Profile for Warren Wiscombe

Title: Research Physical Scientist
Affiliation: NASA Civil Service
Contact: E-mail
Code 613
Greenbelt, MD 20771

Office Phone: 301-614-6190
Fax: 301-614-6307

Publications

Chiu, J., A. Marshak, C.H. Huang, T. Varnai, R. Hogan, D.M. Giles, B.N. Holben, E. OConnor, Y. Knyazikhin, and W.J. Wiscombe (2012). Cloud droplet size retrievals from zenith radiance measurements: examples from the Atmospheric Radiation Measurement Program and the Aerosol Robotic Network.. Atmos. Chem. Phys., 12, 10313-10329..
doi:10.5194/acp-12-10313-2012

Marshak, A., Y. Knyazikhin, C. Chiu, and W. Wiscombe (2012). On spectral invariance of single scattering albedo for water droplets and ice crystals at weakly absorbing wavelengths. J. Quant. Spectrosc. Radiat. Trans., 113(9), 715-720.
doi:10.1016/j.jqsrt.2012.02.021

Marshak, A., Knyazikhin Y., J. Chiu, and W. Wiscombe (2011). Spectrally Invariant Approximation within Atmospheric Radiative Transfer. J. Atmos. Sci., 68(12), 3094-3111.
doi: 10.1175/JAS-D-11-060.1

Yang Y., A. Marshak, S. Palm, T. Varnai, and W. Wiscombe (2011). Cloud Impact on Surface Altimetry from a Spaceborne 532nm Micro-Pulse Photon Counting Lidar: System Modeling for Cloudy and Clear Atmospheres. IEEE Trans. Geos. Rem. Sens., 49(12), 4910-4919.
doi: 10.1109/TGRS.2011.2153860

Yang, Y., A. Marshak, S. P. Palm, T. Varnai, and W. J. Wiscombe (2011). Cloud Impact on Surface Altimetry from a Spaceborne 532-nm Micropluse Photon-Counting Lidar: System Modeling for Cloudy and Clear Atmospheres. Geoscience and Remote Sensing, IEEE Transactions, 49(12), 4910-4919.
10.1109/TGRS.2011.2153860

Chiu J.C., C.-H. Huang, A. Marshak, I. Slutsker, D. M. Giles, B. N. Holben, Y. Knyazikhin, and W.J. Wiscombe (2010). Cloud optical depth retrievals from the Aerosol Robotic Network (AERONET) cloud mode observations. J. Geophys. Res., D14202, 115.
doi:10.1029/2009JD013121

Yang Y., A. Marshak, T. Varnai, W.J. Wiscombe, and P. Yang (2010). Uncertainties in ice sheet altimetry from a space-borne 1064 nm single channel lidar due to undetected thin clouds. IEEE Trans. Geos. Rem.Sens., 48(1), 250-259.
doi:10.1109/TGRS.2009.2028335

Chiu J.C., A. Marshak, Y. Knyazikhin, P. Pilewskie, and W. Wiscombe (2009). Physical interpretation of the spectral radiative signatures in the transition zone between cloud-free and cloudy regions. Atmos. Chem. Phys., 9(4), 1419-1430.
doi:10.5194/acp-9-1419-2009

Marshak A., Y. Knyazikhin, J.C. Chiu, and W.J. Wiscombe (2009). Spectral invariant behavior of zenith radiance around cloud edges observed by ARM SWS. Geophys. Res. Lett., 36(L16802).
doi:10.1029/2009GL039366

Huang D., Y. Liu, and W. Wiscombe (2008). Determination of cloud liquid water distribution with 3D cloud tomography. J. Geophys. Res., 113(D13201).
doi:10.1029/2007JD009133

Ottaviani M., K. Stamnes, J. Koskulics, H. Eide, S. Long, W. Su, and W. Wiscombe (2008). Light reflection from water waves: a polarimetric investigation under controlled laboratory conditions. J. Atmos. Oceanic Tech., 25(5), 715-728.
doi:10.1175/2007JTECHA1049.1

Su W., E. Dutton, T. Charlock, and W. Wiscombe (2008). Performance of commerical radiometers in very low temperature and pressure environments typical of polar regions and the stratosphere: A laboratory study. J. Atmos. Oceanic. Tech., 25(4), 558-569.
doi:10.1175/2007JTECHA1005.1

Yang Y., A. Marshak, J.C. Chiu, W.J. Wiscombe, S.P. Palm, A. B. Davis, D. A. Spangenberg, L. Nguyen, J. D. Spinhirne, and P. I. Minnis (2008). Retrievals of Thick Cloud Optical Depth from the Geoscience Laser Altimeter System (GLAS) by Calibration of Solar Background Signal. J. Atmos. Sci., 3527, 65, 3513.
doi:10.1175/2008JAS2744.1

Chiu J.C., A. Marshak, W.J. Wiscombe, S. C. Valencia, and E.J. Welton (2007). Cloud optical depth retrievals from solar background. IEEE Geosci. Remote Sens. Lett., No. 3, 4, 456-460.
10.1109/LGRS.2007.896722

Turner D. D., A. M. Vogelmann, R. T. Austin, J. C. Barnard, K. Cady-Pereira, J.C. Chiu, S. A. Clough, C. Flynn, M. M. Khaiyer, J. Liljegren, K. Johnson, B. Lin, C. Long, A. Marshak, S. Y. Matrosov, S. A. McFarlane, M. Miller, Q. Min, P. Minnis, Z. Wang, and W. Wiscombe (2007). Thin Liquid Water Clouds: Their Importance and Our Challenge. Bull. Amer. Meteor. Soc., 88, 177-190.

Zhang Z., P. Yang, G. Kattawar, and W. Wiscombe (2007). Single-scattering properties of Platonic solids in geometrical-optics regime. JQSRT, 106, 595-603.

Chiu J.C., A. Marshak, Y. Knyazikhin, W. Wiscombe, H. Barker, J. C. Barnard, and Y. Luo (2006). Remote sensing of cloud properties using ground-based measurements of zenith radiance. J. Geophys. Res., D16201, 111.
10.1029/2005JD006843

Knyazikhin Y., A. Marshak, M. Larsen, W. Wiscombe, J. Martonchik, and R. Myneni (2005). Small-scale drop size variability: Impact on estimation of cloud optical properties. J. Atmos. Sci., 62, 2555-2567.

Marshak A., Yu. Knyazikhin, M. L. Larsen, and W.J. Wiscombe (2005). Small-scale drop size variability: Empirical models for drop-size-dependent clustering in clouds. J. Atmos. Sci., 62, 551-558.

Wiscombe W.J. (2005). Scales, Tools and Reminiscences In A.M. Marshak and A.B. Davis, Springer (Ed.), 3D Radiative Transfer in Cloudy Atmospheres (686pp).

Chiu J.-Y.C., A. Marshak, and W.J. Wiscombe (2004). The effect of surface heterogeneity on cloud absorption estimates. Geoph. Res. Lett. (L15105), 31.
10.1029/2004GL020104

Evans K. F., and W.J. Wiscombe (2004). An algorithm for generating stochastic cloud fields from radar profile statistics. Atmospheric Research, 72, 263-289.
10.1016/j.atmosres.2004.03.016.

Marshak A., Y. Knyazikhin, K. Evans, and W. Wiscombe (2004). The "RED versus NIR" plane to retrieve broken-cloud optical depth from ground-based measurements. J. Atmos. Sci.,., 61, 1911-1925.

Evans K. F., R. Lawson, P. Zmarzly, OConnor D., and W. Wiscombe (2003). In situ cloud sensing with multiple scattering lidar: Simulations and demonstration. J. Atmos. Oceanic Tech., 20, 1505-1522.

Gao B. -C., P. Yang, G. Guo, S. K. Parks, W. Wiscombe, and B. D. Chen (2003). Measurements of water vapor and high clouds over the Tibetan Plateau with the Terra MODIS instrument. IEEE Trans. Geosci. Remote Sens., 41, 895-900.

Gao B. -C., P. Yang, G. Guo, S. K. Park, W.J. Wiscombe, and B. D. Chen (2003). Measurements of water vapor and high clouds over the Tibetan Plateau with the Terra MODIS instrument. IEEE Trans. Geosci. Remote Sens., 41, 895-900.

Lee Y. K., P. Yang, M. I. Mishchenko, B. A. Baum, Y. Hu, H. -L. Huang, W.J. Wiscombe, and A. J. Baran (2003). On the use of circular cylinders as surrogates for hexagonal pristine ice crystals in scattering calculations at infrared wavelengths. Appl. Opt., 42, 2653-2664.

Yang P., M. G. Mlynczak, H. L. Wei, D. P. Kratz, B. A. Baum, Y. X. Hu, W.J. Wiscombe, A. Heidinger, and M. I. Mishchenko (2003). Spectral signature of ice clouds in the far-infrared region: Single-scattering calculation and radiative sensitivity study. J. Geophys. Res. (D18), 4569, 108.
10.1029/2002JD003291

Gao B. -C., P. Yang, W. Han, R. -R. Li, and W. Wiscombe (2002). An algorithm using visible and 1.38-m channels to retrieve cirrus cloud reflectances from aircraft and satellite data. IEEE Trans. Geosci. Remote Sens., 40, 1659-1668.

Knyazikhin Y., A. Marshak, W. Wiscombe, J. Martonchick, and R. Myneni (2002). A missing solution to the transport equation and its effect on estimation of cloud absorptive properties. J. Atmos. Sci., 59, 3572-3585.

Yang P., B. C. Gao, W.J. Wiscombe, M. I. Mishchenko, S.E. Platnick, H. L. Huang, B. A. Baum, Y. X. Hu, D. Winker, S.C. Tsay, and S. K. Park (2002). Inherent amd apparent scattering properties of coated or uncoated spheres embedded in an absorbing host medium. Appl. Opt., 41, 2740-2759.

Gerber H., J. Jensen, A. Davis, A. Marshak, and W. Wiscombe (2001). Spectral density of cloud liquid water content at high frequencies. J. Atmos. Sci., 58, 497-503.

Yang P., B. C. Gao, B. A. Baum, Y. Hu, W.J. Wiscombe, M. I. Mishchenko, D. M. Winker, and S. L. Nasiri (2001). Asymptotic solutions for optical properties of large particles with strong absorption. Appl. Opt., 40, 1532-1547.

Yang P., B. C. Gao, B. A. Baum, W.J. Wiscombe, Y. X. Hu, S. L. Nasiri, P. F. Soulen, A. J. Heymsfield, G. M. McFarquhar, and L. M. Miloshevich (2001). Sensitivity of cirrus bidirectional reflectance to vertical inhomogeneity of ice crystal habits and size distributions for two Moderate-Resolution Imaging Spectroradiometer (MODIS) bands. J. Geophys. Res., 106, 17267-17291.

Yang P., B. C. Gao, B. A. Baum, Y. X. Hu, W.J. Wiscombe, S.C. Tsay, D. M. Winker, and S. L. Nasiri (2001). Radiative properties of cirrus clouds in the infrared (8-13 microns) spectral region. J. Quant. Spectrosc. Radiat. Trans., 70, 473-504.

Esper J., P. Panetta, M. Ryschkewitsch, W. Wiscombe, and S. Neeck (2000). NASA/GSFC nano-satellite technology for Earth Science Missions. Acta Astronautica, 46, 287-296.

Marshak A., Yu. Knyazikhin, A. Davis, W. Wiscombe, and P. Pilewskie (2000). Cloud vegetation interaction: Use of Normalized Difference Cloud Index for estimation of cloud optical thickness. Geophys. Res. Lett., 27, 1695-1698.

Davis A., A. Marshak, H. Gerber, and W. Wiscombe (1999). Horizontal structure of marine boundary-layer clouds from cm-to km scales. J. Geophys. Res., 104, 6123-6144.

Marshak A., L. Oreopoulos, A. Davis, W. Wiscombe, and R. Cahalan (1999). Horizontal radiative fluxes in clouds and accuracy of the Independent Pixel Approximation at absorbing wavelengths. Geophys. Res. Lett., 11, 1585-1588.

Marshak A., W. Wiscombe, A. Davis, L. Oreopoulos, and R. Cahalan (1999). On the removal of the effect of horizontal fluxes in two-aircraft measurements of cloud absorption. Quart. J. Roy. Meteor. Soc., 125, 2153-2170.

Davis A., A. Marshak, R. Cahalan, and W. Wiscombe (1998). Insight into three-dimensional radiation transport from diffusion theory, application to the cloudy atmosphere (111-139). Radiative Transfer, Ed. M. P. Mengue, Begell House, Inc., NY

Gao B. -C., Y. Kaufman, W. Han, and W. Wiscombe (1998). Correction of thin cirrus path radiances in the 0.4-1 micron spectral region using the Sensitive 1.375 Micron Cirrus Detecting Channel. J. Geophys. Res., 103, 32169-32176.

Marshak A., A. Davis, R. Cahalan, and W. Wiscombe (1998). Nonlocal Independent Pixel Approximation, direct and inverse problems. IEEE Trans. Geosci. Remote Sens., 36, 192-205.

Marshak A., A. Davis, W. Wiscombe, and R. Cahalan (1998). Radiative effects of sub-mean-free-path liquid water variability observed in stratiform clouds. J. Geophys. Res. (Atmos.), 103, 19557-19567.

Marshak A., A. Davis, W. Wiscombe, W. Ridgway, and R. Cahalan (1998). Biases in shortwave column absorption in the presence of fractal clouds. J. Climate, 11, 431-446.

Cahalan R.F., A. Davis, A. Marshak, D. Silberstein, and W. Wiscombe (1997). Cloud macrostructure and radiation. Remote Sensing A Scientific Vision for Sustainable Development: LC 97-70575, ISBN 0-7803-3839-1 F01, 41-44.

Davis A., A. Marshak, R.F. Cahalan, and W. Wiscombe (1997). Interactions, solar and Laser beams in stratus clouds, fractals and multifractals in climate and remote sensing studies. Fractals, 5, 129-166.

Davis A., A. Marshak, W. Wiscombe, and R.F. Cahalan (1997). Evidence for net horizontal radiative fluxes in marine stratocumulus. (809-812). IRS'96 Current Problems in Atmospheric Radiation, W. L. Smith and K. Stamnes, Eds., Deepak Publ.

Davis A., D. Winker, A. Marshak, J. Spinhurne, R. Cahalan, S. Love, S. Melfi, and W. Wiscombe (1997). Retrieval of physical and optical cloud thicknesses from space-borne and wide-angle Lidar. Adv. Atmos. Remote Sensing with Lidar, A. Ansmann, R. Neuber, P. Rairoux and U. Wadinger, Eds. Springer-Verlag, 193-196.

Davis A., A. Marshak, R.F. Cahalan, and W. Wiscombe (1997). The Landsat scale break in stratocumulus as a three-dimensional radiative transfer effect: Implications for cloud remote sensing. J. Atmos. Sci., 54, 241-260.

Marshak A., A. Davis, R. Cahalan, and W. Wiscombe (1997). Physical simulation of high-resolution satellite images for fractal cloud model (301-310). Fractal Frontiers. M. M. Novak and T. G. Dewey, Eds., World Scientific

Marshak A., A. Davis, R. Cahalan, and W. Wiscombe (1997). The effect of horizontal fluxes on cloud absorption estimates based on simulated two-aircraft measurements of fractal clouds. IRS'96: Current problems in atmospheric radiation (415-418). W. L. Smith and K. Stamnes, Eds., Deepak Publ.

Marshak A., A. Davis, R.F. Cahalan, and W. Wiscombe (1997). Nonlocal Independent Pixel Approximation for computing radiation fields of inhomogeneous clouds. IRS'96: Current problems in atmospheric radiation (139-142). W. L. Smith and K. Stamnes, Eds., Deepak Publ.

Marshak A., A. Davis, W. Wiscombe, and R. Cahalan (1997). Inhomogeneity effects on cloud shortwave absorption measurements: Two-aircraft simulations. J. Geophys. Res., 102, 16619-16637.

Marshak A., A. Davis, W. Wiscombe, and R.F. Cahalan (1997). Scale-invariance of liquid water distributions in marine stratocumulus. II. Multifractal properties and intermittency issues. J. Atmos. Sci., 54, 1423-1444.

Davis A., A. Marshak, W. Wiscombe, and R.F. Cahalan (1996). Multifractal characterizations of intermittency in nonstionary geophysical signals and fields (97-158). Nonstationary Random Processes and Their Applications, G. Trevino, Ed., World Scientific

Davis A., A. Marshak, W. Wiscombe, and R.F. Cahalan (1996). Scale-invariance of liquid water distributions in marine stratocumulus. I. Spectral properties and stationarity issues. J. Atmos. Sci., 53, 1538-1558.

Ellingson R., and W. Wiscombe (1996). The Spectral Radiance Experiment (SPECTRE): Project description and sample results. Bull. Amer. Meteor. Soc., pages unknown, 77.

Marshak A., A. Davis, W. Wiscombe, and G. Titov (1995). The verisimilitude of the Independent Pixel Approximation used in cloud remote sensing. Remote Sens. Environ., 52, 72-78.

Marshak A., A. Davis, W. Wiscombe, and R.F. Cahalan (1995). Radiative smoothing in fractal clouds. J. Geophys. Res. (Atmos.), 100, 26247-26261.

Wiscombe W. (1995). An absorbing mystery. Nature, 376, 466-467.

Cahalan R.F., W. Ridgway, W.J. Wiscombe, Harshvardhan, and S. Gollmer (1994). Independent pixel and Monte Carlo estimates of stratocumulus albedo. J. Atmos. Sci., 51, 3776-3790.

Cahalan R.F., W. Ridgway, W.J. Wiscombe, T.L. Bell, and J. B. Snider (1994). The albedo of fractal stratocumulus clouds. J. Atmos. Sci., 51, 2434-2455.

Davis A., A. Marshak, and W. Wiscombe (1994). Wavelet-based multifractal analysis of non-stationary and/or intermittent geophysical signals. Wavelets in Geophysics (249-298). E. Foufoula-Georgiou and P. Kumar, Eds., Academic Press

Davis A., A. Marshak, W.J. Wiscombe, and R.F. Cahalan (1994). Multifractal characterizations of non-stationarity and intermittency in geophysical fields: Observed, retrieved, or simulated. J. Geophys. Res., 99, 8055-8072.

Gao B. -C., and W. Wiscombe (1994). Surface-induced brightness temperature variations and their effects on detecting thin cirrus clouds using IR emission channels in the 8-12 mm region. J. Appl. Meteor., 33, 568-570.

Marshak A., A. Davis, R.F. Cahalan, and W.J. Wiscombe (1994). Bounded Cascade Models as non-stationary multifractals. Phys. Rev.E49, 55-69.

Cahalan R.F., and W.J. Wiscombe (1993). Impact of cloud structure on climate (120-124). Current Problems in Atmospheric Radiation. A. Deepak Publishing

Davis A., A. Marshak, and W. Wiscombe (1993). Bi-multifractal analysis and multi-affine modeling of non-stationary geophysical processes: Application to turbulence and clouds. Fractals, 3, 560-567.

Gao B. -C., A. Goetz, and W. Wiscombe (1993). Cirrus cloud detection from airborne imaging spectrometer data using the 1.38 micron water vapor band. Geophys. Res. Lett., 20, 301-304.

Marshak A., A. Davis, R. Cahalan, and W. Wiscombe (1993). Multi-singular and multi-affine properties of Bounded Cascade Models. Fractals, 3, 702-710.

Fiedler-Ferrari N., H. Nussenzveig, and W. Wiscombe (1991). Theory of near-critical angle scattering from a curved interface. Phys. Rev.A43, 1005-1038.

Nussenzveig H., and W. Wiscombe (1991). Complex angular momentum approximation to hard-core scattering. Phys. Rev.A43, 2093-2112.

Warren S., W. Wiscombe, and J. Firestone (1990). Spectral albedo and emissivity of CO2 in Martian polar caps: Model results. J. Geophys. Res., 95, 14717-14741.

Wiscombe W. (1990). Principles of Numerical Modeling with Applications to Atmospheric Radiation. Course on Radiation as It Relates to Climate Westview Press, Boulder, Colorado, pages unknown

Cahalan R.F., M. Nestler, W. Ridgway, W.J. Wiscombe, and T. Bell (1989). Marine stratocumulus spatial structure (19-25). Proc. Fourth Int. Conf. Stat. Clim., IMSC

Mugnai A., and W. Wiscombe (1989). Scattering from nonspherical Chebyshev particles III: Variability of angular scattering patterns. Appl. Opt., 28, 3061-3073.

Luther F., R. Ellingson, Y. Fouquart, S. Fels, N. Scott, and W. Wiscombe (1988). Intercomparison of radiation codes in climate models (ICRCCM): Longwave clear sky results. Bull. Amer. Meteor. Soc., 69, 40-48.

Stamnes K., S.C. Tsay, W. Wiscombe, and K. Jayaweera (1988). Numerically stable algorithm for Discrete-Ordinate-Method radiative transfer in multiple scattering and emitting layered media. Appl. Opt., 27, 2502-2509.

Wiscombe W., and A. Mugnai (1988). Scattering from nonspherical Chebyshev particles II: Means of angular scattering patterns. Appl. Opt., 27, 2405-2421.

Nussenzveig H., and W. Wiscombe (1987). Diffraction as tunneling. Phys. Rev. Lett., 59, 1667-1671.

Mugnai A., and W. Wiscombe (1986). Scattering from nonspherical Chebyshev particles. I: Cross sections, single-scattering albedo, asymmetry factor and backscattered fraction. Appl. Opt., 25, 1235-1244.

Prabhakara C., D. A. Short, W. Wiscombe, R. S. Fraser, and B. Vollmer (1986). Rainfall over oceans inferred from Nimbus-7 SMMR, application to 1982-83 El Nino. J. Climate Appl. Meteor., 25, 1464-1474.

Wiscombe W., and R. Welch (1986). Further comments on the effects of large drops in clouds. J. Atmos. Sci., 43, 401-407.

Warren S., and W. Wiscombe (1985). Dirty snow after nuclear war. Nature, 313, 467-470.

Wiscombe W., and V. Ramanathan (1985). The role of radiation and other renascent subfields in atmospheric science. Bull. Amer. Meteor. Soc., 66, 1278-1287.

Wiscombe W., R. Welch, and W. Hall (1984). The effect of very large drops on cloud absorption I. Parcel models. J. Atmos. Sci., 41, 1336-1355.

Hoffert M., B. Flannery, A. Callegari, C. Hsieh, and W. Wiscombe (1983). Evaporation-limited tropical temperatures as a constraint on climate sensitivity. J. Atmos. Sci., 40, 1659-1668.

Wiscombe W. (1983). Atmospheric radiation: 1975-1983. Rev. Geophys. Space Phys., 21, 997-1021.

Wiscombe W., and S. Warren (1981). Comment on 'Radiative Properties of Snow for Clear Sky Solar Radiation'. Cold Reg. Sci. Tech., 5, 177-180.

Mugnai A., and W. Wiscombe (1980). Scattering of radiation by moderately nonspherical particles. J. Atmos. Sci., 37, 1291-1307.

Nussenzveig H., and W. Wiscombe (1980). Forward optical Glory. Optics Lett., 5, 455-457.

Nussenzveig H., and W. Wiscombe (1980). Efficiency factors in Mie scattering. Phys. Rev. Lett., 45, 1490-1494.

Wiscombe W. (1980). Improved Mie scattering algorithms. Appl. Opt., 19, 1505-1509.

Wiscombe W., and A. Mugnai (1980). Exact calculations of scattering from moderately-nonspherical tn-particles: Comparisons with equivalent spheres Proc. Workshop Light Scattering by Irregularly Shaped Particles, D. W. Schuerman, Ed., Plenum Publishing Corp NY, pages unknown

Wiscombe W., and S. Warren (1980). A model for the spectral albedo of snow I. Pure snow. J. Atmos. Sci., 37, 2712-2733.

Wiscombe W., and S. Warren (1980). A model for the spectral albedo of snow II. Snow containing atmospheric aerosols. J. Atmos. Sci., 37, 2734-2745.

Wiscombe W. (1977). Doubling Initialization revisited. J. Quant. Spectr. and Rad. Trans., 18, 245-248.

Wiscombe W. (1977). Author's reply. J. Quant. Spectr. and Rad. Trans., p. 251, 18.

Wiscombe W. (1977). The Delta-M Method: Rapid yet accurate radiative flux calculations for strongly asymmetric phase functions. J. Atmos. Sci., 34, 1408-1422.

Wiscombe W., and J. Evans (1977). Exponential-sum fitting of radiative transmission functions. J. Comp. Phys., 24, 416-444.

Wiscombe W., and J. Joseph (1977). The range of validity of the Eddington approximation. Icarus, 32, 362-377.

Wiscombe W., and P. Chylek (1977). Mie scattering between any two angles. J. Opt. Soc. Amer., 67, 572-573.

Joseph J., W. Wiscombe, and J. Weinman (1976). The Delta-Eddington Approximation for radiative flux transfer. J. Atmos. Sci., 33, 2452-2459.

Wiscombe W. (1976). Extension of the Doubling Method to inhomogeneous sources. J. Quant. Spectr. and Rad. Trans., 16, 477-489.

Wiscombe W. (1976). On initialization, error and flux conservation in the Doubling Method. J. Quant. Spectr. and Rad. Trans., 16, 637-658.

Wiscombe W., and G. Grams (1976). The backscattered fraction in Two-Stream Approximations. J. Atmos. Sci., 33, 2440-2451.

Wiscombe W. (1975). Solar radiation calculations for Arctic summer stratus conditions Climate of the Arctic, Weller and Bowling, Eds., University of Alaska Press, Fairbanks, Alaska, pages unknown