27 Sep 2022
27 Sep 2022
Status: this preprint is currently under review for the journal AMT.

Retrieving 3D distributions of atmospheric particles using Atmospheric Tomography with 3D Radiative Transfer – Part 1: Model description and Jacobian calculation

Jesse Loveridge1, Aviad Levis2, Larry Di Girolamo1, Vadim Holodovsky3, Linda Forster4, Anthony B. Davis4, and Yoav Y. Schechner3 Jesse Loveridge et al.
  • 1Department of Atmospheric Sciences, University of Illinois, Urbana, 61801, USA
  • 2Computer and Mathematical Sciences Department, California Institute of Technology, Pasadena, 91125, USA
  • 3Viterbi Faculty of Electrical and Computer Engineering, Technion – Israel Institute of Technology, Haifa 3200003, Israel
  • 4Jet Propulsion Laboratory, California Institute of Technology, Pasadena, 91109, USA

Abstract. Our global understanding of clouds and aerosols relies on the remote sensing of their optical, microphysical, and macrophysical properties using, in part, scattered solar radiation. These retrievals assume clouds and aerosols form plane-parallel, homogeneous layers and utilize 1D radiative transfer (RT) models, limiting the detail that can be retrieved about the 3D variability of cloud and aerosol fields and inducing biases in the retrieved properties for highly heterogeneous structures such as cumulus clouds and smoke plumes. To overcome these limitations, we introduce and validate an algorithm for retrieving the 3D optical or microphysical properties of atmospheric particles using multi-angle, multi-pixel radiances and a 3D RT model. The retrieval software, which we have made publicly available, is called Atmospheric Tomography with 3D Radiative Transfer (AT3D). It uses an iterative, local optimization technique to solve a generalized least-squares problem and thereby find a best-fitting atmospheric state. The iterative retrieval uses a fast, approximate Jacobian calculation, which we have extended from Levis et al. (2020) to accommodate open as well as periodic horizontal boundary conditions (BC) and an improved treatment of non-black surfaces.

We validated the accuracy of the approximate Jacobian calculation for derivatives with respect to both the 3D volume extinction coefficient and the parameters controlling the open horizontal boundary conditions across media with a range of optical depths and single scattering properties and find that it is highly accurate for a majority of cloud and aerosol fields over oceanic surfaces. Relative root-mean-square errors in the approximate Jacobian for 3D volume extinction coefficient in media with cloud-like single scattering properties increase from 2 % to 12 % as the Maximum Optical Depths (MOD) of the medium increases from 0.2 to 100.0 over surfaces with Lambertian albedos < 0.2. Over surfaces with albedos of 0.7, these errors increase to 20 %. Errors in the approximate Jacobian for the optimization of open horizontal boundary conditions exceed 50 % unless the plane-parallel media providing the boundary conditions are very optically thin (~0.1).

We use the theory of linear inverse RT to provide insight into the physical processes that control the cloud tomography problem and identify its limitations, supported by numerical experiments. We show that the Jacobian matrix becomes increasing ill-posed as the optical size of the medium increases and the forward scattering peak of the phase function decreases. This suggests that tomographic retrievals of clouds will become increasingly difficult as clouds becoming optically thicker. Retrievals of asymptotically thick clouds will likely require other sources of information to be successful.

In Part 2 of this study, we examine how the accuracy of the retrieved 3D volume extinction coefficient varies as the optical size of the target medium increases using synthetic data. We do this to explore how the increasing error in the approximate Jacobian and increasingly ill-posed nature of the inversion in the optically thick limit affects the retrieval. We develop a method to improve retrieval accuracy in the optically thick limit. We also assess the accuracy of retrieved optical depths and surface irradiances and compare them to retrievals using 1D radiative transfer.

Jesse Loveridge et al.

Status: open (extended)

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Jesse Loveridge et al.

Model code and software

Atmospheric Tomography with 3D Radiative Transfer Loveridge, J., Levis, A., Aides, A., Forster, L., & Holodovsky, V.

Jesse Loveridge et al.


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Short summary
We describe a new method for measuring the 3D spatial variations of water within clouds using the reflected light of the sun viewed at multiple different angles by satellites. This is a great improvement over older methods which typically assume that clouds occur in a slab shape. Our study used computer modeling to show that our 3D method will work well in cumulus clouds where older slab methods do not. Our method will inform us about these clouds and their role in our climate.