3D Radiative Transfer


Clouds, which cover about 68% of the globe, regulate the incident solar radiation field in space and time more than any other atmospheric variable, and they act as a primary greenhouse constituent in our atmosphere. Our ability to accurately compute the interaction of the radiation field with clouds is critically important in the geosciences, including, for example, our ability to predict climate change, to quantify the climate forcing by anthropogenic aerosols through its influence on cloud microphysics, to produce accurate predictions of biogeochemical cycles and the oxidative capacity of our atmosphere, and to monitor environmental change from space. Yet, in all environmental prediction models and in most satellite remote sensing techniques, radiative transfer is computed assuming clouds and their radiative boundary conditions to be plane‐parallel (i.e., horizontally homogeneous out to infinity), hence simplified to 1-D (the vertical) radiative transfer. This makes radiative transfer calculations computationally fast and solutions to the inverse problem faced in satellite remote sensing tangible. However, a simple look at clouds, either from the ground, aircraft or spacecraft reveals that they are often not horizontally homogenous over a wide range of scales, thereby raising questions as to the degree to which the plane‐parallel assumption produces the required accuracy for various applications. Our group’s publication record includes a long list of papers that address issues of cloud heterogeneity on the radiation field, including theory, modeling, and satellite observations. Below are just a couple of examples.


We have extended the open source NASA I3RC community Monte Carlo 3D radiative transfer model to include emission. The code simply goes by IMC+emission and is available though the NASA I3RC project page and through the codes public GitHub maintained by former group member Alexandra Jones:


The code has been extensively benchmarked as described in our Journal of Atmospheric Science publication:


Since the code is an extension of the original I3RC community model developed by Robert Pincus, the quick start start documentation is essentially the same and can be found here.

Satellite Observations

Many studies have given important insight into the applicability of the plane‐parallel assumption, showing significant errors in calculating radiative heating and photochemical reactions, or on satellite remote sensing when applied to heterogeneous cloud fields. Most of these have been either derived over a limited regional domain from observations or from computationally expensive 2‐ or 3‐D radiative transfer calculations applied to only a few simulated heterogeneous cloud fields. The extent to which the results from these studies are globally applicable requires measureable deviations from 1‐D solar radiative transfer for real clouds from global observations. To do so, we combined MISR and MODIS observations to examine how often and to what degree oceanic water clouds can be considered plane-parallel. We showed that the angular distribution of scattered solar radiation measured at 1 km resolution from space are indistinguishable from plane-parallel clouds 24% of the time at the 95% confidence interval of our measurement method. These plane‐parallel clouds occur most frequently within regions dominated by stratiform clouds under solar zenith angles <60°. For all other regions or sun‐angles, the frequency in which clouds are indistinguishable from plane‐parallel drops sharply to as low as a few percent. Our results provide a basis for interpreting space‐time variability within many satellite‐retrieved variables and reveal a need for continued efforts to handle three‐dimensional radiative transfer in environmental modeling and monitoring systems. These results are published in Di Girolamo et al. (2010).

This figure shows the key results from Di Girolamo et al. (2010) described above. The top figures show the frequency in which the angular distribution of scattered sunlight is within 5% of its plane-parallel values (this is well within our ability to measure it) for the months of January and July. The bottom figures shows monthly-mean H_sigma values, defined as the standard deviation of 12×12 275-m 866-nm channel reflectances divided by its mean – a measured representation of the spatial heterogeneity of the cloud field. Clearly, measured angular deviations from plane-parallel are closely related to the spatial heterogeneity of the cloud field.

Atmospheric Tomography with 3D Radiative Transfer

The above figure shows that we need to move away from passive remote sensing techniques of cloud optical and microphysical properties rooted in 1-D radiative transfer to one that is rooted in 3D radiative transfer.

Recently, we introduced AT3D – an Open Source software package that takes in multi-angle imagery to retrieve the 3D (volumetric) distribution of cloud microphysical properties. AT3D is fully described in Loveridge et al. (2023) and shows excellent results when applied to synthetic cumulus cloud fields of low to moderate optical depths.  Unlike retrievals rooted in 1-D radiative transfer, AT3D retrievals are robust against changes in solar zenith angle, as shown for the retrieval of the volume extinction coefficient in the figure below.



Our research has largely been supported by NASA over multiple grants over many years, with NSF support occurring on occasion. The specific grants are listed in the acknowledgment section of the publications.

Peer-reviewed publications on issues of cloud heterogeneity or 3D radiative transfer

De Vera, M.V., L. Di Girolamo, G. Zhao, R.M. Rauber, S.W. Nesbitt, and G.M. McFarquhar, 2024: Observations of the macrophysical properties of cumulus cloud fields over the tropical western Pacific and their connection to meteorological variables. Atmos. Chem. Physical., 24, 5603-5623, https://doi.org/10.5194/acp-24-5603-2024 

Loveridge, J., A. Levis, L. Di Girolamo, V. Holodovsky, L. Forster, A.B. Davis, and Y.Y. Schechner, 2023: Retrieving 3D distributions of atmospheric particles using Atmospheric Tomography with 3D Radiative Transfer – Part 2: local optimization, Atmos. Meas. Tech., 16, 3931-3957, https://doi.org/10.5194/amt-16-3931-2023

Reid, J., et al., 2023: The coupling between tropical meteorology, aerosol lifecycle, convection, and radiation, during the Clouds, Aerosol Monsoon Processes Philippines Experiment (CAMP2Ex). Bull. Am. Meteorol. Soc., https://doi.org/10.1175/BAMS-D-21-0285.1.

Mitra, A., L. Loveridge, and L. Di Girolamo, 2023: Fusion of MISR stereo cloud heights and Terra-MODIS thermal infrared radiances to estimate two-layered cloud properties. J. Geophys. Res. – Atmos., 128,  e2022JD038135, https://doi.org/10.1029/2022JD038135.

Loveridge, J., A. Levis, L. Di Girolamo, V. Holodovsky, L. Forster, A.B. Davis, and Y.Y. Schechner, 2023: Retrieving 3D distributions of atmospheric particles using Atmospheric Tomography with 3D Radiative Transfer – Part 1: Model description and Jacobian calculation, Atmos. Meas. Tech., 16, 1803-1847, https://doi.org/10.5194/amt-16-1803-2023

Fu, D., L. Di Girolamo, R.M. Rauber, G.M. McFarquhar, S.N. Nesbitt, J. Loveridge, Y. Hong, B. van Diedenhoven, B. Cairns, M.D. Alexandrov, P. Lawson, S. Woods, S. Tanelli, O.O. Sy, S. Schmidt, C.A. Hostetler, and A.J. Scarino, 2022: An evaluation of liquid cloud droplet effective radius derived from MODIS, airborne remote sensing and in situ measurements from CAMP2Ex, Atmos. Chem. Phys., 22, 8259-8285, 2022; https://doi.org/10.5194/acp-22-8259-2022

Mitra, A., L. Di Girolamo, Y. Hong, Y. Zhan, and K.J. Mueller, 2021: Assessment and error analysis of Terra-MODIS and MISR cloud-top heights through comparison with ISS-CATS lidar. J. Geophys. Res. Atmos., 126, e2020JD034281. https://doi.org/10.1029/2020JD034281.

Dutta, S., L. Di Girolamo, S. Dey, Y. Zhan, C.M. Moroney, and G. Zhao, 2020: The reduction in near-global cloud cover after correcting for biases caused by finite resolution measurement. Geophys. Res. Lett, 47, e2020GL090313. https://doi.org/10.1029/2020GL090313.

Hong, Y., and L. Di Girolamo, 2020: Cloud phase characteristics over southeast Asia from A-Train satellite observations. Atmos. Phys. Chem., 20, 8267-8291, https://doi.org/10.5194/acp-20-8267-2020.

Fu, D., L. Di Girolamo, L. Liang, and G. Zhao, 2019: Regional Biases in Moderate Resolution Imaging Spectroradiometer (MODIS) marine liquid water cloud drop effective radius deduced through fusion with Multi-angle Imaging SpectroRadiometer (MISR). J. Geophys. Res. Atmos., 124, https://doi.org/10.1029/2019JD031063.

Lee, B., L. Di Girolamo, G. Zhao, and Y. Zhan, 2018: Three-dimensional cloud volume reconstruction from the Multi-angle Imaging SpectroRadiometer. Remote Sens. 10(11), 1858, doi:10.3390/rs10111858.

Werner, F., Z. Zhang, G. Wind, D. Miller, S. Platnick, and L. Di Girolamo, 2018: Improving cloud optical property retrievals for partly cloudy pixels using coincident higher-resolution single band measurements: A feasibility study using ASTER observations. J. Geophys. Res. Atmos. 123doi:10.1029/2018JD028902. (EOS Dec 5, 2018, Editor’s Highlight)

Jones, A.L., and L. Di Girolamo, 2018: Design and verification of a new monochromatic thermal emission component of the I3RC Community Monte Carlo Model. J. Atmos. Sci., 75, 885-906, doi: 10.1175/JAS-D-17-0251.1. (Ogura Award)

Werner, F., G. Wind, Z. Zhang, S. Platnick, L. Di Girolamo, G. Zhao, N. Amarasinghe, and K. Meyer, 2016: Marine boundary layer cloud property retrievals from high–resolution ASTER observations: case studies and comparison with Terra MODIS. Atmos. Meas. Tech., 9, 5869-5894, 2016; doi:10.5194/amt-9-5869-2016.

Zhang, Z., F. Werner, H.-M. Cho, G. Wind, S. Platnick, A. S. Ackerman, L. Di Girolamo, A. Marshak, and K. Meyer, 2016: A framework based on 2-D Taylor expansion for quantifying the impacts of subpixel reflectance variance and covariance on cloud optical thickness and effective radius retrievals based on the bispectral method, J. Geophys. Res. Atmos., 121, doi:10.1002/ 2016JD024837.

Zhao, G., L. Di Girolamo, D.J. Diner, C.J. Bruegge, K. Mueller, and D.L. Wu, 2016: Regional changes in Earth’s color and texture as observed from space over a 15-year period. IEEE Trans. Geosci. Remote Sens.,54(7), 4240-4249, doi:10.1109/TGRS.2016.2538723.

Liang, L. L. Di Girolamo, and W. Sun, 2015: Bias in MODIS cloud drop effective radius for oceanic water clouds as deduced from optical thickness variability across scattering angle. J. Geophys. Res. Atmos., 120, doi:10.1002/2015JD023256.

Cho, H.-M., Z. Zhang, K. Meyer, M. Lebsock, S. Platnick, A.S. Ackerman, L. Di Girolamo, L.C. Labonnote, C. Cornet, J. Riedi, and R.E. Holz, 2015: Frequency and causes of failed MODIS cloud property retrievals for liquid phase clouds over global oceans. J. Geophys. Res. Atmos., 120, doi:10.1002/2015JD023161.

Astin, I., and L. Di Girolamo, 2014: The horizontal scale-dependence of the cloud overlap parameter alpha.  Atmos. Chem. Phys., 14, 9917-9922.

Rauber, R.M., G. Zhao, L. Di Girolamo, and M. Colon-Robles, 2013: Aerosol size distribution and optical property variability near Caribbean trade cumulus clouds – effects of humidity and cloud processing as determined from aircraft measurements. J. Atmos. Sci., 70, 3063-3083.

Davison, J.L., R.M. Rauber, L. Di Girolamo, and M.A. LeMone, 2013: A revised conceptual model of the tropical marine boundary layer. Part III: Bragg scattering layer statistical properties. J. Atmos. Sci. 70, 3047-3062.

Davison, J.L., R.M. Rauber, and L. Di Girolamo, 2013: A revised conceptual model of the tropical marine boundary layer. Part II: detecting relative humidity layers using Bragg scattering from S-band radar. J. Atmos. Sci. 70, 3025-3046.

Davison, J.L., R.M. Rauber, L. Di Girolamo, and M.A. LeMone, 2013: A revised conceptual model of the tropical marine boundary layer. Part I: statistical characterization of the variability inherent in the wintertime trade wind regime over the Western North Atlantic. J. Atmos. Sci. 70, 3005-3024.

Stubenrauch, C.J.,  W.B. Rossow, S. Kinne, S. Ackerman, G. Cesana, H. Chepfer, L. Di Girolamo, B. Getzewich, A. Guignard, A. Heidinger, B. Maddux, P. Menzel, P. Minnis, C. Pearl, S. Platnick, C. Poulsen,  J. Riedi, S. Sun-Mack, A. Walther, D. Winker, S. Zeng, and G. Zhao, 2013: Assessment of global cloud datasets from satellites: Project and Database initiated by the GEWEX Radiation Panel. Bull. Am. Meteor. Soc., 94, 1031 – 1049.

Liang, L., and L. Di Girolamo, 2013: A global analysis on the view-angle dependence of plane-parallel oceanic water cloud optical thickness using data synergy from MISR and MODIS. J. Geophys. Res. Atmos., 118, doi:10.1029/2012JD018201.

Reid, J.S., E.J. Hyer, R. Johnson, B.N. Holben, J. Zhang, J.R. Campbell, S.A. Christopher, L. Di Girolamo, L. Giglio, R.E. Holz, C. Kearney, J. Miettinen, E.A. Reid, F.J. Turk, J. Wang, P. Xian, R.J. Yokelson, G. Zhao, R. Balasubramanian, B.N. Chew, S. Janai, N. Lagrosas, P. Lestari, N.-H.Lin, M. Mahmud, B. Norris, A.X. Nguyen, N.T.K.Oahn, M. Oo, S. Salinas, and S.C. Liew, 2013: Observing and understanding the Southeast Asian aerosol system by remote sensing: An initial review and analysis for the Seven Southeast Asian Studies (7SEAS) program. Atmos. Res., 122, 403-468

Jones, A.L., L. Di Girolamo, and G. Zhao, 2012: Reducing the resolution bias in cloud fraction from satellite derived clear-conservative cloud masks. J. Geophys. Res., 117, D12201, doi:10.1029/2011JD017195.

Minor, H.A., R.M. Rauber, S. Goke, and L. Di Girolamo, 2011: Trade wind cloud evolution observed by polarization radar: relationship to giant condensation nuclei concentrations and cloud organization. J. Atmos. Sci., 68, 1075-1096.

Dey, S., L. Di Girolamo, G. Zhao, A.L. Jones, and G.M. McFarquhar, 2011: Satellite-observed relationships between aerosol and trade-wind cumulus cloud properties over the Indian Ocean. Geophys. Res. Lett., 38, L01804, doi:10.1029/2010GL045588.

Di Girolamo, L., L. Liang, and S. Platnick, 2010: A global view of one-dimensional solar radiative transfer through oceanic water clouds. Geophys. Res. Lett., 37, L18809, doi:10.1029/2010GL044094.

Tackett, J.L., and L. Di Girolamo, 2009: Enhanced aerosol backscatter adjacent to tropical trade wind clouds revealed by satellite-based lidar. Geophys. Res. Lett., 36, L14804, doi:10.1029/2009GL039264.

Zhao, G., L. Di Girolamo, S. Dey, A.L. Jones, and M. Bull, 2009: Examination of direct cumulus contamination on MISR-retrieved aerosol optical depth and angstrom coefficient over ocean. Geophys. Res. Lett., 36, L13811, doi:10.1029/2009GL038549.

Liang, L., L. Di Girolamo, and S. Platnick, 2009: View-angle consistency in reflectance, optical thickness and spherical albedo of marine water-clouds over the northeastern Pacific through MISR-MODIS fusion. Geophys. Res. Lett., 36, L09811, doi:10.1029/2008GL037124.

Snodgrass, E.R., L. Di Girolamo, and R.M. Rauber, 2009: Precipitation characteristics of trade winds clouds during RICO derived from radar, satellite, and aircraft measurements. J. Appl. Meteor. Climatol.,48, 464-483.

Dey, S., L. Di Girolamo, and G. Zhao, 2008: Scale effect on statistics of the macrophysical properties of trade wind cumuli over the tropical western Atlantic during RICO. J. Geophys. Res.,113, D24214, doi:10.1029/2008JD010295.

Yang, Y., and L. Di Girolamo, 2008: Impacts of 3-D radiative transfer effects on satellite cloud detection and their consequences on cloud fraction and aerosol optical depth retrievals. J. Geophys. Res., 113, D04213, doi:10.1029/2007JD009095. (Ogura Award)

Rauber, R.M., B. Stevens, H.T. Ochs, C. Knight, B.A. Albrecht, A.M. Blyth, C.W. Fairall, J.B. Jensen, S. G. Lasher-Trapp,  O. L. Mayol-Bracero,  G. Vali,  J. R. Anderson,  B. A. Baker,  A. R. Bandy,  E. Burnet,  J.-L. Brenguier,  W. A. Brewer,  P. R. A. Brown,  P. Chuang,  W. R. Cotton,  L. Di Girolamo,  B. Geerts,  H. Gerber,  S. Göke,  L. Gomes,  B. G. Heikes,  J. G. Hudson,  P. Kollias,  R. P. Lawson,  S. K. Krueger,  D. H. Lenschow,  L. Nuijens,  D. W. O’Sullivan,  R. A. Rilling,  D. C. Rogers,  A. P. Siebesma,  E. Snodgrass,  J. L. Stith,  D. C. Thornton,  S. Tucker,  C. H. Twohy, and P. Zuidema, 2007: Rain In shallow Cumulus over the Ocean – The RICO campaign. Bull. Amer. Meteor. Soc., 88, 1912–1937.

Zhao, G., and L. Di Girolamo, 2007: Statistics on the macrophysical properties of trade wind cumuli over the tropical western Atlantic. J. Geophys. Res., 112, D10204, doi: 10.1029/2006JD007371. (Ogura Award)

Genkova, I., G. Seiz, G. Zhao, P. Zuidema, and L. Di Girolamo, 2007: Trade wind cumulus cloud top height comparisons from ASTER, MISR, and MODIS. Remote Sens. Environ.,107, 211-222.

Astin, I., and L. Di Girolamo, 2006: The relationship between aand the cross-correlation of cloud fraction. Quart. J. Roy. Metero. Soc., 132, 2475-2478.

Brewer, J., and L. Di Girolamo, 2006: Limitations of fractal dimension estimation algorithms with implications for cloud studies. Atmos. Res., 82, 433-454.

Zhao, G., and L. Di Girolamo, 2006: Cloud fraction errors for trade wind cumuli from EOS-Terra instruments. Geophys. Res. Lett.,33, L20802, doi:10.1029/2006GL027088

Zhao, G., and L. Di Girolamo, 2004: A cloud fraction versus view angle technique for automatic in-scene evaluation of the MISR cloud mask. J. Appl. Meteor., 43, 860-869.

Di Girolamo, L., 2003: Generalizing the definition of the bi-directional reflectance distribution function (BRDF). Remote Sens. Environ., 88, 479-482.

Astin, I., and L. Di Girolamo, 2003: Minimizing systematic error in cloud fraction estimates from cloud radars. J. Atmos. Oceanic Tech., 20, 707-716.

Di Girolamo, L., 2002: Reciprocity principle for radiative transfer models that use periodic boundary conditions. J. Quant. Spectrosc. Radiative Trans. 73, 23-27.

Astin, I., L. Di Girolamo, and H.M. Van de Poll, 2001: Baysian confidence intervals for true fractional coverage from finite transect measurements: implications for cloud studies from space. J. Geophys. Res.106, 17303–17310.

Di Girolamo, L., 1999: A reciprocity principle applicable to reflected radiance measurements and the searchlight problem. Appl. Opt., 38, 3196-3198.

Astin, I., and L. Di Girolamo, 1999: A general formalism for the distribution of the total length of a geophysical parameter along a finite transect. IEEE Trans. Geosci. Remote Sens.,37, 508–512.

Hagen, D., D. Crisp, L. Di Girolamo, J.-F. Blavier and T. Ackerman, 1998: Balloon-based measurements of the profile of downwelling shortwave irradiance in the troposphere. Geophys. Res. Lett., 25, 1887-1890.

Di Girolamo, L., T. Varnai and R. Davies, 1998: Apparent breakdown of reciprocity in reflected solar radiances. J. Geophys. Res., 103, 8795-8803.

Di Girolamo, L., and R. Davies, 1997: Cloud fraction errors caused by finite resolution measurements. J. Geophys. Res.,102, 1739–1756.