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

Loveridge, Jesse; Levis, Aviad; Girolamo, Larry Di; Holodovsky, Vadim; Forster, Linda; Davis, Anthony B.; Schechner, Yoav Y.

doi:10.5194/amt-2022-251

Cited by 6 publications

(35 citation statements)

References 115 publications

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“…We use the approximate Jacobian matrix calculation described in Part 1 to efficiently compute approximate gradients of the cost function using the approximate Jacobian 𝐊 R : Our approximate Jacobian matrix is accurate in the single-scattering limit. In this regime, it has a relative Root Mean Square Error (RMSE) of 4% with respect to finite differencing calculations (Loveridge et al, 2022b), similar to the accuracy of derivatives calculated using a forward-adjoint formulation (Doicu and Efremenko, 2019). The accuracy of the approximate Jacobian degrades as the medium becomes optically thicker, the phase function becomes more isotropic, and as the singlescatter albedo and surface albedo increase (Loveridge et al, 2022b).…”

Section: Introductionmentioning

confidence: 85%

“…In Part 1 of this study (Loveridge et al, 2022b), we described a remote sensing retrieval technique with the potential to meet these needs by providing 3D instantaneous snapshots of volumetric properties of the atmosphere at the resolution of passive imagery. Our method uses multi-angle imagery and the Spherical Harmonics Discrete Ordinates Method (SHDOM) for modelling 3D Radiative Transfer (RT) to constrain the 3D properties of atmospheric particles, such as effective particle radius and mass concentration (Levis et al, 2020;Tzabari et al, 2022), in a process called tomography (Arridge and Schotland, 2009;Martin et al, 2014).…”

Section: Introductionmentioning

confidence: 99%

“…Our retrieval algorithm for the tomography problem directly builds upon earlier work in making such retrievals tangible and computationally efficient through the use of approximate Jacobians of 3D radiative transfer that enable the use of efficient gradient-based local optimization methods (Levis et al, 2015(Levis et al, , 2017(Levis et al, , 2020. We have made our method publicly available in the software package Atmospheric Tomography with 3D Radiative Transfer (AT3D) (Loveridge et al, 2022a), which was developed from the research software used in Levis et al (2015Levis et al ( , 2017Levis et al ( , 2020 called pySHDOM.…”

Section: Introductionmentioning

confidence: 99%

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Retrieving 3D distributions of atmospheric particles using Atmospheric Tomography with 3D Radiative Transfer – Part 2: local optimization

Loveridge

Levis

Girolamo

et al. 2023

Preprint

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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. Current retrievals assume clouds and aerosols form plane-parallel, homogeneous layers and utilize 1D radiative transfer (RT) models. These assumptions limit the detail that can be retrieved about the 3D variability of cloud and aerosol fields and induce biases in the retrieved properties for highly heterogeneous structures such as cumulus clouds and smoke plumes. In Part 1 of this two-part study, we validated a tomographic method that utilizes multi-angle passive imagery to retrieve 3D distributions of species using 3D RT to overcome these issues. That validation characterized the uncertainty in the approximate Jacobian used in the tomographic retrieval over a wide range of atmospheric and surface conditions for several horizontal boundary conditions. Here in Part 2, we test the algorithm’s effectiveness on synthetic data to test whether retrieval accuracy is limited by the use of the approximate Jacobian. We retrieve 3D distributions of volume extinction coefficient (σ3D) at 40 m resolution from synthetic multi-angle, mono-spectral imagery at 35 m resolution derived from stochastically-generated ‘cumuliform’ clouds in (1 km)3 domains. The retrievals are idealized in that we neglect forward modelling and instrumental errors with the exception of radiometric noise; thus reported retrieval errors are lower bounds. σ3D is retrieved with, on average, a Relative Root Mean Square Error (RRMSE) < 20 % and bias < 0.1 % for clouds with Maximum Optical Depth (MOD) < 17, and the RRMSE of the radiances is < 0.5 %, indicating very high accuracy in shallow cumulus conditions. As the MOD of the clouds increases to 80, the RRMSE and biases in σ3D worsen to 60 % and −35 %, respectively, and the RRMSE of the radiances reaches 16 %, indicating incomplete convergence. This is expected from the increasing ill-conditioning of the inverse problem with decreasing mean-free-path predicted by RT theory and discussed in detail in Part 1. We tested retrievals that use a forward model that is better conditioned but less accurate due to more aggressive delta-M scaling. This reduces the radiance RRMSE to 9 % and the bias in σ3D to −8 % in clouds with MOD ~80, with no improvement in the RRMSE of σ3D. This illustrates a significant sensitivity of the retrieval to the numerical configuration of the RT model which, at least in our circumstances, improves the retrieval accuracy. All of these ensemble-averaged results are robust to the inclusion of radiometric noise during the retrieval. However, individual realizations can have large deviations of up to 18 % in the mean extinction in clouds with MOD ~80, which indicates large uncertainties in the retrievals in the optically thick limit. Using the better conditioned forward model tomography can also accurately infer optical depths (OD) in conditions spanning the majority of oceanic, cumulus fields (MOD < 80) as the retrieval provides OD with bias and RRMSE better than −8 % and 36 %, respectively. This is a significant improvement over retrievals using 1D RT, which have OD biases between −30 % and −23 % and RRMSE between 29 % and 80 % for the clouds used here. Prior information or other sources of information will be required to improve the RRMSE of σ3D in the optically thick limit, where the RRMSE is shown to have strong spatial structure that varies with the solar and viewing geometry.

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Section: Introductionmentioning

confidence: 85%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Retrieving 3D distributions of atmospheric particles using Atmospheric Tomography with 3D Radiative Transfer – Part 2: local optimization

Loveridge

Levis

Girolamo

et al. 2023

Preprint

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“…The software described and used in this paper is called Atmospheric Tomography with 3D Radiative Transfer (AT3D). A static archive of the software is available at Loveridge et al (2022;…”

Section: Appendix F: Calculating the Jacobian Matrix By Finite Differ...mentioning

confidence: 99%

“…In this two-part series of papers, we present and validate an extension to the retrieval framework of Levis et al (2020), which we have implemented and made publicly available in the software package Atmospheric Tomography with 3D Radiative Transfer (AT3D; Loveridge et al, 2022). This paper, which is Part 1, is devoted to the description of the retrieval methodology and the underlying theory of the retrieval, along with supporting numerical evidence.…”

Section: Introductionmentioning

confidence: 99%

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

et al. 2023

Self Cite

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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 that 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 in 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 and periodic horizontal boundary conditions (BCs) 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 a 3D volume extinction coefficient in media with cloud-like single-scattering properties increase from 2 % to 12 % as the maximum optical depths (MODs) of the medium increase 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 optically very 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 become optically thicker. Retrievals of asymptotically thick clouds will likely require other sources of information to be successful. In Loveridge et al. (2023a; hereafter Part 2), 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 the increasingly ill-posed nature of the inversion in the optically thick limit affect the retrieval. We also assess the accuracy of retrieved optical depths and compare them to retrievals using 1D radiative transfer.

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Influence of cloud retrieval errors due to three-dimensional radiative effects on calculations of broadband shortwave cloud radiative effect

Ademakinwa,

Tushar,

Zheng

et al. 2024

Atmos. Chem. Phys.

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Abstract. We investigate how cloud retrieval errors due to the three-dimensional (3D) radiative effects affect broadband shortwave (SW) cloud radiative effects (CREs) in shallow cumulus clouds. A framework based on the combination of large eddy simulations (LESs) and radiative transfer (RT) models was developed to simulate both one-dimensional (1D) and 3D radiance, as well as SW broadband fluxes. Results show that the broadband SW fluxes reflected at top of the domain, transmitted at the surface, and absorbed in the atmosphere, computed from the cloud retrievals using 1D RT (F1D∗), can provide reasonable broadband radiative energy estimates in comparison with those derived from the true cloud fields using 1D RT (F1D). The difference between these 1D-RT-simulated fluxes (F1D∗, F1D) and the benchmark 3D RT simulations computed from the true cloud field (F3D) depends primarily on the horizontal transport of photons in 3D RT, whose characteristics vary with the sun's geometry. When the solar zenith angle (SZA) is 5°, the domain-averaged F1D∗ values are in excellent agreement with the F3D, all within 7 % relative CRE bias. When the SZA is 60°, the CRE differences between calculations from F1D∗ and F3D are determined by how the cloud side-brightening and darkening effects offset each other in the radiance, retrieval, and broadband fluxes. This study suggests that although the cloud property retrievals based on the 1D RT theory may be biased due to the 3D radiative effects, they still provide CRE estimates that are comparable to or better than CREs calculated from the true cloud properties using 1D RT.

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

Cited by 6 publications

References 115 publications

Retrieving 3D distributions of atmospheric particles using Atmospheric Tomography with 3D Radiative Transfer – Part 2: local optimization

Retrieving 3D distributions of atmospheric particles using Atmospheric Tomography with 3D Radiative Transfer – Part 2: local optimization

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

Influence of cloud retrieval errors due to three-dimensional radiative effects on calculations of broadband shortwave cloud radiative effect

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