The tropical Atlantic meridional SST gradient index and its relationships with the SOI, NAO and Southern Ocean

Abstract.

The tropical Atlantic meridional SST gradient (TAMG) is a mode of climatic variability known to be largely associated with abnormal rainfall regimes in South America and West Africa. A TAMG index is defined by the difference between area indices of sea surface temperature anomaly north (TN index) and south (TS index) of the meteorological equator (∼5°N). We investigate, for the 1964–1998 period, the decadal variability of the TAMG index and the relationship of its TN and TS components with the Southern Oscillation Index (SOI), the North Atlantic Oscillation (NAO), sea level pressure (SLP) signals in South Atlantic islands, the global NCEP-NCAR SLP field, and sea-ice extent data in the Southern Ocean. We explore the relationship between the SOI and the TN and TS signals, after estimating their fluctuating lags with the cross-wavelet transform technique. The SOI always leads TN with an average time lead of 5.4 months. On the contrary, TS leads the SOI by ∼4 months after 1984. When exploring the origin of such a precursory event of the SOI, observed in TS, it is found that the highest correlation between TS, the global SLP field, and the sea-ice extent around Antarctica is located in the Ross sea, where the ice signal leads the SOI. High correlation between TS and the SLP field is also observed in the western tropical Pacific. The continuous wavelet transform is then used to extract the low-frequency components of the TN and TS signals. These components are strong well-defined oscillations with mean periods at 9.6 years for TN and 14 years for TS. Given this asynchronous non-dipole nature of the TN and TS decadal components, we can anticipate that the TAMG undergoes decadal oscillations that are variable on a longer multi-decadal timescale. These components are also very similar to the low-frequency components of the NAO index, for TN (with the NAO leading TN by 14 months) and SLP anomaly signals at St. Helena and Tristan da Cunha islands, for TS. These results indicate that the TN or TS decadal component is each related to the larger climatic milieu in the same hemisphere, but that the climatic milieu of the South Atlantic is distinct from that of the North Atlantic.

Appendix A

1.1 Cross-wavelet spectrum and estimation of the instantaneous phase difference and time lag between two time series

The continuous wavelet transform (CWT) (e.g. Daubechies 1992; Lau and Weng 1995; Torrence and Compo 1997; Mallat 1998) of a signal x(t) with the analysing wavelet ψ is defined as:

$$ W_x (b,a) = {1 \over a}\int\limits_{ - \infty }^\infty {x(t)\psi ^* } \left( {{{t - b} \over a}} \right)\hbox{d}t $$

(A1)

where a is the dilatation parameter, b is the time translation parameter and * denotes the complex conjugate. We use the complex Morlet wavelet (Morlet 1983):

$$ \psi (t) = \pi ^{- 1/4} \exp (- t^2 /2)\exp (i\omega _0 t) $$

(A2)

with $i = \sqrt {- 1}$ and $\omega _0 = \sqrt {2/\ln 2} \cong 5.34$ (Daubechies 1992). With this wavelet, the wavelet transform coefficient W _x (b, a) may be expressed in terms of real and imaginary parts, modulus and phase, and the relation between the dilatation parameter a and the usual frequency f is f(a) = ω(a)/2π = 0.874/a (Meyers et al. 1993).

The cross-wavelet spectrum of two series x(t) and y(t) is defined as:

$$W_{xy} (b,a) = W_x (b,a)W_y^* (b,a)$$

(A3)

where W _x (b, a) and W _y (b, a) are the CWT of x(t) and y(t) respectively and where * denotes the complex conjugate. The cross-wavelet coefficient W _xy (b, a) is a complex number and may be expressed in terms of real and imaginary parts, modulus and phase difference. Indeed, let us recall that if z ₁ = c ₁ exp(iθ₁) and z ₂ = c ₂ exp(iθ₂) are two complex numbers with phases θ₁ and θ₂, then z ₁ z ₂* = c ₁ c ₂ exp[i(θ₁ – θ₂)] is a complex number with phase: Δθ = θ₁ – θ₂.

Consequently, the cross-wavelet spectrum provides an estimation of the local phase difference Δφ(b, a) between the two series for each point of the (b, a) time-frequency space. This local phase difference is independent of the amplitude of the series in the sense that Δφ(b, a) will not vary substantially if the amplitude of the series is modified for any location parameter b (or time t). These characteristics allow us to estimate the instantaneous phase difference between the two series x(t) and y(t). Keeping in mind that b corresponds to the time t, this phase difference is defined as:

$$ \Delta \Phi (b) = \tan ^{ - 1} {{\int_{a1}^{a2} {\hbox{Im}[W_{xy} (b,a)]\hbox{d}a} } \over {\int_{a1}^{a2} {\hbox{Re}[W_{xy} (b,a)] \hbox{d}a} }} $$

(A4)

where Re[W _xy (b, a)] and Im[W _xy (b, a)] are the real and imaginary parts of W _xy (b, a) and where a ₁ < a ₂ are the lower and upper limits of the dilatation parameter. The instantaneous time lag between x(t) and (t) is then obtained from the relation:

$$T(b) = {{\Delta \Phi (b)} \over {2\pi F(b)}}$$

(A5)

where F(b) is the instantaneous frequency. We define this frequency as the first normalized moment in frequency of W _xy (b, a):

$$ F(b) = {{\int_{a1}^{a2} {f(a)|W_{xy} (b,a)|\hbox{d}a} } \over {\int_{a1}^{a2} {|W_{xy} (b,a)|\hbox{d}a} }} $$

(A6)

where f(a) is the frequency corresponding to the dilatation parameter a and where |W _xy (b, a)| is the modulus of W _xy (b, a).