This review is from Referee #1 of the original manuscript. The authors have made changes in the right direction, but there are still issues to address.
Each model produces a sea-ice floe size distribution (FSD) from which the sea-ice floe perimeter density (P) can be calculated (assuming a shape parameter, gamma). Each satellite image also yields a FSD and P. The authors compare P from models with P from satellite images, which is a perfectly proper and legitimate way to assess the skill of the models. But note that the relationship between P and FSD is a one-way street: given the FSD and shape parameter gamma, one can calculate P; but given P, one can say nothing about the FSD. The results of the analysis show that in general there is very poor agreement between modelled P and observed P, and that's fine -- it simply means that the models are not able to reproduce the observed P. But even if the agreement were good, it would say nothing about the modelled FSDs. That point should be acknowledged or conveyed somewhere.
The perimeter density P is not a proxy for the FSD. A proxy is "a measurement of one physical quantity that is used as an indicator of the value of another" or equivalently "a measured variable used to infer the value of a variable of interest" (to quote two dictionary definitions). Now consider these examples:
1. All floes are circular with radius r0. The FSD is the Dirac delta function, f(r) = delta(r - r0), and P = 2/r0. Suppose r0 = 20 meters = 0.02 km. Then P = 100/km.
2. All floes are circular with uniform distribution on [0,L]. The FSD is f(r) = 1/L and P = 3/L. Suppose L = 30 meters = 0.03 km. Then P = 100/km.
3. All floes are circular with exponential distribution. The FSD is f(r) = (1/lambda)*exp(-r/lambda) and P = 1/lambda. Suppose lambda = 10 meters = 0.01 km. Then P = 100/km.
In all three examples, P = 100/km. If one is simply given that P = 100/km, it is not possible to "go backwards" and find the FSD. The FSD could be anything. Any distribution with a free parameter can be made to have P = 100/km by proper choice of the parameter. P is not a proxy for FSD.
The authors misinterpret the work of Perovich and Jones (2014). At lines 237-238 of the marked-up revised manuscript, the authors write, "P is a useful proxy for FSD and widely used in previous observational studies (e.g. Perovich, 2002; Perovich and Jones, 2014; Arntsen et al., 2015)." In Perovich and Jones (2014) they ASSUME that the FSD follows a power law, and then use the observed P to determine the power-law exponent. In other words, P is not used as a proxy for the FSD -- the FSD is already fixed as a power law. P is used for finding the exponent.
This is what the authors wrote in their response to my comment about perimeter density (PD) and FSD in the original manuscript:
"1) The same PD corresponding to different number FSDs or the same FSD corresponding to different PDs does not mean there is no connection between PD and FSD. In previous studies, Rothrock and Thorndike (1984) first defined the FSD as both number density n(r) and area fraction f(r). These two definitions are related by f(r)=gamma * r^2 * n(r). Now, if we consider a set of circular floes and a set of elliptical floes with semi-major axis "a" and semi-minor axis "b" with the same number FSD n(r) in a given region. But assume that pi*a*b NE pi*r^2. In this situation, although these two groups of floes have the same n(r), their areal FSD f(r) is different. Similarly, if we consider 5 circular floes with the same radius of 10 m and 100 elliptical floes with semi-major axis "a=1 m" and semi-minor axis "b = 5 m" in a given region. Then we can get the same areal FSD, different number FSDs. Even the traditional FSD concepts n(r) and f(r) still shows the same situation that there is not always a unique 1:1 relationship between them. Similarly, it is not abundant evidence to prove that PD is not a metric related to FSD by showing the same PD corresponding to different number FSDs or the same FSD corresponding to different PDs."
Let's analyze some of the statements in the paragraph above.
1. The equation "f(r) = gamma * r^2 * n(r)" is presented but then later "Even the traditional FSD concepts n(r) and f(r) still shows the same situation that there is not always a unique 1:1 relationship between them." But the equation given by the authors shows that once the constant gamma is chosen, there is indeed a 1:1 relationship between n(r) and f(r).
2. "if we consider 5 circular floes with the same radius of 10 m and 100 elliptical floes with semi-major axis a=1 m and semi-minor axis b = 5 m in a given region. Then we can get the same areal FSD, different number FSDs." In the first case, the 5 circular floes of radius 10 m have a total area of 500*pi. In the second case, the 100 elliptical floes also have a total area of 500*pi. Yes, the total area is the same in both cases. And yes, the number of floes in the first case (5) is different than the number of floes in the second case (100). But the authors are mistaken or confused in their use of "FSD" in these examples. Since all the circular floes have radius 10 m, the FSD is n(r) = delta(r-10). Since all the elliptical floes have a=1 m, the FSD is n(a) = delta(a-1). The FSDs are all delta functions. The authors don't seem to understand the difference between "area" and "areal FSD" nor between "number" and "number FSD". This is troubling.
Image Resolution.
The models overestimate P for floes with r < 15 m (Fig. 2). The observed P is based on images with pixel size 1 meter. The authors analyze 5 images with pixel size 0.5 meters, resulting in larger P for small floes (Fig. 4). The authors conclude that inadequate image resolution may be one of the causes of the discrepancy between modelled and observed P for small floes.
Line 23: "the image resolution is not sufficient to detect small floes"
Lines 586-587: "The causes of such differences include ... the limitations within the observations such as the image resolution"
Lines 632-633: "It requires much higher resolution images (e.g., aerial photographs) and further research in the future to properly investigate the effects of the image resolution"
Lines 662-663: "the ability to resolve the shape of the FSD for small floes remains constrained by the limited resolution of satellite images"
A few comments:
1. At lines 600-605, the authors admit that the increase in P in going from 1-m images to 0.5-m images "is still far too small to explain the difference between the observations and model outputs." Nevertheless, the next sentence says: "This suggests that the image resolution could be one of the contributors to the overestimation of modelled P for small floes, but it is still inconclusive whether the limited image resolution is the main contributor or other factors such as model parameterisations contribute to the difference." Really? Can't we conclude that image resolution is NOT the main contributor, given that halving the pixel size from 1 meter to 0.5 meters gives a change in P that is "far too small to explain the difference between observations and model outputs"?
2. Judging by Figure 2, the models simulate floe sizes down to about r=3 meters. The authors suggest that the image resolution of 1 meter (or 0.5 meters) is not sufficient (see quotes above). Apparently centimeter-scale imagery is needed (e.g. from aerial photographs). Wouldn't that result in a mismatch in the scale of comparison, if images resolved floe sizes of r=0.1 meters but models only resolved r=3 meters?
3. In order to explain or account for the difference in modelled P vs. observed P for small floes, the authors look for a potential shortcoming in the data (its resolution) rather than a potential shortcoming in the models. This seems like the wrong approach. In my opinion, 1-meter (or 0.5-meter) image resolution is good enough! I'm not convinced that we need centimeter-scale imagery to properly characterize the FSD and P.
Lines 448-450. "floe welding rate is set to be proportional to the square of SIC in the two prognostic models ... In this section, we present the model-observation comparison results for SIC to validate floe welding for the prognostic models."
The model-observation comparison of SIC does not validate the floe welding parameterization. There are no observations of floe welding presented in this paper. The comparison of SIC validates SIC, not floe welding.
Lines 479-481. "FSDv2-WAVE slightly underestimates SIC by 2-4% compared to the observations in the MIZ (SIC<80%). CPOM-FSD strongly underestimate the SIC by 13%-15% in the MIZ compared to the observations. This difference can be attributed to different atmospheric forcing that is used in the models (Schroder et al., 2019)." I don't see any evidence that the difference in SIC can be attributed to the different atmospheric forcing (NCEP-2 vs JRA55b) used in the models. This sentence simply makes a declaration without any further justification. I looked up the Schroder reference and it uses NCEP-2 but not JRA55b, so I don't see how it supports the claim being made here.
Lines 483-484. "The underestimated SIC from the two prognostic models may be a contributor to the underpredicted floe welding rate during spring and early summer." Since the floe welding rate is proportional to the square of SIC in the two prognostic models (line 448), underestimation of SIC translates directly into underpredicted floe welding rate in the models. It's not "may be a contributor to" but rather "is the cause of". Incidentally, we don't know if the floe welding rate is, in reality, proportional to SIC-squared. That has not been validated in this paper.
Lines 484-485. "A negative bias in spring SIC shown in the prognostic models may partially explain the overestimation of P especially for small floes (Fig. 2)." First, the overestimation of P is ONLY for small floes (Fig. 2) so it's misleading to say "especially for small floes." Second, a negative bias in SIC could be due to too few small floes or too few large floes. Simply knowing that SIC is too low does not automatically imply an overestimation or underestimation of P.
Lines 652-654. "we examined the P in the northern regions where wave-induced breakup is negligible. In these regions, most modelled P match our observations better." There are no observations in the northern CS region.
Figure 6. The caption refers to changes in FSD but the figure shows changes in P.
Table 2. The caption refers to three models but the table lists only two models. |