1. Introduction
Arctic sea ice is an important component of the global climate system, modulating surface radiative fluxes and serving as the interface between atmosphere–ocean processes at high latitudes. Large changes to Arctic sea ice not only have large ramifications for global climate (e.g., Deser et al. 2010; Tomas et al. 2016; Liu and Fedorov 2019; England et al. 2020), but also affect local ecosystems and communities who rely on sea ice throughout the Arctic (e.g., Sakakibara 2008; Meier et al. 2014). Although pointwise observations are available during the historical period (e.g., Walsh et al. 2017), spatially complete observations of Arctic sea ice became available only in the satellite era (starting in 1972). Furthermore, strong external forcing and large and rapid Arctic sea ice declines have been observed during the entirety of the satellite record (Fetterer et al. 2017), making it difficult to understand the relative role of external forcing and internal variability on such declines (e.g., Ding et al. 2017; England et al. 2019). Here we reconstruct Arctic sea ice conditions over the last two millennia using a data assimilation technique and investigate both the significance of the current declines and Arctic sea ice variability under preindustrial conditions.
To date, researchers have relied on three main sources to study presatellite Arctic sea ice conditions and variability: modeling, direct observations, and proxy records. Modeling past Arctic sea ice provides spatially and temporally complete information, yet models are typically not constrained to observations. The combined Coupled Model Intercomparison Project, phase 5 (CMIP5)–Paleoclimate Modeling Intercomparison Project phase 3 (PMIP3) represents a significant modeling effort for understanding climate conditions during the last millennium. Arctic sea ice concentration is included in CMIP5–PMIP3 Last Millennium simulations spanning 850–1849 CE (Schmidt et al. 2011; Taylor et al. 2012) from eight modeling centers. Atwood et al. (2016) used the CMIP5–PMIP3 Last Millennium simulations to investigate the global cooling observed between 1200 and 1850 CE and found a small contribution of Arctic sea ice changes to this cooling via surface albedo feedbacks. However, the authors also point out some key differences between paleoclimate proxy records and model results, and note that large uncertainties in volcanic forcing and insolation over the last millennium prescribed in these model simulations could have a large role in cooling over this time period. Furthermore, Goosse et al. (2013) found that when simulating Arctic sea ice, the same model biases that exist in the modern era also exist when simulating Arctic sea ice of the past. In an attempt to circumvent some of these biases, Schweiger et al. (2019) forced Pan-Arctic Ice Ocean Modeling and Assimilation System (PIOMAS; Schweiger et al. (2011); Zhang and Rothrock 2003), a sea ice–ocean model, with atmospheric reanalysis data and observational data in order to reconstruct sea ice volume from 1901 to 2010. This approach is sensitive to the atmospheric reanalysis used to force it (Lindsay et al. 2014) and to the initial conditions.
Walsh et al. (2017) provide a spatially complete reconstruction of Arctic sea ice coverage from 1850 to 2013 CE at monthly resolution based on a synthesized and curated database of historical observations of sea ice. The Walsh et al. (2017) reconstruction of sea ice extent is based on a priority ordering procedure of the observational datasets available, along with analog and linear interpolation methods to spatially infill regions and times when observations are not available. In particular, before around 1953, observations during winter are especially sparse, and results during that time mainly reflect the infill strategy (Brennan et al. 2020). Here we use an updated version 2 of the Walsh et al. (2019) dataset to compare with our results.
To extend the Arctic sea ice record prior to the historical period, various sea ice–sensitive proxies have been proposed and evaluated (de Vernal et al. 2013). For example, biogenic proxies such as IP25 (e.g., Belt et al. 2007) and sea salt in ice cores (e.g., Wolff et al. 2003) have been used to quantitatively reconstruct Arctic sea ice. However, biogenic and ice core sea ice proxies show strong regional dependencies (Polyak et al. 2010) and as such have been used almost exclusively for regional reconstructions. Given the intricacies of each sea ice proxy record, limited spatial coverage, coarse resolution, and dating uncertainties, they are mainly used to complement other proxy types when reconstructing hemispheric-scale climate conditions (de Vernal et al. 2013). They do however, provide a rare source for comparison of our results on a regional basis, which is particularly useful prior to the twentieth century.
Unlike sea ice–sensitive proxies, temperature-sensitive proxies are numerous and have been under development for many decades. Furthermore, a strong relationship between Arctic and global-mean surface air temperatures (SAT) and Arctic sea ice conditions in both observations and climate models is well documented (Gregory et al. 2002; Winton 2011; Mahlstein and Knutti 2012; Stroeve and Notz 2015; Rosenblum and Eisenman 2017; Olonscheck et al. 2019). Given this relationship, temperature-sensitive proxies have been employed to reconstruct Arctic sea ice. For example, Kinnard et al. (2011) calibrate 69 terrestrial proxy records against historical observations of total Arctic sea ice extent (1979–95) to reconstruct summer Arctic sea ice extent since 561 CE at 5-yr resolution using partial least squares regression. Kinnard et al. (2011) find that the late-twentieth-century decline in Arctic sea ice is unprecedented in both duration and magnitude relative to the rest of the record. Connolly et al. (2017) use presatellite temperature trends to recalibrate sea ice data sources from three regions spanning the Arctic, resulting in a reconstruction of Arctic sea ice extent from 1901 to 2015 on seasonal time scales. They find both a decline of Arctic sea ice during the early-twentieth-century warming (∼1910 to 1940 CE) and the declines starting around 1979, which reverse several decades of increasing Arctic sea ice coverage before that time. Alekseev et al. (2016) use the relationship between summer SAT and Arctic sea ice extent to reconstruct September Arctic sea ice extent from 1900 to 2013 with a linear regression model and find that the reduction of Arctic sea ice extent around 1930–40 is only half that observed in 2012 (the year of minimum Arctic sea ice extent in the satellite record).
Models, direct observations, and proxy records all provide useful information about Arctic sea ice of the past, but discrepancies still exist between each of these sources. Data assimilation (DA) is a statistical technique that combines sparse observations and spatially complete model output to generate a better estimate of climate fields when compared to using models and observations individually. Using DA to reconstruct climate variability has undergone rapid development in recent years (Dirren and Hakim 2005; Annan et al. 2005; Goosse et al. 2006; Ridgwell et al. 2007; Widmann et al. 2010; Bhend et al. 2012; Steiger et al. 2014; Hakim et al. 2016; Tardif et al. 2019), although few studies have used DA techniques to reconstruct sea ice. Klein et al. (2014) reconstruct Arctic sea ice over a 400-yr period in the mid-Holocene with a particle filter that uses a proxy-based reconstruction (based on dinocyst assemblages) to constrain an ensemble of model runs at each time step. Singh et al. (2018) use an ensemble Kalman filter DA approach to reconstruct various climate fields, including Arctic sea ice, in order to investigate Atlantic multidecadal variability over the last two millennia, and find that during a positive phase of the Atlantic multidecadal oscillation, sea ice thins throughout the Arctic and retreats over Greenland, Iceland, and the Nordic seas. Brennan et al. (2020) use an ensemble Kalman filter DA approach to reconstruct Arctic sea ice conditions from 1850 to 2017 by assimilating temperature observations with CMIP5–PMIP3 Last Millennium simulations, and find significant Arctic sea ice decline during the early-twentieth-century warming.
Here, we build on Singh et al. (2018) and Brennan et al. (2020), using an ensemble Kalman filter DA scheme and code base from the Last Millennium Reanalysis (LMR; Hakim et al. 2016) framework to reconstruct Arctic sea ice with annual resolution throughout the Common Era (1–2000 CE). We do this by assimilating a global network of 487 temperature-sensitive proxy records combined with CMIP5–PMIP3 Last Millennium simulations to produce fully gridded, spatially consistent climate fields with a framework for uncertainty quantification (see section 2a). We first quantify the skill of reconstructing Arctic sea ice in an idealized framework (section 3a), followed by results for reconstructions of Arctic sea ice over the past two millennia (section 3b). We then use these reconstructions to investigate how the variability of total Arctic sea ice extent has changed throughout the last two millennia (section 3b). A concluding discussion is provided in section 4.
2. Methods
Paleoclimate DA is implemented using the LMR framework (Hakim et al. 2016) to reconstruct Arctic sea ice concentration (SIC) over the past two millennia. The goal of DA is to objectively combine spatially complete model data with sparse and noisy pointwise observations resulting in spatially complete fields that are representative of the evolution of the climate system over the time period of interest. In sections 2a and 2b we describe the basic DA framework and the specific datasets used for the reconstructions presented, followed by a description of specific experiments and metrics for defining skill in the analysis (sections 2c, 2d, and 2e).
a. Paleoclimate data assimilation
Generally, DA begins with a prior estimate, which can be thought of as an initial “guess” of the climate state for a given time. In a weather setting this guess takes the form of a very accurate short-term forecast, but on the longer time scales considered here (annual) forecasts are both computationally expensive and exhibit low skill. As a consequence, it is common practice to replace the forecast with a random sampling of climate states relevant to the time period being reconstructed (e.g., Hakim et al. 2016). Here this sample takes the form of a 200-member ensemble of annually averaged and randomly drawn years from a last millennium climate model simulation (described in section 2b). We employ an offline (e.g., Oke et al. 2002) ensemble Kalman filter approach using the same random ensemble as the prior for each year, so that all temporal variability and trends in the reconstruction derive from the proxy records.
The Kalman gain allows, in this case, pointwise temperature-sensitive proxy information to influence not only a broader spatial region, but also other variables such as Arctic SIC through the covariance across variables derived from the prior ensemble. Here R is assumed to be a diagonal matrix, meaning that the errors between proxy records are assumed to be uncorrelated. Each diagonal element of R is the variance of the observation error, which is estimated as the variance of regression residuals from the proxy system model calibration. Diagonal R allows for serial observation processing, for which one observation is assimilated at a time, and a simple application of spatial covariance localization (described below), which is used to control spurious long-distance correlations. To solve the updated Eq. (1), we employ a square root ensemble Kalman filter (Whitaker and Hamill 2002), which was also applied in the LMR framework (Hakim et al. 2016). For this technique, the ensemble mean and perturbations are updated separately. Furthermore, this ensemble technique, with serial observation processing, also implies that the full error covariance matrix B never needs to be calculated explicitly [for further details, see Whitaker and Hamill (2002)].
As mentioned above, Kalman filter methods rely on, in this case, the covariance between temperature and SIC derived from the prior ensemble. It is well documented that climate models tend to underestimate the sensitivity of Arctic sea ice variability to temperature (e.g., Stroeve et al. 2007; Winton 2011; Rosenblum and Eisenman 2017). To address this low-sensitivity bias, we inflate the sea ice perturbations from the prior ensemble means for the climate simulations used here, the MPI and CCSM4 Last Millennium simulations (see section 2b), by multiplying each by a factor of 1.8 and 2.6 respectively. We also reduce the effect of spurious long-distance correlations using covariance localization (e.g., Hamill et al. 2001), applying the Gaspari–Cohn fifth-order polynomial function (Gaspari and Cohn 1999) with a localization radius (the distance from observations set to zero influence) of 15 000 km. Both this localization length scale and these inflation factors are taken from Brennan et al. (2020), who determined empirically that these values yield reconstructions from assimilated instrumental temperature observations that best fit the observed total Arctic sea ice extent trend and variability during the satellite era (using both squared correlation and coefficient of efficiency to measure skill). To account for uncertainty in the errors of the prior and proxies, we perform 10 Monte Carlo iterations for each reconstruction (200 ensemble members for each iteration) for which a different random prior ensemble draw is used and 75% of the proxy records are randomly sampled to be assimilated. Including a different subset of the proxy records in each Monte Carlo iteration provides a measure of uncertainty due to the proxy records included in the assimilation, which can help account for unknown error in modeling certain proxies (Hakim et al. 2016). Results shown below pertain to the ensemble mean, averaged across all the ensemble members from 10 Monte Carlo iterations unless specified otherwise.
Since the range of valid SIC values ranges over 0%–100%, and solutions to (1) are not limited to this range, values outside this range are adjusted to 0% and 100%, respectively, for each ensemble member at each grid cell. On average, across all years, ensemble members and Monte Carlo iterations, 1.8% ± 0.6% of the reconstructed values result in concentrations greater than 100% and 0.9% ± 0.3% of reconstructed values are less than or equal to −1% SIC (reported spread is one standard deviation across all years, ensemble members, and Monte Carlo iterations). For all of our Arctic sea ice results, we reconstruct SIC and calculate the total Arctic sea ice area and extent (area of grid cells with concentration greater than 15%) after the above adjustments are made for each ensemble member and across iterations.
b. Data sources
A 200-member prior ensemble (200 random years) of both SAT and SIC fields is randomly drawn from fully forced CMIP5–PMIP3 Last Millennium model simulations spanning the years 850–1849 CE (Schmidt et al. 2011; Taylor et al. 2012). This ensemble size was chosen because it is computationally inexpensive and exhibits small differences from reconstructions performed with a 1000-member prior ensemble as described in Brennan et al. (2020). For this work, all experiments are run using prior ensembles drawn from two different models: the Community Climate System Model version 4 (CCSM4, Last Millennium simulation; Landrum et al. 2013) and Max Planck Institute for Meteorology (MPI-ESM-P, Last Millennium simulation; Jungclaus et al. 2010). These two sets of experiments are used to estimate the sensitivity of the sea ice reconstructions to the climate model prior and thus the sensitivity of the results to model physics and temperature–sea ice covariance structure. All model output is regridded to a 2° × 2° grid.
We assimilate annually resolved temperature-sensitive proxy records from the Past Global Changes Consortium version 2.0.0 (PAGES2kv2; Emile-Geay et al. 2017), including tree rings, ice cores, corals, lake sediments, and bivalve records (see location of proxy records in Fig. S1 in the online supplemental material). For the proxy system models [H in Eq. (1), which predicts proxy values from the model prior], we use a linear model calibrated against instrumental temperature data between 1951 and 1980 CE for all records except tree-ring-width records, for which we use a bilinear model calibrated against both temperature and precipitation from the instrumental records, including seasonality, following Tardif et al. (2019). The calibration datasets for the proxy system models used in this study are the NASA Goddard Institute for Space Studies Surface Temperature Analysis (Hansen et al. 2010) version 4 for temperature and the gridded precipitation dataset from the Global Precipitation Climatology Centre (Schneider et al. 2014) version 6 as the source of monthly information on moisture input over land surfaces.
c. Pseudoproxy experiments
Idealized experiments are performed where a climate model simulation is taken to be the targeted state. Then, a sparse network of pseudo SAT observations is drawn from the target and assimilated by the DA scheme (e.g., Steiger et al. 2014). The resulting Arctic sea ice reconstructions are compared with the target state in order to assess the skill of the setup. Both perfect and imperfect model pseudoproxy experiments are performed. For perfect model experiments, both observations and the prior ensemble are drawn from the same model, which provides a useful upper bound on the performance of a reconstruction for a given observation network. Imperfect model experiments draw observations from one model and the prior ensemble from a different model, which provides a more challenging but realistic test where the prior covariance and observation estimates are drawn from the wrong distribution.
For perfect model experiments, the CCSM4 Last Millennium simulation is taken to be the target state. SAT is drawn from the grid cell in the CCSM4 Last Millennium simulation closest to each proxy location in the PAGES2kv2 network (referred to as pseudo observations) for each year of the Last Millennium simulation (850–1849 CE). A random 200-member prior ensemble is also drawn from CCSM4 Last Millennium simulation. The posterior reconstruction can then be validated against the target state (CCSM4 Last Millennium simulation). Noise is added to the true pseudo observations, equal to the square root of the variance in the PAGES2kv2 proxy observation (same as for the real proxy experiments in section 2a) times a random value drawn from a standard normal distribution. This value of uncertainty was chosen in order to mimic the quantity used in the real proxy experiments. In this setup, the prior ensemble is drawn from the target state, and thus the covariance in the DA step, is perfect within sample error.
Imperfect model experiments take the MPI Last Millennium simulation to be the target state and pseudo observations are drawn from this simulation in the same way as in perfect model experiments. The difference is that the 200-member prior ensemble is drawn from the CCSM4 Last Millennium simulation. The posterior reconstruction can again be compared and evaluated against the target state (MPI Last Millennium simulation). This is a much stricter test of the method, and an important one, given that it mimics real reconstructions where the covariance is estimated from a model that is an imperfect representation of the true (unknown) covariance.
Both of these tests were performed by reconstructing years 850–1849 CE (the entire period of the last millennium simulations) and 10 Monte Carlo iterations were performed for each. Covariance inflation is used for the imperfect model experiments, as described previously, but not for the perfect model experiments given the prior ensemble is drawn from the target state and thus the sensitivity of Arctic sea ice variability to temperature is not underestimated. A localization radius of 15 000 km is used in all experiments. For each of the Monte Carlo iterations, a random sample of 25% of the proxy locations were withheld from the assimilation to simulate the same procedure used in the real proxy-based reconstructions.
d. Fixed proxy experiments
In a stationary offline DA framework, the prior ensemble is constant in time, and thus all temporal variability in the reconstructions comes from the assimilated proxy records. When the number of records assimilated increases, the temporal variability in the posterior also increases until the true variability is reached (assuming the ensemble is well calibrated and uncertainty properly accounted for). To disentangle the changes in temporal variability that are due to changes in proxy count, we perform experiments that assimilate a set of 101 proxy records (from the PAGES2kv2 network) that is fixed in time, where each record in the set has a measurement for every year reconstructed. For these experiments we reconstruct the years 1200–1970 CE using a single Monte Carlo iteration with a 200-member prior ensemble. A map showing the location of the proxy records included in this network is included in Fig. S1.
e. Skill metrics
This quantity has an upper bound of one and is unbounded in the negative direction. A CE value of one indicates the two datasets are identical, namely exhibiting the same relative phasing and amplitude of signal and no bias. A CE value of zero occurs when the sum of squared errors is equal to the variance in the verification data, and negative CE values result from a bias between the two datasets, in either the mean or amplitude of the variability.
3. Results
a. Pseudoproxy experiments
For perfect model experiments, the total Arctic sea ice extent anomalies over the entire reconstructed period (850–1849 CE, the full length of the last millennium simulations) are verified against the target values from the CCSM4 Last Millennium simulation and show an R2 value of 0.51 and a CE value of 0.47 (Fig. 1). Variability in the reconstructed ensemble mean is smaller than in the target state (with a temporal standard deviation of 0.29 × 106 versus 0.57 × 106 km2 in the target state), as expected when comparing an ensemble mean with a deterministic quantity (Leith 1974). The temporal variance of individual ensemble members is larger than the ensemble mean, but much of this temporal variability is noise (different for all ensemble members), so we rely on the ensemble mean throughout the results section since it provides the best estimate of the state relative to any individual ensemble member.
(top) Total Arctic sea ice extent anomalies between 850 and 1849 CE from the target values (black; CCSM4 Last Millennium simulation) and reconstruction (blue). This reconstruction was constructed using a perfect model experiment with pseudo observations and a 200-member prior ensemble drawn from the CCSM4 Last Millennium simulation. The shaded blue region represents the 2.5th–97.5th-percentile spread of ensemble member anomalies. Anomalies are relative to 850–1850 CE. (bottom) Correlation coefficient and coefficient of efficiency are shown from comparing reconstructed and target values of sea ice concentration at each grid cell between 850 and 1849 CE. The gray circles indicate all the proxy locations from the PAGES2kv2 database for various proxy types that are available in this region for some portion of 850–1849 CE. Pseudo proxy observations are drawn from 75% of these proxy locations for each Monte Carlo iteration.
Citation: Journal of Climate 35, 4; 10.1175/JCLI-D-21-0099.1
Spatial performance of the reconstructed SIC shows good performance throughout the Arctic, with the highest performance near the coastlines of North America (particularly around Alaska and the Hudson Bay regions), near Iceland, and throughout the Barents Sea, where proxy observations are plentiful (Fig. 1). Positive CE values are observed everywhere, although their amplitude is smaller than correlation coefficients, as expected, given that CE measures signal amplitude and bias as well as timing. Overall these results indicate that DA can skillfully combine sparse temperature information together with a prior drawn from CMIP5–PMIP3 Last Millennium climate model simulations in order to reconstruct annual Artic SIC in this perfect model framework.
Imperfect model experiments show worse performance than the perfect model experiments, with total Arctic sea ice extent anomalies having both R2 value and CE of 0.43 with the target state (Fig. 2). Note that the model prior (CCSM4 Last Millennium) compared to the target model (MPI Last Millennium), in the absence of assimilation, yields an R2 value of 0.04 and CE of −0.54. Therefore, assimilating observations from this sparse network draws the reconstructed state much closer to the target state than the original model prior. As in the perfect model experiment, the reconstructed ensemble mean underestimates the temporal variability with a standard deviation of 0.42 × 106 km2 as compared to 0.60 × 106 km2 in the target.
(top) Total Arctic sea ice extent anomalies between 850 and 1849 CE from the target values (black; MPI Last Millennium simulation) and reconstruction (blue). This reconstruction was constructed using an imperfect model experiment with pseudo observations drawn from MPI Last Millennium simulation and a 200-member prior ensemble drawn from the CCSM4 Last Millennium simulation. The shaded blue region represents the 2.5th–97.5th-percentile spread of ensemble member anomalies. Anomalies are relative to 850–1850 CE. (bottom) Correlation coefficient and coefficient of efficiency are shown from comparing reconstructed and target values of sea ice concentration anomalies at each grid cell between 850 and 1849 CE. The gray circles indicate all the proxy locations from the PAGES2kv2 database for various proxy types that are available in this region for some portion of 850–1849 CE. Pseudo proxy observations are drawn from 75% of these proxy locations for each Monte Carlo iteration.
Citation: Journal of Climate 35, 4; 10.1175/JCLI-D-21-0099.1
In evaluating the spatial performance of the imperfect model reconstruction, we note large differences in the mean state SIC between the CCSM4 (prior) and MPI (target) Last Millennium simulations (see Fig. S2), which lead to mean-state biases in the reconstructions. Generally, the sea ice edge in the CCSM4 Last Millennium simulation extends farther east of Greenland in the Fram Strait region. There is also more sea ice in Baffin Bay, the Barents Sea, the Kara Sea, and the Sea of Okhotsk in the CCSM4 Last Millennium simulation and less SIC in the Canadian Arctic Archipelago and Bering Sea when compared to the MPI Last Millennium simulation. The reconstructed extent in the imperfect model experiments has a bias of at least 0.2% throughout the Arctic, which results in negative CE values throughout the Arctic. To gain further insights for the imperfect model experiments without bias, we show correlation coefficients and CE values for SIC with the time mean removed at each grid cell in Fig. 2. Overall these results show positive correlation and CE values throughout the Arctic, with the highest performance off the coast of regions where there are more proxy locations, as in the perfect model experiments. Again, the CE values are lower than correlation coefficients and large regions of negative CE values are observed. Given that the mean bias was removed, these regions with low or negative CE values reveal where the reconstructed variability exceeds that in the target state. CE values are particularly low in the North Atlantic and north and northwest Pacific regions where the target state exhibits zero SIC most years, with some isolated years of minimal sea ice coverage. This pattern is difficult to reconstruct given that when there is any variability present in the prior ensemble at a given location, the DA reconstruction will retain variability there for all times.
These imperfect model experiments show that prior bias reduces skill in the reconstructions relative to the perfect model case, but also that the sparse proxy network is sufficient to yield skillful reconstructions particularly of coastal sea ice conditions as well as pan-Arctic coverage. To account for the effect of prior bias on the real-proxy results we perform our analysis on two sets of reconstructions derived using both CCSM4 and MPI Last Millennium priors. Moreover, we define anomalies relative to the satellite era in our proxy-based reconstructions, since that time period is observationally well constrained.
b. Proxy-based reconstructions
Here we present two 2000-yr reconstructions of Arctic sea ice cover, derived from assimilating the full PAGES2kv2 proxy network with a 200-member ensemble drawn from CCSM4 Last Millennium simulation in one experiment, and MPI in the other. Ten Monte Carlo iterations were performed using each model prior to account for uncertainty in the prior ensemble and proxy error, and the results shown are the ensemble mean across all members from all iterations for each metric unless otherwise noted.
1) Validation and comparisons to other records
Given that there are more reconstructions of temperature available relative to sea ice, we begin by comparing our reconstructions of Arctic mean SAT with previous estimates. We compare our reconstructions with McKay and Kaufman (2014) and Anchukaitis et al. (2017), who both use collections of Arctic proxy records to reconstruct Arctic and Northern Hemisphere temperatures respectively (see comparison in Fig. S3). Anchukaitis et al. (2017) reconstructed full spatial fields of Northern Hemisphere May–August temperatures and we use their filtered dataset, which only includes values with a reduction in error greater than zero, to calculate an Arctic mean temperature (area weighted north of 60°N). This comparison shows that the reconstructions using a model prior drawn from MPI Last Millennium simulations compares best with both McKay and Kaufman (2014) and Anchukaitis et al. (2017) with R2 values for 20-yr low-pass filtered datasets of 0.67 and 0.81, respectively (see Table S1 in the online supplemental material).
To validate our reconstructions of sea ice, we first compare the reconstructed total Arctic sea ice extent to that from satellite observations. A similar comparison for total Arctic sea ice area is found in Fig. S4 and Table S3. Reconstructions using prior ensembles drawn from CCSM4 and MPI Last Millennium simulations and proxies from the full PAGES2kv2 proxy network are shown in Fig. 3, and we first note that they strongly agree with one another (R2 and CE value of 0.86 between 1 and 1999 CE; see Table S2). The reconstruction using a CCSM4 Last Millennium model prior verifies better with satellite observations of total Arctic sea ice extent [annually averaged monthly sea ice extent values from Fetterer et al. (2017)] between 1979 and 1999 with an R2 and CE value of 0.60 and 0.58 as compared to values of 0.50 and 0.45 for reconstructions using an MPI Last Millennium model prior. For the rest of the analysis we will present our results using our reconstruction that relies on a prior ensemble drawn from the CCSM4 Last Millennium simulation.
Annual total Arctic sea ice extent anomalies from satellite observations (red; Fetterer et al. 2017) and Walsh et al. (2019) (brown) calculated from monthly values, an annual reconstruction produced by assimilating HadCRUT4 temperature observations and an ensemble drawn from CCSM4 Last Millennium simulation (black; Brennan et al. 2020), and our annual reconstructions produced by assimilating the PAGES2kv2 proxy records and a prior ensemble drawn from the CCSM4 (blue) and MPI (purple) Last Millennium simulations, respectively. The blue, purple, and black shaded regions all represent the 2.5–97.5th-percentile spread of the ensemble member anomalies. Anomalies are relative to 1979–99 CE.
Citation: Journal of Climate 35, 4; 10.1175/JCLI-D-21-0099.1
Comparing our reconstructions of total Arctic sea ice extent to other reconstructions in the instrumental era (1850 to the present), we find good agreement with Brennan et al. (2020), who reconstruct total Arctic sea ice extent by the same method used here, but assimilate temperature observations from the HadCRUT version 4.6.0.0 dataset (HadCRUT4; Morice et al. 2012) with the same Last Millennium climate simulations. All of the validation statistics with satellite observations and other reconstructions shown in Fig. 3 are highlighted in Table 1. The strongest agreement (other than with satellite observations) is with the Brennan et al. (2020) reconstruction using MPI Last Millennium model prior with an R2 value of 0.59 and a CE of 0.49 between 1850 and 1999 CE. It is perhaps surprising that the best agreement with the Brennan et al. (2020) reconstruction uses a different model prior, but we note that results for both model priors also agree well, with R2 and CE values of 0.86 between 1 and 1999 CE. We hypothesize that the minor differences result from different spatial distributions of observations between HadCRUT and PAGES2kv2, especially as they project onto the model covariance patterns.
Squared correlation coefficient and coefficient of efficiency values between previously published records of total Arctic sea ice extent (columns) and the reconstructions presented here drawing prior ensembles from CCSM4 and MPI Last Millennium simulations and proxy records from PAGES2kv2 database (rows). Comparisons were done between 1850 and 1999 CE when compared to records from Brennan et al. (2020) and Walsh et al. (2019) and between 1979 and 1999 CE when compared to satellite data (Fetterer et al. 2017). Anomalies centered about 1979–99 CE.
Both our proxy-based reconstructions and Brennan et al. (2020) show a larger decline of total Arctic sea ice extent during the early twentieth-century warming than that in the Walsh et al. (2019) reconstruction [we annually averaged monthly sea ice extent values from Walsh et al. (2019)]. The proxy-based reconstructions show a decline of approximately 1.0 × 106 km2 in total Arctic sea ice extent between 1910 and 1940 CE, with low values remaining through 1960 before increasing by approximately 0.5 × 106 km2 by around 1965, followed by a persistent decline into the satellite era. This signal differs from the Walsh et al. (2019) reconstruction, which shows relatively constant total Arctic sea ice extent anomalies between 1850 and 1970 CE except for a brief decrease and increase of about 0.5 × 106 km2 between ∼1940 and 1950 CE. Conversely, in the earlier portion of the instrumental era, between 1850 and 1900 CE, both our proxy-based reconstruction and the Walsh et al. (2019) reconstruction show more Arctic sea ice coverage than the Brennan et al. (2020) reconstructions (a maximum difference of approximately 0.5 × 106 km2). During this period, there were relatively fewer temperature observations available in the HadCRUT4 dataset assimilated in the Brennan et al. (2020) reconstructions than in later periods, while the number of proxy records is near its peak. We speculate that the lower coverage of Arctic sea ice indicated in the Brennan et al. (2020) reconstructions may be due to the lower number of temperature observations assimilated during this period. Our reconstructions also disagree with Walsh et al. (2019) between 1950 and 1970 CE, which appears to be related to larger sea ice coverage in Baffin Bay and east of Greenland in the Walsh et al. (2019) reconstruction (see Fig. S8). A comparison of our reconstructed total Arctic sea ice area with satellite data and Walsh et al. (2019) can be found in Fig. S4.
Next, we compare our reconstruction to a gridded passive-microwave-derived SIC satellite product (Peng et al. 2013; Meier et al. 2017) to evaluate the spatial performance of our reconstructions. Figure 4 shows the correlation coefficient and CE values evaluated at each grid cell using the annually averaged, merged satellite product (Meier et al. 2017), regridded to a 2° × 2° grid, and our reconstruction (CCSM4 Last Millennium model prior) between 1979 and 1999 CE. Note that SIC values are infilled with 100% concentration around 85°–90°N in the satellite product, so correlation and CE values are not shown in this region. Elsewhere, we generally see positive correlation values with regions exhibiting negative correlation in Baffin Bay and near the sea ice edge in the Pacific sector. As described in the imperfect pseudo proxy experiment results, mean state biases between the prior and satellite data are inherited in our reconstructions (see Fig. S5), which leads to negative CE values. Consequently, in order to assess variability rather than mean bias, we show CE values comparing anomalies for both reconstructed and satellite values in Fig. 4. In the central Arctic, the regions that show negative CE values in Fig. 4 are regions where variability is overestimated. Similarly, near the sea ice edges, particularly near the Kamchatka Peninsula and Greenland and Barents Seas, regions of negative CE are located near biased estimates in the sea ice edge. In Baffin Bay and the Bering Sea, the negative CE values are due to the signal timing differences between the satellite product and reconstruction. The spatial performance of reconstructions using a prior drawn from an MPI Last Millennium model prior yield similar results and are shown in Fig. S6.
Correlation coefficient and coefficient of efficiency are shown from comparing a merged satellite product (Meier et al. 2017) and reconstructed ensemble-mean (derived using a CCSM4 Last Millennium model prior) sea ice concentration anomalies at each grid cell between 1979 and 1999 CE. Values are only shown where the mean state of the reconstruction between 1979 and 1999 CE exceeds 15% coverage. Note that sea ice concentration values are infilled with 100% concentration around 85°–90°N in the satellite product, therefore these skill metrics are not shown in that region.
Citation: Journal of Climate 35, 4; 10.1175/JCLI-D-21-0099.1
Prior to the instrumental era, various sea ice–sensitive proxy records have been developed to reconstruct regional sea ice conditions. Here we compare three independent records from three different regions to our reconstructions. Regional averages are defined using the regional mask from the National Snow and Ice Data Center as defined in Fig. S7 (regridded to a 2° × 2° grid). Figure 5 shows a comparison of the regional sea ice areas from our reconstructions and Walsh et al. (2019) to two IP25 records from the Barents Sea (Vare et al. 2010) and northern Iceland (Massé et al. 2008) and a combined algal record from the Canadian Arctic (Halfar et al. 2013). Comparisons with proxy records are shown relative to our reconstructions of total Arctic sea ice area because they are a more sensitive measure than extent and better reflect the amount of sea ice coverage in the region that proxy records are sensitive to. Further, given our reconstructions produce annual mean values, there is little variability in the extent in regions within the ice edge because on average most grid cells maintain at least 15% coverage.
Regional sea ice area anomalies from our reconstruction produced by assimilating the PAGES2kv2 proxy records and a prior ensemble drawn from the CCSM4 Last Millennium simulation (black) and 15-yr low-pass filtered ensemble mean (blue). The 15-yr low-pass filtered regional sea ice area from Walsh et al. (2019) is given by the brown line. Anomalies are relative to 1979–99 CE. (a) Normalized IP25 flux in the BASICC-8 sediment core, a proxy for springtime sea ice occurrence in the western Barents Sea (teal; Vare et al. 2010). (b) A combined algal record produced by averaging the normalized annual growth rates and annually averaged Mg/Ca ratios from three samples collected in the Canadian Arctic representing abundance of summer sea ice (plotted on an inverted scale), light green line is the 5-yr moving average; darker green line the 15-yr low-pass filtered annual data as in Halfar et al. (2013). (c) Relative abundance of IP25 in core MD99–2275 (green dots), a proxy for springtime sea ice occurrence along the northern coast of Iceland (Massé et al. 2008).
Citation: Journal of Climate 35, 4; 10.1175/JCLI-D-21-0099.1
Overall there are encouraging similarities between the regional proxies and our reconstruction, particularly on centennial time scales, but in general our reconstructions tend to show better agreement with Walsh et al. (2019) than the proxy records. Our reconstructions share common aspects with the algal proxy records from Halfar et al. (2013) in the Baffin Bay region during the twentieth century, having an R2 value of 0.20 [calculated using 15-yr low-pass Butterworth filtered reconstructed ensemble mean and records from Halfar et al. (2013)]; estimates from Walsh et al. (2019) show a much greater expansion of sea ice centered around 1965 in the region. In the eastern Greenland region, the proxies show minimal spring sea ice cover prior to 1300, and our reconstructions also show low sea ice cover with anomalies comparable to the satellite era between approximately 800 and 1100 CE. Qualitatively, our reconstructions compare well with that presented in Vare et al. (2010) in the Barents Sea, and both indicate a peak in sea ice coverage around 1800 CE. However, the onset of the early twentieth-century warming occurs earlier (around 1910 to 1920 CE) in both our reconstructions and Walsh et al. (2019), as compared to Vare et al. (2010) (around 1940 CE), which also shows no recovery in the 1970s. A comparison of our reconstructions of regional sea ice area to those in Walsh et al. (2019), for all 13 regions of the Arctic, is shown in Fig. S8.
The only pan-Arctic reconstructions of sea ice coverage we are aware of during the Common Era are those of Kinnard et al. (2011) and Singh et al. (2018). While the Singh et al. (2018) reconstruction uses methods similar to ours, they differ in important ways, including no prior inflation or localization, a smaller prior ensemble (100 members rather than 200 members), and, most important, an earlier version of the PAGES2k proxy network. The Singh et al. (2018) reconstruction has considerably less temporal variability, and the R2 value with each of our reconstructions of total Arctic sea ice area is 0.44. Kinnard et al. (2011) produce a record of August Arctic sea ice extent with 5-yr resolution from 563 to 2008 CE. There is substantially more variability in the Kinnard et al. (2011) reconstruction (see Fig. S9), which is likely due to the fact that it is an estimate of the sea ice extent for a single summer month. During this time period our reconstruction with a prior drawn from a CCSM4 Last Millennium simulation is negatively correlated with Kinnard et al. (2011) and has an R2 value of 0.05 (both subjected to a 40-yr low-pass Butterworth filter).
2) Variability of Arctic sea ice in the preindustrial era
We present the full 2000-yr reconstruction in Fig. 6, and remind the reader that given the stationary offline approach, all the temporal variability originates from the assimilated proxy observations. Furthermore our reconstructions show minimal agreement with the last millennium simulations used as ensemble priors for the reconstructions (see Table S2). Notable features include a steady rise in Arctic sea ice extent between approximately 750 and 1820 CE as well as large spikes in Arctic sea ice extent that appear to correspond with large volcanic eruptions. Between 1600 and 1850 CE, the Arctic sea ice extent remains elevated with the exception of a period of retreat and recovery from about 1600 to 1800 CE (Fig. 6). The long-term rise in Arctic sea ice extent between 750 and 1820 CE is consistent with well-documented Northern Hemisphere (e.g., Mann et al. 2008) and high-latitude (e.g., Kaufman et al. 2009) millennial-scale cooling trend in temperature-sensitive proxy records and other climate field reconstructions (e.g., Hakim et al. 2016; Tardif et al. 2019). Previous work has shown that this millennial-scale cooling in the Northern Hemisphere corresponds with a slow reduction of summer insolation in these regions that is amplified by climate feedbacks (e.g., Kerwin et al. 1999; Wanner et al. 2008; Kaufman et al. 2009), while other studies show this cooling was more influenced by volcanic eruptions and greenhouse gas concentration changes (e.g., Hegerl et al. 2007; Schurer et al. 2014). In our reconstructions, as described in section 2d, we note that this time period also corresponds with a steady increase in the number of proxy observations (Fig. 6, lower panel), which could in theory contribute to a trend in the resolved signal. To control for this effect, we perform a fixed proxy experiment (see section 2d) between 1200 and 1970 CE, in which the same 101 proxy records are assimilated at each time. This fixed proxy experiment eliminates artificial temporal variability due to changes in proxy count, although limiting the available records can also reduce the overall variability in the reconstruction. Results for this fixed proxy experiment also have a positive trend between 1200 and 1800 CE (see Fig. S10), statistically different from zero with 99% confidence, which supports the interpretation that the trend of increasing Arctic sea ice extent in our reconstruction is not a result of the changing number of proxy records in time.
(top) Total Arctic sea ice extent anomalies from satellite observations (red, Fetterer et al. 2017), and our reconstruction (black) produced by assimilating the PAGES2kv2 proxy records and a prior ensemble drawn from the CCSM4 Last Millennium simulation. The gray shaded regions represent the 2.5th–97.5th-percentile range of the ensemble member anomalies. The blue line is the 20-yr low-pass filtered ensemble mean of the reconstruction shown in black. Anomalies are relative to 1979–99 CE. (bottom) The total number of proxy locations assimilated in the reconstruction through time.
Citation: Journal of Climate 35, 4; 10.1175/JCLI-D-21-0099.1
Next, we investigate the correspondence of Arctic sea ice extent changes with large volcanic eruptions. First we note that previous work has found evidence of Arctic sea ice expansion in the decade following tropical volcanic eruptions in the sea ice–sensitive (IP25 and alkenone biomarker) proxies (Sicre et al. 2013). In our reconstructions, around 540 CE there is a large spike (Fig. 6), which corresponds with a series of large tropical and Northern Hemisphere volcanic eruptions that are associated with anomalously cool conditions across the Northern Hemisphere, the largest of which resulted in −19.1 W m−2 of global forcing (Sigl et al. 2015). There are other spikes in Arctic sea ice extent that correspond with large tropical eruptions such as those that occurred around 1458 CE (−20.6 W m−2 of global forcing) and 1815 CE (−17.2 W m−2 of global forcing; see Fig. S11). Another notable period of amplified Arctic sea ice extent occurred during the Little Ice Age between around 1600 and 1700 CE, which corresponds with various larger tropical eruptions such as those in 1601 (−11.6 W m−2 of global forcing), 1641 (−11.8 W m−2 of global forcing), and 1695 CE (−10.2 W m−2 of global forcing).
To further investigate the response of Arctic sea ice to volcanic eruptions, we perform composite analysis on the 26 largest temporally distinct eruptions that occurred in the Northern Hemisphere and the tropics between 1 and 1980 CE (Fig. 7). To define these eruptions we started with the tropical and Northern Hemisphere eruptions from the list of 40 largest eruptions over the last two millennia presented in Fig. 3b of Sigl et al. (2015). We then selected the eruptions that were temporally distinct, meaning eruptions without other eruptions on the list at least 10 years preceding or following them. This ensures that the signal in the composite represents the response of Arctic sea ice to a single large eruption. We find that there is a statistically significant (with 95% confidence) increase of total Arctic sea ice extent during the year of the eruption followed by elevated coverage for approximately 3–5 years (Fig. 7). The largest response occurs during the year of the eruption with an increase in total Arctic sea ice extent of approximately 0.19 × 106 km2 in the mean across all 26 eruptions after which the anomalies slowly dampen to zero. This composite is based on the reconstruction from assimilating PAGES2kv2 proxy records and a prior drawn from the CCSM4 Last Millennium simulation. We performed the same composite on a reconstruction using a prior drawn from MPI Last Millennium simulation and found a smaller mean amplification of total Arctic sea ice extent anomalies during the year of the eruptions (∼0.14 × 106 km2), but these elevated anomalies lasted slightly longer (7 years following the eruption were statistically significant from zero at 95% confidence; not shown).
A composite of reconstructed total Arctic sea ice extent anomalies (acquired by assimilating PAGES2kv2 proxy records with a prior drawn from CCSM4 Last Millennium simulation) from the 5 years preceding and 25 years following 26 large eruptions taken from Sigl et al. (2015). Anomalies of total Arctic sea ice extent are relative to the 5 years preceding each eruption, which is indicated by the vertical dashed red line. The light blue lines show the ensemble mean across 2000 ensemble members for each eruption. The dark blue line shows the mean across all 26 eruptions, and the open circles indicate the years that show anomalies that are statistically different from zero with 95% confidence according to a t test. The gray shaded region shows the 2.5th and 97.5th percentiles derived from taking the mean of a composite of 26 random draws from our reconstruction 1000 times.
Citation: Journal of Climate 35, 4; 10.1175/JCLI-D-21-0099.1
Previous work that looked at the response of Arctic sea ice coverage to volcanic eruptions in model simulations has found a much larger response to eruptions and a lag in the response by a year or more with maximum response in the summer months (e.g., Zanchettin et al. 2014; Pauling et al. 2021). Differences in the magnitude of these responses with our reconstructions may be due to a variety of factors, including reduced variability in the ensemble mean response (as compared to individual model simulations), limited proxy availability, especially during the earlier portion of the record, model bias, and limits of annual resolution to detect changes that may be largely seasonal (e.g., Stevenson et al. 2017). Interestingly, when these composites are performed for the eruptions that occur between 850 and 1850 CE with the CCSM4 and MPI Last Millennium simulations, little response is observed in the CCSM4 Last Millennium simulation whereas a large lagged response is observed in the MPI Last Millennium simulation (see Fig. S12). We note that some of these differences are likely due to the fact that not all of the composited eruptions appear in the two different forcing datasets used for these simulations. However, the response in the reconstructions is similar for both model priors used, which further illustrates that this response is coming from information gained by assimilating proxy observations.
3) Twentieth-century Arctic sea ice variability in context
Using 2000-yr reconstructions puts the Arctic sea ice extent changes observed in the twentieth century in broader context (Fig. 6). Here we use our reconstruction to investigate two key questions about Arctic sea ice variability: 1) How significant and for what length of time are the negative trends in the satellite record significant compared to the rest of the last millennium? 2) Has the variability of Arctic sea ice on interannual to decadal time scales changed during the last millennium?
To investigate the significance of observed trends in Arctic sea ice extent in the satellite record, we look at the distribution of trends over sliding 20- and 30-yr windows throughout our reconstructions and satellite observations. For our reconstructions, we calculate trends during all possible 20- and 30-yr overlapping periods for each ensemble member from all Monte Carlo iterations (2000 total ensemble members) for the preindustrial (1000–1850 CE), postindustrial (1850–1979 CE), and satellite era (1979–99 CE). The reconstructed trends during the satellite era are only shown for 20-yr periods because our reconstructions only overlap with the satellite era for 20 years (1979–99 CE). These results are shown as histograms in Fig. 8, and we note that the uncertainty in these trends only accounts for variability in the proxy network.
Distribution of total Arctic sea ice extent trends calculated on individual ensemble members for 20- and 30-yr running windows. The results from our reconstruction of total Arctic sea ice extent (PAGES2kv2 proxy records, CCSM4 Last Millennium model prior) are shown: preindustrial trends (1000–1850 CE) in filled blue, postindustrial trends (1850–1979 CE) in unfilled dark blue, and the satellite era trends (1979–99 CE) in unfilled turquoise in the left panel only. The vertical dashed turquoise line indicates the mean of the distribution of reconstructed satellite-era trends. The distribution of trends calculated from satellite observations (Fetterer et al. 2017) are shown in red near the horizontal axis. The darker blue filled portion of the preindustrial distribution of reconstructed trends represents the 95% confidence interval.
Citation: Journal of Climate 35, 4; 10.1175/JCLI-D-21-0099.1
We first note differences between the reconstructed pre- and postindustrial distributions of trends (Fig. 8). The postindustrial period shows steeper negative trends due to the early-twentieth-century warming, which exhibits large and steep declines of Arctic sea ice extent in our reconstructions. The mean reconstructed 20-yr trend during the satellite era underestimates the magnitude of the trend observed in satellite observations for the equivalent time period (1979–99 CE; vertical dashed red line in Fig. 8). Nevertheless, the mean reconstructed 20-yr satellite era trend falls outside the 95% confidence window of reconstructed preindustrial 20-yr trends indicating that the means of the two distributions are statistically different at the 95% confidence level. Interestingly, the full distribution of sliding 20-yr trends calculated from satellite observations (Fetterer et al. 2017; 1979–2017 CE; shown in red near the horizontal axis in Fig. 8) shows some overlap with the reconstructed preindustrial distribution, indicating that although the means are statistically different, some ensemble members from the preindustrial period show 20-yr trends similar to those observed in the satellite record. For 30-yr trends there is nearly no overlap between the trends in the satellite record and reconstructed preindustrial period. We find that for windows longer than about 30 years for reconstructions using a CCSM4 Last Millennium model prior (35 years for reconstructions using a MPI Last Millennium model prior), the trends in the satellite record are outside the distribution of reconstructed preindustrial trends (see Fig. S13). These results are consistent with previous studies that have shown that greenhouse gas warming impacts tend to exceed internal variability for global mean temperature at greater than 30-yr time scales (e.g., Parsons et al. 2020). The same analysis shown in Fig. 8 performed on reconstructions using a prior drawn from MPI Last Millennium simulations yield similar findings (not shown).
To investigate our second question, whether variability of Arctic sea ice extent has changed in the last millennium, we examine the spectral power of reconstructed total Arctic sea ice extent (Torrence and Compo 1998). We use the first derivative of the Gaussian as the wavelet basis function because we are particularly interested in periods of rapid advance or decline of Arctic sea ice extent. As mentioned previously, with an offline DA approach, the variability in time may depend on the number of proxies assimilated. Therefore wavelet analysis is performed on two different reconstructions of total Arctic sea ice extent: full reconstructions from 1 to 1999 CE with all PAGES2kv2 proxies assimilated, and a fixed proxy reconstruction from 1200 to 1970 CE with the same 101 proxies assimilated at each time.
Figure 9 shows the wavelet power spectrum for both the full and fixed-proxy experiments. Generally, there are two main regions of significant power (exceeding the 95% confidence level) centered at approximately 1550 and the early-twentieth-century warming (∼1900). The sector of high power between 1500 and 1600 CE is significant for periods of approximately 64 years and longer in the fixed proxy experiment and for all periods in the full proxy experiments. Around the start of the early-twentieth-century warming (∼1900), there is significant power for periods greater than approximately 20 years in the fixed proxy experiments and at all periods in the full proxy experiments. There are other isolated sectors of both wavelet power spectra in Fig. 9 with significant power; however, a majority of the power is contained at longer periods in these two regions centered about 1550 and 1900 CE. In the full proxy wavelet spectrum there is very little power prior to about 1400 CE, which is likely due in part to the decreasing proxy count and thus decreasing temporal variability in Arctic sea ice reconstruction going further back in time.
The wavelet power spectrum of total Arctic sea ice extent anomalies using a first derivative of a Gaussian as the wavelet basis function for two different reconstructions: (bottom) full reconstruction using all PAGES2kv2 proxy records (0–1999 CE), and (top) reconstruction using a 101 fixed proxy records (1200–1970 CE). The anomalies of both reconstructions are relative to 1900–40 CE. The black contours enclose regions of greater than 95% confidence for a red noise process with lag-1 coefficients of 0.76 and 0.66 respectively. The gray shaded region represents the so-called cone of influence, where edge effects become important. For the full reconstruction, the analysis was performed on the mean across 200 ensemble members from 10 Monte Carlo iterations (a random sample of 75% of the proxy records was assimilated into each iteration), whereas the analysis of the fixed proxy experiment was performed on the ensemble mean from a single iteration of 200 ensemble members.
Citation: Journal of Climate 35, 4; 10.1175/JCLI-D-21-0099.1
Overall, there is little significant power for shorter periods (10–20 years) in any of the wavelet power spectra in Fig. 9 (except for isolated periods that could be associated with volcanic eruptions) indicating that the postindustrial era is not significantly different from the last 1000 to 2000 years on these time scales. For periods greater than 30 years the power reaches a maximum from around 1800 to 1999 CE, which greatly exceeds the power reached in the rest of the record. This high power in the later portion of the records indicates that rapid growth and decline from 1800 to 1999 CE was more pronounced than what was reconstructed during the rest of the last 1000 to 2000 years.
4. Discussion and conclusions
These results indicate that assimilating temperature-sensitive proxy records with last millennium model simulations can be a useful tool for reconstructing Arctic sea ice over the last two millennia. Furthermore, we find strong agreement between the reconstructions presented here and those from Brennan et al. (2020) (Fig. 3) whose reconstructions relied on temperature observations, which reinforces the fact that proxy records are well equipped to resolve a temperature signal on annual time scales.
As discussed previously, some mean state bias is inherited in our reconstructions from the model prior used. These biases arise mainly due to the fact that the same uninformed prior ensemble, drawn from a last millennium simulation, is used to reconstruct Arctic sea ice conditions throughout the last two millennia. However, there are also differences in model physics and teleconnection patterns (e.g., Bonan and Blanchard-Wrigglesworth 2020) that likely contribute to differences in reconstructions using different model priors.
Using two types of pseudoproxy experiments we found that the DA scheme described here can be used to skillfully reconstruct Arctic sea ice coverage by assimilating pseudo temperature observations and prior ensembles drawn from last millennium model simulations. These experiments show skill in both pan-Arctic quantities such as total Arctic sea ice extent, and also in spatial performance, particularly in coastal regions near proxy locations. When pseudo proxy reconstructions of total Arctic sea ice extent are compared with the true values, perfect model experiments resulted in R2 and CE values of 0.51 and 0.47, respectively, while imperfect model experiments resulted in R2 and CE values of 0.43 and 0.43, respectively.
We present two sets of reconstructions derived by assimilating temperature sensitive proxy records from the PAGES2k network with both CCSM4 and MPI Last Millennium model priors. First, we validate these reconstructions of total Arctic sea ice extent against satellite observations (Fetterer et al. 2017) between 1979 and 1999 CE and find R2 and CE values of 0.60 and 0.58, respectively, when using a CCSM4 Last Millennium model prior and R2 and CE values of 0.50 and 0.45, respectively, for reconstructions using an MPI Last Millennium model prior. Next, we compare our reconstructions of total Arctic sea ice extent to other instrumental era reconstructions between 1850 and 1999 CE. When compared with Brennan et al. (2020), we find R2 values ranging between 0.46 and 0.59 and CE values between 0.023 and 0.49. Our two reconstructions overall show weaker agreement with Walsh et al. (2019), with R2 values of 0.36 and 0.47 and CE values between −0.33 and 0.067 for CCSM4 and MPI model priors, respectively. Generally our reconstructions and Brennan et al. (2020) show larger and longer lasting declines in total Arctic sea ice extent during the early-twentieth-century warming than the Walsh et al. (2019) reconstruction, but both our reconstructions and Walsh et al. (2019) generally show more Arctic sea ice extent between approximately 1850 and 1900 CE than the Brennan et al. (2020) reconstruction. We compare our reconstructed SIC with a merged satellite product (Meier et al. 2017) at each grid cell between 1979 and 1999 CE, and generally find positive correlation everywhere and some regions of negative CE mainly in the central Arctic and near the sea ice edge where our reconstructions overestimate sea ice variability. Finally we also compare our reconstructions to three sea ice–sensitive proxy-based reconstructions in three different regions of the Arctic and generally find similarities between these records and our reconstructions. However, on a regional basis, our reconstructions tend to agree more closely with that from Walsh et al. (2019) than the sea ice–sensitive proxy-based reconstructions.
In our 2000-yr reconstructions, there is a positive trend in total Arctic sea ice extent between approximately 750 and 1820 CE that we determine is not very sensitive to changes in proxy count. We also see large changes in total Arctic sea ice extent throughout the record that correspond with large volcanic eruptions. Through compositing our reconstructions for 26 large and temporally independent volcanic eruptions, we find a mean increase of ∼0.14–0.19 × 106 km2 during the year of an eruption followed by approximately 4–7 years of elevated Arctic sea ice extent conditions depending on the model prior used.
In the postindustrial period, we find that the mean reconstructed satellite trend on 20-yr time scales falls outside the 95% confidence interval of the distribution of reconstructed preindustrial trends. Furthermore, the distribution of trends in total Arctic sea ice extent calculated from satellite observations for 20- and 30-yr time scales shows some overlap with the tails of the distribution of trends calculated from 1000 to 1850 CE in our reconstructions. However, windows longer than 30 years yield a distribution of trends in the satellite observations that has no overlap with that from the preindustrial reconstructions.
Through wavelet analysis, we find that on shorter time scales (less than approximately 20-yr periods) there have been no major changes in Arctic sea ice variability throughout the last two millennia. This indicates that, despite strong external forcing, the variability in recent observations is representative of periods without such strong forcing. On longer time scales (greater than 30-yr time scales) the early-twentieth-century warming shows significantly more power than any other event in the last millennium. There is another event centered about 1550 CE that also shows high power and could be associated with insolation changes and volcanic eruptions, but requires further investigation that is left for future work.
Acknowledgments.
This research was supported by Grants AGS-1702423 from the National Science Foundation (NSF), and 2016-014 from the Heising-Simons Foundation. MKB was also supported by a NSF Graduate Research Fellowship. The CMIP5–PMIP3 data used in this paper were obtained from the Earth System Grid Federation at https://esgf-node.llnl.gov/projects/cmip5/ (last access: 30 May 2019). Some calibration and verification data sets were provided by the NOAA/OAR/ESRL PSD, Boulder, Colorado, USA, from their website at https://www.esrl.noaa.gov/psd/ (last access: 26 June 2019). Walsh et al. (2019) was accessed via the National Snow and Ice Data Center (NSIDC) website at https://nsidc.org/data/g10010, as was the gridded satellite products used for verification from https://nsidc.org/data/G02202/versions/3. The sea-ice proxy data in Fig. 5 were acquired for Halfar et al. (2013) from the NOAA National Centers for Environmental Information website at https://www.ncdc.noaa.gov/paleo-search/study/15454, and for Vare et al. (2010) and Massé et al. (2008) from the “Supplementary Data 4” datafile published with Kinnard et al. (2011). The timing and size of volcanic eruptions used was from the “Source data to Fig. 3” datafile published with Sigl et al. (2015). Python wavelet software was provided by Evgeniya Predybaylo based on Torrence and Compo (1998) and is available at http://atoc.colorado.edu/research/wavelets/. We thank Ed Blanchard-Wrigglesworth for helpful discussion of Arctic sea ice and Andre Perkins and Robert Tardif for their help with development of extensions to the LMR code that contributed to the work reported here. We also thank the three anonymous reviewers for their detailed comments and suggestions, which significantly improved the work. MKB would like to thank Luke Parsons, Jessica Badgeley, Cecilia Bitz, and the rest of the ice and climate research group for their feedback and productive discussion about this project.
Data availability statement.
All data for the reconstructions presented here are available online at Zenodo (https://doi.org/10.5281/zenodo.5809703).
REFERENCES
Alekseev, G., N. Glok, and A. Smirnov, 2016: On assessment of the relationship between changes of sea ice extent and climate in the Arctic. Int. J. Climatol., 36, 3407–3412, https://doi.org/10.1002/joc.4550.
Anchukaitis, K. J., and Coauthors, 2017: Last millennium Northern Hemisphere summer temperatures from tree rings: Part II, spatially resolved reconstructions. Quat. Sci. Rev., 163, 1–22, https://doi.org/10.1016/j.quascirev.2017.02.020.
Annan, J., J. Hargreaves, N. Edwards, and R. Marsh, 2005: Parameter estimation in an intermediate complexity Earth system model using an ensemble Kalman filter. Ocean Modell., 8, 135–154, https://doi.org/10.1016/j.ocemod.2003.12.004.
Atwood, A. R., E. Wu, D. M. W. Frierson, D. S. Battisti, and J. P. Sachs, 2016: Quantifying climate forcings and feedbacks over the last millennium in the CMIP5-PMIP3 models. J. Climate, 29, 1161–1178, https://doi.org/10.1175/JCLI-D-15-0063.1.
Belt, S. T., G. Massé, S. J. Rowland, M. Poulin, C. Michel, and B. LeBlanc, 2007: A novel chemical fossil of palaeo sea ice: IP25. Org. Geochem., 38, 16–27, https://doi.org/10.1016/j.orggeochem.2006.09.013.
Bhend, J., J. Franke, D. Folini, M. Wild, and S. Brönnimann, 2012: An ensemble-based approach to climate reconstructions. Climate Past, 8, 963–976, https://doi.org/10.5194/cp-8-963-2012.
Bonan, D. B., and E. Blanchard-Wrigglesworth, 2020: Nonstationary teleconnection between the Pacific Ocean and Arctic sea ice. Geophys. Res. Lett., 47, e2019GL085666, https://doi.org/10.1029/2019GL085666.
Brennan, M. K., G. J. Hakim, and E. Blanchard-Wrigglesworth, 2020: Arctic sea-ice variability during the Instrumental Era. Geophys. Res. Lett., 47, e2019GL086843, https://doi.org/10.1029/2019GL086843.
Connolly, R., M. Connolly, and W. Soon, 2017: Re-calibration of Arctic sea ice extent datasets using Arctic surface air temperature records. Hydrol. Sci. J., 62, 1317–1340, https://doi.org/10.1080/02626667.2017.1324974.
Deser, C., R. Tomas, M. Alexander, and D. Lawrence, 2010: The seasonal atmospheric response to projected Arctic sea ice loss in the late twenty-first century. J. Climate, 23, 333–351, https://doi.org/10.1175/2009JCLI3053.1.
de Vernal, A., R. Gersonde, H. Goosse, M.-S. Seidenkrantz, and E. W. Wolff, 2013: Sea ice in the paleoclimate system: The challenge of reconstructing sea ice from proxies—An introduction. Quat. Sci. Rev., 79, 1–8, https://doi.org/10.1016/j.quascirev.2013.08.009.
Ding, Q., and Coauthors, 2017: Influence of high-latitude atmospheric circulation changes on summertime Arctic sea ice. Nat. Climate Change, 7, 289–295, https://doi.org/10.1038/nclimate3241.
Dirren, S., and G. J. Hakim, 2005: Toward the assimilation of time-averaged observations. Geophys. Res. Lett., 32, L04804, https://doi.org/10.1029/2004GL021444.
Emile-Geay, J., and Coauthors, 2017: A global multiproxy database for temperature reconstructions of the Common Era. Sci. Data, 4, 170088, https://doi.org/10.1038/sdata.2017.88.
England, M., A. Jahn, and L. Polvani, 2019: Nonuniform contribution of internal variability to recent Arctic sea ice loss. J. Climate, 32, 4039–4053, https://doi.org/10.1175/JCLI-D-18-0864.1.
England, M., L. M. Polvani, L. Sun, and C. Deser, 2020: Tropical climate responses to projected Arctic and Antarctic sea-ice loss. Nat. Geosci., 13, 275–281, https://doi.org/10.1038/s41561-020-0546-9.
Fetterer, F., K. Knowles, W. N. Meier, M. Savoie, and A. K. Windnagel, 2017: Sea ice index, version 3. National Snow and Ice Data Center, accessed 15 February 2019, https://doi.org/10.7265/N5K072F8.
Gaspari, G., and S. E. Cohn, 1999: Construction of correlation functions in two and three dimensions. Quart. J. Roy. Meteor. Soc., 125, 723–757, https://doi.org/10.1002/qj.49712555417.
Goosse, H., H. Renssen, A. Timmermann, R. S. Bradley, and M. E. Mann, 2006: Using paleoclimate proxy-data to select optimal realisations in an ensemble of simulations of the climate of the past millennium. Climate Dyn., 27, 165–184, https://doi.org/10.1007/s00382-006-0128-6.
Goosse, H., D. Roche, A. Mairesse, and M. Berger, 2013: Modelling past sea ice changes. Quat. Sci. Rev., 79, 191–206, https://doi.org/10.1016/j.quascirev.2013.03.011.
Gregory, J. M., P. A. Stott, D. J. Cresswell, N. A. Rayner, C. Gordon, and D. M. H. Sexton, 2002: Recent and future changes in Arctic sea ice simulated by the HadCM3 AOGCM. Geophys. Res. Lett., 29, 2175, https://doi.org/10.1029/2001GL014575.
Hakim, G. J., J. Emile-Geay, E. J. Steig, D. Noone, D. M. Anderson, R. Tardif, N. Steiger, and W. A. Perkins, 2016: The last millennium climate reanalysis project: Framework and first results. J. Geophys. Res. Atmos., 121, 6745–6764, https://doi.org/10.1002/2016JD024751.
Halfar, J., W. H. Adey, A. Kronz, S. Hetzinger, E. Edinger, and W. W. Fitzhugh, 2013: Arctic sea-ice decline archived by multicentury annual-resolution record from crustose coralline algal proxy. Proc. Natl. Acad. Sci. USA, 110, 19 737–19 741, https://doi.org/10.1073/pnas.1313775110.
Hamill, T. M., J. S. Whitaker, and C. Snyder, 2001: Distance-dependent filtering of background error covariance estimates in an ensemble Kalman filter. Mon. Wea. Rev., 129, 2776–2790, https://doi.org/10.1175/1520-0493(2001)129<2776:DDFOBE>2.0.CO;2.
Hansen, J., R. Ruedy, M. Sato, and K. Lo, 2010: Global surface temperature change. Rev. Geophys., 48, RG4004, https://doi.org/10.1029/2010RG000345.
Hegerl, G. C., T. J. Crowley, M. Allen, W. T. Hyde, H. N. Pollack, J. Smerdon, and E. Zorita, 2007: Detection of human influence on a new, validated 1500-year temperature reconstruction. J. Climate, 20, 650–666, https://doi.org/10.1175/JCLI4011.1.
Jungclaus, J. H., and Coauthors, 2010: Climate and carbon-cycle variability over the last millennium. Climate Past, 6, 723–737, https://doi.org/10.5194/cp-6-723-2010.
Kaufman, D. S., and Coauthors, 2009: Recent warming reverses long-term Arctic cooling. Science, 325, 1236–1239, https://doi.org/10.1126/science.1173983.
Kerwin, M. W., J. T. Overpeck, R. S. Webb, A. DeVernal, D. H. Rind, and R. J. Healy, 1999: The role of oceanic forcing in mid-Holocene Northern Hemisphere climatic change. Paleoceanography, 14, 200–210, https://doi.org/10.1029/1998PA900011.
Kinnard, C., C. M. Zdanowicz, D. A. Fisher, E. Isaksson, A. de Vernal, and L. G. Thompson, 2011: Reconstructed changes in Arctic sea ice over the past 1,450 years. Nature, 479, 509–512, https://doi.org/10.1038/nature10581.
Klein, F., H. Goosse, A. Mairesse, and A. de Vernal, 2014: Model–data comparison and data assimilation of mid-Holocene Arctic sea ice concentration. Climate Past, 10, 1145–1163, https://doi.org/10.5194/cp-10-1145-2014.
Landrum, L., B. L. Otto-Bliesner, E. R. Wahl, A. Conley, P. J. Lawrence, N. Rosenbloom, and H. Teng, 2013: Last millennium climate and its variability in CCSM4. J. Climate, 26, 1085–1111, https://doi.org/10.1175/JCLI-D-11-00326.1.
Leith, C., 1974: Theoretical skill of Monte Carlo forecasts. Mon. Wea. Rev., 102, 409–418, https://doi.org/10.1175/1520-0493(1974)102<0409:TSOMCF>2.0.CO;2.
Lindsay, R., M. Wensnahan, A. Schweiger, and J. Zhang, 2014: Evaluation of seven different atmospheric reanalysis products in the Arctic. J. Climate, 27, 2588–2606, https://doi.org/10.1175/JCLI-D-13-00014.1.
Liu, W., and A. V. Fedorov, 2019: Global impacts of Arctic sea ice loss mediated by the Atlantic meridional overturning circulation. Geophys. Res. Lett., 46, 944–952, https://doi.org/10.1029/2018GL080602.
Mahlstein, I., and R. Knutti, 2012: September Arctic sea ice predicted to disappear near 2°C global warming above present. J. Geophys. Res., 117, D06104, https://doi.org/10.1029/2011JD016709.
Mann, M. E., Z. Zhang, M. K. Hughes, R. S. Bradley, S. K. Miller, S. Rutherford, and F. Ni, 2008: Proxy-based reconstructions of hemispheric and global surface temperature variations over the past two millennia. Proc. Natl. Acad. Sci. USA, 105, 13 252–13 257, https://doi.org/10.1073/pnas.0805721105.
Massé, G., S. J. Rowland, M. A. Sicre, J. Jacob, E. Jansen, and S. T. Belt, 2008: Abrupt climate changes for Iceland during the last millennium: Evidence from high resolution sea ice reconstructions. Earth Planet. Sci. Lett., 269, 565–569, https://doi.org/10.1016/j.epsl.2008.03.017.
McKay, N. P., and D. S. Kaufman, 2014: An extended Arctic proxy temperature database for the past 2,000 years. Sci. Data, 1, 140026, https://doi.org/10.1038/sdata.2014.26.
Meier, W. N., and Coauthors, 2014: Arctic sea ice in transformation: A review of recent observed changes and impacts on biology and human activity. Rev. Geophys., 52, 185–217, https://doi.org/10.1002/2013RG000431.
Meier, W. N., F. Fetterer, M. Savoie, S. Mallory, R. Duerr, and J. Stroeve, 2017: NOAA/NSIDC climate data record of passive microwave sea ice concentration, version 3. National Snow and Ice Data Center, accessed 15 September 2020, https://doi.org/10.7265/N59P2ZTG.
Morice, C. P., J. J. Kennedy, N. A. Rayner, and P. D. Jones, 2012: Quantifying uncertainties in global and regional temperature change using an ensemble of observational estimates: The HadCRUT4 data set. J. Geophys. Res., 117, D08101, https://doi.org/10.1029/2011JD017187.
Nash, J. E., and J. V. Sutcliffe, 1970: River flow forecasting through conceptual models part I—A discussion of principles. J. Hydrol., 10, 282–290, https://doi.org/10.1016/0022-1694(70)90255-6.
Oke, P. R., J. Allen, R. N. Miller, G. D. Egbert, and P. M. Kosro, 2002: Assimilation of surface velocity data into a primitive equation coastal ocean model. J. Geophys. Res., 107, 3122, https://doi.org/10.1029/2000JC000511.
Olonscheck, D., T. Mauritsen, and D. Notz, 2019: Arctic sea-ice variability is primarily driven by atmospheric temperature fluctuations. Nat. Geosci., 12, 430–434, https://doi.org/10.1038/s41561-019-0363-1.
Parsons, L. A., M. K. Brennan, R. C. Wills, and C. Proistosescu, 2020: Magnitudes and spatial patterns of interdecadal temperature variability in CMIP6. Geophys. Res. Lett., 47, e2019GL086588, https://doi.org/10.1029/2019GL086588.
Pauling, A. G., M. Bushuk, and C. M. Bitz, 2021: Robust inter-hemispheric asymmetry in the response to symmetric volcanic forcing in model large ensembles. Geophys. Res. Lett., 48, e2021GL092558, https://doi.org/10.1029/2021GL092558.
Peng, G., W. N. Meier, D. J. Scott, and M. H. Savoie, 2013: A long-term and reproducible passive microwave sea ice concentration data record for climate studies and monitoring. Earth Syst. Sci. Data, 5, 311–318, https://doi.org/10.5194/essd-5-311-2013.
Polyak, L., and Coauthors, 2010: History of sea ice in the Arctic. Quat. Sci. Rev., 29, 1757–1778, https://doi.org/10.1016/j.quascirev.2010.02.010.
Ridgwell, A., J. C. Hargreaves, N. R. Edwards, J. D. Annan, T. M. Lenton, R. Marsh, A. Yool, and A. Watson, 2007: Marine geochemical data assimilation in an efficient Earth system model of global biogeochemical cycling. Biogeosciences, 4, 87–104, https://doi.org/10.5194/bg-4-87-2007.
Rosenblum, E., and I. Eisenman, 2017: Sea ice trends in climate models only accurate in runs with biased global warming. J. Climate, 30, 6265–6278, https://doi.org/10.1175/JCLI-D-16-0455.1.
Sakakibara, C., 2008: “Our home is drowning”: Iñupiat storytelling and climate change in Point Hope, Alaska. Geogr. Rev., 98, 456–475, https://doi.org/10.1111/j.1931-0846.2008.tb00312.x.
Schmidt, G. A., and Coauthors, 2011: Climate forcing reconstructions for use in PMIP simulations of the last millennium (v1.0). Geosci. Model Dev., 4, 33–45, https://doi.org/10.5194/gmd-4-33-2011.
Schneider, U., A. Becker, P. Finger, A. Meyer-Christoffer, M. Ziese, and B. Rudolf, 2014: GPCC’s new land surface precipitation climatology based on quality-controlled in situ data and its role in quantifying the global water cycle. Theor. Appl. Climatol., 115, 15–40, https://doi.org/10.1007/s00704-013-0860-x.
Schurer, A. P., S. F. B. Tett, and G. C. Hegerl, 2014: Small influence of solar variability on climate over the past millennium. Nat. Geosci., 7, 104–108, https://doi.org/10.1038/ngeo2040.
Schweiger, A., R. Lindsay, J. Zhang, M. Steele, H. Stern, and R. Kwok, 2011: Uncertainty in modeled Arctic sea ice volume. J. Geophys. Res., 116, C00D06, https://doi.org/10.1029/2011JC007084.
Schweiger, A., K. R. Wood, and J. Zhang, 2019: Arctic sea ice volume variability over 1901–2010: A model-based reconstruction. J. Climate, 32, 4731–4752, https://doi.org/10.1175/JCLI-D-19-0008.1.
Sicre, M.-A., and Coauthors, 2013: Sea surface temperature and sea ice variability in the subpolar North Atlantic from explosive volcanism of the late thirteenth century. Geophys. Res. Lett., 40, 5526–5530, https://doi.org/10.1002/2013GL057282.
Sigl, M., and Coauthors, 2015: Timing and climate forcing of volcanic eruptions for the past 2,500 years. Nature, 523, 543–549, https://doi.org/10.1038/nature14565.
Singh, H. K. A., G. J. Hakim, R. Tardif, J. Emile-Geay, and D. C. Noone, 2018: Insights into Atlantic multidecadal variability using the last millennium reanalysis framework. Climate Past, 14, 157–174, https://doi.org/10.5194/cp-14-157-2018.
Steiger, N. J., G. J. Hakim, E. J. Steig, D. S. Battisti, and G. H. Roe, 2014: Assimilation of time-averaged pseudoproxies for climate reconstruction. J. Climate, 27, 426–441, https://doi.org/10.1175/JCLI-D-12-00693.1.
Stevenson, S., J. T. Fasullo, B. L. Otto-Bliesner, R. A. Tomas, and C. Gao, 2017: Role of eruption season in reconciling model and proxy responses to tropical volcanism. Proc. Natl. Acad. Sci. USA, 114, 1822–1826, https://doi.org/10.1073/pnas.1612505114.
Stroeve, J., and D. Notz, 2015: Insights on past and future sea-ice evolution from combining observations and models. Global Planet. Change, 135, 119–132, https://doi.org/10.1016/j.gloplacha.2015.10.011.
Stroeve, J., M. M. Holland, W. Meier, T. Scambos, and M. Serreze, 2007: Arctic sea ice decline: Faster than forecast. Geophys. Res. Lett., 34, L09501, https://doi.org/10.1029/2007GL029703.
Tardif, R., and Coauthors, 2019: Last Millennium reanalysis with an expanded proxy database and seasonal proxy modeling. Climate Past, 15, 1251–1273, https://doi.org/10.5194/cp-15-1251-2019.
Taylor, K. E., R. J. Stouffer, and G. A. Meehl, 2012: An overview of CMIP5 and the experiment design. Bull. Amer. Meteor. Soc., 93, 485–498, https://doi.org/10.1175/BAMS-D-11-00094.1.
Tomas, R. A., C. Deser, and L. Sun, 2016: The role of ocean heat transport in the global climate response to projected Arctic sea ice loss. J. Climate, 29, 6841–6859, https://doi.org/10.1175/JCLI-D-15-0651.1.
Torrence, C., and G. P. Compo, 1998: A practical guide to wavelet analysis. Bull. Amer. Meteor. Soc., 79, 61–78, https://doi.org/10.1175/1520-0477(1998)079<0061:APGTWA>2.0.CO;2.
Vare, L. L., G. Massé, and S. T. Belt, 2010: A biomarker-based reconstruction of sea ice conditions for the Barents Sea in recent centuries. Holocene, 20, 637–643, https://doi.org/10.1177/0959683609355179.
Walsh, J. E., F. Fetterer, J. S. Stewart, and W. L. Chapman, 2017: A database for depicting Arctic sea ice variations back to 1850. Geogr. Rev., 107, 89–107, https://doi.org/10.1111/j.1931-0846.2016.12195.x.
Walsh, J. E., W. L. Chapman, F. Fetterer, and J. S. Stewart, 2019: Gridded monthly sea ice extent and concentration, 1850 onward, version 2. National Snow and Ice Data Center, accessed 24 May 2021, https://doi.org/10.7265/jj4s-tq79.
Wanner, H., and Coauthors, 2008: Mid- to Late Holocene climate change: An overview. Quat. Sci. Rev., 27, 1791–1828, https://doi.org/10.1016/j.quascirev.2008.06.013.
Whitaker, J. S., and T. M. Hamill, 2002: Ensemble data assimilation without perturbed observations. Mon. Wea. Rev., 130, 1913–1924, https://doi.org/10.1175/1520-0493(2002)130<1913:EDAWPO>2.0.CO;2.
Widmann, M., H. Goosse, G. van der Schrier, R. Schnur, and J. Barkmeijer, 2010: Using data assimilation to study extratropical Northern Hemisphere climate over the last millennium. Climate Past, 6, 627–644, https://doi.org/10.5194/cp-6-627-2010.
Winton, M., 2011: Do climate models underestimate the sensitivity of Northern Hemisphere sea ice cover? J. Climate, 24, 3924–3934, https://doi.org/10.1175/2011JCLI4146.1.
Wolff, E. W., A. M. Rankin, and R. Röthlisberger, 2003: An ice core indicator of Antarctic sea ice production? Geophys. Res. Lett., 30, 2–5, https://doi.org/10.1029/2003GL018454.
Zanchettin, D., O. Bothe, C. Timmreck, J. Bader, A. Beitsch, H.-F. Graf, D. Notz, and J. H. Jungclaus, 2014: Inter-hemispheric asymmetry in the sea-ice response to volcanic forcing simulated by MPI-ESM (COSMOS-Mill). Earth Syst. Dyn., 5, 223–242, https://doi.org/10.5194/esd-5-223-2014.
Zhang, J., and D. A. Rothrock, 2003: Modeling global sea ice with a thickness and enthalpy distribution model in generalized curvilinear coordinates. Mon. Wea. Rev., 131, 845–861, https://doi.org/10.1175/1520-0493(2003)131<0845:MGSIWA>2.0.CO;2.
