1 Introduction and motivation

Interannual and interdecadal oscillations with a regional extent have been found in several areas of the Earth’s oceans and atmosphere. In and near the North Atlantic basin, such oscillations have been identified in many observational studies, including in the oceans’ temperature field and in the atmosphere’s geopotential fields (e.g., Bjerknes 1964; Deser and Blackmon 1993; Dettinger et al. 1995; Hurrell and Van Loon 1997; Moron et al. 1998; Da Costa and Colin de Verdiére 2002; Feliks et al. 2010; Jajcay et al. 2016). The extent to which these oscillations are due to purely oceanic (Dijkstra and Ghil 2005; Berloff et al. 2007, and references therein) purely atmospheric (e.g., Frankignoul and Hasselmann 1977; Frankignoul et al. 1997) or coupled (Vannitsem et al. 2015, and references therein) processes is still a matter of controversy (Dijkstra and Ghil 2005; Ghil and Robertson 2000; Clement et al. 2015; Zhang et al. 2016; Srivastava and DelSole 2017).

Over and near the Pacific Ocean basin, the Pacific Decadal Oscillation (PDO) was extensively studied; see, for instance, the Newman et al. (2016) review. These authors affirm that, in all likelihood, the PDO is not due to a single mechanism but rather to the combination of several different basin-scale processes. The spatial patterns corresponding to these processes are not identical and their characteristic time scales are quite different, but they all project strongly onto the PDO pattern; see also Chao et al. (2000).

Newman et al. (2016) identify three eigenmodes that represent dynamical processes with maxima in the northern, central tropical–northern subtropical, and eastern tropical Pacific, respectively; similar patterns from various analyses have been reported elsewhere (e.g., Barlow et al. 2001; Chiang and Vimont 2004; Guan and Nigam 2008; Compo and Sardeshmukh 2010. The first eigenmode represents largely North Pacific dynamics, while the latter two represent interannual-to-decadal tropical dynamics driving North Pacific variability. Among the proposed mechanisms, several authors (e.g., Deser et al. 1999; Seager et al. 2001; Schneider and Cornuelle 2005; Zhang and Delworth 2015; Wills et al. 2019 suggest that the PDO is primarily an extratropical phenomenon caused by an integrated response to prior Aleutian Low wind stress forcing, while other studies suggest that it represents the long-lived remnants of ENSO variability (e.g.,Zhang et al. 1997; Vimont 2005; Newman et al. 2016,).

In this paper, we focus on significant oscillations with periods in the interannual-to-interdecadal, 2–15-years band studied, for instance, by Moron et al. (1998). Several studies reported oscillations in this band in sea surface temperatures (SSTs), as well as in land surface and atmospheric temperatures. Deser et al. (2002), for instance, addressed decadal recurrence of above-normal sea ice extent anomalies in the Labrador Sea and associated below-normal SSTs in the North Atlantic basin (NAB), with a 1–3-years persistence of these anomalies. They attributed a major role to atmospheric forcing but admitted that the year-to-year SST persistence in the subpolar NAB could not be simulated with a slab mixed-layer ocean. In a rather different spirit, Clement et al. (2015) and Srivastava and DelSole (2017) suggested that the Atlanitic Multidecadal Oscillation and PDO are mainly the oceans’ response to stochastic forcing by the mid-latitude atmospheric circulation, while Zhang et al. (2016) vigorously rebutted the claims of Clement et al. (2015).

Curry and McCartney (2001) and Eden and Jung (2001) showed observational evidence of interannual-to-interdecadal variability in the intensity of the North Atlantic gyre circulation related to the atmospheric North Atlantic Oscillation (NAO) patterns. Eden and Jung (2001), moreover, provided evidence for interdecadal variability in the surface net heat flux forcing associated with the NAO governing interdecadal changes of the North Atlantic circulation. Feliks et al. (2011), though, found a 10.5-years periodicity in the Atlantic SSTs along the North Atlantic Drift near the Grand Banks that affected the atmospheric circulation above. Muller et al. (2013) analyzed average global land surface temperatures and found a significant oscillation with a period of 9-10 yr that correlates well with their Atlantic SST index, while the period is quite close to that of Feliks et al. (2011).

Kondrashov et al. (2005) studied the Nile River water level records for 1–300 years and found statistically significant interannual oscillations with periodicities of 2.2, 4.2 and 7 years. The two shorter ones were attributed to precipitation anomalies over the Ethiopian Plateau due to the effect of the Southern Oscillation on the African easterlies, while the latter was linked to NAO influences. Feliks et al. (2010, 2013) showed that a 2.7-years and a 7–8-years oscillation is present over the NAB, Middle East, the Indian subcontinent and the Tropical Pacific, and that the separate regional modes are synchronized at these two periodicities, at least in part.

Whatever the origin of these oscillations, understanding the complex interactions between the ocean and the overlying atmosphere is crucial for the prediction of the climate system’s LFV (Kushnir et al. 2002; Czaja et al. 2003; Hurrell et al. 2003; Visbeck et al. 2003; Liu 2012; Vannitsem et al. 2015; Pierini et al. 2016). The physics behind the climate’s LFV is still far from elucidated and there are basic questions such as: is the ocean causing the variability and if so, in what regions, and how does it influence the atmosphere? Atmospheric LFV with similar broad periodicities is often found thousands of kilometers away, largely over the land, as in Feliks et al. (2010, 2013, 2016). While the results of Feliks et al. (2004, 2007, 2011) suggest that it is the interannual variability of oceanic thermal fronts, such as the Gulf Stream or Kuroshio front, that give rise to atmospheric LFV above the fronts and further downwind, the amplitude of this LFV is smaller by an order of magnitude than the variance of the synoptic-scale weather systems and of the intraseasonal variability.

Previous studies concentrated on regional or, at most, hemispheric aspects of interannual variability, albeit including teleconnection effects. The purpose of this paper is to examine global modes of interannual variability. We find that two such modes are statistically significant and have periods of 10–12 yr and roughly 3.5 yr. Both are, in fact, consistent with some of the previously described regional modes. The exact mechanism for the way that these two global climate modes arise has to be left for further studies but it seems to be consistent with their being synchronized by propagating waves in the atmosphere and oceans.

Most previous studies used low-resolution general circulation models (GCMs) or highly idealized ones that lacked many important processes in the ocean and the atmosphere. In this paper, we use the Community Earth System Model (CESM: Hurrell et al. 2013; Small et al. 2014), an IPCC-class GCM with a resolution of \(0.1 \times 0.1\) degrees in the ocean and \(0.25 \times 0.25\) degrees in the atmosphere, as recommended by Feliks et al. (2004, 2007) and improved upon by Minobe et al. (2008). Such high resolution is necessary to resolve the ocean’s internal dynamics, particularly in the western boundary currents and their eastward-jet extension, like the Gulf Stream and North Atlantic Drift, as well as resolving the air–sea fluxes and the atmospheric dynamics in regions of narrow SST fronts, cf. Small et al. (2008). The results obtained by analyzing a CESM 100-years simulation are then confronted with those afforded by a study of the NCEP-NCAR reanalysis (Kalnay et al. 1996; Kistler et al. 2001) and of the ECMWF ERA5 reanalysis (Hersbach et al. 2020).

A number of previous papers studied also global modes of variability in the observations or reanalyses on the interannual-to-interdecadal time scale. Thus, Moron et al. (1998) used MSSA to examine the U.K. Meteorological Office’s MOHSST5 data base of SSTs over the 1901–1994 time span and found several interannual oscillations associated with the El Niño–Southern Oscillation (ENSO) and the NAB, as well as an irregular trend with 1910–1940 and 1975–1994 warming and 1940–1975 cooling, especially in the northern hemisphere; see also Ghil and Vautard (1991). The change in trend was preceded in both 1940 and 1975 by the appearance of a small anomaly of opposite sign in the North Atlantic, south of Greenland (Moron et al. 1998, Fig. 3, panels 1936–1940 and 1976–1980).

De Viron et al. (2013) used a comprehensive set of 25 climate indices; their set encompassed not only scalar indices associated with climate variability in large regions, like ENSO or the PDO, but also some that have been associated with much smaller areas, like Sahel rainfall. The various indices extended over time spans of 50–60-years lengths. These authors found that four leading principal components (PCs) captured most of the variability in their dataset; the spectral analysis of these PCs was limited to the shortest interannual modes, namely those associated with ENSO, because of the limited length of their dataset.

Finally, Kravtsov (2017) and Kravtsov et al. (2018) focused on the differences between decadal and multidecadal climate variability in simulations produced by IPCC-class models from the Coupled Model Intercomparison Project Phase 5 (CMIP5: Taylor et al. 2012), on the one hand, and in a number of datasets, such as the indices used by De Viron et al. (2013) and others, and two distinct reanalyses, 20CRv2 (Compo et al. 2011) and ERA-20C (Poli et al. 2016). They did find in the observational datasets a global stadium wave (GSW), which was not present in the model simulations nor was it similar to the decadal wave found in this paper. Gavrilov et al. (2020a) took another look at this GSW by introducing a novel analysis method of the data, based on Linear Dynamical Modes (LDMs).

In Sect. 2, we present the CESM model and its 100-years simulation, as well as the MSSA methodology. The CESM simulation is studied in Sect. 3, emphasizing oscillatory modes in the 2–15-years band. In Sect. 5, we ascertain that the spatio-temporal pattern and the dynamics of the 11-years oscillatory mode is not an artifact of the MSSA methodology and that it can be obtained directly from the data. In Sect. 4, we present the NCEP-NCAR reanalysis and ECMWF ERA5 reanalysis and their interannual oscillations. A summary and conclusions follow in Sect. 6, where we also attempt to address (a) the differences between our results and those of Kravtsov et al. (2018) and Gavrilov et al. (2020b); and (b) the potential role of the solar cycle in the decadal mode described in this paper.

The Electronic Suplementary Material (ESM) complements the information in the paper’s main text. It consists of three short animations for northern hemisphere fields extracted from the CESM model’s simulation:

  1. (i)

    The 11-years oscillatory mode in the surface temperatures (STs);

  2. (ii)

    The 11-years oscillatory mode in the 200-hPa geopotential field; and

  3. (iii)

    The 3.4-years oscillatory mode in the 200-hPa geopotential field.

2 Dataset and methodology

2.1 The Community earth system model (CESM)

CESM is a state-of-the-art, fully coupled ocean–atmosphere GCM (Hurrell et al. 2013). The version used herein is CESM1.1; see also Small et al. (2014). The model components are the Community Atmosphere Model (CAM5), with the Spectral Element dynamical core and 27 vertical levels, and the Community Land Model (CLM4), both with a horizontal resolution of horizontal resolution of \(0.25 \times 0.25\) degrees, which permits mesoscale systems, coupled with the Parallel Ocean Program (POP2) with 62 vertical levels and the Community Ice CodE (CICE), both with a horizontal resolution of \(0.1 \times 0.1\) degrees, These resolutions permit the inclusion of mesoscale systems in the atmosphere and resolve many of the mesoscale eddies in the ocean.

CESM was run for 100 year from an initial state for year 2000 and a short, one-year ocean-ice spin-up from the Gouretski and Koltermann (2004) climatology, based on the World Ocean Circulation Experiment (WOCE) results and other data. Present-day greenhouse gas conditions—e.g., a fixed 367 ppm \(\hbox {CO}_2\) concentration—were used.

The coupled run performed ocean–atmosphere coupling every 6 hr and its atmospheric fields equilibrated to a statistically near–steady state in about 33 years. The subsurface fields in the ocean were still experiencing some climate drift, but the SSTs equilibrated, too, after the CESM run’s first 50 years, as documented in Small et al. (2014, Fig. 1b). The reanalysis datasets studied in Sect. 4 are 68-years and 71-years long, for the NCEP-NCAR and ERA5 reanalysis, respectively; hence, we analyzed the last 66 years of the CESM model simulation using the methodology of the next subsection. The residual SST drift did not seem to affect the LFV in the atmospheric fields that we analyzed.

2.2 Multivariate singular spectrum analysis (MSSA)

To identify complex patterns of spatio-temporal behavior in the CESM simulation summarized above, we rely here on MSSA, which provides an efficient and robust tool to extract dynamics from short, noisy time series. MSSA relies on the classical Karhunen–Loève decomposition of stochastic processes into data-adaptive orthogonal functions. Broomhead and King (1986) introduced MSSA into dynamical system analysis as a robust version of the Mañé–Takens idea to reconstruct the underlying dynamics from a time-delayed embedding of time series; see Ghil et al. (2002) and Alessio (2015, Ch. 12) for a comprehensive overview of the methodology and of related spectral methods. Groth et al. (2017) present some of the algorithmic details that have proven useful in applying MSSA to high-dimensional climatic problems.

The MSSA method essentially diagonalizes the lag-covariance matrix \(\mathbf{M}\) of one or more climatic fields to yield a set of orthogonal eigenvectors and the corresponding eigenvalues. The eigenvectors are referred to as space-time empirical orthogonal functions (ST-EOFs), while the eigenvalues equal the variance that is captured in the direction of a given ST-EOF. The projection of the original data onto the ST-EOF yields the corresponding PCs. A key feature of the MSSA approach is that oscillatory behavior is detected by the presence of so-called oscillatory pairs, that is, ST-EOFs with approximately equal eigenvalues and fundamental frequencies (Vautard and Ghil 1989; Ghil and Vautard 1991; Plaut and Vautard 1994).

To improve the separability of distinct frequencies, we rely here on a subsequent varimax rotation of the ST-EOFs (Groth and Ghil 2011). The presence of oscillatory pairs, though, is not sufficient to reliably identify nearly periodic deterministic behavior in the underlying dynamics. Allen and Smith (1996) provided, therefore, a Monte Carlo–type test against a null hypothesis of red noise for the statistical significance of one or more oscillatory modes, while Allen and Robertson (1996) suggested a multi-channel extension thereof to MSSA. A more rigorous significance test for the multivariate, high-dimensional case considered herein was formulated by Groth and Ghil (2015) and applied to coupled ocean–atmosphere interannual variability by Groth et al. (2017). It is the latter form of the significance test for high-dimensional MSSA that was used throughout the present paper.

3 Interannual oscillatory modes in the CESM model’s simulation

To find the coupled oscillatory modes in the CESM simulation, we examine the global surface temperatures (STs) over sea and land, the sea level pressures (SLPs) and geopotential heights at 200 hPa. Note that CESM does not contain a prognostic equation for the temperature of the interface between the atmosphere and sea or atmosphere and land. Hence, the STs in CESM are computed, over the oceans as well as over the continents, by equating the heat fluxes at each grid point on either side of the interface with the atmosphere.

These three fields represent therewith the land, the sea and the lower and upper layers of the atmosphere. The resolution we used in our ST analysis was about \(0.5 \times 0.5\) degrees, while it was about \(1.0 \times 1.0\) degrees for the SLP and 200 hPa fields. The fact that the resolution cannot be exactly uniform is due to the presence of different horizontal grids near the surface in the atmosphere and in the oceans, which requires interpolation. We normalize each field by its variance so as to analyze the three of them together.

To remove the strong seasonal cycle in the data, we first calculated monthly averages from the daily values. We then applied a 12-month moving-average filter to the monthly time series so obtained. Feliks et al. (2013) examined the response function of this filter and showed that the amplifying or dam** of the periodicities longer than 3 years is very small. Next, we derived annually sampled time series by simply taking all 66 January values from this smoothed time series and checked that the results are almost the same as those reported below when taking another month of the year.

MSSA was then applied with a window width of \(M = 20\) years. In constructing the lag-covariance matrix \(\mathbf{M}\), copies of the available time series are lagged by multiples of 1 years, and the maximum lag equals the method’s window width M, i.e., the matrix \(\mathbf{M}\) is \(M \times M\). This window width is about 1/3 of the length of the time series, as recommended by Vautard and Ghil (1989). The methodology is by now pretty standard in the climate sciences (e.g., Krishnamurthy 2019) and there are many sources for the the algorithmic details (Ghil et al. 2002; Alessio 2015; Groth et al. 2017, and references therein). Only the signals significant at the two-sided 95% level are analyzed further below.

3.1 The CESM model’s decadal mode

The MSSA spectrum of the combined global fields is shown in Fig. 1 together with error bars that indicate the 95% confidence interval with respect to a null hypothesis of red noise. Oscillations with periods of 11 and 3.4 years emerge as statistically significant and are analyzed below. There several points around 0.05 cy/year and below that appear as statistically significant, but these points are associated with periods of 20 years and longer. Since the total length of the time series is \(N = 66\) years, the oscillatory modes corresponding to these points cannot be resolved correctly since they only satisfy—marginally or not at all—the Vautard and Ghil (1989) criterion of \(N \ge 3M\).

Fig. 1
figure 1

Spectral analysis of the time series of the global ST, SLP and 200-hPa fields, as found in the CESM model simulation, after detrending and by using MSSA with a window width \(M = 20\) years, after subtracting the seasonal cycle and applying varimax rotation for better frequency separation (Groth and Ghil 2015; Groth et al. 2017). The estimated variance of each mode in the dataset is shown as a filled red square, while lower and upper ticks on the error bars indicate the \(5{\mathrm{th}}\) and \(95{\mathrm{th}}\) percentiles of a red-noise process constructed from a surrogate data ensemble of 100 time series. Each of the surrogates has the same variance and lag-one auto-correlation as the original record. The surrogate time series were produced by projecting the first 40 principal components (PCs) of the MSSA analysis onto the basis vectors of a red-noise process

Full size image

The oscillatory mode captured by the ST-EOFs (3,4) pair has a period of 11 years and accounts for 6% of the interannual variance, after subtracting the seasonal signal. Phase composites of the corresponding reconstructed components (RCs: Ghil and Vautard 1991; Ghil et al. 2002), denoted by RCs (3,4), are shown in Figs. 2, 5 and 6, for the ST, 200 hPa and SLP fields, respectively. In each of these three figures, the cycle has been divided into eight phase categories, following Moron et al. (1998).

Fig. 2
figure 2

Composites of the 11-years mode of global STs found in the CESM model simulation, in eight phase categories, displayed clockwise and labeled by the epoch at the middle of the category; color bar in degrees Celsius. These composites are based on the MSSA pair (1,2), which captures 6% of the interannual variance. The mean ST field in the middle panel has contour interval (CI)  = 2 K

Full size image

In the ST field of Fig. 2, north of 25 N, the 11-years oscillatory mode is dominated by a superposition of wavenumbers 1–3 in the zonal, east–west direction, with alternating, large-scale warm and cold anomalies. These waves are propagating eastward and poleward around the globe.

For example, the very extensive warm anomaly occurring in phase 4.1 years at longitudes (40 E–320 E) and latitudes (20 N–75 N) shrinks substantially and can be found in phase 6.9 years mainly north of 70 N and over North America. The cold anomaly located in phase 4.1 years at longitudes (70 E–200 E) and latitudes (20 N–40 N) propagates to longitudes (40 E–320 E) and latitudes (40 N–75 N) in phase 8.2 years. So, in phase 9.6 years, the warm and cold anomalies have switched their places with respect to the phase at 4.1 years. This mode is found over vast regions of the Arctic Ocean and the surrounding high-latitude land areas. It would thus appear that the interaction of sea ice with the ocean, atmosphere and land surfaces plays a large role in this oscillation. The propagation of the ST of this mode in most of the northern hemisphere is shown in the animation in Online Resource 1.

The 11-years oscillations in STs over the North Pacific display a tongue-and-horseshoe pattern. This pattern is similar to PDO patterns found in previous studies (e.g.,Newman et al. 2016; Kren et al. 2016). Comprehensive reviews of the different processes that affect the PDO can also be found in Miller and Schneider (2000) and Alexander et al. (2010).

In our results, though, a warm tongue is found in phases 9.6–2.8 years; it starts develo** at 144 W over Japan, and it propagates northeastward. Later, as the tongue reaches the West Coast of North America, the warm anomaly deforms to a horseshoe shape, in phases 2.8–5.5 years. During the latter phases, a cold tongue develops in the western mid-latitudes of the Pacific Ocean; thus, in phases 4.1 years and 5.5 years, a cold tongue in the western basin coexists with a warm horseshoe in the east.

The tongue and horseshoe described herein are spatial features that do appear in the second and third eigenmodes of the PDO, as obtained by Newman et al. (2016); see their Figs. 6b and 6d, respectively. But there are significant differences in the evolution of their modes and ours, and the succession of changes in shape, extent, location and polarity of these features, as shown in Fig. 2 here, cannot be represented by a linear combination,whose coefficients change in time, of the Newman et al. (2016) patterns in their Figs. 6b and 6d; the latter were derived by using a methodology that emphasizes variability in the North Pacific ocean basin, while ours is evenhandedly global.

Thus, for instance, in phases 6.9 years and 1.4 years of our Fig. 2, only a very small tongue is present in the western North Pacific; this state cannot be described by a weighted sum of the second and third eigenmodes of Newman et al. (2016): the second one (their Fig. 6b) has a very large tongue, while the third one (their Fig. 6d) has only a negligible amplitude in the western basin and cannot erase therewith the large area and strength of the second mode there. Hence the North Pacific features of our global 11-years oscillatory mode seem to provide a different picture of the decadal component of the PDO than the Newman et al. (2016) combination of regional mechanisms.

Turning now to the North Atlantic sector, the 11-years oscillatory mode in the Labrador Sea has a warm ST anomaly in the phases 1.4 years–4.1 years and a cold one in phases 6.9 years–9.6 years. We will show further below that the temperatures in the Labrador Sea at depth of 5 m lack these anomalies and are thus led to conclude that this oscillation is probably due to changes in sea ice cover. This mode in our results seems to agree in the Atlantic sector with the decadal variations described by Deser et al. (2002). The latter authors used a simple ice–ocean mixed layer model forced with observed air temperature and wind fields and found that large-scale atmospheric thermodynamic forcing could account for much of the ice extent and SST evolution, but that the year-to-year persistence of SST anomalies in the subpolar Atlantic could not be explained in the absence of an active ocean.

There is a close connection, though, between the eastward propagation of the global decadal mode herein and the temperature anomaly in the Gulf Stream region, as seen in Fig. 2. To highlight this connection, Fig. 3 zooms into the Gulf Stream area within the curvilinear rectangle (35 N–46 N, 287 E–310 E). A cold anomaly is observed in phases 1.4 years–5.5 years, and a warm anomaly in phases 6.9 years–11 years. Further to the northeast in the domain (46 N–60 N, 320 E–330 E), a warm anomaly is observed in phases 2.8 years–5.5 years, and a cold anomaly in phases 8.2 years–11 years as the oscillatory 11-years mode propagates eastward.

Fig. 3
figure 3

Composites of the 11-years mode of global STs shown in Fig. 2, but zooming over the North Atlantic basin (NAB) in the Gulf Stream area (35 N–46 N, 287 E–310 E), in eight phase categories. This area encompasses both the Cape Hatteras and Great Banks regions (CHR and GBR), as defined by Feliks et al. (2011); see text for details

Full size image

This spatial pattern and the eastward propagation in the NAB resemble the oscillatory modes found by Groth et al. (2017) in their MSSA investigation of the SST field from the Simple Ocean Data Assimilation (SODA: Carton and Giese 2008; Giese and Ray 2011) reanalysis. A. Groth and colleagues found highly significant oscillatory modes with periods in the 7.7–13 years band. Similar oscillatory patterns have already been reported in the analysis of instrumental SST records for the NAB. Sutton and Allen (1997) had identified already in their analysis of shipboard observations a northward propagation of SST anomalies Their dominant spectral peak, though, was centered at 12–14 years in the SST power spectrum.

Feliks et al. (2011) found in the Cape Hatteras and Great Banks regions—CHR = (34  N–43.5 N, 75 W–60 W), where the Gulf Stream front associated with the subtropical gyre separates from the coast, and GBR = (42 W–50 N, 55 W–35 W), where the Gulf Stream front diverges abruptly due to the confluence between the subtropical and subpolar gyres—oscillatory modes with periods of 8.5 and 10.5 years, respectively. Siqueira and Kirtman (2016) used SODA data and an older high-resolution model, namely CCSM4. They repeated the analyses of Feliks et al. (2011) over the same two regions, CHR and GBR, by applying MSSA to SODA data and to CCSM4 simulations; the latter used the current IPCC horizontal resolution and the higher resolution recommended by Feliks et al. (2004, 2007) and implemented by Minobe et al. (1994; Jiang et al. 1995a; Ghil and Robertson 2000; Ghil et al. 2002).

Finally, the variance of these global modes is rather small, not exceeding 10% of total interannual variance. Still, they can be useful tools in predicting changes in year-to-year large-scale features, as is certainly the case for the Tropical Pacific and regions teleconnected to it (e.g., Barnston et al. 2012), while longer-range predictions that rely on the decadal mode might require more detailed assessment (e.g., Plaut et al. 1995).

All this being said, we are left with the rather puzzling quandary of the difference between the present results and those of Kravtsov et al. (2018, and references therein): (i) the global decadal mode we find herein, in the CESM simulation and the two reanalyses, does not resemble their GSW; while (ii) these authors do find the GSW in the NCEP-NCAR reanalysis they have relied upon but not in the CMIP5 simulations.

Kravtsov et al. used the same time series analysis methodology, MSSA (Ghil and Vautard 1991; Plaut and Vautard 1994; Plaut et al. 1995; Ghil et al. 2002), as done in the present paper, although there might be some technical details that differ. In fact, their GSW bears some similarity to the multidecadal variability described in previous work by Ghil et al. (e.g., Ghil and Vautard 1991; Plaut et al. 1995; Moron et al. 1998; Chao et al. 2000); see, in particular, see, in particular, (1998, Fig. 3). Moreover, the LDM decomposition of Gavrilov et al. (2020b) found some of their leading LDMs to be associated with regional patterns concentrated either in the Atlantic or the Pacific Ocean.

Concerning the absence of the GSW from the CMIP5 simulations (Kravtsov 2017, Table 1) analyzed by Kravtsov and colleagues, this might be due to the ensemble averaging, which probably included models with insufficient horizontal resolution. Recall, once more, that Feliks et al. (2004, 2007) concluded—by using detailed horizontal resolution experiments in simplified atmospheric models—that a resolution of 50 km or better was necessary to reproduce the effect of oceanic SST fronts, like the Gulf Stream or the Kuroshio, on the atmosphere above and downstream. This conclusion was verified in GCMs with uniformly high resolution by Minobe et al. (1990, 2008, 2012) concentrated on Sun-climate effects upon the Pacific basin’s quasi-decadal variability, with an emphasis on the Tropical Pacific. The latter group started its study with a relatively simple delayed-action oscillator (Graham et al. 1990) and emphasized this oscillator’s resonant response to solar-cycle forcing (White and Liu 2008) in follow-up work with the Fast Ocean-Atmosphere Model (FOAM) fully coupled ocean-atmosphere GCM.

The picture here is somewhat more complex: The decadal-scale evolution of the tongue in the western Tropical Pacific and of the horseshoe in the eastern Pacific do actively participate in our global mode. But we have clearly shown that other large areas of the globe are quite active in this mode. In particular, Fig. 3 illustrated the decadal evolution of gyre-mode–type features in the northwestern sector of the North Atlantic that had been studied over a full hierarchy of oceanic and atmospheric models and several data sets by Feliks et al. Jiang et al. (1995b) through Feliks et al. (2011) and on to Feliks et al. (2016); see the Dijkstra and Ghil (2005) review and recent observational confirmation by Groth et al. (2017).

It appears therewith that separate North Atlantic, Pacific, and high-latitude modes synchronize to give rise to a global decadal mode, as described in Sect. 3 where solar activity was absent and discussed in Sect. 6.2. It is this global mode of purely internal variability that responds resonantly in nature to the very small and somewhat irregular 11-years solar forcing, and it is this resonant response of the intrinsic global decadal mode of Sect. 4 that yields the amplitude and pattern of the mode we found in the reanalysis studied in Sect. 4.

In order to provide further insights into interannual climate LFV and the solar cycle’s role therein, it will be necessary (i) to apply advanced time series analysis tools to both GCM simulations and observational datasets; and (ii) to use a full hierarchy of climate models—from the simplest conceptual models to IPCC-class GCMs (e.g., Ghil 2001, 2019; Held 2005)—to ascertain the mechanisms that give rise to the global oscillatory modes identified and described herein.