|Summary and Main Comments:|
This paper reports on measurements of the growth of single faceted ice crystals grown on a capillary in a new cryogenic chamber. The chamber allows for crystals to undergo growth and sublimation cycles with imaging that has enough detail so that approximate rates of growth can be derived from the data. The data show clear indications of the formation of entrapped air pockets in crystal corners and edges among other interesting features. These pockets appear after periods of sublimation. While the appearance of these pockets has been noted in prior measurements and observations, the authors of this article provide an explanation for the existence with of these pockets with a theory of lateral facet growth by protrusions driven by the flux of molecules across an adjoining facet. The authors show that a physically plausible model of protrusion growth driven by this adjoining flux of mobile surface molecules can explain the rate of lateral facet spreading derived from the data. The authors then make use of theories of lateral growth, and protrusion growth in particular, to provide qualitative explanations (or perhaps hypotheses) for the development of various secondary habits of ice crystals.
This article is the first attempt (that I am aware of) to quantify and explain the lateral growth of crystal facets. At present, there are no quantitative or qualitative models of lateral growth used in the atmospheric sciences. Ice crystal growth models currently used in the atmospheric sciences fit into only two categories: (1) Models that are designed for growth that is normal to the facet. In other words, steps formed by nucleation or by outcrops of dislocations propagate parallel to the facet, causing the facet to grow outward, normally (what the authors refer to as normal growth). These models are used to study the development of single crystalline habits, and they are sometimes used to understand laboratory growth data. (2) Models that treat the growth of ice as if the surface doesn’t matter. These models use the capacitance framework, which is not strictly appropriate for faceted growth. These models have been used to interpret laboratory growth data and are used ubiquitously in atmospheric cloud models. Hence, and as the authors themselves point out, there has been no focus in the atmospheric science community on facet growth that is lateral, however it is clear that this sort of growth must be important. For instance, facets must develop over time anytime an ice crystal nucleates either from a frozen droplet or from a solid aerosol nucleus. This process must include the lateral spreading of facets, a process for which we have very little data and no quantitative models. One can easily imagine where lateral spreading may be important: There are numerous laboratory measurements of the growth rates of ice crystals that begin from a nucleated ice particle. These crystals all probably undergo a period of facet development where lateral spreading, and perhaps protrusions, are likely important. However, lateral growth is never considered when laboratory growth data are interpreted (because, of course, no model of this sort of growth exists at the present time). One can also imagine that lateral growth is important in the modeling of atmospheric clouds: The overall mass growth rates of crystals that are growing laterally are likely quite different than normal growth of crystal facets, and probably very different than the capacitance model growth rates. Substantial differences in the crystal growth rates would naturally lead to impacts on model simulated cloud properties including numbers of nucleated ice crystals, and the mass and thermal energy budget of a cloud layer (through latent heating and crystal sedimentation out of the cloud layer). At the present time, the community lacks measurements, ideas, and theories (even simple ones) to advance the way we think about growing ice crystals and the impacts they may have on clouds. This paper is a nice first step in examining lateral growth and its potential impacts on a variety of complex crystal forms, and I think the paper will stimulate the thinking of those interested in advancing our methods of modeling ice in the laboratory and the atmosphere. I am therefore eager to see this paper published in some form, and I would suggest minor revisions: The paper is quite clearly written and is well argued within the constraints of the available data. While the paper is shorter and clearer than the original discussion paper (I perused this paper as well during my review), and the science appears quite sound, I do have a number of suggestions and questions (see below) related to the presentation of the material, and this is the reason for my recommendation of minor revisions. The above summary of the paper is, of course, my current understanding of the material and I hope that I have not misunderstood the authors’ ideas and intent.
(1) General comment on the introduction/background: While the introduction is quite clear and well written, I do think it may be hard for those who are not quite familiar with the theories of ice crystal growth to place the results here into an atmospheric context. Ice crystal growth theorists and laboratory scientists who measure the growth of crystals will probably be able to grasp the concepts presented in the present paper, but those outside of these areas may have more difficulty even though the material is of general interest (in my view). Perhaps adding a few sentences that place these results into a broader atmospheric context would be worthwhile. I do not think that adding this is critical to the paper, it is a suggestion that may help interested readers see the possible implications of these results.
(2) Line 18, pg2: I may have missed it, but I do not think that I saw the definition of the initialism “BCF” given earlier in the text.
(3) Line 33, pg2: “all thick surface regions leading growth” is a little awkward. I would suggest rewording.
(4) Line 34, pg2: “tend to have a rough edge” perhaps add “indicated by rounding”, as you later point out. I think here you are trying to point out that vapor grown crystals are faceted, meaning that the surfaces are not “rough” but that individual steps can be rough as indicated by their rounded in appearance.
(5) Line 17, pg 3: “Instead, atmospheric ice models usually…” This statement is definitely true for models like Wood et al. (2001), but ice models used for cloud simulations usually do not include any information about the crystal surface. The usual assumption is that the surface is at equilibrium and that no steps exist at all, since they use the capacitance model.
(6) Line 18, pg 3: Should “density” be inserted in “vapor near the step source”?
(7) Caption of Figure 1: The word “sizes” always seems ambiguous to me. Perhaps “diameters”?
(8) Figures in general: A number of the figures show crystals grown in various chambers. I think it might be good to provide some more information on the environmental conditions: Temperature is sometimes given, but what about pressure and supersaturation?
(9) Line 9, pg4: I would insert “diameter” in the parenthetical “(~20 micrometers)” since Gonda’s measurements were of the width of the frozen droplet.
(10) Line 11, pg4: “…show these edges as rough..” Is this indicated by the fact that they are rounded? It might be worth it to point that out.
(11) Line 13, pg4: I have real difficulties seeing the pyramidal facets on Fig 1a,b since the image is a little fuzzy. Perhaps an arrow could be used to indicate the location?
(12) Line 19, pg4: “nucleation of new growth layers”. Is it possible that the facets are growing by dislocations instead of layer nucleation? Gonda and Yamazaki’s (1984) paper shows the growth velocities of the a and c axes of their crystals, and the growth rates are quite close to each other (their Fig. 3). Given that the supersaturation in that case was between 1 and 2% it would seem that the growth would have to have been dominated by dislocations. Otherwise the axis growth rates would have been different I would think (since the critical supersaturations for the basal and prism faces are around 0.5% and 2% respectively at Gonda’s growth temperature of -15C).
(13) Figure 2: I very much like this figure. However, later on in the paper you discuss the vapor gradient near the protrusion. If it wouldn’t make the figure too messy, it might be good to add in isolines of vapor density. I was able to follow your description of the structure of the contours, but an image would certainly help. Especially for those who are not familiar with the way vapor gradients may change near the surface of a crystal.
(14) Line 3-4, pg 6: I personally find it hard to see much in some of the images that Gonda and Yamazaki present in their papers. Would it even be possible to discern small air pockets given the image quality?
(15) Line 34, pg 6: Perhaps you could add “in a later study, both of us (JN and BS) began…” This would provide an implicit reference to BS as an author, since the initials BS are not otherwise defined. And this would be consistent with line 31 of the same page.
(16) Line 2, pg 7: The initialism CC2 should be defined. Are the crystals grown at ambient atmospheric pressure in the new chamber? Can you provide a very brief explanation of how the supersaturation is estimated, since that is required for the growth calculation shown later.
(17) Line 11, pg 8: “after the sublimation”. It seems like the word “period” should be inserted here after sublimation.
(18) Line 12, pg 10: “unusually thin” Are they usually thicker? If so, how much?
(19) Line 23, pg 10: “unusual for a crystal grown at such low supersaturation” Can a reference be provided here?
(20) Lines 5-8, pg 11: Using rings to determine the facet spreading is a nice idea. How is the location of each ring determined? It also might be good to provide an error estimate, which can then be used to provide an error estimate for the rate of spreading shown in Fig. 6.
(21) Concerning Fig 6: On a first glance, I thought that the partial grid behind the data points were actually error bars! However, it would be good to provide some estimate of the error. Since the supersaturation is used in the theoretical calculations, an error estimate on the supersaturation and the calculated growth would be good as well. Finally, the title of the figure led me to believe, initially, that the basal face radius was plotted, but it appears that this is a plot of the ring radius divided by the actual crystal radius. If this is correct, then you may want to clarify the title and, perhaps, use this as the y-axis label instead.
(22) Line 1, pg 15: This sentence was a little confusing to me. Should it read, “….was essential or if it was the greater amount of normal growth…”
(23) Line 20, pg 16: “…form near an edge or corner instead of one.” I was a little confused by this sentence. Do you mean that there can be a single air pocket at a corner, but there can also be a pair of pockets near a corner but along the edge (as in Fig. 10h)?
(24) Line 19, pg 17: “”…the rim is narrower than that just inside the rim”) This is a bit confusing and should probably be reworded.
(25) Figures 11 and 12: One way the discussion of these figures could be made a little clearer is if indications of various feature were made on the images themselves. For instance, on Fig. 12 one could indicate the “fan” like hollow in (a) and the flat terrace in (b).
(26) Line 19, pg 20: “analogous facet” is a bit ambiguous.
(27) Line 24, pg 20: “grown and sublimated in a pure vapor.” It is my understanding that here you mean the situation where gas-phase diffusion becomes unimportant, which happens at very low pressures. However, at high temperatures aren’t the vapor pressures high enough so that diffusion is still an issue? If so then perhaps one should add “near vacuum conditions.”
(28) Line 36, pg 20: “It would be less likely at the much lower-temperature protruding-growth effects found here.” I found this sentence to be a bit awkward and suggest rewording.
(29) Line 30, pg 21: You may want to add a sentence or two here about why a small basal face is all that is needed.
(30) Lines 36-37, pg 21: It may be worth pointing out that scroll forms are also found at lower temperatures (below -20C).
(31) Appendix A: I very much like the model of protrusion growth. It is relatively simple but appears to capture the main physical features of the lateral spreading of a facet. On Line 1, pg 25, I assume this is an infinitesimally thin disk?
(32) Line 2, pg 25: “Shifting and normalizing” What do you mean by “shifting”? Is this just the subtraction of N_infinity? And you may want to be a little more specific about the normalization.
(33) Line 5, pg 25: “can be shown”. Was this shown in Nelson (1994), otherwise it might be good to give a reference to the solution.
(34) Equation A5, pg 25: My understanding of this function is that it provides the appropriate basis function for the area (r-x_s to a) over which the flux of vapor is non-zero. If this is correct, then it might be good to introduce this basis function in this way. Perhaps pointing out that the idea here is to define a basis function for the ring region over which the vapor flux is non zero.
(35) Line 16, pg 25: “derivative of this function” Since there are two functions above this line, the function being referred to should probably be specified. I assume it is Eq. A5.
(36) Line 15, pg 26: “From Eq A3 and A7…” I presume that h_td is replaced with h_tr though? If so then this should be specified.
(37) Line 5, pg 27: The refinements described here sound like they would produce a more precise model, but given that we lack detailed measurements it’s probably not warranted. It seems to me that the present “simplified” model is well-suited for the measurements that were taken from the growth chamber.