# 01.21.11: First analysis of HOT SADCP data¶

I show here a first analysis of the HOT SADCP data. I selected data from the 300-kHz instrument on the Kilo Moana from 2005 to 2007 (the latest most finalized data). Data north of 21.75°N taken during a transit (ship velocity larger than 5 m/s) of at least 75 km have selected (Fig. 1, left). The data cover the whole annual cycle (Fig. 1, right).

Figure 1: (left) Selected tracks and (right) Timing of the data versus latitude over the annual cycle (I still do not know how to put data labels with matplotlib).

In Fig. 2, I show the averaged power density spectrum (PDS) computed at every depth between 0 and 100 m for all cruises and the average over all cruises. In Fig. 3, I show the PDS of the vertically-averaged velocity field over 0-100 m and the average over all cruises. In Fig. 4, I compare the PDS from different depth ranges and different types.

Figure 2: PDS of (left) U and (right) V. The PDS are the averaged PDS computed at every depth between 0 and 100 m for all cruises (red) and the average over all cruises (black).

Figure 3: PDS of (left) U and (right) V. The PDS are that of the vertically averaged field between 0 and 100 m. Individual cruises (red) and average over all cruises (blue).

Figure 4: PDS of (a) u and (b) v for different depth ranges. Plain lines are the averaged PDS computed at every depth within the depth range. The dash lines are the PDS of the velocity averaged within that depth range.

The slopes for the various categories are listed in Tab. 1:

U V
A / 0-100 m -2.38 -2.07
A / 0-50 m -2.64 -2.30
A / 50-100 m -2.13 -1.85
B / 0-100 m -1.96 -1.63
B / 0-50 m -2.49 -2.12
B / 50-100 m -1.89 -1.63
** Table 1:** Slopes of the spectrum averaged all cruises and for different depth ranges. A: the spectrum are calculated at every depth then averaged out; B: the spectra are from the vertically-averaged velocity field. Slopes were calculated by fitting a line to the spectrum between 1e-2 and 4e-1 cpkm.

The spectrum of the zonal velocity is always steeper than that of the meridional velocity, suggesting that there is more energy at small scales in V than in U. The spectra averaged with depth tend also to be steeper than the spectra of the vertically-averaged velocity. The overall average slope is -2.09 ± 0.3. This is larger than the -5/3 slope of SQG theory but flatter than the -3/-4 slope of QG theory.

In Figs. 5 and 6, I show statistics for the Rossby number, defined as the ratio of the along-track gradient of the cross-track velocity over the Coriolis parameter. For each, R is computed from the vertically-averaged velocity between 0 and 100 m and further smoothed with a running mean of 5 km before taking the gradient. Fig. 5 shows the mean of the absolute value of R for each section and Fig. 6 the mean of squared R. The magnitude, but not the temporal evolution, of the statistics changes with shorter or longer smoothing and with different vertical averages.

Figure 5: Mean of the absolute value of R.

Figure 6: Squared R.

Besides some outliers, you could almost start to see some seasonality in the signal (annual and/or semi-annual). Unfortunately, there is no section available in summer and at the beginning of the year when R could be weak given its surrounding values.

This calls for getting more data. I will try next to add the data from the broad-band 38-kHz.

Figs. 1 to 3 and Figs. 5 and 6 were produced with rel_vort_HOT_SADCP.py and Fig. 4 with fig5_012111.py both in RESEARCH/PROJECTS/MARINE_BIOLOGY/SUBMESOSCALE_PROCESSES/SADCP/analysis on ipu1.