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The Iceland-Scotland section runs south from Iceland, southeast across the Iceland Basin to the Rockall-Hatton Plateau, and continues across Rockall Trough to the coast of Scotland (see Figures 3.1 and 3.2b). The entire section is south of the Greenland-Scotland Ridge and so lies within the northeast North Atlantic rather than the Nordic Seas. An estimated level of no motion at 1400!m was suggested by Saunders (2001) and this is used as the initial reference for the geostrophic

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velocities. A first guess of the initial velocity field is derived by applying the LADCP derived reference velocities as a barotropic offset to these geostrophic velocities, following the procedure employed for the other sections.

The initial fluxes derived from the LADCP data indicated there was an imbalance within the initial circulation. The cumulative volume transports in the upper part of the water column suggest a 2!Sv inflow of Atlantic Waters across the section into the Nordic Seas (dashed black line in Figure 4.9). This was confined mainly to the Iceland Basin, and is low compared to the widely accepted values of 6.7!-!7.4!Sv (Hansen and Østerhus, 2000). Initial runs of the inverse also revealed imbalances with extremely low heat transports across the Greenland-Scotland Ridge and inconsistent results particularly when salinity conservation was required within the south box in the layers relating to the Atlantic inflow. In effect, the NAtlC and Atlantic inflow was ‘missing’ from the initial circulation.

To find the cause of the problem the hydrographic properties along the section are examined together with the alternative velocity field provided by the shipboard ADCP data. During this section an alternative estimate of the direct velocities in the upper water column was made by shipboard ADCP. This provided continuous coverage of the velocity field in the upper 500!m, with high spatial (1!–!2!km) and temporal resolution (2 minute ensembles), whereas the LADCP data provided only on-station measurements. The cumulative transports over the upper 500!m of the water column calculated from the average ADCP currents (solid black line in Figure 4.9) show the inflow of Atlantic Water to be confined to the Rockall Trough to the east of the Rockall-Hatton plateau. Turning to the hydrographic properties, the position of the warm and saline NAtlW can be seen to the right of the contoured salinity plot (Figure 5.7b), within the upper waters of the Rockall Trough. This evidence points to the major pathway of the inflow to the Nordic Seas at the time of the section being via the Rockall Trough.

Although the station spacing was such that a reasonable representation of the hydrographic properties along the section can be described, the LADCP data did not adequately capture the circulation of the upper part of the water column. One probable reason for this was that the length scales of variability in the water mass properties are greater than those for variability in the currents. To adjust the initial field to give a reasonable circulation, a further barotropic correction of 0.5!cms-1

directed into the Nordic Seas is applied to station pairs east of the Rockall-Hatton plateau. This adjustment ensured that the transports within the upper part of the water column are comparable to those suggested by the shipboard ADCP data (solid black line in Figure 4.9). The final input field for the inverse model was thus the geostrophic velocity field with a level of no motion at 1400m, with a northwards barotropic correction of 0.5!cms-1 _{to station pairs east of the Rockall-Hatton}

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The circulation of the sub-polar gyre is usually such that the major pathway for the inflow of Atlantic Water to the Nordic Seas is via the Iceland Basin to the west of the Rockall-Hatton plateau (Orvik and Niiler, 2002). However, the data from this section show the inflow to be confined to the Rockall trough during September 1999. This is known to be a second pathway by which warm North Atlantic upper water reaches the Norwegian Sea (Holliday et al., 2000). Although it is unusual for the entire inflow to be via this pathway, considerable variability in this Rockall input has been noted on inter-annual to decadal timescales. Holliday et al. (2000) and White and Heywood (1995) showed how in winter 1993/1994 the “NAtlC zone” moved from the Iceland Basin and entered the Rockall Trough.

The unusual circulation described by the hydrographic data can be attributed to the anomalous wind field in September 1999, at the time of the Iceland-Scotland section. This wind field influenced the circulation of the upper waters of the Iceland Basin so there was no net northwards flow west of the Rockall-Hatton Plateau. Figure 4.10 is a map of the long-term climatological mean sea level pressure for September from NCEP reanalysis (National Center for Environmental Prediction, US National Oceanographic and Atmospheric Administration). It shows the prevailing atmospheric conditions, with westerly winds and an area of low pressure to the southwest of Iceland and an area of high pressure off the west coast of Spain. Figures 4.11 and 4.12 show the mean sea level pressure for September 1999, and the anomaly in sea level pressure for September 1999 from the long term mean (Septembers 1968!-!1996), respectively. These figures show how in September 1999, the region of low pressure had shifted southeast from its mean position and was situated directly over the Rockall Trough region. Figure 4.12 indicates that the range of the anomaly in sea level pressure was greater than the range of the climatological mean for the entire region. Regions of low pressure give rise to cyclonic winds in the northern hemisphere such that the Ekman transport (circulation of the wind-driven layer of the upper ocean) causes divergence of the upper waters and upwelling of the underlying waters. The position of the area of low pressure in September 1999 was such that Ekman pumping caused northward movement of waters in the Rockall Trough region, manifested in the transport of warm Atlantic Waters into the Nordic Seas via the North Atlantic Current. This shift in the atmospheric conditions of the sub-polar gyre forced the northwards flow of the NAtlW to the east from the Iceland Basin into the Rockall Trough.

4.6

The Box Inverse Method

Inverse methods encompass a wide range of statistical techniques which combine observations with dynamical information to estimate unknown features of the ocean circulation (McIntosh and Rintoul, 1997). They have been used to address the classical problem of physical oceanography; the determination of a reference level velocity (which must be added to the thermal wind velocity to give the absolute velocity) (Wunsch, 1978).

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The ‘box inverse’ method (the Wunsch formulation of the inverse problem) has become a commonly used tool for the anaylsis of oceanographic data. In this thesis, this technique is applied to hydrographic data to compute the unknown reference velocities. These are then applied as a barotropic correction to the initial velocity field to give an improved estimate of the circulation. The method itself may be adapted to address a variety of unknown aspects of the circulation (e.g. Naveira Garabato et al., 2002; Sloyan and Rintoul, 2000), and its strength is essentially that any prior information can be incorporated as a constraint.

The method may be applied to a closed circuit (which may include coastline) of station pairs about a volume of ocean divided into horizontal layers defined by pressure, density, potential temperature or salinity. The system is set up as a set of linear simultaneous equations and suitable constraints are applied by requiring conservation of property and volume fluxes in some or all layers (Wunsch, 1996). In particular, it can be ensured that flow through a closed volume is reasonable by requiring zero net mass flux (Hall and Bryden, 1982).

The method assumes that the ocean is in geostrophic balance and that mass and salt are conserved (Bacon, 1996; Wunsch and Grant, 1982). It also assumes that instantaneous hydrographic sections can be used to represent the long-term mean flows. These assumptions are the major limitations or weaknesses of the method. However, if the reality of the oceanic system is to be understood, there is a responsibility to seek the best possible interpretation of the data.

The solution is used to provide valuable information about the reference velocity. If a highly divergent 'first guess' is chosen (such as zero velocity at the bottom), the solution will be large. If a more responsible initial state is used (such that the 'first guess' is as nearly non-divergent as possible) the solution is typically small. There are many possible solutions to an underdetermined problem such as this. To find a solution that departs minimally from the assumed initial state, singular value decomposition (SVD) may be used (Lanczos, 1961). This is a cost function based method where a small solution is ‘good’, and a large solution ‘bad’. It seeks a least squares fit where the ‘best’ answer is the minimum cost function.

If more than one constraint is used it is necessary to truncate the SVD such that the preferred solution degree is selected (e.g. McDonagh and King, 2002). As the solution degree increases the flow field becomes less divergent (according to the constraints being applied by the inversion) at the cost of becoming increasingly noisy. If the full rank solution is chosen a large change in the solution may be forced by small changes in noise. If all constraints are independent (as, for example, when the water column is subdivided into a small number of layers representing distinct water masses) then all of the few resulting eigenvalues contribute to the solution. If, however, there is an overlap of information then the solution will become unreasonable after a certain solution degree. When both salt and volume are conserved, for example, then there is inherent redundancy

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since these conditions are not independent. A variety of approaches may be employed for the selection of the best solution degree (see section 5.6.2).