General Comments:

The overall concept of this study is commendable and very useful, but there are problems with this study that need to be addressed and resolved before this study can be published.  In spite of these problems, the results still appear valid.  For example, the authors attempt to treat cirrus cloud properties (effective radius r_eff or diameter D_eff, IWC and N_ice) using Euclidean geometry (i.e., as spheres), and as with earlier attempts like this, at least one of these variables ends up serving as the “dust bin” (i.e., becomes corrupted, N_ice in this case) due to this flawed approach.  But since it appears that D_eff and IWC are calculated accurately, and the radiation transfer (RT) calculations in libRadtran do not use N_ice, the results of this study still appear valid.

Another major drawback of this study is that the cirrus cloud geometrical thickness Δz is fixed (i.e., it never varies), having a value of 0.20 km.  It appears that Δz is fixed to enable mathematical closure; otherwise Figure 1 is not possible.  More importantly, Δz = 0.2 km is fine for contrails, but not for natural cirrus clouds, which are typically ~ 1.2 km on average.  Since this study claims to be representative of natural cirrus clouds, the authors need a compelling argument to justify using a fixed Δz of 0.2 km for such clouds.

The paper is well written and organized, with good quality of figures, and the results should be useful to the atmospheric radiation community.  I therefore recommend publication after major revisions.  Detailed comments addressing the paper’s drawbacks now follow.

Major Comments:

1. Equation 1: In some conventions, F^↓ is taken to be positive while F^↑ is taken to be negative, in which case ΔF = F_c + F_cf.  To avoid any confusion, please mention that all flux quantities are taken to be positive.

1. Lines 127-128: Cirrus clouds are typically ~ 1 km in geometrical thickness; why was a thickness of 0.2 km selected?  It is not clear how this unrealistic value impacts the analysis under “Results”; please explain why the findings of this study are realistic in relation to this choice for geometrical thickness.

1. Equation 6: Petty and Huang (2011) was consulted for the calculation of ν_eff, where it was discovered that ν_eff has no general analytical solution, making Eq. 6 here unpractical.  If there is an analytical solution, it should be given here.  For the special case of an exponential particle size distribution or PSD, μ = 0 and ν_eff = 1/3, but libRadtran has set μ to a value of 1. 

1. Lines 155-157 and Eq. 7: Please mention that this D_eff definition is the same definition derived in Mitchell (2002, JAS), provided that ice volume V is evaluated at the bulk density of ice (0.917 g/cm³), as shown by the following derivation that begins with Eq. 7:

D_eff = D_V³/D_A² = (6V/π)/(4A/π) = (3/2) (V/A)                                                              (1)

where V is the ice crystal volume at bulk density and A is the mean projected area of the ice crystal, as defined on lines 159-160.  But on line 164, the paper states: “where V and A are the average volume and projected area of the crystal population, respectively”.  It seems like a leap of faith to apply this D_eff derived for an ice crystal to a PSD, but in Mitchell (2002) it is shown that this can be done, so please justify this leap of faith and mention the implicit ice density.

1. Equation 11: This could be done more elegantly and accurately by simply selecting appropriate power-law mass-dimension expressions for aggregates, droxtals, hex-plates.  From Eq. 29 in Mitchell et al. (2006),

N_ice = Γ(μ+1) IWC Λ^β / (α Γ(β+μ+1)) ,                                                                           (2)

where Γ denotes the gamma function, μ and Λ are from Eq. 5 of this paper, and α and β are the prefactor and exponent of the ice particle mass-dimension power law relationship (i.e., m = αD^β).  The r³ dependence in Eq. 11 is an artifact of the Euclidean geometrical framework imposed and leads to false interpretations later in the paper, like the top of page 12.  For example, from Petty and Huang (2011), Λ = 3/r_e for exponential PSDs, giving

N_ice = 3^β IWC/(α Γ(β+1) r_e^β ).                                                                                       (3)

Thus, N_ice has a β dependence on ice particle size (not a cubic dependence as shown in Eq. 11), where β tends to be ~ 2 for aggregates, ~ 2.4 for hex-plates and 3 for droxtals.

1. Lines 199-200: The cloud absorption optical depth is also very important in determining RT in the TIR; please mention this.

1. Equation 13: Is this equation used in libRadtran?  If not, what is the point in mentioning it?  Cloud property input to libRadtran consists of IWC and r_e, suggesting the zero-scattering approximation might be used for TIR hemispheric fluxes:

ε = 1 - exp(-5 τ_abs/3)                                                                                                    (4)

where ε is cloud emissivity and τ_abs is the cloud absorption optical depth.  Please indicate whether ε is calculated in libRadtran, and how it is calculated if applicable.

1. Lines 209 – 213 and Eq. 14: (14) appears flawed since, in principle, there should be an emissivity term (ε) for both the surface and the ice cloud.  But since typically ε ≈ 1 at the surface, does ε in (14) correspond only to the ice cloud?  If so, it would be incorrect to multiply it by T_sfc⁴ (which Eq. 14 does).  Later, ΔF_tir is shown for IWC, r_e, and ice crystal shape, so it appears that ε refers to the ice cloud and therefore ε < 1, but how then does ε depend on IWC, r_e and ice particle shape?  The dependence of ΔF_tir on cloud properties is a complete black-box mystery and this needs to be explained.

1. Figure 1: Fixing the cloud thickness appears to be required to get closure for the system of equations producing these four figures.  If so, this analysis may not be representative of natural cirrus clouds in some respects since the geometric cloud thickness Δz is fixed at 0.2 km corresponding to extremely thin cirrus or contrails.  For example, obtaining a typical range of cirrus cloud optical depth requires anomalously high IWC to compensate for the small Δz, based on the relationship: τ_vis = 3 IWC Δz/(ρ_i D_eff).  At a minimum, the authors should explain how they obtain mathematical closure to produce these plots.

1. Figure 9a: N_ice here has units of cm^-3 with some values exceeding 100 cm^-3.  In natural cirrus clouds, N_ice_ice rarely exceeds ~ 2 cm^-3.  This appears to be a consequence of the r^-3 dependence of N_ice in Eq. 11.  As shown in Eq. 3 above, the dependence of N_ice on r_e is r_e^-β where β typically lies between 1.7 and 3.

1. Lines 258-259: As noted in (1) above, N_ice is related to r_eff by the power of -β (not -3 as stated here).

1. Lines 295-296: How do ice particle shapes affect ΔF_tir, given the above comments in 8?

1. Lines 307-314: The aspect ratio strongly impacts the scattering phase function and therefore the asymmetry parameter g (Fu, 2007, JAS; Van Diedenhoven et al., 2012, AMT; 2013, ACP).  Please consult these studies and revise this discussion accordingly.

1. Figure 3 caption: What do the numbers refer to in Fig. 3 a-c?

1. Lines 327-329: Macke and Grosklaus (1998) addressed lidar (SW radiation).  While their finding about PSDs may be true for SW radiation, Mitchell (2002, JAS) and Mitchell et al. (2011, ACP) found that PSD shape matters considerably for LW radiation.

1. Line 358: This refers to Fig. 5a, correct?  Here the upper boundaries are becoming more negative with increasing θ.

1. Figure 5 caption: What do the numbers next to the boxes indicate?  They appear to correspond to median, 25th and 75th percentile values, but this should be called out.

1. Line 378: As far as I can tell, Fig. 2 shows that r_eff is the primary factor controlling ΔF, not IWC.

1. Lines 506-508: This could have been described more clearly under “Methods” unless I missed something.

Technical Comments:

1. Figure 2 caption: Typo where r_eff = 5 μm; should be 45 μm?

1. Line 349: ΔF_tir => ΔF_net?

General remarks:

The manuscript describes an impressive sensitivity study (very nicely summarized in Figure 2, indeed!)) on the importance of the governing physical parameters of cirrus clouds and contrails on their radiative effects in the climate system. Numerous studies on the influence of various parameters already exist, but not on this scale presented here. The authors also largely correctly refer to the previous literature, but I would have liked to see a somewhat more quantitative presentation here. A table roughly summarizing the parameter variations and effects on the radiation effect of previous work could be helpful.

I understand that even 94,000 radiative transfer simulations cannot cover all cases of real-world clouds and illumination geometries. The authors should therefore make somewhat more prominent (not just at the end of the manuscript) which assumptions in their calculations constrain the phase space. This seems particularly important to me because, while the authors commendably make their data available for further radiative effect studies, there is then a danger that it will be used without further questioning. For example, ice clouds generally have a distinctive vertical structure of crystal sizes and shapes, which affects both solar reflectivity and thermal emission. Horizontal crystal orientation - as often observed - also has an effect, as does 3D radiative transfer for optically thicker ice clouds. Similarly, a crystal size distribution is always also a crystal shape distribution, so distinguishing clouds consisting of only one crystal shape is somewhat unrealistic. It is not for nothing that Baum et al. (2005) combined size and shape distributions to obtain more realistic optical properties. I realize that one cannot account for all of this in a large sensitivity study, but limitations should be clearly pointed out.

Some results are quite obvious, e.g. that the solar cooling effect is determined by the albedo differences of cloud and ground, and the warming effect by the temperature differences of cloud and ground. It is also not necessary to point out several times that the solar parameters do not affect the terrestrial radiation effects and vice versa.

The study of a water cloud underlying the ice cloud seems somewhat contrived to me, see the specific references below.

Would it somehow be possible to reduce the number of figures, e.g. take only those whose results are referred to in the summary at the end? See also my comments below.

Specific remarks:

line 54-56: I agree that liquid water clouds have simpler microphysics. However, this simplification is perhaps surpassed by the problem of 3D radiative transfer in such clouds. Therefore, I would not say that radiative transfer in cirrus clouds is more complex.

68-69: Why distinguish between sensitivity to size and to size distribution?

104-105: ...but then you need to show/cite that 2d or 3d variability is not a driving parameter. And the present work is not even 1d (vertically resolved), but 0d (plane-parallel homogeneous).

135-136: according to the title, the work is about cirrus and contrails. So, do the 3 shapes suffice for cirrus as well? Does the aspect ratio of the hexagonal particles varies with size?

Table 3: I understand that some hard choices have to be made if one is to make sense of the parameter space of the physical properties of cirrus clouds. However, it seems to me that the range of only three cloud temperatures is very limited compared to the parameters that make up the optical thickness (IWC, r_eff). The cloud greenhouse effect is thus much more discretized than the albedo effect.  

167: which r_min and r_max where chosen for the gamma size distribution?

173: isn't the effect of an underlying cloud not somehow accounted for already by varying surface albedo and surface temperature?

190-192 and eq. (11): This rearranging only work if r^3_vol is not a function of r. But I'd think that this parameter is very much a function of r.

220-221: what do you mean with "diagnosed by libradtran"? For a given size and shape, the extinction coefficient should be readily available, given that the extinction efficiency = 2 for large particles.

228: The term "observed" may be misleading as this is about modelling, not observations.

Fig. 1: Since only theoretical relations between the dependent quantities N, IWC, r_eff, and tau are shown here, which are rather clear, one could omit this discussion and refer to a textbook on radiative transfer.

307: "To some extend" -> "For idealized hexagonal columns and plates"

327-328: Macke and Großklaus is about rain drops :), you probably meant:

Macke A, Francis P-N, Mc Farquhar G-M, Kinne S (1998) The role of ice particle shapes and size distributions in the single scattering properties of cirrus clouds. Journal of Atmospheric Sciences 55 (17), 2874-2883.

360-361. wrt the forward peak: The forward peak (0 degree scattering angle) is never directed upward. Are you refering to the forward scattering range?

Figs. 5b and 6b can be omitted.

378: "IWC is the primary factor...": Not according to Fig 2 and your previous explanation that solar and terrestrial effects of IWC cancel out each other. Do I misunderstand something here?

389: "...photon path length ... has an almost negligible impact on the cloud RE in the solar and TIR.": photon path lengths in solar and thermal IR are not the same. 

Did you specifically calculate the mean free path length at the thermal IR? Which wavelength? Water vapor or CO2 absorption might also affect the path length.

418 - 419: "indicates an increase in the sensitivity of ΔFsol, particularly with respect to reff": Wasn't that already obvious from Fig. 2?

3.4.2: The title is "Thermal IR", but the text below is about F_net

3.6: Again, I would think that the radiative boundary conditions that arise from an underlying cloud are covered by the variations in surface albedo and surface temperature, already.

501-502: Of course, F_sol and Delta F_sol = 0 during night. But given this obvious day-night differences in the contributions of F_sol to F_net, wouldn't it not make more sense to study F_net for 24h means?

509: "Delta F_sol is dominated by Delta F_tir": Typo? F_sol -> F_net?

511-512: alpha_srf = 1 is rather unrealistic on this planet. So, I don't think that solar warming ever occurs.

515: "the resulting net RE is a warming.": -> small.

The competition alone does not explain a warming or cooling.

527: "Simultaneously, the TIR heating remains almost constant...": yes, because the cloud top temperature is fixed. The latter could also be subject to variations. In fact, brighter clouds often have larger vertical extend and are thus colder. I suggest to drop this "underlying cloud" study.

528: infinite -> horizontally infinite

This study presents a dataset of radiative transfer simulations with the goal to investigate the sensitivity of the radiative effect of cirrus and contrails. The sensitivity study comprises eight selected parameters: ice crystal effective radius, ice water content, solar zenith angle, surface albedo, liquid water cloud optical thickness of an underlying cloud, three ice crystal shapes, cirrus temperature, and surface temperature. The dataset which is submitted together with the manuscript consists of three netCDF files, one for each ice crystal shape. Results for plane-parallel radiative transfer simulations are provided as upward and downward irradiance for cloudy and clearsky scenes as well as the cloud radiative effect (CRE), integrated over the solar and thermal spectrum. While such a sensitivity study has the potential to provide interesting insights into the driving parameters on CRE of cirrus and the associated data set is useful as a reference, there are a number of major issues which have to be addressed before publication:

(A) The manuscript is missing a discussion of the results and comparison with previous studies which are mentioned in the introduction (Fu and Liou (1993), Yang et al. 2010, Zhang et al. 1999, Mitchell et al. 2011, and Schumann 2012). Are there new insights gained from the selected parameter space?

(B) There are several major issues with the setup of the RT simulations which have to be addressed, especially since the data set is intended for public use:

1. Top of the atmosphere (TOA) is assumed here at 15 km (as stated e.g. in line 90 and Table 1) instead of the commonly used 120 km (Emde et al. 2016). All atmospheric profiles provided in libRadtran and used in this study are defined up to 120 km. The upward and downward irradiances computed in this study are therefore missing important contributions of molecular scattering and absorption. To allow comparison with other studies and make the data set useful for the community, irradiances should be computed at the standard TOA level.
2. Ice cloud optical thickness values are provided for a reference wavelength of 640 nm. The standard reference wavelength, however is 550 nm. Similar as above, to allow comparison with other studies and make the data set useful for the community please use 550 nm as a reference wavelength.
3. The study claims to use the “more recent ice crystal parameterizations” (line 61) but only droxtals were used from Yang et al. 2013, whereas Yang et al. 2000 was used for plates and rough aggregates. Yang et al. 2013 provides optical properties for plates and rough aggregate as well. Why not use the latest optical properties in a consistent way?
4. Furthermore, no explanation or discussion is provided why these specific habits were chosen. Why are e.g. columns or bullet rosettes not included? Please provide motivation to select “droxtal”, “rough-aggregates” and “plates” and cite relevant literature that supports this choice as representative for cirrus, contrails, and contrail cirrus (e.g. Platnick et al. 2016, Forster et al. 2022, Järvinen et al. 2018).
5. It is not explained why libRadtran’s Fortran implementation of DISORT is used for the radiative transfer simulations instead of the faster and more robust C-version (Emde et al. 2016), when the goal is to use the “latest RT models” (line 62).
6. The results including the water cloud below the cirrus are potentially biased: “wc_modify tau set 20” in the input file will set the water cloud optical thickness to 20 at each wavelength which causes the liquid water content to vary across the spectrum. To achieve constant LWC, it has to be be scaled directly to an optical thickness of 20 at 550 nm wavelength.
7. The water cloud layer is fixed with cloud base at 3 km. This implies that the cloud layer is located at a different temperature for each of the 3 atmospheric profiles. As stated in the manuscript (line 174) this places the cloud even at temperatures below freezing for the subarctic winter profile. To be consistent, should the water cloud not rather be fixed at a certain temperature, the same way the altitude of the ice cloud was defined?
8. Information about the setup of the radiative transfer simulations is contradicting in several places in the manuscript, or missing:
   • It is not explained how the surface temperature is set in the RT simulations. The stated temperatures of 273 K for afglsw and 313 K for afglus do not correspond to the surface level temperature of these atmospheric profiles as provided by Anderson et al. 1986.
   • Molecular absorption is stated to be Fu and Liou (1992, 1993) in Table 1, then the text states REPTRAN parameterization in “moderate” resolution (line 110), and the sample input file provided as a supplement uses REPTRAN in “coarse” resolution. Please double-check and explain the choice.
   • In Table 1, and line 109 it is stated that the spectral solar irradiance according to Kurucz 1992 is used. The data provided with libRadtran has a spectral resolution of 1 nm, but the sample input file refers to a version with 5 nm resolution. How was that obtained and why did the authors choose a coarser resolution?

(C) A clear statement of the intended use of the dataset together with assumptions made for the radiative transfer simulations and their impact on the accuracy of the results is missing. The abstract (line 21/22) states: “The data set […] can be used to compute the radiative effect of cirrus clouds, contrails, and contrail cirrus instead of full radiative transfer calculations.” This is a very general statement and it is not clear what potential use cases could be. Although it is very useful to publish the results together with the paper, potential users of the data set would need more guidance: Please provide more details how the data set should be used, limitations, accuracy, possible questions that could be answered.

1. Important information is missing about assumptions used for the radiative transfer simulations which have important implications for potential use cases: Plane-parallel RT instead of 3D RT, assuming TOA at 15 km, assuming randomly oriented ice crystals, parameterization of ice crystal optical properties which assumes a coupling of crystal size and aspect ratio, constant geometric thickness of the cirrus of 0.2 km, etc.
   
   These assumptions have to be stated more prominently in the manuscript to ensure correct usage of the published data.
2. Especially for contrails and contrail-cirrus, but also for cirrus radiative 3D effects have been shown to be non-negligible (e.g. Gounou and Hogan 2007, Kalesse 2009, Forster et al. 2011). If the presented results should be applicable to contrails the bias due to neglecting these 3D effects has to be quantified.

More detailed comments:

1. Abstract line 18: Why is TIR influenced more by ice crystal shape than effective radius? In line 298 it is stated that crystal size has a stronger impact than shape. Please explain in the text.
2. Abstract line 19: “Net RE is controlled by the surface albedo, the solar zenith angle, and the surface albedo in decreasing importance”. Surface albedo is mentioned twice, please correct.
3. Line 69-72: “A comprehensive study of cirrus radiative effects was conducted by Schumann (2012), who aimed to derive an approximate model to estimate the cloud RE. While those studies are valuable, none of them presents a comprehensive sensitivity study across all relevant cloud and environmental input parameters. Therefore, we present a study that separates the effect of eight selected parameters on the cirrus RE.”
   
   This is contradictory: none of the previous studies is “comprehensive”, but the present study focuses on “eight selected parameters”. Are the eight selected parameters of the present study enough to make it “comprehensive”? Should not the driving question be: How many and which parameters are necessary to investigate the main question / support the main statement?
4. Line 85: Please add the equation for DeltaF_net before defining DeltaF_sol and DeltaF_tir
5. Line 95: “The surface albedo is kept constant in this study”. Which value is chosen for the solar spectrum?
6. Line 102: “libRadtran was run as one-dimensional (1D) RT solver…” -> better: “The 1D RT solver DISORT, which is part of libRadtran, assuming horizontally uniform clouds”.
7. Line 119: Why would tropical and desert atmospheric profiles be interchangeable here? The different water vapor profiles affect the thermal RE as mentioned in the subsequent sentence.
8. Line 121: Please double-check the surface temperatures for the subarctic winter and tropical profiles. Surface temperatures for subarctic winter is 257.2 K and 299.7 K for tropical. How is the surface temperature “set” to -40, 0, 40 degC?
9. Line 143: “Our simulations range from 5 to 45 μm for all three shapes and, therefore, focus on young contrails and cirrus.” If so, aged contrails and contrail cirrus should not be mentioned in the abstract and conclusion.
10. Table 3: Range does not add information here, just provide actual values. Add “total number” as last column label.
11. Line 185: “because, as 3D effects are neglected” -> ”as radiative 3D effects are neglected”. This is the first time 3D effects are mentioned, but this information should appear more prominently. Please cite relevant literature and add more discussion on possible biases introduced by the plane-parallel assumption and neglecting 3D RT in this study.
12. Results Fig. 1: it should be noted that these results do not rely on RT simulations but show basic dependencies between microphysical and optical parameters.
13. Line 225: “Going beyond these dependencies…” The sensitivities discussed in the preceding paragraph do not use RT simulations. Now switch to RT results? This should be separated more clearly in the text.
14. Fig. 1c, d: please complete legend information with “r_eff” (1c) and “IWC” (1d)
15. Line 245: why are the parameters for the reference cloud chosen from extreme values of the parameter space? Wouldn’t it be more intuitive to select mean/median values?
16. Please provide a reference from literature which states a representative cirrus optical thickness of 0.18 at 640 nm?
17. Which crystal shape is assumed for the reference cloud?
18. In Fig. 2 it looks like reff=5 um is used for the reference cloud, not 45 um.
19. Figure 2:
    • The scale and grid lines of the y-axis should be comparable between the 3 subplots.
    • Caption: The parameter for the reference case provided here do not match the description in the text.
    • Selecting mean/median values of the parameter space would place the star closer to the mean RE, similar to the IWC case.
    • Is a box plot representative for the 3 distinct ice crystal shape values?
20. Line 249: “For the all Sun geometries…” Please double-check sentence.
21. Line 274: Which values for the surface albedo were selected to investigate the sensitivity of the RE on T_srf, T_ic and tau_wc? The results should be different for alpha=0, and 1.
22. 3.1 Sensitivity on ice crystal shape: When comparing the effect of ice crystal effective radius vs. crystal shape on the cirrus RE, it is important to mention that size and aspect ratio are coupled in the optical property parameterizations by Yang et al. 2000 and 2013. Please add this to the discussion.
23. Figure C1: why not show the phase function for the ice crystal shapes and effective radii which are actually used?

Literature:

• Kalesse, H., 2009. Influence of ice crystal habit and cirrus spatial inhomogeneities on the retrieval of cirrus optical thickness and effective radius (Doctoral dissertation, Mainz, Univ., Diss., 2010).
• Gounou, A. and Hogan, R.J., 2007. A sensitivity study of the effect of horizontal photon transport on the radiative forcing of contrails. Journal of the atmospheric sciences, 64(5), pp.1706-1716.
• Forster, L., Emde, C., Unterstrasser, S., and Mayer, B. 2012. Effects of three-dimensional photon transport on the radiative forcing of realistic contrails. Journal of the atmospheric sciences, 69(7), pp.2243-2255.
• Platnick, S., Meyer, K.G., King, M.D., Wind, G., Amarasinghe, N., Marchant, B., Arnold, G.T., Zhang, Z., Hubanks, P.A., Holz, R.E. and Yang, P., 2016. The MODIS cloud optical and microphysical products: Collection 6 updates and examples from Terra and Aqua. IEEE Transactions on Geoscience and Remote Sensing, 55(1), pp.502-525.
• Forster, L. and Mayer, B., 2022. Ice crystal characterization in cirrus clouds III: retrieval of ice crystal shape and roughness from observations of halo displays. Atmospheric Chemistry and Physics, 22(23), pp.15179-15205.
• Järvinen, E., Jourdan, O., Neubauer, D., Yao, B., Liu, C., Andreae, M.O., Lohmann, U., Wendisch, M., McFarquhar, G.M., Leisner, T. and Schnaiter, M., 2018. Additional global climate cooling by clouds due to ice crystal complexity. Atmospheric Chemistry and Physics, 18(21), pp.15767-15781.