The Kuroshio Current System in the North Pacific displays path transitions on a decadal timescale. It is known that both internal variability involving barotropic and baroclinic instabilities and remote Rossby waves induced by North Pacific wind stress anomalies are involved in these path transitions. However, the precise coupling of both processes and its consequences for the dominant decadal transition timescale are still under discussion. Here, we analyse the output of a multi-centennial high-resolution global climate model simulation and study phase synchronisation between Pacific zonal wind stress anomalies and Kuroshio Current System path variability. We apply the Hilbert transform technique to determine the phase and find epochs where such phase synchronisation appears. The physics of this synchronisation are shown to occur through the effect of the vertical motion of isopycnals, as induced by the propagating Rossby waves, on the instabilities of the Kuroshio Current System.

The Kuroshio Current System (KCS) in the North Pacific plays an important role in climate through
its meridional heat transport

Observations have shown that both the Kuroshio Current (KC) and
the Kuroshio Extension (KE) as part of the KCS exhibit variations in their
path

From a theoretical point of view, the central problem is to explain the KCS path variability
using the building blocks of geophysical fluid dynamics. The existence
of western boundary currents in the ocean (such as the Kuroshio and also the Gulf Stream) is well
explained by the linear Sverdrup–Stommel–Munk model

One piece of the KCS path variability puzzle is clearly the non-stationary atmospheric forcing
of the ocean flow. There is wind stress variability over the eastern Pacific related to the Pacific
Decadal Oscillation (PDO)

Another piece of the puzzle is the strong internal (or intrinsic) variability which can be generated solely
through mixed barotropic–baroclinic instabilities. Studies using a hierarchy (quasi-geostrophic,
shallow-water and primitive equation) of models have indicated that low-frequency path variability
(both in the KC and KE) can occur under a stationary wind forcing

Approaches on combining both forced and internal views have been made as an attempt
to develop a more detailed theory explaining the path transitions of the KCS and its dominant
decadal timescale in terms of the interaction between forced Rossby waves and the
internal variability (including the mesoscale eddies). When a baroclinic Rossby wave model (based on the linear vorticity equation under longwave approximation) is subjected to non-stationary wind stress forcing, no path transitions are found due to the interaction of the Rossby waves and the western boundary current

During the last decade, much has also been learned from the analysis of simulations with
high-resolution ocean general circulation models (OGCMs). The relevance of internal ocean variability
in the climate system was demonstrated by comparing OGCM simulations under realistic
and climatological annual cycle atmospheric forcing

In this paper, we contribute to the understanding of the KCS path variability, refining existing results
of the relation between the wind stress and KCS variability

We start by describing the model data and methods of analysis in Sect.

We analyse output from a 300-year control simulation of the CESM (version 1.0.4) as
performed at SURFsara, the academic computer centre in Amsterdam.
In this control simulation (see also

From the model output, we extracted monthly averaged fields of SSH, zonal
and meridional wind stress, ocean horizontal velocity fields, ocean temperature and ocean
salinity. For analysis these fields were transformed onto a rectangular grid with a horizontal resolution
of

In Fig.

The results in Fig.

Phase synchronisation in chaotic oscillators was introduced by

In order to detect epochs of synchronisation in the KCS, we have to choose two time
series representing the processes which are supposed to synchronise.
For the KE variability, we choose the KE path length time series, as plotted in Fig.

Motivated by the phase synchronisation studies of

A common approach to derive the phase from a scalar time
series

Epochs of phase synchronisation appear as plateaus in the phase difference curve.
To avoid a selection of plateaus in the phase difference evolution purely based
on visual inspection, we follow

In the results below, 1000 iterative amplitude-adjusted Fourier transform (iAAFT)
surrogates

Although many other methods and measures of phase relationships have been used

We first show a brief model–observation comparison in Sect. 3.1 to further demonstrate that the model is fit for the purpose of analysing KCS path variability. Next, the main results of the paper are provided in Sect. 3.2, where the phase synchronisation is studied, and in Sect. 3.3, where the phase synchronisation mechanism is analysed.

Figure

Before determining the Fourier spectrum, each of the time series is
linearly detrended and the seasonal cycle is removed. Surrogate red noise (2000 realisations)
is generated to determine the confidence levels; note that for the wind stress the
lag-one autocorrelation is small, resulting in effectively white-noise surrogates.
Figure

When performing the SSA as described in Sect.

The two-dimensional embedding of the derivative of the observables with its Hilbert transform is
shown in Fig.

Epochs where plateaus in the phase difference occur are confirmed by the statistical test
described in Sect.

By processing the model output data by SSA as in

In the analysis above, only the zonal component of the wind stress is considered, while the wind stress curl directly affects the SSH field through Ekman and Sverdrup dynamics. Therefore, we also performed a phase synchronisation analysis using the wind stress curl over the same domain as the zonal wind stress. The first EOF of the wind stress curl contains 7.6 % of the total variance, which is considerably smaller than the variance explained by the first PC of the zonal wind stress (which is 29.6 %). When conducting SSA on the first PC of the wind stress curl, a significant (95 % confidence level) ST-PC pair was identified with an 8-year period (against red-noise surrogates). A phase synchronisation analysis between the KE path length and the wind stress curl revealed significant plateaus between model years 200 and 240, similar to the results for the zonal wind stress. The similarity of the results for the zonal wind stress and the wind stress curl is expected since the meridional dependency of the zonal wind stress is the dominant component of the wind stress curl.

We also analysed phase synchronisation in the CESM between the NPGO index

Finally, it should be noted that synchronisation cannot be deduced unconditionally by applying a phase synchronisation analysis and by revealing a dependence
between the phases of the observables. Two time series can fulfil the “mathematical” condition of phase synchronisation which is given by the boundedness
of the phase difference even if the observed state arises from other processes or effects

Self-sustained oscillators synchronise through a coupling which allows the adjustment of the phases.
Assessing the processes responsible for the synchronisation is an important but also difficult task,
especially for phase synchronisation detected from observations. A good assessment is therefore
preferably carried out in an “experimental set-up” where parameters can be varied

However, as also mentioned above, here an adequate view of the physics of the system
motivates the exploration for a possible coupling mechanism from the zonal wind stress to the KE path length
through the propagation of SSH anomalies. We specifically also focus on the propagation of
the anomalies of the depth of the 1028 kg m

Hovmöller diagrams of

The Hovmöller diagrams (Fig.

When comparing the 1028 kg m

To determine the effects of the variations in the IPD and the background zonal velocity
on the KC stability, we consider the local EKE of the KC system,
defined here as

We interpret the results in Figs.

Output from a multi-centennial simulation with a high-resolution version of the Community Climate System Model (CESM) was used to study phase synchronisation between path variability in the Kuroshio Current System (KCS) and the wind variability over the North Pacific basin. In particular, by performing an SSA, oscillatory components on decadal scales of the Kuroshio Extension (KE) path length and the first PC of the zonal wind stress field were chosen as representative observables for the proposed oscillators. The length of the CESM simulation is crucial for determining an adequate phase of the KE path length and the zonal wind stress variability. The high spatial resolution of the ocean model component is also needed to adequately represent the internal variability in the KCS. The phase difference evolution, the distributions of the phase difference and results from a statistical test indicate that the KE and the North Pacific zonal wind stress are episodically phase synchronised in CESM.

We interpret this phase synchronisation as an entrainment of an external frequency (that of the
mid-basin wind stress variability) into the variability of a chaotic system (the KCS), as described in Sect. 5.2 of

When this forcing is too large with respect to the intrinsic KCS variability, the period of the external frequency is dominant and hence, in the case of a periodic forcing, the resulting KCS will become periodic in a chaos–destroying synchronisation (as described in

We think that the phase synchronisation as investigated with methods from non-linear dynamics, together with its mechanism as described in
Sect. 3.3, provides a further step to connect the purely Rossby wave
“forced” view of KCS path transitions, as originally advocated

Indications that some periods of observed variability show a much clearer decadal variability
than others are found in the analysis of AVISO data

Analysis scripts and model output are available on request from the corresponding author.

All authors generated the idea for this study and wrote the paper together.

The authors declare that they have no conflict of interest.

The authors thank Michael Kliphuis (IMAU, UU), who performed the CESM simulations, and both reviewers for their excellent suggestions and comments, which improved the manuscript substantially. The computations were done on the Cartesius at SURFsara in Amsterdam. Use of the Cartesius computing facilities was sponsored by the Netherlands Organization for Scientific Research (NWO) under the project 15502.

This paper was edited by Anna Rubio and reviewed by Stefano Pierini and one anonymous referee.