A New Paradigm for South Pacific Climate Variability and Predictability


 Pacific climate variability is largely understood based on El Niño–Southern Oscillation (ENSO), the North Pacific focused Pacific decadal oscillation (PDO) and/or the whole of Pacific region interdecadal Pacific oscillation – which respectively represent the dominant modes of interannual and decadal climate variability. However, the role of the South Pacific, including atmospheric drivers and cross-scale interactions between interannual and decadal climate variability, has received considerably less attention. Here we propose a new paradigm for South Pacific climate variability whereby the Pacific-South American (PSA) mode, characterised by two mid-tropospheric modes (PSA1 and PSA2), provides coherent noise forcing that acts to excite multiple spatiotemporal scales of oceanic responses in the upper South Pacific Ocean ranging from seasonal to decadal. While PSA1 has long been recognised as highly correlated with ENSO, we find that PSA2 is critically important in generating a sea surface temperature (SST) quadrupole pattern in the extratropical South Pacific. This sets up a precursor that optimally determines the predictability and evolution of SST 9 months in advance of the peak phases of both the leading South Pacific SST mode and ENSO. Our results show that the atmospheric PSA mode is the key driver of oceanic variability in the South Pacific subtropics.

Ocean climate variability is potentially predictable on seasonal to interannual time scales. 37 We expect this new knowledge to be of potential benefit to marine conservation, fisheries and 38 aquaculture management practices that utilise climate forecasts for their operations and 39 planning. 40 Pacific decadal variability has been historically understood in terms of the North Pacific-focused 41 Pacific decadal oscillation (PDO [1] ) and by the basin-scale interdecadal Pacific oscillation (IPO 42 [2] ). However, neither the PDO nor the IPO explicitly isolate the South Pacific contribution. 43 Analogous to the PDO, the South Pacific decadal oscillation (SPDO [3,4] ) has been identified and 44 described as the South Pacific centre of action contributing to the entire basin-wide Pacific decadal 45 variability. Refs [4,5] show that the SPDO can be viewed as a combination of different dynamical 46 processes operating on different timescales. Those processes include the atmospheric forcing, 47 tropical El Niño-Southern Oscillation (ENSO) teleconnections, and the internal oceanic dynamics.

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Importantly, the atmospheric forcing associated with the Pacific-South American pattern 1 (PSA1) 49 has been identified as the main stochastic driver of the SPDO [4] (cf Fig.1 (left)). ENSO has been 50 shown to impact extratropical variability via the atmospheric bridge [6] and oceanic pathways [7] .

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Recent studies point out that extratropical ocean dynamics can feed back to the tropical Pacific via 52 a sea surface temperature (SST) quadrupole pattern [8] or a South Pacific meridional mode [9][10][11] .

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These oceanic processes act as extratropical precursors that might potentially guide the 54 predictability and evolution of ENSO.

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In this study, we propose a new paradigm for South Pacific climate variability whereby the pair of 56 atmospheric eastward-propagating PSA modes can excite extratropical South Pacific Ocean 57 responses on multiple time scales ranging from seasonal to decadal. Although the South Pacific 58 Ocean responds to fast-varying atmospheric forcing on distinct timescales, the resultant spatial 59 SST features remain difficult to distinguish from the background state. This suggests that the 60 characterisation and identification of predictable signals, and their sources, require careful 61 separation of the climate signal and relevant noise processes. This remains a necessary but 62 challenging problem.

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The atmospheric Pacific-South American mode 64 The PSA mode is represented by an eastward-propagating wave train extending from eastern 65 Australia to Argentina, characterised in mid-tropospheric geopotential height in terms of two 66 invariant empirical orthogonal function (EOF) patterns with associated principal component (PC) 67 time series (PSA1 and PSA2; see methods section) whose phases are nearly in quadrature with 68 each other and whose explained variances are of nearly equal amplitude [12,13] . In combination, 69 they produce the single propagating PSA mode. The PSA mode is known to strongly influence the 70 Antarctic cryosphere [14] , wind and significant wave heights across the Southern Hemisphere 71 oceans [13] , and the South American monsoon system including rainfall [15] and weather and climate 72 extremes over Brazil [16] .

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The respective PSA1 pattern has been widely recognised as being highly correlated with ENSO, 74 where previous studies argue that it results in part as an atmospheric response to ENSO [15,17,18] .

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While regression analysis shows that there is indeed a very close relationship between PSA1 and 76 ENSO (Fig. 1a), the origin of this relationship remains an active area of research [19,20] . Meanwhile, 77 the connection between the atmospheric PSA2 and tropical SST variability is less clear. Ref [15] 78 argues that PSA2 is responsible for the quasi-biennial component of ENSO (Fig. 1b) Analysis of South Pacific SST shows that the first two modes of SST variability, referred to as the 101 SPDO [3,4] and South Pacific quadrupole SST pattern [8] , are primarily driven by the variability 102 associated with the atmospheric PSA1 and PSA2 patterns (Figs. 1 e and f). Using a univariate first-103 order autoregressive (AR1) model [28,29] , we found that the integrated atmospheric PSA1 and PSA2  A second integration of the AR1 model (following a similar approach to refs [4,30] )with the first 108 integration being from the atmosphere to the surface ocean, and the second integration from the 109 surface ocean to the subsurface oceanreveals that the leading SST mode is further reddened by 110 the extratropical upper ocean (Fig. 1 e). The integrated SPDO signal (blue curve in Fig. 1   The extratropical South Pacific not only responds via reddening processes to the fast-varying 121 atmosphere but also via coherence resonances [31] . Specifically, the forcing due to coherent 122 synoptic scale disturbances in the atmosphere associated with the PSA imprints onto the surface 123 ocean further enhancing internal SST variability at its preferred frequency. To examine this 124 mechanism, we generalised the univariate AR1 model to a higher-dimensional multivariate field  that the atmospheric PSA mode can directly modulate ENSO evolution in the tropics [27] , the 148 indirect influence has nevertheless been widely identified in both observations [11] and model 149 simulations [36,38] via the "atmosphere → extratropical ocean → tropical ocean" pathway. One way 150 in which this indirect influence may occur is through a "seasonal footprinting" mechanism [39] , 151 where the atmospheric forcing drives an extratropical anomalous SST "footprint" in the boreal 152 spring, which persists through the boreal summer, and sustains wind stress anomalies in the tropics 153 that are crucial to initiate ENSO events.

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The LIM approach enables an objective determination of the optimal initial perturbations that 155 maximise, for example, ENSO and SPDO growth. This provides an ideal framework through 156 which to investigate the dynamical precursors and predictability of the peak phases of ENSO and 157 the SPDO. Unlike lead-lag correlations that have been widely applied to identify ENSO precursors 158 [8,9,11] , the LIM represents a multivariate linear stochastically forced model and provides a 159 dynamical approximation (see methods section) that satisfies conditionally causal [40] relationships 160 between the optimal precursors and their peak phases.

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The interactions between the non-normal damping SST modes can give rise to a transient 162 amplification of the variance of the deterministic SST system at a preferred temporal growth scale.

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Such transient amplification is useful in sampling and interpreting errors in initial conditions [41] 164 and explains the actual variance growth in the system [32] . Transient amplification of monthly 165 tropical and South Pacific SST anomalies allows a specific set of initial perturbations to develop 166 into the peak phases that are found to exist at 6-to 10-month lead times [5,9,32,33,42] . Our LIM 167 experimental results show that the optimal growth time of SST anomalies in the tropical and South respectively. The tropical ENSO precursor (Fig. 3 a) has been discussed in previous studies [32, 33, 176 37] and may be associated with the recharge-discharge mechanism as first described by Jin [43] . The 177 extratropical precursor (Fig. 3 c)      The pair of fastest damped noise mode and optimal initial perturbations were estimated using a 391 generalised AR1 model, here referred to as the linear inverse model (LIM) [32] , or alternatively 392 termed principal oscillation pattern (POP) analysis [47] . The LIM can be written in the form of a 393 linear stochastic differential equation: where the evolution of the state vector can be expressed as the sum of the deterministic dynamics,

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, that constitute "slow" processes and the stochastic forcing term, , that constitutes "fast" 397 processes. In this study, we defined the model state vector as given a state vector ( ).

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The damping modes can then be diagnosed by applying eigen-decomposition to the dynamical 419 operator (i.e., = ). Since the matrix is not symmetric, some or all of its eigenvalues 420 and eigenvectors are complex. The damping time scales -1/σ and/or the oscillatory periods 2π/ω 421 of the damping modes can be directly estimated from the corresponding eigenvalues = + ,

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where and are the real and imaginary parts of , respectively. In this study, the pair of complex 423 damping modes that has the fastest damping time scale has been discussed. The optimal growth that maximises the amplification of the variance can be estimated as the variance was found at 9 months.

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The optimal precursor indicates the initial condition that maximises the growth of the state vector 437 over a specified time interval τ (τ = 9 months in this case). The optimal precursor is derived as the 438 corresponding leading eigenvector of T ( ) ( ) when τ = 9 months is specified.