Skillful sea ice drift forecasts are crucial for scientific mission planning and marine safety. Wind is the dominant driver of ice motion variability, but more slowly varying components of the climate system, in particular ice thickness and ocean currents, bear the potential to render ice drift more predictable than the wind. In this study, we provide the first assessment of Arctic sea ice drift predictability in four coupled general circulation models (GCMs), using a suite of “perfect-model” ensemble simulations. We find the position vector from Lagrangian trajectories of virtual buoys to remain predictable for at least a

More than 120 years has passed between Nansen's empirical “rule of thumb” about sea ice drifting

Initialized predictions inevitably come with errors and uncertainty. In this work, we differentiate between

Recent studies have assessed both the current skill of sea ice drift forecasts and the potential to improve them, mostly for the Arctic Ocean.

In these forecast skill assessments, all aforementioned sources of errors and uncertainty are imprinted on the forecast accuracy. While the forecast skill horizon can be pushed towards longer lead times by more sophisticated data assimilation and forecast calibration methods, more efficient and more accurate numerical integration schemes, and improved model physics, the uncertainty due to the sensitive dependence on the initial conditions is an inherent feature of the climate system and introduces an upper limit for forecasting skill (see, for instance,

While we are not aware of studies about the potential predictability of sea ice drift, the predictability of various other sea ice properties has been assessed in several recent studies, presented in the following. These are all based on data from the Arctic Predictability and Prediction on Seasonal-to-Interannual TimEscales (APPOSITE) project (see Sect.

Sea ice extent and sea ice volume were found to be predictable for up to 3 years in four coupled general circulation models (GCMs) by

Note that these studies use different metrics for predictability, tailored to the predictand in question. Therefore, the term “predictable for up to” not only is influenced by sample size, as mentioned above, but also implicitly includes choices on the metric and climatological normalization (see Sect.

The substantial derivative, that is, the material change in sea ice momentum with time, can be described by

While the wind is the primary driving force setting the ice into motion, the ocean drag mainly acts to counteract the wind-induced motion. This simplified relation does not hold where notable (sub-)surface ocean currents occur. Nevertheless, particularly in the open ocean and on the timescales of days, more than two-thirds of the ice velocity variance is explained by geostrophic winds

It thus appears plausible that the predictability of near-surface wind determines the predictability of ice drift to a large part. However, ocean drag, which is influenced by ocean currents, and the rheological response, which is influenced by ice thickness and concentration, also affect the persistence of and variability in sea ice drift and thus its predictability. Given that ocean currents as well as ice thickness vary on longer timescales than atmospheric winds, we hypothesize that the motion of sea ice is more predictable than the (near-surface) wind field. Moreover, as atmospheric circulation patterns, ice thickness, and ocean currents vary regionally and seasonally, we expect to find regional and seasonal differences in ice drift predictability. The main goals of this work are testing these hypotheses and quantifying the relative importance of the described effects.

With this study, we provide the first estimates of initial-value predictability of Arctic sea ice drift in global climate models. We use a suite of perfect-model ensembles following a common experimental protocol, which further enables an assessment of the model diversity regarding inherent ice drift uncertainty. We present the topic from both a Lagrangian perspective, i.e., the predictability of a time-dependent position of a virtual buoy, and an Eulerian point of view, i.e., the predictability of ice drift vectors at a fixed position, and explore possible explanations for regional and seasonal differences while considering lead times from days to a few months. The Eulerian perspective allows us to compare ice drift predictability directly with corresponding wind predictability, and thus to quantify if and to what degree ice drift is more predictable than the wind. Our results will help to clarify how different processes act on sea ice drift predictability and put current forecast skill into perspective.

This paper is structured as follows. In Sect.

As part of the Arctic Predictability and Prediction on Seasonal-to-Interannual TimEscales (APPOSITE) project, perfect-model experiments have been carried out with seven general circulation models

AWI-CM1

GFDL-CM3

HadGEM1.2

MPI-ESM

Simulations from MPI-ESM and GFDL-CM3 were submitted to the Coupled Model Intercomparison Project Phase 5 (CMIP5) in the same configuration as for the APPOSITE project. Note that AWI-CM1 and MPI-ESM share the same atmospheric component, ECHAM6. In some other publications, AWI-CM1 may be referred to as E6F, a temporary former name.

For each of the selected models, a control simulation of at least

These control simulations provide statistical properties of the individual model climates. Depending on the model, up to

We use daily averaged model output for sea ice velocity, sea ice concentration (SIC), and sea ice thickness (SIT) from all four models and near-surface (

Brief summary of the APPOSITE simulations used in this study. The columns are, from left to right, model name, number of control simulation years (

We calculate kinematic trajectories for virtual buoys (targets) from the velocity fields with a numeric integration method of second-order accuracy. Trajectories

Assuming that the given initial-value problem fulfills the requirements for the Picard–Lindelöf theorem, unique analytical solutions are given by

As AWI-CM1 computes on an unstructured triangular grid, we implemented the integration method for that type of mesh and applied it to curvilinear and rectilinear grids by cutting the quadrilateral boxes into two adjacent triangles. The method uses an adaptive time step which ensures that no triangular elements are skipped during one time step, thus avoiding a loss of velocity information. We use barycentric coordinates for the spatial interpolation between nodes and a common linear interpolation in time. The trajectory tool is a side product of this publication and made openly available in the R package “spheRlab” (

Map of all initial positions for trajectory computation (red crosses and circles). The initial positions with a solid red circle constitute the common subset of initial positions for all models after the filtering process outlined in Sect.

We use 347 initial positions distributed evenly over the Arctic Ocean (see Fig.

In this study, we determine and analyze the potential predictability of Lagrangian target positions and Eulerian velocity vectors. We express the predictability as the ratio of the uncertainty in the ensemble mean of the initialized prediction to a reference ensemble constructed by drawing randomly from the climatological background (see below). It is therefore necessary to measure the uncertainty in an ensemble prediction. For scalar quantities, such as temperature or ice speed, the normalized root mean square error (NRMSE; see

To account for the bivariate nature of velocity vectors, we describe ensemble spread at a given lead time by the corresponding covariance matrix

For the normalization, we construct a climatological reference ensemble by drawing randomly from the control run. For a specific initial position and season from AWI-CM1, for example, we compile an ensemble of the same size as the initialized predictions (i.e.,

The normalized uncertainty

We obtain a time series of normalized uncertainty for the whole common subset by averaging over the index

Note that potential predictability is often defined via

We follow the same approach for the position vectors, except that these vectors in geographical coordinates are projected onto a local Cartesian coordinate system (with units of

Here we present the main characteristics of climatological variables related to sea ice momentum and motion, namely sea ice thickness; ice velocity and speed; and, where available, wind. We further present key aspects of the interannual ice drift variability, based on the calculated trajectories. We focus on the results of January and July, as the ensemble predictions were initialized in these months.

Relative frequency distribution for ice drift speed

Maps of average ice thickness for the months of March and September are presented in

The aforementioned order also holds for ice thickness (see Table

For the two models providing wind data, we investigate the climatological annual cycle of the relation of ice speed and wind speed on the analysis grid. For AWI-CM1, there is a pronounced phase shift of monthly mean ice speed and wind speed: while ice speed is lowest in April and maximal in August, wind speed is lowest in June and July and peaks in the cold season between August and February (Fig.

The differences between all four models regarding the climatological ice drift speed, as well as the differences between AWI-CM1 and HadGEM1.2 regarding the magnitude of the climatological wind forcing, already hint at potential differences in the growth of uncertainty in ice drift predictions between models, seasons, and regions.

Annual cycles of monthly mean wind and drift speeds on the common subset of initial positions. The numbers indicate the respective months. Please note the strongly different scaling on the axes.

We now consider the trajectories from the control simulations. For each initial position, we derive the orientation and axis ratio of the variance ellipse for the climatological distribution of

Variance ellipses (here scaled for showing the 20

The same as Fig.

The temporal evolution of the spatially averaged climatological reference uncertainty used for normalization (obtained by bootstrapping; see Sect.

We begin with the analysis of the target position predictability, measured by the normalized spread (uncertainty) of the point clouds that correspond to individual lead times of the trajectory ensembles. We use the term uncertainty interchangeably with normalized uncertainty. As explained above, an uncertainty of 0 implies perfect predictability, whereas an uncertainty of 1 implies the complete loss of predictability.

The spatial characteristics are presented for a 45

The uncertainty exhibits smooth spatial gradients in all models (Fig.

There are distinct regions with significantly higher uncertainty for July initializations than for January initializations in AWI-CM1, GFDL-CM3, and HadGEM1.2 (Fig.

Normalized uncertainty in target position predictions for all initial positions that fulfill the selection criteria 1–3 (see Sect.

Constraining the examined region to the common analysis grid, we find that the spatially averaged normalized uncertainty has qualitatively the same temporal evolution in all four models: a slow increase in uncertainty in the first days, a relatively steep increase within a roughly 4-week lead time, and then a deceleration of normalized uncertainty growth (Fig.

Despite the qualitatively different spatial distributions, the averaged normalized uncertainty is very similar across AWI-CM1, GFDL-CM3, and HadGEM1.2 (see Table

None of the models reaches the climatological saturation value for target position uncertainty within a 90

Regarding the last point, we calculated trajectories for AWI-CM1 with a

Instead of following virtual ice parcels on Lagrangian trajectories like in the previous section, we perform a similar analysis for sea ice drift velocity vectors at fixed positions, which enables a direct comparison with the near-surface winds at the same locations (see Sect.

As for the Lagrangian point of view, all models also exhibit spatial gradients for uncertainty for the drift velocity vectors (not shown). These gradients are smooth, though intermittent over time, in that qualitative regional characteristics change within days. Significantly larger uncertainties for summer initializations can only be detected in HadGEM1.2, as comparably large interannual variability renders any differences in the mean uncertainties statistically insignificant for AWI-CM1 and GFDL-CM3.

In contrast to the Lagrangian perspective, where a considerable level of predictability appears to remain at comparably long lead times, from the Eulerian perspective the uncertainty reaches the climatological uncertainty for all models in both seasons within 3 to 4 weeks (Fig.

Mean normalized uncertainties on the common set of initial positions at a 45 and 12 d lead time for the Lagrangian (LAGR) and Eulerian (EULE) perspective, respectively, with 1 standard error.

As trajectories are obtained by applying a time integral to the velocity field (Eq.

The initial normalized uncertainty in the lagged trajectories matches the uncertainty in the Eulerian velocity vectors at the respective original lead time very closely (Fig.

The uncertainty in the lagged Lagrangian trajectories then grows more slowly than for the Eulerian velocity vectors, bounded below from the uncertainty in the non-lagged trajectories. Figuratively speaking, the time integration leads to an “inheritance” of the low uncertainty from early time steps for the Lagrangian trajectories, whereas subsequent time steps in the Eulerian perspective do not transport information in time. As displacements of buoys within a few time steps are small compared to the scale of spatial coherence of the ice velocity field in the analyzed models, the Eulerian and Lagrangian perspectives tell a similar story – yet at a different pace. This feature may raise confidence that properties of the Eulerian ice velocity predictability can be partly transferred to the Lagrangian target position predictability and vice versa.

Finally, this experiment displays how an initial uncertainty in the velocity field influences the growth of uncertainty in the target position, which has practical consequences for operational forecasts; the smaller the initial uncertainty in the ice velocity, the later the uncertainty growth rate of initialized forecasts attains the climatological growth. This underlines the important role of data assimilation.

Lagged-initialization experiment with AWI-CM1: we set virtual buoys at the same initial positions as before but delay the release by 4, 7, 10, 15, and 20 d. The colored lines show the normalized uncertainty on the non-lagged time axis. The dashed lines show the uncertainty for the Eulerian perspective and the dotted line the uncertainty in non-lagged Lagrangian trajectories (“Lag 00”). The initial uncertainty in the lagged Lagrangian trajectories matches closely the uncertainty in the Eulerian perspective at the respective time of buoy release.

In summary, we find that the spatial distribution of the normalized target position varies between the models and, within the same model, also between summer and winter initializations. For the Lagrangian perspective, normalized uncertainties are not saturated within the considered time periods, although an experiment with longer integration times shows that this happens at even longer lead times. The uncertainty in Eulerian velocity vectors on the other hand is saturated within 4 weeks for all investigated models while exhibiting intermittent spatial characteristics. A lagged-initialization experiment highlights the close connection between both points of view. It furthermore illustrates how the target position uncertainty is inherited from the Eulerian velocity vector uncertainty. In the following, we examine what drives the observed regional and seasonal differences.

Wind forcing is known to be one main driver of ice drift variability, particularly in the open ocean, and it is therefore likely to play a key role in ice drift predictability. The APPOSITE data set includes daily average near-surface wind velocities for two of the considered models, AWI-CM1 and HadGEM1.2, of which we make use in this section. We calculate the normalized uncertainty for the two-dimensional near-surface wind vectors in the Eulerian perspective like for the ice velocities before.

Indeed, we find a close correspondence of the temporal evolution of wind and ice drift vector uncertainty (Fig.

Normalized uncertainty in near-surface wind vectors in Eulerian perspective for AWI-CM1

The spatial distribution of wind vector uncertainty, albeit being intermittent as well, matches closely the patterns of the uncertainty in ice drift vectors (not shown). Moreover, there is a significant positive correlation of wind vector uncertainty and ice vector uncertainty at most initial positions in both models and both seasons, again taking the available number of initializations per initial position as the sample (Fig.

Here, we examine the relation of initial ice thickness and the uncertainty in the target position (Lagrangian perspective). For each initial position, we calculate the correlation coefficient for initial ice thickness and the target position uncertainty at a

Correlation of target position normalized uncertainty at

For July, there is virtually no significant correlation of initial ice thickness and uncertainty in all models; small patches with significant differences cover barely more than

While the temporal evolution of spatially averaged uncertainty is qualitatively similar across the models, the spatial characteristics, the quality of seasonal differences, and the response to initial ice thickness are not. We attribute this to different representations of the forces acting on the ice, as well as different sea ice physics implementations. This makes it difficult to generalize our results but stresses the importance of using not one but a variety of models to study the predictability of the climate system.

The local correlation of Eulerian wind vector uncertainty to ice drift uncertainty in HadGEM1.2 and AWI-CM1 and the fact that ice drift is barely more predictable than wind are strong indications of a dominant influence of atmospheric variability on ice drift predictability. Regarding our hypothesis of sea ice drift being less uncertain (that is, more predictable) than wind vectors, we find ambiguous results. Slightly enhanced predictability of ice drift versus wind is found for AWI-CM1 in both January and July for up to at least a 2-week lead time, but this is less clear for HadGEM1.2, raising the question of what drives possible differences in the relation of ice drift and wind predictability between these two models. As presented in Sect.

It is unfortunate that no daily near-surface wind data are available for GFDL-CM3 and MPI-ESM. As a consequence, it is not possible to examine for example if the divergence of atmospheric states in MPI-ESM is delayed compared to the other models, which could explain the increased ice drift predictability compared to the other models (see Figs.

While monthly mean ice speeds for January and July did not exhibit noteworthy linear trends, we again mention that the models were not in an equilibrium state after the spin-up period. This might have a more meaningful effect on possible future studies on the relation of ice speed (predictability) and the mean ice state.

Another data-related caveat is that there are no daily (sub-)surface ocean velocity data available for the four examined models within the APPOSITE data set, so we cannot offer a view on the results in regard to the variability in ocean currents. Given that ocean drag is an important forcing term for sea ice motion on the timescales considered in this study, this should be examined in future studies.

One shortcoming of analyzing Lagrangian trajectories is the loss of virtual buoys close to the ice edge. Therefore, owing to the chosen trajectory selection, the variability in the marginal ice zone, which is one very dynamic part of the ice cover, cannot be represented adequately.

Furthermore, there are other choices for quantifying the uncertainty or information (or loss thereof) contained in an ensemble prediction. We also performed large parts of the analyses using two other measures for uncertainty, namely the normalized root mean square error (NRMSE; see

We suggest that future studies should quantify the predictability of specific (scalar) components of the ice drift separately. For example, the drift speed could be the aspect of ice drift that is the most sensitive to the initial ice thickness and could thus reveal such a dependence more readily. It would also be interesting to account for the predominant wind direction in coastal areas to examine if ice strength (and thus thickness) plays a larger role in determining drift uncertainty when wind drag is directed towards the shore, compared to winds directed offshore or parallel to the coast.

In addition to that, the significance of ice thickness anomalies for ice drift uncertainty can be scrutinized more thoroughly following the approach of

In this work, we determined and analyzed the uncertainty in initialized Arctic sea ice drift predictions in four global climate models. We made use of a set of perfect-model experiments carried out in the APPOSITE project and calculated trajectories of virtual ice floes with a newly implemented open-source trajectory tool.

For the Lagrangian target position, spatial gradients of the uncertainty develop within a few days. Spatial patterns vary between the models and from summer to winter. The spatially averaged uncertainty for a common subset (across all four models) of initial positions does not reach the climatological saturation value for at least

While the wind variability explains large fractions of the uncertainty in the ice velocity vector, the initial ice thickness as a proxy for ice strength and internal forces was found to play a statistically significant but quantitatively small role regarding the target position predictability. There remain open questions, particularly about the origin of the spatial patterns of uncertainty and the summer-to-winter variation and about the role of (sub-)surface ocean currents, that call for additional studies on the predictability of sea ice drift.

We estimate the uncertainty in the ensemble mean of Eulerian velocity vectors by the spectral norm, that is, the square root of the largest eigenvalue, of the covariance matrix in

Let

For the Lagrangian target positions we follow the same approach, except that we project the (spherical) geographical coordinates onto a (Cartesian)

Climatological monthly mean sea ice thickness for January (top) and July (bottom), derived from the control run.

Maximum and selected percentiles for sea ice thickness on the common subset of initial positions, derived from the control simulations.

Temporal evolution of climatological uncertainty, i.e., the length of the semi-major axis of the variance ellipse. Note the square root horizontal axis.

Additional simulation for AWI-CM1 with longer lead times. The time series shows the normalized uncertainty for the initial positions on the inset map. The asterisk marks the lead time when the climatological saturation value is attained for the first time (one-sided

Maps of the correlation coefficient of the normalized uncertainties in Eulerian ice drift and near-surface wind vectors at

APPOSITE data are available at

HFG and SFR planned the research. SFR implemented the trajectory tool and performed the APPOSITE data processing and the trajectory calculations. SFR and HFG analyzed, interpreted, and discussed the results. SFR wrote the manuscript, with contributions from HFG.

The contact author has declared that neither of the authors has any competing interests.

Publisher's note: Copernicus Publications remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

We thank the two anonymous referees for their helpful and constructive suggestions and feedback, which helped to improve this paper. This work was carried out as part of the Young Investigator Group Seamless Sea Ice Prediction (SSIP), funded by the Federal Ministry of Education and Research of Germany (grant no. 01LN1701A). Data storage and computational resources were kindly provided by the German Climate Computing Center (DKRZ). We thank the coordinators of and contributors to the APPOSITE project for making their data set available and Ed Blanchard-Wrigglesworth for valuable discussions during the early stage of the project.

This research has been supported by the Bundesministerium für Bildung und Forschung (grant no. 01LN1701A). The article processing charges for this open-access publication were covered by the Alfred Wegener Institute, Helmholtz Centre for Polar and Marine Research (AWI).

This paper was edited by Jari Haapala and reviewed by two anonymous referees.