A review of interactions between ocean heat transport and Arctic sea ice

Arctic sea ice has been retreating at fast pace over the last decades, with potential impacts on the weather and climate at mid and high latitudes, as well as the biosphere and society. The current sea-ice loss is driven by both atmospheric and oceanic processes. One of these key processes, the influence of ocean heat transport on Arctic sea ice, is one of the least understood due to the greater inaccessibility of the ocean compared to the atmosphere. Recent observational and modeling studies show that the poleward Atlantic and Pacific Ocean heat transports can have a strong influence on Arctic sea ice. In turn, the changing sea ice may also affect ocean heat transport, but this effect has been less investigated so far. In this review, we provide a synthesis of the main studies that have analyzed the interactions between ocean heat transport and Arctic sea ice, focusing on the most recent analyses. We make use of observations and model results, as they are both complementary, in order to better understand these interactions. We show that our understanding in sea ice - ocean heat transport relationships has improved during recent years. The Barents Sea is the Arctic region where the influence of ocean heat transport on sea ice has been the largest in the past years, explaining the large number of studies focusing on this specific region. The Pacific Ocean heat transport also constitutes a key driver in the recent Arctic sea-ice changes, thus its contribution needs to be taken into account. Although under-studied, the impact of sea-ice changes on ocean heat transport, via changes in ocean temperature and circulation, is also important to consider. Further analyses are needed to improve our understanding of these relationships using observations and climate models.


Context
Observations show that the annual mean Arctic air surface temperature has increased more than twice as fast as the global average since the late twentieth century, a process called 'Arctic amplification' (Chapman and Walsh 1993, Cohen et al 2020, IPCC 2021. Together with this warming, the annual mean Arctic sea-ice area decreased by 2 million km 2 between 1979 and 2020 (figure 1), corresponding to a relative loss of 18% over that time period, based on the Ocean and Sea Ice Satellite Application Facility (OSI SAF) observations (Lavergne et al 2019). This loss has been more pronounced in summer (−3.2 million km 2 in September, i.e. −48%) compared to winter (−1.4 million km 2 in March, i.e. −9%), as shown in figures 1 and 2 and previous studies (Onarheim et al 2018, Stroeve and Notz 2018, Meredith et al 2019, IPCC 2021. Sea ice has also thinned since 1980 (Lindsay and Schweiger 2015, Kwok 2018, Meredith et al 2019, leading to a decrease in annual mean Arctic sea-ice volume of 12 000 km 3 (relative loss of 49%) between 1979 and 2020, based on the Pan-Arctic Ice-Ocean Modeling and Assimilation System (PIOMAS; figure 3). The absolute loss in sea-ice volume is relatively similar across seasons, while the relative loss is stronger in summer (−77% in September) compared to winter (−34% in March), due to smaller initial volume in summer compared to winter (figure 3).   Arctic warming and sea-ice reduction have had large impacts on the Arctic ecosystem with subsequent effects on societies and local communities. With the reduction of sea ice, new shipping routes through the Arctic have opened and the exploitation of natural resources (such as oil and gas) has become more economically feasible, but these have put our environment at risk (Meredith et al 2019). Although debated, Arctic sea-ice reductions have been linked to changes in weather and climate conditions at lower latitudes (McCusker et al 2016, Ogawa et al 2018, Koenigk et al 2019, Cohen et al 2020. Especially, a more frequent occurrence of cold winter weather conditions over Eurasia and North America has been associated with sea-ice loss (Francis and Vavrus 2012, Mori et al 2019, Cohen et al 2020. Thus, changes in Arctic sea-ice conditions are not only relevant for local Arctic climate conditions but are also of potential importance for climate at lower latitudes.
The recent changes in Arctic sea-ice area and volume are driven by both anthropogenic global warming and internal climate variability (Kay et al 2011, Notz and Marotzke 2012, Swart et al 2015, Notz and Stroeve 2016, England et al 2019, Meredith et al 2019, Olonscheck et al 2019. Both anthropogenic global warming and internal variability influence Arctic sea ice via different atmospheric (Ding et al 2017) and ocean (Carmack et al 2015) processes. Ocean processes are probably the least understood causes due to the more difficult accessibility of the ocean compared to the atmosphere, thus deserving particular attention. It has recently been recognized that poleward ocean heat transport has a strong influence on the recent changes in Arctic sea ice (Arthun et al 2012, Polyakov et al 2017, Serreze et al 2019. The two oceans that bring warm water to the Arctic regions are the Atlantic and Pacific oceans. Heat from the Atlantic Ocean enters the Arctic Ocean through three main gateways ( figure 2(b)).
The Barents Sea Opening, located between northern Norway and Bear Island (south of Svalbard), is the most important Arctic gateway with an annual mean ocean heat transport of 73 TW based on moorings (Smedsrud et al 2010). Observations show that Atlantic Water heat transport at the Barents Sea Opening has increased by 2.4 TW decade −1 over 1998-2016, due to both strengthening and warming of Atlantic Water inflow, leading to substantial loss in Barents sea-ice area (Arthun et al 2012, Docquier et al 2020. The two other Arctic gateways on the Atlantic side are Fram Strait and Davis Strait, with annual mean ocean heat transports of 36 TW (Schauer and Beszczynksa-Möller 2009) and 20 TW (Curry et al 2011), respectively. The positive trend in ocean heat transport at Fram Strait since 1997 has been mainly driven by increased ocean temperature (Beszczynska-Möller et al 2012, Wang et al 2020, while there has been no significant change through Davis Strait (Curry et al 2011). The only Arctic gateway on the Pacific side is Bering Strait (figure 2(b)), with an annual mean ocean heat transport of 14 TW (Woodgate 2018). Despite this fairly modest contribution, an increase in ocean heat transport at Bering Strait has been observed since 1990, mainly due to increased flow (Woodgate 2018).

Motivation and structure
As described in section 1.1, Arctic sea ice has been dramatically retreating in the past decades, and part of this retreat has been due to enhanced poleward ocean heat transport, justifying the need to better understand the relationships between the two. However, our understanding of these relationships is far from being complete and many uncertainties are linked to the observational and modeling systems used. Also, there is more and more evidence that the Pacific Ocean, which provides a smaller contribution of heat transport to the Arctic compared to the Atlantic Ocean, also greatly impacts Arctic sea ice (Serreze et al 2019). Additionally, recent studies also show an effect of sea-ice changes on ocean heat transport and circulation (Sévellec et al 2017). Thus, a review summary on the interactions between the two major oceans (Atlantic and Pacific) and Arctic sea ice is necessary. Carmack et al (2015) provide a review on the role of ocean heat transport on Arctic sea ice based on observations, mainly mooring-based for ocean heat transport and satellite-based for sea ice. Here, we update their findings including research on this topic in the last years from both observational and modeling studies. In addition, we review the latest findings on the potential influence of Arctic sea ice on ocean heat transport.
In section 2, we present the criteria used to select the featured articles, as well as the main tools used for observing and modeling Arctic sea-ice concentration and thickness, and ocean heat transport. In section 3, we present key recent studies analyzing interactions between ocean heat transport and Arctic sea ice. In our study, we define the Arctic Ocean in its broad sense as the ocean centered around the North Pole that is covered by sea ice at least in winter (figure 2(a)). For ocean heat transport, we mainly focus on the four Arctic gates described in section 1.1 and depicted in figure 2(b), but we do not strictly restrict our analysis to them. Sections 3.1 and 3.2 focus on the impact of ocean heat transport from the Atlantic and Pacific, respectively, on Arctic sea ice, while section 3.3 looks at the reverse influence of Arctic sea ice on ocean heat transport. A summary and outlook is provided in section 4.

Article selection criteria
A series of criteria have been used to select the featured articles: • Article relevance: articles that are directly connected to the topic have been considered. Other articles that are indirectly connected have also been considered depending on their importance to convey the key messages of our review. • Robustness: the goal of the review is to provide a global picture of the interactions between ocean heat transport and Arctic sea ice. Thus, we have insisted more on the results that are confirmed by multiple studies and are derived from different sources (observations and models, or independent measurements, or multiple models), and less on the results that are only confirmed by one or a few studies, in agreement with the Intergovernmental Panel on Climate Change (IPCC) confidence levels. We have ensured that contradicting results are adequately represented. • Recent articles: we have mainly focused on the most recent analyses, updating the review from Carmack et al (2015), but we have also taken into account important articles that have been published earlier on.

Observations
In this section, we shortly describe the availability of recent observations of sea-ice concentration and seaice thickness (which are used to compute Arctic seaice area and volume) and ocean heat transport at the Arctic gates, as well as the methods to retrieve these observations. Observations of Arctic sea-ice concentrations have mainly come from satellite passive microwave radiometers for more than four decades. They have started in late 1978 with the Scanning Multichannel Microwave Radiometer (SMMR), continued with the Special Sensor Microwave Imager (SSM/I) from 1987, and then with the Special Sensor Microwave Imager/Sounder (SSMIS) since 2009 (Stroeve and Notz 2018). Several algorithms have been developed to convert the brightness temperature retrieved by radiometers into sea-ice concentration, with weaker performance in summer partly due to the presence of melt ponds (Ivanova et al 2015). The Arctic seaice area is computed by summing the product of sea-ice concentration and grid-cell area over all grid points included in the Arctic Ocean. An alternative diagnostic to sea-ice area is sea-ice extent, which is the total ocean area including all grid points with at least 15% sea-ice concentration. While sea-ice extent allows to partly remove the observational uncertainty related to melt ponds, sea-ice area is a preferred diagnostic when comparing climate models to observations due to uncertainties related to grid geometry (Notz 2014).
Changes in Arctic sea-ice thickness have not been monitored with such a long-term and consistent record. Until the end of the twentieth century, only in-situ data were available, including measurements of sea-ice draft (ice depth below the waterline) by the US Navy submarine cruises between 1975 and 2000 (Rothrock et al 2008). It was only in 1993 that satellite altimeter observations started with ESA's ERS-1/2, although the spatial coverage was limited up to 81.5 • N. Near Arctic-wide observations of seaice thickness have been obtained since 2003, thanks to the NASA's Ice, Cloud and land Elevation Satellite (ICESat) satellite laser altimeter. However, the ICESat record is limited to October-November and Since late 2018, Arctic-wide ice thickness measurements have also come from ICESat-2 (Petty et al 2020). Note, however, that large uncertainties affect satellite observations of sea-ice thickness, due to errors in snow depth and densities of snow, ice and water as these quantities are used to convert the measured sea-ice freeboard (ice thickness above the waterline) into sea-ice thickness.
Combining sea-ice concentration and sea-ice thickness allows to compute Arctic sea-ice volume. Due to the spatial and temporal gaps of sea-ice thickness measurements and the relatively large uncertainty inherent to thickness retrievals (Stroeve et al 2014, Zygmuntowska et al 2014, reanalysis data have also been used for sea-ice volume. In particular, PIOMAS has provided data since 1979 Rothrock 2003, Schweiger et al 2011). These data agree relatively well with satellite observations over the central Arctic (Schweiger et al 2011) and simulate sea-ice thickness with error statistics similar to the observational uncertainty (Schweiger et al 2019).
As ocean heat transport at a specific transect is derived from the product of ocean temperature and velocity integrated over this transect, the two latter quantities need to be known. Ocean temperature is obtained via hydrographic stations and moorings and ocean velocity is measured through current meter moorings. In-situ moorings have been deployed since 1990 at Bering Strait and have offered year-round observations of ocean velocity and temperature (Woodgate 2018 (Curry et al 2011). Due to the short observational time period, uncertainties related to these measurements (e.g. mesoscale eddies, extrapolation of each current meter to represent boxes with uniform velocity, coverage of part of the transects; Ingvaldsen et al (2004)), mooring under-sampling and the relatively long time period of internal variability, the use of climate models is a good complement to these observations.

Models
In this section, we briefly describe the climate models used to represent Arctic sea ice, ocean heat transport and their interactions. We mainly focus on global climate models as these models take into account largescale interactions between ocean heat transport and Arctic sea ice. But we also discuss results from regional models, which might improve the representation of smaller-scale ocean-sea ice interactions at the ice edge. A distinction needs to be done between oceanonly models, including sea ice, that are driven by atmospheric forcing on one hand, and coupled models that include ocean, sea ice, atmosphere and land on the other.
Climate models use mathematical equations to characterize the exchanges of energy, momentum and water in different parts of the ocean, sea ice, atmosphere and land. They divide the globe into a three-dimensional grid of cells in which the equations representing the different components of the climate system are computed. A finer grid size (higher resolution) allows us to provide a more detailed representation of climate processes but requires larger computer resources. Climate models are used to better understand the key climate processes, including the interactions between ocean heat transport and Arctic sea ice, and to provide insights into the future by making projections.
In recent years, three different modeling approaches to better understand the climate system have been designed. The first method is to combine a large set of models. The primary example is the Coupled Model Intercomparison Project (CMIP), which also informs the IPCC. In particular, the three phases CMIP3, CMIP5 and CMIP6 have provided multi-model frameworks to simulate the climate in the recent past and future following the same protocol (Meehl et al 2007, Taylor et al 2012, Eyring et al 2016. The second approach is to carry out sensitivity experiments with one or several climate models, in which certain aspects of the climate system or model parameters are modified. The third approach is to perform a large ensemble of simulations with the same model starting from slightly different initial states in order to reduce the uncertainty related to internal variability (Deser et al 2020). In our review, we take into account the three approaches as they are complementary.
Arctic sea-ice concentration and thickness are directly computed in the sea-ice component of climate models. As for observations, the modeled ocean heat transport at a specific transect is computed via ocean temperature and velocity, which are computed in each model grid cell in the ocean component. The main advantage of a global climate model over observations is that it covers the whole globe and a much longer time period, allowing to separate internal variability from external forcing. However, it suffers from uncertainties related to incomplete understanding and inadequate representation of the climate system, and grid-size limitations.

Influence of Atlantic Ocean heat transport on Arctic sea ice
In this section, we review the recent literature related to the influence of heat transport from the Atlantic Ocean on Arctic sea ice from both observational and modeling perspectives.

Observations
Relationships between Atlantic Ocean heat transport and Arctic sea-ice conditions have been recognized for more than a century (Helland-Hansen and Nansen 1909) and a number of studies since then Table 1. Sensitivity of Barents and Arctic sea-ice area (SIA) to an increase in ocean heat transport (OHT) (unit: km 2 per 10 TW) according to observational and modeling studies. For the Barents SIA sensitivity, we use OHT at the Barents Sea Opening (BSO), and for the Arctic SIA, we use the total Arctic OHT. The period over which the sensitivity is computed is provided in brackets. For multi-model/multi-member studies, the multi-model/ensemble mean is provided. The observations and models used are provided below the author names for each study. We also indicate the number of years by which OHT leads SIA in the computation of the sensitivity if there is a lead-lag correlation.

Studies
Barents have shown a role of Atlantic warming on sea-ice reduction (Steele and Boyd 1998, Dickson et al 2000, Furevik 2001, Vinje 2001, Polyakov et al 2004, Francis and Hunter 2007, Schlichtholz 2011, Spielhagen et al 2011. However, the influence of Atlantic Ocean heat transport on Arctic sea ice has only been recently quantified, focusing on the Barents Sea (Arthun et al 2012). The Barents Sea occupies a key position between the warm Atlantic Water and the cold Arctic Ocean, favoring substantial heat loss to the atmosphere, without which this sea would be largely ice free in winter (Smedsrud et al 2013). Arthun et al (2012) show that the reduction in Barents sea-ice area between 1998 and 2008 is correlated with an increase in Atlantic Water heat transport at the Barents Sea Opening. They find a decrease of 145 000 km 2 in Barents sea-ice area per 10 TW increase in ocean heat transport (table 1, ocean heat transport leading sea-ice area by two years) using hydrographic data and current meter moorings from the Institute of Marine Research (IMR, Norway; Ingvaldsen et al (2004)). The increased heat transport at the Barents Sea Opening has been caused by both strengthening and warming of the Atlantic Water inflow (Arthun et al 2012). As the Barents Sea is practically ice free in summer, most recent changes have happened in winter, with a decrease in sea-ice area of >50% since 1979 (figure 2(c)) (Onarheim and Arthun 2017). The influence of Atlantic Water heat transport on sea ice has been further demonstrated by skillful predictions of Barents sea ice-area based on observed sea-ice area in the Barents Sea and ocean heat transport at the Barents Sea Opening one or two years in advance (Onarheim et al 2015). The predicted Barents sea-ice area computed from this framework shows good agreement with observations, with 50% of the variance explained and a correct increase/decrease in sea-ice cover 88% of the time. The skill of the prediction is further increased by including meridional winds. This framework is supported by a 60 yr simulation from a regional ice-ocean model (Onarheim et al 2015).
There is also evidence that the Atlantic Water inflow has had an influence on sea ice in the western Nansen Basin (<70 • E), located north of Barents Sea, between Svalbard and Franz Joseph Land, after the mid-1990s. In particular, local zones of thinner ice and lower ice concentration mirror the pathway of the Fram Strait branch of Atlantic Water (Ivanov et al 2012). The fact that winter minimum sea-ice thickness occurs in the ice pack interior above the Atlantic Water path shows that a substantial amount of Atlantic Water heat in the western Nansen Basin has contributed to ice melting from below. Ivanov et al (2012) hypothesize that the delivering of warm water from deep to under-ice layers comes from winter convective mixing.
Until recently, the heat brought by the Atlantic Water had been isolated from the surface in the eastern Eurasian Basin (>70 • E) by large vertical density gradients associated with the Arctic halocline (Polyakov et al 2020). However, the conditions previously identified by Ivanov et al (2012) in the western Nansen Basin are now observed in the eastern Eurasian Basin (as far as 125 • E). In particular, large sea-ice loss in the eastern Eurasian Basin since 2011 has also been linked to Atlantic Water inflow (Polyakov et al 2017). This eastward progression of Atlantic Water inflow is called 'atlantification' (Arthun et al 2012). The recent increased penetration of Atlantic Water into the eastern Eurasian Basin, as shown by moorings and buoys deployed in 2013-2015 (Polyakov et al 2017) and 2015-2018 (Polyakov et al 2020), is associated with stratification weakening, increased vertical mixing and pycnocline warming. This has led to enhanced upward Atlantic Water heat flux to the ocean surface, and thus to a reduction in ice growth in winter (Polyakov et al 2017). This process has continued at an increasing rate in more recent years, with ocean heat flux greater than 10 W m −2 for the winters of 2016-2018, compared to 3-4 W m −2 for 2007-2008, leading to a more than two-fold reduction of winter ice growth (Polyakov et al 2020).

Models
As for observations, the main region of interest in terms of ocean heat transport-Arctic sea ice relationships in modeling studies has been the Barents Sea as it has experienced the largest relative winter sea-ice loss in the past years compared to other Arctic seas (Onarheim et al 2018), combined with increased ocean heat transport through the Barents Sea Opening (Arthun et al 2012). We first review the literature associated with the influence of Atlantic Ocean heat transport on the Barents Sea ice, and then the one related to the impact of Atlantic Ocean heat transport on other Arctic seas. We decide to focus on the studies that provide a quantification of the influence of ocean heat transport on Arctic sea ice, but we acknowledge that additional modeling studies suggest an influence of ocean heat transport on sea ice without a clear quantification (Yang and Neelin 1997, Holland et al 2001, Holland and Bitz 2003, Hwang et al 2011.

Barents Sea
The global coupled atmosphere-ocean-sea ice model ECHAM5/MPIOM (European Center for Medium-Range Weather Forecasts Hamburg/Max Planck Institute Ocean Model) has been run over nearly 500 yr with pre-industrial external forcing to investigate seasonal to interannual variability in the Barents Sea (Koenigk et al 2009). Results from this simulation provide evidence that ocean heat transport into the Barents has a minor importance for interannual sea-ice variations, which are mostly driven by sea-ice import through local winds, but it starts to become more important at longer time scales.
However, other studies have later found that ocean heat transport at the Barents Sea Opening has an influence on Barents sea-ice area at seasonal, interannual and decadal time scales. Results with the regional ocean-sea ice model HAMSOM (Hamburg Shelf Ocean Model) forced by NCEP/NCAR atmospheric reanalysis suggest that there is a one-year leadlag correlation between ocean heat transport and Barents sea-ice area, with a sea-ice retreat of 70 000 km 2 per 10 TW increase in ocean heat transport over the period 1948-2007 (table 1) (Arthun and Schrum 2010, Arthun et al 2012). The Regional Ocean Modeling System (ROMS) also shows evidence of a direct role of Atlantic Water heat transport at the Barents Sea Opening, associated with local winds, on Barents sea ice within seasons (Lien et al 2017).
Model simulations with the coupled global climate model EC-Earth2.3 using the CMIP5 forcing provide evidence that the largest Arctic warming over 1850-2100 occurs in the Barents Sea (Koenigk et al 2013). This leads to strong reductions in sea-ice concentration and thickness in the Barents Sea with varying amplitude depending on the emission scenario. Concurrently, the ocean heat transport at all Arctic straits, and especially at the Barents Sea Opening, increases in all simulations, mainly via increased temperature of the Atlantic Water (Koenigk et al 2013, Koenigk and Brodeau 2014). The increased ocean heat transport leads to enhanced bottom ice melt in these simulations, contributing to sea-ice retreat (Koenigk and Brodeau 2014).
Over the period 1979-2015, the trend in CMIP5 multi-model mean March Barents sea-ice extent (−2700 km 2 per year) is much weaker than that observed (−9700 km 2 per year) (Li et al 2017). Also, the trends in CMIP5 March Barents sea-ice extent have little correlation with the trends in global mean surface air temperature across all CMIP5 models (R = −0.2), but they are strongly anti-correlated with the trends in annual mean Atlantic Water heat transport at the Barents Sea Opening (R = −0.8). Results from Li et al (2017) suggest that enhanced ocean heat transport at the Barents Sea Opening associated with regional internal variability have had a major role in reducing the winter sea-ice cover in the Barents Sea since 1979.
The use of seven coupled global climate models that followed the High Resolution Model Intercomparison Project (HighResMIP) protocol (which is one of the CMIP6-endorsed MIPs), with at least two different horizontal resolutions for each model, confirms the strong anti-correlation between annual mean ocean heat transport at the Barents Sea Opening and March Barents sea-ice area (Docquier et al 2020). The sensitivity of March Barents sea-ice area to ocean heat transport at the Barents Sea Opening is −80 000 km 2 per 10 TW on average (table 1, ocean heat transport leading sea-ice area by one year), with large variations between models (−18 000 to −137 000 km 2 per 10 TW). This study reveals that an increased ocean resolution allows us to better represent the different ocean currents flowing into the Barents Sea as well as the Atlantic Water heat transport at the Barents Sea Opening. A higher ocean resolution also improves the strong water cooling at the sea-ice edge and further formation of warm intermediate Atlantic Water. However, no clear impact of model resolution on sea ice-ocean heat transport relationships is found. Another multi-model study with eight different ocean-only models and one fully coupled model finds that a stronger wind forcing over the Greenland Sea leads to an increased ocean heat transport at the Barents Sea Opening and a reduced sea-ice extent in the Barents and Kara Seas (Muilwijk et al 2019). In particular, an average reduction of 50 000 km 2 in sea-ice area in the Barents and Kara Seas combined is found for an increase in ocean heat transport of 10 TW (table 1)

Other Arctic seas
Ocean heat transport at the Barents Sea Opening does not only influence sea ice in the Barents Sea but appears to also influence the whole Arctic Ocean. In particular, the Community Earth System Model (CESM) Large Ensemble (LE), constituted of 40 members run over 1920-2100, provides evidence that heat transport at the Barents Sea Opening is a major source of internal Arctic sea-ice variability during winter (Arthun et al 2019). This relationship remains strong in the future, using the Representative Concentration Pathway (RCP) 8.5, and weakens as sea ice retreats. The future increase in ocean heat transport in these experiments is reflected in a northward penetration of warm water into the Arctic Ocean, resulting in a strong reduction in sea-ice thickness (−1.2 m in the eastern Arctic Ocean on average).
An analysis using different model projections from the Community Climate System Model version 3 (CCSM3) shows that abrupt reductions in the Arctic sea-ice extent occur when ocean heat transport to the Arctic rapidly increases through the twenty-first century (Holland et al 2006). These rapid 'pulse-like' events in ocean heat transport lead changes in sea ice (particularly sea-ice thickness) by about 1-2 years via increased melt rate. Increased ocean heat transport is associated with strengthened ocean currents and warmer waters entering the Arctic Ocean (Holland et al 2006).
Results from the NorESM1-M global coupled climate model provide evidence that the increased ocean heat transport at the Barents Sea Opening causes a reduction in Barents sea-ice area through reduced basal growth, while sea-ice area reduction in the central Arctic is mostly controlled by increased ocean heat transport to the Arctic through Fram Strait, resulting in increased bottom melting (Sando et al 2014). The CESM-LE large ensemble (1850-2100, using RCP8.5 scenario) suggests that ∼80% of the rapid sea-ice declines in the Arctic are correlated with increased ocean heat transport, mainly at the Barents Sea Opening and Bering Strait (Auclair and Tremblay 2018). A rapid sea-ice decline is a period of ⩾4 yr during which the trend in the 5-year running mean minimum sea-ice extent is ⩽−0.3 million km 2 yr −1 (Auclair and Tremblay 2018). A set of sensitivity experiments performed with EC-Earth3 and starting from present-day climate confirms that an increased total ocean heat transport at all Arctic gates leads to a large reduction in Arctic sea-ice area (Docquier et al 2021). In these experiments, the sea-surface temperature is artificially increased in different parts of the North Atlantic and North Pacific Oceans, leading to enhanced ocean heat transport into the Arctic. Sea-ice loss is mainly driven by reduced basal growth along the sea-ice edge and enhanced basal melt in the central Arctic, in agreement with Sando et al (2014).
Three other multi-model studies compute the northward ocean heat transport at a specific latitude (between 60 • N and 70 • N), instead of the typical Arctic gates, and analyze its relationship with Arctic sea ice. The first analysis focuses on ∼20 CMIP3 models and shows that models that simulate a stronger poleward ocean heat transport at 60 • N also have a smaller September Arctic sea-ice extent (Mahlstein and Knutti 2011). According to Mahlstein and Knutti (2011), the northward ocean heat transport largely contributes to the uncertainty in future Arctic climate projections. The second study finds that the Arctic warming between 1961 and 2099 is driven by the net atmospheric surface flux in about half of the models and by the meridional ocean heat flux at 66 • N in the other half of the models, based on 26 CMIP5 models (Burgard and Notz 2017). A significant negative correlation between Atlantic Ocean heat flux and Arctic sea-ice area is found across all models (R = −0.4). The third analysis confirms the strong decline in Arctic sea-ice area with enhanced poleward Atlantic Ocean heat transport north of 60 • N at interannual time scales using five HighResMIP models at different horizontal resolutions over the historical period (1950-2014) (Docquier et al 2019).
Additionally, a finer ocean resolution results in lower Arctic sea-ice area and volume and generally enhances Atlantic Ocean heat transport, with the limitation that three models used in this study have the same ocean component.

Influence of Pacific Ocean heat transport on Arctic sea ice
Although the contribution of the Pacific Ocean to the total Arctic Ocean heat transport is relatively small compared to the Atlantic Ocean (∼10% according to the observational estimates provided in section 1.1), its influence on Arctic sea ice is important because the Pacific water enters the Arctic at depths closer to the surface compared to Atlantic water (Woodgate 2018). In this section, we review the recent literature associated with this influence from both observational and modeling perspectives.

Observations
Inflowing Pacific water through the Bering Strait dominates upper surface water masses in the Chukchi and Beaufort Seas. The reduction in sea-ice concentration in these Arctic seas over the past decades has been associated with enhanced ocean heat transport at the Bering Strait, which has been recorded since 1990 , Woodgate 2018. The acceleration of the sea-ice concentration decrease after 1997-1998 is associated with increased Pacific water temperature and upward heat flux in the Chuckchi and Beaufort Seas, which delayed sea-ice formation (Shimada et al 2006).
Since 1990, almost without interruption, yearround measurements have been maintained in the Bering Strait region, typically at 2-3 sites (Woodgate 2018). Over the period 1990-2015, the increase in ocean heat transport at the Bering Strait has been ∼0.2 TW yr −1 , with lows in 2001 and 2012 (∼10 TW) and highs in 2007 and 2015 (∼17 TW), and has been mainly driven by volume transport increase (Woodgate 2018). The increase in ocean heat transport at the Bering Strait between 2001 and 2004 had a sea-ice melt potential of ∼640 000 km 2 for a 1 m thick ice layer . The almost doubling of the Bering Strait heat transport between 2001 and 2007 acted as a trigger for the onset of the large Arctic sea-ice melt that occurred in 2007 (Woodgate et al 2010).
In the Chukchi Sea, the dates of ice retreat (first day of the year when the mean sea-ice concentration within this sector is less than 30%) and advance (first day after the seasonal ice extent minimum when the average sea-ice concentration in this sector exceeds 30%) have moved to ∼25 d earlier and ∼55 d later, respectively, between 1979 and 2014 (Serreze et al 2016). The resulting increased open-water period (+80 d) has been strongly related to ocean heat transport through the Bering Strait, and especially the transport in April-June, which explains 68% of the variance in the timing of sea-ice retreat in the Chukchi Sea (Serreze et al 2016).
Relatively high water temperatures in the Bering Strait have been recorded in 2017, resulting in a large ocean heat transport, thus partly explaining the early sea-ice retreat in the Chukchi Sea in autumn 2017 (Serreze et al 2019). Also, based on satellite measurements between 2002 and 2018, the November sea-surface temperature over the Chukchi and Bering Seas was at its highest value in 2018, as a response to an episode of previous atmospheric blocking over the Bering Sea (Kodaira et al 2020). Consequently, less sea ice formed in the Chukchi Sea in November 2018.

Models
The influence of the Pacific Ocean heat transport on the large Arctic sea-ice melt event that occurred in the summer of 2007, mentioned in section 3.2.1, is further supported by a modeling study performed with PIOMAS, forced by NCEP/NCAR atmospheric reanalysis (Steele et al 2010). The modeling results provide evidence that in summer 2007 the ocean gained twice the amount of ocean heat averaged over the previous seven years, in agreement with observations (Woodgate et al 2010). In the early summer, top melt from the atmosphere dominated the total seaice melt in the Pacific sector, while bottom melt due to ocean heat transport dominated later in the summer, with values 34% larger relative to the previous seven years (Steele et al 2010). Ocean heat transport is only one factor that contributed to the record minimum sea-ice extent in 2007, together with warm air temperatures, low initial sea-ice thickness, changes in atmospheric circulation, ice motion, clouds, and solar heating of leads (Perovich 2011). Koenigk and Brodeau (2014) suggest that the contribution from Bering Strait in the increase in ocean heat transport is small compared to the contribution from the Barents Sea Opening over the twentyfirst century using EC-Earth2.3. However, the Pacific water transported through the Bering Strait has a lower salinity than Atlantic water and stays closer to the ocean surface, thus contributing more substantially to bottom sea-ice melt than Atlantic water (Koenigk and Brodeau 2014). This is confirmed by a later study with EC-Earth3, in which bottom seaice melt is enhanced at the Bering Strait when the sea-surface temperature is artificially increased in the North Pacific Ocean (Docquier et al 2021). Combined with atmospheric warming of the North Atlantic Ocean, this leads to a more efficient melting of Arctic sea ice when the sea-surface temperature increases in the North Pacific Ocean compared to the North Atlantic Ocean. The loss in September Arctic sea-ice area is ∼610 000 km −2 per 10 TW increase in total Arctic Ocean heat transport when the sea-surface temperature is increased in the North Pacific Ocean (table 1), roughly twice more than if the increase comes from the North Atlantic (Docquier et al 2021).
The rapid sea-ice declines identified by Auclair and Tremblay (2018) using CESM-LE over 1920-2100 are correlated either with the Bering Strait or Barents Sea Opening ocean heat transport. The correlation between changes in annual mean Bering Strait ocean heat transport and September sea-ice concentration is of similar amplitude as between the Barents Sea Opening ocean heat transport and September sea-ice concentration. This seems counter-intuitive since the annual mean ocean heat transport at the Bering Strait is smaller than the one at the Barents Sea Opening. Auclair and Tremblay (2018) suggest that this could be due to the fact that Pacific water enters the Arctic over a broader shallow shelf compared to Atlantic water. This further highlights the importance of the Bering Strait in controlling sea-ice changes.

Influence of Arctic sea ice on ocean heat transport
In this section, we review the recent literature related to the influence of Arctic sea ice on ocean heat transport from both observational and modeling perspectives. As this influence has been under-studied compared to the reverse impact of ocean heat transport on Arctic sea ice presented in sections 3.1 and 3.2, we merge observational and modeling studies in the same section.
Some early studies report connections between formation of sea ice and ocean circulation, in particular deep ocean convection in the Labrador Sea (Dickson et al 1988, Goosse and Fichefet 1999, Belkin 2004. Bitz et al (2006) investigate the influence of changes in sea ice on ocean heat transport using CCSM3. They artificially decrease sea-ice albedo to mimic a strong reduction in Arctic sea ice. Following the reduction in Arctic sea-ice cover, the ocean warms in a 200 m layer just below the surface of the Arctic Ocean. This subsurface warming results from enhanced Atlantic Ocean heat transport (Bitz et al 2006).
The Atlantic Meridional Overturning Circulation (AMOC) is closely linked to the meridional transport of heat by the Atlantic Ocean (Marshall et al 2015, Weijer et al 2019, thus its monitoring is highly relevant to understand changes in ocean heat transport. In particular, it has been shown that the AMOC has slowed down since 2008 using data from an array of instruments at 26.5 • N (Smeed et al 2018), potentially weakening the meridional ocean heat transport farther north, although the connection between the AMOC at 26.5 • N and Arctic Ocean heat transport is complex and requires further analyses (Oldenburg et al 2018). Using the global ocean model NEMO (Nucleus for European Modelling of the Ocean) and the global climate model CESM, a recent study suggests that the Arctic sea-ice decline may explain at least part of the recent AMOC slowdown (Sévellec et al 2017). The potential underlying mechanism is that the current loss in Arctic sea ice increases the open-water area, resulting in strong anomalous solar heat flux into the ocean and subsequent warming. Additionally, the Arctic sea-ice decline and Greenland ice-sheet loss add freshwater into the Arctic Ocean. Together, these two processes would cause an AMOC slowdown via southward advection of buoyancy anomalies, and a reduction of poleward ocean heat transport (Sévellec et al 2017).
As the most rapid Arctic warming has occurred in the Barents Sea, experiencing the largest winter sea-ice loss (Stroeve and Notz 2018), it makes sense to ask what is the impact of sea-ice retreat in this specific region on ocean heat transport. Hydrographic observations from 1970 to 2016 show a sharp increase in ocean heat content in the upper 100 m from the mid-2000s, the 2010-2016 average being 3.8 standard deviations above the 1970-1999 average (Lind et al 2018). In parallel, net sea-ice import to the Barents Sea (mainly from the Kara Sea) has decreased since 2002-2003. The findings of Lind et al (2018) show that the reduced sea-ice import has resulted in less melt water, reduced stratification and more vertical mixing in the upper part of the water column, leading to increased upward heat and salt fluxes and finally enhanced ocean heat content in the upper 100 m.
Model results with the unstructured-grid Finite Element Sea ice Ocean Model (FESOM) provide evidence that following sea-ice decline in the Arctic, seaice export through the Fram Strait decreases and salinity in the Greenland Sea increases (Wang et al 2020). This link between Fram Strait ice export and Greenland Sea salinity is in agreement with previous modeling studies (Haak et al 2003, Koenigk et al 2006. The increase in Greenland Sea salinity lowers sea-surface height and strengthens the cyclonic gyre circulation in the Nordic Seas, resulting in increased volume transport of Atlantic water into the Arctic Ocean through the Fram Strait (Wang et al 2020). Thus, ocean heat transport through the Fram Strait increases and potentially melts more sea ice, so this is a positive feedback.

Conclusions
In this review, we have synthesized the information on the influence of ocean heat transport on Arctic sea ice, as well as the reverse impact of Arctic sea ice on ocean heat transport, based on the most recent literature. Our key results are the following: (a) Major advances in understanding the ocean heat transport-Arctic sea ice relationships have been done using multiple observations and climate models. Despite an early attested influence of ocean heat transport on Arctic sea ice, a more precise quantification of this impact is relatively recent (∼ten years) thanks to improved observational and modeling systems. On the Atlantic side, an eastward progression of Atlantic water inflow, called 'atlantification' , is currently underway, associated with reduced ice growth in winter. On the Pacific side, some episodes of large ocean heat transport have been recorded in 2007 and 2017, resulting in sea-ice retreat, especially in the Chukchi Sea. However, knowledge gaps still exist. From an observational perspective, this is partly due to the relatively difficult access of the deeper layers of the ocean, which hinders a fully accurate measurement of ocean heat transport. Also, the systematic pan-Arctic measurement of ocean heat transport and key sea-ice variables (concentration and thickness) is relatively new (from the late 1970s for seaice concentration, and from the 1990s for seaice thickness and Arctic Ocean heat transport), which does not provide a long temporal window of observations. From a modeling point of view, an incomplete representation of key climate processes in the Arctic and a too coarse grid resolution lead to uncertainties in the simulation of ocean heat transport and its interaction with Arctic sea ice. (b) The sensitivity of Barents sea-ice area to an increase in ocean heat transport at the Barents Sea Opening amounts to ∼−145 000 km 2 per 10 TW over the period 1998-2008, based on observations (Arthun et al 2012). Caution needs to be taken with respect with this number as it involves a relatively small time period, annual mean sea-ice area and data are not detrended. We have computed this sensitivity using a longer time period (1998)(1999)(2000)(2001)(2002)(2003)(2004)(2005)(2006)(2007)(2008)(2009)(2010)(2011)(2012)(2013)(2014)(2015)(2016) and detrended data from IMR for annual mean ocean heat transport and OSI SAF for March sea-ice area (as this is the period when most changes happened in the Barents Sea in past years). We obtain a value ten times smaller (−12 000 km 2 per 10 TW), which indicates the large sensitivity of this computation depending on the time period and the methodology used. Modeling studies have found a sensitivity ranging between −30 000 and −80 000 km 2 per 10 TW (table 1). Despite the uncertainty in the precise quantification of this sensitivity, ocean heat transport at the Barents Sea Opening has been shown to be a good predictor for Barents sea-ice conditions. (c) While the Atlantic Ocean heat transport influence on Arctic sea ice is relatively well attested by observations and models (section 3.1), a considerably smaller amount of studies exists related to the impact of the Pacific Ocean heat transport (section 3.2). This is partly due to the fact that the contribution of the ocean heat transport at Bering Strait is only ∼10% of the total Arctic Ocean heat transport. Thus, changes happening there have been smaller in absolute value compared to changes on the Atlantic side. However, this does not mean that there is no impact on Arctic sea ice; on the contrary, significant changes in sea ice (especially in the Chukchi Sea) have been reported in past years due to enhanced ocean heat transport at the Bering Strait (Serreze et al 2019). (d) The influence of Arctic sea ice on ocean heat transport (section 3.3), and the possibility of a feedback loop between the two, has been understudied compared to the reverse impact of ocean heat transport on Arctic sea ice. As several studies have shown that the recent sea-ice reduction have triggered changes in ocean circulation and temperature, thus impacting ocean heat transport, this influence also needs to be considered.
Based on the above results, we make the following recommendations for future work: (a) The continuation of the ongoing efforts in observing ocean heat transport to the Arctic through the four main gates and Arctic seaice concentration and thickness is crucial to extend the current time series. In order to better understand the pathways of ocean heat entering the Arctic, it is especially important to monitor under-sea ice ocean observations. This would enable us to better quantify the risk that large amounts of inflowing warm water (e.g. from the intermediate warm Atlantic Water) come into contact with Arctic sea ice in the near future. (b) Climate models need to be improved to incorporate the latest model developments and enhance our understanding of the interactions between Arctic sea ice and ocean heat transport. The inclusion of a more realistic runoff from land-water storage and ice-sheet melt is important in order to have a more realistic description of the ocean current system and its changes in the future, including the northward ocean heat transport. A finer model resolution will also allow us to gain precision into the different ocean and sea-ice processes. Additionally, the three approaches consisting in comparing multiple climate models together (such as CMIP), performing sensitivity experiments and carrying out large model ensemble simulations could be combined more effectively. (c) More emphasis could be put on the influence of Bering Strait ocean heat transport on Arctic sea ice, as well as the impact of Arctic sea ice on ocean heat transport via changes in ocean temperature and circulation, as these processes are clearly important for the Arctic climate system. (d) Maybe as important as improving observations and climate models, the techniques to evaluate and analyze observations and model data also need to be carefully designed. For example, the analysis of the influence of ocean heat transport on Arctic sea ice (and the reverse) would benefit from tools coming from nonlinear sciences.
In particular, the study of causal links between ocean heat transport and Arctic sea ice would enable us to go beyond classical correlation analyses (Liang 2014, Runge et al 2019. Arctic sea ice is rapidly retreating and thinning, and ocean heat transport to the Arctic is increasing. Also, model projections suggest a continuation of the ongoing processes, with more or less intensity depending on the greenhouse gas emission scenario we will follow (SIMIP Community 2020, IPCC 2021). As these changes are having and will continue to have impacts on the climate system, the biodiversity and our societies, observing and modeling interactions between ocean heat transport and Arctic sea ice have never been as important as now.

Data availability statement
The data that support the findings of this study are openly available. The observed sea-ice concentration from OSI SAF (Lavergne et al 2019), used for producing figures 1 and 2, can be accessed via http:// dx.doi.org/10.15770/EUM_SAF_OSI_0008 (OSI SAF, 2017) for the period 1979-2015 and https://osi-saf. eumetsat.int/products/osi-430-b-complementingosi-450 for data from 2016. The PIOMAS Rothrock 2003, Schweiger et al 2011) sea-ice volume data, used to produce figure 3, can be accessed via the Polar Science Center of the University of Washington: http://psc.apl.uw.edu/research/projects/arcticsea-ice-volume-anomaly.