## 1. Introduction

Over the last few years, interest in Arctic sea ice predictability has grown mainly as a consequence of the recent decline in Arctic sea ice. Stakeholders include groups as diverse as resource extraction, shipping, and local traditional hunting industries. The extreme melt in 2007 triggered an organization of yearly summer forecasts called the Sea Ice Outlook project under the auspices of the Study for Environmental Arctic Change (SEARCH). The outlook project has become an international effort to provide a community-wide summary of the expected September Arctic sea ice minimum, and thus combines a wide range of forecasting techniques representative of the field’s status (Stroeve et al. 2014). To date, most efforts have focused on pan-Arctic forecasts, that is, the total sea ice extent. It is clear, however, that the practicality of a pan-Arctic forecast is limited— indeed, most stakeholders are only interested in regional forecasts. While SEARCH has recognized this issue and encouraged the submission of regional forecasts, in 2012 there were 23 submissions of pan-Arctic forecasts compared to just 6 submissions of regional forecasts. The chief reason for this disparity is that regional prediction is a more complex problem than pan-Arctic prediction owing to factors such as local-scale ice advection and small-scale influences on sea ice processes.

Seasonal prediction of Arctic sea ice extent is an initial condition problem (Blanchard-Wrigglesworth et al. 2011b). Results from both modeling (e.g., Holland et al. 2011) and statistical (e.g., Lindsay et al. 2008) studies indicate that sea ice thickness offers key predictive information for sea ice extent. This results from the combination of a much longer time scale of sea ice thickness anomalies relative to sea ice extent anomalies, and the forcing of sea ice thickness anomalies on sea ice extent anomalies particularly during the summer and fall (Blanchard-Wrigglesworth et al. 2011a).

Skillful predictability of regional sea ice extent anomalies is thus conditioned by the skillful prediction of regional sea ice thickness anomalies. At the same time, a skillful prediction of regional sea ice thickness anomalies will depend on the correct characterization and initialization of regional sea ice thickness in the framework of the predictive system being used.

Unfortunately, measurements of ice thickness in observations (and especially ice thickness anomalies) are limited both spatially and temporally (pan-Arctic satellite measurements of thickness are only sporadically available since 2003 and not available in real time). It is not known what the typical length scale of ice thickness anomalies might be, and thus it is not known how many independent observing stations would be needed to monitor sea ice thickness in the Arctic. Using ice thickness data output from an ice-ocean model forced with observations, Lindsay and Zhang (2006b) estimated that just three optimally placed stations were needed to monitor 90% of the variance of the basinwide mean thickness, but it is not known how model dependent this result might be.

We thus wish to investigate the spatial and temporal characteristics of Arctic sea ice thickness in models that are used to predict or estimate the observed state of Arctic sea ice: fully coupled GCMs and ice–ocean models (IOMs) that are forced with an estimate of the observed atmosphere. We compare GCMs and IOMs for two reasons. First, we wish to evaluate what impact coupling the ice–ocean system with the atmosphere system has on the overall behavior of sea ice thickness. Second, given the scarcity of observed thickness data, hindcasts of sea ice thickness from IOMs with data assimilation have been used to initialize and validate GCM prediction runs and to give an estimate of observations. It is thus of paramount importance to assess how an IOM performs relative to a GCM given identical sea ice physics in both models.

To gain a better understanding of the differences between the GCM and the IOM, we investigate the separate thermodynamic and dynamic ice thickness tendencies in the CCSM4 GCM and IOM. From these two variables, we can reconstruct two synthetic time series of ice thickness solely due to thermodynamic and dynamic forcings respectively. Traditionally, many studies have attempted to characterize sea ice thickness variability using thermodynamic-only (or column) models of sea ice (e.g., Thorndike 1992; Bitz et al. 1996), yet it is clear that ice dynamics are likely to play a significant role in determining sea ice thickness variability. Our analysis allows us to gain an understanding of the interplay between the thermodynamics and dynamics of sea ice, and points to significant differences in this interplay between the GCM and IOM that result in different sea ice thickness characteristics.

## 2. Methods and data

We characterize Arctic sea ice thickness anomalies using output from an array of GCMs and two IOMs. A further detailed analysis is given of one GCM and the two IOMs. We use GCM output from the Community Climate System Model, version 4 (CCSM4; see Gent et al. 2011) twentieth-century runs. The CCSM4 data we analyze are from a seven-member ensemble run for the period 1961–2000. CCSM4 captures successfully many aspects of the Arctic climate (e.g., Jahn et al. 2012). We also examine sea ice thickness output for the period 1961–2000 from the historical twentieth-century simulations of 16 additional GCMs that have been submitted to the Coupled Model Intercomparison Project phase 5 (CMIP5) archive. The full list of GCMs is displayed in Table 1. One of the IOMs we study is composed of the ice and ocean components of CCSM4 run with surface atmospheric forcing developed in Large and Yeager (2004) for the Common Ocean–Ice Reference Experiments (CORE). We call this the CCSM4IO (IO for ice ocean) model hereafter. The other IOM is the Pan-Arctic Ice Ocean Model and Assimilation System (PIOMAS; see Zhang and Rothrock 2003). PIOMAS is an ice–ocean model that is forced with the National Centers for Environmental Prediction (NCEP)–National center for Atmospheric Research (NCAR) atmospheric reanalysis and that assimilates satellite-observed sea ice concentration using nudging (Lindsay and Zhang 2006a). Its ice thickness agrees well with observed in situ and satellite ice thickness estimates (Schweiger et al. 2011). We analyze the period 1979–2012. PIOMAS has extensively been used to investigate the variability and decline of sea ice thickness (e.g., Lindsay and Zhang 2006b; Schweiger et al. 2011) and to initialize numerical models for seasonal forecasts (e.g., for the Sea Ice Outlook), motivating us to investigate it within the context of other models.

List of models used.

We first remove the seasonal cycle and linearly detrend all time series since we want to eliminate the long-term forced response from the variability, yet still consider decadal variability. We only do this for grid points in which mean sea ice thickness at the time of summer minimum is greater than 0.1 m. Since we are interested in ice thickness variability in the Arctic Ocean basin (rather than sub-Arctic, seasonally ice-covered seas) this arbitrary threshold achieves this goal. When analyzing output from multiple-run ensembles (as for the CCSM4 described above), we first compute each metric of interest for each individual run and calculate ensemble means as a final step. When pan-Arctic means are shown, these are area-weighted means of the metric of interest calculated at individual grid points. We compute the standard deviation of sea ice thickness as a measure of variability. We characterize the spatial extent of sea ice anomalies by creating one-point correlation maps for a series of points across the Arctic. In other words, we calculate the correlation of the time series of thickness anomalies at a given point with the time series of monthly thickness anomalies at all grid points. To calculate the spatial length scale of thickness anomalies from a given point, we calculate the mean *e*-folding distance (mean distance at which the correlation drops to 1/*e*). We do this by calculating the area over which the correlations are greater than 1/*e*, and calculating the radius of a circle that yields that area. We use this method because it is computationally more efficient than calculating individual distances to all grid points. (We illustrate our methodology in Fig. A1 in the appendix.) We repeat this procedure for an array of points of sufficient density to capture the pattern of spatial length scale of the thickness anomalies across the Arctic.

*e*-folding time (the time it takes for the autocorrelation to decay to 1/

*e*) at the fixed reference grid point. The other, which we call the Lagrangian lifetime, is the

*e*-folding time when tracking the point of maximum correlation in lag time, which allows us to account for the dynamic nature of sea ice. The Eulerian and Lagrangian correlations at a grid point

*i*are computed as

*h*

_{it}denotes the ice thickness anomaly at grid point

*i*for time

*t*,

*σ*

_{i}is the standard deviation of ice thickness at grid point

*i*,

*t*is the lag in months, and max

_{j}indicates the maximum correlation is taken over

*j*grid points within 500 km of the point of maximum correlation at the previous time step. This 500-km limit eliminates remote points that might randomly have high correlations with the

*i*th grid point, yet this distance is large enough to account for monthly sea ice displacement.

## 3. Results

We present a more thorough comparison of sea ice thickness anomalies in CCSM4, PIOMAS, and CCSM4IO. In some instances we bring in the CMIP5 models to consider robustness across a wider set of models.

### a. Time mean and variability

Some initial insight into the origin of the patterns of variability can be gained by investigating the mean annual thickness fields (see Fig. 1). In terms of mean pan-Arctic thickness, CCSM4 has thicker ice than PIOMAS and CCSM4IO. CCSM4IO is particularly striking in terms of how thin the ice is. Table 2 shows the pan-Arctic annual mean thickness for all three models. To address differences in variability between CCSM4 and CCSM4IO that may result from differences in mean ice thickness, we also include in our analysis the CCSM4 twenty-first century representative concentration pathway 8.5 (RCP8.5) forced simulations. The RCP8.5 is a high-emission scenario with direct radiative forcing reaching 8.5 W m^{−2} (~1370 ppm CO_{2} equivalent) in 2100. In the CCSM4, this five-member ensemble simulates a decline in sea ice throughout the twenty-first century. We use model data for the period when the ice thickness is similar to that in CCSM4IO (which are model years 2031–60). We call this CCSM4-21c.

Mean annual Arctic ice thickness and variability (standard deviation), and *e*-folding length scale and time scale in months. We limit the area over which we compute the mean to grid cells that have at least an annual mean value of 0.1 m.

In all three models the overall pattern is similar, with thickest ice north of Greenland and the Canadian Arctic Archipelago, and thinner ice in the eastern portion of the Arctic basin. Available satellite-derived observations of ice thickness (Kwok and Rothrock 2009; Fig. 1d) show a similar pattern, yet are thinner than both CCSM4 and PIOMAS. However, the Ice, Cloud, and Land Elevation Satellite (ICESat) data are only available for October, November, February, and March 2003–08, and are biased thin relative to the 1979–2012 period (Kwok and Rothrock 2009).

We illustrate the variability of the sea ice thickness with maps of the standard deviation of annual thickness anomalies in Fig. 2. Mean standard deviations for the Arctic basin are shown in Table 2. Overall, ice thickness variability is significantly larger in CCSM4 than in the IOMs. In all models, the regions of largest thickness variability tend to lie along the Arctic basin coastlines, despite rather different mean thickness states among the models (see Fig. 1).

Standard deviation of annual sea ice thickness anomalies (m) in (a) CCSM4, (b) CCSM4-21c, (c) PIOMAS, and (d) CCSM4IO, and ratio of standard deviations of (e) CCSM4 and PIOMAS and (f) CCSM4 and CCSM4IO.

Citation: Journal of Climate 27, 21; 10.1175/JCLI-D-14-00345.1

Standard deviation of annual sea ice thickness anomalies (m) in (a) CCSM4, (b) CCSM4-21c, (c) PIOMAS, and (d) CCSM4IO, and ratio of standard deviations of (e) CCSM4 and PIOMAS and (f) CCSM4 and CCSM4IO.

Citation: Journal of Climate 27, 21; 10.1175/JCLI-D-14-00345.1

Standard deviation of annual sea ice thickness anomalies (m) in (a) CCSM4, (b) CCSM4-21c, (c) PIOMAS, and (d) CCSM4IO, and ratio of standard deviations of (e) CCSM4 and PIOMAS and (f) CCSM4 and CCSM4IO.

Citation: Journal of Climate 27, 21; 10.1175/JCLI-D-14-00345.1

In CCSM4, the areas of highest thickness variability are the East Siberian Sea and the Canadian Arctic Archipelago coastline. In PIOMAS, ice thickness is still highly variable in the East Siberian Sea and Canadian Arctic Archipelago, yet the high variability areas are more constrained to the coastline and less extensive than in CCSM4. Smaller areas of high variability can be seen along the Atlantic sector archipelagos (Svalbard and Franz Josef). In CCSM4IO, only the Canadian Arctic Archipelago has relatively high variability, while the maxima found in the other models along the Siberian coastline are absent. In CCSM4-21c ice thickness is significantly less variable than CCSM4, yet more variable than CCSM4IO. In all models the central Arctic has the lowest variability within the Arctic basin. Figures 2e and 2f show the ratio of variability between CCSM4 and PIOMAS and CCSM4 and CCSM4IO respectively. The larger variability of CCSM4 compared to the two IOMs particularly along the eastern Arctic is immediately apparent, with values 2–3 times larger than PIOMAS and 3–5 times larger than CCSM4IO.

We find a relationship between mean ice thickness and ice thickness variability, with regions of thicker ice within the basin associated with higher variability (not shown). This relationship however is more constrained in the simulations with thinner ice (CCSM4-21c and CCSM4IO). The link between mean ice thickness and variability is also observed when comparing mean values across the suite of GCMs in the CMIP5 archive. Figure 3 shows mean pan-Arctic values of the variability of ice thickness anomalies for 17 different CMIP5 GCMs (including CCSM4), CCSM4-21c, CCSM4IO, and PIOMAS plotted against the annual-mean pan-Arctic sea ice thickness. Models with thicker ice tend to have more variable ice thickness. The relationship between mean sea ice thickness and variability appears to be more constrained for thinner models, which agrees with the intramodel results (further illustrated in Fig. A2 in the appendix). The spread across models is much larger than the spread across ensemble runs within a single model (as illustrated by CCSM4 and CCSM4-21c in Fig. 3) and thus cannot be accounted for by natural variability alone.

Scatterplots of mean annual Arctic sea ice thickness and mean annual thickness variability in 16 different CMIP5 GCM models. Values are also shown for CCSM4 (green cross), CCSM4-21c (green-crossed circle), CCSM4IO (red circle), and PIOMAS (black circle). The pan-Arctic mean thickness is defined as in Table 2. Error bars are shown for CCSM4 and CCSM4-21c and represent the spread across ensemble runs within each GCM.

Citation: Journal of Climate 27, 21; 10.1175/JCLI-D-14-00345.1

Scatterplots of mean annual Arctic sea ice thickness and mean annual thickness variability in 16 different CMIP5 GCM models. Values are also shown for CCSM4 (green cross), CCSM4-21c (green-crossed circle), CCSM4IO (red circle), and PIOMAS (black circle). The pan-Arctic mean thickness is defined as in Table 2. Error bars are shown for CCSM4 and CCSM4-21c and represent the spread across ensemble runs within each GCM.

Citation: Journal of Climate 27, 21; 10.1175/JCLI-D-14-00345.1

Scatterplots of mean annual Arctic sea ice thickness and mean annual thickness variability in 16 different CMIP5 GCM models. Values are also shown for CCSM4 (green cross), CCSM4-21c (green-crossed circle), CCSM4IO (red circle), and PIOMAS (black circle). The pan-Arctic mean thickness is defined as in Table 2. Error bars are shown for CCSM4 and CCSM4-21c and represent the spread across ensemble runs within each GCM.

Citation: Journal of Climate 27, 21; 10.1175/JCLI-D-14-00345.1

Having described the general regional characteristics of sea ice mean thickness and its variability, we now investigate correlations in space and time to better understand the persistence of sea ice thickness anomalies.

### b. Length and time scales in CCSM4, CCSM4IO, and PIOMAS

Figure 4 shows the *e*-folding length scale of sea ice anomalies for all three models. For CCSM4 and CCSM4-21c, the mean length scale is ~700 and ~720 km respectively. For PIOMAS, the mean length scale is ~940 km, and for CCSM4IO it is ~1100 km. These differences between the GCMs and IOMs are significant and have profound implications as we discuss below in section 4. The lack of significant change in the length scale of anomalies in CCSM4-21c relative to CCSM4 means that the difference in length scale between CCSM4 and CCSM4IO cannot be accounted for by the difference in mean thickness between the two simulations.

Length scale (km) of sea ice thickness anomalies in (a) CCSM4, (b) CCSM4-21c, (c) PIOMAS, and (d) CCSM4IO.

Citation: Journal of Climate 27, 21; 10.1175/JCLI-D-14-00345.1

Length scale (km) of sea ice thickness anomalies in (a) CCSM4, (b) CCSM4-21c, (c) PIOMAS, and (d) CCSM4IO.

Citation: Journal of Climate 27, 21; 10.1175/JCLI-D-14-00345.1

Length scale (km) of sea ice thickness anomalies in (a) CCSM4, (b) CCSM4-21c, (c) PIOMAS, and (d) CCSM4IO.

Citation: Journal of Climate 27, 21; 10.1175/JCLI-D-14-00345.1

We define the footprint of an anomaly as the square of the length scale multiplied by *π*. Hence anomalies in CCSM4IO (PIOMAS) are on average 2.47 times (1.8 times) larger than in CCSM4. Taking the area of the central Arctic basin to be about 10^{7} km^{2}, and dividing by the footprint area, these values would imply thickness anomalies with 6 degrees of freedom in CCSM4, but only 3 degrees of freedom in CCSM4IO.

There are significant differences between the time scales of pan-Arctic mean thickness and regional sea ice thickness anomalies, and it is known that ice transport affects persistence (e.g., Bitz et al. 1996; Blanchard-Wrigglesworth et al. 2011b). By exploring the Lagrangian and Eulerian time scales, we expect to evaluate the effect that transport has on persistence. Figure 5 shows the Eulerian *e*-folding time scales for thickness anomalies. Mean *e*-folding values for the Arctic basin are shown in Table 2. Lagrangian time scales tend to be about one season longer than Eulerian, while anomalies in the IOMs and CCSM4-21c are about 2 months shorter lived than in CCSM4.

Eulerian time scales (months) of sea ice thickness anomalies in (a) CCSM4, (b) CCSM4-21c, (c) PIOMAS, and (d) CCSM4IO.

Citation: Journal of Climate 27, 21; 10.1175/JCLI-D-14-00345.1

Eulerian time scales (months) of sea ice thickness anomalies in (a) CCSM4, (b) CCSM4-21c, (c) PIOMAS, and (d) CCSM4IO.

Citation: Journal of Climate 27, 21; 10.1175/JCLI-D-14-00345.1

Eulerian time scales (months) of sea ice thickness anomalies in (a) CCSM4, (b) CCSM4-21c, (c) PIOMAS, and (d) CCSM4IO.

Citation: Journal of Climate 27, 21; 10.1175/JCLI-D-14-00345.1

In CCSM4, there is a maximum of *e*-folding times on the Canadian side of the central Arctic, with Eulerian (Lagrangian) *e*-folding times around 20 (30; not shown) months. For the IOMs, these time scales are smaller. Additionally, the region of highest values is displaced, lying closer to the Canadian Arctic Archipelago. In contrast, the shorter time scales tend to be areas closest to the coastline. As discussed in Blanchard-Wrigglesworth et al. (2011b), sea ice dynamics play a large role in limiting the time scales of thickness anomalies—in CCSM4, the highest Eulerian time scales are located in the region of lowest sea ice motion velocities (not shown), while the highest Lagrangian time scales are located downstream (in an advective sense) from the Eulerian maxima (not shown).

In addition, mean ice thickness also plays a role in determining the time scale of sea ice anomalies, particularly in the IOMs. Scatterplots for Eulerian time scales and mean thickness at each grid point for each model indicate a positive correlation prevails (not shown). The relationship between mean thickness and time scale also helps explain the intermodel difference in mean time scales, with CCSM4 having thicker ice and longer-lived thickness anomalies relative to CCSM4-21c, CCSM4IO, and PIOMAS.

### c. Length and time scales in CMIP5 models

The extent to which mean thickness helps explain the variations in length and time scales can be examined across the suite of GCMs in the CMIP5 archive. Figure 6 shows mean pan-Arctic values of the length scale and time scale of ice thickness anomalies for 17 different CMIP5 GCMs (including CCSM4), CCSM4-21c, CCSM4IO, and PIOMAS plotted against the annual-mean pan-Arctic sea ice thickness. While there is considerable scatter, models with thicker ice tend to have smaller length scales and longer time scales, although the correlation is weak and only significant at the 90% level. The twofold to threefold range in variability in both fields (length and time scale) across the models is indeed remarkable.

Scatterplots of mean annual Arctic sea ice thickness (m) and (left) length scale (km) and (right) Eulerian time scale (months) in 16 different CMIP5 GCM models. Values are also shown for CCSM4 (green cross), CCSM4-21c (green circle), CCSM4IO (red circle), and PIOMAS (black circle). The pan-Arctic mean thickness is defined as in Table 2.

Citation: Journal of Climate 27, 21; 10.1175/JCLI-D-14-00345.1

Scatterplots of mean annual Arctic sea ice thickness (m) and (left) length scale (km) and (right) Eulerian time scale (months) in 16 different CMIP5 GCM models. Values are also shown for CCSM4 (green cross), CCSM4-21c (green circle), CCSM4IO (red circle), and PIOMAS (black circle). The pan-Arctic mean thickness is defined as in Table 2.

Citation: Journal of Climate 27, 21; 10.1175/JCLI-D-14-00345.1

Scatterplots of mean annual Arctic sea ice thickness (m) and (left) length scale (km) and (right) Eulerian time scale (months) in 16 different CMIP5 GCM models. Values are also shown for CCSM4 (green cross), CCSM4-21c (green circle), CCSM4IO (red circle), and PIOMAS (black circle). The pan-Arctic mean thickness is defined as in Table 2.

Citation: Journal of Climate 27, 21; 10.1175/JCLI-D-14-00345.1

In terms of length and time scales, the difference in mean thickness helps explain the difference in time scale between CCSM4 and CCSM4IO (since CCSM4-21c and CCSM4IO agree on their time scales) but does not explain the difference in length scale, since they remain significantly different between CCSM4-21c and CCSM4IO. In terms of ice thickness variability, approximately 75% of the difference in ice thickness variability between CCSM4 and CCSM4IO may be attributed to the difference in mean thickness (see Table 2). The residual 25% difference is statistically robust as shown in the appendix (Fig. A2).

To gain a better understanding of the residual 25% difference between the models we now inspect the partition of ice thickness tendency into thermodynamic and dynamic terms and the surface forcing of sea ice.

### d. Thermodynamic and dynamic thickness tendency

Ice thickness tendency can be partitioned into thermodynamic growth (or melt) and dynamic transport. While the former involves a net transfer of energy vertically in or out of a point (or model grid cell), the latter involves horizontal movement of mass in or out of a point (or model grid cell). Despite this difference, atmospheric processes that affect one (e.g., increased downwelling longwave radiation) are likely tied to processes that affect the other (e.g., increased winds) via atmospheric patterns that affect both variables (e.g., winter storms producing warming and cloud cover, and thus enhanced downwelling longwave radiation and enhanced surface winds).

Additionally, thermodynamic and dynamic thickness tendencies may be more likely to be linked in certain regions. For example, one can imagine a cold offshore wind blowing sea ice (that is growing) away from the coast, yielding a negative dynamic thickness tendency. At the same time, however, strong turbulent heat losses from the resulting open water produce strong ice growth, yielding a positive thermodynamic thickness tendency.

We wish to know the relative importance of these two driving terms for the patterns of sea ice thickness variability shown in Fig. 2, and whether the interaction between the terms can help explain the difference in total sea ice variability between the GCMs and IOMs. We create three synthetic time series of ice thickness reconstructed separately from the monthly output of thermodynamic tendency, dynamic tendency, and thermodynamic plus dynamic tendency data. We refer to these as reconstructed thermodynamic thickness, dynamic thickness, and total thickness. The reconstructed total thickness for CCSM4 is in close agreement with thickness in CCSM4 (*r* > 0.98; not shown), serving as a check for our methodology. We explain this in depth in the appendix below. After annually averaging and detrending each of the three reconstructed time series, we calculate their standard deviation (Fig. 7).

Standard deviation of the anomalies (m) in the reconstructed annual ice thickness time series from the (a),(d) thermodynamic, (b),(e) dynamic, and (c),(f) thermodynamic plus dynamic tendency terms in (top) CCSM4 and (bottom) CCSM4IO.

Citation: Journal of Climate 27, 21; 10.1175/JCLI-D-14-00345.1

Standard deviation of the anomalies (m) in the reconstructed annual ice thickness time series from the (a),(d) thermodynamic, (b),(e) dynamic, and (c),(f) thermodynamic plus dynamic tendency terms in (top) CCSM4 and (bottom) CCSM4IO.

Citation: Journal of Climate 27, 21; 10.1175/JCLI-D-14-00345.1

Standard deviation of the anomalies (m) in the reconstructed annual ice thickness time series from the (a),(d) thermodynamic, (b),(e) dynamic, and (c),(f) thermodynamic plus dynamic tendency terms in (top) CCSM4 and (bottom) CCSM4IO.

Citation: Journal of Climate 27, 21; 10.1175/JCLI-D-14-00345.1

The variability in the reconstructed thermodynamic and dynamic thickness is comparable between CCSM4 and CCSM4IO: while there are regional differences, overall they tend to have similarly high variability along the coastlines and low variability in the central Arctic. The pan-Arctic averages are also comparable between them.

Variability in total thickness, however, is not simply the sum of the variability in the reconstructed thermodynamic and dynamic thickness, but depends crucially on the covariance between these two terms. Figure 8 shows the correlation between the reconstructed annual (detrended) thermodynamic and dynamic thickness time series in CCSM4 and CCSM4IO.

Correlation between the reconstructed annual thermodynamic and dynamic ice thickness time series in (a) CCSM4 and (b) CCSM4IO.

Citation: Journal of Climate 27, 21; 10.1175/JCLI-D-14-00345.1

Correlation between the reconstructed annual thermodynamic and dynamic ice thickness time series in (a) CCSM4 and (b) CCSM4IO.

Citation: Journal of Climate 27, 21; 10.1175/JCLI-D-14-00345.1

Correlation between the reconstructed annual thermodynamic and dynamic ice thickness time series in (a) CCSM4 and (b) CCSM4IO.

Citation: Journal of Climate 27, 21; 10.1175/JCLI-D-14-00345.1

In CCSM4, the two fields are only modestly anticorrelated over large sections of the central Arctic (*r* ~ −0.6), whereas in CCSM4IO, the two fields are strongly anticorrelated over the whole Arctic (*r* < −0.9), which decreases the variance in the total ice thickness field. This different behavior in coupling is not entirely due to the lack of feedbacks between the ice/ocean components and the overlying atmosphere in CCSM4IO; calculations of the coupling between the thermodynamic and dynamic time series in CCSM4 in the twenty-first century simulation show that as the sea ice becomes thinner, the anticorrelation grows stronger. Despite this behavior, at the time when the sea ice in CCSM4 is equivalent in thickness to CCSM4IO, the anticorrelation is still weaker in CCSM4 (pan-Arctic average of *r* = −0.86 in CCSM4 and *r* = −0.94 in CCSM4IO).

Figure 9 shows spatial maps of the correlation between the reconstructed thermodynamic and dynamic thickness and the total ice thickness for CCSM4 and CCSM4IO. Variability in the CCSM4 is driven mainly by dynamic variability. The regions where dynamic variability is smaller tend to be the regions with lower mean ice speeds, especially in the Beaufort Gyre region and in the inlets of the Canadian Arctic Archipelago. In these regions, thermodynamic variability dominates thickness variability. In the CCSM4IO, however, there are no clear patterns, and neither the dynamic nor thermodynamic variability dominates thickness variability overall.

Spatial maps of the correlation at each grid point between total and reconstructed (left) dynamic and (right) thermodynamic thickness in the (a),(b) CCSM4 and (c),(d) CCSM4IO models.

Citation: Journal of Climate 27, 21; 10.1175/JCLI-D-14-00345.1

Spatial maps of the correlation at each grid point between total and reconstructed (left) dynamic and (right) thermodynamic thickness in the (a),(b) CCSM4 and (c),(d) CCSM4IO models.

Citation: Journal of Climate 27, 21; 10.1175/JCLI-D-14-00345.1

Spatial maps of the correlation at each grid point between total and reconstructed (left) dynamic and (right) thermodynamic thickness in the (a),(b) CCSM4 and (c),(d) CCSM4IO models.

Citation: Journal of Climate 27, 21; 10.1175/JCLI-D-14-00345.1

## 4. Discussion and conclusions

Our study of sea ice thickness anomalies and their origin reveals that models with a thicker mean ice cover tend to have more variable ice thickness. Regionally, ice thickness tends to be most variable along Arctic coastlines and in regions of thickest ice. The length and time scale of these anomalies are also related, albeit weakly, to the mean ice thickness, with smaller yet longer-lived anomalies in models with thicker ice. Therefore estimations of the number of stations (or measuring points) needed to monitor variability of Arctic ice thickness will be model dependent. The upper bound given by the suite of models studied is yielded by the model with the smallest footprint anomalies, and translates into 14 stations (or degrees of freedom). The Lagrangian approach to investigating thickness anomalies offers promise over the Eulerian approach, given that the Lagrangian persistence is about a season longer than the Eulerian persistence. Nevertheless, ice thickness time scales tend to be shortest close to the coastlines, where thickness information might be most useful for stakeholder needs (e.g., Hawkins et al. 2014, manuscript submitted to *Quart. J. Roy. Meteor. Soc.*). In CCSM4, ice thickness variability is primarily driven by dynamic processes. This agrees with results from Tietsche et al. (2014), who found that ice thickness predictability in the Arctic basin was dominated mainly by dynamic processes over thermodynamic processes. We note that models do not simulate landfast ice, which may lead to unrealistic, dynamically driven sea ice thickness variability along coastlines where landfast ice is present in observations, as landfast ice is static and thus its growth and decay are dictated by thermodynamics alone.

We have compared ice thickness variability in the fully coupled and ice–ocean-only model versions of CCSM4 and found that variability is more damped in the case of the ice–ocean model, even when the bias in mean ice thickness is taken into account and despite the individual thermodynamic and dynamic tendency terms being comparable in both models. Stronger damping is a result of near-complete cancellation between dynamic and thermodynamic influences on ice thickness. The damping illustrates the importance that coupling has on the interaction and feedbacks among the sea ice and ocean and the overlying atmosphere. As such, coupling also affects the overall variability of the system. It is plausible that any GCMs that employ data assimilation will also have damped sea ice thickness anomalies.

One possible reason for this discrepancy between GCM and IOM may originate from the influence that sea ice cover has on air surface temperatures in the cold season (outside the summer months when the air temperature is locked at 0°C). We imagine an area (or grid cell) in the central Arctic, where the degree of cancelation between dynamic and thermodynamic processes in the GCM and IOM differs most. Here the ice is mainly perennial with ice concentrations that are always close to 100%, yet leads are not uncommon. These leads in winter are areas of strong thermodynamic growth of sea ice, since the turbulent heat loss from the ocean to the atmosphere is much higher than in ice-covered regions. If we imagine a situation where a lead opens by dynamic means (e.g., by diverging winds), then the dynamics create a negative thickness tendency. The open lead regrows, thus creating a positive thermodynamic tendency. The net result is a negative correlation between the dynamic and thermodynamic tendencies. However, another effect takes place in the GCM. Once the lead opens the heat loss from the ocean to the atmosphere warms the near-surface air temperature. This would result in a more moderated thermodynamic growth of ice and a more modest anticorrelation between the dynamic and thermodynamic terms. The reanalysis fields that are used to drive IOMs tend to lack the degree of coupling between winds, ice cover, and air temperature that occurs in the real world and GCMs because sea ice in atmospheric reanalysis models is motionless. Additionally, a lack of regional complexity in the reanalysis fields might help explain the large length scales in the central Arctic seen in the IOMs, which cannot be explained by a difference in mean ice thickness.

The differences in character of sea ice anomalies across GCMs and IOMs lead to considerations that must be addressed for sea ice prediction (hindcast or forecast) experiments. First, initializing a GCM with sea ice thickness anomalies derived from an IOM without any scaling may result in initial conditions having too little impact on the forecast (since variability in IOMs tend to have damped variability compared to GCMs). Further, any GCM using data assimilation in the atmosphere up to the point of forecast is also likely to suffer from this issue.

Second, the expected continued decline of the Arctic ice cover in coming decades is likely to affect the spatial and time scale characteristics of ice thickness anomalies throughout the twenty-first century. It is unclear how these changes may affect potential predictability: while the expanding spatial scale of anomalies may enhance sea ice predictability, shortening persistence times should decrease predictability. Declining sea ice thickness variability may offer less predictive information at initialization. Of course, to address these questions it is paramount to consider the relationship between ice thickness and ice extent anomalies, which is known to be nonstationary (e.g., Gregory et al. 2002; Notz 2009; Stroeve et al. 2012).

Third, the link between the mean state of a GCM in terms of its sea ice thickness and its sea ice thickness variability (in space, time, and amplitude) means that GCMs that have a strong bias in mean ice thickness relative to observations are likely inappropriate tools for the purposes of sea ice forecasts. Given the link between persistence and predictability (e.g., Day et al. 2014), the large spread in time scales across GCMs is a likely candidate for helping explain the spread in predictability that is seen across GCMs (Tietsche et al. 2014).

## Acknowledgments

We thank Jennifer Kay, Kyle Armour, and Marika Holland for insightful discussions, Jinlun Zhang for providing PIOMAS data, Alex Jahn for sea ice motion data, and David Bailey for assistance on retrieving CCSM4IO data. This work was supported by NSF Grant ARC-0909313 and ONR Grant N000141310793.

## APPENDIX

### In-Depth Methodology and Robustness

#### a. One-point correlation maps and length scales

To illustrate the calculation of mean length scale of anomalies we show in Fig. A1 a one-point correlation map of thickness anomalies for a grid point at 82°N, 175°E. The correlation at that point is one, and drops as we move farther away. Only values greater than 1/*e* or lower than −1/*e* are shown. To calculate the mean length scale, we compute the area of grid points with correlation greater than 1/*e* and the radius of the circle that yields that area. This circle is plotted centered at the grid point. The radius of the circle is the mean length scale of ice thickness anomalies for that grid point.

One-point correlation map of thickness anomalies for a grid point at 82°N, 175°E, marked by an X. A circle with an area equal to that covered by grid cells with a correlation greater than 1/*e* is plotted centered on the X.

Citation: Journal of Climate 27, 21; 10.1175/JCLI-D-14-00345.1

One-point correlation map of thickness anomalies for a grid point at 82°N, 175°E, marked by an X. A circle with an area equal to that covered by grid cells with a correlation greater than 1/*e* is plotted centered on the X.

Citation: Journal of Climate 27, 21; 10.1175/JCLI-D-14-00345.1

One-point correlation map of thickness anomalies for a grid point at 82°N, 175°E, marked by an X. A circle with an area equal to that covered by grid cells with a correlation greater than 1/*e* is plotted centered on the X.

Citation: Journal of Climate 27, 21; 10.1175/JCLI-D-14-00345.1

#### b. Ice thickness variability as a function of mean ice thickness

To illustrate the robustness in the link between ice thickness variability and mean ice thickness we show in Fig. A2 a scatterplot of mean thickness and ice thickness variability in CCSM4 (from both the twentieth-century historical ensemble and the twenty-first-century RCP8.5 ensemble) for consecutive 30-yr periods. We also include the data point for CCSM4IO.

Scatterplot of mean annual sea ice thickness and annual standard deviation of ice-thickness anomalies area-weight averaged in the Arctic basin. Values are shown for individual CCSM4 twentieth-century ensemble runs (blue; 35-yr periods), for individual CCSM4-21c ensemble runs (green), and for CCSM4IO (black diagonal cross). The departure of CCSM4IO from the CCSM4-21c data is significant at the 99% level.

Citation: Journal of Climate 27, 21; 10.1175/JCLI-D-14-00345.1

Scatterplot of mean annual sea ice thickness and annual standard deviation of ice-thickness anomalies area-weight averaged in the Arctic basin. Values are shown for individual CCSM4 twentieth-century ensemble runs (blue; 35-yr periods), for individual CCSM4-21c ensemble runs (green), and for CCSM4IO (black diagonal cross). The departure of CCSM4IO from the CCSM4-21c data is significant at the 99% level.

Citation: Journal of Climate 27, 21; 10.1175/JCLI-D-14-00345.1

Scatterplot of mean annual sea ice thickness and annual standard deviation of ice-thickness anomalies area-weight averaged in the Arctic basin. Values are shown for individual CCSM4 twentieth-century ensemble runs (blue; 35-yr periods), for individual CCSM4-21c ensemble runs (green), and for CCSM4IO (black diagonal cross). The departure of CCSM4IO from the CCSM4-21c data is significant at the 99% level.

Citation: Journal of Climate 27, 21; 10.1175/JCLI-D-14-00345.1

#### c. Ice thickness reconstruction from the dynamic and thermodynamic ice tendency data

The CCSM4 outputs mean monthly dynamic and thermodynamic ice growth tendencies for each month. We reconstruct monthly time series of ice thickness due to both processes by averaging the tendencies between successive months (taking into account the different number of days per month) and then adding this number to the previous month thickness. For the first month of the time series, we take the thickness from the raw data. In other words, the thermodynamic ice thickness for February is the January thickness value, plus the mean thermodynamic thickness tendency in January and February (weighted by the number of days in each month) times the total number of days between successive months (i.e., January and February in this case). We do not expect the reconstruction to be perfect, since our averaged tendency value is a linear approximation to the change in thickness between successive months. Nevertheless, the mean Arctic-wide correlation between both time series is *r* = 0.98.

As a sample at an arbitrary point, we show the raw and reconstructed thickness time series at 85°N, 130°E in Fig. A3. We also show the individual thermodynamic and dynamic time series (Fig. A3b). Throughout this 40-yr period, ice grows thermodynamically and is lost (advected out) dynamically. This is a basic characteristic of the Arctic as a whole (Maykut 1985), as it functions as a net ice factory that is then advected out of the Arctic, mainly through the Fram Strait.

(a) Total (blue) and reconstructed (black) ice thickness at an arbitrary point (85°N, 130°E). The correlation between total and reconstructed monthly thickness time series is *r* = 0.98, equal to the mean Arctic value. (b) The individual thermodynamic (blue) and dynamic (black) thickness. The sum of both (red) is the reconstructed thickness in (a).

Citation: Journal of Climate 27, 21; 10.1175/JCLI-D-14-00345.1

(a) Total (blue) and reconstructed (black) ice thickness at an arbitrary point (85°N, 130°E). The correlation between total and reconstructed monthly thickness time series is *r* = 0.98, equal to the mean Arctic value. (b) The individual thermodynamic (blue) and dynamic (black) thickness. The sum of both (red) is the reconstructed thickness in (a).

Citation: Journal of Climate 27, 21; 10.1175/JCLI-D-14-00345.1

(a) Total (blue) and reconstructed (black) ice thickness at an arbitrary point (85°N, 130°E). The correlation between total and reconstructed monthly thickness time series is *r* = 0.98, equal to the mean Arctic value. (b) The individual thermodynamic (blue) and dynamic (black) thickness. The sum of both (red) is the reconstructed thickness in (a).

Citation: Journal of Climate 27, 21; 10.1175/JCLI-D-14-00345.1

In Fig. A4 we show the monthly anomalies of the time series shown in Fig. A3. This figure shows that monthly anomalies in total thickness are driven principally by anomalies in the dynamic component (*r* = 0.80), while the thermodynamic component has a weaker influence (*r* = 0.34). These values are representative of the central Arctic as seen in Fig. 9. At the same time, the dynamic and thermodynamic components are only weakly anticorrelated (*r* = −0.30).

Total (black) and reconstructed (gray), and dynamic (blue) and thermodynamic (red) monthly thickness anomalies for an arbitrary point (85°N, 90°E).

Citation: Journal of Climate 27, 21; 10.1175/JCLI-D-14-00345.1

Total (black) and reconstructed (gray), and dynamic (blue) and thermodynamic (red) monthly thickness anomalies for an arbitrary point (85°N, 90°E).

Citation: Journal of Climate 27, 21; 10.1175/JCLI-D-14-00345.1

Total (black) and reconstructed (gray), and dynamic (blue) and thermodynamic (red) monthly thickness anomalies for an arbitrary point (85°N, 90°E).

Citation: Journal of Climate 27, 21; 10.1175/JCLI-D-14-00345.1

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