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10.20.2012: Comparison of time and space spectrum in potential density and horizontal velocity

Figs. 1 and 2 show the temporal (plain) and spatial (dashed) averaged spectra of potential density and horizontal velocity in the HYCOM model, respectively. Spectral slopes appear to be conserved between time and space for potential density (Fig. 1) but this is less clear for the horizontal velocity field (Fig. 2). In the latter case, it may be because of the shallowing of the time spectra toward high frequency. This shallowing occurs because of a wave field present in velocity but not in density. The wave field has a period of about 5 days, a relatively large scale (1-2 deg.), is found mostly in the upper 500 m but its horizontal pattern is not well structure in space (I don’t see a well defined horizontal periodic structure associated with this field). The temporal and vertical structure of the wave field in U is presented in Fig. 3 and shows the signal in the upper 500 m. Interestingly, the phase is propagating downward suggesting its energy is propagating upward. I speculate that this wave field may arise directly from wind forcing but it may not be realistic as we don’t see this peak in the spectrum of the horizontal velocity field observed at WHOTS (not shown).

The two figures, however, are consistent with Capet et al. (2008)’s results and seem consistent with the interpretation that dynamics, with a slope of -2, are submesoscale within the surface mixed layer (SML) and, with a slope of -3, interior quasi-geostrophic below the SML.


Figure 1: Temporal (plain) and spatial (dashed) averaged spectra of potential density in the HYCOM model at 10 m depth (red) and 200 m depth (blue). The temporal spectrum has been obtained from 8 non-overlapping 100-day long segments from 8 locations around WHOTS that are at least 2° apart (dof=171). The spatial spectrum has been obtained from 27 zonal sections at two different latitudes (22.5°N and 24.5°N); these segments are 30-day apart in time (the time scale at which the lag auto-correlation of the horizontal velocity becomes zero) and are thus considered independent. All segments are detrended in space or time and a Hanning window is applied to each of them before Fourier decomposition. 95% confidence interval for the temporal or spatial spectra have been computed following von Storch and Zwiers (1999) and are shown with the vertical black bars in the lower left corner. The slanted plain and dashed black lines indicate -2 and -3 slopes, respectively.


Figure 2: Same as Fig.1 but for horizontal velocity instead.


Figure 3: Zonal velocity at 201°E and 22.5°N: (upper) full and (lower) high-passed (T<14 days) filtered component.


Capet, X., et al., 2008: Mesoscale to submesoscale transition i the California current system. Part I: Flow structure, eddy flux, and observational tests. J/ Phys. Ocean., 38, 29–43. doi:10.1175/2007JPO3671.1