Tratamientos Urbanísticos

Any time series in the ocean reveals barotropic variability related to astronomical constituents (tides). Tides can be expressed as the sum of tidal constituents. An expression can be used to build a sum of harmonic constituents that represent a time series and can be written individually as follows:

(2.2)

where A is the amplitude of the constituent, G is the phase lag, w is the angular speed and V the astronomical argument composed of combination of s (Moon's mean longitude), h (Sun's mean longitude), p (longitude of Moon's perigee), N (longitude of the Moon's ascending node) and p' (longitude of Sun's perigee). Time (t) used is elapsed time in hours. The astronomical argument is essentially to combine the factors determining phase to provide parameterization values on the day of the tidal observation (Cartwright, 1985). TIRA software (Bell et al, 2000) has been used to find tidal constituents by harmonic analysis. TIRA is basically used to study tidal constituents in sea level measurements; here it is used for current (analysed as components, separately North-South and East-West) and temperature time series.

In order to apply harmonic analysis on the time series a set of components (Z0, MSF, 2Q1, O1, K1, OO1,MU2, M2, S2, M3, M4, MS4, S4, M6, 2MS6 and 2SM6) were proposed (input file from TIRA software proposed for time series with length around 15 days). Other components were related to these in the analysis (PI1, P1, S1, PSI1 and PHI1 to K1; N2, NU2 and L2 to M2; T2 and K2 to S2; Q1 and RHO1 to O1; SIG1 to 2Q1, J1 to OO1, 2N2 to MU2). The time series length was approximately 21 days. Components with a strong signal, and residuals (time series without the contribution of tidal components solved for), were used to interpret results.

33 a)

b)

Figure 2.9: TIRA analysis results for M2 astronomical constituent. Each set of four panels shows the ellipse properties: major axis (black line, cm/s), minor axis (red line, cm/s), major axis orientation (blue line, degrees relative to the North) and rotation (green line, anticlockwise if 180º > rotation angle [p2-p1] > 0º; black line shows 180º). Panels refer to a) A1, b) A3, c) A4 and d) A5.

34 c)

d)

Figure 2.9: TIRA analysis results for M2 astronomical constituent. Each set of four panels shows the ellipse properties: major axis (black line, cm/s), minor axis (red line, cm/s), major axis orientation (blue line, degrees relative to the North) and rotation (green line, anticlockwise if 180º > rotation angle [p2-p1] > 0º; black line shows 180º). Panels refer to a) A1, b) A3, c) A4 and d) A5.

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Results from the tidal harmonic analysis are summarised here. M2 is the strongest in all series, but not as large at A5 as at the other sites, as shown in Figure 2.9. The major axis magnitude appears to be slightly different (1-3 cm/s) between the top and bottom records (except at A1), however major axis orientation is observed to be uniform in all profiles. M2 orientation is observed to be East-West (except at A1 where it is to the North-East), and with clockwise rotation. The residual from the tidal analysis was found still to contain some tidal signal and remained energetic (reaching 10 cm/s).

A low pass filter is applied, which passes low frequency signals and reduces the amplitude of signals with frequencies higher than the cutoff frequency ( hrs) (Emery and Thomson, 2001). The filter is a Fourier transform with a finite number of coefficients and specific interval frequency ( ), where components with amplitudes from frequencies bigger than the cutoff frequency can be eliminated by averaging them. Filter analysis can be used to build a filter to pass a specific frequency band or bands. Low pass filtering using Fourier transforms was originally proposed by Lanczos (1956).

Residuals from low pass filtering of the currents confirm that the MOW is flowing mainly to the North-West (Figure 2.10). At A1, the residual is towards the West. In all records, the current measured over the depth range has a uniform current profile direction slightly changing near the bottom. Also currents increase with water depth and are less close to the bottom. The filtered series reveal that the record starts with the ending of a strong signal of MOW (April 19th-20th). Three days later (April 23th-25th) the strongest MOW signal occurs, sooner on records from A4 and A5 (more clearly on the bottom records). The last MOW signal is detected around April 30th with a long duration (around 9 days). Strong MOW signal have a time lag of around one day between sites A3 to A1 and A5 to A4. Strong MOW events seem to start early on deeper (A4-A5) records, however high temperature on records seems to pass (Figure 2.10) site A1. Also, not all events of high temperature are happening during strong current events at all sites.

36 a)

b)

Figure 2.10 Residuals (cm/s) from low pass filter applied to original ADCP time series are plotted as arrows at nominal depth above seabed (y-axis). Filter removes any signal below 24 hours period (i.e. high frequencies). A set of panels show nominal depths (metres) above seabed on the y-axes and each site has used different scale due to strength of the signal. Panels refer to a) A1, b) A3, c) A4 and d) A5.

37 c) d)

Figure 2.10 Residuals (cm/s) from low pass filter applied to original ADCP time series are plotted as arrows at nominal depth above seabed (y-axis). Filter removes any signal below 24 hours period (i.e. high frequencies). A set of panels show nominal depths (metres) above seabed on the y-axes and each site has used different scale due to strength of the signal. Panels refer to a) A1, b) A3, c) A4 and d) A5.

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