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?

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 smoothing

l. 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".