We use the SI³ sea ice model Sea Ice modelling Integrated Initiative, coupled with the Boussinesq hydrostatic ocean model NEMO Nucleus for European Modelling of the Ocean,. SI3 is an Eulerian continuous thermodynamical model of sea ice that we use here with five different thickness categories. In this model, the drift and deformation of sea ice are solely horizontal and the heat transfer is only vertical due to the scale ratio between the width (O(100–1000 km)) and the thickness of the sea ice (O(1 m)).

We use a regional configuration of SI³-NEMO covering the Arctic region, from the Bering Strait down to about 40° N in the Atlantic Ocean (the model domain is partially shown in Fig. , with truncation indicated by the grid-point ticks on the x and y axes). The configuration is based on a horizontal resolution of 1/4° (i.e. about 10 km in the central Arctic region) and 31 vertical levels for the ocean. This regional configuration is the same as in , who have implemented and evaluated an elasto-brittle formulation for sea ice rheology i.e. the BBM formulation, as described in in addition to the already existing elasto-visco-plastic formulation aEVP,.

We take advantage of this single modeling framework (i.e. SI³-NEMO) in which either the BBM or the aEVP rheology formulation can be set to test the impact of rheology on the short-term predictability properties of the system. Forecast experiments are thus run both with the BBM and aEVP rheology, while all other settings are kept the same in the modeling framework – namely same atmospheric forcing, same ocean model parameters, same grid resolution and time-step – allowing for a clean comparison framework (see a summary of the main parameters and settings in Table ). The only exception is the air–ice drag coefficient (parameter rn_Cd_i in the SI³-NEMO namelist), which we have adjusted separately in the experiments with BBM and aEVP, as also done by , to establish a fair comparison framework and ensure that both configurations had a realistic mean drift over the period of interest. The air–ice drag parameter plays an important role in computing the surface momentum fluxes based on the sea ice state and the prescribed surface atmospheric forcing. Previous studies showed that the simulated drift of sea ice is sensitive to the way air-ice drag is set e.g., and recommended fitting its value according to an observed metric typically based on sea ice drift or deformation. In this study, we used a drag coefficient of 2.10×10-3 in the BBM-based experiments and 1.10×10-3 with aEVP. These values were tuned so that the mean simulated sea ice drift in the BBM and aEVP configurations – averaged over January–February–March 1997 and over the pack-ice region (Fig. ) – matches the corresponding observed mean (i.e., 5.2 km / 24 h) within ±0.2 km / 24 h, which was estimated from the EUMETSAT OSI-SAF daily gridded sea ice drift product OSI-455,. Note that since our predictability analysis presented in Sect. 3 follows a “perfect-model” approach, in which the predictability scores quantify the evolution of ensemble members relative to one another rather than against observations, the tuning of the drag coefficient does not directly affect these scores, as the same value is used across all members of a given ensemble. The qualitative results presented in this study are therefore expected to hold for different values of the drag coefficient. Our choice of values was primarily guided by the criteria of realism and fairness of comparison between the BBM and aEVP configurations.

Building on the work of , we focus on the same 1997 winter season in January–March as their study, where they implemented the BBM rheology formulation in the SI³ model and thoroughly compared the resulting sea ice scaling properties of deformation with those of the standard aEVP formulation and with the RGPS (RADARSAT Geophysical Processor System Lagrangian trajectories) observation dataset available for that year . We provide below some additional evaluation of the regional model on local sea ice drift as seen from a Lagrangian-drifter point of view (Sect. ).

Our predictability study aims to contrast the behavior of BBM and aEVP models, and thus focuses on the winter months (January to March), when friction and internal forces in the sea ice – in other words, rheology – play a crucial role in how the ice behaves, compared to later in the season when the so-called “free drift” regime may take over when the ice responds more directly to the wind forcing as a consequence of low internal stresses within the ice .

Predictability is assessed by running a set of 10 d ensemble forecasts with N=20 members initialized with perturbed sea ice states. The number of members in the ensemble is a compromise between computational cost and the robustness of the obtained ensemble statistics. We built on who showed, in a similar context (but with a different model), that their ensemble forecast statistics converged when the ensemble size exceeded 20. Note that for readability, we use the term “forecast” throughout, even though the experiments are conducted over a past period for which the actual sea ice state is known (i.e., technically a hindcast framework).

The experimental protocol is depicted in Fig. . The ensemble forecasts are initialized at different start dates sampled within the 1997 January–March season so that eight consecutive, non-overlapping 10 d ensemble forecasts are run in total over the period. These periods are labeled P1, P2, …, P8 hereafter, and their start dates are summarized in Table  and in Fig. . The sea-ice-ocean initial state of each of these periods is extracted from a single, unperturbed simulation of 3 months (hereafter the “unperturbed reference simulation”) based on the BBM rheology formulation. It is important to note that all the ensemble forecasts run in this study, using either the BBM or the aEVP rheology formulation, are initialized from exactly the same set of initial states taken from the BBM-based reference simulation and subsequently perturbed. This choice ensures that the extracted initial states include a realistic level of heterogeneities and LKFs as it would be in an operational context where data assimilation would assimilate high-resolution observations as envisaged by, e.g. or .

The reference simulation begins on 1 January, initialized with the GLORYS12 reanalysis product for both ocean and sea ice states. The first ensemble forecast run over P1 (start date on 16 January) is thus started after a spinup of 15 d. Given the rapidity with which the dynamics of sea ice evolve in the BBM-based configuration, this short spinup was enough for most sea ice variables, as will be shown by the results of this study. Only for sea ice thickness, we have observed in our results some indications that the modeled thickness had not reached its equilibrium regime, even though it does not limit our ability to draw some conclusions regarding predictability (as discussed in Sect. ). Regarding the ocean state, the short spinup may similarly result in some adjustment of ocean currents; however, given that our study focuses on short-term predictability (<10 d) in winter conditions with high sea ice concentration covering the Arctic, this is unlikely to significantly affect our results. Under such conditions, internal ice stress is known to dominate the momentum budget and wind forcing accounts for the majority of sea ice drift variance, making the ocean current adjustment a second-order effect compared to the sea ice dynamical response to atmospheric forcing .

Ensemble scores are finally computed from the ensemble forecast to assess the predictability horizon in the BBM-based and aEVP-based configurations. The ensemble scores are all computed from hourly-averaged model outputs unless stated otherwise. For this reason, in our results, the time indication t0 corresponds to the state of the model averaged over the first hour of simulation (which is not strictly equivalent to the initial state, but close enough to make the approximation, except where explicitly noted in the text).

The initial states sampled from the unperturbed simulation are perturbed to initialize the ensembles with positional errors and mimic possible misfits in the position of the sea ice features at initial time in an operational context. We do so by generating maps of random displacements Δx(x,y), Δy(x,y) that are then applied to perturb consistently the initial condition of all the sea ice variables (i.e. using the same maps of displacements for all the variables). Compared to more standard perturbation methods, which usually apply Gaussian perturbations to the model variables in a specific modal subspace, (Empirical Orthogonal Functions, singular vectors, bred vectors, etc.), the proposed method has the originality to produce non-Gaussian perturbations of the geophysical fields through Gaussian displacement perturbations. It is particularly relevant in the context of this study, where we aim to investigate specifically the sensitivity of the system to small displacements in the location of sea ice structures (LKFs, leads, etc) rather than to large amplitude variations in the sea ice fields.

In practice, we use the Lu-generator python package to generate and apply these perturbations to the SI³ initial sea ice states. In this study, only the sea ice state is perturbed; the ocean state is left unperturbed. While the same displacement maps could in principle be applied consistently to ocean variables, this would require additional constraints to avoid displacing water masses beyond bathymetry boundaries (analogously to the coastal masking applied to sea ice, as described below). The simpler choice that is made here is to only perturb the position of the sea ice features with respect to the atmospheric forcing and the ocean underneath can be viewed as representative of the inconsistencies that may arise in the atmosphere–ice–ocean momentum balance in operational systems, when sea ice and ocean states are not corrected consistently by data assimilation.

We generate a set of N=20 maps for Δx(x,y) and Δy(x,y), consisting of normal isotropic random vectors with a spatial correlation scale of 500 km (about 1/5th of the size of the Arctic basin) and a standard deviation of 1, 10, or 50 km, corresponding to the 3 amplitudes of displacement (small/medium/large) that will be used in the experiments. In practice, for better comparison, we use the same sample of 20 displacement maps to initialize all the ensemble experiments (all start dates and all three amplitudes), with a simple rescaling of the standard deviation for each amplitude. The “small”, 1 km perturbation is scaled to about 1/10th of the size of a grid cell in our system, to represent a lower bound error, where initial sea ice features are only very slightly displaced relative to the system resolution. On the other hand, the “medium” and “large” perturbations (10 and 50 km resp.) represent shifts of about 1 (resp. 5) grid cells on average. We will comment further on the amplitude of these initial perturbations when analyzing the different ensemble scores and relate them to existing errors in the current operation systems for comparison, when this information is available in the literature.

An example of the resulting perturbed initial states is shown in Fig.  for the concentration and the U-component of the drift, plotting the unperturbed fields (left column) and the difference between two perturbed members (right columns). Leads, LKFs, and patterns of positive/negative drift in the initial fields are slightly shifted and distorted between the two ensemble members, in order to take into account some uncertainty in their exact location at initial time. This positional uncertainty is by design scaled to the imposed displacements. Note that the perturbations are applied everywhere in the domain, except over land and at and near the coast, where they are damped to zero to avoid displacing the sea ice unrealistically at the coast and over land. The damping coefficient is set to zero at the coast and grows exponentially offshore to 1 with a characteristic distance of about 25 grid points (about 250 km).

Our perturbation method does not enforce local mass conservation as it only applies local random displacements on the x and y directions. But these perturbations are only applied to the initial state, where uncertainty in the initial mass is a physically reasonable assumption. Moreover, those displacements are applied consistently across all sea ice variables, ensuring that a given physical feature (for example an open lead) is displaced or distorted identically in all variables in which it appears (e.g. sea ice concentration, thickness, ice drift, etc.). This stands in contrast to previous studies that perturbed only a single sea ice variable e.g. sea ice thickness in , sea ice cohesion in , and.

We first focus on the predictability of the position of the sea ice edge. The sea-ice edge marks the boundary between the ocean covered with ice and the open ocean. As such, it is a widely used proxy for sea-ice extent and its variability in climate and seasonal prediction studies e.g.,, and at shorter lead times it is a routinely-evaluated forecast product from operational sea-ice prediction systems e.g.,. In this study, based on the ensemble forecast experiments, we can compute a probabilistic version of the Integrated Ice-Edge Error IIEE,, namely the Spatial Probability Score applied to the sea ice edge thereafter SPS,. It is defined as: 1SPS=∫x∫y[P[c>0.15](x,y)-P[c>0.15]ref(x,y)]2dxdy where it represents the spatial integral of the square difference between P[c>0.15](x,y) the probability of having a concentration greater than 0.15 at a given location (x,y) in the ensemble forecast, and P[c>0.15]ref(x,y) the same probability but for a given reference. We use the usual 0.15 concentration threshold to define the location of the ice edge, as in, e.g., . The probabilities P[c>0.15] and P[c>0.15]ref are estimated from the discretized frequency of the event. Since we follow a perfect model approach, the reference is taken alternatively as a member of the ensemble and P[c>0.15]ref takes the value of 0 or 1. P[c>0.15] is computed considering the 19 remaining members of the ensemble and can take a continuum of values between 0 and 1. Examples of the corresponding probability maps are depicted in a subregion near Svalbard in Fig.  and will be commented on in more detail in the following.

Our method of perturbing the initial state acts consistently on all sea ice fields and not specifically on the ice edge. An example is given in Fig.  to illustrate how the initial perturbations of concentration, drift, thickness, etc., translate into an ensemble spread in the position of the local sea ice edge in a subregion near Svalbard. Overall, the initial spread in the position of the sea ice edge is consistent with the scaling of the positional displacements applied to the sea ice state: when the perturbation is scaled to 1 km (about 1/10th of the size of the model cell), the sea ice edge shows almost no spread in its local position (Fig. a). For a perturbation scaled to 10 km, the edge of the sea ice is spread locally by a few grid cells between the ensemble members (Fig. b). In the 50 km case (Fig. c), the position of the sea ice edge can differ by up to 15–20 grid cells locally (up to 200 km).

Integrated across the entire domain, the initial spread between members, quantified by the SPS score in Fig. , ranges from 0.15 to 47×104 km2 depending on the initial date and ensemble members. It should be noted that the largest initial errors we generate in the SPS in this study are of the same order of magnitude as the practical initial errors in the coupled climate systems (atmosphere–ice-ocean) of the subseasonal-to-seasonal (S2S) database investigated by , where the initial error ranges between 20 and 70×104 km2 and their climatological reference is about 55×104 km2. In their climate-coupled setups, the initial error in the sea ice edge is highly influenced by the initialization strategies of the 3-D ocean (which differ from one coupled system to another) and can lead to relatively large errors, close to (or sometimes even larger than) the climatological reference. Regional operational sea ice forecasting systems, such as NeXtSIM-F can do better to initialize the sea ice edge in a single sea ice configuration forced by the operational regional ocean product TOPAZv4 . For reference, the initial error in the IIEE (which is the deterministic version of the SPS) is given to about 7–10×104 km2 for the January–March period of year 2019 in , which falls again in the range of the initial errors we have generated on the sea ice edge. Overall, we thus verify here that the approach we propose in this paper generates initial errors in the SPS whose amplitudes range from those typically observed in current climate and operational sea ice forecasting systems to very small local errors in the ice-edge position (kilometer scale, i.e., smaller than a model grid cell). This makes us able to study the sensitivity of the sea ice system to initial errors.

The evolution of the SPS error in the ensemble forecasts is plotted as a function of lead time, for the BBM and aEVP experiments separately (Fig. ). Each plotted curve corresponds to the SPS score for one of the eight forecast periods, computed by taking one member of the 20 ensemble members as the pseudo-truth (resulting in a total of 8 periods × 20 scores = 160 curves in each panel of Fig. ). In all experiments, we find that the SPS error systematically decreases with time (or remains nearly constant for the smallest initial perturbations), indicating that the ensemble members tend to converge towards a more similar sea ice edge position within the 10 d forecast period (illustrated in Fig. b). Contrary to what might be expected from a chaotic behavior, no exponential growth of the error is observed for this metric. Instead, the initially-introduced positional errors of the ice edge are damped with time. The largest initial errors are typically reduced by about half within ten days of forecast, while the smallest perturbations – on the order of one-tenth of a model grid cell – remain nearly constant throughout the forecast period. However, the impact of initial errors persists through the 10 d forecasts, with the large initial errors leading to larger SPS errors after 10 d than the small initial errors. In that sense, some predictability in the position of the sea ice edge persists until the end of the 10 d. This behavior of the ensemble members to converge toward a similar sea ice edge position demonstrates the strong constraint exerted by the boundary conditions of the sea ice system on the ice edge position. In our configuration, only the sea ice is perturbed at initialization. The atmospheric forcing remains unperturbed: the same exact atmosphere is seen by all the ensemble members. The ocean component is also initially unperturbed but is coupled to the perturbed sea ice. However, at its resolution (1/4°, ∼10 km in the Arctic), it does not seem to respond sufficiently to the local initial displacements of the ice-edge position to induce a growing spread of the ocean-ice solutions in the different ensemble members. However, it is possible that a higher-resolution ocean model – with more active mesoscale turbulence – could lead to a different behavior. Overall, these results indicate that the short-term evolution of the SPS in our simulations reflects primarily the deterministic adjustment of the ice edge position to the imposed oceanic and atmospheric boundary conditions (in common to all the ensemble members). In other words, we find that at the resolution of our system, forecast performance on the sea ice edge position depends more strongly on the quality of the external oceanic and atmospheric conditions than on an accurate initial position of the sea ice edge. This is also why the SPS error was found to grow with time-lag in fully coupled atmosphere-sea-ice-ocean systems initialized with perturbed atmosphere and Sea Surface Temperature e.g..

Finally, no significant differences are found in the predictability behavior of the SPS between the two rheologies explored in this study (Fig. ). It suggests that, for short-term forecasts, the evolution of the sea ice edge position is more constrained by thermodynamic interactions with the underlying ocean and the above atmosphere than by internal dynamical processes.

In this section, we extend the analysis to the predictability of some of the main dynamical and thermodynamical properties of the pack ice: sea ice concentration, thickness, drift, and deformation. Leads, pressure ridges, and high-deformation linear features are manifestations of the heterogeneity of winter fields that remain a challenge to accurately forecast e.g.. We focus on the pack ice region as delimited in Fig. , excluding on purpose the coastal areas and the Marginal Ice Zone (MIZ), where landfast ice and small ice floes, respectively, might behave differently than the central pack ice with respect to predictability and would require adequate metrics. We evaluate here the forecast accuracy using the Continuous Ranked Probability Score (CRPS; e.g., ), a widely-used metric in atmospheric and oceanic ensemble forecasting e.g.,. The CRPS provides a spatially-integrated measure of the grid-point mismatch between a probabilistic forecast and a reference value. It is defined as the expected value of Δ, calculated at each grid point as: 2Δ=∫-∞+∞|F(m)-Fref(m)|dm and in practice the expectation of Δ is approximated here by its spatial average over the region of interest (cf. Fig. ). F is, at each point in the model grid, the cumulative distribution function of the predicted physical quantity m, and Fref the reference function to compare with. In our perfect model ensemble approach, the reference value – or pseudo-truth – is alternately taken as each individual ensemble member, while the remaining 19 members are used to estimate the forecast distribution. F is defined as a stepwise function that increases by 1/19 at each of the 19 forecast values. Fref is a Heaviside function that varies from 0 to 1 at the value of the reference member. Thus, Δ can be seen as the area between the two cumulative distribution functions, and the CRPS can be interpreted as a generalized absolute error for the ensemble forecasts, accounting for both the bias and the spread of the ensemble and sharing the same unit as the forecasted physical quantity. Note, however, that in the perfect-model context where the pseudo-truth is taken from the ensemble itself, the CRPS primarily reflects the ensemble spread, or in other words the forecast uncertainty.

In the following, we investigate the evolution of the CRPS for sea ice concentration, thickness, drift, and deformation on average and individually for the eight 10 d forecast periods P1, …, P8. The purpose is to quantify the evolution of the ensemble spread, i.e. the forecast uncertainty, in positioning accurately the heterogeneous features of the pack ice. We first investigate the results based on the Elasto-Brittle (BBM) experiments, and then we contrast these results with those based on the Elasto-Viscous (aEVP) experiments.

In this section, we complement the previous CRPS analysis, which evaluated the model skills in an Eulerian framework, by now considering predictability from a Lagrangian perspective. We showed in the previous section that, at the grid-cell level, the drift of sea ice becomes fully decorrelated between the ensemble members within a few days (1–5 d) in the BBM model, while in the aEVP configuration the members of the ensemble tend to converge towards a more similar and spatially smooth solution. Here, we document how these contrasting behaviors translate into the divergence of Lagrangian trajectories computed from the simulated sea-ice drift fields of the two configurations. Such Lagrangian metrics might be more meaningful in an operational context of search-and-rescue, for example. They also allow us to relate our approach more directly to the studies of and .

We make use of the virtual buoys generated from all the ensemble forecasts (i.e. the eight time periods and three perturbation amplitudes) with the two model configurations, as described in Sect. . An example of these virtual buoy trajectories is given in Fig.  and some statistics on the 101 ensembles of trajectories are provided in Fig. . More specifically, the figure displays the temporal evolution of the ensemble spread, measured by the area of the ellipse defined by the 95 % confidence contour of the distribution (assumed to be bivariate normal). Note that the range of the y axis is ten times larger in Fig. a than in Fig. b. The spread between the virtual buoys grows with lead time for both BBM and aEVP models, as expected from passive tracers advected by velocity fields that themselves differ. Lagrangian trajectories accumulate differences at every time step because they are advected by distinct velocity fields in each ensemble member. Even in the case where the velocity fields of different ensemble members become more similar with lead time and the level of heterogeneity decreases (aEVP case), the Lagrangian trajectories still diverge because they integrate past differences along their paths. However, the statistics in Fig.  confirm what is already apparent from the example cases (Figs.  and ): the spread of the virtual buoys grows significantly larger in the BBM configuration than in aEVP. After 10 d, the ellipse area is on average around 90 km2 in the ensembles initialized with the larger perturbations (STD 50 km) and about 60 km2 in the ensemble initialized with the smaller perturbations (STD 1 and 10 km). By contrast, the virtual buoys from the aEVP forecasts have on average spread roughly an order of magnitude less: about 10 km2 with the largest initial perturbation, while below 1 km2 with the smaller initial perturbations. For reference, the dispersion found after 10 d in previous studies focused on the uncertainty caused by the surface wind or by some model parameters is approximately 800 km2 and 200 km2, respectively, in (defined by the 99 % confidence ellipse in their case) and 190 km2 in from the wind uncertainty scaled to a variance three times as small as in. Our results thus confirm previous work that initial uncertainty has quantitatively less impact on the spread of Lagrangian trajectories than uncertainty in the wind forcing at least when its variance is scaled as in , and. However, we also find that in the BBM configuration the effect of initial positional uncertainty on buoy dispersion is roughly an order of magnitude larger than in the aEVP configuration, making it comparable in magnitude to wind- and model-induced uncertainty. This implies that initial-condition uncertainty – when interacting with a highly sensitive rheology such as BBM – constitutes a non-negligible source of trajectory spread. In operational contexts such as search-and-rescue, where all sources of uncertainty accumulate along Lagrangian paths, this contribution may thus have important practical implications.

Our study proposes an ensemble framework based on the SI³+NEMO sea ice ocean model with a horizontal resolution of 1/4° (∼10 km in the central Arctic) to investigate the predictability of the sea ice system on daily-to-weekly timescales, focusing on the sensitivity to initial uncertainty in the position of sea ice features. We compare this sensitivity for two model configurations based on different sea ice rheology formulations: the elastic–viscous–plastic (aEVP) formulation and the more recently developed brittle Bingham–Maxwell (BBM) formulation . The implementation and evaluation of both configurations were presented in for the same 1997 winter season. Our study additionally provides a brief evaluation of the modeled sea ice drift against available Lagrangian sea ice IABP drifters to confirm that both adequately reproduce the observed drift and provide an appropriate framework for comparing their sensitivity to initial conditions.

Our approach is based on 10 d ensemble forecasts of N=20 members over eight non-overlapping time periods in January–April 1997. Those ensemble forecasts are initialized with perturbed initial states where Gaussian perturbation displacements Δx(x,y), Δy(x,y) in x and y directions are generated and applied consistently to all the sea ice variables, resulting in non-Gaussian perturbations of those variables to mimic mispositioned and distorted sea ice features (leads, LKFs, etc) that can arise at initialization in an operational system. The perturbations are scaled to three different magnitudes of displacement (STD of 1, 10, and 50 km), and exactly the same perturbed states are used to initialize the ensemble forecasts with the BBM and aEVP rheology.

By design, only the initial sea ice state is perturbed (the ocean state and atmospheric forcing are not), in order to isolate the response of the coupled ice–ocean system to initial positional uncertainty in the sea ice features alone. These initial errors can be viewed as representative of the inconsistencies that may arise in the atmosphere–ice–ocean momentum balance in operational systems when sea ice and ocean states are not corrected consistently by data assimilation.

In that sense, we focus on an upper bound for predictability (or a potential predictability) that will, in practice, be lower when additional sources of uncertainty, such as atmospheric forcing, ocean initial state, or model parameters, are taken into account. This upper bound is nonetheless relevant in itself to characterize the behavior of the modeled sea ice, and we expect the qualitative contrasts identified between rheologies to remain relevant for operational forecasting even as quantitative predictability limits are reduced.

Potential predictability is assessed by measuring the response of the system, for a given evaluation metric, to small initial perturbations (misplacements of the order of 1/10th of a grid cell) as compared to larger errors (misplacements of tens of grid cells). We consider that the system has fully lost its potential predictability when the initial perturbations no longer have an impact on how much the ensemble solutions diverge. In practice, this happens at the lead time when the ensemble members, initialized with slightly perturbed conditions, have become as spread as when initialized with large perturbations.

This approach has been applied to several commonly-used metrics, each highlighting a different aspect of the sea-ice forecasts: (i) the Spatial Probability Score (SPS), a probabilistic integrated measure of local positional errors of the ice edge; (ii) the Continuous Ranked Probability Score (CRPS) for concentration, thickness, drift, and deformation, which provides a generalized absolute-error metric for ensemble forecasts, integrated over the pack-ice region; and (iii) Lagrangian metrics quantifying the spread of virtual sea-ice drifter trajectories generated from the ensemble simulations.

Regarding the ice edge position, our results do not show a non-linear, chaotic-like response of the ensemble forecasts to small positional uncertainties. Instead, initial errors tend to decay, reflecting a strong constraint from the imposed atmospheric forcing and the ocean's state. After 10 d, the forecasts still retain a memory of the initial error amplitude, while the ensemble members tend to converge toward a more similar ice-edge position. We found that this behavior is largely independent of rheology, indicating that ice-edge predictability in our system is primarily controlled by thermodynamic forcing rather than internal ice dynamics. In that regard, improving operational forecasts of the sea-ice edge is unlikely to be achieved through a changed rheology or through more accurate assimilation of its observed initial position alone, but rather through better initialization of the underlying ocean and more realistic atmospheric forcing – at least at the present model resolution. Our results do not exclude, however, that at higher resolution, a more turbulent ocean circulation that includes better-resolved mesoscale features may introduce additional nonlinearity in the coupled ice–ocean response, potentially increasing the sensitivity to initial position errors.

Unlike the above results for the sea ice edge position, the CRPS metric for concentration, deformation, and drift displays a strong non-linear, chaotic-like sensitivity to initial positional errors when using the BBM-based model. For these quantities, predictability rapidly degrades, and the CRPS evolution loses memory of the initial perturbations after only a few days: five to ten days for concentration, one to five days for deformation and drift, and longer than ten days for thickness (as it is primarily driven by thermodynamic processes operating on longer timescales compared to dynamics). Importantly, this intrinsic limit arises even under perfect atmospheric forcing, demonstrating that sea-ice dynamics alone can set a short predictability horizon for LKFs and other dynamical features, independently of its interaction with the chaotic atmosphere. In contrast, the system based on the aEVP rheology exhibits little sensitivity to positional errors: heterogeneities are quickly smoothed out, the ensemble members converge, and the CRPS metric decreases with lead time. Although this implies higher potential predictability, it also reflects a loss of dynamical variability and a weaker representation of the observed sea-ice heterogeneity.

We have also illustrated some practical consequences of these contrasted potential predictability limits, showing that the two types of rheology produce fundamentally different uncertainty structures in both the local probability of high-deformation events and the dispersion of Lagrangian trajectories. Specifically, the BBM configuration generates large and weakly-predictable heterogeneities in the deformation field, which translate into a high probability of encountering at least one intense deformation event within 24 h (i.e. LKF formation) over large areas of the central Arctic. By contrast, the aEVP configuration produces much smoother deformation fields, leading to narrow zones of elevated risk surrounded by broad regions where the likelihood of such events remains low. Similarly, virtual-buoy experiments show that initial uncertainties in the Eulerian sea ice drift fields amplify rapidly under BBM dynamics – resulting in an order-of-magnitude larger Lagrangian spread than in aEVP after 10 d – whereas the aEVP system largely damps these initial differences.

These contrasted behaviors are not merely academic, they also matter for practical applications, such as field operations or search-and-rescue response, where understanding uncertainty is often as important as the forecast itself e.g.. A system that strongly amplifies small initial errors (as documented here for BBM) may offer lower deterministic predictability yet provides more realistic – and therefore more useful – information about the range of plausible trajectories or the local likelihood of severe deformation. Conversely, a system that smooths heterogeneity (as in aEVP) may appear more predictable and also easier to handle for technical operational purposes (e.g. data assimilation), but it risks underestimating extreme outcomes. Such contrasts reinforce the value of ensemble forecasting for sea ice: in a highly nonlinear and only weakly predictable medium, ensembles provide not only an estimate of the forecast state but also a quantification of the risk associated with user-relevant events.

While these results carry clear practical relevance, a number of important considerations regarding the scope and generalizability of our findings merit discussion. The quantitative estimates derived in this study are based on a single forecast season (winter 1997) and on a specific model configuration and spatial resolution. They should therefore be viewed as indicative rather than universal.

For example, the exact values quantifying the predictability limits for different sea ice variables derived from the CRPS scores are, strictly speaking, only representative of our 1997 winter forecast cases. We expect these values to vary somewhat from year to year due to interannual variability in wind forcing and sea ice conditions. Longer-term changes in sea ice conditions may also play a role, such as the observed decreasing trend in sea ice thickness, or the so-called regime shift, documented to occur around 2007 and references therein. Since within the elasto-brittle framework, thinner sea ice breaks up more easily as thickness influences the mechanical strength of the ice and thus its resistance to fragmentation, e.g., we expect even shorter predictability limits than those reported here for 1997 with BBM (i.e. 1–5 d for deformation and drift, 5–10 d for concentration) in more recent years within the “thinner-ice” regime. A systematic investigation of the interannual variations in predictability and their relationship with sea ice thickness changes lies beyond the scope of the present study and is left for future work.

Furthermore, our results are representative of the difference in the predictability behavior between the BBM and aEVP rheology in a model configuration at a horizontal resolution of 1/4°. The dependence of the results on resolution, and in particular the discrepancy in sensitivity between aEVP and BBM, was not explored in this study and would certainly merit further investigation, since each rheology is known to respond differently to resolution changes e.g.. Nonetheless, we expect the qualitative contrast between the two rheologies (i.e., the fact that BBM exhibits non-linear error amplification associated with LKFs while aEVP does not) to persist across resolutions, as it likely stems from a structural difference in how the two rheologies represent deformation. In contrast, quantitative metrics, such as the specific timescales of predictability loss, are likely to be more sensitive to resolution change. Furthermore, at higher resolutions, ocean dynamics may also play a growing role: the better resolution of mesoscale eddies would introduce additional variability beneath the ice, potentially acting as an extra source of uncertainty for the sea ice and thus further constraining its predictability limits. This, however, remains to be verified and quantified in future work.

Finally, note that our study remains focused on potential predictability, i.e. related solely to initial errors. This constitutes a first step toward characterizing the intrinsic behavior of the sea-ice system before accounting for additional external sources of uncertainty. Beyond intrinsic predictability, operational forecast skill is also constrained by additional sources of uncertainty. In particular the surface wind forcing uncertainty, known as a major contributor introducing its own constraints on the predictability limits of the sea ice system (known to be one to two weeks in the atmosphere; e.g., ). Surface wind uncertainty could be approached as in previous studies using a perturbation method e.g., using ensemble atmospheric analyses or forecasts e.g., or even coupling the sea-ice model to an atmosphere or atmospheric boundary-layer model, which would relax the current assumption of prescribed one-way atmospheric forcing and allow atmosphere–ice two-way feedbacks to shape the forecast uncertainty more realistically. Notably, the modeling framework used in this study is well suited to incorporate these additional sources of uncertainty, including wind forcing and model parameters, and to systematically compare their respective impacts within a unified framework, opening promising avenues for future investigation.