Remotely forced variability in the tropical Atlantic Ocean

Abstract

An ensemble of eight hindcasts has been conducted using an ocean-atmosphere general circulation model fully coupled only within the Atlantic basin, with prescribed observational sea surface temperature (SST) for 1950–1998 in the global ocean outside the Atlantic basin. The purpose of these experiments is to understand the influence of the external SST anomalies on the interannual variability in the tropical Atlantic Ocean. Statistical methods, including empirical orthogonal function analysis with maximized signal-to-noise ratio, have been used to extract the remotely forced Atlantic signals from the ensemble of simulations. It is found that the leading external source on the interannual time scales is the El Niño/Southern Oscillation (ENSO) in the Pacific Ocean. The ENSO signal in the tropical Atlantic shows a distinct progression from season to season. During the boreal winter of a maturing El Niño event, the model shows a major warm center in the southern subtropical Atlantic together with warm anomalies in the northern subtropical Atlantic. The southern subtropical SST anomalies is caused by a weakening of the southeast trade winds, which are partly associated with the influence of an atmospheric wave train generated in the western Pacific Ocean and propagating into the Atlantic basin in the Southern Hemisphere during boreal fall. In the boreal spring, the northern tropical Atlantic Ocean is warmed up by a weakening of the northeast trade winds, which is also associated with a wave train generated in the central tropical Pacific during the winter season of an El Niño event. Apart from the atmospheric planetary waves, these SST anomalies are also related to the sea level pressure (SLP) increase in the eastern tropical Atlantic due to the global adjustment to the maturing El Niño in the tropical Pacific. The tropical SLP anomalies are further enhanced in boreal spring, which induce anomalous easterlies on and to the south of the equator and lead to a dynamical oceanic response that causes cold SST anomalies in the eastern and equatorial Atlantic from boreal spring to summer. Most of these SST anomalies persist into the boreal fall season.

Appendix

1.1 The empirical orthogonal function analysis with maximized signal-to-noise ratio

The description of the empirical orthogonal function analysis with maximized signal-to-noise rario (MSN EOF) follows the exposition in Venzke et al. (1999). Suppose an ensemble mean is composed of a forced and a random part (i.e., X _M =X _F +X _R ), we want to find the dominant pattern of X _F , despite of the presence of X _R . The bold letters represent matrix or vectors here and in following text. If X _F and X _R are temporally uncorrelated with each other, the covariance matrix of X _M can be separated to a forced and a residual noise covariance matrices, i.e., C _M = C _F +C _R . In our case, C _R is 1/8 of the average noise covariance matrix (C _N ) from the 8 ensemble members. To find the eigenvectors of C _F , the key procedure is to eliminate the spatial covariance of noise. Mathematically, this is equivalent to a transformation F such that F _T C _R F = I, where I is identity matrix. This is referred to as the “prewhitening” transformation in the literature because the internal variations become spatially white noise in the transformed matrix F _T C _M F, which guarantees that F _T C _F F and F _T C _M F have identical eigenvalues.

In practice, F is estimated from the first K weighted EOF patterns of the deviations ${\mathbf{{X}'}}_{{\text{i}}} = {\mathbf{X}}_{{\mathbf{i}}} - {\mathbf{X}}_{{\mathbf{M}}}$ , where i denotes the ith member within the ensemble. The matrix of eigenvectors (E) of F _T C _M F contains a set of noise filters, which can be restored into physical space by ${\mathbf{\tilde{E}}} = {\mathbf{FE}}.$ The optimal filter (the 1^st column vector ${\mathbf{\tilde{e}}} = {\mathbf{\tilde{E}}}$ maximizes the ratio of the variances of the ensemble mean and within-ensemble deviations. In this study, we examine this most dominant response only. The optimally filtered time series of X _M (i.e., its projection onto ${\mathbf{\tilde{e}}}$ gives the 1^st MSN principal component (PC). (In practice, one can simply first project X _M onto F to form the prewhitened data in the noise EOF space and then conduct an SVD to get both E and all MSN PCs simultaneously.) The 1^st MSN EOF pattern, which represents the dominant spatial response, is derived by projecting X _M onto the 1^st MSN PC.

The prewhitening operator F and hence the MSN EOF are dependent upon the truncation level (K) of the noise EOF modes. It is necessary to retain enough modes both to treat the noise and to adequately resolve the forced signals in the retained EOF space. On the other hand, not well-determined higher EOF modes should be avoided. Moreover, since the number of forced patterns is limited, an excessive truncation may lead to an ill-posed problem. We took a trial-and-error approach to find a range of K with stable result. Using seasonal averaged SST anomalies and applying the method separately to each season, we examined the sensitivity with K changing from 10 to 40 at an increment of 5. We find that the calculated 1^st mode is nearly unchanged when K is within the range of 20 to 40. We present the result for K equals 30.

The statistical significance of an estimated MSN EOF mode (Venzke et al. 1999) can be tested as following: If there is no true forced signal and a derived mode is purely due to sampling, the ratio of the variance (σ² _M ) of the time series (y _M ) by projecting X _M onto ${\mathbf{\tilde{e}}}$ and the averaged within-ensemble variance (σ² _N ) of the time series (y _k ) by projecting ${\mathbf{{X}^{\prime}}}_{{\text{k}}}$ onto ${\mathbf{\tilde{e}}}$ obeys an F-distribution:

$$ n\frac{{\sigma ^{2}_{M} }} {{\sigma ^{2}_{N} }} = n\frac{{\frac{1} {{m - 1}}{\mathbf{y}}^{{\mathbf{T}}}_{{\mathbf{M}}} {\mathbf{y}}_{{\mathbf{M}}} }} {{\frac{1} {{(m - 1)(n - 1)}}{\sum\limits_k {{\mathbf{y}}^{{\mathbf{T}}}_{{\mathbf{k}}} {\mathbf{y}}_{{\mathbf{k}}} } }}} \sim F_{{m - 1,(m - 1)(n - 1)}} $$

(A1)

Here m is the number of sampling times and n the total members within the ensemble. We will only consider those modes that pass the 95% significance level in this test.