This review was posted by the editor on behalf of one of the anonymous reviewers.

Review of “Retrieving 3D distributions of atmospheric particles using Atmospheric Tomography with 3D Radiative Transfer – Part 1: Model description and Jacobian calculation” by Jesse Loveridge, Aviad Levis, Larry Di Girolamo, Vadim Holodovsky, Linda Forster, Anthony B. Davis, Yoav Y. Schechner.

This is a well written and informative paper that evaluates the capabilities and limitations of passive multi-angle observations for the 3D reconstruction of extinction fields.  The authors make good use of the formalism introduced by Martin et al. (2014), but fail to differentiate their own approach from that presented therein.  Martin et al. (2014) uses the adjoint formalism to calculate the gradient of a cost function and never expresses the Jacobian in this manner.  The author’s use of the adjoint formulation to construct the Jacobian is therefore different to that of Martin and is interesting in its own right and that difference should perhaps be highlighted. 

It would probably benefit the paper if before Eq. (63) the authors note that it is a calculation of the Jacobian and include the dF/da term in the expression of the equation to remind the reader that is what it is and that it comes from Eq.(42) (we’re 20 equations further in so a reminder is helpful).  Also, given the later discussion of how areas that have strong illumination and “observation” are more sensitive/well constrained it would be worth noting after Eq.(43) how the “volume source vector of the modified RTE for the derivatives of the radiance field” depends strongly on the strength of the direct and diffuse radiance. This can then be emphasized after Eq.(63) where is it is apparent that it is the combination of the strength of the adjoint sources and the illumination (via the volume source) that determine which areas of the cloud will contribute significantly to the Jacobian.  The identification of this fact within the formalism of the adjoint calculation of the Jacobian is helpful in explaining the results that are described later in terms of delta-M transmission from solar and viewing directions.

The authors clearly demonstrate the issues associated with tomography for optically very thick clouds and plane parallel/stratiform clouds.  They also note cloud types for which the condition and stability of the tomographic reconstruction should be good are extremely common.  It would therefore be helpful if a little more care was given to discussing the performance of the Jacobian approximation for opacities associated with those cloud types, particularly for physically thicker cumulus clouds where one might expect the approximation to cause problems. 

While it is asserted that tomography should work for optically thin stratiform clouds such as cirrus clouds given the Jacobian’s condition number, Figure 17 showing the 16 stream stratiform results gives cause to doubt that is the case. Since this study has not actually done tomographic retrievals of cirrus clouds assertions regarding capabilities to apply tomographic retrievals to such clouds should be given appropriate caveats.

Minor Editorial Comments

The delta-M method and the Nakajima and Tanaka correction are mentioned in different places.  It would probably be best to describe what is actually done in SHDOM when that code is described at the beginning and note that whenever you say delta-M you are referring to the treatment in the SHDOM code.

Line 55: “at the full resolution of the sensors.” would be more realistically “that makes complete use of the full resolution of the sensors.”

Line 60: “efficiently” should probably be “effectively”

Line 79: “there is no way to identify” is an exaggeration.  Aerosol above clouds, cirrus above liquid cloud, multi-layered clouds are all things that have been done with IPA and passive remote sensing.

Line 154: Could not find previous definition of LES

Line 285: Should note that logarithmic and other transformations of data are often used to help stabilize fitting.

Line 331: “controlled by the singular value spectrum of K.”  Should caveat by noting that it is particularly the case for diagonal, or block diagonal error covariance matrices.  Very strongly correlated measurements can significantly modify the spectrum of the Fisher information matrix compared with that of the Jacobian matrix.

Line 417: do not bold face 1.

Line 430: Is this notation correct? The first term should probably not have a second (r,omega) parenthesis.

Line 481:  TOP, BOT and SIDE

Line 816: Effective variance is probably not 10. Give correct value. 0.1?

Line 825: Why is theta_sun here in parenthesis?  You have given the value of its cosine.  Delete or put (theta_sun=xx°).

Line 882: Reference to Eq. (60) is given.  It’s wrong.  I think it’s Eq. (63), but please fix.

Line 958: “extend” should be “extent”