Eddy kinetic energy

The ocean circulation has two principal geostrophic com ponents: a quasi-stationary large-scale com ponent reflecting the m ean flow, and a m esoscale eddy com ponent on

spatial scales o f 100-1000 km [Menard, 1983]. It is the variability associated w ith the

latter w hich we aim to observe in the altim eter data and ocean m odel output in this section.

6.3.1 Eddy kinetic energy from altimetry

The m ethod adopted for the estim ation o f eddy kinetic energy from ER S-2 sea surface heights is sim ilar to that o f M enard [1983], w ith additional quality control checks included. This m ethod uses the geostrophic relation to deduce surface eddy velocities from the sea surface height fields, and then estim ates the eddy kinetic energy as the variance o f the velocity, assum ing isotropy o f the eddy field. A sim ilar m ethod was

em ployed by H eyw ood et al. [1994] w ho show ed that the isotropic approxim ation

does not significantly affect the result.

M enard [1983] defined a quantity called the eddy velocity, w hich is taken to be the difference betw een the instantaneous geostrophic com ponent o f surface velocity and the m ean velocity. This can sim ply be com puted from the instantaneous sea surface height anom aly using the geostrophic relation (retaining the notation o f section 6.2.1):

w here is the eddy velocity in the cross-track direction at point j for orbit repeat

num ber i. g is the gravitational acceleration, a n d / = 2Q sin0, the C oriolis param eter (Q is equ al to the rotation rate o f the Earth, and 6 is the latitude). The partial derivative is taken in the along-track direction, and was com puted using least squares fitting to 5 consecutive data points (corresponding to an along-track distance o f 27 km).

T he v elo city variance in the cro ss-track d irectio n, <7j(v^), is then co m p u ted according to:

=

6.4

The eddy kinetic energy at point j , Ej, is then simply given by:

6.5

assuming that the velocity variance is isotropic. Ej was computed at each reference point, y, from two years o f ERS-2 data (cycles 001 to 021), and then gridded on a 0.25° X0.25“ grid. The resulting eddy kinetic energy map can be seen in figure 6.5.

400 320 240 2 / _ 2 c m /s 160

Figure 6.5 Eddy kinetic energy map of the Arctic Ocean computed from cycles 001 to 021 of ERS-2 sea surface height data.

Eddy kinetic energy values for the North Atlantic, as indicated in figure 6.5, are

consistent with the observations from Geosat and E R S -1 presented by Heywood et al.

[1994]. As was the case for the variability calculation, an increase in the background eddy kinetic energy signal on moving from ice-free to ice-covered seas is clearly

visible. As described by Sandwell and Zhang [1989], calculations o f along-track

slopes from altimetry enhances the short wavelength altimeter noise, and so we expect this method to be sensitive to residual noise on the elevation signal in ice-covered regions. Even if we do not trust the num erical values of eddy kinetic energy

com puted using this m ethod, a num ber o f very interesting qualitative features can be isolated.

T he altim etry reveals that eddy activity is generally restricted to the shallow shelf regions o f the A rctic O cean. In the B eaufort Sea and w estern C an ad a B asin, we observe eddy kinetic energies which are considerably higher than the rem ainder o f the relatively low energy A rctic O cean interior. This is consistent w ith the view s o f

M anley and H unkins [1985], A agaard and Carm ack [1994] and P lueddem ann et a l

[1998], deduced from in situ observations of the eddy field structure.

A aga ard and Carm ack [1994] suggest that the eddies are form ed in the m argins o f the A rctic O cean, and provide an im portant m echanism for the transport and m ixing o f

w ater properties in the otherw ise low energy interior. M anley and H unkins [1985]

ob serv e eddy d iam eters o f 10 to 20 km , co n sisten t w ith the lo cal rad iu s o f deform ation, at depths o f betw een 50 and 300 m. W e m ight therefore expect very little surface signature indicating the presence o f these subsurface eddies. They also estim ate that eddies occupy at least a quarter o f the available surface area in the B eaufort Sea, and that they are generated north o f Point Barrow , A laska, as a result o f instability in the eastw ard flow ing A laskan C oastal C urrent. A n o th er regio n o f

significant eddy kinetic energy is the East G reenland shelf. Johannessen et a l [1987]

describe observations o f 14 m esoscale eddies in both deep and shallow w ater betw een 78°N and 81°N. The altim eter also reveals high eddy kinetic energy in this region.

6.3.2 Model eddy kinetic energy and comparisons with altimetry

E stim ates o f m odel eddy kinetic energy w ere calculated from the slopes o f the sea surface height fields to allow for a consistent com parison with the altim eter estim ates.

M cC lean et a l [1997] adopted a sim ilar approach for com paring eddy kinetic energy estim ates from the PO C M and PO P m odels w ith TO PEX /PO SE ID O N results. This involves calculating the sea surface slope at each grid location, using a least squares fit through the sea surface height at the grid location and the two adjacent cells in the x-direction o f the grid. A sim ilar calculation is perform ed in the y-direction, and the tw o slopes are co nverted to surface geostrophic velocities using the g eo strophic equation. T he tw o com ponents o f velocity are then com bined, and their variance calculated. A ssum ing isotropy o f the velocity variances, as we did for the altim eter data, w e arrive at an estim ate o f eddy kinetic energy at each g rid location. The resulting eddy kinetic energy maps on 0.25° x 0.25° grids are shown in figure 6.6.

cm^/s'

Figure 6.6 Eddy kinetic energy maps of the Arctic Ocean as calculated from (a) the OCCAM model (1992-1993), and (b) the NPS model (1993-1994).

From figure 6.6, it is clear that there is considerably more mesoscale energy in the OCCAM model than in the NFS model. Qualitatively however, the results from the two models are quite similar, and reveal that most of the energy in the Arctic resides in the continental shelf regions, with very little energy in the interior o f the ocean. The im portance o f the bottom topography in controlling the current systems within the Arctic is also highlighted.

It is clear by comparing figures 6.5 and 6.6 that the altimeter estimates of eddy kinetic energy in the Arctic Ocean are significantly higher than those o f the models. The general pictures are how ever sim ilar, with high energies predicted in the East Greenland and Eurasian continental shelf regions, and relatively low energies in the central Arctic. Table 6.3 compares the mean eddy kinetic energies from ERS-2 and the two ocean models for the same four regions as table 6.2, and highlights the substantial differences.