Correlated K-distribution Method Research Articles

Numerical Performance of Correlated-k Distribution Method in Atmospheric Escape Simulation

Atmospheric escape is crucial to understanding the evolution of planets in and out of the solar system and to interpreting atmospheric observations. While hydrodynamic escape simulations have been actively developed incorporating detailed processes such as UV heating, chemical reactions, and radiative cooling, the radiative cooling by molecules has been treated as emission from selected lines or rotational/vibrational bands to reduce its numerical cost. However, ad hoc selections of radiative lines would risk estimating inaccurate cooling rates because important lines or wavelengths for atmospheric cooling depend on emitting conditions such as temperature and optical thickness. In this study, we apply the correlated-k distribution (CKD) method to cooling rate calculations for H2-dominant transonic atmospheres containing H2O or CO as radiative species, to investigate its numerical performance and the importance of considering all lines of the molecules. Our simulations demonstrate that the sum of weak lines, which provides only 1% of the line emission energy in total at optically thin conditions, can become the primary source of radiative cooling in optically thick regions, especially for H2O-containing atmospheres. Also, in our hydrodynamic simulations, the CKD method with a wavelength resolution of 1000 is found to be effective, allowing the calculation of escape rate and temperature profiles with acceptable numerical cost. Our results show the importance of treating all radiative lines and the usefulness of the CKD method in hydrodynamic escape simulations. It is particularly practical for heavy-element-enriched atmospheres considered in small exoplanets, including super-Earths, without any prior selections for effective lines.

Assessment of various Full-Spectrum Correlated K-distribution methods in radiative heat transfer in oxy-fuel sooting flames

Thermal radiation plays an important role in heat transfer process in oxy-fuel sooting flame (OFS). The accuracy of Full-Spectrum Correlated K-distribution (FSCK) methods with the original scheme (Modest and Zhang, 2002), the improved one (Cai and Modest, 2014), and the rank correlated one (Solovjov and Webb, 2018) is evaluated in two OFSs. As a comparison, two oxy-fuel non-sooting flames (OFNSs) are constructed as well. The performance of these three schemes in OFSs is basically consistent with that in OFNSs except for the original scheme in the high-soot-concentration regions. The original scheme displays larger errors than the other two schemes in the high-temperature regions, especially in the high-soot-concentration regions, though the error is quite small. The improved scheme provides excellent accuracy in the high-temperature regions, but significant errors in the low-temperature regions, which results in an overestimation of temperature by 38.8 K. The rank correlated scheme displays the best accuracy in both OFSs and OFNSs. Furthermore, the reference (or Planck) temperature has obvious impacts on the accuracy of original scheme, but has much weaker effects on the improved and rank correlated schemes.

An Improved nongray-wall emissivity-absorptivity model for the Full-Spectrum Correlated K-distribution method

In practical combustion chambers, the emissivity of wall materials in general varies spectrally and inappropriate treatments may lead to significant errors in modeling radiative heat transfer. To reduce the error of the Full-Spectrum Correlated K-distribution (FSCK) method in practical problems involving nongray walls, a nongray-wall model is proposed by reordering the wall emissivity and absorptivity separately, in which the Planck function at the wall temperature and an effective mean temperature is used as the weight function of wall emissivity and absorptivity, respectively. As a result, this new model preserves the wall emission and considers the spectral radiative property of the wall. Radiative heat transfer calculations in 1D and 3D configurations bounded by nongray walls are simulated to evaluate the accuracy of this new model. The results show that this new model is in general more accurate than the recently developed nongray-wall model (Liu et al., Int. J. Heat Mass Transf. 2021), especially in cases where the wall-to-wall radiative heat transfer plays an important role. It is also showed that this new model is less sensitive to the choice of the effective mean temperature and the medium blackbody emission-averaged temperature is recommended.

Rapid, accurate computation of narrow-band sky radiance in the 940\xa0nm gas absorption region using the correlated k-distribution method for sun-photometer observations

We developed lookup tables for the correlated k-distribution (CKD) method in the 940 nm water vapor absorption region (WV-CKD), with the aim of rapid and accurate computation of narrow-band radiation around 940 nm (10,000–10,900 {mathrm{cm}}^{-1}) for ground-based angular-scanning radiometer data analysis. Tables were constructed at three spectral resolutions (2, 5, and 10 {mathrm{cm}}^{-1}) with quadrature values (point and weight) and numbers optimized using simulated sky radiances at ground level, which had accuracies of ≤ 0.5% for sub-bands of 10 {mathrm{cm}}^{-1}. Although high-resolution WV-CKD requires numerous quadrature points, the number of executions of the radiative transfer model is reduced to approximately 1/46 of the number used in the line-by-line approach by our WV-CKD with a resolution of 2 {mathrm{cm}}^{-1}. Furthermore, we confirmed through several simulations that WV-CKD could be used to compute radiances with various vertical profiles. The accuracy of convolved direct solar irradiance and diffuse radiance at a full width at half maximum (FWHM) of 10 nm, computed with the WV-CKD, is < 0.3%. In contrast, the accuracy of convolved normalized radiance, which is the ratio of diffuse radiance to direct solar irradiance, at an FWHM of 10 nm computed with the WV-CKD is < 0.11%. This accuracy is lower than the observational uncertainty of a ground-based angular-scanning radiometer (approximately 0.5%). Finally, we applied the SKYMAP and DSRAD algorithms (Momoi et al. in Atmos Meas Tech 13:2635–2658, 2020. https://doi.org/10.5194/amt-13-2635-2020) to SKYNET observations (Chiba, Japan) and compared the results with microwave radiometer values. The precipitable water vapor (PWV) derived with the WV-CKD showed better agreement (correlation coefficient γ = 0.995, slope = 1.002) with observations than PWV derived with the previous CKD table (correlation coefficient γ = 0.984, slope = 0.926) by Momoi et al. (Momoi et al., Atmos Meas Tech 13:2635–2658, 2020). Through application of the WV-CKD to actual data analysis, we found that an accurate CKD table is essential for estimating PWV from sky-radiometer observations.

Assessment of Various Full-Spectrum Correlated K-Distribution Methods in Radiative Heat Transfer in Oxy-Fuel Sooting Flames

Assessment of Various Full-Spectrum Correlated K-Distribution Methods in Radiative Heat Transfer in Oxy-Fuel Sooting Flames

A nongray-wall emissivity model for the full-spectrum correlated k-distribution method based on uniform media assumption

The walls of high-temperature combustion devices are usually assumed to be black or gray in radiative heat transfer calculations to save computing resources; however, this simplification may introduce large errors. To improve the accuracy of the Full-Spectrum Correlated K-distribution (FSCK) method in calculations of nongray-wall radiative heat transfer problems without reducing the computational efficiency, a nongray-wall emissivity model for the FSCK method is proposed based on uniform-medium assumption. The accuracy of this nongray-wall emissivity model and the commonly used Planck-function-weighted gray-wall emissivity model is evaluated in 1D isothermal and homogeneous cases, 1D non-isothermal and inhomogeneous cases, and 3D flames bounded by walls coated with fly-ash deposit or soot deposit. The results show that the nongray-wall emissivity model for FSCK demonstrates much better accuracy than the gray-wall one, especially for cases of low wall temperatures. The nongray-wall emissivity model provides good accuracy over a wide range of optical depth, while the accuracy of the gray-wall emissivity model is highly dependent on the optical depth. The nongray-wall emissivity model based on the uniform-medium assumption can be applied to non-isothermal and inhomogeneous radiative heat transfer problems involving nongray walls.

A Proof-of-Concept Algorithm for the Retrieval of Total Column Amount of Trace Gases in a Multi-Dimensional Atmosphere

An algorithm for the retrieval of total column amount of trace gases in a multi-dimensional atmosphere is designed. The algorithm uses (i) certain differential radiance models with internal and external closures as inversion models, (ii) the iteratively regularized Gauss–Newton method as a regularization tool, and (iii) the spherical harmonics discrete ordinate method (SHDOM) as linearized radiative transfer model. For efficiency reasons, SHDOM is equipped with a spectral acceleration approach that combines the correlated k-distribution method with the principal component analysis. The algorithm is used to retrieve the total column amount of nitrogen for two- and three-dimensional cloudy scenes. Although for three-dimensional geometries, the computational time is high, the main concepts of the algorithm are correct and the retrieval results are accurate.

Radiative transfer in the [formula omitted] A-band - a fast and accurate forward model based on the [formula omitted]-distribution approach

An efficient method based on accurate transmissivity calculations to account for gaseous absorption in Monte Carlo / quasi-Monte Carlo radiative transfer codes is presented. The modeling approach is based on an improved non-uniform transmission formulation, called the ℓ-distribution method. The technique is founded on two components: 1/ an original uniform method to tabulate band averaged transmissivities of gaseous paths and 2/ its extension to non-uniform paths, based on the Godson-Weinreb-Neuendorffer’s (GWN) approximation that consists of the definition of effective scaling factors to relate gaseous spectra in distinct states. As the GWN method is known to provide results dependent on the ordering of the gas layers, two path reordering strategies are introduced and compared. One of them is founded on results from statistical theory and requires the introduction of a new coefficient (Kendall’s Ke). This coefficient together with its role on the path reordering strategy is introduced, detailed and analyzed. The two schemes are then assessed against Line-By-Line calculations in line-of-sight geometries. Two configurations representative of radiative transfer in the O2 A-band for scattering atmospheres are then studied: the first one only considers molecular (Rayleigh) scattering and the second one involves various cloud configurations (single or bi-layer clouds located at various altitudes). For these calculations, the ℓ-distribution methods based on the two path reordering schemes were implemented in the 3D Monte Carlo code 3DMCPOL. Results of the ℓ-distribution method are compared with solutions provided by the Correlated k-distribution method and assessed against Line-By-Line calculations. The ℓ-distribution approach combined with the Kendall’s reordering strategy is shown to provide results more accurate than k-distributions at smaller calculation costs. The ℓ-distribution method is shown to be a relevant candidate for radiative transfer in the atmosphere, both for remote sensing applications but also for weather forecasting or radiative budget studies, with or without scattering phenomena.

A Spectral Acceleration Approach for the Spherical Harmonics Discrete Ordinate Method

A spectral acceleration approach for the spherical harmonics discrete ordinate method (SHDOM) is designed. This approach combines the correlated k-distribution method and some dimensionality reduction techniques applied on the optical parameters of an atmospheric system. The dimensionality reduction techniques used in this study are the linear embedding methods: principal component analysis, locality pursuit embedding, locality preserving projection, and locally embedded analysis. Through a numerical analysis, it is shown that relative to the correlated k-distribution method, PCA in conjunction with a second-order of scattering approximation yields an acceleration factor of 12. This implies that SHDOM equipped with this acceleration approach is efficient enough to perform spectral integration of radiance fields in inhomogeneous multi-dimensional media.

A nongray-wall emissivity model for the Wide-Band Correlated K-distribution method

The walls of combustion systems are usually assumed to be black or gray in radiative calculations, which may cause large errors. The Planck-function-weighted emissivity is usually used as the gray-wall emissivity when using the Wide-Band Correlated K-distribution method. This approach can demonstrate good accuracy when coupled with the emissivity-based optimized band interval approach proposed by Solovjov et al., 2013. To improve computational efficiency without losing accuracy, a nongray-wall emissivity model and an absorption-coefficient-based method for determining the band interval are proposed. The accuracy of nongray-wall and gray-wall emissivity models along with different approaches to determine the band intervals is evaluated in three 1D isothermal and homogeneous cases bounded by fly-ash deposit, a high-temperature alloy, and soot deposit and a 3D fuel-air flame bounded by fly-ash deposit. The results show that the nongray-wall emissivity model is much more accurate than the gray-wall one when the number of bands is greater than 1. Coupled with the absorption-coefficient-based band interval approach, the nongray-wall emissivity model becomes more accurate when the number of bands is larger than 2, especially for low-temperature walls. It is sufficient to divide the entire spectrum into 4 bands for the cases tested here.

Effects of the K-value solution schemes on radiation heat transfer modelling in oxy-fuel flames using the full-spectrum correlated K-distribution method

Radiation heat transfer in oxy-fuel flames is more important than in conventional fuel-air flames. The Full-Spectrum Correlated K-distribution methods (FSCK) with the original correlated-K solution scheme (Modest and Zhang, 2002) and a newly proposed one (Cai and Modest, 2014), and the Rank Correlated Full-Spectrum K-distribution method (RC-FSK) are used in radiative calculations of oxy-fuel flames. Twelve one-dimensional flames, including fuel-air, dry and wet oxy-fuel flames with various length scales, as well as a two-dimensional dry oxy-fuel flame are studied. The results show that the reference temperature has a non-negligible impact on the accuracy of original scheme and the emission-weighted temperature leads to a good accuracy. The accuracy of the new scheme is almost unaffected by the reference temperature, except for small-scale dry oxy-fuel flames. The error of the new scheme is mainly in the low-temperature region, and its accuracy depends on the length scale of computational domain. A hybrid correlated-K scheme using either the original or the new scheme according to local temperature is proposed. It combines the advantages of two schemes in different temperature regions, and is independent of the reference temperature. In addition, the RC-FSK demonstrates almost the same accuracy as FSCK with the hybrid scheme when the Planck temperature is set equal to the reference temperature.

A grouping strategy for the multi-group full-spectrum K-distribution method in gas mixtures

The Multi-Group Full-Spectrum K-distribution method (MGFSK) is a promising method for efficient and accurate thermal radiation calculations in participating media with strong temperature inhomogeneity. The current MGFSK method cannot be used for modeling radiative transfer in gas mixtures since it is applicable only to a single radiating gas. To make MGFSK applicable to mixtures without losing efficiency, a new grouping strategy for gas mixtures is proposed based on a scaling function of the mixture. Several one-dimensional two-layer systems with large temperature gradient and a two-dimensional oxy-fuel flame are simulated to demonstrate the accuracy of the modified MGFSK method (MGFSK-M). The simulation results are compared with those of the Line-by-Line model, the Full-Spectrum Correlated K-distribution method (FSCK) and the Rank Correlated Full-Spectrum K-distribution method (RC-FSK). MGFSK-M significantly outperforms both FSCK and RC-FSK in the two-layer systems. For the oxy-fuel flame, RC-FSK and MGFSK-M offer similar accuracy and both perform better than FSCK.

Alternate Mapping Correlated k-Distribution Method for Infrared Radiative Transfer Forward Simulation

The alternate mapping correlated k-distribution (AMCKD) method is studied and applied to satellite simulations. To evaluate the accuracy of AMCKD, the simulated brightness temperatures at the top of the atmosphere are compared with line-by-line radiative transfer model (LBLRTM) or the observed data which are from Advanced Himawari Imager (AHI) on board the Himawari-8, as well as Medium Resolution Spectral Imager (MERSI) on board the Fengyun-3D. The result of AMCKD is also compared with the algorithm of Radiative Transfer for the Television Observation Satellite Operational Vertical Sounder (RTTOV). Under the standard atmospheric profiles, the absolute errors of AMCKD in all longwave channels of AHI and MERSI are bounded by 0.44K compared to the benchmark results of LBLRTM, which are more accurate than those of RTTOV. In the most cases, the error of AMCKD is smaller than the NEDT at ST, while the error of RTTOV is larger than the instrument noise equivalent temperature (NEDT) at scene temperature (ST). Under real atmospheric profile conditions, the errors of AMCKD increase, because the input data from ERA-Interim reanalysis dataause bias in the satellite remote sensing results. In the most considered cases, the accuracy of AMCKD is higher than RTTOV, while the efficiency of AMCKD is slightly slower than RTTOV.

Radiative transfer models for retrieval of cloud parameters from EPIC/DSCOVR measurements

In this paper we analyze the accuracy and efficiency of several radiative transfer models for inferring cloud parameters from radiances measured by the Earth Polychromatic Imaging Camera (EPIC) on board the Deep Space Climate Observatory (DSCOVR). The radiative transfer models are the exact discrete ordinate and matrix operator methods with matrix exponential, and the approximate asymptotic and equivalent Lambertian cloud models. To deal with the computationally expensive radiative transfer calculations, several acceleration techniques such as, for example, the telescoping technique, the method of false discrete ordinate, the correlated k-distribution method and the principal component analysis (PCA) are used. We found that, for the EPIC oxygen A-band absorption channel at 764 nm, the exact models using the correlated k-distribution in conjunction with PCA yield an accuracy better than 1.5% and a computation time of 18 s for radiance calculations at 5 viewing zenith angles.

Linearized radiative transfer models for retrieval of cloud parameters from EPIC/DSCOVR measurements

In this paper, we describe several linearized radiative transfer models which can be used for the retrieval of cloud parameters from EPIC (Earth Polychromatic Imaging Camera) measurements. The approaches under examination are (1) the linearized forward approach, represented in this paper by the linearized discrete ordinate and matrix operator methods with matrix exponential, and (2) the forward-adjoint approach based on the discrete ordinate method with matrix exponential. To enhance the performance of the radiative transfer computations, the correlated k-distribution method and the Principal Component Analysis (PCA) technique are used. We provide a compact description of the proposed methods, as well as a numerical analysis of their accuracy and efficiency when simulating EPIC measurements in the oxygen A-band channel at 764 nm. We found that the computation time of the forward-adjoint approach using the correlated k-distribution method in conjunction with PCA is approximately 13 s for simultaneously computing the derivatives with respect to cloud optical thickness and cloud top height.

A new k-interval optimization technique for atmospheric upwelling radiance calculation in infrared absorption bands

A new optimization technique is proposed to generate the k-interval parameters including the quadrature weights and their corresponding equivalent absorption coefficients when using correlated k-distribution method for computations of spectrally integrated atmospheric upwelling radiances in infrared absorption bands. The main feature of this technique is the introduction of the upwelling contribution function (UCF) both in expressing the atmospheric upwelling radiance and in constructing the merit function for fitting, so that the optimization for the band radiance smoothly turns into the optimization for the band UCF of each atmospheric sublayer. The performance of the proposed technique is illustrated by comparing with the Δlog(k) technique and the Gauss–Legendre quadrature technique at three different band settings in both the US standard atmosphere and the tropical atmosphere, and the line-by-line results are treated as the reference. Results show that there are less relative errors by the proposed optimization technique than by the other two techniques under the same number of k-intervals. In most cases, the computational efficiency can be improved by more than 10% under the same precision requirement in upwelling radiance calculations, and even 80% in some preferable conditions.

Improved full-spectrum k-distribution implementation for inhomogeneous media using a narrow-band database

A new implementation to determine the correlated k values as used in full-spectrum correlated k-distribution methods for inhomogeneous media is presented, which conserves radiative emission and significantly improves the accuracy of the full-spectrum correlated k-distribution method in strongly inhomogeneous media. In addition, an update of a previous high-accuracy, compact narrow-band k-distribution database is given. The new narrow-band database utilizes the latest spectroscopy databases to ensure accuracy at elevated temperatures and pressures. Differences between the two versions of narrow-band k-distribution databases as a result of the change of spectroscopy databases are illustrated.

Quantification of model-form uncertainty in the correlated-k distribution method for radiation heat transfer

The full-spectrum correlated-k distribution method has been shown to be exact for thermal radiation in molecular gas-particulate mixtures which obey the correlation assumption. Unfortunately, this assumption breaks down for molecular gases with strong temperature or concentration gradients. There has previously been no way to effectively quantify the model-form uncertainty introduced by the failure of the correlation assumption. This paper examines the effect of temperature gradients in CO2 and proposes a technique to generate probability density functions for the gray-gas absorption coefficients used in the full-spectrum correlated-k distribution method. The uncertainty in the absorption coefficients may then be propagated forward to ascertain confidence intervals for important quantities such as heat flux or intensity distributions.

K-bin and k-IR: k-distribution methods without correlation approximation for non-fixed instrument response function and extension to the thermal infrared—Applications to satellite remote sensing

k-distribution methods are efficient tools for large spectral band radiation transfer simulations in the atmosphere. A weakness of classical k-distribution method (correlated k-distribution method) is the simulation of layered atmosphere with variable gas absorption. This weakness is due to the use of the correlation approximation. We can avoid the use of the correlation approximation using a spectral mapping for the construction of the k-distribution intervals. This already-existing method is known as Spectral Mapping Transformation (SMT). Within SMT k-distribution, k-distribution is built to suit all the atmospheric layers. This difference of method, compared to the correlated k-distribution methods, leads to a loss of rapidity but to a gain of precision. Particularly, SMT k-distribution methods permit a balance between rapidity and precision by decreasing or increasing the number of bins (spectroscopically similar k-distribution intervals). Within this article, we recapitulate the main principles of SMT k-distribution methods and present two improvements: the k-IR method, which is an adaptation of an SMT k-distribution method to the thermal infrared, and k-bin, which is an adaptation of an SMT k-distribution method that allows the user to simulate narrow-band satellite channels with a non-fixed spectral response function. k-IR permits a modeling of the absorption and emission by gases, even if the spectral variability of the Planck function is completely different from the spectral variability of absorption/emission coefficients. This is achieved by associating to each bin (spectroscopically similar k-distribution interval) a precomputed value of the bin-averaged blackbody radiance. Within this paper, we outline k-IR and apply it for the simulation of Channel 3 (12.05μm) of the Imaging Infrared Radiometer (IIR) aboard the CALIPSO satellite. Results show that the accuracy steadily increases with an increasing number of bins. This will allow us to reach the instrument precision. k-bin, otherwise, is a more stringent approach of the k-distribution method. The major difference between a conventional k-distribution and k-bin is that, for a given spectral interval no assumption about the shape of the sensor weighting function has to be incorporated a priori. For a given spectral interval, any sensor response function can be constructed from a set of radiative transfer simulations. This requires somewhat different constraints in the way the subdivision in bins is performed, namely we must ensure that not only the band-averaged transmission is resembled to high accuracy, but also the transmission in each bin. Within this paper we outline k-bin method and apply it to high-resolution spectroscopic simulations in the oxygen A-band. k-bin allows for a representation of any channel (with a resolution of 0.04nm or lower) within the oxygen A-band with an accuracy of 0.2% or better with less than 600 simulations. This corresponds for the Orbiting Carbon Observatory-2 (OCO-2) to a computational cost of 0.6 simulations per channel.

Retrieving Clear-Sky Surface Skin Temperature for Numerical Weather Prediction Applications from Geostationary Satellite Data

Atmospheric models rely on high-accuracy, high-resolution initial radiometric and surface conditions for better short-term meteorological forecasts, as well as improved evaluation of global climate models. Remote sensing of the Earth’s energy budget, particularly with instruments flown on geostationary satellites, allows for near-real-time evaluation of cloud and surface radiation properties. The persistence and coverage of geostationary remote sensing instruments grant the frequent retrieval of near-instantaneous quasi-global skin temperature. Among other cloud and clear-sky retrieval parameters, NASA Langley provides a non-polar, high-resolution land and ocean skin temperature dataset for atmospheric modelers by applying an inverted correlated k-distribution method to clear-pixel values of top-of-atmosphere infrared temperature. The present paper shows that this method yields clear-sky skin temperature values that are, for the most part, within 2 K of measurements from ground-site instruments, like the Southern Great Plains Atmospheric Radiation Measurement (ARM) Infrared Thermometer and the National Climatic Data Center Apogee Precision Infrared Thermocouple Sensor. The level of accuracy relative to the ARM site is comparable to that of the Moderate-resolution Imaging Spectroradiometer (MODIS) with the benefit of an increased number of daily measurements without added bias or increased error. Additionally, matched comparisons of the high-resolution skin temperature product with MODIS land surface temperature reveal a level of accuracy well within 1 K for both day and night. This confidence will help in characterizing the diurnal and seasonal biases and root-mean-square differences between the retrievals and modeled values from the NASA Goddard Earth Observing System Version 5 (GEOS-5) in preparation for assimilation of the retrievals into GEOS-5. Modelers should find the immediate availability and broad coverage of these skin temperature observations valuable, which can lead to improved forecasting and more advanced global climate models.