the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 10 Jul 2025
A neural-network-based fast forward operator for polarized 3D radiative transfer in low-level Arctic mixed-phase clouds
Abstract. Clouds generally have a complex three-dimensional geometry. However, realistic three-dimensional radiative transfer simulations of clouds are computationally expensive, so most retrievals of cloud properties assume one-dimensional clouds, which introduces retrieval biases. In this work, a fast forward operator for polarized 3D radiative transfer in the visible wavelength range is presented. To this end, a new approximation for 3D radiative transfer, the InDEpendent column local halF-sphere ApproXimation (IDEFAX), is introduced. The basic idea behind this approximation is similar to the independent column approximation assuming plane-parallel clouds. However, every column is approximated by an independent 3D half-spherical cloud instead of a plane-parallel homogeneous cloud. The half-spherical cloud is defined by the local cloud surface orientation angles and embedded in a cloud field with a given cloud fraction. Thus, IDEFAX has only three more parameters compared to the plane-parallel approximation. To obtain a fast forward operator, artificial neural networks were trained for both, the plane-parallel and the half-spherical cloud assumptions. IDEFAX as well as the neural network forward operators were validated against polarized 3D radiative transfer simulations with MYSTIC for low-level Arctic mixed-phase clouds using a realistic cloud field simulated with the WRF model. The use of IDEFAX significantly improves the representation of 3D radiative effects in the simulated radiance fields compared to the plane-parallel independent column approximation. Due to the implementation of the forward operator with neural networks, the computation time for both approximations is comparable and about five orders of magnitude faster than real 3D radiative transfer simulations for the shown example. The introduced neural network forward operators are constructed to be used in retrievals of cloud properties with the specMACS instrument. However, the methods are also applicable to other measurements in the visible wavelength range as well as to model data.
Competing interests: At least one of the (co-)authors is a member of the editorial board of Atmospheric Measurement Techniques. The peer-review process was guided by an independent editor, and the authors also have no other competing interests to declare.
Publisher's note: Copernicus Publications remains neutral with regard to jurisdictional claims made in the text, published maps, institutional affiliations, or any other geographical representation in this paper. While Copernicus Publications makes every effort to include appropriate place names, the final responsibility lies with the authors. Views expressed in the text are those of the authors and do not necessarily reflect the views of the publisher.-
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The requested preprint has a corresponding peer-reviewed final revised paper. You are encouraged to refer to the final revised version.
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Interactive discussion
Status: closed
-
RC1: 'Referee comment on egusphere-2025-2554', Anonymous Referee #2, 26 Jul 2025
- AC1: 'Reply on RC1', Anna Weber, 15 Aug 2025
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RC2: 'Comment on egusphere-2025-2554', Anonymous Referee #1, 09 Aug 2025
General comments:
This paper does more than what is described in its title. A whole new approximation to 3D radiative transfer (RT) in clouds at solar wavelengths is introduced, going by the whimsical name of IDEFAX (InDEpendent column local halF-sphere ApproXimation). It is an alternative to the well-known ICA (Independent Column Approximation) with 3 extra parameters to accomodate broken cloud fields. However, even these approximate 3D RT models are too cumbersome to use operationally due to their large parameter spaces, hence look-up tables (LUTs), with 11 and 14 dimensions, respectively, for ICA and IDEFAX. Therefore, the authors invoke a neural net (NN) model trained to accelerate either ICA or IDEFAX.
Both the new (IDEFAX) and old (ICA) approximations are tested against synthetic clouds and observations using the NCAR Weather Research and Forecasting (WRF) model followed by detailed computational 3D RT using the LMU MYSTIC code to estimate the intensity (Stokes I) and polarized (Stokes U and Q) radiances. The present application is for low-level mixed-phase Arctic clouds and the simulated observations are for LMU's airborne specMACS sensor.
The research is new and timely, and the paper is well-written. In this reviewer's opinion, it can be published in AMT after a revision that addresses the following questions.
Specific comments:
The most innovative part of this work is the IDEFAX model described in Section 4 and validated against high-fidelity (WRF+MYSTIC) vector 3D RT simulations in Section 6. That should be emphasized rather than the (more and more common) NN implementations in the revised title.
Also, we hear about the ~5 orders-of-magnitude speedup of the NN models compared to MYSTIC. However, the more relevant speedup factors are IDEFAX or ICA vs MYSTIC and the NN implementations vs (LUT-based) IDEFAX and ICA. Please provide.
I may have missed this, but we'd like to know exactly how many WRF realizations of the Arctic clouds were used in the NN training. It feels like there is only one, which I doubt.
Lastly, does the new cloud fraction parameter not have an upper limit that is less than unity? 78.5% for hemispheres on a square cartesian grid, or 81.4% for closely packed hemispheres.
Technical corrections:
p. 1, l. 9: Remove 2nd coma.
p. 1, l. 25: either roughening and smoothing --> both roughening and smoothing
or --> either roughening or smoothingl. 30: most retrievals --> most operational retrievals
l. 75: Word "used" is unnecessary.
l. 111, and many times after this: 1000m --> 1000 m, with unbreakable space before unit
Fig. 2: Would be beneficial to show lines of equal scattering angle here and in similar figures.
l. 146: Need either comas or parentheses or both in "radiances respectively Stokes vectors".
l. 271: Remove first "the".
l. 300, 1st sentence: Best to separate clauses with a coma. Elsewhere too, e.g., often before "which" (unless it should be "that").
l. 325, and elsewhere: Referring to "real" clouds is misleading, better to use "realistic" or "WRF".
Citation: https://doi.org/10.5194/egusphere-2025-2554-RC2 - AC2: 'Reply on RC2', Anna Weber, 15 Aug 2025
Interactive discussion
Status: closed
-
RC1: 'Referee comment on egusphere-2025-2554', Anonymous Referee #2, 26 Jul 2025
The paper by Weber et al. addresses a very important research topic: the accurate and efficient simulation of atmospheric radiation fields for complex cloud scenarios (including polarisation).
Such radiative transfer models are important for the interpretation of remote sensing measurements and for the quantification of the atmospheric radiation budget. So far, usually 1D models are applied, which assume horizontally homogenous atmospheric properties. For many scenarios, they can not properly describe the atmospheric radiation fields.
The authors of this paper introduce a new method to describe the effects of 3D clouds using a simplified parameterisation for 3D clouds (half spherical clouds). Moreover, they also developed a fast neural network, which is trained on the simulations using the half spherical cloud parameterisation. Both new models are evaluated against a full 3D radiative transfer model, and a (slight) improvement with respect to the 1D cloud simulations was found.
The paper is scientifically sound and within the scope of AMT. However, the writing is sometimes confusing and has repetitions; also some quantities are not clearly defined (see also the minor points below).
After addressing my comments, the paper might be published in AMT.
Major comments
1) While I see the benefits of the choice of the half sphere concept, it stays unclear why the authors have chosen this concept. The authors should motivate their choice and also discuss which other simple parameterisations might have been used instead. They might also discuss which more sophisticated concepts might be useful in improved future applications.
2) Several important aspects are not clear:
-are the clouds in a pixel represented by one half spherical cloud (as stated in line 6) or by a field of half spherical clouds (as stated in line 63)?
-what is the size of one pixel? Does the size depend on the measurement properties and/or the grid of the RTM simulations?
3) The improvement of the new-methods over the 1D cloud approximation is rather small (Fig. 7): The correlation coefficient increases from 0.81 to 0.87 and from 0.85 to 0.86, respectively.
With such a small improvement, it remains unclear why a user should take the effort and use the new-methods instead of 1D cloud models.
The authors should explore, why the improvement is so small, and which model improvements (see my first comment) could be applied to increase the agreement to the full 3D simulations.
Minor points:
-line 24/25: what is meant with roughening or smoothening of the brightness field? Could you add a suitable reference?
-line 39: what is meant here with ‚high’ and ‚low’ resolution? Could you give numbers; maybe add a reference?
-line 55: what are the wavelength ranges for the three channels? What is the spatial resolution? Please add this information.
-line 61: the ‚forward operator’ should be introduced / defined; maybe a new subsection could be inserted starting with line 61?
-line 103: what is meant with ‚the domain visible in the radiative transfer simulations?
(also for the figure caption of Fig. 6)
-Fig. 3: the pixel size should be graphically indicated in the figure. Is a cloud in a pixel represented by one half spherical cloud or by a field of half spherical clouds?
-Fig. 3 and text: what is the procedure if one cloud covers several pixels?
-Table 1 and text: please make clear for which area the cloud fraction defined? Is this done on a pixel basis, or for a larger area?
Citation: https://doi.org/10.5194/egusphere-2025-2554-RC1 - AC1: 'Reply on RC1', Anna Weber, 15 Aug 2025
-
RC2: 'Comment on egusphere-2025-2554', Anonymous Referee #1, 09 Aug 2025
General comments:
This paper does more than what is described in its title. A whole new approximation to 3D radiative transfer (RT) in clouds at solar wavelengths is introduced, going by the whimsical name of IDEFAX (InDEpendent column local halF-sphere ApproXimation). It is an alternative to the well-known ICA (Independent Column Approximation) with 3 extra parameters to accomodate broken cloud fields. However, even these approximate 3D RT models are too cumbersome to use operationally due to their large parameter spaces, hence look-up tables (LUTs), with 11 and 14 dimensions, respectively, for ICA and IDEFAX. Therefore, the authors invoke a neural net (NN) model trained to accelerate either ICA or IDEFAX.
Both the new (IDEFAX) and old (ICA) approximations are tested against synthetic clouds and observations using the NCAR Weather Research and Forecasting (WRF) model followed by detailed computational 3D RT using the LMU MYSTIC code to estimate the intensity (Stokes I) and polarized (Stokes U and Q) radiances. The present application is for low-level mixed-phase Arctic clouds and the simulated observations are for LMU's airborne specMACS sensor.
The research is new and timely, and the paper is well-written. In this reviewer's opinion, it can be published in AMT after a revision that addresses the following questions.
Specific comments:
The most innovative part of this work is the IDEFAX model described in Section 4 and validated against high-fidelity (WRF+MYSTIC) vector 3D RT simulations in Section 6. That should be emphasized rather than the (more and more common) NN implementations in the revised title.
Also, we hear about the ~5 orders-of-magnitude speedup of the NN models compared to MYSTIC. However, the more relevant speedup factors are IDEFAX or ICA vs MYSTIC and the NN implementations vs (LUT-based) IDEFAX and ICA. Please provide.
I may have missed this, but we'd like to know exactly how many WRF realizations of the Arctic clouds were used in the NN training. It feels like there is only one, which I doubt.
Lastly, does the new cloud fraction parameter not have an upper limit that is less than unity? 78.5% for hemispheres on a square cartesian grid, or 81.4% for closely packed hemispheres.
Technical corrections:
p. 1, l. 9: Remove 2nd coma.
p. 1, l. 25: either roughening and smoothing --> both roughening and smoothing
or --> either roughening or smoothingl. 30: most retrievals --> most operational retrievals
l. 75: Word "used" is unnecessary.
l. 111, and many times after this: 1000m --> 1000 m, with unbreakable space before unit
Fig. 2: Would be beneficial to show lines of equal scattering angle here and in similar figures.
l. 146: Need either comas or parentheses or both in "radiances respectively Stokes vectors".
l. 271: Remove first "the".
l. 300, 1st sentence: Best to separate clauses with a coma. Elsewhere too, e.g., often before "which" (unless it should be "that").
l. 325, and elsewhere: Referring to "real" clouds is misleading, better to use "realistic" or "WRF".
Citation: https://doi.org/10.5194/egusphere-2025-2554-RC2 - AC2: 'Reply on RC2', Anna Weber, 15 Aug 2025
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Anna Weber
Gregor Köcher
Bernhard Mayer
The requested preprint has a corresponding peer-reviewed final revised paper. You are encouraged to refer to the final revised version.
- Preprint
(6423 KB) - Metadata XML
The paper by Weber et al. addresses a very important research topic: the accurate and efficient simulation of atmospheric radiation fields for complex cloud scenarios (including polarisation).
Such radiative transfer models are important for the interpretation of remote sensing measurements and for the quantification of the atmospheric radiation budget. So far, usually 1D models are applied, which assume horizontally homogenous atmospheric properties. For many scenarios, they can not properly describe the atmospheric radiation fields.
The authors of this paper introduce a new method to describe the effects of 3D clouds using a simplified parameterisation for 3D clouds (half spherical clouds). Moreover, they also developed a fast neural network, which is trained on the simulations using the half spherical cloud parameterisation. Both new models are evaluated against a full 3D radiative transfer model, and a (slight) improvement with respect to the 1D cloud simulations was found.
The paper is scientifically sound and within the scope of AMT. However, the writing is sometimes confusing and has repetitions; also some quantities are not clearly defined (see also the minor points below).
After addressing my comments, the paper might be published in AMT.
Major comments
1) While I see the benefits of the choice of the half sphere concept, it stays unclear why the authors have chosen this concept. The authors should motivate their choice and also discuss which other simple parameterisations might have been used instead. They might also discuss which more sophisticated concepts might be useful in improved future applications.
2) Several important aspects are not clear:
-are the clouds in a pixel represented by one half spherical cloud (as stated in line 6) or by a field of half spherical clouds (as stated in line 63)?
-what is the size of one pixel? Does the size depend on the measurement properties and/or the grid of the RTM simulations?
3) The improvement of the new-methods over the 1D cloud approximation is rather small (Fig. 7): The correlation coefficient increases from 0.81 to 0.87 and from 0.85 to 0.86, respectively.
With such a small improvement, it remains unclear why a user should take the effort and use the new-methods instead of 1D cloud models.
The authors should explore, why the improvement is so small, and which model improvements (see my first comment) could be applied to increase the agreement to the full 3D simulations.
Minor points:
-line 24/25: what is meant with roughening or smoothening of the brightness field? Could you add a suitable reference?
-line 39: what is meant here with ‚high’ and ‚low’ resolution? Could you give numbers; maybe add a reference?
-line 55: what are the wavelength ranges for the three channels? What is the spatial resolution? Please add this information.
-line 61: the ‚forward operator’ should be introduced / defined; maybe a new subsection could be inserted starting with line 61?
-line 103: what is meant with ‚the domain visible in the radiative transfer simulations?
(also for the figure caption of Fig. 6)
-Fig. 3: the pixel size should be graphically indicated in the figure. Is a cloud in a pixel represented by one half spherical cloud or by a field of half spherical clouds?
-Fig. 3 and text: what is the procedure if one cloud covers several pixels?
-Table 1 and text: please make clear for which area the cloud fraction defined? Is this done on a pixel basis, or for a larger area?