Introduction

The Arctic climate system has been changing rapidly over the last decades, as witnessed by a rapid rise in surface air temperature and a reduction in sea ice extent and thickness (Druckenmiller et al. 2022), melting of the Greenland ice sheet (The IMBIE Team 2020), the "Atlantification" of the Eurasian basin (Polyakov et al. 2017), and freshwater (FW) content accumulation in the Beaufort Gyre (Proshutinsky et al. 2019). Because of the Arctic amplification, the Arctic is the region on the globe where the largest increase in surface air temperature is expected to occur by the end of the century (IPCC 2021). All of these ongoing changes manifest themselves in changes in the Arctic climate system components such as atmosphere, ocean, and cryosphere. Ultimately, these changes are driven by the exchange of heat and FW across the lateral boundary of the Arctic atmosphere and ocean due to large-scale atmospheric circulation and ocean circulation (von Schuckmann et al. 2020). Among the CMIP5 global climate models, it is not clear whether atmospheric circulation or oceanic circulation will be the primary driver of continued future Arctic warming (Burgard and Notz 2017).

In the North Atlantic Ocean, the basinwide Atlantic meridional overturning circulation (AMOC) brings heat to the north well into the Arctic, and exports FW and dense water from the Arctic to the south (Dickson et al. 2008). The North Atlantic Current, which originates from the Gulf Stream, flows northward, and the portion of the Atlantic Water (AW) that crosses the Greenland-Scotland Ridge and enters the Norwegian Sea experiences substantial cooling and densification. A portion of it flows into the Arctic Ocean via the Barents Sea Opening (BSO) and Fram Strait and experiences further water-mass transformations. The other part recirculates in Fram Strait, partially subducts beneath surface water and returns south along the East Greenland Current (EGC) in the Nordic seas (Mauritzen 1996). In addition, about one-third of the dense water is formed in the Iceland Sea (Våge et al. 2011), which, merged with the dense water in the EGC, flows toward the Greenland-Scotland Ridge as headwaters of the overflow water, eventually feeding the lower limb of the AMOC (Hansen and Østerhus 2000). It has been shown that about half of the Polar Water exiting the Arctic participates in the overturning circulation (Le Bras et al. 2021) but how much water-mass transformation occurs in the Arctic Ocean and how that may change in the future is still unclear.

There are a few sustained basinwide scale mooring arrays in the North Atlantic to monitor the temporal variability of AMOC and the associated heat transport (HT) and FW transport (FWT; Frajka-Williams et al. 2019). Going from south to north, they include the "RAPID" array across the subtropical gyre since 2004 (Cunningham et al. 2007), the Overturning in Denotes content that is immediately available upon publication as open access.

Supplemental information related to this paper is available at the Journals Online website: https://doi.org/10.1175/JPO-D-23- 0056.s1.

the Subpolar North Atlantic Program (OSNAP) array across the subpolar gyre since 2014 (Lozier et al. 2019), the Greenland-Scotland Ridge array since 1992 (Østerhus et al. 2019), and the Arctic boundary array since 2004 (Dickson et al. 2008). To quantify the HT and FWT, one needs to measure all inflow and outflow branches at the same time. The HT can then be quantified as the temperature difference between the inflow and outflow and is proportional to the strength of the ocean circulation (Hall and Bryden 1982;Ganachaud and Wunsch 2000). In a similar manner, FWT can be quantified as the salinity difference between the inflow and outflow scaled by the ocean circulation (Ganachaud and Wunsch 2003).

Although there are many numerical models available at increasingly better resolutions, there are still significant discrepancies relative to the observations and among models. This not only holds for climate models that deliver future climate projections (Wang et al. 2016;Ilıcak et al. 2016) but also for data assimilation models to assess the state of the ocean in the present and past (Uotila et al. 2018;Mayer et al. 2019). Moreover, the Arctic Ocean lacks sufficient observation-based datasets to validate these numerical ocean and climate models. For the net Arctic Ocean transports, there are only a few datasets available that cover the entire Arctic Ocean. Considering the ongoing fast changes in the Arctic climate, there is an urgent need to establish and update the observation-based Arctic Ocean transport estimates.

The Arctic Ocean is delineated from the rest of the ocean by (from east to west) Fram Strait between Greenland and Svalbard, BSO between Svalbard and Norway, Bering Strait between Siberia and Alaska, Fury and Hecla Strait between the Canadian mainland and Baffin Island, and Davis Strait between Baffin Island and Greenland, of which Fury and Hecla Strait can be ignored to estimate the water-mass exchanges between the Arctic Ocean and the surrounding seas (Tsubouchi et al. 2012;Bacon et al. 2022). To quantify the Arctic Ocean transports, synoptic hydrographic data from these four Arctic gateways were analyzed using a box inverse model (Tsubouchi et al. 2012). This inverse box model was then applied to the mooring data from the Arctic gateways to obtain a 1-yr-long estimate between September 2005 and August 2006 (Tsubouchi et al. 2018. This study employs the same inverse method to extend the time series from 1 year (T2018) to 6 years (2004-10) to quantify representative seasonal cycles and investigate interannual variability. We also exploit the mass and salt conserved velocity field to estimate the overturning circulation in the Arctic Ocean and its temporal variability.

Data and methods

In this section, we first present the datasets used in this study. We then describe the method to generate gridded monthlymean properties and velocity fields. Third, we show the inverse model method and then HT and FWT calculations.

a. Data

Our main oceanographic measurements consist of 1165 moored instrument records in Davis, Fram, and Bering Straits and the BSO (Fig. 1). The moored instruments comprise devices measuring point measurements of temperature, salinity and pressure; acoustic Doppler current profilers (ADCPs); and single-point current meters. Their typical deployment duration is 1 or 2 years, with sampling rates of 10-60 min. The mooring array configuration from summer 2005 to summer 2006 was presented in Fig. 1 of T2018, and a similar configuration was maintained from summer 2004 to summer 2010. Due to various reasons, the number of observational records of good quality at each mooring site varied from year to year (Fig. S1 in the online supplemental material). Details of the in situ mooring data in terms of measurement locations and durations, type of instruments, measurement accuracy, original sampling rate, and so on, can be found as follows: Davis Strait in Curry et al. (2014); the western side of Fram Strait in de Steur et al. (2014) with the data at de Steur (2019); the central and eastern side of Fram Strait in Beszczynska-Möller et al. (2012) with the data at Beszczynska-Möller et al. (2015); BSO in Ingvaldsen et al. (2004);and Bering Strait in Woodgate (2018).

In addition, for the BSO, 37 repeat CTD sections between Bear Island and Tromsø in Norway (i.e., around 6 occupations per year) are also included to compensate for the relatively small number of moored instrument records in BSO. Each CTD section comprises around 20 stations in ;30-km horizontal distance and has 1-dbar resolution in vertical coverage.

Sea ice thickness, sea ice temperature, and velocity data are obtained from the Pan-Arctic Ice Ocean Modeling and Assimilation System (PIOMAS; Zhang and Rothrock 2003). We choose to use this data assimilation product to obtain continuous sea ice transport estimates without data gaps. Model biases are evaluated as 8% in sea ice velocity and 9% in ice thickness with available buoy and submarine observations (Zhang and Rothrock 2003), and model ice thickness biases depend on ice thickness itself (model overestimate ice thickness of thinner than ;2 m; Johnson et al. 2012). These monthly data are used to quantify the sea ice volume transport, HT, and FWT through the four Arctic gateways.

b. Construction of monthly gridded fields

Based on the point measurements of temperature, salinity, and velocity at moored instrument locations, initial coast-tocoast and surface-to-bottom temperature, salinity, and crosssectional velocity fields are obtained at monthly resolution. We focus on the period from October 2004 to May 2010 when most of the moored instrument records overlapped; several, but not all, arrays started earlier and/or have been continued thereafter. As in T2018, grid resolution is 3 km in the horizontal axis, and it has 75 vertical layers. There are, however, two major differences between this study and T2018: the treatment of missing data periods and unobserved variability outside of the mooring arrays. Details of the mooring data treatment, the gridding procedure, and major features of the gridded fields can be found in section a of the online supplemental material.

c. Box inverse model

The box inverse model employed in this study is the same as in T2018. It contains a set of linear equations that represent mass and salt conservation for each defined model layer. Each equation considers four different types of physical mechanisms that exchange mass and salt. They are horizontal ocean circulation and sea ice export across the Arctic boundary (i.e., the four gateways), and surface FW flux through the sea surface of the Arctic Ocean, and diapycnal fluxes between model layers. The surface FW flux represents all FW that goes into the Arctic Ocean through the sea surface bounded by the four gateways. It is a sum of precipitation 2 evaporation (P 2 E) and river discharge from Eurasia, North America, the Canadian Arctic Archipelago, and Greenland. Since the accuracy of these transport estimates are different, the box inverse model objectively modifies these transport estimates according to the size of these uncertainties to achieve mass and salt conservation in each defined model layer.

We use the mooring data across the four Arctic gateways to estimate the first guess of horizontal ocean circulation, and PIOMAS data to estimate the first guess of horizontal sea ice export. Smaller uncertainties are assigned on these two terms (3-month standard deviation of moored velocity measurements and 10% magnitude of initial sea ice velocities, respectively). In We define five model layers (Table 1): Surface Water (SURF) layer, Upper Atlantic Water (UAW) layer, Atlantic Water (AW) layer, Intermediate Water (IW) layer, and Deep Water (DW) layer. The water-mass definitions are the same as in T2018, with one change in model layer interface definitions. The model layer interface between AW and IW is now defined by the 28C isothermal and that between IW and DW is defined by a fixed depth of 1500 m instead of isopycnal definitions. This change is motivated by the fact that there are only three point measurements of salinity in Fram Strait below 750 m during this period. The 28C isotherm in the eastern T S U B O U C H I E T A L .

and central Fram Strait mostly coincides with potential density isopycnal of 27.97 kg m 23 , which defines the AW lower boundary (Beszczynska-Möller et al. 2012). These choices avoid defining unrealistic shapes of layer interfaces between AW and IW and between IW and DW due to the sparse salinity measurements.

The inverse model has 12 constraints that come from volume and salt transport constraints for the full depth and the 5 defined layers and 1287 unknowns that represent the four different types of physical mechanisms that exchange mass and salt. The 1287 unknowns are categorized into bottom velocities at 3 km grid points (639 unknowns), sea ice advections at these grid points (639 unknowns), surface FW flux (1 unknown), and diapycnal velocities across defined water-mass interfaces (8 unknowns). Row and column weights are set to prescribe uncertainties both on constraints and unknowns. The row-and column-weighted matrix was then solved by the singular value decomposition (SVD). A posteriori uncertainties were calculated based on the Gauss-Markov formalism (Wunsch 1996). Details of the box inverse model setting are provided in appendix A in T2018.

The box inverse model solutions in this study are similar to that in T2018. The eight leading SVD modes are used to solve the 12 conservation equations that yield a stable solution in which the inverse model solution for the unknowns remains within a priori uncertainties. Overall, reference velocities are modified by mean and peak perturbations of 2 and 10 mm s 21 , respectively. Larger modification is introduced over Belgica Bank in Fram Strait and north of Bear Island in BSO where moored observations do not exist. As discussed in the online supplemental material (see Fig. S3), most of the full-depth initial imbalances stem from below 1500 m in Fram Strait. Thus, most of the inverse adjustment occurs in Fram Strait and accounts for 2.8 6 1.7 Sv [mean 6 standard deviation (std)]. Adjustments in other gateways are minor: BSO for 0.1 6 0.4 Sv, Davis Strait for 0.0 6 0.1 Sv, and Bering Strait for 0.0 6 0.0 Sv (mean 6 std). Sea ice transport adjustments are also minor, equivalent to 0.5 mSv on average with a peak of 3 mSv. The surface FW flux adjustment and the diagnosed diapycnal flux adjustments are larger. The former is equivalent to 20 mSv with a peak of 300 mSv. The latter is equivalent to 1-3 Sv on average with a peak of 6 Sv.

d. HT and FWT calculation

HT through the Arctic boundary is calculated as (following T2018)

where r o is density of seawater (1027 kg m 23 ), c o p is specific heat capacity of seawater (3.987 3 10 3 J kg 21 K 21 ), y is the cross-sectional velocity anomaly from the mean y , and u is the potential temperature difference from its reference value u. Note that y is not zero. It is a small number [O(10 24 ) m s 21 ] that balances with the surface FW flux in the mass conservation. Superscripts o and i refer to liquid ocean and sea ice, respectively. The r i is density of sea ice (930 kg m 23 ), c i p is specific heat capacity of sea ice, c f is latent heat of freezing (3.347 3 10 5 J kg 21 ), y is the cross-sectional velocity, z is depth, and x is the alongboundary coordinate. Similarly, FWT through the Arctic boundary is calculated as

where S is the salinity difference from its reference value S.

The reference values u and S are calculated for each individual month as the appropriate boundary-mean potential temperature and salinity, respectively (Bacon et al. 2015). To estimate the FWT related to sea ice, a sea ice salinity of 6 is assumed, which represents the salinity of first year sea ice (Kovacs 1996).

Results

a. Mass and salt balanced velocity fields and gateway volume transports

Figures 2a-c show the 68-month mean mass and salt balanced absolute velocity field, along with cumulative full depth and water-mass specific volume transports. Positive values indicate inflow into the Arctic Ocean. Table 2 summarizes volume transport estimates through the four gateways and the overturning cells (the latter will be discussed in the next section). The mean absolute velocity field captures major features of ocean circulation around the Arctic boundary. The major export of water happens on both sides of Greenland. In the western Davis Strait water is exported as the SURF water mass (1.8 Sv). In the western Fram Strait, export of SURF is small (0.7 Sv) and the EGC primarily exports IW (4.0 Sv) and DW (1.5 Sv). AW is transported into the Arctic Ocean by the WSC (3.5 Sv) through the eastern Fram Strait and through the BSO (1.1 Sv). BSO also imports 1.1 Sv of the SURF and What is new here is that the obtained volume transport time series satisfies mass and salt conservation at any given month. The net volume transport (black line in Fig. 3) is small and balances with sea ice export through the four gateways and the surface FW flux. We find that the transport in each gateway is subject to substantial interannual variability and has a clear seasonality as summarized in Table 2, which was not obvious from 1-yr data presented in T2018. BSO inflow is the strongest in winter at 2.9 Sv [January-March (JFM) mean], and the weakest in spring at 1.

b. Overturning circulation in the Arctic Ocean

The transport obtained across the Arctic Ocean boundary is converted into temperature-salinity space and illustrates the water-mass transformation that occurs in the Arctic Ocean (Fig. 4a). Most of the inflow takes place in the AW inflow between 2.08 and 7.58C in potential temperature and 34.8 to 35.2 in salinity shown by the red colors. This AW inflow is transformed into the salty-cold deeper outflow (potential density greater than 27.8 kg m 23 ) and into fresher upper outflowing Polar Water (which we define as the sum of SURF and UAW, i.e., with potential density less than 27.5 kg m 23 ). The volume transport as a function of potential density provides the overturning streamfunction in the Arctic Ocean (black line in Fig. 4b). Contributions to the mean overturning circulation in the Arctic Ocean from the four Arctic gateways are shown individually in different colors. The mean overturning streamfunction crosses zero transport twice, at about 26.6 and 27.7 kg m 23 , indicating that there are three overturning cells. The upper cell appears in density less than 26.6 kg m 23 with a maximum of 0.3 Sv around 26.3 kg m 23 . This cell transforms the Pacific water inflow through Bering Strait into the Polar Water outflow through both Davis Strait and Fram Strait, with the outflow being denser than the inflow. Since this water comes from the Pacific Ocean and exits to the North Atlantic via the Labrador Sea and Nordic seas, it does not constitute an overturning cell in the classical sense (i.e., water returning to the basin from where it came from, after the density transformation occurred). The intermediate cell has a strength of 21.1 Sv around 27.5 kg m 23 , which is the interface between UAW and AW. The negative value of the strength of the cell implies that this cell represents the transformation of the (relatively) denser AW inflow through the BSO and Fram Strait into the (relatively) lighter Polar Water outflow through Davis Strait and Fram Strait. The transformation is accomplished within the Arctic Ocean by mixing of AW with sea ice meltwater and river freshwater runoff and precipitation. The lowest cell has a maximum of 2.7 Sv around 28.0 kg m 23 , that is, the interface between AW and IW. This cell transforms AW inflow through Fram Strait and BSO into denser waters (IW and DW), which exit the Arctic Ocean through Fram Strait. The monthly time series of the strength of the three cells and their corresponding seasonal cycles are shown in Figs. 4c and 4d, respectively. Throughout the observational period the upper cell (blue line) shows the smallest variability, whereas the lower cell (green line) shows the largest. While the upper cell mostly displays (intra)seasonal variability, the intermediate and deep ones also feature interannual changes. Occasionally, the strengths of both the upper and intermediate cells drop to 0 Sv. We next examine the seasonal cycle of the overturning circulation. The intermediate overturning cell (AW to SURF/ UAW conversion in red line) is strongest in winter (February-March) and weakest in summer (August). The lower cell (AW FIG. 3. (a) Ocean volume transport time series (Sv) in the four Arctic main gateways from October 2004 to May 2010: Davis Strait in blue, Fram Strait in green, BSO in red, and Bering Strait in cyan. The sum of these is shown in black. (b) Their mean seasonal cycles.

TABLE 2. Mean and standard deviation (std) of ocean volume transports (Sv) in the four Arctic main gateways and of the three overturning cells between October 2004 and May 2010 (column 2) and their seasonal averages (columns 3-6). Sign conventions for the four main gateways are positive means inflow to the Arctic Ocean and negative means outflow from the Arctic Ocean. For the overturning cells, positive means that inflow density is lighter than outflow density, and vice versa. Note that we consider Polar Water as the sum of SURF 1 UAW.

Seasonal averages Mean 6 std (Sv) JFM AMJ JAS OND Four main gateways Davis Strait 21.9 6 1.0 21.8 22.2 22.4 21.2 Fram Strait 21.4 6 1.2 22.0 20.4 21.2 21.9 BSO 2.2 6 1.0 2.9 1.3 2.2 2.4 Bering Strait 1.0 6 0.5 0.8 1.3 1.4 0.7 Overturning cells Pacific Water to Polar Water (SURF 1 UAW) 0.7 6 0.6 0.1 0.7 1.2 0.4 AW to Polar Water 21.4 6 0.8 21.9 21.3 20.4 21.1 AW to both IW and DW 2.9 6 1.2 3.1 1.8 2.5 3.7

to IW/DW conversion in green line) follows a similar pattern but reaches its extreme values slightly earlier (maximum in January; minimum in June). While it can be expected that IW formation is maximum in wintertime during the massive cooling of both the BSO inflow over the shallow Barents Sea and of the Fram Strait branch of Atlantic Water inflow, this does not necessarily lead to a maximum IW outflow during winter in Fram Strait, as water masses formed in the Arctic Ocean can take many years before being exported. Rather, we expect the seasonality observed in the two AW-related overturning cells to be primarily wind driven: Fig. 3b demonstrates the BSO inflow peak occurring in January, which is mostly wind driven, to coincide with the timing of maximum AW-IW/DW overturning.

The summertime maximum of the upper overturning cell in Fig. 4d coincides with the maximum in low-density inflow through Bering Strait and the maximum outflow through Davis Strait at that time of the year in Fig. 3b.

Table 2 summarizes the overturning circulation in the Arctic Ocean. A total of 2.2 Sv Polar Water outflow is fed by three sources: 0.7 Sv Pacific water inflow, 0.15 Sv surface FW flux, and 1.4 Sv AW. The lower limb of the overturning circulation of 2.9 Sv is fed by the AW inflow. Note that these transport numbers are the 68-month averages of the monthly time series of the three overturning cells in Fig. 4c, which is higher than the two maxima and the one minimum of the mean overturning function in Fig. 4b. See Fig. S4 in the online supplemental material for the details.

c. HT and FWT time series

Another main result of this study is the HT and FWT time series from October 2004 to May 2010 (Fig. 5). Table 3 summarizes the 68-month mean and annual mean values. Here, positive values of HT mean the Arctic Ocean gains heat from the surrounding seas. As the 6-yr mean, the Arctic Ocean imports 180 6 57 TW (mean 6 std) of heat, with an ocean contribution of 151 6 48 TW and a sea ice contribution of 29 6 21 TW. It has a large month to month variability ranging from ;80 to ;290 TW (Fig. 5b). It also shows a clear seasonality with a maximum in November around ;260 TW, and minimum in May around ;110 TW. The seasonality is primarily driven by ocean heat transport. In addition, there is substantial interannual variability. The largest annual mean HT of 195 TW was observed in 2009, while the lowest of 155 TW in 2008. This interannual variability seen here is dictated by the ocean heat transport and not that of sea ice. 3). The month-to-month variability is large, ranging from 240 mSv (net import of FW) to 1320 mSv (net export of FW). The seasonal variability has higher values of ;230 mSv in winter months (November-March) and minima as lower values ;40 mSv in summer months (July-August). Approximately two-thirds of the monthly and seasonal variabilities come from the ocean and the other one-third comes from the sea ice. FWT also shows large interannual variability: the largest annual mean FWT of 177 mSv occurred in 2005 and the lowest annual mean of 127 mSv in 2008. The ocean FW transport explains 87% of the total year to year FW transport variability.

We now compare our result with T2018 to estimate potential offsets in HT and FTW due to the unobserved variability by moored instruments. T2018 uses the same data and same inverse model method for one year (i.e., 2005/06), but has different treatment of missing data periods and of the unobserved variability. T2018 estimates the unobserved variability above the shallowest moored instruments in Davis Strait, Fram Strait and Bering Strait using the vertical gradients of temperature, salinity and velocity from NEMO model output, for example (see the online supplemental material of T2018 for full details). Thus, we anticipate our FWT estimate may underestimate the transport by neglecting these unobserved ). This comes from different missing data treatment, such as inclusion of F17 mooring data (Fig. S1), highlighting uncertainty associated with the data gaps and interpolation methods. To conclude, this study likely underestimates the FWT by ;30 mSv by omitting unobserved variability over the shallowest moored instruments in western Davis Strait. The Belgica Bank in Fram Strait is also still a major source of uncertainty and likely is responsible for significant offsets in FWT (Karpouzoglou et al. 2023), but we do not have the means to investigate these in detail here. Uncertainty of the obtained ocean HT and FWT stem from two different sources: (i) accuracy and representativeness of the measurements in the property and velocity fields, and (ii) unobserved variability both in the velocity and property fields with the mooring array configuration. We consider the accuracy and representativeness uncertainty (i) in the velocity fields based on the a posteriori error estimate of the inverse model that is originally prescribed as an a priori error in the boundary velocity fields based on the standard deviation of velocities measured by the moored instruments over three months as in Tsubouchi et al. (2012). We quantify this uncertainty in heat transport to be 626 TW and that in FW transport to be 644 mSv for a single month. For the unobserved variability uncertainty (ii), we adopt the uncertainty estimates from T2018, which is 67 TW for HT and 652 mSv for FWT. T2018 estimates this unobserved variability in FWT stems from three sources and their uncertainties are ;30 mSv each. They are the upper water column in western part of Davis Strait, the Belgica Bank in western Fram Strait, and sparse deep salinity measurements in the EGC region in Fram Strait. By combining these two different uncertainty estimates in a root sum square sense, we obtain that the total uncertainty for heat is 627 TW and that for FW is 668 mSv for a single month. To estimate the uncertainty for the long-term mean transport, we assume the former uncertainty to be half random and half systematic while the latter uncertainty is systematic. Random uncertainty can be reduced by frequent sampling with factor of n 21/2 , where n is the number of degrees of freedom. By calculating the random uncertainty with n 5 68 and combining that with the systematic uncertainties in a root sum square sense, we estimate the long-term mean uncertainty for HT and FWT as 620 TW and 661 mSv, respectively.

d. Water-mass transformation

To better understand the HT and FWT variability and its relation to surface fluxes and storage fluxes, we view them from a water-mass transformation perspective as described in T2018. Unlike examining each gateway contribution individually, this approach is not affected by the choice of reference values. The Arctic heat and FW budgets can be expressed as

where F Surf H and F Surf vol are surface heat and FW fluxes, respectively; F Stor H and F Stor FW are heat and FW storage fluxes, respectively; V in is the inflow volume transport associated with the water-mass transformation in the Arctic Ocean; Q in and S in are transport-weighted inflow potential temperature and salinity, respectively; and Q oi out and S oi out are transport-weighted outflow potential temperature and salinity including the sea ice contribution, respectively. See T2018 for the derivations.

The overall mean seasonal cycles of inflow and outflow water properties from October 2004 to May 2010 are shown in Fig. 6. As indicated by T2018 with 1-yr data, Q in and S in have around 3-5-months phase difference in their seasonal cycles. Whereas Q in has maxima in August-October and minima in April-May, S in has maxima in January-March and minima in July-August. The average seasonality in Q in ranges between 28 and 58C, and that in S in ranges between 34.4 and 34.8. The seasonality of Q oi out and S oi out are mostly in phase as they form a nearly straight line on the u-S plane. Although most of these features were identified in T2018, this study confirms these are the prominent signals in seasonality by using nearly 6 years of data.

We point out this temperature-salinity space diagram is a useful metric to diagnose the performance of different numerical ocean models and climate models. This single diagram presents the water-mass properties of the inflow and outflow, and the overall water-mass transformation that happens in the Arctic Ocean due to the surface heat flux and surface FW flux as summarized by Haine (2021). Mayer et al. (2019) already exploit our HT estimates to gain our understanding on the performance of reanalysis models (note that our HT and FWT estimates were published on Pangaea as a dataset in 2019; Tsubouchi et al. 2019). By comparing our HT estimate described in this study with that in various reanalysis models, Mayer et al. (2019) identify that reanalysis models tend to underestimate ocean heat transport to the Arctic Ocean by 10%-20% (i.e., surface heat loss from the ocean to the atmosphere in the models tend to be weak, indicating that models may be struggling to capture some processes correctly). Direct comparison of the estimated mean water-mass properties of the inflow and outflow (such as in, e.g., Fig. 6) with reanalysis models will shed light on where the differences may come from.

Discussion

a. Fram Strait deep water

We first discuss our estimate of the lower limb of the overturning circulation in the Arctic. Our estimate of 2.9 Sv is probably too large considering the overflow that crosses the Greenland-Scotland Ridge (Østerhus et al. 2019) and watermass transformation that takes place in the Nordic seas by deep water formation in the Greenland Sea (Swift and Aagaard 1981) and densification of Atlantic Water in the Norwegian Sea (Mauritzen 1996). Based on over 20 years of historical observations, Østerhus et al. (2019) estimate that the total dense overflow across the Greenland-Scotland Ridge is 5.8 Sv. Exploiting Østerhus et al.'s (2019) historical observations with an inverse model, Tsubouchi et al. (2021) estimates that the Nordic seas can produce up to 4.0 Sv of overflow water and the Arctic Ocean including the Barents Sea may produce around 1.5 Sv of overflow water. This estimate of 1.5 compares to the estimate of 2.9 in this study. The large value obtained in the current study for the lower limb overturning cell in the Arctic is likely related to our large estimate of 1.4 Sv of southward flow in DW (below 1500 m), where we expect near-zero net volume transport. Based on historical hydrographic observations in the Greenland Sea and the Eurasian Basin of the Arctic Ocean, Somavilla et al. (2013) We discuss the meaning of the obtained boundary transports, in terms of their relation to the surface fluxes in absence of storage within the Arctic Ocean. Although this is already addressed in T2018, we discuss this topic to highlight its value and to address future improvements to the inverse model. Our inverse model does not account for the storage flux terms both in mass and salt. This means that horizontal salt transport across the gateway boundary is always balanced each month because there is no salt input by surface FW flux. At the same time, net export of seawater by the ocean plus sea ice volume transport [;O(0.1 Sv)] is balanced with the surface FW flux each month through mass conservation. This is achieved as the lower salinity outflow including sea ice (S oi out ) from the Arctic Ocean carries the same amount of salt that is imported to the Arctic Ocean by the inflow with higher salinity (S in ). In this way, our surface FW flux is an "inferred" quantity derived from the pan-Arctic hydrographic sections. For the heat, surface heat flux is "inferred" by the temperature difference between inflow and outflow. These inferred surface fluxes are valuable because these quantities are poorly observed and poorly constrained by numerical models (Bacon et al. 2022). These inferred surface heat and FW flux were already used to validate surface heat fluxes in reanalysis models (Mayer et al. 2019) and surface FW fluxes in reanalysis models (Winkelbauer et al. 2022) that helps to identify which reanalysis products represent the surface fluxes better in the Arctic Ocean.

We note our "inferred" surface FW flux of 156 6 61 mSv likely has a negative bias of ;30 mSv as discussed in section 3c. In addition, our study period of 2004-10 is associated with a period of accumulation of FW content in the Beaufort gyre (Proshutinsky et al. 2019) and a period of reduced FW export through Davis Strait inferred from downstream hydrographic measurements on the Labrador Shelf over seven decades (Florindo-López et al. 2020). These conditions could explain the difference between our surface FW flux estimate and the state-of-art reanalysis and GRACE based estimate of atmospheric and terrestrial FW flux of 6560 km 3 yr 21 (equivalent to 208 mSv) over the period of 1993-2018 by Winkelbauer et al. (2022).

For future improvements of the Arctic boundary transports, we recommend to include Arctic Ocean storage estimates in obtaining the monthly solutions as well as to include the observed overflow water estimates across the Greenland-Scotland Ridge (Østerhus et al. 2019) as an additional constraint. As discussed by Bacon et al. (2022), measurements are available to estimate the storage fluxes of heat and FW. These are satellite measurements of GRACE and altimeter, and hydrographic measurements by ice-tethered profiler (ITP). Rabe et al. (2014) quantify the long-term change of FW content in the Arctic Ocean from 1992 to 2012, and of which an update to 2018 is currently on its way (M. Vredenborg et al. 2023, unpublished manuscript). In addition, Armitage et al. (2016) show the possibility to measure FW content change with remote sensing. Errors and uncertainties of these quantities need to be assessed to quantify the storage flux terms. For the inclusion of overflow estimates across the Greenland-Scotland Ridge as an additional constraint, additional unknowns for specific water masses may need to be considered so that adjustments on DW export will, for example, not directly affect the well observed AW inflow through Fram Strait. Errors on the additional overflow water constraints and uncertainties between vertically uniform adjustments and water-mass-specific adjustments need to be examined.

c. Ambiguity of reference values

It is widely recognized that the relative temperature transport and relative FW transport estimates through single gateways are heavily dependent on the choice of reference values (e.g., Dickson et al. 2007;Schauer and Beszczynska-Möller 2009;Tsubouchi et al. 2012;Bacon et al. 2015). Schauer and Losch (2019) urge to abandon the use of relative temperature transport and relative FW transport in single gateways completely in climate science. Yet, there are many studies that quantify the relative ocean temperature and relative FW transport estimates through single gateways and discuss their role related to ongoing Arctic climate changes. In this study, we have obtained the 68-month mean mass and salt balanced velocity field (Fig. 2), which we use to demonstrate the problems. Although this is already done by Tsubouchi et al. (2012) with summer 2005 hydrographic data, it is worthwhile to demonstrate this again with the nearly 6-yr mooring-based hydrographic sections that capture the main features of the ocean circulation through the Arctic boundary.

Figure 7a shows the cumulative relative temperature transport around the Arctic Ocean boundary with different reference temperatures. We demonstrate results using 1.018 6 0.188C (boundary mean potential temperature that changes from one month to another), 0.08C, and seawater freezing temperature of 21.88C. By integrating across the boundary all three lines end up with the same point of 151 TW that is the long-term mean ocean HT. In contrast, the integration results across part of the section differ significantly. Thus, integrated temperature transport does not change with the choice of the reference temperature, but temperature transport in each individual portion of the boundary, i.e., individual gateways, does change. For example, for the WSC in eastern Fram Strait, it changes from 33 TW-equivalent (TW-eq) with reference temperature of 1.018 6 0.188C to 113 TW-eq with reference temperature of 21.88C.

Figure 7b shows the cumulative relative FWT around the boundary with different reference salinity, such as 34.70 6 0.02 (boundary mean salinity that changes from one month to another), 34.8, and 35.0. The relative FWT has a similar caveat to that of relative ocean temperature transport. The integrated relative FWT around the boundary is hardly affected by the choice of the reference salinity and comes out as 102 mSv (the longterm mean ocean FWT), but the relative FWTs in each portion of the section (and hence each individual gateway) differ significantly. For the EGC in western Fram Strait, for instance, it changes from 24 6 11 mSv-equivalent (mSv-eq) using reference salinity of 34.70 6 0.02 to 56 6 13 mSv-eq using reference salinity of 35.0. To be precise, the integrated relative FWT around the boundary is also affected by the choice of reference salinity. This is because the reference salinity appears in the denominator of the relative FWT equation. As discussed in Tsubouchi et al. (2012), a "sensible" choice of the reference salinity (between 34.8 and 35.2) only introduces an error of ;1% in the integrated relative FWT.

Here is our standpoint on the reference value issue: Scientists must be aware of the ambiguities and caveats of quantified relative ocean temperature transport and relative FW transport estimates in single gateways. We urge the use of different terms and units to distinguish between the two different quantities depending on their sensitivity to reference values, such as HT (W) versus relative temperature transport (W-eq) for heat and FWT (mSv) versus relative FWT (mSv-eq) for FW. This was already done by Talley (2003), Talley (2008), and T2018. The relative temperature transport and relative FWT in single gateways can be very different, both their mean values and temporal variabilities [Figs. 3 and 4 in Schauer and Losch (2019)]. We argue that it is not useful to interpret relative temperature and FW transports in single gateways in the context of their impact on heat and FW storage (or changes therein) in the Arctic Ocean.

Summary and conclusions

This study provides observation-based estimates of the overturning circulation in the Arctic Ocean and associated Last, there are a few sustained basinwide scale mooring arrays in the North Atlantic to continuously monitor the temporal variability of the AMOC and associated HT and FWT (Frajka-Williams et al. 2019). Together with insights from these sustained observations, the overturning circulation in the Arctic Ocean and associated HT and FWT time series should be 1) extended over the entire past observational period up to present, 2) updated regularly in the future, and 3) considered to be improved with including storage terms in the Arctic Ocean. These will provide vital information to better understand the variability of the AMOC and allow us to identify trends or potential shifts that may happen in the future. collected by University of Washington, Seattle, Washington, and the University of Alaska Fairbanks, Fairbanks, Alaska (PIs R. Woodgate and T. Weingartner), with funding from NSF Grant (NFS-0856786), and the NOAA-RUSALCA program. The BSO mooring data were collected by IMR, Bergen, Norway (PI R. Ingvaldsen). The Fram Strait mooring data from 2004 to 2010 were collected by AWI, Bremerhaven, Germany (PI U. Schauer), and NPI, Tromsø, Norway (PI E. Hansen). "DOBOX 4.2" (Morgan 1995) is used for the box inverse model. Support for this study came from the Alfred Wegener Institute, Helmholtz Centre for Polar and Marine Research, and from the Helmholtz Infrastructure Initiative FRAM. Author T. Tsubouchi was funded by the EU Horizon 2020 Marie Skłodowska-Curie Grant ARCGATE (652757).