A previous North Pacific Ocean circulation model forced by climatological winds is extended here to include a time-dependent North Pacific Oscillation (NPO) forcing. The Kuroshio Extension (KE) decadal bimodal cycle (which is a self-sustained intrinsic relaxation oscillation in the climatologically forced case) is now excited by the NPO forcing. Both the timing of the cycles and the Rossby wave teleconnection mechanism that is found to govern the synchronization from 1993 to 2012 are in good agreement with altimeter observations. Sensitivity numerical experiments are carried out by varying the zonal location and amplitude of the NPO forcing, and the lateral eddy viscosity. The emergence of the KE bimodality with a correct timing is found to be extremely sensitive to changes in the dissipative parameterization; the implications of such sensitivity for deficiencies found in more realistic North Pacific Ocean general circulation models are discussed. The dynamical mechanism that emerges from this study is explained as a case of intrinsic variability in an excitable dynamical system triggered, and therefore paced, by an external forcing.
The first two dominant decadal time-scale modes of the sea level pressure variability in the North Pacific drive the oceanic Pacific decadal oscillation (PDO; e.g., Mantua et al. 1997; Schneider and Cornuelle 2005) and North Pacific Gyre Oscillation (NPGO; e.g., Di Lorenzo et al. 2008; Chhak et al. 2009), which are, in turn, the main modes of variability of the North Pacific Ocean. It is well known that the Rossby wave trains that propagate the PDO and NPGO signatures from the central and eastern North Pacific into the Kuroshio Extension (KE) region synchronize the KE bimodal decadal variability with those modes (e.g., Qiu 2003; Qiu and Chen 2005, 2010, hereafter QC05 and QC10, respectively; Ceballos et al. 2009). Starting from 1993 two KE bimodal cycles (BCs) have been fully documented by altimeter data: QC10 showed that during the positive PDO (or negative NPGO) phase, the intensified Aleutian low generates negative sea surface height (SSH) anomalies in the eastern North Pacific that propagate to the west as baroclinic Rossby waves: their arrival in the KE region is found to be in phase with the weakening and southward shift of the KE jet, which marks the beginning of the so-called (convoluted) contracted mode (Qiu 2002), characterized by a weak, highly variable, and convoluted jet with a reduced zonal penetration. This state is then followed by the so-called elongated mode, characterized by a zonally elongated, fairly stable, and energetic quasi-stationary meandering jet.
This complex climate phenomenon raises a first fundamental question: is the KE low-frequency variability directly shaped by the incoming Rossby wave field, or is it because of a nonlinear intrinsic mode of the ocean system? The KE jet is a sharp ocean front, so the dramatic changes observed in its BC cannot be due to a linear superposition of a spatially broad field of Rossby waves, as clearly shown by QC05. On the other hand, an idealized KE reduced-gravity jet obtained in a eddy-permitting primitive equation process study with steady climatological wind forcing (Pierini 2006, hereafter P06) yielded a self-sustained chaotic decadal relaxation oscillation (RO; i.e., a highly nonlinear intrinsic mode of the system manifesting through a fast relaxation phase followed by a slow destabilizing dynamics) in substantial agreement with altimeter observations (as shown in Pierini et al. 2009, hereafter PEA09). This supports the hypothesis that the KE bimodality is essentially due to an RO, in which the basic state (essentially the contracted mode) evolves through the various stages of the BC until the original state is recovered, the gross features of such evolution being basically unaffected by the wind forcing. Substantially the same hypothesis was also supported by OGCM hindcasts (Taguchi et al. 2007, 2010).
In this scenario the KE bimodality must therefore be the manifestation of a nonlinear intrinsic ocean mode excited by a Rossby wave train. Based on eddy-resolving global OGCM for the Earth Simulator (OFES) hindcasts, Taguchi et al. (2007) suggested that the broad-scale Rossby waves generated by the basin-scale wind variability excite intrinsic modes of the KE jet, thus reorganizing the SSH variability in space. QC10 and Taguchi et al. (2010) share the same view, and point to the role played by mesoscale eddies and related feedbacks in the KE dynamics (see also Nonaka et al. 2006, 2012). An approach to the problem based also on the powerful concepts of dynamical systems theory (DST) was adopted by Pierini (2010, hereafter P10): the KE RO of P06 was shown to emerge either spontaneously (self-sustained oscillation) in a parameter range past a homoclinic bifurcation in state space [a tipping point (TP)] or under an appropriate red noise wind forcing below that bifurcation (according to the coherence resonance mechanism; e.g., Pikovsky and Kurths 1997). To study the same problem on a more conceptual level, a low-order ocean model was developed (Pierini 2011): the combined effect of coherence resonance and of a periodic forcing could then be analyzed.
Although a consensus on the validity of this dynamical mechanism seems to have been reached, it is rather surprising that model studies showing a correct combination of KE bimodality and timing seem to be not yet available (see section 4). In connection to this, a process study based on the P06 model is presented here, yielding a KE bimodality and corresponding synchronization with the North Pacific oscillation (NPO; the second dominant mode in atmospheric sea level pressure known to drive the NPGO; e.g., Walker and Bliss 1932; Chhak et al. 2009) in significant agreement with altimeter observations. The nonlinear reduced-gravity primitive equation ocean model from P06 is extended to include a time-dependent wind forcing derived from the NPGO index (section 2). In the reference simulation the model is shown to capture the main features of both the KE bimodality and its teleconnection with the NPO variability via the Rossby wave field. In section 3 three sets of sensitivity numerical experiments are presented. The third one shows that the emergence of the KE bimodality with a correct timing is extremely sensitive to changes in the dissipative parameterization; such sensitivity is conjectured to be a cause of the absence of a correct KE low-frequency variability in more realistic OGCMs (section 4).
2. Reference simulation
The ocean model used here is the same as in P06: it is based on the shallow water reduced-gravity equations with an eddy-permitting resolution (20 km) that in the original implementation included a steady climatological wind stress forcing (see Fig. 1 for the map of its curl). The domain of integration (Fig. 1) has a correct zonal extension that insures a realistic total Sverdrup transport in the oceanic interior, and includes schematic but relatively realistic western coastlines [both aspects are shown to be crucial by Pierini (2008)]. Horizontal dissipation is provided by the Laplacian eddy viscosity (with coefficient ) and by a quadratic interfacial friction (see P06 for further details). The present implementation differs from P06 only in the values of and in the presence of an additive time-dependent component in the wind forcing.
The KE bimodality was found to be teleconnected with both the PDO (QC05) and the NPGO (Ceballos et al. 2009). QC10 noted that, in fact, the PDO- and NPGO-related wind forcings are virtually linearly correlated from 1988 to present period. On the other hand, the NPGO is the oceanic expression of the NPO (Chhak et al. 2009). Thus, the total surface wind stress is chosen as
where the time-dependent component represents the NPO through a schematic wind stress field to conform with the P06 process-oriented approach: gives the spatial structure, is its time dependence, and is a constant amplitude. To define a streamfunction is first determined analytically on the basis of the regression map of the NPGO index with the National Centers for Environmental Prediction (NCEP) North Pacific sea level pressure anomalies (SLPAs) of Chhak et al. (2009, see their Fig. 4c) under the assumption that the NPGO reflects the NPO with no lag. The wind velocity is then derived to insure dynamical consistency, and is finally computed, and normalized according to (see Fig. 2a). Figures 1a and 1b show and , respectively ( is shown by the arrows; the low-latitude gyre is correctly centered at 31.5°N, 150°W). Also, is defined as an analytical low-pass fit to the NPGO index as shown in Fig. 3d, and is normalized as shown in Fig. 2b. Neglecting the high-frequency part of the NPGO and even the higher-frequency part of the NPO is not expected to be relevant according to the analysis of colored noise on the KE bimodality in the same model by Pierini (2010).
In (1), is determined as follows. Qiu (2002) showed that the North Pacific Sverdrup transport Q calculated from monthly wind stress curl data of the NCEP–National Center for Atmospheric Research (NCAR) reanalysis (Kalnay et al. 1996) and averaged in the band 29°–32°N varied from 1990 between approximately 34.5 and approximately 47.5 Sv, that is, with Sv (1 Sv ≡ 106 m3 s−1). Thus, thanks to the adopted normalizations, a rough estimate is adopted (in section 3 it will be shown that the oceanic response is weakly sensitive to changes of this parameter).
As for , the reference simulation of P06 (for which the KE RO was self-sustained) had the value m2 s−1, but for higher values the RO did not emerge. PEA09 developed a complete DST analysis, determining the exact parameter ranges (separated by a TP) in which these behaviors occur. P10 later showed that even below the TP the RO is present in the system's dynamics, and can emerge under an appropriate time-dependent noise forcing: an analysis for the non-self-sustained value m2 s−1 was then carried out [see Pierini (2011, 2012) for analogous studies based on a low-order ocean model]. The same value is therefore used now (but see the next section for an analysis of the dramatic changes occurring when this parameter is varied). Here, unlike in P10, the system is subject to a deterministic NPO forcing instead of a red wind noise.
Following QC05 and QC10, all the numerical results will be characterized by the upstream KE path length evaluated between 141° and 153°E (see section 4b of P06 and section 2b of PEA09 for a detailed model–data comparison based on this parameter). Figure 3a shows calculated from altimeter data (updated time series to QC05 and QC10; B. Qiu 2013, personal communication). In about 1995 and about 2006 the arrival of a negative SSH anomaly carried by Rossby waves in the KE region excites the recharging phase of the KE RO, corresponding to a convoluted contracted mode with large oscillations of accompanied by a high regional eddy kinetic energy level. At the end of this phase (around 2002 and around 2010) a stable elongated jet with two well-defined main crests appears. From now on is much less variable and with a smaller average, but the subsequent evolution eventually leads to the abrupt disruption of the elongated mode followed by the appearance of a stable contracted mode. The transition to a convoluted contracted mode (and relative beginning of a new BC) starts with the arrival of a new negative SSH anomaly (this behavior is documented by QC05 and QC10; in P06 the self-sustained cycle is modeled).
The corresponding model result is shown in Fig. 3b (the previous evolution was forced by the 14-yr period oscillation present until t = 2004.5 yr, and the model spinup ended decades before t = 1990 yr). The recharging phase, shown by the large-amplitude oscillations in , starts almost a year before (after) the actual beginning in the first (second) BC, and its duration is shorter than the real one (as already noted by PEA09), but overall the synchronization is significant and the variability and mean value are in good agreement as well (see the numerical experiment SE3 below for a discussion on the dependence of timing on ). Figure 3c shows the Hovmöller diagram of the SSH anomaly at 35°N, evidencing that the Rossby wave teleconnection and lag with the NPO observed in altimeter data are very well captured by the model (Fig. 3d reports the time dependence of the NPO forcing). Also in the model the arrival of a negative SSH anomaly (weakening the KE jet) marks the transition from a stable contracted mode to an unstable convoluted contracted mode, which is then followed by the elongated mode. Hence, also in this more realistic implementation the approach of P06 turns out to provide a consistent minimal model of the KE bimodality.
3. Sensitivity numerical experiments
Three sets of sensitivity numerical experiments (SE1, SE2, and SE3; Fig. 4) are now presented. SE1 aims at verifying that the synchronization and teleconnection evidenced in the reference simulation are real and robust model features and not a mere coincidence. In SE1 cases Figs. 4a–g the zonal location of the NPO forcing is shifted by 100 km with respect to the previous simulation: the synchronization is in fact retained, with an analogous shift in the initiation of the recharging phase because of the different paths the Rossby waves have to cover (the dashed lines stress the differential Rossby wave travel time).
In SE2 the NPO amplitude is varied. Within the range of α from 0.1 to 0.3 no substantial changes emerge: this is clearly because of the manifestation of an intrinsic phenomenon that is only slightly affected by the time-dependent forcing, whose main effect is to pace the RO. On the other hand, for 0.025 and 0.05 the response is completely different: again, this is because of the intrinsic nature of the RO. Since with m2 s−1 the corresponding autonomous system yields small-amplitude chaotic oscillations with a typical time scale yr (see PEA09), which is what is expected for a sufficiently small NPO amplitude: SE2 cases in Figs. 4h,i reveal exactly this behavior in terms of . Naturally, using a more realistic wind forcing would introduce changes in the response, and perhaps improve the synchronization shown in Fig. 3, but the basic sensitivity shown in SE2 is not expected to change, and can be understood much better in the present simplified framework.
In SE3 is varied. Unlike and , which represent robust dynamical effects, measures a rough parameterization of unresolved small-scale processes, so understanding its effect is fundamental from a modeling viewpoint. To interpret SE3 one must refer to the bifurcation diagram of the autonomous system (see Fig. 4 of PEA09). In SE3 cases of Figs. 4r,s the system is below but not far from the TP, yielding moderate amplitude oscillations: thus, ROs (which are latent in the system; e.g., P10, Pierini 2012) can efficiently be excited. In SE3 cases of Figs. 4t,u ROs are self-sustained in the autonomous case (SE3 case in Fig. 4t with would correspond to the reference simulation of P06): this shows that the tendency of ROs to be self-sustained distorts the synchronization, leading to an unrealistic response. Finally, SE3 cases in Figs. 4o–q correspond to very small-amplitude limit cycles of the autonomous system, which now is too far from the TP for ROs to be excited (but in the intermediate case, Fig. 4q, the first RO does emerge). It is impressive to note that these three completely different scenarios arise for a change of just around 15% of . Another less dramatic but remarkable sensitivity concerns the timing: disregarding the character of the emerged ROs, in SE3 cases of Figs. 4p–u the oscillations arise systematically later as increases: a possible explanation is that the larger the horizontal dissipation, the smaller the amplitude of the anomaly carried into the KE region by the Rossby waves (whose arrival time is virtually independent of ), and, therefore, the longer it takes for the same anomaly (e.g., negative SSH in Fig. 3c) to reach a sufficient level to excite the RO. This is confirmed by the delay of the RO timing in SE2 case of Fig. 4j compared to the higher wind amplitude case in Fig. 4k (in SE2 cases of Figs. 4k–n the effect of the amplitude increase saturates, so no time shift occurs).
The extreme sensitivity found in SE3 seems paradoxical if compared with the KE BC–NPO synchronization observed for two successive cycles in the real ocean. We conjecture that that is a model artifact that, however, does not affect the realism of the modeled KE bimodality in consideration of the good model–data comparison shown in P06 and PEA09. Is this the case also for the more realistic OGCMs? See the next section for a comment on this.
In this paper a previous model of the KE bimodality forced by climatological winds (P06) is extended to include a time-dependent NPO forcing. In the reference simulation the system is excitable (i.e., it is set below the TP); hence the KE ROs do not emerge spontaneously. On the other hand, the NPO forcing efficiently excites the oscillations, whose timing and teleconnection with NPO are in good agreement with the altimeter data of QC10. This shows that the intrinsic nature of the KE bimodal cycle and the deterministic appearance of the latter are not in conflict: the forced and intrinsic variability views of the KE low-frequency variability (Pierini and Dijkstra 2009) are, in fact, reconciled in this model study.
The emerged dynamical mechanism is explained as a case of intrinsic variability in an excitable dynamical system triggered, and therefore paced, by an external forcing (this behavior is likely to be fairly common in climate dynamics; e.g., Otterå et al. 2010; Crucifix 2012). Although it is clear that the real phenomenon is much more complex than it is represented in this model, that simple paradigm points to the essential features that regulate the extremely intricate KE phenomenology, and may help controlling more realistic model results.
In connection to this last point, it is surprising that more sophisticated North Pacific ocean models do not produce a correct KE bimodality (e.g., Douglass et al. 2012; Kurogi et al. 2013; Wang et al. 2013; H. A. Dijkstra 2013, personal communication) or produce the bimodality but not the correct timing (e.g., Taguchi et al. 2010), while the present simple model does. Simulation SE3 (section 3) may suggest possible causes of those deficiencies. For example, in the eddy-resolving OFES (e.g., Nonaka et al. 2006; Taguchi et al. 2010) the adopted horizontal resolution and mixing (given by a biharmonic operator with fixed values of the viscosity and diffusivity) produce an eddy kinetic energy level in the KE region that can be roughly related to a value of in the present modeling framework. Now, if OFES were found to be sensitive to those model details in a way similar to what was determined for in SE3, then an appropriate tuning could lead to a better phasing of the KE bimodality or, conversely, even to the disappearance of the latter. In general, the main conclusion that can be drawn from SE3 is that in excitable models in which highly nonlinear intrinsic ROs arise, the sensitivity to dissipative effects (both parameterized and resolved) should be assessed; otherwise, fundamental aspects of the variability could be missed.
I wish to thank Bo Qiu and Emanuele Di Lorenzo for useful discussions and for having kindly provided the time series reported in Figs. 3a and 3d. Thanks are also due to two anonymous reviewers, whose detailed comments helped improve the manuscript.