the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 06 Feb 2025
The next generation sea-ice model neXtSIM, version 2
Abstract. While many large-scale sea ice models can represent regional to global sea ice evolution, their representation of sea ice dynamics varies little between models. This is because they all use rheologies based on the hypothesis that sea ice behaves as a visco-plastic solid. This works reasonably well for several quantities (e.g. sea ice volume) but fails to capture sea ice deformation features at coarse and moderately high resolutions (i.e. coarser than about 5 km resolution). This may be problematic since these deformations result in the formation of leads and ridges, which likely play an essential role in ice-atmosphere-ocean interactions, and because these are the resolutions at which sea ice models run in coupled models such as Earth System Models. An alternative is to use brittle rheologies that better capture these features independently of the resolution. The neXtSIM model has been at the core of the effort by its developers and users to explore the usage of brittle rheologies and new modelling approaches in geophysical scale simulations of sea ice. Here, we document neXtSIM, now in version 2 of its development, to foster its use for the sea ice community and release a public version of the model. We describe the sea ice dynamics and the core of the model in detail and give insights into the parameters specific to the brittle rheologies included in neXtSIM. We also document the model's specificity associated with its Lagrangian framework and how it affects the coupling with other components of Earth system models. We hope that the insights provided in this study and the public release of the model will trigger innovative research in the sea ice modelling community.
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RC1: 'Comment on egusphere-2024-3521', Anonymous Referee #1, 15 Apr 2025
I welcome the effort to present the description of the current version of neXtSIM, but I think the paper needs to be improved in several directions before I can recommend it.
1. I miss a good description of the numerical part of the model, in particular its time stepping, details of the spatial discretization and the general workflow. The authors cite their previous work where I guess some explanation can be found. However, the value of technical papers in GMD is precisely that they provide an opportunity to document the model and describe details that would enable others to learn and to follow. Many quantities are left undefined in section 2. For example, the stress tensor appears in (1), and on line 54, but then disappears. Instead, there are undefined components, and finally there is the \sigma but without the boldface. Please be precise, it is almost impossible for a general reader to follow. The quantity K (bold face) is not defined, and \eta appears as sea surface height in (1), then as viscosity in (3), and \eta_0 is not specified. This continues in section 2.2, there are undefined strain rate invariants, the parameters e and P* are not specified, the equation for velocity is written (17), but no discrete equation for the stresses, and the reader is referred to other papers for \alpha, \beta and \beta' and \tau.
2. The presentation of section 3.1 should also be improved, and the iterative procedure for the drag coefficients needs to be presented in more detail.
3. The explanation in section 4.2 needs a figure showing (defining) the geometry of the procedure.
4. Many technical steps in the model are related to the decision to use a moving mesh. First, it would be worthwhile to discuss why this choice is necessary and compare it with other possibilities. Remeshing should be equivalent to some diffusion, and if the choice made by the authors is motivated by the desire to keep the damage fields localized, the question is whether a comparable result can be achieved by using a high-order advection scheme. This would simplify many things (but make the advection more complicated). Second, I do not see any discussion of how mesh deformation will affect vector and tensorial quantities.
5. In the discussion of the test case (section 5.1) the authors compare the performance of two damage update schemes. While the field in 2c contains more detail, it is a discrete implementation and grid-scale details cannot be interpreted reliably. I would be suspicious of any features that are the size of several grid cells. Similarly, Fig. 3a and c show that there is grid-scale noise in normal stresses where damage tends to 1, meaning that the stresses are not really differentiable. Please, include discussion of these issues. From a numerical point of view, I would be concerned about the appearance of noise in solutions and consider some measures that restore smoothness.
6. I also miss some general discussion of how the BBM and EVP compare with each other in both the simulated sea ice state and the requirements on time step and computational expenses. This would help the reader to see the differences and decide where the BBM rheology leads to advantages.
Minor points:
3,4 'but fails ...' But should it? At these resolutions the scales where truncation errors are small are perhaps 25 km or larger, and these scales are already too large for most leads.7,8 'independently of resolution'? Why one needs leads and ridges if a mesh is coarse? Do they correspond to any physical reality?
11 'give insights ...' This is what I do not really see
Introduction gives emphasis on historical aspect, and the time intervals of simulations that are mentioned there are discouraging (ten days, an entire year...). I would not not mention this, as it only tells that the model was not really ready.
64 'on any' ?
68 'In it' What is it?
74 cascade Marsan
95 P_max is very similar to the sea ice strength in Hibler's rheology, do you select similar parameters as in (16)? Please specify
119 (P0) and (P1) should be explained. Also it should be explained how derivatives are computed, and there are other things, see
145 Why n+1 in the absolute value |u_w-u^{n+1}|? I hope a linearized version is used.
147 'donates'?
156 stress tensor was boldface initially, please be consistent, there are several places before
168 'particularly after' It would be better to cite some examples.
formula (22) C? it was Ch and Cm before
406 10^5 seems to be rather limiting, a 1/12 degree mesh has already much more cells in the Arctic.
468 'Some loss ...' Can it be quantified?
481 'This sampling ...' Why this sentence is needed?
527 'Such rapid change ....' See my point 5.
Fig. 2, caption, 100 by 100? (It is 1000 by 1000 in the text).
Also add an explanation for b and c.
Fig. 3, caption, why a,c,e and b,d,f are grouped together? Please arrange consistently. Also in the text (line 508, a and f?).Citation: https://doi.org/10.5194/egusphere-2024-3521-RC1 -
RC2: 'Comment on egusphere-2024-3521', Harry Heorton, 21 Jul 2025
This paper documents the recent development and state of the neXtSIM sea ice model. The paper is linked with a code release and is a useful documentation of this high quality sea ice model. The model description appears to be complete and is accompanied by some example simulations in stand-alone configurations. These simulations are well described with generally well documented plots.
The paper does need a lot of minor edits though. There are many undefined (or not clearly located definitions) for key terms in the many equations. The equations seem to be all present and correct, but as it is, it is cumbersome to understand them all as I had to a lot of searching around to find the key terms, and in several cases make large assumptions about what is represented.
Another aspect that seems missing are some overview plots from the 15 year run. All the observational comparisons are well documented, but there is limited documentation of the results of the model that emphasise the unique aspect of neXtSIM – the damage based rheology and Lagrangian grid. Can some extra figures be included that show the mean Arctic wide drift fields (that can be compared to observations), mean damage (winter only seems most appropriate) and stress states?
Minor edits:
Many equations are missing citations - this is not an issue for the accuracy of the paper, but these documentations are often used for the design of other models. In this case it is essential to be able to search for the derivation of the equations or for more complex forms if this is needed. A table of notation may be a useful addition. While sizable for a paper, it may really help with complexities. It will also make future use or adaptation of these equations much easier.
The link between Lagrangian moving mesh and the overall resolution is not clearly defined. The adaptable grid will gain higher or lower resolution as it distorts. It looks like this is all considered as the grid adapts, but is a target resolution (like the 10km for the square example) encoded into this process? Resolution is very important when setting the solver frequency of fixed mesh grids and is generally designed alongside stability and dimensionality. Is there a similar process here?
Specific edits:
Abstract,
The opening 5 sentences here are very vague and do not sell this paper well. It needs opening statements on what sea ice is and why dynamical sea ice models exist. Feltham (2008) is a good place to get this narrative and leads well into the intent of neXtSIM to make the link between continuum and Basin scale circulation and the sub grid cell length and observed sea ice deformational features. This is attempted in lines 5-8, but it is all lacking a detailed context.
L 22 – ten simulated days I assume?
L 23 these technical terms and the reference to the equation need the equation to be included here. The chosen historical intro is nice, but as it is it needs to have the technical terms removed. A summary of the general improvements and simplified assumptions will help here, with just references to later sections. It may also help to include the definition of Lagrangian, which while a base theory, is an important specification of this particular model.
33 – the mix of acronym and citation is awkward to understand at first reading.
35 – citation is in the wrong format or missing words.
42 – this sentence is unnecessarily long – can it be rewritten with the word ‘documented’ only once?
45 ‘most important’ does this mean that it is of the authors opinion that RS obs are more important than in-situ or experimental data? Or that this model design focusses on RS obs matching rather than other obs?
48 ‘the momentum eq’ this suggests that there is only one form of this eqn, the next sentence says that one has been selected for this model – reword. Perhaps say that the core equation conserves momentum?
50 Aph –A is undefined here.
59 – EVP and mEVP are not defined
70 – stating ‘Elasticity E’ will make the next eqn better defined.
72 – ‘[. [‘
73 - if d is in [0,1] starts at d=0, how can d then be reduced?
73 – does a local increase in d represent damage to the sea ice? (this may be obvious, but stating the obvious can be helpful early in a paper).
74 how does this damage reduction occur from a stress point of view? Is it due to the damage and eqn 2 causing stresses to not be transferred across the damaged grid cell?
75 – observed in RS data or in the model behaviour?
76 – I’m not sure what is meant by ‘a dashpot’
80 is \eta the viscosity? I don’t’ think this has been defined yet?
87 P is yet to be defined – so thus Pmax is not defined here.
91 – sigma has a dot in eqn 4, but not in the definition. This suggest one is not meant to be a rate of change.
93 – see above for P definition.
Eqn5 do the three options for P here relate to the 3 stages in figure1? Can the stages here be directly linked in the text to the parts of the equation? This will help the understanding of this complex rheology.
96 – why is there a scaling about h_0 = 1m? For this value h_0 disappears from eqn 6 which suggests that is useful as a parameter later, otherwise why is it here? (other than dimensionality consistency)
Eqn 7 is the top of this eqn related to the defn of lambda in line 91? If so it is not clear what parameters are put into this equation – what is delta tEK? In particular K? Similar for the bottom line (but this may just be values).
Eqn 8 is this just a solver step, or does this change in d have a differential equation form for the rate of change in damage?
Eqn 9 is this the crucial step of the rheology where damage is related to stress? Is this numerically where damage to sea ice is caused by imposed, and thus internal stresses? If so then can the selection of N be explained?
130 is the conceptual form of P the same for both rheologies?
Eqn 17 – this split line form has gone wrong somehow
147 - can all the elements of F be seen in eqn 1?
Eqn 18 – how does beta’ in line 146 relate to beta here and on line 153?
168 Hunke citation and text is confusing – the wrong way around perhaps?
173 – it is not clear if the beginning of this paragraph is for ice models in general or specific to NextSim
Eqn 19 - this look similar to the Lepperanta 1993 review where the thermos model for sea ice is derived. Is this the source for this version and does it have a similar derivation from the original heat equations?
194 - for the two layer model – how is the lower layer solved?
Eqns 20-21 these need citations.
207 - the difference between C, Ch and Cm is not defined – I can’t find where Cm is used up to this point. Eqn 22 does not have a way to differentiate between Cm and Ch. There is also Cb in eqn 1.
Eqn 23 k and g undefined here
225 – it looks like Cm,h develop in time from this statement, but the previous eqns do not make it clear why and how this happen – what is the reason why they are not just calculated at each time step and therefore need to develop?
260 is this figure 9 and 10 in Webster et al or here?
300 are there citations for where these assumptions come from or are they new?
305 – is level-ice a separate tracer class, or just a theoretical area for the conservation law? – edit - can this section begin with which of the following S,H,R are recorded by the model?
318 while the above list and equations are both clearly written can the prior points be referred to here to improve clarity? Or the whole section can be formatted into a list so the equations are linked to the prior numbered laws? As it is the list is repeated again for each equation.
375 where do such open boundaries occur? Later text suggests it is the sea ice edge, but perhaps for a reduced domain?
377 From a previous point – the recorded tracers are defined here – a reference to this point in the earlier sections will help.
386 can the adaptation mentioned here refer back to previous list where it is first mentioned?
Algorithm 1 – while this is complete and the description accurate- it will be really help the reader if the separate blocks of the pseudo-code can be referred to in the text to link the description to the relevant parts. Perhaps line numbers can be added here and referred to in the text?
472 in this sentence it is unclear whether this describes two outputs, or a single one with two forms of data, can numbers be added to split them? (assuming it describes two outputs – I think it does?)
502 – can a physical or rheology description of the difference between these two experiments be added here (it Is touched upon later)? This will make the following descriptions have stronger context.
503 figure two shows deflection of the ice drift - this suggests a coriolis acceleration, is this true? What value/global location is used here?
521 – does this refer to the green line in 3c?
Figure2 – the caption needs to show what time point these figures represent (it is in the text but needs to be here too). similar point for figure 3.
526 - why is higher damage localisation better?
528 this next sentence suggests that small scale deformation lines are a problem?
5.2 - tuning is mentioned later when discussing the results. What tuning was performed prior to this model run, or was the experiment repeated at all with alternate parameters?
Figure 5 and near line 575. Can you comment on the think ice near the Siberian coast that is not seen in the observations? Is this related to drift at all? Why are no maps of mean drift speed presented ?
Feltham, Daniel L. ‘Sea Ice Rheology’. Annual Review of Fluid Mechanics 40, no. 1 (January 2008): 91–112. https://doi.org/10.1146/annurev.fluid.40.111406.102151.
Leppäranta, Matti. ‘A Review of Analytical Models of Sea‐ice Growth’. Atmosphere-Ocean 31, no. 1 (1 March 1993): 123–38. https://doi.org/10.1080/07055900.1993.9649465.
Citation: https://doi.org/10.5194/egusphere-2024-3521-RC2
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