Search for Trends and Periodicities in Inter-hemispheric Sea Surface Temperature Difference

Abstract

Understanding the role of coupled solar and internal ocean dynamics on hemispheric climate variability is critical to climate modelling. We have analysed here 165 year long annual northern hemispheric (NH) and southern hemispheric (SH) sea surface temperature (SST) data employing spectral and statistical techniques to identify the imprints of solar and ocean–atmospheric processes, if any. We reconstructed the eigen modes of NH-SST and SH-SST to reveal non-linear oscillations superimposed on the monotonic trend. Our analysis reveals that the first eigen mode of NH-SST and SH-SST representing long-term trend of SST variability accounts for ~ 15–23% variance. Interestingly, these components are matching with first eigen mode (99% variance) of the total solar irradiance (TSI) suggesting possible impact of solar activity on long-term SST variation. Furthermore, spectral analysis of SSA reconstructed signal revealed statistically significant periodicities of ~ 63 ± 5, 22 ± 2, 10 ± 1, 7.6, 6.3, 5.2, 4.7, and 4.2 years in both NH-SST and SH-SST data. The major harmonics centred at ~ 63 ± 5, 22 ± 2, and 10 ± 1 years are similar to solar periodicities and hence may represent solar forcing, while the components peaking at around 7.6, 6.3, 5.2, 4.7, and 4.2 years apparently falls in the frequency bands of El-Nino-Southern Oscillations linked to the oceanic internal processes. Our analyses also suggest evidence for the amplitude modulation of ~ 9–11 and ~ 21–22 year solar cycles, respectively, by 104 and 163 years in northern and southern hemispheric SST data. The absence of the above periodic oscillations in CO₂ fails to suggest its role on observed inter-hemispheric SST difference. The cross-plot analysis also revealed strong influence of solar activity on linear trend of NH- and SH-SST in addition to small contribution from CO₂. Our study concludes that (1) the long-term trends in northern and southern hemispheric SST variability show considerable synchronicity with cyclic warming and cooling phases and (2) the difference in cyclic forcing and non-linear modulations stemming from solar variability as a possible source of hemispheric SST differences.

Appendix: Amplitude Modulation (AM)

In amplitude modulation (AM), the information signal (here after signal) modifies the amplitude of the carrier wave. The instantaneous amplitude of the carrier changes in accordance with the amplitude and frequency variations of the modulating signal. In the case of a simple single frequency sine wave signal $\vartheta_{\text{m}} = a_{\text{m}} \sin 2\pi f_{\text{m}} t$ modulating a higher frequency sine wave carrier $\vartheta_{\text{c}} = a_{\text{c}} \sin 2\pi f_{\text{c}} t$, the resulting signal amplitude ($\vartheta$) is given by

$$\vartheta = a_{\text{c}} \sin 2\pi f_{\text{m}} t + \left( {a_{\text{m}} \sin 2\pi f_{\text{m}} t} \right)\left( {\sin 2\pi f_{\text{c}} t} \right)$$

(3)

where $\vartheta_{\text{m}} , \vartheta_{\text{c}}$ are the instantaneous amplitudes, $a_{\text{m}} , a_{\text{c}}$ are the peak amplitudes, and $f_{\text{m}} , f_{\text{c}}$ are the frequencies of modulating and carrier signals, respectively. Using the trigonometric equalities, the above equation can be re-written as follows:

$$\vartheta = a_{\text{c}} \sin 2\pi f_{\text{c}} t + \frac{{a_{\text{m}} }}{2}\left( {\cos 2\pi t\left( {f_{\text{c}} - f_{\text{m}} } \right) - \frac{{a_{\text{m}} }}{2}\cos 2\pi t\left( {f_{\text{c}} + f_{\text{m}} } \right)} \right).$$

(4)

The term $a_{\text{c}} \sin 2\pi f_{\text{c}} t, \frac{{a_{\text{m}} }}{2}\left( {\cos 2\pi t(f_{\text{c}} - f_{\text{m}} } \right)\;{\text{and}}\; \frac{{a_{\text{m}} }}{2}\left( { \cos 2\pi t(f_{\text{c}} + f_{\text{m}} } \right)$ represents the original carrier, lower side band (LSB), and upper side band (USB) frequencies, respectively. The pictorial representation of modulated signal ($\vartheta$) in the frequency domain is shown in Fig. 15.

Fig. 15

Spectral content of amplitude modulated signal represented by Eq. (4)

We have estimated the phase and frequency contents of the modulated component ‘y’ identified in the SSA reconstructed Eigen modes to compute f_c and f_m. Then, we have used matlab function z = amdemod(y, f_c, f_m) to demodulate the amplitude modulated signal y to recover the signal. Here, f_c and f_m must satisfy f_m > 2(f_c + B_W), where B_W is the bandwidth of the original signal that was modulated.