The two-stream model is the fastest radiative transfer model among those based on the discrete ordinate method. Although its accuracy is not high enough to be used in applications, the two-stream model gets more attention in computationally demanding tasks such as line-by-line simulations in the gaseous absorption bands. For this reason, we designed the cluster low-streams regression (CLSR) technique, in which a spectrum computed with a two-stream model, is refined by using statistical dependencies between two- and multistream radiative transfer models. In this paper, we examine the efficiency of this approach for computing Hartley-Huggins, O2 A-, water vapour and CO2 bands at the presence of aerosols. The numerical results evidence that the errors of the CLSR method is not biased and around 0.05 %, while the performance enhancement is two orders of magnitude. 1. Dubovik O., Li Z., Mishchenko M.I., Tanrй D., Karol Y., Bojkov B., Cairns B., Diner D.J., Espinosa W.R., Goloub P., Gu X., Hasekamp O., Hong J., Hou W., Knobelspiesse K.D., Landgraf J., Li L., Litvinov P., Liu Y., Lopatin A., Marbach T., Maring H., Martins V., Meijer Y., Milinevsky G., Mukai S., Parol F., Qiao Y., Remer L., Rietjens J., Sano I., Stammes P., Stamnes S., Sun X., Tabary P., Travis L.D., Waquet F., Xu F., Yan C., Yin D. Polarimetric remote sensing of atmospheric aerosols: Instruments, methodologies, results, and perspectives// Journal of Quantitative Spectroscopy and Radiative Transfer, 2019, # 224, pp. 474–511. doi:10.1016/j.jqsrt.2018.11.024, https://doi.org/10.1016/ j.jqsrt.2018.11.024.
2. Chan K.L., Valks P., Slijkhuis S., Kuhler C., Loyola D. Total column water vapour retrieval for global ozone monitoring experience‑2 (GOME‑2) visible blue observations//Atmospheric Measurement Techniques, 2020, 13(8), pp. 4169–4193. doi:10.5194/amt‑13–4169–2020, https://doi.org/10.5194/amt‑13–4169–2020
3. Zeng Z.C., Chen S., Natraj V., Le T., Xu F., Merrelli A., Crisp D., Sander S.P., Yung Y.L. Constraining the vertical distribution of coastal dust aerosol using CO2 and O2 A-band measurements// Remote Sensing of Environment, 2020, 236, 111494. doi:10.1016/j.rse.2019.111494, https://doi.org/10.1016/j. rse.2019.111494.
4. Schuster A. Radiation through a foggy atmosphere// The Astrophysical Journal 1905, 21, 1. doi:10.1086/141186, https://doi.org/10.1086/141186
5. Spurr R., Natraj V. A linearized two-stream radiative transfer code for fast approximation of multiplescatter fields// Journal of Quantitative Spectroscopy and Radiative Transfer, 2011, Vol. 112, #16, pp. 2630–2637. doi:10.1016/j.jqsrt.2011.06.014.
6. Barker H.W., Cole J.N.S., Li J., Yi B., Yang P. Estimation of errors in two-stream approximations of the solar radiative transfer equation for cloudy-sky conditions// Journal of the Atmospheric Sciences, 2015, Vol. 72,
#11, pp. 4053–4074. doi:10.1175/jas-d‑15–0033.1, https://doi.org/10.1175/jas-d‑15–0033.1.
7. Afanas’ev V., Basov A.Y., Budak V., Efremenko D., Kokhanovsky A. Analysis of the discrete theory of radiative transfer in the coupled “ocean–atmosphere” system: Current status, problems and development prospects// Journal of Marine Science and Engineering, 2020, Vol. 8, #3, 202. doi:10.3390/jmse8030202.
8. Budak V.P., Zheltov V.S., Lubenchenko A.V., Freidlin K.S., Shagalov O.V. A fast and accurate synthetic iteration-based algorithm for numerical simulation of radiative transfer in a turbid medium// Atmospheric and Oceanic Optics, 2017, Vol. 30, #1, pp. 70–78. doi:10.1134/s1024856017010031.
9. Clough S.A., Rinsland C.P., Brown P.D. Retrieval of tropospheric ozone from simulations of nadir spectral radiances as observed from space// Journal of Geophysical Research, 1995, 100 (D8), 16579. doi:10.1029/95jd01388
10. Fomin B.A. A k-distribution technique for radiative transfer simulation in inhomogeneous atmosphere: 2. FKDM, fast k-distribution model for the shortwave// Journal of Geophysical Research, 2005, 110 (D2). doi:10.1029/2004jd005163.
11. Fu Q., Liou K. On the correlated k-distribution method for radiative transfer in nonhomogeneous atmospheres// Journal of the Atmospheric Sciences, 1992, Vol. 49, # 22, pp. 2139–2156. doi:10.1175/1520–0469(1992)049<2139: OTCDMF>2.0.CO;2
12. Ambartzumyan V. The effect of the absorption lines on the radiative equilibrium of the outer layers of the stars// Publ. Obs. Astron. Univ. Leningrad 1936, 6, pp. 7–18.
13. Boesche E., Stammes P., Preusker R., Bennartz R., Knap W., Fischer J. Polarization of skylight in the O2 A band: effects of aerosol properties// Applied Optics, 2008, 47 (19), 3467. doi:10.1364/ao.47.003467.
14. Natraj V., Jiang X., Shia R., Huang X., Margolis J., Yung Y. Application of the principal component analysis to high spectral resolution radiative transfer: A case study of the O2 A-band// Journal of Quantitative Spectroscopy and Radiative Transfer, 2005, Vol. 95, #4, pp. 539–556. doi:10.1016/j.jqsrt.2004.12.024
15. del Águila A., Efremenko D.S., Molina Garcia V., Xu J. Analysis of two dimensionality reduction techniques for fast simulation of the spectral radiances in the Hartley-Huggins band// Atmosphere, 2019, Vol. 10, #3, 142. doi:10.3390/atmos10030142.
16. Efremenko D.S., Loyola D.G., Doicu A., Spurr R.J.D. Multi-core-CPU and GPU-accelerated radiative transfer models based on the discrete ordinate method// Computer Physics Communications, 2014, Vol. 185, #12, pp. 3079–3089. doi:10.1016/j.cpc.2014.07.018
17. Efremenko D., Doicu A., Loyola D., Trautmann T. Optical property dimensionality reduction techniques for accelerated radiative transfer performance: Application to remote sensing total ozone retrievals// Journal of Quantitative Spectroscopy and Radiative Transfer, 2014, 133, pp. 128–135. doi:10.1016/j.jqsrt.2013.07.023
18. Kopparla P., Natraj V., Limpasuvan D., Spurr R., Crisp D., Shia R.L., Somkuti P., Yung Y.L. PCA-based radiative transfer: Improvements to aerosol scheme, vertical layering and spectral binning// Journal of Quantitative Spectroscopy and Radiative Transfer, 2017, Vol. 198, pp. 104–111. doi: https://doi.org/10.1016/j.jqsrt.2017.05.005.
19. Natraj V. A review of fast radiative transfer techniques// Light Scattering Reviews, 2013, Vol. 8, pp. 475–504. Springer Berlin Heidelberg. doi: https://doi.org/10.1007/978–3–642–32106–1_10.
20. del Águila A., Efremenko D.S., Trautmann T. A review of dimensionality reduction techniques for processing hyperspectral optical signal// Light & Engineering, 2019, Vol. 27, #3, pp. 85–98. doi:10.33383/2019–017
21. del Águila A., Efremenko D.S., Molina Garcia V., Kataev M.Y. Cluster low-streams regression method for hyperspectral radiative transfer computations: Cases of O2 A- and CO2 bands// Remote Sensing, 2020, 12(8), 1250. doi:10.3390/rs12081250.
22. Doicu A., Trautmann T. Discrete-ordinate method with matrix exponential for a pseudo-spherical atmosphere: Scalar case. Journal of Quantitative Spectroscopy and Radiative Transfer, 2009, Vol. 110, #1–2, pp. 146–158. doi:10.1016/j.jqsrt.2008.09.014.
23. Efremenko D.S., Molina Garcia V., Gimeno Garcia S., Doicu A. A review of the matrix-exponential formalism in radiative transfer// Journal of Quantitative Spectroscopy and Radiative Transfer, 2017, 196, pp. 17–45. doi:10.1016/j.jqsrt.2017.02.015.
24. Molina Garcia V., Sasi S., Efremenko D., Doicu A., Loyola D. Radiative transfer models for retrieval of cloud parameters from EPIC/DSCOVR measurements// Journal of Quantitative Spectroscopy and Radiative Transfer, 2018, 213, pp. 228–240. doi:10.1016/j.jqsrt.2018.03.014.
25. Schreier F., Gimeno Garcia S., Hochstaffl P., Städt S. Py4cats – PYthon for computational atmospheric spectroscopy// Atmosphere, 2019, Vol. 10, #5, 262. doi:10.3390/atmos10050262.
26. Gordon I., Rothman L., Hill C., Kochanov R., Tan Y., Bernath P., Birk M., Boudon V., Campargue A., Chance K., Drouin B., Flaud J.M., Gamache R., Hodges J., Jacquemart D., Perevalov V., Perrin A., Shine K., Smith M.A., Tennyson J., Toon G., Tran H., Tyuterev V., Barbe A., Császár, A., Devi V., Furtenbacher T., Harrison J., Hartmann J.M., Jolly A., Johnson T., Karman T., Kleiner I., Kyuberis A., Loos J., Lyulin O., Massie S., Mikhailenko S., Moazzen-Ahmadi N., Müller H., Naumenko O., Nikitin A., Polyansky O., Rey M., Rotger M., Sharpe S., Sung K., Starikova E., Tashkun S., Auwera J.V., Wagner G., Wilzewski J., Wcisło P., Zak E. The HITRAN2016 molecular spectroscopic database// Journal of Quantitative Spectroscopy and Radiative Transfer, 2017, 203, pp. 3–69. doi:10.1016/j.jqsrt.2017.06.038
27. Bodhaine B., Wood N., Dutton E., Slusser J. On Rayleigh optical depth calculations// Journal of Atmospheric and Oceanic Technology, 1999, Vol. 16, #11, pp. 1854–1861. doi:10.1175/1520–0426(1999)016<1854: orodc>2.0.co;2.
28. Hess M., Koepke P., Schult I. Optical properties of aerosols and clouds: The software package OPAC// Bulletin of the American Meteorological Society, 1998, Vol. 79, # 5, pp. 831–844 (1998). doi:10.1175/1520–0477(1998)079<0831: opoaac>2.0.co;2.
29. Nanda S., de Graaf M., Veefkind J.P., Sneep M., ter Linden M., Sun J., Levelt P.F. A first comparison of TROPOMI aerosol layer height (ALH) to CALIOP data// Atmospheric Measurement Techniques, Jun. 2020, Vol. 13, # 6, pp. 3043–3059. doi:10.5194/amt‑13–3043–2020, https://doi.org/10.5194/amt‑13–3043–2020.
30. Liu C., Yao B., Natraj V., Kopparla P., Weng F., Le T., Shia R.L., Yung Y.L. A spectral data compression (SDCOMP) radiative transfer model for high-spectral-resolution radiation simulations// Journal of the Atmospheric Sciences, 2020, Vol. 77, # 6, pp. 2055–2066. doi:10.1175/jas-d‑19–0238.1, https://doi.org/10. 1175/jas-d‑19–0238.1
31. O’Dell C.W. Acceleration of multiple-scattering, hyperspectral radiative transfer calculations via lowstreams interpolation// Journal of Geophysical Research, 2010, 115 (D10). doi:10.1029/2009jd012803.
32. Sasi S., Natraj V., Garcia V.M., Efremenko D.S., Loyola D., Doicu A. Model selection in atmospheric remote sensing with application to aerosol retrieval from DSCOVR/EPIC, part 2: Numerical analysis// Remote Sensing, 2020, 12 (21), 3656. doi:10.3390/rs12213656, https://doi.org/10.3390/rs12213656.
33. Kokhanovsky A. Cloud Optics// Springer Netherlands, 2006. doi:10.1007/1–4020–4020–2.
34. Budak V.P., Zheltov V.S., Lubenchenko A.V., Freidlin K.S., Shagalov O.V. A fast and accurate synthetic iteration-based algorithm for numerical simulation of radiative transfer in a turbid medium// Atmospheric and Oceanic Optics, 2017, Vol. 30, # 1, pp. 70–78. doi:10.1134/s1024856017010031.

• Previous article
• Next article

• cluster low-streams regression method
• hyperspectral data
• regression model
• radiative transfer
• aerosol models
• line-by-line model