Análisis “La Chimioterapia”

4.2

Detection and identification of Rossby waves

The Q-GCM is run for 200 model years at two central latitudes φ = 30◦ and 40◦, for the parameters listed in Table 3.1. Oceanic and atmospheric variables are saved every 10 days in order to have a dense temporal sampling, useful for the statistical techniques used later on in the study and enabling direct comparisons with satellite measurements such as TOPEX/Poseidon, which provides observations approxim- ately every 10 days.

We are then ready to identify the propagation of the oceanic Rossby waves gen- erated by the unsteady winds in the model (Fig.3.2) and their basic properties. We begin by plotting Hovmöller diagrams (time-longitude plots at a given meridional position in the ocean basin domain) of the second interface height (OCH2), cor- responding to thermocline displacements. The Hovmöller shown are for the north subtropical gyre, for correspondence with the real oceans at these latitudes; never- theless, they show similar patterns at different locations.

As we are interested in westward propagating waves, we apply a westward filter to the data (Cipollini et al., 2000), the results of which are shown in Fig.4.1 for a particular time interval. Here, clear signals of crests and troughs are visible with a strong zonal variation in both amplitude and propagating speed. For comparison purposes, we also plotted the results from a previous run, with the same character- istics, at φ = 20◦. By following crests we can estimate an approximate velocity of the dominant signals, and a simple inspection of the diagrams reveals the theoret- ical increase in phase speed as we move towards lower latitudes. With this crude estimation, at φ = 30◦ the phase speed is around 6.5 cm/s and at φ = 40◦ around 5 cm/s. These are relatively high phase speeds since in the simulations our Rossby radii give us velocities of 5.2 and 2.9 cm/s at 30◦ and 40◦ respectively for the first baroclinic Rossby wave mode.

The high phase speeds identified seem to agree with some observations, for in- stance Osychny and Cornillon (2004), who find differences in wave propagation stronger at higher latitudes. Hovmöller plots of SST anomalies reveal similar results for all central latitudes.

Another fundamental feature in Fig.4.1 is the apparent breaking and instability of waves, which is stronger as we move away from the Equator. In fact, at lower latitudes crests and troughs are very well defined and consistent throughout their propagation in single beams. However, as we increase the central latitudes in our simulations, faster waves start to appear, generated from an original “mother wave”, breaking and destroying their source as they get stronger with latitude.

4.2 Detection and identification of Rossby waves 54

Figure 4.1: Hovmöller plots of the second interface heights OCH2 (in meters), representative of the thermocline displacements, for three different central latitudes (φ = 20o_,30o_,40o_{). Note the increasing breaking of the waves as the latitude in-} creases.

(2004) in which Rossby waves are subject to a latitude-dependent baroclinic in- stability, resulting in faster barotropic Rossby waves. In fact, a time series of the two interface heights in a point in the western side of the basin where these faster waves are found, reveals the barotropicity of the signal, with interface height dis- placements travelling with a barotropic vertical structure, suggesting that we are in presence of the LaCasce-Pedlosky’s instability mechanism.

A complementary and more accurate identification of the spectral characteristics of the Rossby waves identified is achieved through a Fast Fourier Transform (FFT) of the westward-filtered data, resulting in frequency-wavenumber spectra. To this purpose we applied a temporal band-pass filter to the data between 1 and 5 years at every spatial location in order to suppress the high frequencies and the decadal- interdecadal signals.

The FFT analysis plotted in Fig.4.2 reveals Rossby waves propagating much faster than the unperturbed (dashed lines) and the perturbed dispersion relation (solid lines) predict, with mean peaks showing phase speeds around twice the un-

4.2 Detection and identification of Rossby waves 55 −20 0 2 4 6 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Total fr equ en c y [yrs −1 ] −2 0 2 4 6 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 East −2 0 2 4 6 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 West wavenumber [10-4 _km-1_] −20 0 2 4 6 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Total fr equ en c y [yrs −1 ] −2 0 2 4 6 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 West wavenumber [10-4 _km-1_] −2 0 2 4 6 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 East

Figure 4.2: Frequency-wavenumber spectra of OCH2 anomalies at φ = 30◦ (top panels) and φ = 40◦ (bottom panels) for the entire basin (first), the western side (second) and the eastern side (third panels). Magnitude is normalised by its max- imum value for each case. The broken line represents the theoretical dispersion relation at the two central latitudes computed from the theoretical dispersion relation with the model’s Rossby radii. The solid lines are the computed perturbed dispersion relation with the inclusion of a zonal mean flow (See Appendix B). The mean flow speed-up is about 1.2 for typical examples, close to the suggested value of 1.4 by de Szoeke and Chelton (1999).

4.2 Detection and identification of Rossby waves 56

perturbed values at both central latitudes. Here, we will refer to “perturbed solution” to the dispersion relation computed with the inclusion of a zonal mean flow while the “unperturbed solution” correspond to the classical linear dispersion relation (For computations of perturbed solutions see Appendix B. The mean flow computed at the location A in Fig.B.1, typical for the latitudes considered, correspond to the solid line in Fig.4.2 ). In our 3-layer system we found only small variations in the dispersion relation when including the model zonal mean flows. Following the theory of de Szoeke and Chelton (1999), and making use of our density jumps and mean layer depths, we should reach a speed-up of about 1.4. However, in the calculations given in Appendix B, the maximum speed-up was found to be of around 1.22 and this corresponds to the solid lines in Fig.4.2.

As we move polewards, more and more high-frequency waves appear in the west- ern part of the basin, indicating the generation of fast barotropic waves probably due to baroclinic instability processes. For the case at φ= 30◦ (upper panels of Fig.4.2) we find wave speeds ranging from 6 to 9 cm/s, all of them much higher than the unperturbed and perturbed theory would predict. The main peak in the spectra has a period, P, of about 2.5 yr and is shared by the total, western and eastern side spectrum. Another peak, with a period of about 1.5 yr and speed of 9-9.5 cm/s, is present only in the spectrum of the western side of the basin, identifying the fast barotropic waves. We can see that spectral peaks fall into the long nondispersive range, where the phase speed is well approximated by cx = −βa2 and tend to di-

verge from the linear dispersion relation as the wavelength decreases, consistently with Wunsch and Zang (1999), Osychny and Cornillon (2004) and Killworth and Blundell (2005b), meaning that shorter waves travel faster than the longer ones and there is evidence of both linear and non-linear activity in the spectrum. It is also evident from the FFT analysis that the western side is more energetic and presents more variability at all frequencies than the eastern side.

One might argue that, because the resolution is quite coarse, the phase speeds present in these data are not properly taking into account the wave-mean flow inter- action and the baroclinic mean flow speed-up is not fully reflected in these results. However, if we believe the theory by LaCasce and Pedlosky (2004), the fast baro- tropic waves should travel at approximately the double of the linear baroclinic speed, and this is reflected in our data at both central latitudes.

For the central latitude φ = 40◦ (lower panels of Fig.4.2) the results are qual- itatively very similar. The main peak is around P= 3-3.5 yr with phase speeds of about 4-4.5 cm/s. The extra peak in the western side of the ocean basin has a period of 2 years and phase speeds of 7.5-8 cm/s. The wavenumber of the main peaks is around 2×10−7m−1, which corresponds to a wavelengthλ= 5×106_{m. Al-}