensing of the Earth, separation of the path radiance (atmosphere-only contribution) from the surface reflection remains a “significant challenge”. Recent literature names it among the gaps in radiative transfer (RT) topics that “require continued research in the near future”. The challenge comes from multiple reflections (bouncing) between the atmosphere and surface – radiative interaction. In this paper we use a known RT technique, the matrix-operator method (MOM), and a new modification of the monochromatic vector RT (vRT) code IPOL (Intensity and POLarization) to simulate the interaction of a plane-parallel atmosphere and a few widely used surface reflection models.Following the idea of the Green's function method, IPOL no longer takes the surface model parameters on input. Instead, it provides the path radiance, and the atmospheric reflection and transmission matrices as output. Despite many RT codes use the MOM formalism, this output does not seem common. The surface reflection matrix is computed externally. Therefore, this paper extends the Green's function atmospheric correction technique to the case of polarized light.Aiming clarity rather than performance, we explain in Python the structure of the surface matrices for the isotropic (Lambertian), directional unpolarized, and polarized ocean reflection models. We then combine these surface matrices and the precomputed IPOL output to get numerically accurate signal at the top of atmosphere (TOA) and test it vs. published benchmarks. Then, for each benchmark scenario we show how to get the surface from the TOA signal, i.e. perform the RT-based atmospheric correction.

The Shapes of Stellar Spectra

Stellar atmospheres separate the hot and dense stellar interiors from the emptiness of space. Radiation escapes from the outermost layers of a star, carrying direct physical information. Underneath the atmosphere, the very high opacity keeps radiation thermalized and resembling a black body with the local temperature. In the atmosphere the opacity drops, and radiative energy leaks out, which is redistributed in wavelength according to the physical processes by which matter and radiation interact, in particular photoionization. In this article, I will evaluate the role of photoionization in shaping the stellar energy distribution of stars. To that end, I employ simple, state-of-the-art plane-parallel model atmospheres and a spectral synthesis code, dissecting the effects of photoionization from different chemical elements and species, for stars of different masses in the range of 0.3 to 2 M⊙. I examine and interpret the changes in the observed spectral energy distributions of the stars as a function of the atmospheric parameters. The photoionization of atomic hydrogen and H− are the most relevant contributors to the continuum opacity in the optical and near-infrared regions, while heavier elements become important in the ultraviolet region. In the spectra of the coolest stars (spectral types M and later), the continuum shape from photoionization is no longer recognizable due to the accumulation of lines, mainly from molecules. These facts have been known for a long time, but the calculations presented provide an updated quantitative evaluation and insight into the role of photoionization on the structure of stellar atmospheres.

Synthesizing Spectra from 3D Radiation Hydrodynamic Models of Massive Stars Using Monte Carlo Radiation Transport

Observations indicate that turbulent motions are present on most massive star surfaces. Starting from the observed phenomena of spectral lines with widths that are much larger than their thermal broadening (e.g., micro- and macroturbulence), and considering the detection of stochastic low-frequency variability (SLFV) in the Transiting Exoplanet Survey Satellite photometry, these stars clearly have large-scale turbulent motions on their surfaces. The cause of this turbulence is debated, with near-surface convection zones, core internal gravity waves, and wind variability being proposed. Our 3D gray radiation hydrodynamic (RHD) models previously characterized the convective dynamics of the surfaces, driven by near-surface convection zones, and provided reasonable matches to the observed SLFV of the most luminous massive stars. We now explore the complex emitting surfaces of these 3D RHD models, which strongly violate the 1D assumption of a plane-parallel atmosphere. By post-processing the gray RHD models with the Monte Carlo radiation transport code Sedona, we synthesize stellar spectra and extract information from the broadening of individual photospheric lines. The use of Sedona enables the calculation of the viewing angle and temporal dependence of spectral absorption line profiles. By combining uncorrelated temporal snapshots together, we compare the turbulent broadening from the 3D RHD models to the thermal broadening of the extended emitting region, showing that our synthesized spectral lines closely resemble the observed macroturbulent broadening from similarly luminous stars. More generally, the new techniques that we have developed will allow for systematic studies of the origins of turbulent velocity broadening from any future 3D simulations.

Effects of rotation on the spectra of brown dwarfs

ABSTRACT Measured rotational speeds of giant planets and brown dwarfs frequently constitute appreciable fractions of the breakup limit, resulting in centrifugal expansion of these objects at the equator. According to models of internal energy transport, this expansion ought to make the poles of a rotator significantly hotter than the equator, so that inclination of the rotational axis greatly affects both spectral shape and total flux. In this paper, we explore the dependence of a substellar object’s observables on its rotational speed and axis inclination. To do so, we combine picaso (Planetary Intensity Code for Atmospheric Spectroscopy Observations) with software pars (Paint the Atmospheres of Rotating Stars). The former computer program models radiative transfer within plane-parallel planetary atmospheres, while the latter computes disc-integrated spectra of centrifugally deformed gaseous masses. We find that the specific flux of a typical fast-rotating brown dwarf can increase by as much as a factor of 1.5 with movement from an equator-on to a pole-on view. On the other hand, the distinctive effect of rotation on spectral shape increases toward the equator-on view. The latter effect also increases with lower effective temperature. The bolometric luminosity estimate for a typical fast rotator at extreme inclinations has to be adjusted by as much as ${\sim} 20{{\ \rm per\ cent}}$ due to the anisotropy of the object’s observed flux. We provide a general formula for the calculation of the corresponding adjustment factor in terms of rotational speed and inclination.

Polarized discrete ordinate adding approximation for infrared and microwave radiative transfer

A POLarized Discrete ordinate aDding Approximation (POLDDA) is proposed to solve the vector thermal radiative transfer equation in a vertically inhomogeneous plane-parallel atmosphere. The discrete ordinates method is employed to find the single-layer solution for vector thermal radiative transfer; this is an extension of the approach for scalar radiative transfer, with the I- and Q-components being dealt with in a parallel way by using a doubled dimension in the discrete ordinate space. Chandrasekhar’s invariance principle is used to drive the adding process for the connection of multiple layers. This adding process has no restriction on the layer optical properties. The accuracy and efficiency of POLDDA are evaluated under different atmospheric conditions for different number of computational quadrature angles (streams). It is shown that the relative differences between POLDDA (using 32 or 16 streams) and the benchmark calculations (PolRadtran/RT3 with 32 streams, a typical model based on the adding-doubling method) are negligible for both I- and Q-components. When 8 streams are used, the accuracy of POLDDA slightly decreases, but still higher than that of 8-stream RT3. The computational efficiency of POLDDA is much higher than RT3, especially for large optical depths and when a large number of streams (≥ 16) are used. Unlike RT3, the computational time of POLDDA is always the same regardless of the optical depth.

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.

Computation of longwave radiative flux and vertical heating rate with 4A-Flux v1.0 as an integral part of the radiative transfer code 4A/OP v1.5

Abstract. Based on advanced spectroscopic databases, line-by-line and layer-by-layer radiative transfer codes numerically solve the radiative transfer equation with very high accuracy. Taking advantage of its pre-calculated optical depth lookup table, the fast and accurate radiative transfer model Automatized Atmospheric Absorption Atlas OPerational (4A/OP) calculates the transmission and radiance spectra for a user-defined layered atmospheric model. Here, we present a module called 4A-Flux, which is developed and implemented into 4A/OP in order to include the calculation of the clear-sky longwave radiative flux profiles and heating rate profiles at a very high spectral resolution. Calculations are performed under the assumption of local thermodynamic equilibrium, a plane-parallel atmosphere, and specular reflection on the surface. The computation takes advantage of pre-tabulated exponential integral functions that are used instead of a classic angular quadrature. Furthermore, the sub-layer variation of the Planck function is implemented to better represent the emission of layers with a high optical depth. Thanks to the implementation of 4A-Flux, 4A/OP models have participated in the Radiative Forcing Model Intercomparison Project (RFMIP-IRF) along with other state-of-the-art radiative transfer models. 4A/OP hemispheric flux profiles are compared to other models over the 1800 representative atmospheric situations of RFMIP, yielding an outgoing longwave radiation (OLR) mean difference between 4A/OP and other models of −0.148 W m−2 and a standard deviation of 0.218 W m−2, showing a good agreement between 4A/OP and other models. 4A/OP is applied to the Thermodynamic Initial Guess Retrieval (TIGR) atmospheric database to analyze the response of the OLR and vertical heating rate to several perturbations of temperature or gas concentration. This work shows that 4A/OP with 4A-Flux module can successfully be used to simulate accurate flux and heating rate profiles and provide useful sensitivity studies including sensitivities to minor trace gases such as HFC134a, HCFC22, and CFC113. We also highlight the interest for the modeling community to extend intercomparison between models to comparisons between spectroscopic databases and modeling to improve the confidence in model simulations.

Numerical results for polarized light scattering in a spherical atmosphere

We report numerical results for polarized light reflection from the top of a Rayleigh scattering spherical atmosphere with height-dependent single scattering albedo over a dark surface. Michael Mishchenko considered this scenario back in the 1990’s, for a plane-parallel atmosphere of unit optical thickness (OT = 1), for which radiance errors arising from neglecting polarization reaches their highest values. To further extend Mishchenko's results, we consider a value of OT = 0.25, for which the effect of atmospheric curvature is pronounced. New results are generated using three state-of-the art radiative transfer (RT) codes. These are: the MYSTIC and MCSSA models, which simulate light scattering in a true-spherical atmosphere using Monte Carlo methods; and the discrete ordinate code VLIDORT, operating with a new multiple-scatter spherical correction designed to deliver reasonable approximations to spherical-medium scattering. In this work, we report results for both single and multiple scattering; this will help to support the validation of existing and future polarized spherical RT codes, especially those using approximative methods to deal with sphericity.

Atmospheric and Fundamental Parameters of Eight Nearby Multiple Stars

We present the complete set of atmospheric and fundamental parameters, in addition to the masses, for the individual components of eight stellar systems. The list of the systems, whose orbital solutions were published recently, includes seven binaries (HIP 14524, HIP 16025, HIP 46199, HIP 47791, HIP 60444, HIP 61100, HIP 73085) and one triple system (HIP 28671). The systems were analyzed using a spectrophotometric computational technique known as Al-Wardats method for analyzing binary and multiple stellar systems, which makes use of ATLAS9 line-blanketed plane-parallel model atmospheres. Using these estimated parameters, the positions of the components were located on the Hertzsprung–Russell diagram, evolutionary tracks and isochrones to estimate their ages, the range depending on the uncertainties in their metallicities. Five systems were found to be pre-main-sequence stars (HIP 14524, HIP 46199, HIP 60444, HIP 61100, HIP 73085), two were main-sequence stars (the zero-age HIP 28671 and the 6.3 Gyr HIP 16025), and one is a subgiant system (HIP 47791) with an age of 1.4 Gyr. Fragmentation is proposed as the most probable formation process for the eight systems. A comparison between the estimated masses and the dynamical ones lead to new dynamical parallaxes for four systems: (28.63 ± 0.56) mas for HIP 14524, (15.6 ± 0.63) mas for HIP 16025, (9.73 ± 0.26) mas for HIP 47791, and (16.53 ± 0.59) mas for HIP 73085. Hence, the orbital solutions were reclassified. We conclude that Gaia DR3 parallaxes are more precise than those given by Gaia DR2 and Hipparcos 2.

A practical guide to writing a radiative transfer code

Using our decades-long experience in radiative transfer (RT) code development for Earth science, we endeavor to reduce the knowledge gap of bringing RT from theory to code quickly. Despite numerous classic and recent literature, it is still hard to develop an RT code from scratch within a few weeks. It is equally hard to understand, not to mention modify, an existing “monster” RT code, for which the developer is either located remotely or has retired. Following the format of “Numerical Recipes” by Press et al., we collocate in this paper small pieces of necessary theory with corresponding small pieces of RT code. These are arranged in an order that is natural for code development, which is often opposite of the natural order for laying out the theoretical basis. We focus on the transfer of unpolarized monochromatic solar radiation in a plane-parallel atmosphere over a reflecting surface. Both the surface and the atmosphere are homogeneous (uniform) at all directions. The multiple scattering is numerically solved using the deterministic method of Gauss-Seidel iterations. Except for the presented Python-Numba open-source RT code gsit, the paper does not report any new scientific results, but rather serves as an academic demonstration. If development time is an issue or the reader is familiar with basic concepts of RT theory, we recommend proceeding directly to Sec. 3 “RT code development”. Program summaryProgram title: gsit (pronounced “jeezit”)CPC Library link to program files:https://doi.org/10.17632/d3zt5zhx49.1Developer's repository link:https://github.com/korkins/gsitLicensing provisions: MITProgramming language: Python 3Nature of problem: We present a tutorial code in Python for deterministic (non-stochastic) numerical simulation of multiple scattering of monochromatic solar light in a plane-parallel Earth atmosphere bounded from below by a reflecting surface. The problem is solved in a simplified form (i.e., uniform atmosphere, no polarization, uniform surface reflectance, etc.) to better explain numerical features, rather than physics, of propagation of light in the atmosphere.Solution method: The method of Gauss-Seidel iterations. It relies on the Fourier decomposition of the Radiative Transfer Equation over azimuth, Gauss quadrature for numerical integration over the zenith and iterative process for integration over height (optical depth) with analytical (hence known) single scattering approximation being the starting point. The method is relatively simple to code and does not require any external libraries.

Can the Earth–Moon Distance Influence the Accuracy of Lunar Irradiance with the Plane-Parallel Assumption in Atmospheric Radiative Transfer at Night?

AbstractThe plane-parallel atmosphere as an underlying assumption in physics is appropriately used in the rigorous numerical simulation of the atmospheric radiative transfer model (RTM) with incident solar light. The solar irradiance is a constant with the plane-parallel assumption, which is attributed to the small difference in the distance between any point on Earth’s surface to the sun. However, at night, atmospheric RTMs use the moon as a unique incident light source in the sky. The Earth–moon distance is approximately 1/400 of the Earth–sun distance. Thus, the varying Earth–moon distance on Earth’s surface can influence the top of atmosphere (TOA) lunar irradiance for the plane-parallel atmosphere assumption. In this investigation, we observe that the maximum biases in Earth–moon distance and day/night band lunar irradiance at the TOA are ±1.7% and ±3.3%, respectively, with the plane-parallel assumption. According to our calculations, this bias effect on the Earth–moon distance and lunar irradiance shows a noticeable spatiotemporal variation on a global scale that can impact the computational accuracy of an RTM at night. In addition, we also developed a fast and portable correction algorithm for the Earth–moon distance within a maximum bias of 18 km or ±0.05%, because of the relatively low computational efficiency and the large storage space necessary for the standard ephemeris computational software. This novel correction algorithm can be easily used or integrated into the atmospheric RTM at night.