## Abstract

A linear diagnostic model, solving for the time-mean large-scale circulation in the Nordic seas and Arctic Ocean, is presented. Solutions on depth contours that close within the Nordic seas and Arctic Ocean are found from vorticity balances integrated over the areas enclosed by the contours. Climatological data for wind stress and hydrography are used as input to the model, and the bottom geostrophic flow is assumed to follow depth contours. Comparison against velocity observations shows that the simplified dynamics in the model capture many aspects of the large-scale circulation.

Special attention is given to the dynamical effects of an along-isobath varying bottom density, which leads to a transformation between barotropic and baroclinic transport. Along the continental slope, enclosing both the Nordic seas and Arctic Ocean, the along-slope barotropic transport has a maximum in the Nordic seas and a minimum in the Canadian Basin with a difference of 9 Sv (1 Sv ≡ 10^{6} m^{3} s^{−1}) between the two. This is caused by the relatively lower bottom densities in the Canadian Basin compared to the Nordic seas and suggests that most of the barotropic transport entering the Arctic Ocean through the Fram Strait is transformed to baroclinic transport. A conversion from barotropic to baroclinic flow may be highly important for the slope–basin exchange in the Nordic seas and Arctic Ocean.

The model has obvious shortcomings due to its simplicity. However, the simplified physics and the agreement with observations make this model an excellent framework for understanding the large-scale circulation in the Nordic seas and Arctic Ocean.

## 1. Introduction

The Nordic seas and the Arctic Ocean, also known as the Arctic Mediterranean, are dominated by a highly complex topography (Fig. 1). It is a well-known fact that topography plays an important role in this area where the large-scale currents are strongly steered along isobaths (Helland-Hansen and Nansen 1909; Poulain et al. 1996; Orvik and Niiler 2002; Jakobsen et al. 2003). In addition, the Arctic Mediterranean is characterized by depth contours closing on themselves within the domain. This may lead to exceptionally strong flow as the currents will spin up until friction balances the forcing (Greenspan 1968; Nøst and Isachsen 2003; Isachsen et al. 2003; Nilsson et al. 2005). An understanding of the key processes controlling the large-scale circulation becomes crucial to predict how the Arctic Mediterranean will respond to a changing climate.

Recent simplified analytical models solving for the leading-order circulation in the Nordic seas and Arctic Ocean describe remarkably well the observed large-scale circulation. Nøst and Isachsen (2003) and Isachsen et al. (2003) find solutions for the local circulation by analyses of the integral vorticity balances within areas enclosed by *f/H* contours, where *f* is the Coriolis parameter and *H* is the depth. In both models, bottom friction plays an essential role. Isachsen et al. (2003) focuses on the temporal variability of the wind-driven homogenous flow, assuming that the depth-averaged velocity is aligned with *f/H.* This barotropic model is able to predict large parts of the seasonal-to-annual time variability of the flow. Closely related, the steady-state circulation of a stratified ocean was modeled by Nøst and Isachsen (2003), relying on the bottom geostrophic velocity to follow *f/H* contours, but with no such restrictions on the flow above the bottom. Their modeled surface circulation field, estimated from climatological hydrography and wind stress data, captures most of the surface circulation pattern obtained from drifting buoy data in the Nordic seas (Poulain et al. 1996; Orvik and Niiler 2002; Jakobsen et al. 2003). The modeled bottom geostrophic velocities also compare well with observations of bottom currents. They capture the pronounced and narrow cyclonic boundary current in the Arctic Ocean and the weaker flows within the basins (Aagaard 1989).

Topographically steered currents have often been related to eddies. Bretherton and Haidvogel (1976) show that an initial 2D turbulent field above topography will approach a state of minimum enstrophy for a given kinetic energy. This state is characterized by topographically steered currents, cyclonic around basins and anticyclonic around seamounts. Statistical mechanics gives a similar result, predicting that mean currents above a sloping topography are given by a state of maximum entropy (Salmon et al. 1976). Based on statistical mechanics, a parameterization of the interaction between eddies and topography was introduced by Holloway (1987, 1992) and has been widely used in the Arctic Ocean to improve the representation of topographically trapped currents (Nazarenko et al. 1998; Nazarenko and Tausnev 2001; Polyakov 2001; Holloway et al. 2007). The parameterization, also named “the Neptune effect,” drives cyclonic currents in basins with sloping topography. However, also noneddying mean flow will favor a cyclonic circulation, rather than anticyclonic, over a sloping topography (Nycander and LaCasce 2004; Nøst et al. 2008; LaCasce et al. 2008). Nøst et al. (2008) show that as long as the Rossby number is larger than the Ekman number, anticyclonic flow in basins will develop large cross-slope components and topographical steering of the flow breaks down.

It is interesting to note that the simple analytical model by Nøst and Isachsen (2003) captures the topographically steered boundary currents without including any parameterizations. The reason for this is that the model has no cross-slope exchange of vorticity. This raises the following question: Is the boundary flow in the Arctic Ocean mainly cyclonic due to the Neptune effect or is it simply driven by the cyclonic winds in the Nordic seas, as suggested by Nøst and Isachsen (2003)? Neptune effect contra directly cyclonic wind forcing was also discussed by Isachsen et al. (2003).

In Isachsen et al. (2003), the barotropic transport between two depth contours changes in time corresponding to the time variability of the wind forcing. But at a certain time, or in the steady-state model of Nøst and Isachsen (2003), the barotropic transport is conserved along the slope. However, according to Walin et al. (2004), along-slope variations in bottom density will lead to along-slope variations in the barotropic transport between two depth contours. In brief, their theoretical analysis considers the geostrophic dynamics in a steady-state boundary current, which consists of a seaward baroclinic jet stream and a barotropic slope current—similar to the Norwegian Atlantic Current off the coast of Norway (see Orvik et al. 2001). As the density increases downstream (northward in the case of the Norwegian Atlantic Current), a thermal wind arises toward shallower depth, draining the baroclinic jet stream. Through interaction with the sloping topography, the thermal wind is transformed into a barotropic flow restricted to be aligned with the slope. This interaction between baroclinic and barotropic flows gives rise to variations of the barotropic transport along the sloping bottom.

The barotropic flow variations due to a variable bottom density field are further investigated by Nilsson et al. (2005). They present a simplified analytical model solving for the *f*-plane geostrophic circulation in a stratified basin with closed depth contours. As in Nøst and Isachsen (2003) and Isachsen et al. (2003), the near-bottom geostrophic flow is assumed to follow isobaths and bottom friction plays an essential role. Nilsson et al. (2005) show that an along-isobath varying bottom density field alone is able to induce an isobath-following bottom velocity, even in the absence of wind forcing.

The importance of the along-isobath bottom density gradient to the geostrophic circulation is investigated in the Fram Strait region of the East Greenland Current by Schlichtholz (2002, 2005). He combines hydrographic data along the continental slope with theoretical considerations using the depth-integrated vorticity equation and finds that a downstream bottom density increase of 0.01 kg m^{−3} is responsible for a velocity increase of 0.03 m s^{−1} of the southward bottom geostrophic velocity. These studies indicate that even the relatively weak along-isobath variabilities of bottom density, observed in the Arctic Mediterranean, might affect the barotropic velocity field considerably.

In other investigations of the interaction between the density field and bottom slope, the term for the Joint Effect of Baroclinity and Relief (JEBAR) is often used. JEBAR is used when the depth-averaged vorticity equation is turned into an equation for the depth-averaged velocity. The topographic vortex stretching is then expressed by the depth-averaged velocity instead of the bottom velocity (e.g., Mertz and Wright 1992).

In the present study, we extend the model of Nøst and Isachsen (2003) by adding the effect of an along-isobath variation of bottom density. The purpose of this is to investigate the influence of such a contribution to the large-scale circulation in the Nordic seas and Arctic Ocean. Because the vorticity balance in our derivations directly involves the bottom velocities instead of the depth-averaged velocity, the terminology of JEBAR is bypassed entirely.

The theory in the present work differs from the study of Nilsson et al. (2005) by making no *f*-plane assumption. In addition, the design of the model by Nøst and Isachsen (2003) is changed due to the inclusion of the effects of a variable bottom density. For this reason, we choose to present a full theory section (section 2). The climatological data, used to force the model, and the method for extracting bottom densities are presented in section 3. Model results are presented in section 4, followed by a discussion in section 5. Summary and conclusions are presented in section 6.

## 2. The model

### a. Geostrophic velocities

For large-scale circulation in steady state, the horizontal linearized momentum equations become

where ** υ** is the horizontal velocity vector,

**is the vertical unit vector,**

*k**f*is the Coriolis parameter,

*ρ*

_{0}is a reference density,

*p*is pressure,

**∇**represents the horizontal gradient operator, and

**is the frictional stresses. We assume**

*τ***is confined to thin Ekman layers at the surface and bottom. This leaves the ocean interior to be in geostrophic balance with the geostrophic velocity**

*τ*For reasons to be clarified below, it is useful to define a density anomaly *ρ*′ as

where *ρ* is the density and *ρ _{r}* =

*ρ*(

_{r}*H*) is a constant reference density for each isobath. Using Eq. (3), the following expression for pressure at depth

*z*is obtained from the hydrostatic balance

where *g* is the gravitational acceleration and *p _{b}* =

*p*(

*x*,

*y*, −

*H*) is the bottom pressure.

By inserting *p* from Eq. (4) into Eq. (2) and making use of Leibnitz’s rule for differentiation of integrals, the geostrophic velocity can be written as

Here *υ** _{s}* is the baroclinic velocity component recognized as the depth-integrated thermal wind

The bottom geostrophic velocity *υ** _{b}* is expressed by

where *υ*_{ρb} and *υ*_{0} are given as

and

Here, *ρ*′* _{b}* =

*ρ*′(

*x*,

*y*, −

*H*) and

*p*

_{0}is an arbitrary function of (

*x, y*).

^{1}Note that the density-related component

*υ*_{ρb}is directed along the isobaths, whereas

*υ*_{0}has no such restriction. The

*υ*_{0}is written in the form of a geostrophic velocity as in Eq. (2), meaning that

**∇**·

*f*

*υ*_{0}= 0. On the other hand, as long as

*ρ*′

*(or*

_{b}*ρ*) is varying along an isobath and

_{b}**∇**

*H*≠ 0, neither

*υ*_{ρb}nor

*υ**can be written as a geostrophic velocity. Instead, the sum*

_{s}

*υ*_{ρb}+

*υ**fulfills the geostrophic balance, which gives*

_{s}Because *υ*_{ρb} is a depth-independent barotropic velocity component and *υ** _{s}* is a baroclinic velocity, Eq. (10) describes an interaction between barotropic and baroclinic flows induced by along-isobath variations in bottom density. A divergence (convergence) in

*f*

*υ*_{ρb}is associated with a convergence (divergence) in

*f*

*υ**(see Fig. 2). This interaction between barotropic and baroclinic flows is previously described by Schlichtholz (2002, 2005, 2007) and Walin et al. (2004).*

_{s}Assuming that the density field is known from data, finding *υ** _{g}* requires solving for

*υ*_{0}, which is the only unknown component in Eq. (5). The procedure for doing this is presented in the following section, where we take advantage of the closed depth contours in the Nordic seas and Arctic Ocean.

### b. Solving for the bottom velocity on closed depth contours

#### 1) Depth-integrated vorticity equation

The depth-integrated vorticity equation can be found starting from the conservation of volume, which in a steady state is expressed as **∇** · ** V** = 0, where

**= ∫**

*V*^{0}

_{−H }

*υ**dz*. The

**can be split into geostrophic and ageostrophic components:**

*V*The first two terms on the right-hand side of the equation make up the geostrophic transport. The density-related geostrophic component *V** _{Q}* is defined as

where the baroclinic transport *V** _{s}* is given by (using integration by parts)

and the depth-independent *υ*_{ρb} is given by Eq. (8).

The ageostrophic component *V** _{E}* is the horizontal Ekman transport integrated over the two boundary layers and is given by

Taking the divergence of Eq. (11) and using **∇** · ** V** = 0, we get the depth-integrated vorticity equation

where curl( ) = **k** · **∇** × ( ). Here, we have used **∇** · ( *f**V** _{Q}*) = 0 (see appendix A), which gives the following equality used in Eq. (15):

In addition, the divergence of the Ekman transport is given by

Because *τ** _{b}* is a function of

*υ**, the unknown barotropic pressure*

_{b}*p*

_{0}is included in both terms on the left-hand side of Eq. (15), whereas the right-hand side is assumed known from data.

Note that for the case with negligible bottom velocity, Eq. (15) is recognized simply as the Sverdrup balance.

#### 2) Area-integrated balance within closed depth contours

To enable an extraction of *p*_{0}, it is useful to integrate Eq. (15) over the area *A* spanned by a closed isoline *C.* If the isolines are closed contours of *f* /*H*, the first term on the left-hand side of Eq. (15) becomes identically zero. In the present analysis, we integrate over the area *A*(*H*) enclosed by depth contours instead of *f* /*H* contours to facilitate the mathematical expressions and interpretation of the terms involving **k** × **∇***H*. However, in the Nordic seas and Arctic Ocean, *f* /*H* is to a large degree dominated by the topography so that the relative difference between *A*(*H*) and the corresponding *A*( *f* /*H*) is small. Therefore, the first term on the left-hand side of Eq. (15) has negligible influence on the area-integrated balance within closed depth contours and can be ignored (see appendix B). The area-integrated balance of Eq. (15) then reduces to

Here, the area integral associated with *τ** _{b}* has been transformed into a line integral by the use of Stokes’s theorem, where

**represents the tangent unity vector to**

*t**C*in a counterclockwise direction.

We will in the following make the assumption that *υ** _{b}* to leading order follows topography. This assumption of an along-isobath bottom geostrophic flow is used in several other studies. For instance, Nøst and Isachsen (2003) show by a scale analysis that the cross-topographic component of

*υ**is about 100 times smaller than the magnitude of*

_{b}

*υ**itself. Therefore, Eq. (7) can be written as*

_{b}where the unknown barotropic pressure *p*_{0} is now a function of *H* only. We choose a linear friction relation,

with the constant friction parameter *R.* Equations (19) and (20) are now used together with Eq. (18) to obtain an expression for *dp*_{0}/*dH:*

The notation 〈 〉 denotes the weighted average on a closed isobath. For an arbitrary variable *F* = *F*(*x*, *y*), we have

We now define

which together with Eq. (3) gives

where *υ*_{ρb} is given by Eq. (8) with *ρ _{r}* defined by Eq. (23). On average, the magnitude of

*υ**along an isobath is given by the integrated forcing terms, which are constant on each depth contour (see gray arrows in Fig. 2). But locally, the bottom flow also depends on the behavior of*

_{b}*ρ*along the isobath (see black thick arrows in Fig. 2). These two components, plus the effect of the local topographic slope [Eq. (25)], add up to give the total bottom flow.

_{b}Note that in the case of a constant *ρ _{b}* along isobaths,

*υ*_{ρb}= 0 and

*V**=*

_{Q}

*V**, which makes the expression of*

_{s}

*υ**in Eq. (25) identical to the expression of*

_{b}

*υ**found in Nøst and Isachsen (2003), with the only difference in the choice of*

_{b}*H*contours instead of

*f*/

*H*contours. Note also that if

*f*is constant, Eq. (25) becomes equal to the result of Nilsson et al. (2005).

### c. Solving for the bottom velocity on open depth contours

In the more shallow regions, many depth contours are not closing on themselves within the domain. To solve for *υ** _{b}* on open depth contours, the method described in the previous section cannot be used to estimate

*dp*

_{0}/

*dH*. Instead, we need to initialize from observations, again assuming that

*dp*

_{0}/

*dH*is constant along depth contours. We initialize

*ρ*to be equal to

_{r}*ρ*in a region where current meter data near bottom are available. Now,

_{b}*dp*

_{0}/

*dH*can be found on the open contours from Eq. (19) as

Here, is the observed bottom flow with shallow water to the right.

## 3. Data and data processing

According to Eq. (25), the input parameters needed for calculating the bottom geostrophic velocity on closed depth contours are wind stress, hydrography, and topographic data. Additionally, we need observations of the near-bottom flow to estimate *υ** _{b}* on open depth contours [Eqs. (19) and (26)]. The constants are set to

*g*= 9.81 m s

^{−2},

*R*= 2 × 10

^{−4}m s

^{−1}(Haidvogel and Beckmann 1999), and

*ρ*

_{0}= 1030 kg m

^{−3}, and the Coriolis parameter is given as

*f*= 2Ω sin

*θ*, where Ω is the rotation rate of earth and

*θ*is latitude.

### a. Topographic data

The topography we have used the merged International Bathymetric Chart of the Arctic Ocean–5-minute gridded elevations/bathymetry for the world (IBCAO–ET0P05) global topographic data product from Holland (2000) with a grid spacing of 1/12°. First, the topography was smoothed by setting the depth at each point equal to the mean of all surrounding points inside a 20 km × 20 km box. Next, to solve for the bottom velocity according to Eq. (25), we selected a set of closed depth contours at depths between 500 and 4250 m, with intervals of 250 m (Fig. 1). The shallowest contour that encircles both the Arctic Ocean and the Nordic seas is at 750 m (any closed contours at 500 m encircle seamounts). In addition, for estimating the bottom velocity on the shallower part of the continental slope, we include the open depth contours at 400-, 500-, 600-, and 700-m depths.

### b. Climatological data

As wind forcing we have used an average, over the period 1948–2005, of monthly mean wind stress acquired from the National Centers for Environmental Prediction– National Center for Atmospheric Research (NCEP–NCAR) reanalysis project (Kalnay et al. 1996), provided by the NOAA/OAR/ESRL PSD, Boulder, Colorado. Available online at http://www.cdc.noaa.gov). The spatial resolution of the data is about 2° × 2°. The Ekman pumping, to be used in Eq. (25), is calculated from curl[*τ** _{s}*/(

*ρ*

_{0}

*f*)] using spherical coordinates. The Ekman pumping for the Arctic Mediterranean is presented in Fig. 3 and is seen to be of the order of 10

^{−6}m s

^{−1}. The Nordic seas are dominated by positive Ekman pumping (upward velocities), which contribute to cyclonic bottom flow in these basins according to Eq. (25).

Density is extracted from the annual mean Polar Science Center Hydrographic Climatology (PHC), version 3.0 (Steele et al. 2001). The PHC is a combination of mainly two datasets, the *World Ocean Atlas* (*WOA*) (Conkright et al. 1998) and the *Arctic Ocean Atlas* (*AOA*) (Timokhov and Tanis 1998, 1997). Its horizontal resolution is 1° × 1°. In the vertical, 33 standard depths are used with 10-m separations near the surface and 500-m intervals beneath 2000 m. Using salinity and temperature (in situ) data, we calculate the seawater density with pressure corresponding to the standard depths of the dataset.

To attain *ρ _{b}* from the hydrography,

*ρ*is interpolated horizontally onto the depth contours. If, for a certain depth contour, no corresponding standard depth exists in the hydrography,

*ρ*on that contour is instead extracted from the nearest standard level above. As it is the horizontal density anomalies that are important, not the absolute values, this approach turned out to be better than a linear extrapolation in the vertical. Finally, a low-pass filter is used on each isobath to remove noise generated in the interpolation process. The low-pass window that we have used is 500 km. Now,

*ρ*′

_{b}can be found from Eqs. (3) and (23). The

*ρ*′

_{b}is shown in Fig. 4.

Figure 5 shows the divergence of the density-related transport *V** _{Q}*, which depends on

*ρ*′

_{b}[Eq. (12)]. This divergence, together with the Ekman pumping velocity (Fig. 3), make up the right-hand side of Eq. (15) and the integrated forcing terms in Eq. (25). Comparing Figs. 3 and 5, we see that these forcing terms are of the same order of magnitude. However, their spatial distributions are very different and, therefore, the two terms on the right-hand side of Eq. (15) do not cancel out each other. This indicates that the Sverdrup balance is not an appropriate balance in this region.

### c. Current meter data

For the purpose of the initialization of Eq. (26), and for later comparisons of model results with observations, we use a global compilation of current meter data introduced by Holloway (2008, and references therein). In addition, we use near-bottom data from S. Østerhus (2008, personal communication), Hughes et al. (2006), Aagaard (1989), and Woodgate et al. (2001). All data are based on records of at least one month’s duration. Due to the numerous data records from the West Spitsbergen Current in the Fram Strait (e.g., Schauer et al. 2004), we chose this location as our initialization region.

## 4. Model results and comparison with observations

### a. Bottom geostrophic velocity

Using the data described in the previous section, the bottom geostrophic velocities are calculated on closed depth contours [Eq. (25)] and on open contours [Eqs. (19) and (26)], with initialization in the eastern Fram Strait. First, we describe the resulting velocity field by introducing the scalar velocity field *t*, defined as

Here*, t* is a scalar measure of the along-slope flow, where *t* becomes positive (negative) for flow with shallow water to the right (left). The distribution of *t* calculated from the modeled bottom flow for the Arctic Ocean and Nordic seas is seen in Fig. 6.

We see that the entire domain is dominated by cyclonic bottom circulation,^{2} apart from the Canadian Basin and the Makarov Basin, which contain anticyclonic circulation inside the cyclonic Arctic Circumpolar Boundary Current (ACBC) (for a description of ACBC, see Rudels et al. 1999). The ACBC appears as a narrow and strong cyclonic slope current. In general, the strongest flows are along the steeper slopes, such as the continental slopes, the slopes of the Lomonosov Ridge, and on the subbasin slopes in the Nordic seas. In these slope regions, the magnitude of *υ** _{b}* is on the order of 10

^{−1}m s

^{−1}, which is in good agreement with magnitudes of the near-bottom velocities reported from observations (e.g., Aagaard 1989; Woodgate et al. 1999; Orvik et al. 2001; Fahrbach et al. 2001; Woodgate et al. 2001; Newton and Coachman 1974; Newton and Sotirin 1997). Along the shallowest part of the Norwegian continental slope,

*t*is noticed being negative, corresponding to a southward-directed bottom flow. This is contradictory to observations, and the possible reasons for this are a topic in the discussion.

Next, the modeled bottom geostrophic velocity fields are shown together with observations of the deep circulation in Figs. 7 –9. In addition to showing the velocity fields from model and observations, Figs. 7 and 8 also visualize the geographical distributions of the observations. Figure 9 shows a more detailed comparison between modeled and observed deep circulation. For each observation, we find a corresponding model result of *υ** _{b}* from criteria of both lateral position and depth.

^{3}Then we calculate the scalar velocity according to Eq. (27) with the topographic gradient extracted from the model topography. Despite the simplicity of the model and the obvious uncertainties arising when comparing a steady-state model with point observations of various record lengths and from different time periods, the first impression from Figs. 7 –9 is that the model results show a generally good agreement with the observations. The comparisons between observations and model results are discussed in more detail in the following.

In the calculations of the scalar velocity (Fig. 9), we assume that the current meter data are aligned with depth contours to reduce noise coming from the topographic uncertainties. Still, some disagreements of the sign of *t* between observations and model results are expected due to the fact that not all topographic features are correctly resolved in the smoothed topographic data. In Fig. 9, we include two versions of the model results, one according to the full expression [Eq. (25)] and the other where the effect of an along-slope varying bottom density has been excluded by setting *ρ*′_{b} = 0. The latter solution corresponds to the model of Nøst and Isachsen (2003) and is included here to emphasize the importance of *ρ*′_{b}. In the following, we refer to the full model results when nothing else is mentioned.

The observed values of *t* are seen to vary in magnitude from about −0.2 to 0.3 m s^{−1} in the Nordic seas and from about −0.1 to 0.2 m s^{−1} in the Arctic Ocean (Fig. 9). The model results are within the same ranges of magnitude. Furthermore, the subregions show clear differences in their observed flow characteristics. At the slope in the Greenland Sea and the Eurasian Basin the currents are relatively strong compared with other regions, whereas elsewhere in the Arctic Ocean currents are relatively weak. All these characteristic features are captured by the model.

According to Fig. 9, there appears to be larger differences between model results and observations on open depth contours than on closed contours. In the eastern Fram Strait, the model does well on open contours (index 69–70 in Fig. 9), which is expected, as this is the region where the currents have been initialized with observations (see sections 2c, 3c). South of this region, the model has a tendency to underestimate the cyclonic flow on open contours. This is seen as southward bottom flow in the Faroe–Shetland Channel and in the Svinøy section and slightly weaker flow magnitudes than observed in the Barents Sea opening (Fig. 9). However, in the Arctic Ocean, the western Fram Strait, and the Greenland Sea (downstream of the initialization region), the model overestimates the flow on open contours (Fig. 9). Farther south in the Denmark Strait the model again underestimates the magnitude of the bottom flow on open contours.

The model results on the closed contours in the Svinøy section (Fig. 9) are almost identical with the observations, apart from the results at the depth of 900–1000 m (index 9–11), where the direction of the bottom flow differs between model and observations. The reason for this disagreement is not clear.

For the Fram Strait, where data are sorted by ascending longitude, the model results are seen to give a very good fit at the eastern slope (index 64–70), not only on open contours (where they are initialized by the observations) but also on closed contours. The flow magnitude increases toward shallower depth. However, at the western slope (index 44–54), the model mainly overestimates the bottom flow. The two peaks in velocity, at indexes 50 and 52 at the western slope, are both displaced southward of the standard Fram Strait transect, and they clearly appear to have stronger velocities than measurements just north of them. Such downstream increase of the bottom flow within the western Fram Strait region is reported by Schlichtholz (2002, 2005) and is captured by the model, despite the overestimated absolute values. In the center of the strait (index 55–63), both observed and modeled flow magnitudes are in the order of 10^{−2} m s^{−1}, but their directions appear to differ.

In general, the modeled velocity field presented here (Figs. 7, 8) shows the same large-scale features as the result of Nøst and Isachsen (2003, their Figs. 8, 12). This is to be expected as the two models are very similar. However, an interesting new feature achieved from the present model is the relatively high influence of an along-slope varying bottom density, an effect not included by Nøst and Isachsen. In Fig. 9, the effect of *ρ*′_{b} is seen to considerably improve the results in the Arctic Ocean by slowing down the bottom flow. At several places along the Beaufort slope (BS), weak or negligible flows are measured at about 1000-m depth (indexes 36, 46, 48, 61, and 65). Due to the effect of *ρ*′_{b}, these are all seen to be represented very well in the present model (Fig. 9). In other regions, the effect of *ρ*′_{b} seems negligible on the bottom flow, and in the western Fram Strait the results of the bottom flow seem to deviate even more from observations when including the effect of *ρ*′_{b}.

### b. Variations of along-slope barotropic transport

To quantify the along-slope transport variations, induced by a variable bottom density along the slope, we introduce the barotropic transport between two depth contours as

where *x* is used to denote the coordinate axis perpendicular to the bottom flow direction and *υ** _{b}* is the bottom flow with shallow water to the right. The

*T*is estimated, according to Eq. (28), from the modeled

*υ*on the continental slope between the 750- and 2250-m depth contours that encircle both the Arctic Ocean and the Nordic seas. This barotropic transport varies between −2 and 6.9 Sv (1 Sv ≡ 10

_{b}^{6}m

^{3}s

^{−1}) along the slope, as seen in Fig. 10. In general,

*T*is lower in the Arctic Ocean than in the Nordic seas. Especially along the slope of the Canadian Basin, we find the minimum values of

*T*almost all being negative. Other characteristic transport features are the downstream increase of the East Greenland Current through the Fram Strait and a corresponding downstream decrease of the West Spitsbergen Current from the Barents Sea Opening toward the Fram Strait. In addition, we see changes of

*T*where the continental slope current passes the Lomonosov Ridge. These represent a strong downstream decrease of

*T*north of the Laptev Sea and an increase north of Greenland. Finally, a local minimum in transport is found near St. Anna Trough and near the Lofoten Basin.

## 5. Discussion

### a. Uncertainties and weaknesses in the model dynamics

The use of climatological data (i.e., hydrography and wind stress) allows us to calculate the bottom geostrophic flow from Eq. (25). However, there are errors and uncertainties in the climatological data that will influence our results. For instance, Holfort and Hansen (2005) pointed out that the PHC hydrography has large errors in the western Fram Strait. These errors may be the cause of the overestimation of the bottom flow in this region (Fig. 9). However, except for calculations of *υ** _{ρb}*, the use of climatological data in the expression for bottom velocity [Eq. (25)] is always within integrals over areas spanned by closed depth contours. This area integration is likely to make the model results less dependent on local errors and coarse resolution in the climatological data. Errors are also introduced by using the NCEP–NCAR wind stress over ice-covered regions. This will probably cause too strong wind forcing in the regions north of Greenland, due to strong internal forces in the ice (see discussion by Nøst and Isachsen 2003).

The largest uncertainties occur when making comparisons of model results against point measurements. Each observational data are affected by specific conditions, such as local irregularities in topography and density distribution. In addition, our model is forced with climatological data averaged over 50 yr, while current measurements may be down to a month’s duration. Despite the possibility for many sources of uncertainties and errors, the model results are in remarkably good agreement with observations, considering the simplicity of the model.

Our linear model solution relies heavily on the topographic steering of *υ** _{b}*. A vitally important assumption is that

*p*

_{0}is a function of the topography,

*H*, only, and that the relative vorticity is always small compared to

*f*. As variations in

*f*/

*H*are mainly caused by variations in

*H*, along-slope barotropic flow will conserve its potential vorticity. However, if a cross-slope transport should occur at one location and significantly change the along-slope transport, our model results will not be able to correctly describe the flow. Similarly, if cross-slope exchange of relative vorticity becomes important, our linear solution will not be valid.

In linear dynamics, it makes no difference to the behavior of the flow whether it has shallow water on the left or right. However, according to Nycander and LaCasce (2004) and Nøst et al. (2008), nonlinearity will remove this symmetry. By the use of laboratory experiments and numerical simulations, Nøst et al. (2008) demonstrate that cyclonic flow in a basin (shallow water on the right) will strictly follow topography, while for anticyclonic flow (shallow water on the left) locations of strong cross-slope flow develop when the Rossby number is larger than the Ekman number (Ro ≫ Ek). When cross-slope flow occurs, the observed flow is completely different from the linear solution because the assumption that *p*_{0} is a function of *H* is no longer valid. In the following, we use conclusions of Nøst et al. (2008) to test the validity of our linear model results.

Our model results for the Nordic seas and Arctic Ocean are mainly cyclonic due to the mainly cyclonic wind stress. According to Nøst et al. (2008), we expect these results to be good and well described by the linear model. In the Canadian Basin, the forcing is anticyclonic, giving rise to circulation with shallow water on the left in the model solution. Is this solution realistic? At the slope of the Chukchi Plateau, the model results show a strong and narrow anticyclonic bottom flow (Figs. 6, 8). The Ekman number is given by Ek = *R*/*fH* ≈ 10^{−3}, where we have used *R* ≈ 10^{−4} m s^{−1}, *f* ≈ 10^{−4} s^{−1}, and *H* ≈ 1000 m. The anticyclonic flow is very narrow (about 10 km) in this slope region and its strength is about 0.2 m s^{−1}, which gives a Rossby number Ro = *U*/*f L* ≈ 10^{−1}. For this flow we then have Ro ≫ Ek, and according to Nøst et al. (2008), the linear solutions will not be a good representation of this flow, meaning that the strong anticyclonic flow following the depth contours is probably not realistic in this region.

Near-bottom flow with shallow water on the left is also found in the model results along the entire Norwegian continental slope (Fig. 6). A detailed study of the model results in this region (not shown) reveals that the southward-directed bottom flow appears on the open contours at 400–500-m depths along the entire Norwegian coastline. On the deeper contours, between 600–750 m, a southward-directed bottom flow is, however, found only near the Lofoten Basin. As these contours include a closed contour as well as open contours, the reversal of the flow direction in this region is not an effect solely due to the initialization. Instead, it is a result of the strong localized minimum of *ρ*′_{b} (Fig. 4), which is part of the general deepening of warm saline Atlantic water in the Lofoten Basin (Mauritzen 1996; Orvik 2004). The southward flow is in contradiction to the observed northward bottom flows at corresponding depths in the Svinøy section and in the Faroe–Shetland Channel (Figs. 7, 9. This strong (∼0.3 m s^{−1}), narrow (∼10 km) flow with shallow water to the left fulfills the criteria of Ro ≫ Ek (with Ek ≈ 10^{−3} as above). Therefore, following Nøst et al. (2008), development of cross-slope flow is expected to occur. This suggests that our linear model breaks down somewhere along the Norwegian coast.

Another characteristic of the model results is that the velocities on open contours generally differ more from the observations than calculations on closed contours (Fig. 9). Because the calculations of the bottom flow on open contours depend on the initialization, the absolute values of *υ** _{b}* may be forced to fit with some other regions by changing the region of initialization. However, the large variations of the modeled bottom flow (where the model seems to both underestimate and overestimate the observations along the same open depth contour) are due to the along-slope variations of

*ρ*on open contours [Eq. (19)] and will not be removed by changing the initialization region. This means that initializing the velocity on open contours from current meter data in, for example, the Svinøy section will give a better fit to observations of the shallow slope current off the coast of Norway but, on the other hand, it will cause even larger overestimates of

_{b}

*υ**in the Arctic Ocean and along the east Greenland slope.*

_{b}The too-large variations of *υ** _{b}* occurring on open contours might be caused by uncertainties in the forcing data but more probably by inadequacy in the model dynamics. Ocean dynamics near the continental shelf break are complicated, and both eddies and tides are likely to play a role. This might cause a cross-slope vorticity exchange, which cannot be described by our simplified model. Another region with complicated dynamics is the Faroe Bank Channel, known for its strong overflow of deep waters (Hansen and Østerhus 2000). Even though the values of

*ρ*′

_{b}here are extreme, we have not discussed the dynamics of this area. The reason for this is simply that we do not believe that our simplified dynamical model gives a good description of the circulation in this dynamically complex area.

### b. Barotropic/baroclinic transport interactions and slope–basin exchange

The along-slope variations of the barotropic transport (Fig. 10) are part of an interaction between the barotropic transport *H**υ*_{ρb} and the baroclinic transport *V** _{s}*, as discussed by Walin et al. (2004). This interaction between barotropic and baroclinic flow can be illustrated by combining Eqs. (12) and (16) to get

Here, we ignore terms involving **∇***f* because scalings show that these are negligible compared to transport divergences for north–south length scales on the order of 10^{3} km or smaller. Equation (29) tells us that whenever the bottom density is varying along a sloping topography, a transition between the topographically steered transport *H**υ** _{ρb}* and the baroclinic transport

*V**occurs. Where*

_{s}*H*

*υ*_{ρb}converges (diverges), barotropic (baroclinic) transport will be transformed into baroclinic (barotropic) transport. Because the transformation between barotropic and baroclinic transports is a geostrophic process, it does not involve any vertical motion. The process, therefore, works as a horizontal redistribution of the flow. As the baroclinic transport is not necessarily following topography, the water mass, which is transformed from barotropic transport into a baroclinic transport, might leave the continental slope region and thereby contribute to cross-slope exchange. To determine if the transformation contributes to the slope–basin exchange, we turn to a plot of the baroclinic transport (

*V**) shown in Fig. 11. Comparing Figs. 10 and 11, the regions of cross-slope baroclinic transport mainly agree with the regions of along-slope variations in the barotropic transport*

_{s}*T*. We also see that the cross-slope component of the baroclinic transport extends well into the basin centers in several places, suggesting that the baroclinic/barotropic transport interactions may be an important contributor to the slope–basin exchange.

West of Svalbard, the northward transport of Atlantic water is almost entirely barotropic (Fahrbach et al. 2001), and one may think that this transport will be trapped to the continental slope as it flows around the Arctic Ocean. However, our results show that this transport is largely transformed into baroclinic transport, which is partly directed across the slope (Figs. 10, 11). One example of such a transformation is at the continental slope near St. Anna Trough. Here, large along-slope variations of density are found, where the Barents Sea branch of modified Atlantic water enters the Arctic Ocean and confluences with the Fram Strait branch of Atlantic water (Schauer et al. 1997). The along-slope density gradients in this region give rise to a pronounced convergence of the barotropic transport (Fig. 10). Thus, the barotropic transport is transformed into a baroclinic transport, which near St. Anna Trough is directed from the slope into the basin according to Fig. 11.

Observations show that the magnitude of the East Greenland Current changes along the east Greenland slope, from the Fram Strait to the Denmark Strait, with a maximum flow at about 75°N (Fahrbach et al. 1995; Woodgate et al. 1999). The total southward transport in the Fram Strait is 12–13 Sv (Schauer et al. 2004) compared to about 16 Sv calculated at ∼75° in a cross section extending to approximately the same depth as in the Fram Strait. This transport increase of 3–4 Sv from the Fram Strait to the Greenland Sea corresponds well with the modeled barotropic transport variations of about 3 Sv induced by the variable bottom density (Fig. 10). The link between the observed velocity variations along the East Greenland Current and along-slope bottom density variations has recently been presented by Schlichtholz (2007). He also finds that the along-slope velocity variations are supported by cross-slope baroclinic transports estimated from the annual PHC hydrography.

One of the most pronounced differences between the results presented here and the results of Nøst and Isachsen (2003) is the ACBC in the Canadian Basin, which is clearly weaker in the present results due to the additional velocity component *υ*_{ρb}. When comparing the two model results (with/without *υ*_{ρb}) against several bottom flow measurements along the Beaufort slope (Fig. 9), we see that the inclusion of the dynamical effect of bottom density clearly improves the bottom flow representation in this region. In addition, Aagaard (1989) concludes, from current measurements in the Beaufort and Eurasian Basin slope regions, that the ACBC in the Canadian Basin does not extend as deep as in the Eurasian Basin. This agrees with our results, showing that the barotropic transport on the Beaufort slope is much weaker than the barotropic transport on the Eurasian Basin slope (Fig. 10). According to the simplified dynamics, this transport decrease is an effect of along-slope variations in *ρ*′_{b}, which means that the barotropic transport along the Eurasian Basin slope is transformed into a baroclinic transport before reaching the Beaufort slope.

## 6. Summary and conclusions

We have investigated the large-scale circulation pattern in the Nordic seas and Arctic Ocean by using a simplified model of the large-scale circulation. The model is similar to the model developed by Nøst and Isachsen (2003), but it includes the effect of a variable bottom density. Bottom density variations along the slope will cause an interaction between barotropic and baroclinic flows (Walin et al. 2004; Nilsson et al. 2005). The purpose of our work is to quantify this process in the Nordic seas and Arctic Ocean. To do this we have derived the model equations for a variable Coriolis parameter and forced the model with climatological wind stress and a prescribed climatological density field.

The model is successful in reproducing the main large-scale features of the circulation in the Nordic seas and Arctic Ocean. Density variations along the depth contours play an essential role and lead to large variations of the along-slope barotropic flow field. The along-slope barotropic transport is increasing southward along the east Greenland coast from the Fram Strait and decreases northward along the continental slope off the coast of Svalbard. It has local minimum at the slope near Lofoten and at the slope near the St. Anna Trough. Low densities in the Canadian and Makarov Basins lead to a pronounced reduction of the Arctic Circumpolar Boundary Current in these regions compared to the Eurasian Basin and Nordic seas. The maximum barotropic transport between the 750- and the 2250-m depth contours occurs in the Nordic seas, where it reaches a value of 6.9 Sv. In the Canadian Basin the barotropic transport between the same two depth contours is as low as −2 Sv. This suggests that 9 Sv of the barotropic flow in the Nordic seas is converted to baroclinic transport on its way through the Arctic Ocean. As the baroclinic flow can be directed across the slope, the interaction between barotropic and baroclinic flows may cause a barotropic transport to finally leave the slope, after being converted to a baroclinic flow. The interaction between barotropic and baroclinic flows may therefore be important for the slope–basin exchange in the region.

## Acknowledgments

We wish to thank Greg Holloway for providing the global compilation of current meter data in the Arctic Ocean and Nordic seas, and Svein Østerhus for making available the current meter data around the Faroe Islands and at the Vøring Plateau slope. We also thank Vigdis Tverberg and Johan Nilsson for useful discussions, and thanks to K. A. Orvik and one anonymous reviewer for their comments that helped to improve the article. S. Aaboe was funded by the Norwegian Research Council as part of the Polar Climate Research Program (ProClim).

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### APPENDIX A

#### Divergence of fVQ

We here show that **∇** · ( *f**V** _{Q}*) = 0. Making use of Leibnitz’s rule for differentiation of integrals the sum of

*υ**[Eq. (6)] and*

_{s}

*υ*_{ρb}[Eq. (8)] can be written as

Inserting this expression of *υ** _{s}* +

*υ*_{ρb}in Eq. (12), we get (using integration by parts)

where *q̃* = −½*gH*^{2}(*d**ρ*_{r}/*dH*). Because *q̃* is a function only of *H*, we can define a new variable, *q*, by *dq*/*dH* = *q̃*, and the last term in Eq. (A2) can now be given as (1/*ρ*_{0} *f* )**k** × **∇***q*. From this it is straight forward to express *V** _{Q}* as

with

### APPENDIX B

#### Neglected Terms in the Area-Integrated Balance

The topographic vortex-stretching term in Eq. (15) (first term on the left-hand side of the equation) can be shown to have negligible influence on the area-integrated balance, even though it is important in the local balance [Eq. (15)] (Nøst and Isachsen 2003; Schlichtholz 2002, 2005). When the topographic vortex-stretching term is integrated over the area *A*( *f* /*H*), enclosed by *f* /*H* contours, it becomes zero. This is seen by using Gauss’s theorem twice:

In the Arctic Mediterranean, *f/H* is to a large degree dominated by the topography (see, e.g., Fig. 3 in Isachsen et al. 2003). Therefore, the relative difference between the area *A*(*H*) spanned by closed *H* contours and the area *A*( *f* /*H*) spanned by the corresponding *f* /*H* contours is small. By defining *δA* such that *A*(*H*) = *A*( *f* /*H*) + *δA*, the area-integrated balance of Eq. (15) with respect to closed depth contours becomes

Scalings show that the terms in the depth-integrated vorticity equation [Eq. (15)] are of equal magnitude (Nøst and Isachsen 2003). But in Eq. (B2), the first term on the left-hand side is integrated over a much smaller area than the other terms because *δA* ≪ *A*. Therefore, this term has negligible influence on the integrated balance, and Eq. (B2) then reduces to Eq. (18).

## Footnotes

*Corresponding author address:* Signe Aaboe, Norwegian Polar Institute, Polar Environmental Center, N-9296 Tromsø, Norway. Email: signe.aaboe@npolar.no

^{1}

Actually, *υ*_{0} = (*g*/*ρ*_{0} *f* )*ρ*_{r}**k** × **∇***H* + (1/*ρ*_{0} *f* )**k** × **∇***p*_{b}. Because *ρ _{r}* is a function only of

*H,*we can define a new variable,

*q,*by

*dq/dH*= −

*gρ*so that −(

_{r}*g*/

*ρ*

_{0}

*f*)

*ρ*

_{r}

**k**×

**∇**

*H*can be written as (1/

*ρ*

_{0}

*f*)

**k**×

**∇**

*q*. Therefore,

*p*

_{0}=

*q*+

*p*+

_{b}*C*, where

*C*is an arbitrary constant.

^{2}

Note that for *H* encircling a basin, positive values of *t* mean cyclonic circulation, whereas for a topographic rise or islands (e.g., Jan Mayen Island or the Lomonosov Ridge just north of Greenland) cyclonic circulation is represented by negative *t* values.

^{3}

The selected model result is closest horizontally to the position of the observation while at the same time being vertically within ±500 m of the current meter depth.