I’d like to thank the authors for their efforts developing this new model for cryoconite hole depth, which is well presented along with useful sensitivity experiments and some validation. As the authors point out, changes in cryoconite hole dynamics can influence ice surface albedo – so this is an important topic, given that SMB is one of the key controls on Greenland’s sea-level contribution. I imagine this model could easily be driven by either AWS data or climate model output, making it a useful tool for investigating how cryoconite holes could influence albedo under climate warming anywhere in Greenland or indeed Antarctica given some basic observations of typical hole dimensions (which are already available for many places). Other applications would include supraglacial hydrology (changes in water storage) and ice surface microbial processes.

The model calculates changes in hole depth by considering energy balance at the centre of the hole. Validation with some field observations yields an encouraging match overall, with some discrepancies as we would expect.

There are two important aspects which I think need to be considered further before publication, given the application of this model in regions with generally large zenith angles. On that basis I have ticked the major revisions box, but I’m hoping it’s not a lot of work to implement these changes. Elsewhere there are some minor points requiring additional clarification, and the manuscript needs language editing by a native English speaker as there are numerous grammatical errors and a few sentences which are a little hard to follow. Apart from the language itself, the paper is clear and easy to follow.

I’m not very up to date with the relevant literature so I just reviewed this study on its own merits and not in relation to other recent work.

Main points

(1)

Refraction is not considered when the direct SW component passes from air to water. I wonder if that would change your conclusion that the diffuse component dominates over the direct component. If the zenith angle (in the air) is theta_a, and the refractive indices of air and water are n_a = 1 and n_w = 1.33, then the zenith angle in the water (theta_w) would be estimated from Snell’s law, i.e.,

n_a * sin(theta_a) = n_w * sin(theta_w).

This is worth considering, since your range of zenith angles in air (noted as 56 to 85deg: Line 305) would become 38 to 48deg in water, so it’s much more likely that the direct SW can reach the hole centre. You might also want to consider reflection by the water surface.

Refraction along the transmitted (air-ice-water) pathway would also be worth considering but I imagine would be harder to implement.

I think it would be quite easy to adjust the model to account at least for this air-water refraction and hopefully not a lot of work to re-run the plotting scripts so we can see if this is important or not.

(2)

Only melt at the hole centre is considered. This makes sense from the validation perspective as the measurements were collected at the centre. However, in Greenland or Antarctica as the sun goes round and round quite low in the sky it is plausible the hole centre is never directly illuminated but that the outer parts are illuminated directly for several hours. I think the two ‘extremes’ to quantify this would be the northern and southern edges of the hole bottom. Could some of the melt rates be repeated for these locations, with a simple adjustment to the geometry calculation? If it turns out the melt rate is actually quite uniform across the bottom of the hole, that would itself be an interesting result as it would compare well with the generally flat hole bottoms and would support the model simply being applied to the centre and not the edges. This is related to the first point, since if the diffuse component is dominant then the melt rate should be quite uniform. On the other hand if the direct component has been underestimated then the melt rate could vary quite considerably across the hole bottom.

Other points.

Hole widening: I don’t think this is specifically mentioned. However, the direct component is sensitive to hole diameter (because of shading) so it’s certainly worth some discussion even if not included in this first version of CryHo. Later versions should probably attempt to track both the hole depth and the diameter. Is there some positive feedback? As the hole gets wider, more and more of the vertical wall gets illuminated, presumably causing further widening, and additionally a greater water surface area for turbulent heat transfer (noting the area increases as diameter^2 while the wall circumference for melting only increases linearly with diameter). As the hole widens, the bottom is also less shaded. Could that explain how cryoconite holes can sometimes grow quite large, eventually coalescing? Hole widening might mitigate collapse, to some extent, if it can help to increase depth.

L25: “wind speed”. Technically should this be the turbulent heat transfer (which of course is a function of wind speed, but also other factors such as roughness, humidity, air temp etc).

L40-50: Our study from west Greenland also reported CH collapse and debris dispersal following warm/windy conditions (Chandler et al. 2005 TC; our Section 3.1). Also note we used four bare ice types rather than three (clean ice, dirty ice, CH, water).

Section 2: throughout the paper it would be better to write the equations in SI units, to avoid awkward conversion factors, even if you have used these other units in the model code for convenience.

Eq 7: Mc = t_h * Q_Mc / l_M … the units don’t balance here, I think there is a rho missing? Please could you double check all the equations for typos / consistent units (I haven’t checked all of them).

Eq 9-10: A diagram showing the ray paths of the four SW components would be handy here – maybe add a panel to Fig 1?

Eq 18: Does it matter that the hole is full of water, in your LW calculations?

L145: Why is the CH bottom temperature equal to the surface temperature? Shouldn’t it simply be the melting point of ice? In cold conditions, under your assumption you would end up with the bottom of a water-filled hole cooling below 0C.

Section 2.4: I would encourage the authors to consider in more detail the influence of partial shading as I noted earlier, and also the change in zenith angle as the radiation enters the water.

Also, does the transmittance through ice account for the low-density weathering crust? Maybe it doesn’t matter for the deeper holes that are well below it, but something to consider in CryHo V2…

Section 3.3: I am quite untrusting of ablation measurements made using metal stakes, as they tend to melt into the ice unless they are installed deeply enough to be definitely remain well frozen at the bottom – could you comment further, or note it as a possible source of error (I think plastic tubes are better, but I acknowledge that opinions vary!)

L296: A climate model can be used directly as a boundary condition rather than requiring any coupling, this is one of the great applications I can see for CryHo.

L298: I didn’t follow that sentence.

 L385: Conclusion that diffuse component dominates, may need to be revised depending on what you find if accounting for refraction or partial shading as noted above.

Table 1: great if the symbols are listed alphabetically.

Fig 5: you have plotted a single model run based on some estimated parameters. Could you use several runs, covering a range of plausible parameters, and plot the range or stdev of resulting hole depths as a shaded band? It would help interpret the discrepancy between model and obs.

Supplement: It would be great if this could be avoided completely. Figs S1-S4 could be combined as a multipart fig in the main text. The text on extinction coeffs could also be moved to the main text, it’s an interesting part of the model. Fig S5 can join Fig 3.

Fig S6 (move to main text), can the individual Rs components also be plotted separately?

General statement: 

The albedo of the Greenland Ice Sheet is of central importance to the surface energy budget.  In the ablation area, the albedo is determined by whether debris is uniformly distributed or instead confined in cryoconite holes (CHs), so modeling the evolution of CHs is a worthwhile research project. The inputs to the model could be obtained from climate-model output. This paper could therefore be important, but in its current form it is difficult to read, so few readers will get through it.

The abstract could be improved by adding some key points, which are noted as they occur in the major comments below.

Major comments:

(1) CHs develop because the albedo of cryoconite material (ac) is lower than the albedo of the surrounding bare ice (ai).  It would therefore be good to explicitly examine the dependence of equilibrium CH depth on this difference (ai-ac), and add these results to the abstract.

(2) Equation 13. It is strange to compute the diffuse ratio under cloud from the net longwave at the surface, because the causality is backward: in reality the downward longwave is a consequence of cloud thickness.

(3) Eq. 15 (and other equations). These equations apply only to the center point of the CH. But parts of the bottom will still be in shadow for any nonzero solar zenith angle. There’s no need to expand your calculations, but at least point out that you are ignoring this complication.

(4) Eq. 20 and elsewhere.  The factor of 1000 is distracting, and it is not necessary; the user just needs to keep track of the units of k and D.

(5) Equation 21 for RStfc is wrong, because the path length of diffuse transmission into ice is taken to be just the vertical distance (as pointed out on lines 155-156). Instead you need to use the diffusivity factor (for example Liou 1980 p 97 eq 4.26): The effective path length for diffuse flux is the product of the vertical distance and the average secant for diffuse radiation, which varies with depth, but is often taken to be the secant of 53 degrees, i.e. 1.66.

(6). Lines 320-324 point out that the CH depth is uncorrelated with CH diameter. This is an important result which should be included in the abstract.

(7) Lines 334-336. The positive feedback of low ice-albedo (ai), causing CHs to collapse and therefore causing further lowering of ai, is important and should be included in the abstract.

(8) Line 332: “Our results highlight for the first time the importance of both ai and ac”. The key variable is probably neither ai nor ac, but rather their difference (ai-ac). It would be good to add a figure plotting equilibrium depth versus (ai-ac) for the standard values of other inputs. This is related to comment (1).

(9) I cannot make sense of lines 341-348; they need to be rewritten. For example, I don’t understand “the direct component of shortwave radiation is transmitted throughout the ice rather than the diffuse component.”  Also, how can “diffuse” be “direct”, as in this statement: “The CH bottom is directly accessible by a part of the diffuse component.”

(10) Lines 370-371. The observation that CHs decay under overcast cloud is probably not because of the diffuse nature of the incident radiation.  Under a cloud, the total downward shortwave is dramatically reduced, which means that turbulent fluxes become a larger fraction of the total energy budget, leading to CH decay.

(11) Figure 1b. Only part of the CH bottom is shaded; the rest is sunlit.

(12) Figure 3 is completely mysterious to me, so it needs to be redrawn.  The long dark bars (apparently meaning LH?) extend on both sides of zero; what does that mean? The long dark bars are shaded where they are above zero; what does that mean? Some of the long dark bars have a short gap just below the zero line, then they continue as a tiny black box below the gap; what does that mean? What are the short dark bars at the top of some of the bars? Which bars are net radiation?

(13) The paper is difficult to read, partly because the reader needs to keep track of the non-intuitive subscripts on the variables.  Unfortunately, I don’t have useful suggestions on what to do about this.

Minor comments:

Line 49. Is “bare ice” uncontaminated, or does it contain distributed cryoconite material?

Line 76. “latent heat flux”. Point out that HLi is restricted to the latent heat of evaporation; it does not include the latent heat of melting.

Lines 79-80. “Heat conduction from the glacier ice . . . assumed to be negligible.” This is valid if Ta is never colder than Ts. Figure 3 shows that this condition holds during the summer: whenever Ta is negative, Ts likewise is negative and approximately equal to Ta. But in spring and autumn they might differ. This “Ts” in Figure 3 is probably what is called “Ti” in the text, neither of which is defined in Table 1.

Line 85. Give a reference for the value of bulk coefficient.

Line 96 Eq 7 for Mc.  The units don’t match.  LHS is mm/hour, but RHS is kg m^-2 hr^-1. The missing factor is density, kg m^-3.

Line 112. Change “distinguish” to “separate”.

Line 121.  Niwano et al. 2015 is missing from the reference list.

Line 155. Change “pass length” to “path length”.

Line 171. RSfd and RSfs are undefined; they do not appear in Table 1.

Line 177. Eq (25). To say that rd=1.0 is equivalent to assuming that the incident radiation becomes rapidly diffused in the topmost millimeters of the ice, which is probably true.

Line 236. “Lapse rate” is the rate of decrease of temperature with height. If temperature decreases with height, the lapse rate is therefore positive. So remove the minus-sign, unless you mean a temperature-inversion.

Line 428 says that KF designed the study, but then the next sentence says that it was instead YO, NT, and TA who designed the study.

Table 1. Does C have units?

Figure 3 caption line 601, “Ts”. In Table 1 you instead use Ti.

Figure 5. Depth and diameter have unnecessary zeros after the decimal points.  For example, change 39.0 to 39.

Figure 7a,f,g,h. Reverse the order of the legends to correspond with the order of curves. For example, in 7a the red curve is on top, so the legend should have the red legend (+3) on top.

Figure S3. The horizontal azis is labeled theta-0. In the text it is theta-z.

Figure S6. Three of the plots are labeled “control”; what does that mean?

Reference:

Liou, K.N., 1980: An Introduction to Atmospheric Radiation. Academic Press.