Heat and freshwater budgets of the Nordic seas computed from atmospheric reanalysis and ocean observations

Transcription

1 JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 116,, doi: /2011jc006939, 2011 Heat and freshwater budgets of the Nordic seas computed from atmospheric reanalysis and ocean observations O. H. Segtnan, 1 T. Furevik, 1 and A. D. Jenkins 1 Received 5 January 2011; revised 22 July 2011; accepted 10 August 2011; published 3 November [1] The heat and freshwater budgets of the Nordic seas are computed from atmospheric reanalysis data and ocean observations, mainly taken during the period The total heat loss is 198 TW and the freshwater gain 52 msv (1 Sv = 10 6 m 3 s 1 ), with residuals equal to 1 TW and 3 msv, respectively. Budgets are also computed for three subregions within the Nordic seas: the Norwegian Sea, the Barents Sea and the Greenland/ Iceland Sea. Without accounting for transfer of heat and freshwater across the Arctic Front, which separates the Greenland/Iceland Sea from the Norwegian Sea, the residuals of the heat and freshwater budgets range from 36 TW to 34 TW and from 16 msv to 19 msv, respectively. To close the budgets of all subregions cross frontal fluxes of 35 TW and 17 msv, caused either by eddy shedding along the Arctic Front or ocean currents not accounted for, must be included. Combined with observations of the average temperature and salinity on both sides of the Arctic Front these values indicate a rate of cross frontal water exchange of approximately 4 Sv. The most intense water mass modifications occur in the Norwegian Sea, where ocean heat loss and freshwater input are equal to 119 TW and 41 msv, respectively. Citation: Segtnan, O. H., T. Furevik, and A. D. Jenkins (2011), Heat and freshwater budgets of the Nordic seas computed from atmospheric reanalysis and ocean observations, J. Geophys. Res., 116,, doi: /2011jc Introduction [2] Bordered by the Arctic Ocean in the north and the North Atlantic Ocean in the south, the Nordic seas act as a buffer zone between the cold and fresh Arctic Water and the warm and saline Atlantic Water. Their climate is strongly influenced by the properties of the Norwegian Atlantic Current and the East Greenland Current, resulting in higher temperatures and salinities on the eastern side than on the western side (Figure 1). Toward the north the distinct characteristics of the Atlantic Water are gradually reduced through local processes such as atmospheric cooling, production and melting of sea ice and mixing with other water masses [Mauritzen, 1996a; Furevik, 2001; Eldevik et al., 2009]. The different components of the complex system may all affect the oceanographic conditions in the Nordic seas, and strong interannual variability has been documented in ocean temperature and salinity [Furevik, 2001; Saloranta and Haugan, 2001; Blindheim and Østerhus, 2005], sea ice extent [Bjørgo et al., 1997; Johannessen et al., 1999; Kvingedal, 2005], air temperature, precipitation and winds [Hanssen Bauer and Førland, 2000; Furevik and Nilsen, 2005]. The variability is to a large extent linked to the North Atlantic Oscillation or the closely related Arctic Oscillation [Dickson et al., 2000; Furevik and Nilsen, 2005], but details of all underlying processes are still not fully determined. 1 Geophysical Institute, University of Bergen, Bergen, Norway. Copyright 2011 by the American Geophysical Union /11/2011JC [3] Insights into the mechanisms controlling the temperature and salinity of the ocean may be provided by studies of the heat and freshwater budgets. Heat budgets based on ocean transports to and from the Nordic seas have been presented in a number of studies [Mosby, 1962; Worthington, 1970; Wowinckel and Orvig, 1970; Hopkins, 1991], whereas more detailed studies with the surface heat loss included for individual subregions in the Nordic seas were made by Simonsen and Haugan [1996] and Mauritzen [1996b]. Since these studies many new and more detailed data sets, expected to increase the accuracy of the budgets, have become available. Atmospheric reanalysis data is now frequently applied to study exchanges of heat, freshwater and momentum at the sea surface [Furevik and Nilsen, 2005; Richter et al., 2009; Serreze et al., 2006, 2007], several large EU projects (e.g. Nordic WOCE, VEINS, ASOF MOEN; see Dickson et al. [2008a] for a review) have provided more than 10 years of monitoring data from the key branches, and a large quantity of old and new hydrographic observations have recently been compiled into a hydrographic data set for the region [Nilsen et al., 2008]. [4] In this study we will apply atmospheric reanalysis data and available ocean observations, which include hydrographic observations, results from long term current measurements and surface currents derived from drifters, to calculate the heat and freshwater budgets of three subregions within the Nordic seas. The paper is organized as follows: In section 2 the Nordic seas area, mean circulation and the subregions under consideration are presented, the applied data sets described and the budget framework outlined. The majority 1of17

2 Figure 1. Depth averaged (top) temperature and (bottom) salinity distributions of the upper 500 m depth, computed from the NISE data set [Nilsen et al., 2008]. Values are the average over the period The isobaths are drawn for 500 m and 2500 m depth. of the applied data is from the period 1990 to 1999, which will be the time period considered in this study. In order to complete the budgets data from outside this period will, however, also be included. Results for heat and freshwater budgets are presented in sections 3 and 4, respectively. In section 5 relevance to the climatic conditions in the Nordic seas are addressed. We here discuss water mass transformation and which processes that dominate the modification of water traveling the Nordic seas. The main findings are summarized and the paper concluded in section Study Area, Data Sources, and Methods 2.1. Study Area Defining the Nordic Seas Area and the Subregions [5] The Nordic seas consist of a number of deep basins and shallow shelf areas (Figure 2). The ridge from the eastern coast of Greenland via Iceland and the Faroe Islands to the Shetland Islands, hereafter referred to as the Greenland Scotland Ridge, separates the Nordic seas from the North Atlantic Ocean, whereas the boundary with the North Sea is roughly aligned with the 61 N parallel from the Shetland Islands to the coast of Norway. The boundary with the Arctic Ocean follows the Fram Strait, defined as the 79 N parallel from the coast of Greenland to Svalbard, the 80 N parallel from Svalbard to Franz Josef Land and the opening between Novaya Zemlya and Franz Josef Land. The opening between Novaya Zemlya and the Russian mainland (the Kara Gate) separates the Nordic seas from the Kara Sea. [6] We divide the Nordic seas into the following subregions: the Norwegian Sea, the Barents Sea and the Greenland/Iceland Sea. The boundaries follow the ridge system: the Jan Mayen, Mohn and Knipovich ridges separate the Norwegian Sea from the Greenland/Iceland Sea. The boundary between the Barents Sea and the Norwegian Sea is defined by the section from the southern tip of Svalbard via Bear Island to the Norwegian coastline at 19 E. The surface areas and average depths of the subregions are listed in Table Ocean Circulation and Considered Cross Sections [7] The Atlantic inflow to the Nordic seas occurs over the Greenland Scotland Ridge along three branches: west of Iceland (Section 1; Iceland branch), between Iceland and the Faroe Islands (Section 2; Faroe branch) and through the Faroe Shetland Channel (Section 3; Shetland branch). As shown in Figure 2, Sections 1 and 2 are located in the interior of respectively the Iceland Sea and the Norwegian Basin, where measurements have been taken, rather than at the open boundaries. Thus, for budget considerations it has to be assumed that the water masses entering the Nordic seas along the Iceland and Faroe branches are not much modified before crossing Sections 1 and 2. This is obtained by only considering the flux of Atlantic Water through the sections using a mixing model based on properties of the different water masses involved [Hansen et al., 2003; Østerhus et al., 2005]. [8] After entering the Nordic seas a fraction of the Atlantic inflow in the Shetland branch takes a detour into the North Sea, where it gains freshwater and looses some heat, before it returns to the Nordic seas as the Norwegian Coastal Current [Furnes et al., 1986]. This exchange takes place at the opening between Shetland and the Norwegian coastline (Section 4). However, the majority of the Atlantic inflow to the Nordic seas forms the two branch Norwegian Atlantic Current, that to the west of the Norwegian Coastal Current is carrying warm salty waters toward the Arctic Ocean [Orvik and Niiler, 2002]. The fate of the Atlantic inflow in the Iceland branch, on the other hand, is less clear. North of Iceland it mixes with colder and fresher water masses [Hansen and Østerhus, 2000], thus reducing its temperature and salinity. From surface drifters it appears that this mixture either turns westward and leaves the Nordic seas through the Denmark Strait (Section 11) or continues eastward toward the Norwegian Sea (Section 12) [Valdimarsson and Malmberg, 1999]. [9] At the western entrance of the Barents Sea the eastern branch of the Norwegian Atlantic Current bifurcates into the West Spitsbergen Current that continues toward the Fram Strait, and the North Cape Current that turns eastward toward the Barents Sea together with the Norwegian Coastal Current, and enters the Barents Sea through the opening between the Norwegian coast and Bear Island (Section 5). The majority of the Barents Sea through flow enters the Arctic Ocean through the opening between Novaya Zemlya and Franz Josef Land (Section 7) [Loeng et al., 1997; Gammelsrød et al., 2009], whereas a smaller fraction exits the Barents Sea through the Kara Gate (Section 6) [Panteleev 2of17

3 Figure 2. The subregions defined in section 2.1, the cross sections that are used to calculate the ocean fluxes (gray lines labeled 1 14) and the main features of the surface circulation in the Nordic seas after Hansen and Østerhus [2000], showing the northward flow of Atlantic and Coastal Water (solid red and dashed green lines) and the southward flow of Polar Water (solid purple lines). Also illustrated is the flow of deep water through Sections 9, 10, 11, 12, 13 and 14 (black arrows). Depths are shaded at 500 m depth interval. The boundary between the Norwegian Sea and the Greenland and Iceland seas are roughly aligned with the Arctic Front. et al., 2004]. Fluxes through the other openings of the Barents Sea are not well described from measurements, but are assumed small [Loeng et al., 1997] and will not be considered in this study. [10] Most of the water following the West Spitsbergen Current enters the Arctic Ocean through the eastern part of the Fram Strait (Section 8), whereas a smaller amount recirculates in the Fram Strait and enters the Greenland Sea from the Lofoten Basin (Section 9) [Rudels et al., 2000; Cisewski et al., 2003]. In addition to water of Atlantic origin, also transport of deep water takes place through the Fram Strait [Schauer et al., 2004]. After cyclonic loops in the Arctic Ocean the water that entered the Arctic Ocean through Sections 6, 7 and 8 re enters the Nordic seas through the western part of the Fram Strait (Section 10) together with the water that entered the Arctic Ocean through the Bering Strait [Hansen and Østerhus, 2000]. It then continues southward parallel to the shelves east of Greenland. North of Jan Mayen some water is transported eastward toward the Norwegian Sea [Jónsson, 2003; Voet et al., 2010], whereas the remaining water either leaves the Nordic seas through the Denmark Strait (Section 11) or is advected eastward with the East Icelandic Current [Jónsson, 2003, 2007; Mauritzen, 1996a; Hansen and Østerhus, 2000]. Transport of dense water from the Norwegian Sea to the North Atlantic occurs in the deepest openings between Iceland and the Faroe Islands (Section 13) and through the Faroe Shetland Channel (Section 14). The circulation scheme is shown in Figure 2 whereas published estimates of volume transports through twelve of the sections are summarized in Table Data Sources Atmospheric Data [11] Surface data applied in this study were obtained from two atmospheric reanalysis products that are commonly applied in climate studies: The European Centre for Medium Range Weather Forecasts (ERA 40) [Uppala et al., 2005] and the National Centers for Environmental Prediction/ Department of Energy (NCEP 2) [Kanamitsu et al., 2002]. The ERA 40 data set spans the period September 1958 to August 2002 and is at a spatial resolution of 2.5 longitude 2.5 latitude. The NCEP 2 data set covers the period January 1979 to the present date. Outputs are given at a 1.9 longitude 1.9 latitude resolution. Both data sets are re analyses of meteorological observations, but with no direct assimilation Table 1. Area and Average Depth of the Regions Defined in Section 2.1 Based Upon the ETOPO5 Data Set Subdomain Area (10 6 km 2 ) Average Depth (m) Norwegian Sea Barents Sea Greenland/Iceland Sea Nordic seas of17

4 Table 2. Volume Fluxes (V), Average Temperature (T), and Average Salinity (S) of Water Flowing Through Selected Cross Sections in the Nordic Seas Based on the Literature (See Figure 2)a Section V (Sv) T ( C) S (PSU) Period Sep Aug Jun Jun Oct Sep Reference Aug Aug. 2005/Jul Jul Sep Sep Oct Sep Sep Jul Jónsson and Valdimarsson [2005] Hansen et al. [2003] Turrell et al. [2003] Furnes et al. [1986] Skagseth [2008]/Skagseth et al. [2011] Panteleev et al. [2004] Gammelsrød et al. [2009] Schauer et al. [2004] Sep Aug Schauer et al. [2004] Jun Jun Jónsson [2007] Østerhus et al. [2008] Hansen and Østerhus [2007] Nov May a The values are the average over the given periods. The flows through Sections 1, 2, 3, 4, 6, 7, 8, 10, 13 and 14 are defined positive toward the Nordic seas, the flow through Section 5 is positive toward the Barents Sea and the flow through Section 12 is positive toward the Norwegian Sea. of the turbulent surface heat fluxes. Instead these are calculated from bulk flux algorithms, with different parameterizations applied by ERA 40 and NCEP 2 (see e.g. Renfrew et al. [2002] for an overview). Another difference between the two reanalyses is that ERA 40 assimilates raw satellite data into the model, thereby eliminating errors associated with the retrieval processes, whereas NCEP 2 uses retrieved properties. For both data sets the fields after 1979 are the most reliable due to the inclusion of satellite data. In this study we restrict our analysis to the period, due to the time spans of the other data being used Hydrographic Data [12] A high resolution temperature and salinity observational data set for the Nordic seas has been made available through the Norwegian Iceland Seas Experiment (NISE) project [Nilsen et al., 2008; Eldevik et al., 2009; Segtnan et al., 2010]. The time frame for the data set is from 1900 to 2006, with the majority of samples taken after Due to the presence of sea ice during large parts of the year, hydrographic observations on the shelves east of Greenland and in the northern part of the Barents Sea are not available in the winter period. The temporal and spatial data resolution of observations taken during the period are shown in Figure 3. Whereas the annual variations in data coverage are relatively low, monthly variability is considerable. This is not only due to sea ice, since also in the ice free regions, such as the Norwegian Sea, the data coverage is higher in summer (not shown). To construct gridded temperature and salinity maps, the hydrographic data has been interpolated to a 1 longitude 1 latitude grid, using the objective analysis scheme described by Barnes [1964]. The radius of influence is set equal to 168 km Ocean Surface Currents [13] A gridded climatology of near surface currents derived from satellite tracked surface drifting buoy observations has become available at a one degree resolution [Lumpkin and Figure 3. Number of individual measurements included in the NISE data set in the Nordic seas between 1990 and 1999, given by (a) depth, (b) month, and (c) year. (d) Station locations. 4 of 17

5 Garraffo, 2005]. The drifters have a holey sock drogue, centered at 15 m depth, that is designed to minimize the slip relative to the ocean currents at this depth. The data set also includes an estimate of the geostrophic component of the flow, where the motion related to direct wind forcing has been removed using daily winds from the NCEP/NCAR reanalysis [Kalnay et al., 1996]. Velocities contained in the data set have been low passed filtered at five days to remove high frequency variability, by fitting the data to cyclical components and minimizing the residual (eddy noise) caused by e.g. tides or inertial oscillations [Lumpkin and Garraffo, 2005]. Estimates of the surface currents are not available in ice covered regions Formulation and Computation of Heat and Freshwater Budgets Heat Budget [14] From the internal energy and salt equations for a fixed volume [Gill, 1982] the equations expressing the heat and freshwater budgets of an ocean volume can be derived [Serreze et al., 2006, 2007]. The volumes considered in this study extend from the seafloor to the sea surface, and are horizontally limited by the boundaries of the subregions defined in section 2.1. It is assumed that the net flow with the major branches toward and away from the volume is captured by calculating the flow through a finite number (N) of cross sections at the boundary of the volume (crosssections are shown in Figure 2). Most of the cross sections have a vertical extent from the sea surface to the seafloor, but for Sections 1 and 2, which are located in the interior of the Nordic seas and not on the open boundary, only the Atlantic Water has been considered. The flow through the Faroe Shetland Channel has been split into flow from the North Atlantic to the Nordic seas and return flow. Hence the flow of Atlantic Water (Section 3) and overflow water (Section 14) will be calculated separately. The heat budget for each individual subregion may then be written X N j¼1 i w c p V j T j T ref þ I j T f T ref i L f I j w ¼ F sfc þ R h ; where the bar denotes the time mean (a R D t a dt/dt). r w and r i are respectively the density of seawater and sea ice, c p the specific heat capacity of seawater, L f the latent heat of fusion, all assumed constant, and T f is the freezing temperature of seawater ( 1.9 C). V j and I j are respectively the oceanic volume and sea ice transports through each cross section ( j =1,, N), positive toward the volume. T j is the transport weighted average temperature value of the oceanic part of the flow through the cross section under consideration (Section j), and is calculated from the relation T j ¼ Rx 2 R h x 1 Rx 2 R h x 1 Tvdz dx v dz dx ¼ R x2 x 1 R h ð1þ Tvdxdz V j ; ð2þ where x 1 and x 2 are the boundary points that define the crosssection, T and v are respectively the oceanic temperature and velocity normal to the section, and h is the thickness of the layer. The reference temperature, T ref, is arbitrary for a closed volume/mass budget and is here set equal to 0 C. N is the number of cross sections at the boundary of the ocean volume required to cover all branches of the mean current field. F sfc is the mean surface heat flux integrated over the sea surface area, given as the sum of longwave and shortwave radiation and turbulent sensible and latent heat fluxes, defined to be positive upward. [15] The smallest terms of the heat budget have been included in the mean heat budget residual, R h. Since an approximately steady state is assumed (Dt 10 years), the mean rate of change in heat content has been included in R h, together with mean ocean heat fluxes caused by molecular diffusion, mean heat fluxes due to precipitation, evaporation and runoff from land, mean heat flux due to temperature variations of sea ice, and the mean heat flux through the seafloor (e.g. thermal heating). In addition to the smallest terms of the heat budget, also the mean ocean heat flux through the part of the open boundary where the flow has not been measured has been included in R h, since this term cannot be calculated from the available data sets. When the flow with the major branches is captured by the N crosssections this contribution will be due to the eddy heat flux, r w c p V T, where the prime denotes time fluctuations Freshwater Budget [16] The freshwater budget of the ocean volume, averaged over Dt, can be expressed S ref S j V j þ i S ref S ice I j S j¼1 ref w S ref ¼ P E þ R þ Rf ; ð3þ XN where P and E are respectively the mean precipitation and evaporation rates integrated over the sea surface, R is the mean total runoff from land toward the ocean volume, and S j is the transport weighted average salinity value of the mean flow through the cross section under consideration. S j is given as S j ¼ R Rx 2 h x 1 Rx 2 R h x 1 Svdz dx v dz dx ¼ Rx 2 x 1 R h Svdxdz V j ; ð4þ where S is the ocean salinity. S ice is the salinity of sea ice, assumed to be constant, and S ref is the reference salinity, here set equal to Since we in this study have simplified the mass budget to a balance between ocean and sea ice transports through the open boundaries, the value chosen for S ref in equation (3) is in principle not arbitrary. However, freshwater fluxes are not very sensitive to the choice of reference salinity. For example, increasing S ref from 34.9 to 35 will modify the freshwater flux by less than 0.3%. The residual term, R f, includes the ocean fluxes due to molecular freshwater diffusion, the freshwater flux through the seafloor, the rate of change in depth integrated freshwater content and the eddy freshwater flux through the part of the open boundary where the flow has not been measured. 5of17

6 Table 3. Sea Ice Transports (I) Through Sections 7 and 10 Based on the Literature a Section I Period Source km 3 yr Korsnes et al. [2002] km 3 yr Widell et al. [2003] a Section numbers refer to Figure 2. Values are positive toward the Nordic seas Estimating the Terms of the Heat and Freshwater Budgets [17] The surface heat, F sfc, and freshwater, P E, fluxes are calculated from the two re analysis products presented in section 2.2, and estimates of the runoff term, R, are available from the literature (see Table 5). Transport of sea ice takes place through Sections 7, 10 and 11. Estimates of sea ice fluxes from the literature applied in this study are shown in Table 3. The estimate across Section 7 also includes the ice flux through the opening between Svalbard and Franz Josef Land. For Section 11, no direct observations of sea ice fluxes are available. The sea ice flux through the section is obtained by assuming that the melt rate of sea ice flowing through the Fram Strait is proportional to the ice flux, (d I/d y = ci) and that the sea ice flux is reduced by approximately 50% from 79 N to 73 N, as suggested by Aagaard and Carmack [1989]. This gives a sea ice transport of approximately 505 km 3 yr 1 from the Nordic seas to the North Atlantic Ocean. Heat and freshwater fluxes due to sea ice are presented in Table 4. [18] For most of the cross sections considered in this study oceanic heat and freshwater fluxes have been presented in the literature. Fluxes through Sections 2, 3, 5, 7 and 14 are calculated from the values and studies presented in Table 2. Also the oceanic heat fluxes through Sections 8 and 10 are calculated from the values listed in the table. Although some water flows through the eastern part of the Fram Strait in the lower layer [Schauer et al., 2004], all transport of deep water through the strait (northward and southward) has in this study been included in the volume flux through Section 10. This is because we assume that the deep circulation does not to play an active role in the heat and freshwater budgets: deep circulation through Section 8 will be due to a volume flux from the Greenland/Iceland Sea, caused by a leakage from the internal circulation in the Greenland Basin [Voet et al., 2010], and we will assume that this water will enter and leave the Norwegian Sea at the same temperature and salinity. The freshwater fluxes through the Fram Strait in liquid form follows Rabe et al. [2009]. Converted to S ref = 34.9 the liquid freshwater fluxes through Sections 8 and 10 become 2 msv and 78 msv, respectively (for information about the direction of the fluxes see Table 4). [19] The freshwater flux through Section 6 is calculated from the values listed in Table 2, but in order to obtain a closed volume budget for the Barents Sea we have modified the volume transport through Section 6 by 0.1 Sv, from 0.7 Sv to 0.6 Sv. This value is within the range indicated by Loeng et al. [1997]. The average temperature of the flow through the Kara Strait is set equal to 0.0 C [Karcher et al., 2004]. For the Atlantic Water flowing through Section 1 we apply mean weighted average temperature and salinity values of 6.0 C and 35, as indicated by the results of Østerhus et al. [2005]. [20] In the circulation scheme assumed in the present study there is no net volume transport through Section 4, but a part of the water that crosses the Greenland Scotland ridge takes a detour into the North Sea where it mixes with fresher and colder water before it returns to the Nordic seas as the Norwegian Coastal Current. This results in non zero heat and freshwater transports through the section. The freshwater flux of 22 msv is taken from Aure and Østensen [1993]. To estimate the heat flux it is assumed that the temperature is reduced by approximately 1.5 C in the North Sea, as suggested by Mauritzen [1996a], whereas a flow of 1 Sv is applied [Furnes, 1980]. This gives a heat flux equal to 6 TW. For the flow of Atlantic Water through Section 9 we apply a volume flux equal to 0.5 Sv [Cisewski et al., 2003] and assume that this water has the same temperature and salinity as the Atlantic Water flowing through Section 8 ( 2.3 C, 34.9 [Schauer et al., 2004;Rabe et al., 2009]). In order to obtain mass balance for the Norwegian and Greenland/Iceland seas the same amount of water must be transported in the opposite Table 4. Mean Ocean Volume Fluxes, V (Sv; 1 Sv = 10 6 m 3 s 1 ), Heat Fluxes, H (TW), and Freshwater Fluxes, FW (msv), Through Sections 1 14 (See Figure 2), Split Into the Contribution From Mean Ocean Currents (V o, H o, F o ) and From Sea Ice (V i, H i, F i ) a V H FW Section V o V i V tot H o H i H tot F o F i F tot a Also shown are the net fluxes (V tot, H tot, F tot ). Oceanic heat fluxes and freshwater fluxes are calculated relative to 0 C and a salinity of 34.9, respectively. Fluxes through Sections 1, 2, 3, 4, 6, 7, 8, 10, 11, 13 and 14 are defined positive toward the Nordic seas, the flux through Section 5 positive toward the Barents Sea and the fluxes through Sections 9 and 12 are positive toward the Norwegian Sea. V i is the sea ice flux in water equivalent. For details about the flux calculations see section of17

7 [22] In order to give an estimate of the heat and freshwater fluxes in liquid form through Section 11, where only the deep part of the flow has been extensively measured, we calculate the ocean flow field using the thermal wind equation following the method of Mork and Skagseth [2010]. In combination with temperature and salinity observations the heat and freshwater fluxes may be estimated, since we are then able to calculate the mean weighted average temperature and salinity values from equations (2) and (4). Using the thermal wind equation the geostrophic velocity component normal to the cross section is given as vz ðþ¼v s þ g w f Z x dz ; Figure 4. Mean values of the (left) ERA 40 and (right) NCEP 2 sensible (Sen. HF), latent (Lat. HF), net longwave radiative (LWR), net shortwave radiative (SWR) and net (Net HF) surface heat flux over the Nordic seas between 1990 and Values are positive upward. Units are W m 2. direction. The model results of Spall [2010] indicate that such a flow will take place in the deepest openings. As it is assumed that there is no flow of deep water through Section 8, this flow must then contribute to the transport through Sections 13 or 14. For the deep flow through Section 9 we apply the same temperature as for the deep water in the Fram Strait ( 0.4 C [Schauer et al., 2004]), whereas a salinity of 34.9 is used [Farrelly et al., 1985]. Due to the compensating flows there will be no net flow through the cross section. [21] The flow through Section 12 consists of a relatively fresh surface flow, and transport of more saline and colder water in the deep and intermediate layers. The volume flux in the surface layer is about 0.8 Sv and the water has a salinity close to 34.7 [Jónsson, 2007]. Based on the hydrography and velocity maps shown in Jónsson [2007] a mean temperature of 2 C for the surface flow is assumed. For the deep and intermediate part of the flow through Section 12 ( 1.7 Sv) we again apply the same temperature and salinity values as for the deep water in the Fram Strait of 0.4 C and 34.9, which appears to be in agreement with the temperature and salinity maps presented by Jónsson [2007]. For the temperature and salinity of water flowing through Section 13 we apply the same values as used for the Faroe Bank Channel Overflow (Section 14). where v s is the geostrophic velocity at the sea surface (z = z s ), f is the Coriolis parameter, g is the acceleration due to gravity and r/ x is the density gradient along the section. Estimates of the geostrophic component of the surface velocity is obtained from drifter observations, whereas the density gradient in the thermal wind balance is calculated from hydrographic observations. Due to sparse data coverage, only data from summer and autumn has been applied. In particular, observations on the shelf (shallower than 400 m depth) are from September 1991 only. [23] In order to obtain mass balance for the Nordic seas, we assume an oceanic volume flux equal to 5.2 Sv through Section 11. To achieve this value for the derived volume flux v s is multiplied by a constant factor of 0.85, thus decreasing the surface velocities obtained from drifters with 15%, without changing the baroclinic part of the flow. The mean weighted average temperature and salinity of the water flowing through the Denmark Strait are then calculated from equations (2) and (4). Using this method we find that the transport weighted temperature and salinity of the flow through the Denmark Strait are equal to approximately 0.25 C and PSU, respectively. [24] The constants r w, r i, c p, L f and S ice in equations (1) and (3) are set equal to respectively 1027 kg m 3, 917 kg m 3, 4000 J kg 1 C 1, Jkg 1 and 3 PSU. Obtained values for ocean heat (sensible and latent) and freshwater (solid and liquid) fluxes through Sections 1 14 are shown in Table Heat Budget Calculations 3.1. Surface Heat Flux [25] In Figure 4 we have plotted the mean values of the sensible, latent, longwave radiative, shortwave radiative and net surface heat fluxes during the period , using ERA 40 and NCEP 2 data. With the exception of the ice covered regions east of Greenland and in the northernmost part of the Barents Sea, the sensible heat flux is everywhere positive as heat is lost from the ocean to the colder atmosphere, and largest in the vicinity of the sea ice edge. For the latent heat flux, the highest values are found over the Lofoten Basin and over the southwestern part of the Barents Sea. For the shortwave radiation flux the largest (least negative) values are found over the ice covered regions, where shortwave radiation is reflected, and at the highest latitudes. For this component there is a noticeable difference between the 7of17

8 Figure 5. Mean values of the surface heat flux from (a) ERA 40 and (b) NCEP 2, (c) the mean ocean heat convergence and heat budget residual with surface heat fluxes from (d) ERA 40 and (e) NCEP 2, integrated over the Norwegian Sea, Barents Sea and Greenland/Iceland Sea. Units are TW. The surface heat flux is defined as positive upward. ERA 40 and the NCEP 2 data sets, with more incoming solar radiation in the NCEP 2 data. In comparison to the other surface heat flux components, the longwave radiation is much more homogeneous. Considering the net surface heat flux, the greatest surface cooling occurs over the Norwegian Sea, but cooling is also pronounced over the southwestern part of the Barents Sea. The surface heat loss over the Iceland Sea, on the other hand, is relatively low, in particular in the area northeast of Iceland. For the Nordic seas as a whole, NCEP 2 is seen to have a larger net heat loss than ERA 40, as the higher incoming solar radiation is more than compensated for by larger heat loss as sensible heat flux, latent heat flux and longwave radiation. [26] The net surface heat flux, i.e. the first term on the right hand side of equation (1), integrated over the three subregions are shown in Figures 5a and 5b. The surface heat flux is everywhere positive, indicating that heat is lost to the atmosphere. It is seen that the estimated surface heat fluxes 8of17

9 a residual of 11 TW, whereas the residual of the ERA 40 based budget is only 1 TW. Thus the Barents Sea heat budget is almost closed when ERA 40 data is applied. In the other two subregions, however, the residuals are considerable. In the Greenland/Iceland Sea it is of the same order as the surface heat flux. The eastern side of the Nordic seas have positive values for the residual, whereas the opposite is the case for the subregion in the western part (Greenland/Iceland Sea). Using ERA 40 data the residuals have almost the same magnitude. When integrated over the entire Nordic seas area, the residual of the heat budget becomes respectively 1 TW (ERA 40) and 3 TW (NCEP 2), or respectively 0.5% and 1.5% of the ocean heat convergence. Figure 6. Mean values of the (left) ERA 40 and (right) NCEP 2 precipitation rate (P), evaporation rate ( E) and precipitation rate minus evaporation rate (P E) over the Nordic seas between 1990 and Values are positive downward. Units are mm d 1. from the two reanalysis products are in relatively good agreement. Over the Norwegian Sea and over the Greenland/ Iceland Sea the value given by NCEP 2 is approximately 10% larger than that from ERA 40, whereas over the Barents Sea it is approximately 15% lower. Integrated over the entire Nordic seas area, the mean surface heat fluxes estimated using ERA 40 and NCEP 2 are 199 TW and 201 TW, respectively, during the period Ocean Heat Convergence [27] From the heat fluxes listed in Table 4 the mean ocean heat convergence integrated over the three subregions under consideration, i.e. the left hand side of equation (1), is computed. Results are presented in Figure 5c. Highest values are seen in the eastern part of the Nordic seas. In the Barents Sea the ocean heat convergence is equal to 74 TW, and in the Norwegian Sea it is 119 TW. A much lower value is seen on the western side of the Nordic seas, where the ocean heat convergence is close to zero. When integrated over the entire Nordic seas area, the ocean heat convergence becomes 198 TW Heat Budget Residual [28] The residuals of the mean heat budgets for the three subregions, R h, given as the difference between ocean heat convergence and the net heat flux through the sea surface, are shown in Figures 5d and 5e. With relatively small differences between the ERA 40 and NCEP 2 mean surface heat fluxes, the difference between the residuals of the two heat budgets never exceeds 10 TW. In the Barents Sea NCEP 2 data gives 4. Freshwater Budget Calculations 4.1. Precipitation and Evaporation [29] In Figure 6 we show the mean precipitation and evaporation rates during the period from ERA 40 and NCEP 2 data. Although more precipitation is seen in the ERA 40 data compared to NCEP 2, both data sets indicate that there is more precipitation over the southern part of the Nordic seas, compared to the areas farther north. For the evaporation rate, the largest values are found over the Norwegian Sea and over the southwestern part of the Barents Sea. Large differences are seen between the ERA 40 and NCEP 2 data, with the evaporation rates in the latter data set being considerably larger over the eastern part of the Nordic seas. This is also reflected when plotting the precipitation minus evaporation rate. Whereas the ERA 40 data set indicates a net freshwater flux toward the ocean over the bulk part of the Nordic seas, NCEP 2 data shows net evaporation over most of the area. [30] The net surface freshwater input, P E, which is the first term on the right hand side of equation (3), integrated over the three subregions, is shown in Figures 7a and 7b. A considerable difference between the two data sets is seen, as ERA 40 gives positive values for all subregions, whereas the estimates from NCEP 2 are negative over the Norwegian and Barents seas. According to the ERA 40 data the surface freshwater input over the Norwegian Sea, Barents Sea and Greenland/Iceland Sea are equal to 11 msv, 6 msv and 9 msv, respectively, whereas the corresponding values of the NCEP 2 data are 6 msv, 1 msv and 2 msv. The net surface freshwater input integrated over the Nordic seas are thus 26 msv (ERA 40) and 5 msv (NCEP 2) Runoff From Land [31] The major runoff to the Nordic seas, i.e. the second term on the right hand side of equation (3), comes from Norway, Russia and Greenland. River runoff from the islands in the Nordic seas, most noticeable northern Iceland and Spitsbergen is assumed negligible in comparison. Applying the estimates of Tollan [1976] gives a freshwater flux equal to 11 msv toward the Norwegian Sea. For the runoff to the Barents Sea from the major rivers we apply the estimate presented by Aagaard and Carmack [1989] of 8 msv. The runoff to the Greenland/Iceland Sea follows Rignot et al. [2008] and is set equal to 4 msv. Applied estimates are shown in Table 5 and results for the three subregions have also been summarized in Figure 7c. 9of17

10 Table 5. Runoff From Land Based on the Literature a Subdomain Runoff From Land (msv) Period Reference Norwegian Sea Tollan [1976] Barents Sea 8 Aagaard and Carmack Greenland/Iceland Sea [1989] Rignot et al. [2008] a Values denote the net freshwater input from land to the subregion (see Figure 2) Ocean Freshwater Divergence [32] Analogue to the ocean heat convergence, the mean ocean freshwater divergence in solid and liquid forms, i.e. the left hand side of equation (3), is calculated from the mean ocean freshwater transports listed in Table 4. In Figure 7d the freshwater divergence integrated over the three subregions under consideration is shown. With the exception of the Greenland/Iceland Sea, where the freshwater divergence is 3 msv, positive values are seen, indicating that the mean ocean currents transport more freshwater away from than Figure 7. Mean values of the net surface freshwater input from (a) ERA 40 and (b) NCEP 2, (c) runoff from land, (d) the mean ocean freshwater divergence in solid and liquid phases, and freshwater budget residual with surface freshwater input from (e) ERA 40 and (f) NCEP 2, integrated over the Norwegian Sea, Barents Sea and Greenland/Iceland Sea. Units are msv. 10 of 17

11 toward these subregions. The freshwater divergence integrated over the entire Nordic seas area is equal to 52 msv Freshwater Budget Residual [33] The residual of the freshwater budgets, R f, given as the difference between ocean freshwater divergence and the net freshwater input from precipitation, evaporation and runoff from land, is shown in Figures 7e and 7f. It is found that the residuals of both the ERA 40 and NCEP 2 based budgets are negative in the Greenland/Iceland Sea and positive in the Norwegian Sea. Using surface freshwater fluxes from NCEP 2 the freshwater budget residual is positive also in the Barents Sea. In the ERA 40 based budget, on the other hand, the residual is zero in the Barents Sea, and hence a closed freshwater budget is obtained. The residuals of the Nordic seas freshwater budget (integrated over all subregions) are 3 msv (ERA 40) and 34 msv (NCEP 2). 5. Discussion 5.1. Accuracy of the Computed Heat and Freshwater Budgets Ocean Data [34] The ocean heat convergence and freshwater divergence are calculated from the fluxes presented in Table 4. It is thus assumed that the considered cross sections cover the total flow to and from the three subregions. From analysis of surface drifters this appears to be correct for the surface currents, at least in the Norwegian Sea where the majority of the drifters were released [Orvik and Niiler, 2002]. The heat and freshwater fluxes associated with the flow are again dependent on both the magnitude of the volume flux and the temperatures and salinities of the water flowing through the sections. The value of 7.45 Sv for the inflow from the North Atlantic Ocean that is applied in this study, is based on long term measurements at the Greenland Scotland Ridge [Turrell et al., 2003; Hansen et al., 2003; Jónsson and Valdimarsson, 2005] and is therefore considered to be the best estimate available. The estimate for the period found by Østerhus et al. [2005] is somewhat larger, with a value of 8.4 Sv. This may be a result of temporal variability or caused by uncertainties related to determining the fraction of Atlantic Water. This is especially a challenge for Sections 1 and 2, which are located in the interior of the Nordic seas rather than at the open boundaries. [35] The volume flux through the Denmark Strait was calculated as the residual of a closed volume budget for the Nordic seas, based on available estimates of the flow through the other cross sections under consideration. The overflow component of the volume flux has been measured by the use of moored instruments. Estimates are ranging from 2.7 Sv to 3.7 Sv southward [Dickson et al., 2008b]. The greatest flow was found during the period [Macrander et al., 2005], when also the Atlantic inflow to the Nordic seas may have been larger than the average value. During a July August, 2004 cruise, Sutherland and Pickart [2008] estimated the flow with the East Greenland Current and East Greenland Coastal Current through five cross sections between 60 N and 68 N, using a vessel mounted acoustic Doppler current profiler. When adjusting for wind effects the flow was found to be approximately 2 Sv southward. Assuming that this value is representative for the surface flow through the Denmark Strait, a mean value of 5.2 Sv for the total flow through the section is within the available estimates. [36] Errors in the mean weighted average temperature and salinity values, T j and S j, of the inflowing and outflowing water masses may be introduced when different time periods for the temporal averages are used, or if an erroneous flow field, and hence wrong weighting of the temperature and salinity data, is applied. The effect of using different temporal averages to calculate T j and S j is difficult to estimate for most sections, due to few observations. For the Atlantic inflow across the Greenland Scotland Ridge, where estimates from different time periods are available, we find that the values applied in this study are almost identical to those presented by Østerhus et al. [2005]. For Sections 6 and 11, on the other hand, we may expect a seasonal bias since the hydrographic data used to calculate the fluxes were taken during summer and autumn months only. For example, the temperature of surface water flowing through Section 11 may be overestimated due to solar heating, and also the amount of liquid water transported through the section may vary throughout the year. [37] For some of the cross sections explicit values of T j and S j have not been presented in the literature. In particular, in order to close the Nordic seas heat and freshwater budgets, the flow field used in equations (2) and (4) to calculate the mean weighted temperature and salinity values of water masses flowing through the Denmark Strait have been derived from hydrography in combination with drifter data. Since the flow through this section is relatively high ( 70% of the inflow from the North Atlantic) the effect of errors on the heat and freshwater budgets may be considerable. Sutherland and Pickart [2008] reported a maximum freshwater flux at 63 N, assumed to include melted sea ice. Calculated relative to a salinity of 34.9 the freshwater flux becomes 109 msv. Since the salinity of the overflow water is roughly in the range [Macrander et al., 2007], this would indicate a freshwater flux that is 10 msv to 20 msv less than the estimate based on the geostrophic approach. A possible reason for the discrepancy is temporal variability. In particular, most of the freshwater transported through the Denmark Strait has been advected with the East Greenland Current from the Fram Strait, where observations indicate that both the sea ice transport and liquid freshwater flux vary considerably [Widell et al., 2003; Rabe et al., 2009]. The lower value reported by Sutherland and Pickart [2008] compared to the estimate applied in this study could also be due to horizontal mixing with the more saline Irminger Current, that flows to the east of the East Greenland Current [Våge et al., 2011]. In fact Sutherland and Pickart [2008] found that the freshwater flux was decreasing somewhat from 63 N to 60 N, indicating that such a mixing may take place. [38] Another way to assess the derived freshwater flux is to compute a separate budget for the East Greenland Current, as was done by Jónsson [2003]. It was found that the Jan Mayen Polar Current and the East Iceland Current transport approximately 15 msv of freshwater away from the East Greenland Current when calculated relative to a salinity of Ocean transports toward the East Greenland Current, e.g. recirculation of Atlantic inflow with the Iceland branch, should also be considered in the budget. However, assuming that these water masses have a salinity close to 34.9, this 11 of 17

12 will have little effect on the freshwater budget. On the shelves east of Greenland, defined by the eastern coast of Greenland and the 800 m isobath, both ERA 40 and NCEP 2 give a net freshwater flux through the sea surface close to 4 msv. Together with the runoff of 4 msv from the Greenland ice sheet considered in this study, this gives a net freshwater loss of approximately 7 msv for the East Greenland Current between the Fram Strait and the Denmark Strait. In this estimate zonal transports of sea ice toward the interior parts of the Greenland/Iceland Sea have been neglected. With a freshwater flux of 140 msv through the Fram Strait, a freshwater flux through the Denmark Strait equal to 133 msv is obtained. This is 3 msv larger than the value presented in Table 4. [39] In order to estimate errors of the computed heat convergence and freshwater divergence (ocean part) of the three subregions we apply an error estimate of 10% for all volume fluxes, which is the value Hansen et al. [2003] reported as the uncertainty for the calculated flow with the Faroe branch. If we increase/decrease all volume fluxes listed in Table 4 by 10% the Nordic seas heat convergence and freshwater divergence will change by respectively ±22 TW and ±11 msv. Here uncertainties in the mean weighted average temperature and salinity of the inflowing and outflowing water masses have not been accounted for, and it has been assumed that relative changes in the volume flux are equal for all branches. In order to give a more complete assessment of uncertainties in the budget calculations we must also included uncertainties in the average temperature and salinity. Error estimates of S j are set equal to ±0.05 PSU for Sections 6 and 11, where uncertainties in the average salinity are assumed largest, and to ±0.025 PSU for the remaining sections. For T j uncertainties are again expected to be largest for the flow through Sections 6, 11, and also for the surface flow through Section 12. Here error estimates of ±0.5 C are used, whereas error estimates of T j for the other cross sections are set equal to ±0.25 C. Assuming that all values within the error estimate interval are equally likely, a statistical distribution of the errors may be calculated, using a Monte Carlo approach. The expected error of heat convergence and freshwater divergence of a subregion within the 95% confidence interval may then be estimated. Using this approach the calculated error estimates become equal to approximately ±16 TW and ±8 msv (Norwegian Sea), ±9 TW and ±3 msv (Barents Sea) and ±15 TW and ±12 msv (Greenland/Iceland Sea). Since we here have assumed that the volume flux, temperature and salinity have even distributions (all values in the considered intervals are equally likely), these error estimates are conservative compared to if Gaussian distributions were assumed Sea Ice Data [40] Since the sea ice transport through open boundaries is difficult to measure and vary on inter annual timescales, estimates given in literature vary considerably. Recent observational based estimates of the mean sea ice transport through the Fram Strait ranges from 1859 km 3 yr 1 [Korsnes et al., 2002] to 2850 km 3 yr 1 [Vinje et al., 1998]. The estimate of 2400 km 3 yr 1 given by Widell et al. [2003] is the average value over the period , and therefore preferred in the present study. Estimated errors were found to be 480 km 3 yr 1, corresponding to heat and freshwater transport equal to 5 TW and 12 msv. Errors in the sea ice transport through the Fram Strait will also affect the calculated fluxes through the Denmark Strait (Section 11), thus reducing the error estimates of the heat and freshwater convergence of the Greenland/Iceland Sea. However, corresponding values are probably less than uncertainties related to the applied melt rate. [41] Similar to the Fram Strait sea ice export, also estimates of the sea ice transport to the Barents Sea found in literature vary considerably. The values listed by Korsnes et al. [2002] range from 72 km 3 yr 1 to 418 km 3 yr 1, and the standard deviation was found to be 125 km 3 yr 1, about 70% of the mean value for the period. For the freshwater flux due to sea ice transport, also the value chosen for S ice will have an effect. In this study we have applied the value 3 PSU, as was also the value used by Prange and Gerdes [2006]. If we instead use a value of 4 PSU, as suggested by Serreze et al. [2006], we would decrease the freshwater flux through the Fram Strait by 2 msv, whereas for the other sections the effect would be less than 0.5 msv Steady State Assumption [42] In the budget calculations we have assumed that changes in heat and freshwater content of the subregions during the 1990s may be neglected, i.e. the average temperature and salinity values of the subregions at the end of the study period were approximately equal to those at the beginning. Skagseth et al. [2008] presented time series of temperature and salinity in the core of Atlantic Water for three different sections: West of the Norwegian coastline at approximately 62 N (Svinøy Section), the western entrance of the Barents Sea, and south of the Fram Strait (Sørkapp). Although inter annual variations are evident at all sections, no clear trend is seen in the temperature or salinity during the 1990s, and values are similar at the beginning and end of the period. [43] Using the NISE data set the heat and freshwater content for the Norwegian Sea may be computed. Due to less observations in the two other subregions, this cannot be done for the Barents and Greenland/Iceland seas. Since most of the hydrographic observations are from the summer months, we calculate the storage terms for each year in the period from measurements taken in July and August only. As seen from Figure 3, many observations were also taken in May, but most of the measurements were made south of 72 N. [44] From Figure 8 it is seen that the heat content was increasing the first two years of the study period, followed by five years when the heat content was decreasing, before it increased again from The mean rate of change in heat content over the period is found to be 2 TW. Also the rate of change in freshwater content is varying between positive and negative values, with a mean value of 1 msv for the period Although the temperature and salinity distribution may be affected by fluctuations in the front, since measurements are from July and August only, and the mean rate of change in heat and freshwater content has not been calculated for the Barents and Greenland/Iceland seas, the low values indicate only minor errors associated with the steady state assumption for the period under consideration Closing the Mean Heat and Freshwater Budgets Additional Transport Terms [45] For both the heat and freshwater budgets we find that the residuals are non zero and relatively large in magnitude 12 of 17