{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,9,23]],"date-time":"2024-09-23T04:32:12Z","timestamp":1727065932449},"reference-count":71,"publisher":"MDPI AG","issue":"23","license":[{"start":{"date-parts":[[2023,11,27]],"date-time":"2023-11-27T00:00:00Z","timestamp":1701043200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"NOAA Joint Polar Satellite System (JPSS-STAR) Product System\u2019s Development and Implementation (PSDI), Proving Ground and Risk Reduction"},{"name":"Cal\/Val Programs"},{"name":"NOAA\/NESDIS\/STAR Satellite Meteorology and Climatology Division"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Remote Sensing"],"abstract":"Accurate thermal infrared (TIR) fast-forward models are critical for weather forecasting via numerical weather prediction (NWP) satellite radiance assimilation and operational environmental data record (EDR) retrieval algorithms. The thermodynamic and compositional data about the surface and lower troposphere are derived from semi-transparent TIR window bands (i.e., surface-sensitive channels) that can span into the far-infrared (FIR) region under dry polar conditions. To model the satellite observed radiance within these bands, an accurate a priori emissivity is necessary for the surface in question, usually provided in the form of a physical or empirical model. To address the needs of hyperspectral TIR satellite radiance assimilation, this paper discusses the research, development, and preliminary validation of a physically based snow\/ice emissivity model designed for practical implementation within operational fast-forward models such as the U.S. National Oceanic and Atmospheric Administration (NOAA) Community Radiative Transfer Model (CRTM). To accommodate the range of snow grain sizes, a hybrid modeling approach is adopted, combining a layer scattering model based on the Mie theory (viz., the Wiscombe\u2013Warren 1980 snow albedo model, its complete derivation provided in the Appendices) with a specular facet model. The Mie-scattering model is valid for the smallest snow grain sizes typical of fresh snow and frost, whereas the specular facet model is better suited for the larger sizes and welded snow surfaces typical of aged snow. Comparisons of the model against the previously published spectral emissivity measurements show reasonable agreement across zenith observing angles and snow grain sizes, and preliminary observing system experiments (OSEs) have revealed notable improvements in snow\/ice surface window channel calculations versus hyperspectral TIR satellite observations within the NOAA NWP radiance assimilation system.<\/jats:p>","DOI":"10.3390\/rs15235509","type":"journal-article","created":{"date-parts":[[2023,11,27]],"date-time":"2023-11-27T08:35:06Z","timestamp":1701074106000},"page":"5509","source":"Crossref","is-referenced-by-count":2,"title":["Physically Based Thermal Infrared Snow\/Ice Surface Emissivity for Fast Radiative Transfer Models"],"prefix":"10.3390","volume":"15","author":[{"ORCID":"http:\/\/orcid.org\/0000-0002-6914-5537","authenticated-orcid":false,"given":"Nicholas R.","family":"Nalli","sequence":"first","affiliation":[{"name":"IMSG, Inc., NOAA\/NESDIS Center for Satellite Applications and Research (STAR), College Park, MD 20740, USA"},{"name":"National Geospatial-Intelligence Agency (NGA), Springfield, VA 22150, USA"}]},{"given":"Cheng","family":"Dang","sequence":"additional","affiliation":[{"name":"University Corporation for Atmospheric Research (UCAR), Boulder, CO 80301, USA"},{"name":"Joint Center for Satellite Data Assimilation (JCSDA), Boulder, CO 20740, USA"}]},{"given":"James A.","family":"Jung","sequence":"additional","affiliation":[{"name":"Cooperative Institute for Meteorological Satellite Studies (CIMSS), University of Wisconsin-Madison, Madison, WI 53706, USA"}]},{"ORCID":"http:\/\/orcid.org\/0000-0003-1934-7672","authenticated-orcid":false,"given":"Robert O.","family":"Knuteson","sequence":"additional","affiliation":[{"name":"Space Science and Engineering Center, University of Wisconsin-Madison, Madison, WI 53706, USA"}]},{"given":"E. Eva","family":"Borbas","sequence":"additional","affiliation":[{"name":"Space Science and Engineering Center, University of Wisconsin-Madison, Madison, WI 53706, USA"}]},{"given":"Benjamin T.","family":"Johnson","sequence":"additional","affiliation":[{"name":"University Corporation for Atmospheric Research (UCAR), Boulder, CO 80301, USA"},{"name":"Joint Center for Satellite Data Assimilation (JCSDA), Boulder, CO 20740, USA"},{"name":"NOAA\/NWS National Centers for Environmental Prediction (NCEP), College Park, MD 20740, USA"}]},{"ORCID":"http:\/\/orcid.org\/0000-0002-9766-2080","authenticated-orcid":false,"given":"Ken","family":"Pryor","sequence":"additional","affiliation":[{"name":"NOAA\/NESDIS\/STAR, College Park, MD 20740, USA"}]},{"ORCID":"http:\/\/orcid.org\/0000-0001-6232-2871","authenticated-orcid":false,"given":"Lihang","family":"Zhou","sequence":"additional","affiliation":[{"name":"NOAA JPSS Program Office, Lanham, MD 20706, USA"}]}],"member":"1968","published-online":{"date-parts":[[2023,11,27]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"5587","DOI":"10.1029\/JD095iD05p05587","article-title":"Characterization and error analysis of profiles retrieved from remote sounding measurements","volume":"95","author":"Rodgers","year":"1990","journal-title":"J. Geophys. Res."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"744","DOI":"10.1016\/j.rse.2013.10.011","article-title":"Community Radiative Transfer Model (CRTM) applications in supporting the Suomi National Polar-orbiting Partnership (SNPP) mission validation and verification","volume":"140","author":"Liu","year":"2014","journal-title":"Remote Sens. Environ."},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Saunders, R., Rayer, P., Brunel, P., von Engeln, A., Bormann, N., Strow, L., Hannon, S., Heilliette, S., Liu, X., and Miskolczi, F. (2007). A comparison of radiative transfer models for simulating Atmospheric Infrared Sounder (AIRS) radiances. J. Geophys. Res. Atmos., 112.","DOI":"10.1029\/2006JD007088"},{"key":"ref_4","unstructured":"Han, Y., van Delst, P., Liu, Q., Weng, F., Yan, B., Treadon, R., and Derber, J. (2006). JCSDA Community Radiative Transfer Model (CRTM)\u2014Version 1, National Oceanic and Atmospheric Administration (NOAA). NOAA Technical Report NESDIS 122."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"2717","DOI":"10.5194\/gmd-11-2717-2018","article-title":"An update on the RTTOV fast radiative transfer model (currently at version 12)","volume":"11","author":"Saunders","year":"2018","journal-title":"Geosci. Model Dev."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"201","DOI":"10.1364\/AO.45.000201","article-title":"Principal component-based radiative transfer model for hyperspectral sensors: Theoretical concept","volume":"45","author":"Liu","year":"2006","journal-title":"Appl. Opt."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"303","DOI":"10.1109\/TGRS.2002.808244","article-title":"An overview of the AIRS Radiative Transfer Model","volume":"41","author":"Strow","year":"2003","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"E570","DOI":"10.1175\/BAMS-D-20-0126.1","article-title":"Validation and Utility of Satellite Retrievals of Atmospheric Profiles in Detecting and Monitoring Significant Weather Events","volume":"103","author":"Kalluri","year":"2022","journal-title":"Bull. Am. Meteorol. Soc."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"12734","DOI":"10.1002\/2013JD020344","article-title":"Suomi NPP CrIS measurements, sensor data record algorithm, calibration and validation activities, and record data quality","volume":"118","author":"Han","year":"2013","journal-title":"J. Geophys. Res. Atmos."},{"key":"ref_10","first-page":"9","article-title":"IASI Infrared interferometer for operations and research","volume":"Volume 19","author":"Chedin","year":"1993","journal-title":"NATO ASI Series"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"911","DOI":"10.1175\/BAMS-87-7-911","article-title":"AIRS: Improving weather forecasting and providing new data on greenhouse gases","volume":"87","author":"Chahine","year":"2006","journal-title":"Bull. Am. Meteorol. Soc."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"eaaw9883","DOI":"10.1126\/sciadv.aaw9883","article-title":"The polar regions in a 2 \u00b0C warmer world","volume":"5","author":"Post","year":"2019","journal-title":"Sci. Adv."},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Harries, J., Carli, B., Rizzi, R., Serio, C., Mlynczak, M., Palchetti, L., Maestri, T., Brindley, H., and Masiello, G. (2008). The far-infrared Earth. Rev. Geophys., 46.","DOI":"10.1029\/2007RG000233"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"6530","DOI":"10.1002\/2014GL061216","article-title":"Sensitivity of modeled far-IR radiation budgets in polar continents to treatments of snow surface and ice cloud radiative properties","volume":"41","author":"Chen","year":"2014","journal-title":"Geophys. Res. Lett."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"705","DOI":"10.1175\/1520-0450(1988)027<0705:GVSTMR>2.0.CO;2","article-title":"GOES-VAS Simultaneous Temperature-Moisture Retrieval Algorithm","volume":"27","author":"Hayden","year":"1988","journal-title":"J. Appl. Meteorol."},{"key":"ref_16","unstructured":"Liu, E.H., Collard, A., Bi, L., Liu, H., Tong, M., Jung, J., Johnson, B., Chen, M., Liu, Q., and Zhu, T. (2019). EMC contributions to CRTM development and validation. JCSDA Q., 63."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"1691","DOI":"10.1175\/2009WAF2222201.1","article-title":"Introduction of the GSI into the NCEP Global Data Assimilation System","volume":"24","author":"Kleist","year":"2009","journal-title":"Weather. Forecast."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"D12208","DOI":"10.1029\/2012JD017667","article-title":"On the angular effect of residual clouds and aerosols in clear-sky infrared window radiance observations: Sensitivity analyses","volume":"117","author":"Nalli","year":"2012","journal-title":"J. Geophys. Res."},{"key":"ref_19","first-page":"376","article-title":"Sensitivity of sea surface temperature retrieval to sea surface emissivity","volume":"10","author":"Wu","year":"1996","journal-title":"ACTA Meteorol. Sin."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"328","DOI":"10.1109\/TGRS.2007.912712","article-title":"Regression of Surface Spectral Emissivity From Hyperspectral Instruments","volume":"46","author":"Zhou","year":"2008","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_21","doi-asserted-by":"crossref","unstructured":"Borbas, E., Hulley, G., Feltz, M., Knuteson, R., and Hook, S. (2018). The Combined ASTER MODIS Emissivity over Land (CAMEL) Part 1: Methodology and High Spectral Resolution Application. Remote Sens., 10.","DOI":"10.3390\/rs10040643"},{"key":"ref_22","doi-asserted-by":"crossref","unstructured":"Feltz, M., Borbas, E., Knuteson, R., Hulley, G., and Hook, S. (2018). The Combined ASTER MODIS Emissivity over Land (CAMEL) Part 2: Uncertainty and Validation. Remote Sens., 10.","DOI":"10.3390\/rs10050664"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"767","DOI":"10.1364\/AO.4.000767","article-title":"Directional reflectance and emissivity of an opaque surface","volume":"4","author":"Nicodemus","year":"1965","journal-title":"Appl. Opt."},{"key":"ref_24","doi-asserted-by":"crossref","unstructured":"Hapke, B. (2012). Theory of Reflectance and Emittance Spectroscopy, Cambridge University Press. [2nd ed.].","DOI":"10.1017\/CBO9781139025683"},{"key":"ref_25","doi-asserted-by":"crossref","unstructured":"Vollmer, M., and M\u00f6llmann, K.P. (2018). Infrared Thermal Imaging: Fundamentals, Research and Applications, Wiley-VCH. [2nd ed.].","DOI":"10.1002\/9783527693306"},{"key":"ref_26","doi-asserted-by":"crossref","unstructured":"Nicodemus, F.E., Richmond, J.C., Hsia, J.J., Ginsberg, I.W., and Limperis, T. (1977). Geometrical Considerations and Nomenclature for Reflectance, U.S. Department of Commerce. National Bureau of Standards.","DOI":"10.6028\/NBS.MONO.160"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"838","DOI":"10.1364\/JOSA.44.000838","article-title":"Measurements of the roughness of the sea surface from photographs of the sun\u2019s glitter","volume":"44","author":"Cox","year":"1954","journal-title":"J. Opt. Soc. Am."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1109\/TGRS.2023.3248490","article-title":"Reducing biases in thermal infrared surface radiance calculations over global oceans","volume":"61","author":"Nalli","year":"2023","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"111196","DOI":"10.1016\/j.rse.2019.05.015","article-title":"The ECOSTRESS spectral library version 1.0","volume":"230","author":"Meerdink","year":"2019","journal-title":"Remote Sens. Environ."},{"key":"ref_30","doi-asserted-by":"crossref","unstructured":"Berger, R.H. (1979). Snowpack Optical Properties in the Infrared, U. S. Army Cold Regions Research and Engineering Laboratory. CRREL Report 79-11.","DOI":"10.21236\/ADA071004"},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"2712","DOI":"10.1175\/1520-0469(1980)037<2712:AMFTSA>2.0.CO;2","article-title":"A model for the spectral albedo of snow. I: Pure snow","volume":"37","author":"Wiscombe","year":"1980","journal-title":"J. Atmos. Sci."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"24241","DOI":"10.1029\/94JB01560","article-title":"Modeling thermal infrared (2\u201314 \u03bcm) reflectance spectra of frost and snow","volume":"99","author":"Wald","year":"1994","journal-title":"J. Geophys. Res."},{"key":"ref_33","first-page":"20180161","article-title":"Optical properties of ice and snow","volume":"377","author":"Warren","year":"2019","journal-title":"Philos. Trans. R. Soc. Lond. Ser. A"},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"323","DOI":"10.1109\/JSTARS.2010.2050300","article-title":"Comparison of Radiative Transfer Models for Simulating Snow Surface Thermal Infrared Emissivity","volume":"3","author":"Cheng","year":"2010","journal-title":"IEEE J. Sel. Top. Appl. Earth Obs. Remote Sens."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"1424","DOI":"10.1029\/WR018i005p01424","article-title":"Effect of viewing angle on the infrared brightness temperature of snow","volume":"18","author":"Dozier","year":"1982","journal-title":"Water Resour. Res."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"7673","DOI":"10.5194\/gmd-14-7673-2021","article-title":"SNICAR-ADv3: A community tool for modeling spectral snow albedo","volume":"14","author":"Flanner","year":"2021","journal-title":"Geosci. Model Dev."},{"key":"ref_37","unstructured":"Holton, J.R. (2003). Encyclopedia of Atmospheric Sciences, Academic Press."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"1048","DOI":"10.1175\/1520-0469(1970)027<1048:TTOSIT>2.0.CO;2","article-title":"The transfer of solar irradiance through inhomogeneous turbid atmospheres evaluated by Eddington\u2019s approximation","volume":"27","author":"Shettle","year":"1970","journal-title":"J. Atmos. Sci."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"2452","DOI":"10.1175\/1520-0469(1976)033<2452:TDEAFR>2.0.CO;2","article-title":"The Delta-Eddington approximation for radiative flux transfer","volume":"33","author":"Joseph","year":"1976","journal-title":"J. Atmos. Sci."},{"key":"ref_40","unstructured":"Chandrasekhar, S. (1950). Radiative Transfer, Dover."},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"2171","DOI":"10.1175\/JAS-D-18-0246.1","article-title":"Diffusivity-Factor Approximation for Spectral Outgoing Longwave Radiation","volume":"76","author":"Feng","year":"2019","journal-title":"J. Atmos. Sci."},{"key":"ref_42","doi-asserted-by":"crossref","unstructured":"Thomas, G.E., and Stamnes, K. (1999). Radiative Transfer in the Atmosphere and Ocean, Cambridge University Press. Atmospheric and Space Science.","DOI":"10.1017\/CBO9780511613470"},{"key":"ref_43","doi-asserted-by":"crossref","unstructured":"Warren, S.G., and Brandt, R.E. (2008). Optical constants of ice from the ultraviolet to the microwave: A revised compilation. J. Geophys. Res. Atmos., 113.","DOI":"10.1029\/2007JD009744"},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"2520","DOI":"10.1016\/j.jqsrt.2011.06.017","article-title":"Temperature dependence of ice optical constants: Implications for simulating the single-scattering properties of cold ice clouds","volume":"112","author":"Iwabuchi","year":"2011","journal-title":"J. Quant. Spectrosc. Radiat. Transf."},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"3573","DOI":"10.1175\/JAS-D-15-0276.1","article-title":"Effect of Snow Grain Shape on Snow Albedo","volume":"73","author":"Dang","year":"2016","journal-title":"J. Atmos. Sci."},{"key":"ref_46","unstructured":"M\u00e4tzler, C. (2002). MATLAB Functions for Mie Scattering and Absorption, Institut f\u00fcr Angewandte Physik, Universitas Bernensis. Research Report 2002-08."},{"key":"ref_47","doi-asserted-by":"crossref","first-page":"1408","DOI":"10.1175\/1520-0469(1977)034<1408:TDMRYA>2.0.CO;2","article-title":"The Delta-M Method: Rapid Yet Accurate Radiative Flux Calculations for Strongly Asymmetric Phase Functions","volume":"34","author":"Wiscombe","year":"1977","journal-title":"J. Atmos. Sci."},{"key":"ref_48","unstructured":"Briegleb, B.P., and Light, B. (2007). A Delta-Eddington Mutiple Scattering Parameterization for Solar Radiation in the Sea Ice Component of the Community Climate System Model, University Corporation for Atmospheric Research. Technical Report NCAR\/TN-472+STR."},{"key":"ref_49","doi-asserted-by":"crossref","first-page":"129","DOI":"10.1016\/j.jqsrt.2008.09.009","article-title":"A comparison of two-stream DISORT and Eddington radiative transfer schemes in a real atmospheric profile","volume":"110","author":"Lu","year":"2009","journal-title":"J. Quant. Spectrosc. Radiat. Transf."},{"key":"ref_50","unstructured":"Kingery, W.D. (1962). Ice and Snow, The MIT Press."},{"key":"ref_51","doi-asserted-by":"crossref","first-page":"24235","DOI":"10.1029\/94JB00579","article-title":"Measurements of thermal infrared spectral reflectance of frost, snow, and ice","volume":"99","author":"Salisbury","year":"1994","journal-title":"J. Geophys. Res. Solid Earth"},{"key":"ref_52","doi-asserted-by":"crossref","first-page":"486","DOI":"10.1016\/j.rse.2005.11.001","article-title":"In-situ measured spectral directional emissivity of snow and ice in the 8\u201314 \u03bcm atmospheric window","volume":"100","author":"Hori","year":"2006","journal-title":"Remote Sens. Environ."},{"key":"ref_53","doi-asserted-by":"crossref","first-page":"7243","DOI":"10.1364\/AO.52.007243","article-title":"Modeling angular-dependent spectral emissivity of snow and ice in the thermal infrared atmospheric window","volume":"52","author":"Hori","year":"2013","journal-title":"Appl. Opt."},{"key":"ref_54","unstructured":"Stephens, G.L. (1994). Remote Sensing of the Lower Atmosphere: An Introduction, Oxford University Press."},{"key":"ref_55","doi-asserted-by":"crossref","first-page":"130","DOI":"10.1016\/j.jqsrt.2013.03.007","article-title":"Quasi-specular reflection from particulate media","volume":"131","year":"2013","journal-title":"J. Quant. Spectrosc. Radiat. Transf."},{"key":"ref_56","doi-asserted-by":"crossref","first-page":"313","DOI":"10.1016\/0034-4257(88)90032-6","article-title":"Emissivity of pure and sea waters for the model sea surface in the infrared window regions","volume":"24","author":"Masuda","year":"1988","journal-title":"Remote Sens. Environ."},{"key":"ref_57","doi-asserted-by":"crossref","first-page":"1343","DOI":"10.1364\/AO.40.001343","article-title":"Quasi-specular model for calculating the reflection of atmospheric emitted infrared radiation from a rough water surface","volume":"40","author":"Nalli","year":"2001","journal-title":"Appl. Opt."},{"key":"ref_58","doi-asserted-by":"crossref","first-page":"25789","DOI":"10.1029\/98JE01898","article-title":"Effect of surface roughness on bidirectional reflectance of Antarctic snow","volume":"103","author":"Warren","year":"1998","journal-title":"J. Geophys. Res."},{"key":"ref_59","doi-asserted-by":"crossref","first-page":"2734","DOI":"10.1175\/1520-0469(1980)037<2734:AMFTSA>2.0.CO;2","article-title":"A Model for the Spectral Albedo of Snow. II: Snow Containing Atmospheric Aerosols","volume":"37","author":"Warren","year":"1980","journal-title":"J. Atmos. Sci."},{"key":"ref_60","unstructured":"Nalli, N.R. (2023). Field Measurements for Passive Environmental Remote Sensing: Instrumentation, Intensive Campaigns, and Satellite Applications, Elsevier. [1st ed.]. Chapter 6."},{"key":"ref_61","doi-asserted-by":"crossref","first-page":"994","DOI":"10.1175\/1520-0426(2001)018<0994:TMAERI>2.0.CO;2","article-title":"The Marine-Atmospheric Emitted Radiance Interferometer (M-AERI): A high-accuracy, sea-going infrared spectroradiometer","volume":"18","author":"Minnett","year":"2001","journal-title":"J. Atmos. Ocean. Technol."},{"key":"ref_62","doi-asserted-by":"crossref","unstructured":"Taylor, J.K., Revercomb, H.E., Best, F.A., Tobin, D.C., and Gero, P.J. (2020). The Infrared Absolute Radiance Interferometer (ARI) for CLARREO. Remote Sens., 12.","DOI":"10.3390\/rs12121915"},{"key":"ref_63","doi-asserted-by":"crossref","unstructured":"Nikolla, E., Knuteson, R., and Gero, J. (2023). Hyperspectral Infrared Observations of Arctic Snow, Sea Ice, and Non-Frozen Ocean from the RV Polarstern during the MOSAiC Expedition October 2019 to September 2020. Sensors, 23.","DOI":"10.3390\/s23125755"},{"key":"ref_64","unstructured":"Loveless, M., Adler, D., Best, F., Borbas, E., Huang, X., Knuteson, R.O., L\u2019Ecuyer, T., Nalli, N.R., Olson, E., and Revercomb, H. (2023). Ground-based far infrared emissivity measurements using the Absolute Radiance Interferometer. Earth Space Sci., submitted."},{"key":"ref_65","unstructured":"Liou, K.N. (1992). Radiation and Cloud Processes in the Atmosphere: Theory, Observation, and Modeling, Oxford University Press. Number 20 in Oxford Monographs on Geology and Geophysics."},{"key":"ref_66","unstructured":"Nalli, N.R. (2000). A Physical Multispectral Method for the Retrieval of Ocean and Lake Surface Temperatures via Scanning Spectrometer. [Ph.D. Thesis, Department of Atmospheric and Oceanic Sciences, University of Wisconsin-Madison]."},{"key":"ref_67","unstructured":"Wiscombe, W.J. (1977). The Delta-Eddington Approximation for a Vertically Inhomogeneous Atmosphere, National Center for Atmospheric Research (NCAR). NCAR Technical Report 121 [NTIS PB 270618]."},{"key":"ref_68","doi-asserted-by":"crossref","first-page":"362","DOI":"10.1016\/0019-1035(77)90008-2","article-title":"The range of validity of the Eddington approximation","volume":"32","author":"Wiscombe","year":"1977","journal-title":"Icarus"},{"key":"ref_69","doi-asserted-by":"crossref","unstructured":"Hapke, B. (1993). Theory of Reflectance and Emittance Spectroscopy, Cambridge University Press. [1st ed.]. Topics in Remote Sensing.","DOI":"10.1017\/CBO9780511524998"},{"key":"ref_70","unstructured":"Wylie, C.R.J. (1951). Advanced Engineering Mathematics, McGraw-Hill Book Company, Inc."},{"key":"ref_71","unstructured":"Tenenbaum, M., and Pollard, H. (1963). Ordinary Differential Equations: An Elementary Textbook for Students of Mathematics, Engineering, and the Sciences, Harper & Row. Dover 1985 Edition."}],"container-title":["Remote Sensing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2072-4292\/15\/23\/5509\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,12,26]],"date-time":"2023-12-26T13:53:43Z","timestamp":1703598823000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2072-4292\/15\/23\/5509"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,11,27]]},"references-count":71,"journal-issue":{"issue":"23","published-online":{"date-parts":[[2023,12]]}},"alternative-id":["rs15235509"],"URL":"https:\/\/doi.org\/10.3390\/rs15235509","relation":{},"ISSN":["2072-4292"],"issn-type":[{"value":"2072-4292","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,11,27]]}}}