The accurate calculation of fluxes and transports require an absolute velocity field. Volume flux, for example, is calculated as the area integral of velocity across each section. Since the velocity shear calculable from hydrographic data represents only the relative velocity between two depths, the absolute geostrophic velocity profile for any station pair is defined as the sum of the geostrophic and reference velocities. This reference velocity is an offset derived either from some known velocity at some known depth or an estimate of the barotropic (depth averaged) velocity. The classical technique is to use a level of no motion defining the velocity to be zero at some depth as suggested by water mass boundaries or the absence of velocity shear. An alternative technique is the use of direct velocity measurements (from current meters, for example) to reference the flow. These various methods inevitably result in different absolute geostrophic velocity fields (Pickart and Lindstrom, 1993).
Traditional methods of referencing geostrophic velocities based upon water mass distributions do not always accurately represent the velocity field (Donohue et al., 2000), since the density structure alone is insufficient to fully describe the ocean circulation. The circulation of the Nordic Seas is strongly influenced by topography (Chapter 2), and much of the flow is concentrated over slopes with a strong barotropic component. In many regions, levels of no motion either do not exist, or there is no objective way of determining them (Hansen and Østerhus, 2000).
LADCP measurements made on hydrographic stations have successfully been used as a referencing method (Beal and Bryden, 1997; Cunningham et al., 2003; Naveira Garabato et al., 2002). The question remains as to whether direct, instantaneous velocities are typical of the long-term mean. However, LADCP measurements can identify robust features of the circulation that may not be
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apparent from the hydrographic data alone. For example, using full-depth LADCP profiles Beal and Bryden (1999) discovered that the Agulhas Current velocity signal extends to the sea-bed and that there exists an equatorward Agulhas Undercurrent. These features had never been inferred from hydrographic measurements alone, and since they were found in three different LADCP velocity sections they are considered to form part of the long term mean circulation (Donohue et al., 2000). The direct velocity field can be rather difficult to interpret since it is a ‘snapshot’ of the currents, and an exact agreement between the direct (LADCP) and geostrophic velocity fields cannot be expected (Joyce et al., 2001). Firstly, actual LADCP velocities will include ageostrophic components throughout the water column due to inertial oscillations, internal waves, and internal tides. Secondly, the station pair LADCP profiles are the average of two sets of instantaneous velocity measurements. Thirdly, there are errors associated both with the measurement of LADCP data (see section 3.6.2), and with the calculation of the geostrophic velocity field (see section 3.5 for accuracy of the hydrographic data).
There is, as yet, no consensus on the best technique by which LADCP data can be used to reference geostrophic velocities. With the data available for this thesis, the alternatives are:
(i) use of a near-bottom velocity derived from BT data (ii) use of a near-bottom velocity derived from WT data (iii) use of an offset derived from the full depth WT data.
The WT offset, together with the WT and BT near-bottom velocities, provide three estimates of the reference velocity. Over the full dataset, the differences between the WT and BT near-bottom velocities (Figure 4.7) have a mean of 0.45!cm!s-1, and an RMS deviation of 2.5!cm!s-1. The mean
difference is not significantly different from zero at the 98% confidence limit. The normal probability plot shows that, excepting outliers greater than about 4!cm!s-1, the differences between
estimates follow a normal (random) distribution. However,
(i) on some station pairs there are large differences between the LADCP derived estimates of the reference velocity;
(ii) the shears of the geostrophic and WT profiles differ greatly in some regions;
(iii) over steep topography station pairs have large differences in bottom depth of their constituent stations leading to uncertainty in the interpolation of the WT and BT near- bottom velocities on station pair positions.
For this thesis, alternative initial velocity fields were created using a ‘best guess’ of the reference velocity (a subjective choice between the LADCP alternatives and no adjustment). For this, a subjective selection of reference velocity was made on a station by station basis. The choice was
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made by inspection of the WT and BT profiles for each station in the pair, together with the station pair geostrophic profile (section 4.4). An exact agreement between the LADCP and geostrophic velocity fields cannot be expected (Joyce et al., 2001). Firstly, actual LADCP velocities include ageostrophic components and secondly, the station pair LADCP profiles are an average of two sets of instantaneous velocity measurements. For each station pair, a constant velocity offset was sought such that when added to the geostrophic estimate, the difference between the two profiles over some depth range is minimised. Hence, although BT data is more accurate than WT data over their common depth range (section 3.6.2) it was often desirable to use the full depth WT data over the full duration of the cast, rather than the shorter BT record. The WT offset was used here on the majority of stations, although the BT near-bottom velocity was selected for some shallow water station pairs. For shallow station pairs with particularly noisy LADCP/CTD comparisons (due to large ageostrophic effects), and for those station pairs where there was large divergence in the shear between the WT and geostrophic profiles, no adjustment was made.
The initial geostrophic velocity field was referenced to zero velocity at the bottom (see section 4.5.2 for the Iceland-Scotland section). Over much of the Nordic Seas there are strong barotropic currents (Cisewski et al., 2003) with significant bottom velocities, hence in many regions a zero bottom velocity is an unreasonable assumption. The LADCP derived reference velocity for each station pair was then applied as a barotropic offset to the full depth geostrophic profile creating the velocity fields used in the initial flux calculations (section 5.5). For station pairs without LADCP data, the reference velocity was set to the average of the LADCP derived reference velocities for the adjacent station pairs. The reference velocity was set to zero for those station pairs where it was decided to make no adjustment. Across the Barents Sea Opening, O’Dwyer et al. (2001) use vertically averaged ADCP velocities to study the velocity field. Since the thermal wind shear is weak, these can also be taken as an initial estimate of near-bottom reference velocities and were used in this work to reference the geostrophic field due to the absence of LADCP data.
To give an example of the alternative velocity fields created, Figure 4.8 illustrates station pair 81 at 68.1°N 6.5°E in the Norwegian Sea (Table 3.1). The geostrophic profile (referenced to zero at the bottom), full depth WT profile, and the geostrophic profiles adjusted to the WT LADCP are shown. On this station pair the shears of the geostrophic and full-depth WT profiles are well matched.