This review has been done jointly with V. Dansereau.
Following the comments of the different referees, the authors carefully answered to most of them, and substantially modified the original manuscript, which, in our opinion, significantly improved. We have now only one comment that should be taken into account before publication, plus minor comments and some clarifications on their answer. Once these comments taken into account, this manuscript should be suitable for publication in The Cryosphere.
>> Mechanical redistribution is taken into account in our simple 1-category model (i.e. ice or open water). When A=1 and sea ice convergence occurs, the mean ice thickness increase (see continuity Eq. 4 in the manuscript), but since A=1 is capped at one, this leads to the actual thickness of ice in a grid cell (h/A) to increase, i.e. ridging. A simple 1-category model does not resolve the ITD per se, unless the variability in ice thickness is resolved (i.e. unless the model is run at O(1m) resolution, at which sea ice no longer behaves as a 2D material.
This mechanical redistribution scheme is still not mentioned in section 2.1 of the revised manuscript and, apparently, nowhere else (?). This should be corrected.
In the meantime, we do not agree with their view that a 1-category model does not resolve the ITD: there is no a priori and unique spatial scale associated to the Ice Thickness Distribution, which can either be calculated (a PDF) from a modelled field or set of observational data. The difference in the scale of measurements and that of current model resolution however do differ substantially and so one must be careful when comparing modelled and observed ITD.
Please note that we are not talking here about the subgrid-scale parametrization often referred to as ITD (the equations of which are typically cast in 2-dimensions). This is a minor comment.
>> The paper of Dansereau et al. (2016) have a factor of 1/(1+v)(1-2v) in the stress-strain relationship, indicating that the authors have used the plane-strain assumption. Dansereau et al. (2017) however do use the plane stress assumption, as pointed out by the reviewer. In the revised manuscript, we remove the reference to the plane-strain assumption in Dansereau et al. (2016), for conciseness.
This statement is still false:
In Dansereau et al., 2016, p. 1343, section 3.1, the "factor" indicated is nu/((1+nu)(1-2nu)).
Please note that at the top of this paragraph, you find the sentence “Here we apply this idea of stress dissipation to a TWO- or THREE-dimensional, compressible, elastic continuous solid (…). Equation 4 just below this sentence does not make any distinction between a 3D or 2D case. Then, the equation for the elastic stiffness tensor, given just below, does not make any distinction between the 2D plane stresses or the plane strains approximation. Indeed, it is written “the (dimensionless) elastic stiffness tensor K is defined in terms of nu, (…) such that for all THREE-dimensional symmetric tensor epsilon [deformation rate] (…)” and there comes the factor you are referring to, which is the indeed the right one for linear elasticity in 3D. Thus, in this section of the paper, no assumption is chosen between 3D, 2D plane stresses or 2D plane strains to represent sea ice on the large scale. This assumption is rather stated in section 4, but the factor is not explicitly written there. Again, the correct 2D, plane stress version of this factor was used in the simulations of Dansereau et al., 2015, 2016 and 2017. |