Current Meters

I have chosen to sample two current meter sites in the Labrador Sea which were previously studied by Wunsch (1997). Site 91 is in the convecting region and site 89 is near the North Atlantic Current. The two current meters were originally reported by Fu et. al (1982) and Clarke (1996) respectively. I will review their eddy kinetic energy profiles and the partition of energy into vertical dynamical modes.

Site 91
The model's vertical profile of eddy kinetic energy at the gridpoint near site 91 has strongly intensified surface energy rapidly decaying with depth and a mid-depth local maximum of energy at 1500 meters (see Fig. 21). The surface energy is the same order of magnitude as T/P data but only extends to 20 meters depth. This seems to be a product of the superheated surface layer that develops with the restratification of the water column after convection. The mid-depth local maximum in kinetic energy is related to strong event that occurs in March. The mixed layer begins deepening in February and eventually reaches as deep as 2000 meters in late March. Temperature and salinity cross sections show that a mid-depth warm eddy passes across the mooring site in the model . The eddy appears to be shed off the rim current of a $150 km^2$ ``mixed patch'' of intense convection. The model's site 91 is on the southeast edge of this mixed patch. Mid-depth velocity profiles show an enhanced westward flow for 40 days followed by a strong reversal to eastward flow (see Fig. 22). The meridional velocity profile shows a similar although weaker shift from southward to northward velocities at the same time. This is consistent with a cyclonic eddy moving northwest. The eddy acts to smooth the lateral inhomogeneities caused by the deep convection. A previous study (Khatiwala and Visbeck, 2000) has shown that lateral mixing from boundaries to the interior Labrador Sea is extremely effective in the Labrador Sea. The effect of lateral mixing can be seen immediately after convection in the model here.

Because the current meter at site 91 had 4 instruments all below 900 meters depth and a record length of only 207 days, it is not an ideal source of data to make comparisons. In fact, large seasonal changes in stratification and the associated mode structure also occurred with this current meter, and the results in Wunsch, 1997, were severly downweighted. However, the data can still be used to get the general magnitude of energy and the vertical structure at depth. The magnitude of meridional eddy kinetic energy is one to two orders of magnitude too small in the model compared to the observations. A comparison of the mean kinetic energy also reveals that the model is much too quiet. In fact, it was noted earlier in the comparisons with the T/P altimeter that the model's interior Labrador Sea does not have enough background variability. Using the vertical mode structure calculated from Levitus climatology and fitting the observed velocities by the Gauss-Markov theorem, it is possible to extrapolate the shape of the observed $K_{E}$ profile from the four measurements. No confidence should be put into the exact shape of the profile in the upper layers because of the lack of data there and the strongly surface intensified baroclinic modes. The Gauss-Markov results are intrinsically unstable above the top instrument. Mooring 91 is also quite anomalous due to the incredible amounts of mode coupling. Mode coupling acts to decrease the eddy kinetic energy near the surface. Mode-coupled surface energy is 200 times smaller than energy calculated under the assumption of temporally uncorrelated mode coefficients. However, it is interesting to note a mid-depth relative maximum of eddy kinetic energy at 2200 meters depth in the extrapolated profile. The feature is robust with different 'a priori' statistics specified in the Gauss-Markov problem. The maximum has neither the right positioning nor the right vertical extent, however, and is not explicitly resolved by the current meter instruments. The extrapolated profile can not prove that the model's profile is correct, but it shows that the model's vertical structure is reasonable with the information we now have. The actual partition of energy into vertical modes will be discussed in conjunction with mooring 89 below.

Site 89
The model's vertical profile of kinetic energy at site 89 also has a surface intensified region decaying with depth to a relatively constant background energy at mid-depth (see Fig. 23). The eddy kinetic energy becomes unexpectedly energetic in the 500 meter layer above the bottom. Site 89 is not near any topographic features so a bottom trapped wave is not reasonable in this area. The model gridpoints between the shelfbreak and site 89 do not show any bottom intensification. Velocity timeseries show that the bottom intensified events continue throughout the year. In the general model domain, bottom intensification occurs in a few patchy spots of the interior Labrador Sea (see Fig. 24). Model site 89 is located in a $50 km^2$ patch with bottom intensified eddy kinetic energy. The reason for this bottom intensification remains obscure but it has been reported before in models which use bottom friction such as this one. The southwest corner of the model domain, including the North Atlantic Current, is dominated by eddy kinetic energies which are very similar between 1500-3000 meters. This should be expected in a region of mostly barotropic motion, as reported by Wunsch, 1997. The model's Labrador rim current has typically much larger energies at 1500 meters than 3000 meters. This may be consistent with a current that is known to be baroclinically unstable after the convective season. The model at site 89 captures roughly half the magnitude of eddy kinetic energy observed. Observations from mooring 89 also verify that large energies exist at great depth, and some bottom intensified motions actually occur. However, mooring 89 experienced large vertical fluctuations in the instruments during strong barotropic events and should only be considered a preliminary comparison.

To calculate the quantitative partition of energy, the density structure from Levitus climatology is used for the stratification profile. Levitus data primarily reflects the summer season in the Labrador Sea, and is known to be of poor quality. Other attempts to use the model's time-averaged stratification at the mooring sites yield results that are within 10 percent of the partitioning presented here. Work is not yet completed on a seasonally-varying mode structure and the consequent energy partition. 30 vertical levels of model velocity were used; the surface intensified velocities at 7.5 and 22.5 meters did not fit the mode structure hypothesis. The surface velocities are large enough that nonlinear terms must be important and the geostrophic relation breaks down. With 30 vertical levels being used to compute the first five vertical modes, the system is overdetermined and results are insensitive to the a priori specifications of the Gauss-Markov method. The first five modes consistently capture over 95 percent of the total energy, and the largest noise residuals are on the order of 0.5 cm/s. One exeption is the fit of zonal velocity at model site 91 between 3000-3400 meters. Only 50 percent of the energy is captured in the modal fitting, but this is because the signal energy level, $0.25 cm^2/ s^2$, is simply so small. These noise levels technically break our a priori noise assumption because the model output does not include any instrumental error. I believe that the time variability of the modal shapes primarily contributes to this noise, although the signal to noise ratio is very high and our results still tell a coherant picture of the energy partition. In the model, the total energy is overwhelmingly barotropic (see Table 1). The two sample model sites are roughly 70-80 percent barotropic, and 10 percent of the energy resides in both the 1st and 2nd baroclinic modes. It is reassuring to see that little energy is left in the higher baroclinic modes. Extrapolation to the surface yields different results for model sites 89 and 91. The surface expression at site 91 in the interior Labrador Sea is predominantly due to the 2nd baroclinic mode; surface kinetic energy at site 89 near the North Atlantic Current is mostly in the 1st baroclinic mode. It is typical for the surface kinetic energy to reflect changes in the main thermocline height. This result implies that the surface velocity in the interior Labrador Sea depends upon the movement of the highly stratified regions both above and below the homogeneous layer of Labrador Sea Water. Previous results from Wunsch, 1997, also conclude that the bulk of surface energy in the Labrador Sea is not in the 1st baroclinic mode, unlike most of the world ocean. In conclusion, it is encouraging to see that the vertical structure of the model is very barotropic, as would be expected in the high latitudes.

#		Lat	Lon	D	M	u0	u1	v0	v1	uF0	uF1	uF2	vF0	vF1	vF2
91	Mod	57.0	-51.6	360	30	76	14	67	11	21	12	59	11	6	67
91	Obs	57.0	-51.6	207	4	57	14	49	19	9	7	-	7	9	-
89	Mod	51.1	-44.6	360	30	83	15	74	24	36	50	10	25	64	7
89	Obs	51.1	-44.6	259	3	75	17	78	13	13	23	-	41	24	-

Table 1: Partition of energy into vertical modes. For each mooring, there is (Mod) for model output; (Obs) for results of Wunsch, 1997, from observations; (D) for number of days of the record length; (M) for number of depths with instruments; (h) the water depth; (u0,u1) the percent of the total zonal component of energy in the barotropic and 1st baroclinic modes; (v0,v1) total energy percentages in the meridional component; (uF0,uF1,uF2) the percentages of surface kinetic energy in the barotropic through 2nd baroclinic modes; (vF0,vF1,vF2) the percentages of surface kinetic energy in the corresponding meridional components of the vertical modes.