Toward a method for downscaling sea ice pressure

Abstract. Sea ice pressure poses great risk for navigation; it can lead to ship besetting and damages. Contemporary large-scale sea ice forecasting systems can predict the evolution of sea ice pressure. There is, however, a mismatch between the spatial resolution of these systems (a few km) and the typical dimensions of ships (a few tens of m) navigating in ice-covered regions. In this paper, we investigate the downscaling of sea ice pressure from the km-scale to scales relevant for ships. Results show that sub-grid scale pressure values can be significantly larger than the large-scale pressure (up to ∼ 4× larger in our numerical 5 experiments). High pressure at the sub-grid scale is associated with the presence of defects (e.g. a lead). Numerical experiments show that a ship creates its own high stress concentration by forming a lead in its wake while navigating. These results also highlight the difficulty of forecasting the small-scale distribution of pressure and especially the largest values. Indeed, this distribution strongly depends on variables that are not well constrained: the rheology parameters and the small-scale structure of sea ice thickness (more importantly the length of the lead behind the ship). 10

is placed at the end of the simulated lead and the simulated ice pressures on the ship are recorded.
Model simulations are documented showing the changing ice stresses for a number of cases. First the model is tested for the case of no-ship, with the expected deformation rates related to an analytical case. Cases with leads of various sizes and for various model resolutions are also tested.
Additional ice features are also added to the domain, showing that the shape of the largest lead is the controlling factor for the highest ice pressures in the model. A ship is then positioned at the end of the largest lead and the stresses upon the ship are documented. Multiple experiments are performed varying the lead length (and also introducing a refrozen sea surface to the lead), ice strength parameter and the compressive and shear strengths of the ship itself. The authors conclude that the defects within a sub climate model grid cell are the greatest controller of sea ice pressure.
They lead this conclusion to suggest that the pressure stress on a beset ship at the end of a lead of its own making will reduce as the lead surface consolidates. I can see how the results in this paper will help inform the navigation of ice covered seas.
The paper is in general very well written and the introduction and description are easy to follow. I suggest that is published with some additional explanations. Also the title of the paper show be changed to reflect the specific situation that is being simulated.
Improvements can be made to text in the form of overall motivation of the study. Explicitly saying in the introduction and methods and results that aim of the paper is to focus on the increased ice pressure at the tip of a lead where a ship is likely to be present would be a beneficial addition to the paper. Also the paper needs to clearly state that this study models a single instantaneous stress field for a particular setup. This limitation also needs to be addressed in the conclusions when the case of lead closure is discussed. Whilst the authors mention that waiting for a lead to consolidate will reduce the stress on the ship, how likely is it that the lead will close mechanically before then? Also the authors state that care has been made to avoid all deformation within the model gird, what limitations does this put on the study? The authors mention that there is vast literature on ships navigating ice, does any of this describe the situation being simulated? In particular it would be helpful to discuss whether the modelled setup of a lead created by a ship within ice under uniform pressure, results in the lead remaining open and thus increased lead tip pressure existing as modelled here, is a likely and realistic scenario. I am not convinced that ice under uniform external pressure, when passed through by a ship will not result in lead closure, thus allowing the modelled setup to be encountered. I find the results and numerical stability sections confusingly arranged. Further sub sectioning to break apart the various studies in the results will help. Collecting together all the cases where the model resolution was varied would be beneficial. After I had worked out what experiments had been performed and how they related to each I found them clear and well documented.
Title I find that the title is not an accurate description of the paper content. The paper is focusing particularly on recreating the internal ice stresses at lead tips during constant ice compression for the case of ice stresses being low enough to not cause the closing of the lead. The paper content doesn't give a general method of downscaling as all the model setup is directly for the model case presented. The paper title should reflect this.
Abstract -L6 Can you explain what form of numerical experiments you perform in this study within the abstract? A little extra depth on the nature of the methods used will be helpful here.
L10 The information within the parenthesis doesn't correspond well to the rest of the sentence. Do you mean that your study reveals that that the lead length is particularly important? L13 I will be helpful here to clearly indicate that ice pressure is a horizontal 2d force. L149 An overview explanation here will make the following equations much easier to follow. From what I can tell you impose the total normal and shear stresses. The equations that follow enable you to give the components of the gradient of the internal stress tensor. Is this correct?
L159 does this mean that v(1m) will be solved for in the model? Can you list the components that need to be imposed for this side of the grid structure and those which will be left free?
L165 what happens to this simulation when the normal stress on the east and west side are not equal? I assume that there will be a large E-W ice drift which i understand is best avoided for your study. This information will be very helpful for those who wish to recreate your model setup.
L168 This information doesn't require its own section, though including it is very useful. Perhaps put it with the coarse grain results, or in the previous or following section. Actually if all the methods are placed in a 'methods' section and subsections are used the paper format will be easier to navigate. Can you include some basic information about the model setup either here or back in section 3?
What model simulations are you seeking? It seems that you are looking for static solutions, invariant in time, or a snap shot of ice stress, is this the case? What are you hoping to show us with these validations? You are comparing to idealised numbers of ice pressure. Do these validations show that the numerical model generates the correct pressures for a static field? For the lead cases presented here i was expecting to see the closing of the lead, though this makes little sense if the simulations just show the immediate pressure field of ice with a lead present.
From reading ahead to the results it appear you are particularly interested in the increased stresses in the ice at the end of a lead, which a location where a ship is likely to be present. Informing the reader of this before the validation section will show why you are checking the pressure states to show that these regions are correctly simulated.

L207 how is it obtained from the model?
L222 what conclusions will you be seeking in the results section? The validations show that your model is good for the stress states you hope to test, but to fully show this you need to state what these stress states are and why the model and its setup work for them.
L350 my understanding is that the model gives the solution of a single 'snap-shot' of ice stress. The acceleration argument then surely does not matter?