Approximate Radiative Transfer Research Articles

Computing enhancement of the nonlinear SPN approximations of radiative heat transfer in participating material

Anisotropic mesh adaptation is an efficient procedure for controlling the output error of finite element simulations, particularly when used for three-dimensional problems. In this paper, we present an enhanced computational algorithm based on an anisotropic mesh adaptation for nonlinear SPN approximations of radiative heat transfer in both two- and three-dimensional enclosures. Using an asymptotic analysis for the optical scale in the radiative transfer, the integro-differential equation is replaced by a series of partial differential equations of elliptic type. The nonlinear coupling between the heat transfer and radiation in the SPN equations does not depend on the direction ordinates. In an anisotropic participating media, internal boundary layers with different magnitudes occur for each direction and developing an efficient numerical algorithm to accurately resolve them is a challenging task. In the present study, we propose an adaptive finite element method using an efficient hierarchical error estimator. A second-order scheme is used for the time integration and a Newton-type solver is implemented for the fully coupled nonlinear system. The proposed method has the potential to use large timesteps in the simulations for radiative heat transfer in anisotropic media at high temperatures. To demonstrate the viability of the method, several examples are presented for two- and three-dimensional problems. The numerical results confirm the capability of the proposed method to efficiently solve the nonlinear SPN approximations of radiative transfer in anisotropic media.

Predictions of the P1 approximation for radiative heat transfer in heterogeneous granular media

The P1 approximation is a computationally efficient model for thermal radiation. Here, we present a P1 formulation in the context of the combined computational fluid dynamics and discrete element method (CFD-DEM), including closures for dependent scattering and coarse-graining. Using available analytical and semi-analytical solutions, we find agreement for steady-state and transient quantities in size-disperse systems. Heat flux is identified as the most sensitive quantity to predict, displaying unphysical spatial oscillations. These oscillations are due to a temperature slip at the locations of abrupt change in solid fraction. We propose two techniques that mitigate this effect: smoothing of the radiative properties, and pseudo-scattering. Furthermore, using up to a million times enlarged particles, we demonstrate practically limitless compatibility with coarse-graining. Finally, we compare predictions made with our code to experimental data for a pebble bed under vacuum conditions, and in presence of nitrogen. We find that a carefully calibrated simulation can replicate trends observed in experiments, with relative temperature error of less than 10%.

Approximation of Radiative Transfer for Surface Spectral Features

Remote sensing hyperspectral and more generally spectral instruments are common tools to decipher surface features in Earth and Planetary science. While linear mixture is the most common approximation for compounds detection (mineral, water, ice, etc...), the transfer of light in surface and atmospheric medium are highly non-linear. The exact simulation of non-linearities can be estimated at very high numerical cost. Here I propose a very simple non-linear form (that includes the regular linear area mixture) of radiative transfer to approximate surface spectral feature. I demonstrate that this analytical form is able to approximate the grain size and intimate mixture dependence of surface features. In addition, the same analytical form can approximate the effect of Martian mineral aerosols. Unfortunately, Earth aerosols are more complex (water droplet, water ice, soot,...) and are not expected to follow the same trend.

Thermal discrete dipole approximation for near-field radiative heat transfer in many-body systems with arbitrary nonreciprocal bodies

The theoretical study of many-body effects in the context of near-field radiative heat transfer (NFRHT) has already led to the prediction of a plethora of thermal radiation phenomena. Special attention has been paid to nonreciprocal systems in which the lack of the Lorentz reciprocity has been shown to give rise to unique physical effects. However, most of the theoretical work in this regard has been carried out with the help of approaches that consider either point-like particles or highly symmetric bodies (such as spheres), which are not easy to realize and explore experimentally. In this work we develop a many-body approach based on the thermal discrete dipole approximation (TDDA) that is able to describe the NFRHT between nonreciprocal objects of arbitrary size and shape. We illustrate the potential and the relevance of this approach with the analysis of two related phenomena, namely the existence of persistent thermal currents and the photon thermal Hall effect, in a system with several magneto-optical bodies. Our many-body TDDA approach paves the way for closing the gap between experiment and theory that is hindering the progress of the topic of NFRHT in many-body systems.

Empirical Dust Attenuation Model Leads to More Realistic UVJ Diagram for TNG100 Galaxies

Dust attenuation varies substantially from galaxy to galaxy and as of yet cannot be reproduced from first principles in theoretical models. In Nagaraj et al., we developed the first Bayesian population model of dust attenuation as a function of stellar population properties and projected galaxy shape, built on spectral energy distribution fits of nearly 30,000 galaxies in the 3D-HST grism survey with broadband photometric coverage from the rest-frame UV to IR. In this paper, we apply the model, named “DustE,” to galaxies from the large-volume cosmological simulation TNG100 at z = 1. We produce a UVJ diagram and compare it with one obtained in previous work by applying approximate radiative transfer to the simulated galaxies. We find that the UVJ diagram based on our empirical model is in better agreement with observations than the previous effort, especially in the number density of dusty star-forming galaxies. We also construct the intrinsic dust-free UVJ diagram for TNG100 and 3D-HST galaxies at z ∼ 1, finding qualitative agreement but residual differences at the 10%–20% level. These differences may be caused by the finding that TNG100 galaxies have, on average, 29% younger stellar populations and possibly higher metallicities than observed galaxies.

Dynamics of tangent-hyperbolic nanoliquids configured by stratified extending surface: Effects of transpiration, Robin conditions and dual stratifications

A mathematical study is presented to evaluate double stratification effects on the dual convected flow of a non-Newtonian (tangent-hyperbolic) nanoliquid persuaded by porous stretching surface. Thermal radiation along with transpiration (wall suction/injection) and heat source/sink are included. Buongiorno's model is employed for nanoscale effects and a Rosseland diffusion approximation for nonlinear radiative heat transfer. Appropriate similarity transformations are deployed to alter the dimensional governing nonlinear PDEs (partial differential equations) to a nonlinear differential one with physically viable boundary conditions. The transformed dimensionless BVP (boundary value problem) is computed analytically by a HAM (homotopic analysis method) algorithm and a symbolic software. Validation with earlier studies employing the numerical method (Runge-Kutta-Fehlberg) is included. The evolution in velocity, thermal and solutal (nanoparticle) fields are interpreted through graphical outcomes for the impact of significant sundry parameters. Tabular outcomes are also presented for skin-friction, local Nusselt and Sherwood numbers. A rise in material variable (Weissenberg number), the flow is decelerated while it is accelerated with increasing nonlinear thermal convective parameter, mixed convection parameter and buoyancy ratio values. Temperatures are boosted with increment in radiative, thermophoresis, Brownian motion, thermal Biot number and heat generation parameters whereas they are reduced with increasing thermal stratification parameter. Nanoparticle concentration values are suppressed with higher Schmidt number, Brownian movement and solutal stratification variable however they are boosted with greater values of thermophoresis and concentration Biot number. Local Sherwood number is improved with Schmidt number, concentration stratification parameter and concentration Biot number. Local Nusselt number is strongly increased with greater Prandtl number, thermal stratification number, thermal Biot number and radiative parameter. The study finds applications in thermal nano-polymeric coating flows in materials processing operations.

The effects of local stellar radiation and dust depletion on non-equilibrium interstellar chemistry

ABSTRACT Interstellar chemistry is important for galaxy formation, as it determines the rate at which gas can cool, and enables us to make predictions for observable spectroscopic lines from ions and molecules. We explore two central aspects of modelling the chemistry of the interstellar medium (ISM): (1) the effects of local stellar radiation, which ionizes and heats the gas, and (2) the depletion of metals on to dust grains, which reduces the abundance of metals in the gas phase. We run high-resolution (400 M⊙ per baryonic particle) simulations of isolated disc galaxies, from dwarfs to Milky Way-mass, using the fire galaxy formation models together with the chimes non-equilibrium chemistry and cooling module. In our fiducial model, we couple the chemistry to the stellar fluxes calculated from star particles using an approximate radiative transfer scheme; and we implement an empirical density-dependent prescription for metal depletion. For comparison, we also run simulations with a spatially uniform radiation field, and without metal depletion. Our fiducial model broadly reproduces observed trends in H i and H2 mass with stellar mass, and in line luminosity versus star formation rate for [C ii]$_{158 \rm {\mu m}}$, [O i]$_{63 \rm {\mu m}}$, [O iii]$_{88 \rm {\mu m}}$, [N ii]$_{122 \rm {\mu m}}$, and H α6563Å. Our simulations with a uniform radiation field predict fainter luminosities, by up to an order of magnitude for [O iii]$_{88 \rm {\mu m}}$ and H α6563Å, while ignoring metal depletion increases the luminosity of carbon and oxygen lines by a factor ≈ 2. However, the overall evolution of the galaxy is not strongly affected by local stellar fluxes or metal depletion, except in dwarf galaxies where the inclusion of local fluxes leads to weaker outflows and hence higher gas fractions.

Publisher's Note: “The gray body approximation for radiative heat transfer in evacuated tube solar collectors: Effects of envelope infrared transparency” [J. Appl. Phys. 131, 125001 (2022)

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The gray body approximation for radiative heat transfer in evacuated tube solar collectors: Effects of envelope infrared transparency

A theoretical and experimental analysis is carried out of radiative heat transfer in the coaxial geometry of evacuated tube solar collectors. The gray body approximation implicit in the use of an effective emissivity does not strictly apply to evacuated tube solar collectors due to selective absorber coating and partially transmitting outer glass in the thermal infrared, especially when constructed from borosilicate. We develop analytic expressions for the heat transfer through the outer envelope and show the equations no longer follow a simple form where an effective emissivity for the system can be defined. To test all approximations in practice, an experiment is performed using an evacuated solar collector manufactured in the 1980s by the Nitto Kohki company in Japan using the effective emissivity approximation to determine the typical heat transfer characteristics using net radiative heat flows in both directions. This method enabled a good fit to temperature–time data for cooling and heating of the inner tube for temperatures between 10 and 85 °C. The results confirm that the effective emittance method can be used in situations with typical glass wall thickness and temperatures. At temperatures greater 100 °C, the spectral distribution of the emitted radiation falls significantly within the transmitting region of the outer glass and can no longer be neglected. The work has verified the stability of the vacuum in this type of collector as the tube still functions well, maintaining a low emissivity and good vacuum after approximately 40 years in storage conditions.

Deep-learning-based post-process correction of the aerosol parameters in the high-resolution Sentinel-3 Level-2 Synergy product

Abstract. Satellite-based aerosol retrievals provide global spatially distributed estimates of atmospheric aerosol parameters that are commonly needed in applications such as estimation of atmospherically corrected satellite data products, climate modelling and air quality monitoring. However, a common feature of the conventional satellite aerosol retrievals is that they have reasonably low spatial resolution and poor accuracy caused by uncertainty in auxiliary model parameters, such as fixed aerosol model parameters, and the approximate forward radiative transfer models utilized to keep the computational complexity feasible. As a result, the improvement and reprocessing of the operational satellite data retrieval algorithms would become a tedious and computationally excessive problem. To overcome these problems, we have developed a machine-learning-based post-process correction approach to correct the existing operational satellite aerosol data products. Our approach combines the existing satellite retrieval data and a post-processing step where a machine learning algorithm is utilized to predict the approximation error in the conventional retrieval. With approximation error, we refer to the discrepancy between the true aerosol parameters and the ones retrieved using the satellite data. Our hypothesis is that the prediction of the approximation error with a finite training dataset is a less complex and easier task than the direct, fully learned machine-learning-based prediction in which the aerosol parameters are directly predicted given the satellite observations and measurement geometry. Our approach does not require reprocessing of the satellite retrieval products; it requires only a computationally fast machine-learning-based post-processing step of the existing retrieval product. Our approach is based on neural networks trained based on collocated satellite data and accurate ground-based Aerosol Robotic Network (AERONET) aerosol data. Based on our post-processing approach, we propose a post-process-corrected high-resolution Sentinel-3 Synergy aerosol product, which gives a spectral estimate of the aerosol optical depth at five different wavelengths with a high spatial resolution equivalent to the native resolution of the Sentinel-3 Level-1 data (300 m at nadir). With aerosol data from Sentinel-3A and 3B satellites, we demonstrate that our approach produces high-resolution aerosol data with clearly better accuracy than the operational Sentinel-3 Level-2 Synergy aerosol product, and it also results in slightly better accuracy than the conventional fully learned machine learning approach. We also demonstrate better generalization capabilities of the post-process correction approach over the fully learned approach.

Fundamental Definition of Two-Stream Approximation for Radiative Transfer in Scattering Atmosphere

The two-stream approximation (TSA) is a primary method for tackling radiative transfer in a scattering atmosphere, which has wide applications in radiation balance evaluation, atmospheric simulation, and remote sensing data assimilation. This article defines fundamental TSA (F-TSA) by introducing the TSA conversion function, which reveals the causal characteristics of various existing specific TSA (S-TSA) models. The unified diffuse irradiance equations and their solutions are obtained based on F-TSA. The properties of the conversion function and the coefficients of irradiance equations are analyzed. It is proven that the weighted average of different conversion functions is also a conversion function. The specified conversion functions and scattering phase function treatments of six existing and four newly proposed S-TSA models are described. These S-TSA models and their typical combinations are evaluated and compared for incident lights from different directions and atmospheric layers with different optical depths. The main results are: 1) the accuracy of an S-TSA model depends on which one of transmissivity and reflectivity is concerned, and is affected by multiple factors such as the specified conversion function, the phase function processing, the single scattering albedo, the optical depth, and the direction of incident light; 2) the proper combination of different S-TSA models can improve the TSA accuracy significantly, and both the delta function and phase function B models combined with the modified Eddington model are recommended; and 3) applying proper combined S-TSA models instead of the delta transformed S-TSA models to calculate radiation flux may be beneficial.

Effect of ground-based environmental conditions on the level of dangerous ultraviolet solar radiation

An analytical model is suggested to determine the contribution of solar radiation scattered by dispersed layers of weakly absorbing highly-porous media on the surface of the earth to the local UV-index, which characterizes harmful ultraviolet irradiation. The transport approximation for the single-scattering phase function and the two-flux method for approximate radiative transfer calculations were used to calculate an additional UV irradiance due to multiple scattering in the layer of a substrate medium. Three important environment conditions are considered in the case problems: the snowpack in a mountain ski resort of Provo (Utah), the salt layer in the Great Salt Lake desert, and the layers of sand typical of sand resorts and beaches. The optical properties of the media were calculated using the data for spectral optical constants of substances in the near-ultraviolet and analytical geometrical optics solution for large spherical particles of a weakly absorbing material. The resulting spectral single-scattering transport albedo of the medium was used to determine an additional harmful UV radiation. It was found that corrected values of the UV-index in all three cases are substantially higher than those calculated without account for the light reflected from a scattering medium on the earth surface. The model of the present paper can be used for different dispersed media in a wide range of physical parameters.

New boundary conditions for the approximate flux-limited diffusion radiative transfer in circumstellar environments

Context. In order to constrain the models describing circumstellar environments, it is necessary to solve the radiative transfer equation in the presence of absorption and scattering, coupled with the equation for radiative equilibrium. However, solving this problem requires much CPU time, which makes the use of automatic minimisation procedures to characterise these environments challenging. Aims. In this context, the use of approximate methods is of primary interest. One promising candidate method is the flux-limited diffusion (FLD), which recasts the radiative transfer problem into a non-linear diffusion equation. One important aspect for the accuracy of the method lies in the implementation of appropriate boundary conditions (BCs). We present new BCs for the FLD approximation in circumstellar environments that we apply here to spherically symmetric envelopes. Methods. At the inner boundary, the entering flux (coming from the star and from the envelope itself) may be written in the FLD formalism and provides us with an adequate BC. At the free outer boundary, we used the FLD formalism to constrain the ratio of the mean radiation intensity over the emerging flux. In both cases we derived non-linear mixed BCs relating the surface values of the mean specific intensity and its gradient. We implemented these conditions and compared the results with previous benchmarks and the results of a Monte Carlo radiative transfer code. A comparison with results derived from BCs that were previously proposed in other contexts is presented as well. Results. For all the tested cases, the average relative difference with the benchmark results is below 2% for the temperature profile and below 6% for the corresponding spectral energy distribution or the emerging flux. We point out that the FLD method together with the new outer BC also allows us to derive an approximation for the emerging flux. This feature avoids additional formal solutions for the radiative transfer equation in a set of rays (ray-tracing computations). Conclusions. The FLD approximation together with the proposed new BCs performs well and captures the main physical properties of the radiative equilibrium in spherical circumstellar envelopes.

Influence of atmospheric adjacency effect on top-of-atmosphere radiances and its correction in the retrieval of Lambertian surface reflectivity based on three-dimensional radiative transfer

In satellite-based and airborne imagery, the observed radiances reflected by a certain pixel at the surface are additionally influenced by reflections from the neighboring surface pixels and multiple scatterings due to atmospheric components (mainly cloud and aerosol particles) into the observational solid angle of the imaging camera. This phenomenon is commonly referred to as the atmospheric adjacency effect. This three-dimensional (3D) radiative transfer effect is caused by spatial inhomogeneities of the surface reflectivity and the atmospheric properties. Based on the recently published 3D radiative transfer code LEIPSIC (Light Estimator Including Polarization, Surface Inhomogeneities, and Clouds), a new atmospheric correction (AC) algorithm is proposed to consider for the atmospheric adjacency effect when estimating the surface reflectivity from satellite or airborne imagery. The effectiveness of the new AC algorithm is quantified and compared to the results based on the independent pixel approximation (IPA) radiative transfer approach. It is shown that the image blurring caused by the atmospheric adjacency effect and the error of reflectivity retrievals are reduced by 80% using the new AC algorithm. Furthermore, the simulations demonstrate that the vertical profile of the atmospheric properties is crucial in determining the quality of the AC.

Asymptotic PN Approximation in Radiative Transfer Problems

We study the validity of the time-dependent asymptotic PN approximation in radiative transfer of photons. The time-dependent asymptotic PN is an approximation which uses the standard PN equations with a closure that is based on the asymptotic solution of the exact Boltzmann equation for a homogeneous problem, in space and time. The asymptotic PN approximation for radiative transfer requires careful treatment regarding the closure equation. Specifically, the mean number of particles that are emitted per collision () can be larger than one due to inner or outer radiation sources and the coefficients of the closure must be extended for these cases. Our approximation is tested against a well-known radiative transfer benchmark. It yields excellent results, with almost correct particle velocity that controls the radiative heat-wave fronts.

Coupling Mesoscopic Boltzmann Transport Equation and Macroscopic Heat Diffusion Equation for Multiscale Phonon Heat Conduction

ABSTRACT Phonon heat conduction has to be described by the Boltzmann transport equation (BTE) when sizes or sources are comparable to or smaller than the phonon mean free paths (MFPs). When domains much larger than MFPs are to be treated or when regions with large and small MFPs coexist, the computation time associated with full BTE treatment becomes large, calling for a multiscale strategy to describe the total domain and decreasing the computation time. Here, we describe an iterative method to couple the BTE, under the Equation of Phonon Radiative Transfer approximation solved by means of the deterministic Discrete Ordinate Method, to a Finite-Element Modeling commercial solver of the heat equation. Small-size elements are embedded in domains where the BTE is solved, and the BTE domains are connected to a domain where large-size elements are located and where the heat equation is applied. It is found that an overlapping zone between the two types of domains is required for convergence, and the accuracy is analyzed as a function of the size of the BTE domain. Conditions for fast convergence are discussed, leading to the computation time being divided by more than five on a study case in 2D Cartesian geometry. The simple method could be generalized to other types of solvers of the Boltzmann and heat equations.

Using two-stream theory to capture fluctuations of satellite-perceived TOA SW radiances reflected from clouds over ocean

Abstract. Shortwave (SW) fluxes estimated from broadband radiometry rely on empirically gathered and hemispherically resolved fields of outgoing top-of-atmosphere (TOA) radiances. This study aims to provide more accurate and precise fields of TOA SW radiances reflected from clouds over ocean by introducing a novel semiphysical model predicting radiances per narrow sun-observer geometry. This model was statistically trained using CERES-measured radiances paired with MODIS-retrieved cloud parameters as well as reanalysis-based geophysical parameters. By using radiative transfer approximations as a framework to ingest the above parameters, the new approach incorporates cloud-top effective radius and above-cloud water vapor in addition to traditionally used cloud optical depth, cloud fraction, cloud phase, and surface wind speed. A two-stream cloud albedo – serving to statistically incorporate cloud optical thickness and cloud-top effective radius – and Cox–Munk ocean reflectance were used to describe an albedo over each CERES footprint. Effective-radius-dependent asymmetry parameters were obtained empirically and separately for each viewing-illumination geometry. A simple equation of radiative transfer, with this albedo and attenuating above-cloud water vapor as inputs, was used in its log-linear form to allow for statistical optimization. We identified the two-stream functional form that minimized radiance residuals calculated against CERES observations and outperformed the state-of-the-art approach for most observer geometries outside the sun-glint and solar zenith angles between 20 and 70∘, reducing the median SD of radiance residuals per solar geometry by up to 13.2 % for liquid clouds, 1.9 % for ice clouds, and 35.8 % for footprints containing both cloud phases. Geometries affected by sun glint (constituting between 10 % and 1 % of the discretized upward hemisphere for solar zenith angles of 20 and 70∘, respectively), however, often showed weaker performance when handled with the new approach and had increased residuals by as much as 60 % compared to the state-of-the-art approach. Overall, uncertainties were reduced for liquid-phase and mixed-phase footprints by 5.76 % and 10.81 %, respectively, while uncertainties for ice-phase footprints increased by 0.34 %. Tested for a variety of scenes, we further demonstrated the plausibility of scene-wise predicted radiance fields. This new approach may prove useful when employed in angular distribution models and may result in improved flux estimates, in particular dealing with clouds characterized by small or large droplet/crystal sizes.

Consistently Simulating a Wide Range of Atmospheric Scenarios for K2-18b with a Flexible Radiative Transfer Module

Abstract The atmospheres of small, potentially rocky exoplanets are expected to cover a diverse range in composition and mass. Studying such objects therefore requires flexible and wide-ranging modeling capabilities. We present in this work the essential development steps that lead to our flexible radiative transfer module, REDFOX, and validate REDFOX for the solar system planets Earth, Venus, and Mars, as well as for steam atmospheres. REDFOX is a k-distribution model using the correlated-k approach with the random overlap method for the calculation of opacities used in the δ-two-stream approximation for radiative transfer. Opacity contributions from Rayleigh scattering, UV/visible cross sections, and continua can be added selectively. With the improved capabilities of our new model, we calculate various atmospheric scenarios for K2-18b, a super-Earth/sub-Neptune with ∼8 M ⊕ orbiting in the temperate zone around an M star, with recently observed H2O spectral features in the infrared. We model Earth-like, Venus-like, and H2–He primary atmospheres of different solar metallicity and show resulting climates and spectral characteristics compared to observed data. Our results suggest that K2-18b has an H2–He atmosphere with limited amounts of H2O and CH4. Results do not support the possibility of K2-18b having a water reservoir directly exposed to the atmosphere, which would reduce atmospheric scale heights, and with it the amplitudes of spectral features, making the latter inconsistent with the observations. We also performed tests for H2–He atmospheres up to 50 times solar metallicity, all compatible with the observations.

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.