The coherence of the oceanic heat transport through the Nordic seas: oceanic heat budget and interannual variability

Atlantic Water is the main source of the heat and salt in the Arctic. On the way to the Arctic Ocean via the Nordic Seas, it interacts and mixes with other water masses which affects sea ice extent and deep water formation. The Atlantic Water heat transported into the Nordic Seas has a significant impact on the local climate and is investigated here along with its inter15 annual variability using the ARMOR3D dataset, which is a collection of 3D monthly temperature, salinity and geostrophic velocities fields, derived from in situ and satellite data on a regular grid since 1993. The study region includes the eastern part of the Nordic seas, i.e., seven latitudinal transects from Svinoy section (65° N) to the northern part of the Fram Strait (78.8° N). The Atlantic Water heat advection decreases northwards, as a significant amount of heat is lost to the atmosphere and due to mixing with surrounding waters. As observed, the imbalance of heat fluxes in the upper layer leads to an increase in the 20 upper ocean mean temperature over most of the study region. The correlations of the interannual variations of the advective heat fluxes rapidly drop from Svinoy to Jan Mayen sections and between Bear Island and Sorkapp sections. This is a result of a differential damping of periodicities (the 2–3 year and 5–6 year oscillations), as well as of different signs of the tendencies over the latest decades. The heat fluxes at all sections show a consistent change with meridional (C) and western (W) weather types, which is due to the different direction of the Ekman pumping associated with each of the weather types. A certain link 25 to the NAO, AO and EA atmospheric indices is observed only at the southern sections.

ocean and the atmosphere, often coupled (Jungclaus and Koenigk, 2010;Schlichtholz, 2011, Bucklay andMarshall, 2016;Bashmachnikov et al., 2018). A significant amount of the northward directed oceanic heat is released in the Nordic and the Barents seas and in the Whaler's Bay north of Spitsbergen (Piechura and Walczowski, 2009;Moore et al., 2012;Smerdsrud 35 et al., 2013;Bosse et al., 2018). Previously, the subsurface Atlantic water (AW) was believed to not affect the Arctic climate after submerging and entering the Arctic (Lenn et al., 2009;Sirevaag and Fer, 2012;Rudels et al., 2013). However, recent studies show that the AW can reach the upper mixed layer in the Atlantic sector of the Arctic which can be associated with the recent warming of the Arctic, thus becoming an important factor for the Arctic climate change (Schlichtholz, 2013;Tverberg et al., 2014;Carmack et al., 2015;Polyakov et al., 2017). 40 Warm and saline AW is transported north across the Nordic Seas to the Arctic along the continental margin of Norway by the Norwegian Atlantic Slope Current (NwASC) and along the Jan Mayen Fracture zone and Mohn-Knipovich ridges by the Norwegian Atlantic Front Current (NwAFC) (Poulain et al., 1996;Orvik and Niiler, 2002;Skagseth et al., 2004). There is practically no AW transport from the Barents Sea to the Arctic Ocean (Smerdsrud et al., 2013;Mahotin and Ivanov, 2016); most of the oceanic heat enters the Arctic Ocean through the Fram Strait (Rudels, 1987(Rudels, , 2015Schauer et al. 2004;Beszczynska-45 Möller et al., 2012). The West Spitsbergen Current (WSC), a continuation of the NwASC, has a complex structure near the Fram Strait, where it is split into several branches and recirculations (Aagaarda et al., 1987;Gascard et al., 2011;. Two main paths, the Svalbard branch along the Spitsbergen slope (limited by the 400 meters isobaths) and the Yermak branch along the western flank of the Yermak Plateau, enter the Arctic, while the recirculation pattern turns southwestwards, back to the Nordic Seas (Saloranta and Haugan, 2004;Cokelet et al., 2008;. 50 On its way through the Nordic Seas to the Arctic Basin, the AW undergoes dispersion in several recirculations and density transformation through heat loss to the atmosphere and mixing with surrounding waters (Chafik et al., 2016;Polyakov et al., 55 2017;Muilwijk et al., 2018;Bosse et al., 2018). The Faroe, East Icelandic and West Icelandic currents carry a total of about 8.0-9.0 Sv, which merge into the Norwegian Current (the NwAFC, the NwASC and the Norwegian Atlantic Coastal Current -NwACC) ( Fig.1 1) (Dickson et al., 2008;Rossby et al., 2017). A total of 260-300 TW (reference T = 0 ° C) of heat is brought from the mid-latitude Atlantic to the Norwegian Sea located in the eastern Nordic Seas Rossby et al., 2017). Across the Svinoy Section located further north in the Norwegian Sea, the Norwegian Current carries an average of 60 4.0-6.0 Sv (Mork and Skagseth, 2010) and around 150 TW of heat (the estimates vary from 100 to 200 TW, Skagseth et al., 2008 ;Bacon et al., 2015). Therefore, approximately half of the incoming AW heat is released to the atmosphere or heats the Arctic waters coming from the Greenland Sea, even before reaching the Lofoten Basin of the Norwegian Sea known as a region with large winter heat loss (Segtnan et al., 2011).
The NwACC and a part of the NwASC enter the Barents Sea along the northern shelf of Scandinavia as the Nordkapp and 65 Murmansk (Norwegian Coastal) currents with a total average transport of 2.0 Sv (from 1.0 to 3.0 Sv; Smerdsrud et al., 2013); the average annual flow of oceanic heat into the Barents Sea (reference T = 0 °C) is around 50 TW (from 30 to 60-70 TW, Skagseth et al., 2008;Smerdsrud et al., 2010;Skagseth et al, 2011;Bashmachnikov et al., 2018). From 1998, a monotonous increase in the average heat flux (1.5 TW per year) is observed, which is associated with an increase in the volume transport, rather than temperature of the AW (Schauer et al., 2008;Kalavichchi, Bashmachnikov, 2019). 70 The total flow through the Fram Strait to the north of the West Spitsbergen Current (WSC) is 6.0-11.0 Sv with a characteristic inter-annual variability of about 5.0 Sv (Schauer et al., 2004(Schauer et al., , 2008Beszczynska-Möller et al., 2012;Rudels et al., 2013). The difference in the estimates is due to a complex flow structure and difficulty in evaluating the strong recirculations in the Fram Strait. Using a reference temperature of 1.0 °C, the mean heat flux to the north of Spitsbergen during latest decades was estimated to be 30-40 TW (Schauer et al., 2008;Fahrbach, 2006, Schauer andBeszczynska-Möller, 2009;75 Rudels et al., 2013) and was found to increase since 1980 (Dickson et al., 2008). Along the WSC the overall transport increases During the recent decades, the time-series of the AW temperature in the Fram Strait and the Barents Sea Opening show a prominent long-term positive trend in the AW core temperature (around 1° C per decade in the WSC) (Schauer et al., 2008), as well as interannual fluctuations with the characteristic periods of 5-6, 8-10 years (Skagseth et al., 2008;Vesman et al., 2017;Muilwijk et al., 2018;Bashmachnikov et al., 2018). The volume and heat fluxes are re-distributed between the Barents Sea and the Fram Strait, governed by the regional wind patterns through variations of the sea-level anomalies (Lien et al., 85 2013).
In this paper we analyze the space-time variations in advective heat fluxes along the pathways of the AW into the Arctic. https://doi.org/10.5194/os-2020-109 Preprint. Discussion started: 3 December 2020 c Author(s) 2020. CC BY 4.0 License.

ARMOR3D dataset
The latest version of the ARMOR3D dataset used in this study is a collection of global gridded monthly 3D fields of 90 temperature, salinity and geostrophic currents based on in situ and satellite observations at standard depth-levels and with 0.25° x 0.25°spatial resolution. The data from 1993 are available through the CMEMS web portal (Verbrugge et al., 2017). Joint analysis of satellite (sea-level and sea surface temperature (SST) anomalies) and sub-satellite historical data through a multiple linear regression provides temperature and salinity values on a regular grid at different depth levels. These "synthetic" temperature and salinity profiles are combined with historical data in the optimal interpolation procedure to obtain the final 95 monthly 3D thermohaline fields (Guinehut et al., 2004. Geostrophic currents are calculated by extrapolating the seasurface altimetry currents downwards using the thermohaline fields of the previous step and the thermal wind equations (Mulet et al., 2012).

Mooring data 100
To validate the volume and heat fluxes derived from ARMOR3D, data from the moorings deployed in the Fram Strait by Alfred Wegener Institute (Beszczynska-Möller et al., 2012, 2015 were used. The dataset consists of the temperature, salinity and currents speed information from 10 moorings stations deployed along 78.8° N from 8.70° E to 2.10° W during 1997-2011. The datasets are available online from PANGEA database . All available precalculated oceanic heat fluxes data from NACLIM project for the Hornbanki station located at 66.50° N 21.30° W (Jonsson and 105 Valdimarsson, 2012) were also used.

Atmospheric data
The ocean-atmosphere heat exchange, as well as short/long-wave radiation balance is derived from the ERA-Interim reanalysis (Dee et al., 2011) distributed by the European Centre for Medium-range Weather Forecasts (ECMWF). Turbulent 110 heat fluxes across the upper boundary, i.e., to/from the atmosphere, were calculated using the COARE 3.5 algorithm. COARE 3.5 is a modified version of the COARE 3.0 algorithm (Fairall et al, 2003) based on the CLIMODE, MBL, and CBLAST experiments (Edson et al., 2012).

Atmosphere circulation indexes 115
The North Atlantic Oscillation (NAO), Arctic Oscillation (AO) and East Atlantic (EA) indices were obtained from the NOAA National Weather Service Climate Prediction Center. The statistical links between the oceanic heat transport and the typical atmospheric pressure patterns, characterized by these indices, were estimated.
In 1933, Vangengeim suggested a set of indices characterizing atmospheric circulation. He introduced the concept of an elementary synoptic process (ESP). ESP was understood as the process during which, within the Atlantic-European sector, the 120 geographic distribution of the sign of anomalies of the pressure field and the direction of the main air transportations are preserved. ESP could be generalized in three main types of atmospheric circulation: -the western (W), -the eastern (E) and meridional (C) (Girs, 1978;Prokhorova and Svyashchennikov, 2016). During type W, zonal components of the air circulation at mid-latitudes are strengthened and meridional are weakened. This type of circulation leads to a significant reduction in the interactions of the air masses between the tropics and high latitudes. During the circulation pattern of type C, the Icelandic and 125 Aleutian Lows are practically nonexistent due to development of the high-pressure anomaly over the north Atlantic, the so called Atlantic Ridge. Further east, the Siberian Anticyclone strengthens and becomes connected with the Polar Anticyclone.
Type E features strong meandering of the mid-latitude jet, as in C, but the main high-pressure ridges change to troughs and vice versa. In this type, the Icelandic Low is well developed and the stationary anticyclones are observed over Europe and America (Bezuglova & Zinchenko, 2009). Vangengeim -Giers classification helps to highlight variations of the wind patterns 130 over the study region, only partly captured by the atmospheric indices above.
The Atlantic Multidecadal Oscillation (AMO) index, shaping the long-term variability of water temperature in the tropical to mid-latitude North Atlantic, i.e. the temperature of the waters entering the Nordic Seas, was also downloaded from NOAA National Weather Service Climate Prediction Center.

The study region
The transects for calculation of the oceanic advective heat fluxes are drawn across the main pathways of the AW in the Nordic Seas, from the latitude of the Svinoy section at 65° N to the northern part of the Fram Strait at 78.8° N (Fig. 2). The position of the transects may have a significant effect on the absolute values of the heat flux estimates. The sections were drawn to be approximately perpendicular to the direction of the mean currents, i.e. to the continental slope and the underwater ridges, as 140 the currents are strongly bottom trapped. The continental shelf was assumed as the eastern boundary for most of the sections.
The selection of the western limits of the zonal section is an ambiguous task. In this study the western limits correspond to a point with the minimum velocity of the NwAFC, before the sign of the mean meridional flow is reversed (Fig. 2). This minimizes the effect of the return flow and an unstable part of the jet flow dominated by eddies .  the current minimum on the west (red), see Figure 2) The heat fluxes through the western boundaries of the regions are most challenging to calculate with sufficient precision. Due to the instability of the NwAFC, combined with a relatively larger (monthly) period of data averaging and medium resolution of the available data, even a small change in the position of the transect can lead to a significant change in the integral flux 160 through the section, e.g., from 10 to 75 TW for the Svinoy-Voring section. These uncertainties must be taken into account when calculating balances within the studied areas.
where 0 =1030 kg m -3 is the mean sea water density; p c = 3900 J kg -1 C -1 is the specific heat of water; Ti is the sea water 170 temperature in each grid-point and on each depth level, Tref is the "reference temperature" of sea water, Vi is the current speed module perpendicular to the transect, dx is the distance between the stations, dz is the thickness of the water layer.
When comparing the values of heat fluxes given by various authors (Skagseth et al., 2008;Smedsrud et al. 2013), it is necessary to take into account various choices of the "reference temperature". There is no justified algorithm for selection of the reference temperature (Schauer and Beszczynska-Möller, 2009). Here as the "reference temperature", we use Tref = 0 °C, as in most of 175 the previous studies in the region , Skagseth et al., 2008Smedsrud et al. 2013, Bacon et al., 2015Walczowski, 2014). Experiments show that modification of the absolute value of the heat fluxes and different choice of the reference temperature have only minor effects on the interannual variations, which are of primary interest here. In this study we integrate the advective heat fluxes over the Atlantic water layer (described in Table 1).

The Atlantic water in the eastern Nordic Seas
Although the term "Atlantic Water" is widely used in a number of studies, there is no common criterion for the definition of AW in the Nordic Seas. Depending on the goals and research areas, different criteria based on temperature, salinity, potential density and other parameters, as well as different threshold values were used (Table 1) (2007), we limit the AW from below using the potential density threshold, which largely corresponds to the temperature and salinity thresholds, used in alternative studies. Furevik et al. (2007) give a rather broad range of the threshold potential density values, increasing northwards. Due to the densification of the AW as it moves north 190 (Latarius and Quadfasel, 2016), it is necessary to choose different parameters for different regions. To select the optimal density threshold values, the time-mean depths of various isopycnals from this range were overlaid on the vertical distribution of temperature and salinity at the transects across the Norwegian Atlantic Current (NwAC) (Fig. 4.). This allows testing the criteria against temperature and salinity thresholds used to define AW in different areas of the Nordic Seas in other studies (Walczowski, 2014, Beszczynska-Möller et al, 2012, K.A. Mork and Skagseth, Ø., 2010. From our analysis, 27.

Vertical mixing
Vertical turbulence heat flux through the base of the upper layer is estimated as: https://doi.org/10.5194/os-2020-109 Preprint. Discussion started: 3 December 2020 c Author(s) 2020. CC BY 4.0 License.
Where T is the temperature differences between the lower boundary of AW and surrounding waters; z = 100 m. Two methods were used for obtaining Kz values: (1) Kz = const = 10 -5 m 2 s -1 (Fer et al., 2018) and (2) Kz was estimated through the Richardson number (Timmermann and Beckmann, 2004), which combines Pacanowski and Philander (1981) parameterisation 210 with a diagnostic scheme using the Monin-Obukhov length.
In the second case (Pacanowski and Philander, 1981)), the diffusion coefficient is estimated as: where ℎ′ is the vertical scale of the length defined by the Monin-Obukhov length. In the case of our study no convective mixing 220 through the lower interface was registered, so we set = 0 .
Substituting all coefficients to the eqs. 3-5, we obtain: As currents in the ARMOR3D dataset are geostrophic, we calculate the Richardson number from the horizontal density gradients using the geostrophic relations: 225 The results of Kz estimation using the methods suggested in (Fer et al., 2018) and (Timmermann, R. and Beckmann, A., 2004) were found to be similar.

Validation of ARMOR3D heat fluxes
To validate the ARMOR3D estimates, we compare the statistical properties of all available mooring observations in the Fram Strait (AWI F1-F10) with those in the nearest grid-point of the ARMOR3D dataset. To obtain more homogeneous data series suitable for further comparison, a preliminary filtering is applied to the moorings data. The processing steps include removal https://doi.org/10.5194/os-2020-109 Preprint. Discussion started: 3 December 2020 c Author(s) 2020. CC BY 4.0 License. of outliers and monthly averaging of the data to cope with the ARMOR3D temporal resolution. Then the ARMOR3D and the 235 moorings data are binned to 100 m vertical bins, centered on the position of the available moored instruments. Figure 5 shows an example of statistical comparison of the time series of temperature, velocity and heat fluxes for the two datasets at mooring F5 (located in the eastern Fram strait 78,5° N and 6° E). The Taylor diagrams (Taylor, 2001) show that the temperature variability is well reproduced by the ARMOR3D dataset (the correlation coefficient is 0.7). On the other hand, current velocity (and the heat flux) derived from ARMOR3D, shows lower interannual and seasonal absolute values, as well as variability, 240 compared to in situ data. However, the seasonal pattern of the heat fluxes, as well as the interannual one, are reproduced in ARMOR3D with reasonable accuracy (the correlation coefficient is 0.6). The meridional velocity component is much better reproduced by ARMOR3D, compared to the zonal one, which is because the main geostrophic flow in the region is directed northward. Therefore, we may expect a higher accuracy of the heat fluxes across the zonal sections, compared to the nearmeridional ones. 245 In the areas with the presence of the drifting ice (the East Greenland Current) and at deeper water levels, the performance of ARMOR3D in comparison to the mooring data naturally decreases. This is due to a decrease in the accuracy of the satellite altimetry in areas with sea ice and accumulation of the errors while integrating the density gradient downwards. For the present study, focused on the upper 500-meter layer and in the regions with no winter ice cover, we consider the results from the ARMOR3D dataset reasonably well representing the interannual variability of the heat fluxes. 250 https://doi.org/10.5194/os-2020-109 Preprint. Discussion started: 3 December 2020 c Author(s) 2020. CC BY 4.0 License. Figure 5. Validation of ARMOR-3D (blue) against in situ data at mooring F5 (red) located in the WSC at 78,5° N 6° E: awater temperature ( o C), bzonal current velocity U (cm s -1 ) and cmeridional current velocity V (cm s -1 ). Left -Taylor diagrams (ARMOR-3D is point B, in situpoint A), centerdata time series, right -seasonal cycles. Data are averaged in 50-150 m layer. 255

Temporal variability of heat fluxes along the NwAC
Svinoy section is one of the main sites where AW inflow into the Nordic Seas is monitored continuously (Orvik and Niiler, 2002;Raj et al., 2018). The heat fluxes are calculated over AW layer limited from below by the isopycnals presented in Section 2.7. The heat advection across the section is split between three main cores of the AW: the coastal branch at 10° E (NwACC), the slope branch between 5 and 6° E (NwASC) and the polar frontal branch between 2 and 3° E (NwAFC). Our analysis shows 260 https://doi.org/10.5194/os-2020-109 Preprint. Discussion started: 3 December 2020 c Author(s) 2020. CC BY 4.0 License. that the largest heat flux is directed northward along with the NwASC. From the Svinoy (406 TW) to the Jan Mayen sections (341 TW) the heat advection decreases by about 1/3. This is consistent with the observed significant heat loss of NwAC to the interior of the Lofoten Basin, the main heat reservoir in the Nordic seas (Bjork, 2001;Bosse et al., 2018). Mean integrated heat fluxes have more or less similar seasonal patterns at all transects and for all years: the heat flux decreases in summer and increases in winter. The seasonal cycle is regulated by the seasonal variability of the current velocity, which is higher in winter. 265 This is in line with the previous results on the heat transport in the area (Skagseth et al., 2004(Skagseth et al., , 2008Mork and Skagseth, 2010). The winter maximum of the NwASC is explained by a higher sea-level gradient caused by an increased Ekman pumping associated with stronger northerly winds along the Scandinavian coast (Skagseth et al., 2008;Mork and Skagseth, 2010). of heat is lost due to the vertical mixing across the AW boundary (Fig. 6), in particular in the Lofoten Basin, where convection across the AW lower boundary is episodically observed (Bosse et al., 2018;Fedorov et al., 2019). The main components of 285 the heat balance of the regions A-D are schematically shown in Fig. 6. The imbalances obtained account to 10-20 % of the incoming heat fluxes. These reflect the warming of the AW in the Norwegian Sea. We also should take into account uncertainties of the estimated oceanic heat advection. Due to the uncertainty in the reference temperature, Schauer and Beszczynska-Möller (2009) suggest treating the oceanic heat fluxes in terms of their variability, rather than relying on their absolute values. 290 https://doi.org/10.5194/os-2020-109 Preprint. Discussion started: 3 December 2020 c Author(s) 2020. CC BY 4.0 License. Figure 6. Components of the heat balance for the Regions A-D. Straight red (blue) arrows represent the oceanic heat fluxes entering (leaving) the study regions, dashed arrows represent latent and sensible heat fluxes from ocean to atmosphere (blue) and radiation from atmosphere to ocean (red), curved arrow represents vertical turbulent heat flux. 295 On its way north AW changes its properties through mixing with the surrounding water and the ocean-atmosphere exchange.
Propagating at different rates, which vary in time, these multiple transformations contribute to the loss of correlations between heat fluxes across the transects (Fig. 7). Skagseth et al. (2008) found a certain coherence between the temperature and salinity variations at the Svinoy and the Sorkapp/BSO sections on decadal time scales. Our results show that there is a significant loss of correlations along the AW pathway, dropping to insignificant levels north of the Sorkapp section. The strongest loss of 300 correlation is found between Svinoy and Jan Mayen sections, as well as between Sorkapp and Isfjord. The loss of a consistent interannual variability between Svinoy and Jan Mayen sections along the NwAC can be explained by high activity of oceanic eddies which redistribute the heat over the Lofoten basin (Dugstad et al., 2019;Raj and Halo, 2016). The same explains the correlation loss between Isfjord and Sorkapp sections . A drop in correlation value may result from 1-1.5 year period, which is the time required for an anomaly to propagate from 63 to 76° N, given the mean anomaly 305 propagation velocity of 3 cm s -1 (Walkzowski, 2014). However, the cross-correlation analysis suggests the maximum correlations at zero time lag, which suggests rather simultaneous forcing at all the sections.
After removing the trend in the deseasoned data, the cross-correlation between the sets of the southern sections (Svinoy to Jan Mayen) and the northern sections (Sorkapp to Fram) increases, while this procedure does not affect the correlations between https://doi.org/10.5194/os-2020-109 Preprint. Discussion started: 3 December 2020 c Author(s) 2020. CC BY 4.0 License.
Svinoy and Jan Mayen (Figure 7b). This indicates the different signs of the long-term variability in the southern and the 310 northern sections (also present in Figure 9). The results above suggest different mechanisms controlling heat transport at the southern and northern sections along the NwASC. Skagseth et al. (2008) and Raj et al. (2018) suggest NAO to be the principal agent in modulating the AW transport along the southwestern Scandinavian coast. On the other hand, Lien et al. (2013) have shown that the relative strengths of the branches of AW along the western Spitsbergen and in the Barents Sea are strongly affected by a regional atmospheric circulation pattern over the Spitsbergen and the northwestern Barents Sea: a higher AW transport in the Barents Sea is 320 accompanied by a lower transport through the Fram Strait. Hence, we hypothesize that NAO is more affecting the southern part of the AW pathway, while the local atmospheric circulation pattern in the Nordic Seas impacts the northern part of the AW pathway. Only the heat fluxes across the southern sections show significant moderate positive correlations with the NAO, AO and EA indices (0.34 -0.47) ( Table 2). Previously, Chafik et al. (2015) showed that NAO is not the driving mode for the AW influx through the Fram Strait and that the regional atmospheric circulation is the main driving factor. For the northern 325 sections the correlations go to zero.
A consistent sign of the correlations is obtained between the advective heat fluxes at all sections and the weather types C and W (Table 2), although only the correlations with the heat fluxes across the southernmost and the northernmost sections are significant. Even though not always significant, the correlation coefficients are always positive with the western weather type W and are always negative with the central weather type C. This suggests a possible existence of the large-scale forcing pattern, 330 responsible for the in-phase variations along the NwAC. With the weather type W, the winds are intensified along the Scandinavian coast accumulating the water along the coast and intensifying the NwASC (Fig. 8a). The intensification of the northern NwAFC may result from a stronger gradient of the wind speed west of Spitsbergen, which provides the sea-level drop across the NwAFC due to the divergence of the Ekman fluxes. With the weather type C, the main winds are directed towards https://doi.org/10.5194/os-2020-109 Preprint. Discussion started: 3 December 2020 c Author(s) 2020. CC BY 4.0 License.
the Scandinavian coast, thus the Ekman transport is directed south which decreases the NwASC (no water accumulation along 335 the Scandinavian coast), whereas the weak gradients of the wind speed west of Spitsbergen reduce the Ekman divergence which is not favorable for the intensification of the NwAFC (Fig. 8c). The lack of correlation with type E can be explained by the overall weaker winds over in the eastern Nordic Seas (Fig. 8b).  From 1993 to 2017 there are no pronounced positive or negative long-term trends (Fig. 9 a,b) in the heat flux across most of the sections (apart from the BSO section, where the consistent tendency of the heat flux to grow is observednot shown, see Kalavichchi, Bashmachnikov, 2019). At Svinoy section there is a certain tendency of oceanic heat advection to grow, the most pronounced since 2010. This is in line with the recent warming of the AW after 2010-2011 in the Norwegian Sea derived from 350 the Argo float profiles (Mork et al., 2019). However, at the Fram section, the heat advection increases only in the beginning of the 2000s, and since 2005 it started to decrease. Thus, despite the general increase in the water temperature in the south of the region, the northern section does not demonstrate a positive trend in the heat fluxes during the latest decades. This is one of the factors reducing the correlations.
To detect the hidden periodicities in the heat fluxes, the wavelet analysis with the Morlet mother wavelets is applied (Torrence 355 and Compo, 1998). In all the transects we distinguish the main periodicities of 3 years and of 5-6 years (Fig. 9c,d). The wavelet amplitudes decrease northwards, along with the decrease of the mean heat fluxes. The cross-wavelet diagram shows a high coherence of heat fluxes in the Svinoy and Fram Strait sections at time-periods of 2-5 years, the variability at these periods occurs in phase. This suggests that on intra-decadal time scales there is a certain coherence in the oceanic heat advection along the NwAC. W and C indexes have similar variability with the time scales of 2-3 and 5-7 years, which further supports the 360 existence of the link between the oceanic heat advection along the NwAC and the W-C weather patterns.

Conclusions
The present analysis suggests a certain consistency of the heat fluxes along the path of the NwAC through the Nordic Seas.
This consistency results from the high cross-wavelet coherence between the heat fluxes at the southern and the northern https://doi.org/10.5194/os-2020-109 Preprint. Discussion started: 3 December 2020 c Author(s) 2020. CC BY 4.0 License. sections at some interannual time scales. This coherence results from 3 and 5-6 year oscillations dominating the short-term interannual variability. Wind patterns corresponding to the C and W weather types may serve the forcing mechanism, 370 increasing/decreasing the heat advection along the whole path of the NwAC.
However, there are notable differences in the heat fluxes which result in a decrease of the correlations. Particularly strong drops of correlations are observed across the Lofoten Basin (between the Svinoy and Jan Mayen sections) and north of the Bear Island. The reasons are the opposite tendencies in the long-term variability (after the mid 2000s) and differential damping of the detected oscillations (the longer oscillations are damped more effectively while progressing north: the amplitude of the 375 5 years oscillation drops by 50% from Svinoy to the Bear Island and further on by 60% from the Bear Island to the Fram section, while the amplitude of the 3 years oscillation drops by 40% progressing from Svinoy to the Bear Island and further on only by 8% from the Bear Island to the Fram section). One of the reasons for this behavior may be the dependence of the heat fluxes across the southern sections on NAO type patterns, while it practically does not influence the northern sections. In turn, the northern sections depend on the variability of the local cyclonic wind patterns, centered in the north-western Barents Sea 380 (Lien et al., 2013;Chafik et al., 2015). The observed variability of the heat fluxes is mostly shaped by the variations in the current velocity and is only marginally influenced by the changes in temperature of the AW.
The oceanic heat inflow in the regions (A-D) is largely balanced by the heat release to the atmosphere and by vertical mixing.
The first dominates in the northern part of the study region (west of Spitsbergen), while the secondin its southern part (the Lofoten Basin). The imbalances form from 10 to 20% of the incoming heat and encompass the heat fluxes by the mesoscale 385 eddies (Raj et al., 2020;Bashmachnikov et al, 2020). The imbalances lead to the observed warming of the eastern Nordic Seas.
Discussing the balances, the errors in the heat fluxes should be taken into consideration. In particular, the positions of the transects highly affect the results. However, these errors in the absolute values of the fluxes practically do not affect the interannual variability discussed above. https://doi.org/10.5194/os-2020-109 Preprint. Discussion started: 3 December 2020 c Author(s) 2020. CC BY 4.0 License.