1. Introduction
The North Atlantic (NA) region exhibits pronounced multidecadal variability such as that in sea surface temperature (SST) (Folland et al. 1986; Kushnir 1994; Knight et al. 2005; Álvarez-García et al. 2008), hurricane activity (Goldenberg et al. 2001), or Sahel rainfall (Folland et al. 1986; Zhang and Delworth 2006). There is an ongoing debate about the mechanisms underlying the multidecadal variability in the NA region, and external and internal factors have been proposed to explain the variability (e.g., Latif and Keenlyside 2011; Ting et al. 2014; Bellomo et al. 2018; Zhang et al. 2019). Unfortunately, instrumental data are limited, hindering understanding the origin of the multidecadal variability. For example, instrumental SSTs with relatively good spatial coverage or station-based sea level pressure (SLP) data only are available for about the last 150 years, which is too short to investigate in detail the causes and characteristics of multidecadal climate variability. Records of other quantities such as subsurface ocean temperatures or ocean circulation parameters are even shorter. Observations of the Atlantic meridional overturning circulation (AMOC) at 26.5°N (Cunningham et al. 2007; Kanzow et al. 2007) or moored observations of the deep western boundary current (DWBC) in the northwest Atlantic (Toole et al. 2017), for example, only had started in 2004. At 53°N, the western boundary current system of the Labrador Sea has been measured by moorings since 1997 (Zantopp et al. 2017), allowing us to merely resolve multiyear to decadal changes. Some insight into the nature of the multidecadal variability in the NA, however, was obtained from long-term surface observations, and these suggest that ocean circulation is the major factor influencing NA SST variability at decadal to multidecadal time scales whereas the atmosphere drives the NA SST variability on shorter time scales (Bjerknes 1964; Latif et al. 2006; Gulev et al. 2013; Bryden et al. 2020). This picture is supported by ocean–sea ice general circulation models that have been forced by time-dependent atmospheric surface observations. Álvarez-García et al. (2008), for example, report that the observed multidecadal SST variability during 1958–2000 exhibits a close link to the ocean model’s AMOC.
The limited observations are the reason why heavy use is being made of multicentennial to millennial control integrations of climate models to explore the nature of internal multidecadal variability in the Atlantic. Additional insight into the mechanisms of multidecadal variability is obtained from historical simulations with climate models, in which estimates of observed external forcing 1850–2014 is specified (Taylor et al. 2012; Zhang and Wang 2013; Weyer et al. 2020). However, climate models have generally been unable to simulate atmospheric anomalies in the extratropics as strong as the observed such as that in the North Atlantic Oscillation (NAO) in either coupled (Gillett 2005) or in forced mode with specified observed boundary conditions (Scaife et al. 2009). Moreover, climate models suffer from biases that are particularly prominent in the subpolar NA, with large errors in mean-state SST and sea surface salinity (SSS), which in turn may bias decadal variability (Menary et al. 2015). In fact, climate models disagree with regard to the origin of the multidecadal variability in the NA, its periodicity, and its spatial structure.
In many climate models, midlatitude and subpolar multidecadal SST variations are significantly correlated with fluctuations in the AMOC (e.g., Ba et al. 2014; Sun et al. 2020), suggesting a link to northward heat transport changes, consistent with the early studies of Delworth et al. (1993); Timmermann et al. (1998) and Latif et al. (2004). Some studies link interdecadal AMOC variability in a variety of models to westward propagating baroclinic Rossby waves (te Raa and Dijkstra 2002; Frankcombe et al. 2008; Sévellec and Fedorov 2013). Besides, a coupled upper ocean–atmosphere–sea ice mode (Escudier et al. 2013) may interact with the westward propagating anomalies (Ortega et al. 2015). However, all these mechanisms might be model dependent.
The subpolar gyre (SPG), also in line with Delworth et al. (1993), interacts with the AMOC (Zhang 2008; Lohmann et al. 2009) and plays an important role in preconditioning the density structure in the NA sinking region in a number of climate models. Meanwhile, some observational and modeling studies suggest that specific SST anomalies in the NA can induce a winter NAO response, which will influence the AMOC by affecting oceanic deep convection (Sutton et al. 2018). Therefore, there may be important dynamical ocean–atmosphere interactions operating in the multidecadal variability over the NA region (Grossmann and Klotzbach 2009; Sun et al. 2019).
Comparisons between slab ocean and fully coupled general circulation model simulations are commonly used for understanding the relative roles of atmospheric forcing and ocean dynamics on SST. The role of the ocean circulation in driving multidecadal SST variability in the Atlantic, which is termed Atlantic multidecadal oscillation (AMO) or Atlantic multidecadal variability (AMV), has been challenged by Clement et al. (2015), arguing that the main features of the observed AMO are reproduced in models where the ocean heat transport is prescribed. Allowing the ocean circulation to interact with the atmosphere does not significantly alter the characteristics of the AMO in the analyzed climate models. The results of Clement et al. (2015) suggest that the AMO is the response to stochastic forcing from the midlatitude atmospheric circulation. Finally, external forcing, natural and anthropogenic, also has been suggested to explain some of the multidecadal climate variability observed in the NA region (e.g., Otterå et al. 2010; Booth et al. 2012; Muthers et al. 2016).
Here we present a control integration of a version of the Kiel Climate Model (KCM), in which variability of the ocean circulation and dynamical ocean–atmosphere coupling are crucial in producing a quasi-oscillatory multidecadal mode with an irregular period of 25–50 years over the NA region that clearly sticks out above red noise, where the multidecadal time scale is set by the ocean circulation. The atmosphere locally responds to the SST anomalies in the SPG region, thereby reinforcing ocean circulation change and lengthening the time scale.
The multidecadal mode can be understood within the stochastic climate model framework that can be considered as null hypothesis for the generation of internal climate variability. This conceptual model has been originally formulated in a rather general manner by Hasselmann (1976), and different versions of the model have been applied to explain some aspects of the variability in the NA on a variety of time scales (Frankignoul 1985; Saravanan and McWilliams 1997). Mecking et al. (2014) studied an ocean–sea ice general circulation model (NEMO) that was driven using white noise forcing associated with the NAO. The AMOC and SPG strength in that simulation both exhibit enhanced power at low frequencies but no dominant time scale, and thus provide no evidence for an oscillatory ocean-only mode of variability. Here we study the variability in a control integration of a coupled atmosphere–ocean–sea ice general circulation model, the KCM, that employs an ocean–sea ice component of the NEMO family. Therefore, our coupled simulation, in some way, can be understood as an extension of the uncoupled study by Mecking et al. (2014).
We address the following questions in this study: first, what is the role of the Atlantic Ocean circulation, wind-driven and buoyancy-driven, in the multidecadal variability? Second, how do the SPG and AMOC interact? Third, what is the role of dynamical ocean–atmosphere coupling in the multidecadal variability? Finally, is the multidecadal variability consistent with the stochastic climate model framework? And if so, what stochastic model applies to the multidecadal variability simulated by the KCM, what is the stochastic forcing, and what spectral characteristics does it exhibit?
The paper is organized as follows. Section 2 gives an overview of the data and methods used in this study. The results are presented in section 3. The major findings of this study are summarized and discussed in section 4.
2. Material and methods
a. Data
Observations are used to calculate long-term climatologies for model comparison (Fig. 1). The SST climatology for 1955–64 is from the World Ocean Atlas 2018 (WOA18) with 1° × 1° resolution (Locarnini et al. 2018; https://www.nodc.noaa.gov/OC5/woa18/). Observed SLPs during 1900–2012 with 5° × 5° resolution are from the Hadley Centre Sea Level Pressure dataset (HadSLP2r; Allan and Ansell 2006).
(a) Long-term annual-mean SST (°C) in the KCM. (b) SST bias relative to the long-term annual-mean SST derived from observations 1955–64 provided by WOA18. (c) Long-term annual-mean SLP (Pa) in the KCM. (d) SLP bias relative to the long-term annual-mean SLP observations 1900–2012 calculated from HadiSLP2r. The observations have been linearly detrended. All 3000 years of the control run were used in computing the means of the KCM.
Citation: Journal of Climate 34, 16; 10.1175/JCLI-D-20-0725.1
We analyze a multimillennial, 3000-yr-long, preindustrial control integration of a version of the Kiel Climate Model using a CO2 concentration of 286 ppm. A list of references of published studies employing different versions of the KCM, originally described in Park et al. (2009), can be obtained from https://www.geomar.de/kcms. The KCM version that is used here employs ECHAM5 (Roeckner et al. 2003) as atmospheric component, with a horizontal resolution of T42 (2.8° × 2.8°) and 19 vertical levels. The ocean–sea ice component is NEMO (Madec 2008) on a 2° Mercator mesh (ORCA2) horizontally, with increased meridional resolution of 0.5° near the equator and 31 vertical levels. The atmosphere model is coupled to the ocean–sea ice model via OASIS (Valcke et al. 2006). A surface freshwater flux correction (FWC) is applied to the model over the NA (10°–80°N), which not only largely eliminates upper-ocean salinity biases over that region but also considerably reduces the cold SST and upper-ocean temperature biases over the NA (Park et al. 2016).
The simulated long-term annual mean SSTs (SLPs) over the NA and the biases relative to the long-term climatologies from observations are shown in Figs. 1a and 1b (Figs. 1c,d). There is still an obvious cold SST bias over the NA (Fig. 1b), indicating that the FWC, although removing sea surface salinity biases, does not completely eliminate the cold SST bias. The remaining cold SST bias is comparable to the multimodel ensemble-mean cold SST bias calculated from models participating in phases 3, 5, and 6 of the Coupled Model Intercomparison Project (CMIP3, CMIP5, and CMIP6) (see Fig. 3 in Bock et al. 2020). The SLP climatology is an indicator of the mean low-level atmospheric circulation, and the KCM’s SLP climatology clearly depicts the Icelandic low and the Azores high (Fig. 1c). SLP biases are on the order of several hectopascals in the pressure centers (Fig. 1d).
Additionally, a 700-yr-long sensitivity experiment is conducted with the KCM, in which daily wind stress is randomly chosen from a 700-yr-long chunk of the control run, but obeying the seasonal cycle, and specified over the global ocean (Wrandom hereafter). Annual anomalies are used for the analyses throughout the paper unless otherwise stated.
b. POP analysis
The principal oscillation pattern (POP) analysis (Hasselmann 1988; von Storch et al. 1988, 1995) is a multivariate statistical technique designed to infer simultaneously the characteristic patterns and time scales of a vector time series. POPs are defined as the normal modes of a linear dynamical representation of the data in terms of a first-order autoregressive vector process with residual noise forcing. Let X(t) represent an n-dimensional stochastic process. For practical purposes, the original process is usually reduced into the subspace of leading empirical orthogonal function (EOFs; Lorenz 1956). Hence, X is composed of the leading principal components (PCs). The evolution of X is represented as a first-order multivariate Markov process: X(t + 1) =
We link the variability associated with the leading POP mode, which we have derived from PSI, MOC, and SLP, to other variables over the NA by means of lag regression analysis.
c. Statistical methods and definition of climate indices
We depict maps of linear regression coefficients of different variables on selected indices, calculated at different time lags, where the indices have been normalized by their respective standard deviation σ. An F test is used to test the significance of the regression coefficients. The Student’s t test and Monte Carlo simulation based on nonparametric random phase (Ebisuzaki 1997) are applied to test the significance of the correlation coefficients. Cross-spectral analysis is used to investigate the relationship between two time series in the frequency domain. Sun et al. (2020) used the method to investigate the links of area-averaged North Atlantic SST indices to some of their mechanistic drivers. For the computation of cross-spectra, we use the Hamming window and set the window length to 200 samples with an overlap of 120 samples (e.g., von Storch and Zwiers 2001). Welch’s method of overlapped averaged periodogram is applied (Welch 1967). The power spectrum estimate is obtained by applying the Daniell window with length m to smooth the raw periodogram (Bloomfield 2004). The upper 90% and 95% confidence levels of the power spectra are calculated according to the chi-squared distribution of the variance of the background noise. If the lag-1 autocorrelation coefficient is negative or close to zero, white noise is chosen as the background spectrum; otherwise red noise is chosen [see details in Gilman et al. (1963)].
Several indices are used in this study. We primarily make use of the coefficient time series of the real part of the leading POP mode to obtain regression patterns of selected variables at different phases of the POP cycle. We note that theoretically the real and imaginary part time series of a (complex) POP mode are in quadrature. Further, we use an NAO index defined as the PC of the leading EOF of the SLP anomalies in winter [December–March (DJFM)] over the North Atlantic region (20°–80°N, 90°W–40°E), following Hurrell et al. (2013), which accounts for 52.7% of the variance. We additionally define a Greenland SLP index (GI), which is the area mean of the SLP anomalies over the southern Greenland region (54.4°–68.4°N, 60°–22.5°W), where only ocean grid points are used in the calculation of the index. The reason for defining the GI is given in section 3 when discussing the atmospheric response to the SST anomalies south of Greenland. An SST index is defined as the PC of the leading EOF of the SST anomalies over the extratropical NA (20°–70°N, 80°W–0°E), which is termed PC1SST and accounts for 21.4% of the total variance (the regression pattern shown in Fig. 6e is very similar to the leading EOF). In Wrandom, the leading SST EOF is very similar to that in the control run and accounts for 19.5% of the variance. An AMOC index is defined as the maximum of the overturning streamfunction at 40°N (Zhang 2008). Finally, an SPG index is defined as the inverted area average of the barotropic streamfunction anomalies over the subpolar NA (50°–58°N, 42°–26°W), similar to a previous study (Lohmann et al. 2009).
3. Results
a. Power spectra
As shown in Park et al. (2016), the Atlantic Ocean circulation simulated in the control run exhibits strong multidecadal variability. The power spectrum of the SPG index (Fig. 2a) and that of the AMOC index (Fig. 2b) are red with increasing variance toward longer time scales. Both spectra exhibit a statistically significant peak above the 95% confidence level (relative to red noise) at periods of 25–50 years. We note that the spectrum of the AMOC index is characterized by a steeper increase than the SPG spectrum, which is in line with the findings of Mecking et al. (2014). The spectrum of the GI (Fig. 2c) exhibits an almost even variance distribution across time scales, which is largely consistent with a white-noise type spectrum. There is, however, enhanced power at multidecadal time scales (relative to red noise) above the 95% confidence level in the spectrum of the GI, consistent with the spectra of the two ocean circulation indices. The spectrum of PC1SST (Fig. 2d) also exhibits significantly enhanced variability in the range 25–50 years.
(a)–(d) Power spectrum of indices from the KCM’s control run. The window length m for smoothing is 51 points. (a) SPG index spectrum (blue solid curve), and the 90% confidence level (green dotted curve) and 95% confidence level (red dotted curve) with reference to a fitted red-noise process (black dashed curve). (b) As in (a), but for the AMOC index. (c) As in (a), but for the Greenland SLP index (GI). (d) As in (a), but for PC1SST. Also shown are power spectra of the indices from the KCM’s random wind stress experiment (Wrandom): (e) SPG index, (f) AMOC index, (g) GI, and (h) PC1SST. The window length m for smoothing is 11 points. The indices have been normalized by their respective standard deviations prior to computing the spectra. All 3000 years of the control run were used in (a)–(d), and all 700 years of Wrandom in (e)–(h).
Citation: Journal of Climate 34, 16; 10.1175/JCLI-D-20-0725.1
Spectra of the same indices are shown from the sensitivity experiment Wrandom in Figs. 2e–h. In this experiment, the wind stress feedback on the ocean is inhibited. To resolve the multidecadal variability a different window length m is applied in calculating the spectra from Wrandom than in the control run, as the choice of m depends on the length of the time series. The power over the multidecadal time scale (25–50 years) in the spectra of the SPG index (Fig. 2e) and AMOC index (Fig. 2f) is strongly reduced compared to the control run with less prominent peaks, whereas the spectra of the GI index (Fig. 2g) and of PC1SST (Fig. 2h) do not exhibit any significant peaks exceeding the 95% confidence level in the range 25–50 years. The differences between the spectra indicate robust dynamical ocean–atmosphere interactions in the control run but not in the experiment Wrandom. We conclude that the multidecadal ocean circulation variability in Wrandom can be understood as an ocean-only mode that is strongly damped and merely sticks out above red noise. It is the dynamical coupling between the ocean and the atmosphere through the SST–wind stress feedback, which enhances the multidecadal variability and extends the variability toward longer time scales in the fully coupled run.
b. Combined principal oscillation pattern analysis
POP analysis is applied jointly to the barotropic streamfunction (PSI), the meridional overturning streamfunction (MOC), and the sea level pressure (SLP), where all 3000 years are used in the analysis. The leading POP mode (POP1) is complex and accounts for 23.7% of total joint variability. POP1 has a rotation period of 38 years and decay time (e-folding time) of 11 years. The second most energetic POP mode (POP2) accounts for 15% of the total variance. POP2 has a rotation period of 18.9 years and decay time of 6 years. Here we concentrate on the multidecadal variability and only discuss the variability associated with POP1.
We note that a POP analysis also has been performed jointly only on PSI and MOC (not shown). In that analysis, the leading POP mode accounts for 40.1% of the joint variability; it has a rotation period of 40.7 years and an e-folding time of 9.3 years, and the PSI and MOC patterns are very similar to those shown below from the POP analysis with the SLP included. Finally, a POP analysis of PSI, MOC, and SLP from Wrandom has been conducted. Overall, the leading POP mode calculated from Wrandom is similar to that derived from the control run. The most important difference between the leading POP modes calculated from the two simulations is the e-folding time amounting to only 5.7 years in Wrandom, which is about half of that in the control run. This further supports the important role of the wind stress–SST feedback for maintaining the multidecadal oscillation.
Only the last 300 years of the (complex) coefficient time series (PC) of POP1 are shown in Fig. 3a. However, both the real-part (PC1r) and imaginary-part (PC1i) exhibit marked multidecadal variability throughout the 3000-yr-long integration, as exemplified by the power spectra of PC1r and PC1i, which were calculated over all 3000 years and both exhibit statistically significant peaks near the rotation period of 38 years (Figs. 3b,c). The power drops but remains large at centennial time scales in both spectra. PC1i clearly leads PC1r (Fig. 3a). However, the phase difference at the rotation period slightly deviates from π/2, which is expected from the POP concept, as derived from cross-spectral analysis of the two time series (Fig. 3d), indicating some asymmetry in the POP cycle. Finally, there is highly significant squared coherence between PC1r and PC1i at multidecadal time scales (Fig. 3d).
(a) Last 300 years of the real-part (PC1r) and imaginary-part coefficient time series (PC1i) of the leading POP mode (POP1) derived from the control run. (b) Power spectrum of PC1r. (c) Power spectrum of PC1i. The window length m for smoothing is 51 points. The time series have been normalized by their respective standard deviations prior to computing the spectra. The 90% confidence level, 95% confidence level, and fitted red noise process are labeled as in Fig. 2. (d) Squared coherence (blue) and phase spectrum (orange stars) between PC1r and PC1i. The phase only is shown when the squared coherence exceeds the 95% confidence level (black dotted line). A phase lag of zero indicates that the two time series vary in phase (orange dotted line), while a positive (negative) phase lag indicates that PC1r leads (lags). All 3000 years of the control run were used in (b)–(d).
Citation: Journal of Climate 34, 16; 10.1175/JCLI-D-20-0725.1
The real and imaginary part patterns of POP1—POP1r and POP1i—are shown in Fig. 4, where the normalization has been changed back. POP1r exhibits quite large loadings in MOC, PSI, and SLP (Figs. 4a–c, respectively). This phase can be considered as the extreme phase of the POP cycle with respect to MOC. The MOC anomalies linked to POP1r (color shading in Fig. 4a) represent an anomalously strong AMOC with a basinwide positive overturning streamfunction anomaly (see also Fig. 5e) similar to that described in the context of the Atlantic multidecadal variability simulated in the original KCM version (Park and Latif 2008). Explained variances (contours in Fig. 4a) amount to about 80% in the center of the overturning anomalies and 30% near the equator. Moreover, PC1r is strongly correlated with the AMOC index (defined at 40°N). The correlation coefficient between the two time series is largest at zero lag and amounts to 0.8, which is significant at 95% confidence level.
Spatial patterns of POP1: (left) MOC (meridional overturning circulation streamfunction; Sv), (center) PSI (barotropic streamfunction; Sv), and (right) SLP (sea level pressure; Pa). Shown are the (a) real part pattern of MOC, (b) real part pattern of PSI, (c) real part pattern of SLP, (d) imaginary part pattern of MOC, (e) imaginary part pattern of PSI, and (f) imaginary part pattern of SLP. Color indicates loadings and contours explained variances. Explained variance is shown with a contour interval of 0.1 for MOC and PSI, and 0.01 for SLP.
Citation: Journal of Climate 34, 16; 10.1175/JCLI-D-20-0725.1
(a)–(i) Regression maps of the meridional overturning streamfunction (MOC) upon PC1r, and (j)–(r) of the barotropic streamfunction (PSI; color) with depth-integrated (50–500 m) ocean currents superimposed (arrows) from lag = −8 to lag = +8 years (at 2-yr intervals). Regression coefficients are calculated based on one standard deviation (σ) of PC1r. Color indicates the regressions; contours in (a)–(i) indicate explained variances shown with a contour interval (CI) of 0.1.
Citation: Journal of Climate 34, 16; 10.1175/JCLI-D-20-0725.1
The pattern of PSI linked to POP1r (Fig. 4b) exhibits large negative anomalies in the center of the SPG, describing an anomalously strong SPG. The largest explained variances are located in the Labrador Sea where they amount to about 60%. The correlation coefficient between PC1r and the SPG index amounts to 0.34 at zero lag and 0.44 when the SPG index leads by 5 years where the correlation is largest, both significant at the 95% confidence level. We additionally computed the correlation function between the SPG index and the AMOC index, which also yields a time lag of 5 years at the correlation maximum with the SPG index leading (not shown). South of the negative barotropic streamfunction anomalies, positive anomalies along the western boundary are observed (Fig. 4b), which will be addressed below when discussing the mechanism of the multidecadal variability.
The salient feature of the SLP anomalies linked to POP1r is the localized low pressure system over the southern Greenland area (Fig. 4c). PC1r accounts for a rather small fraction of the variance in the SLP (less than 10%), which is not surprising given the chaotic nature of the atmospheric variability. The atmosphere in the middle and high latitudes contains many chaotic subsystems spanning many different time scales, ranging from days to centuries, which is demonstrated by the spectrum of the GI exhibiting nearly white-noise shape (Fig. 2c). Therefore, the contour interval for the explained variance has been chosen as 0.01 in Fig. 4c (and Fig. 4f).
The imaginary part patterns of POP1 (i.e., the MOC, PSI, and SLP anomalies related to POP1i) are shown in Figs. 4d–f, respectively. PC1i leads PC1r by a quarter of the rotation period [Eq. (1)] (i.e., by about a decade), so that the patterns given by POP1i can be considered as precursor patterns with respect to the patterns given by POP1r. MOC exhibits large-scale negative anomalies south of about 40°N with explained variances on the order of 20% and relatively small positive anomalies in the region 50°–60°N (Fig. 4d). With respect to PSI (Fig. 4e), POP1i exhibits relatively large anomalies in the subpolar NA that account for a substantial fraction of the variance in the barotropic streamfunction. In particular, there is a dipole anomaly in PSI around the southern tip of Greenland, with positive anomalies in the west and negative anomalies in the east. Explained variances amount to about 30% in the two poles. The negative PSI anomalies bend in a southwestern direction. The transition from POP1i to POP1r thus describes southward propagating overturning anomalies and an intensifying SPG.
The SLP pattern linked to POP1i (Fig. 4f) exhibits low pressure anomalies over the midlatitude NA, centered over the eastern part, and high pressure anomalies to the north, centered over the Labrador Sea and Nordic seas. The magnitude of the SLP anomalies, however, is much smaller than that in POP1r (Fig. 4c), so that the evolution of the SLP anomalies to first order can be understood as a standing oscillation. Overall, the anomalies related to POP1 exhibit rather complex propagation characteristics with regard to MOC and PSI and interactions between them, and also suggests an atmospheric role in the multidecadal oscillation. These aspects will be discussed in more detail in the following subsections.
To understand the mechanisms behind the multidecadal variability described by POP1, we address the following questions: first, how do the oceanic overturning and gyre circulations change? Second, in which way do the ocean circulation changes influence the SST? Third, is the atmosphere sensitive to the SST changes? Fourth, if so, how does the atmosphere feed back onto the ocean? Fifth, how do the SPG and AMOC interact with each other? Sixth, what is the role of stochastic forcing in the multidecadal cycle? To address these questions, we primarily calculate maps of local regression coefficients of selected variables on PC1r at different time lags, ranging from lag = −8 years to lag = +8 years with a time step of 2 years, representing approximately half a cycle (Figs. 5–12). The regressions are based on a one standard deviation change (σ) in PC1r.
c. Ocean circulation change
Lag = 0 years represents the conditions associated with the real-part phase of POP1, namely POP1r, when MOC, PSI, and SLP are well developed and explain the most variance in the respective fields over the subpolar NA (Figs. 4a–c). As a consistency check, we first calculate the regression patterns of MOC (Figs. 5a–i) and PSI (Figs. 5j–r). The MOC and PSI regression patterns at lag = 0 years (Figs. 5e and 5n, respectively) well reproduce the POP1r patterns (Figs. 4a,b), and the regression patterns at lag = −8 years (Figs. 5a,j) are very similar to the POP1i patterns (Figs. 4d,e). Thus, the lag regression method appears to be well suited to investigate the space–time structure of oceanic and atmospheric anomalies that are associated with POP1, irrespective of whether or not the considered variable has been part of the POP analysis.
A small positive MOC anomaly first develops at lag = −8 years in the region 50°–60°N (Fig. 5a), which does not account for much variance at this time. The positive MOC anomaly strengthens in place and accounts there for most of the variance in the overturning streamfunction at lag = 0 years with values of about 80% (Fig. 5e). Furthermore, the positive MOC anomaly expands southward and remains relatively strong south of 40°N until lag = +8 years (Fig. 5i). At this time, first signs of a negative MOC anomaly develop in the subpolar NA. Overall, the MOC anomalies at lag = +8 years are similar to those at lag = −8 years but with opposite signs. In summary, the regressions of the overturning streamfunction anomalies on PC1r from lag = −8 to lag = +8 years illustrate the development of an anomalously strong AMOC and its subsequent weakening.
The regression maps of the PSI anomalies associated with PC1r have the anomalous depth-integrated (50–500 m) ocean currents superimposed as arrows (Figs. 5j–r). At lag = −8 years, there is a cyclonic (negative) barotropic streamfunction anomaly centered south of Greenland, which reaches southward to about 40°N. The cyclonic PSI anomaly in the SPG region subsequently intensifies and remains relatively strong without changing shape until lag = +2 years (Figs. 5j–o). Explained variances are not shown in Figs. 5j–r. As indicated by the two POP patterns (Figs. 4b,e), the explained variances in PSI are large in the subpolar NA throughout the POP cycle, amounting to up to 60% in localized regions. The small positive barotropic streamfunction anomalies off the coast of North America to the southwest of the large negative anomalies at lag = −8 years (Fig. 5j) strengthen during the subsequent years. There are two parts of the positive PSI anomalies that can be distinguished. The part close to the western boundary propagates southward along the western boundary (Figs. 5k–o), whereas the zonally elongated part propagates eastward and then northward east of the negative PSI anomaly (Figs. 5k–o). The meridional dipole structure in PSI from lag = +2 to lag = +6 years (Figs. 5o–q) represents an anomalously strong Gulf Stream/North Atlantic Current (NAC) system, consistent with the study of Koul et al. (2020) analyzing observations and a simulation with another global climate model. At lag = +8 years (Fig. 5r), positive PSI anomalies have replaced the negative PSI anomalies in the SPG region observed at lag = −8 years (Fig. 5j), indicating that the SPG has now weakened relative to its climatological mean state.
d. Influence of ocean circulation on SST
We next address the SST and net surface heat flux variability associated with POP1r. Major SST anomalies (Figs. 6a–i) go along with negative net heat-flux anomalies during all phases (Figs. 6j–r), indicating that the SST anomalies are driven by ocean dynamics as the atmosphere acts as a damping; that is, the ocean releases (takes up) heat when the SST anomalies are positive (negative). We conjecture that the warm SST anomalies observed in the subpolar NA from lag = −8 to lag = −2 years are mostly due to the anomalously strong gyre circulation (Figs. 4j–m). The strengthening AMOC (and associated heat transport) is suggested by the SST anomalies developing in the southwestern subtropical NA around lag = −2 years that subsequently propagate eastward and northward (Figs. 6d–i). At lag = +4 and lag = +6 years, the SST anomaly pattern is very similar to that when regressing the SST anomalies on an AMOC index (Sun et al. 2020, their Fig. 2g).
(a)–(i) Regression maps of sea surface temperature (SST) upon PC1r, and (j)–(r) of the net surface-heat flux (color) from lag = −8 to lag = +8 years (at 2-yr intervals). Regression coefficients are calculated based on one standard deviation (σ) of PC1r. Color indicates the regressions and contours indicate explained variances (CI is 0.1).
Citation: Journal of Climate 34, 16; 10.1175/JCLI-D-20-0725.1
e. Sensitivity of the atmosphere to SST anomalies
The atmospheric response to extratropical SST anomalies is still controversial (Czaja et al. 2019). Two types of response can be distinguished in atmospheric general circulation models, a linear baroclinic and a nonlinear barotropic response (Kushnir et al. 2002). Here, the linear atmospheric response appears to apply, which operates without synoptic eddy involvement. The linear response to surface heating is characterized by low-level wind convergence, with an associated cyclonic circulation, and an upper-level wind divergence, with an associated anticyclonic circulation (Thomson and Vallis 2018). At lag = −8 years, there is a positive SST anomaly east of the southern tip of Greenland (Fig. 6a). The positive SST anomaly grows and expands to the northeast and to the west during the following years (Figs. 6b–d). As the SST anomalies grow, atmospheric heating (negative heat flux anomalies) also becomes larger (Figs. 6k–m). We assume that the surface heating is linearly related to the SST anomaly south of Greenland. The cross-correlation function between PC1r, which is correlated with PC1SST at about 0.8 when PC1r leads by 1 year, and a near-surface (10 m) wind divergence index, defined as the area average over the southern Greenland region (57.2°–73.9°N, 56.25°–22.5°W), recovers the multidecadal periodicity and exhibits the largest negative correlation amounting to −0.3 (the 95% confidence level is 0.037) when PC1r leads by two years (not shown). At lag = 0 years, the magnitude of the correlation only is slightly smaller. The peak correlation increases to about 0.6 when applying an 11-yr running mean filter to the time series, whereby the structure of the cross-correlation function does not change. Thus, the SST anomaly south of Greenland goes along with low-level wind convergence over the southern Greenland area, supporting the notion of a linear atmospheric response.
We note the strong meridional gradient at the southern flank of the SST anomaly south of Greenland at lag = 0 years (Fig. 6e). Therefore, we also attempt to obtain insight into the role of surface baroclinicity changes in the atmospheric response. For this purpose, we only use winter averages (DJFM), as synoptic eddy activity is strongest during this part of the year. The correlation of the GI with the meridional gradient at the southern flank of the SST anomaly (evaluated over the region 51.6°–60°N, 53.4°–30.9°W), which serves as a measure of surface baroclinicity change, is insignificant. The result remains virtually unchanged when moving the box, over which the meridional gradient of the SST anomaly is calculated, by ±2° latitude. We finally note that the vertical structure of the atmospheric pressure changes is baroclinic (not shown), with anomalously high pressure aloft, also indicating that the atmospheric response is dominated by the linear regime.
f. Low-level atmospheric variability and its feedback on the ocean
We now investigate in more detail the low-level atmospheric changes and their feedback on the ocean. Regression maps of the SLP anomalies upon PC1r are shown in Figs. 7a–i, and regression maps of the wind stress (arrows) and wind stress curl anomalies (color shading) in Figs. 7j–r. Explained variances are small with values typically less than 10%, as discussed above. This is why the contour interval for the explained variance in the SLP regression maps is set to 0.01 in Figs. 7a–i, while it is 0.1 otherwise. The SLP regression map at lag = 0 years well reproduces the POP1r pattern (Fig. 4c), and the regression map at lag = −8 years is similar to the POP1i pattern (Fig. 4f). The salient feature in the SLP regression maps is the anomalously low pressure over large regions of the NA. This pattern is not the NAO pattern, but it projects on it. Most important to our discussion concerning the mechanism underlying the variability linked to POP1 is the deepening of the low pressure anomaly over the southern Greenland area from lag = −8 years to lag = −2 years (Figs. 7a–d). The low pressure anomaly starts weakening after lag = −2 years and has disappeared at lag = +8 years (Fig. 7i), when SLP anomalies are small over the entire NA. Anomalous surface westerlies are observed on the southern flank of the low pressure anomaly center, which are particularly well developed from lag = −4 years to lag = 0 years (Figs. 7l–n). The associated wind stress curl (color shading) is positive south of the southern tip of Greenland and provides cyclonic vorticity to the ocean, which explains the strengthening of the barotropic streamfunction during this time (Figs. 5l–n). In the experiment Wrandom in which the wind stress feedback is inhibited, the PSI and SLP regressions upon PC1r (from the POP analysis of Wrandom) are similar in structure from lag = −6 to lag= −2 years but weaker by about 40%–50%. This again demonstrates the importance of the positive wind stress (curl) feedback on the SPG in the control run.
(a)–(i) Regression maps of sea level pressure (SLP; only shown over ocean points) upon PC1r, and (j)–(r) of the wind stress curl (color) with wind stress vectors superimposed (arrows) from lag = −8 to lag = +8 years (at 2-yr intervals). Regression coefficients are calculated based on one standard deviation (σ) of PC1r. Color indicates the regressions and contours in (a)–(i) indicate explained variances (CI is 0.01).
Citation: Journal of Climate 34, 16; 10.1175/JCLI-D-20-0725.1
At this stage of the analysis, the following points can be made about the multidecadal variability described by POP1 (Figs. 5–7): first, there are major changes in the ocean circulation, horizontal and vertical (Fig. 5), with the SPG leading the AMOC. Second, it is the changes in the ocean circulation that drive the major SST changes, as the surface heat fluxes act as a damping (Fig. 6). Third, the atmosphere responds to the SST anomalies south of Greenland in the form of a rather localized low pressure anomaly (Figs. 7a–i) centered over southern Greenland. Fourth, the associated changes in the wind stress curl (Figs. 7j–r) add cyclonic vorticity to the ocean, which intensifies the SPG. Fifth, the stronger SPG reinforces the SST anomaly south of Greenland, which in turn further deepens the low pressure anomaly. Thus, there is a positive feedback loop between the SST, SLP, wind stress (curl), and SPG, as already indicated by the spectral analyses (Fig. 2), through which anomalies in these quantities grow from about lag = −6 to lag = −2 years. Sixth, the AMOC (Figs. 5a–i) intensifies over the years, with very first signs in the subpolar NA at lag = −8 years, and the AMOC is suggested to drive the surface warming over most of the NA beyond lag = 0 years (Figs. 6a–i), keeping in mind that the surface heat fluxes act as a damping on the SST anomalies throughout the POP cycle.
g. SPG–AMOC interaction
How do the gyre and the overturning circulation interact with each other? We calculate the regression maps of sea surface salinity (SSS) and freshwater flux (FW) anomalies upon PC1r (Fig. 8). The major SSS anomalies must be due to ocean circulation changes, because the SSS and FW anomalies generally have the same sign (i.e., anomalously high SSS goes along with anomalously high freshwater input and vice versa). We note that sea ice variability cannot explain the size of the SSS anomalies (not shown). Further, the anomaly patterns of the net heat flux (Figs. 6j–r) and of the freshwater flux (Figs. 8j–r) bear some resemblance, suggesting that both fluxes are part of the atmospheric response to the SST anomalies south of Greenland. Positive SSS anomalies first appear at lag = −8 years in the Greenland Sea and in the Irminger Sea. The SSS anomalies expand thereafter and at lag = −4 years positive SSS anomalies are observed in all three deep convection sites of the NA (Fig. 8c), in the Labrador Sea, Irminger Sea, and Greenland Sea [see Park et al. (2016) for the deep convection sites in the KCM version used here]. The SSS anomalies intensify until about lag = −2 years (Fig. 8d), along with the strengthening SPG. We therefore attribute the positive SSS anomalies during this time to the enhanced gyre transporting more salinity into the NA’s sinking region. From lag = 0 years onward (Figs. 8e–i), positive SSS anomalies also appear in the midlatitudes, which is likely due to the strengthening AMOC (Figs. 5e–i) through enhanced meridional transport, keeping in mind that the FW anomalies (Figs. 8n–r) cannot account for the increasing SSS. Farther south, near the western boundary, negative SSS anomalies are observed that propagate northward along the boundary (Figs. 8e–i). The origin of these negative SSS anomalies is unclear. As the local FW anomalies are negative, as well as the rainfall anomalies (not shown), direct atmospheric forcing can be excluded. One plausible explanation for the negative SSS anomalies could be the stronger upper ocean currents (Figs. 5o–r) associated with the stronger AMOC, which reduce the time over which the surface waters are exposed to the net evaporation prevailing in this region, which will show up as negative SSS anomalies.
(a)–(i) Regression maps of sea surface salinity (SSS) upon PC1r, and (j)–(r) of the freshwater flux from lag = −8 to lag = +8 years (at 2-yr intervals). Regression coefficients are calculated based on one standard deviation (σ) of PC1r. Color indicates the regressions and contours indicate explained variances (CI is 0.1).
Citation: Journal of Climate 34, 16; 10.1175/JCLI-D-20-0725.1
We next investigate the surface density and mixed layer depth (MLD) anomalies (Fig. 9). The regression patterns of the surface density anomalies (Figs. 9a–i) are similar to that of the SSS anomalies (Figs. 8a–i). Large positive surface density anomalies in the regions of oceanic deep convection are simulated from lag = −4 to lag = 0 years (Figs. 9c–e), which also are the regions of large SSS anomalies (Figs. 8c–e). Because the positive SST anomalies observed in these regions reduce the surface density, the higher surface density must be due to the anomalously high SSSs. In response to the enhanced density, the MLD increases in the deep convection sites of the NA (Figs. 8k–m). Larger MLD implies intensified deep convection, which in turn strengthens the AMOC (Figs. 5a–i). After lag = 0 years, the surface density begins to decline in the sinking region (Figs. 9f–i), which is presumably due to the weakening SPG (Figs. 5o–r), and MLD anomalies begin to reduce (Figs. 9o–r). The MLD anomalies south of Greenland become negative at lag = +4 years (Fig. 9p), which will slow the AMOC.
(a)–(i) Regression maps of sea surface density upon PC1r, and (j)–(r) of the mixed layer depth (MLD) from lag = −8 to lag = +8 years (at 2-yr intervals). Regression coefficients are calculated based on one standard deviation (σ) of PC1r. Color indicates the regressions and contours indicate explained variances (CI is 0.1).
Citation: Journal of Climate 34, 16; 10.1175/JCLI-D-20-0725.1
To assess the relative importance of the different deep convection sites on the ocean circulation two MLD indices are defined, whereby the definition is guided by regressing the MLD upon PC1r (Fig. 10a). A south Greenland index (S-GI) is defined as the area average of the MLD over the Irminger Sea and Labrador Sea (box A) and a Greenland Sea index (GSI) as the area average of the MLD over the Greenland Sea (box B). The SPG index and the AMOC index are regressed upon the two MLD indices (Figs. 10b and 10c, respectively). Both ocean circulation indices are significantly related to the MLD in the two regions, consistent with the MLD regressions upon PC1r (Fig. 9). We conclude that both deep convection regions are important in driving the SPG and the AMOC, whereby the S-GI region (box A) appears to have a stronger influence on the multidecadal ocean circulation variability. The SPG index approximately varies in phase with whereas the AMOC index lags the MLD anomalies in the two deep convection regions, where the time lags between the MLD indices and the AMOC index are consistent with previous modeling studies (Msadek and Frankignoul 2009; Danabasoglu 2008).
(a) Regression map of MLD upon PC1r at lag = 0 years. Regression coefficients are calculated based on one standard deviation (σ) of PC1r. Color indicates the regressions and contours indicate explained variances (CI is 0.1). The South Greenland MLD index (S-GI) is defined as the area average over box A and the Greenland Sea MLD index (GSI) as the area average over box B. (b) Lag-regression functions between the SPG index and S-GI (blue curve) and GSI (orange curve). Filled dots indicate that the correlations are significant at the 95% level. (c) As in (b), but for the AMOC index.
Citation: Journal of Climate 34, 16; 10.1175/JCLI-D-20-0725.1
A stronger AMOC transports more heat from the subtropics northward into the upper midlatitude and subpolar NA (Msadek et al. 2013). Specifically, the NAC component of the AMOC advects more warm and salty water from the subtropical gyre into the eastern part of the SPG, as already suggested by the SST and SSS (Figs. 6a–i and 8a–i, respectively). The top 700-m ocean heat content (OHC) regression maps depict a slow transition from negative (Fig. 11a) to positive anomalies (Fig. 11i) in the eastern part of the midlatitude and subpolar NA. This transition is due to the strengthening AMOC. We note that the dipole OHC anomalies, with negative anomalies in the southwest and positive anomalies in the northeast, observed from lag = 0 to lag = +8 years (Figs. 11e–i), are also typical of an anomalously strong AMOC in another climate model (Zhang 2008). The reverse pattern would be characteristic of an AMOC slowing, as suggested by a set of climate models (Saba et al. 2016). This relationship between weak AMOC and reduced OHC also exists in the KCM version used here, as described by Latif et al. (2019), who discuss fast decadal AMOC-slowing events.
(a)–(i) Regression maps of upper-ocean (0–700 m) heat content (OHC) upon PC1r, and (j)–(r) of the upper-ocean (0–700 m) salt content (OSC) from lag = −8 to lag = +8 years (at 2-yr intervals). Regression coefficients are calculated based on one standard deviation (σ) of PC1r. Color indicates the regressions and contours indicate explained variances (CI is 0.1).
Citation: Journal of Climate 34, 16; 10.1175/JCLI-D-20-0725.1
The top 700-m ocean salt content (OSC) exhibits large positive anomalies in the deep convection sites of the NA from lag = −4 to lag = 0 years (Figs. 11l–n). These OSC anomalies are instrumental in driving the stronger AMOC given the opposing influence of the positive OHC anomalies on upper-ocean density (Figs. 11c–e).
In Fig. 12, we depict the regression maps of the sea surface height (SSH; Figs. 12a–i) and top 700-m ocean dynamic height (ODH; Figs. 12j–r) anomalies. Although SSH is an ocean surface parameter, it integrates ocean variability from bottom to surface and is connected to the ocean interior changes (e.g., three-dimensional large-scale ocean circulation). From lag = −4 to lag = 0 years, the SSH anomalies are strongly negative in the sinking region of the NA (Figs. 12c–e). The changes in the SSH can result either from changes in the mass or mean density of the water column. As mass change by the FW is small, the negative SSH anomalies represent the increased formation of North Atlantic Deep Water (NADW), consistent with the MLD anomalies (Figs. 9l–n). The NADW is exported southward along the western boundary, as seen by the negative SSH anomalies off the coast of North America, and eventually reaches the tropical Atlantic exhibiting negative SSH anomalies from lag = +2 years onward (Figs. 12f–i). To the east of the negative SSH anomalies, positive SSH anomalies start to develop around lag = 0 (Fig. 12e). While the negative SSH anomalies are associated with the southward flowing deep cold water branch of the AMOC, the positive SSH anomalies are linked to the upper northward flowing warm water branch of the AMOC. The upper AMOC branch is emphasized by the top 700-m depth-integrated ODH anomalies that were calculated directly from the hydrostatic balance with referenced pressure level of 2000 dbar (Figs. 12n–r). Because the ODH is determined by the dynamical balance associated with ocean density distribution, it can show the temperature and salinity variations impacts. The ODH anomalies here must be due to the OHC anomalies (Figs. 11e–i), which exhibit a great resemblance regarding the spatial pattern. Moreover, the OSC anomalies are positive, as pointed out above (Figs. 11n–r), and thus cannot explain the ODH anomalies.
(a)–(i) Regression maps of sea surface height (SSH) upon PC1r, and (j)–(r) of the upper-ocean (0–700 m) dynamic height referenced to 2000 dbar (ODH) from lag = −8 to lag = +8 years (at 2-yr intervals). Regression coefficients are calculated based on one standard deviation (σ) of the PC1r. Color indicates the regressions, and contours indicate explained variances (CI is 0.1).
Citation: Journal of Climate 34, 16; 10.1175/JCLI-D-20-0725.1
At lag = +8 years, the phase reversal is almost completed: the positive ODH anomalies in the north give rise to a weaker SPG. At this time, the SLP and wind stress anomalies over the SPG region are relatively small (Figs. 7i,r), as they are at lag = −8 years. The weaker SPG reduces the salinity transport into the sinking region of the NA, which lowers the SSS and surface density, and in turn the MLD (Fig. 9). Finally, as reduced MLD is an indicator of less intense oceanic deep convection, the AMOC will slow with a time delay.
The important processes and time scales involved in the multidecadal variability over the NA, as described by POP1, are summarized schematically in Fig. 13. First, there is a fast positive ocean–atmosphere feedback involving the SPG, SST, SLP, and wind stress (curl). We infer from the regression maps that the positive feedback operates for about 4 years, from lag = −6 to lag = −2 years. The sequence of processes associated with the positive ocean–atmosphere feedback can be described as follows: the enhanced SPG drives positive SST anomalies south of Greenland through increased oceanic heat advection from the south, noting that the surface heat fluxes act as a damping on the SST anomalies. The positive SST anomalies drive a low pressure SLP anomaly that is centered over southern Greenland. The rather persistent and localized low pressure anomaly goes along with positive wind stress curl anomalies that add cyclonic vorticity to the ocean, thereby further intensifying the SPG.
Schematic diagram of the processes and time scales involved in the multidecadal oscillation described by the leading POP mode (POP1). The fast positive ocean–atmosphere feedback (red color) involving the SPG, SST, SLP, and wind stress (curl) operates for about 4 years. Enhanced SPG drives positive SST anomalies around south of Greenland through increased oceanic heat advection from the south, in turn driving a low pressure SLP anomaly centered over southern Greenland. The positive wind stress curl anomaly associated with the low pressure anomaly adds cyclonic vorticity to the ocean, thereby further intensifying the SPG. The delayed negative feedback is shown in the blue color. The SPG leads AMOC by about 5 years due to the density changes in the sinking region that are forced by the SPG. Anomalously strong AMOC influences the SPG by enhancing the upper-ocean heat content in the subpolar NA, which weakens the SPG. In response, the upper-ocean salinity transport into the sinking region diminishes and upper-ocean density reduces. According to the POP clock (1), the evolution from an anomalously strong AMOC to a “normal” AMOC is described by the transition from POP1r (lag = 0 years in the regressions) to the negative of POP1i (approximately lag = +8 years).
Citation: Journal of Climate 34, 16; 10.1175/JCLI-D-20-0725.1
Second, there is a slow adjustment of the AMOC to the density changes in the NA’s sinking region that provides the delayed negative feedback necessary for the oscillation. We note, however, that there is some overlap of the fast and slow feedback processes. The change in the AMOC influences the SPG in a way eventually bringing about the phase reversal by enhancing the upper ocean heat content in the subpolar NA, which weakens the SPG. In response, the upper ocean salinity transport into the NA’s sinking region diminishes and upper ocean density reduces. According to the POP clock (1), the evolution from an anomalously strong AMOC to a “normal” AMOC is described by the transition from POP1r (lag = 0 years in the regressions) to the negative of POP1i, which takes a quarter of the rotation period (i.e., about a decade). It is the SPG that connects AMOC change with oceanic deep convection, whereby the latter drives the AMOC that in turn influences the SPG. We infer from cross-correlation analysis that the SPG index leads the AMOC index by about 5 years (not shown), which together with the AMOC’s adjustment time scale of about a decade gives rise to the multidecadal periodicity. Additionally, the coupled ocean–atmosphere feedback between the SST and wind stress (curl) extends the multidecadal variability into longer time scales.
h. Stochastic forcing of the multidecadal oscillation
On the one hand, the atmosphere responds to the SST changes south of Greenland as part of the multidecadal variability linked to POP1, as indicated, for example, by the near-surface wind divergence anomalies over southern Greenland that are significantly correlated with the SST anomalies. The atmospheric response acts as a damping on the multidecadal SST anomalies, as shown by the corresponding surface heat flux anomalies. In the following, we show that on the other hand, the stochastic heat flux forcing by the atmosphere over the subpolar NA is driver of the multidecadal variability and essential to continuously exciting POP1 exhibiting a decay time of about a decade that is considerably smaller than the rotation period of 38 years.
Previous studies suggested that the NAO, which is the dominant mode of atmospheric variability over the NA sector in winter, is an important driver of low-frequency ocean circulation variability through associated heat flux variability (e.g., Eden and Jung 2001; Mecking et al. 2014; Delworth and Zeng 2016). We apply an EOF analysis to the KCM’s winter-mean (DJFM) net surface-heat flux anomalies over the extratropical NA (20°–70°N, 90°W–40°E). The first EOF (EOF1Qnet; Fig. 14a) accounting for 24.8% of the total variance is closely related to the model’s winter NAO, with a correlation coefficient of the corresponding principal component (PC1Qnet) with the wintertime NAO index amounting to 0.83. Further, a cross-spectral analysis between the two time series reveals highly significant squared coherence over a broad range of time scales with zero phase difference (Fig. 15a). EOF1Qnet exhibits a tripolar pattern, which is consistent with observations when the heat fluxes are caused by the positive phase of the NAO (Czaja and Marshall 2001). The negative heat flux anomalies (enhanced oceanic heat loss) over the Labrador Sea are most important here, as they were shown to drive the AMOC in a number of climate models and also in the KCM (Park et al. 2016). The power spectrum of PC1Qnet is consistent with white noise, exhibiting almost the same level of variance across time scales (Fig. 14b). We note the statistically significant multidecadal peak (relative to white noise) in the spectrum of PC1Qnet, which indicates that the atmospheric response to the multidecadal SST variability projects on the NAO. However, the major SLP response is a more localized pattern over the southern Greenland area, as described above (Fig. 7).
(a) Pattern of the leading EOF of winter-mean (DJFM) net surface-heat flux anomalies from the KCM’s control run. (b) Power spectrum (σ2) of the corresponding PC1 (blue curve), 90% confidence level (green dotted curve), and 95% confidence level (red dotted curve) with reference to a fitted white-noise process (black dashed curve). The time series has been normalized by its standard deviation prior to computing the spectrum.
Citation: Journal of Climate 34, 16; 10.1175/JCLI-D-20-0725.1
(a) Squared coherence (blue curve) and phase spectrum (orange stars) between the winter-NAO index (DJFM) and the PC of the leading net surface-heat flux EOF (DJFM), labeled PCQnet. The phase only is shown when the squared coherence exceeds the 95% confidence level (black dotted line). A phase lag of 0 indicates that the two time series vary in phase (orange dotted line), while a positive (negative) phase lag indicates that PCQnet lags (leads). (b) As in (a), but with the AMOC index. (c) As in (a), but with the real-part POP coefficient time series, PC1r. (d) As in (a), but with the SPG index.
Citation: Journal of Climate 34, 16; 10.1175/JCLI-D-20-0725.1
Next, cross-spectral analysis is performed between PC1Qnet and the AMOC index (Fig. 15b). The two indices only exhibit large squared coherence near the rotation period of POP1 with a phase difference close to zero, indicating an equilibrium response of the AMOC at this time scale. At the other frequencies, the squared coherence is relatively small. Thus, the AMOC only responds to the heat flux variability associated with EOF1Qnet in a narrow frequency range. Such behavior is consistent with the stochastic excitation of a multidecadal eigenmode by the nearly white noise heat flux forcing linked to EOF1Qnet that is related to the NAO. The results of the cross-spectral analysis are similar when replacing the AMOC index by PC1r (Fig. 15c), the POP coefficient time series of POP1r, which, as noted above, is closely related to the AMOC index with a correlation coefficient of 0.8 at zero lag. The cross-spectral analysis between PC1Qnet and the SPG index (Fig. 15d) also exhibits a squared-coherence peak near the rotation period but with a phase shift in the range of π/4 and π/2 (i.e., 4–8 years), with the SPG leading. This is consistent with the SPG leading the AMOC by several years and the atmosphere quickly responding to the SST anomalies south of Greenland, as shown above.
4. Summary and discussion
In this study, we investigate a multimillennial preindustrial control integration of a version of the Kiel Climate Model (KCM) and describe the mechanism underlying the simulated multidecadal climate variability in the North Atlantic (NA) sector. Specifically, we address the interactions between the subpolar gyre (SPG), the Atlantic meridional overturning circulation (AMOC), and the atmosphere. A principal oscillation pattern (POP) analysis is applied jointly to the barotropic streamfunction (PSI), meridional overturning streamfunction (MOC), and sea level pressure (SLP) to derive the leading modes of coupled variability in the NA sector. The leading POP mode accounting for 23.7% of the joint variance, which only is described in this study, is multidecadal with a rotation period (cycle length) of 38 years and a damping time of about a decade. We find that in the KCM, the interactions among the SPG, AMOC, and atmosphere are essential to understanding the nature of the multidecadal climate variability in the NA region. In principle, the eigenmode can be understood as an “ocean-only” mode, but the atmosphere plays an essential role by considerably enhancing the multidecadal variability.
The SPG is important in linking the AMOC to the atmosphere. Changes in SPG strength have two effects. First, they drive SST changes south of Greenland and second, they control the salinity transport into the sinking region of the NA. The SST change influences the atmosphere, where the atmospheric response primarily consists of a localized SLP anomaly centered over the southern Greenland area. The wind stress curl anomaly associated with the SLP change reinforces the SPG change. Thus, the SPG, SST, SLP, and wind stress form a positive feedback loop, and this amplifying feedback is important in enhancing and maintaining the multidecadal variability, as shown by a sensitivity experiment in which the wind stress feedback is inhibited.
Second, the change in the salinity transport in response to the altered SPG influences the upper-ocean density and in turn oceanic deep convection and, with a time delay, the AMOC. The adjustment of the AMOC provides the delayed negative feedback, which drives the phase reversal from one phase of the oscillation to the other by influencing the SPG in a manner that the resulting change is opposite to the initial SPG change. Some of the elements of the multidecadal variability observed in the KCM have also been described from a version of the Hadley Centre climate model by Dong and Sutton (2005) and in other climate models. To our knowledge, however, the three-way interaction between the SPG, the AMOC, and the atmosphere, which operates in the KCM, has not been previously described.
The mechanism in this study is different to that described in previous studies in which the AMOC variability is related to westward propagating baroclinic Rossby waves (e.g., Sévellec and Fedorov 2013). When the density anomalies associated with the Rossby waves reach the western boundary, the resulting zonal density gradient will lead to an AMOC anomaly according to the thermal wind balance. This relationship, however, cannot be established in observations, and climate models suggest it operates on shorter time scales than multidecadal. In our study, although a similar pattern is observed, for example in the OHC (Fig. 11), the dipole is not related to westward propagating density anomalies. The density gradient may influence the AMOC, but it is not the main driver of the AMOC.
This study supports the interpretation of the KCM’s multidecadal variability in the NA region as a stochastically forced eigenmode. Latif et al. (2002) introduced a concept composed of three stochastic models: the simple first-order model, in which the ocean mixed layer is stochastically forced by the surface fluxes; the stochastic excitation of an eigenmode of the ocean circulation; and the stochastic excitation of an eigenmode of the coupled ocean–atmosphere system. The multidecadal variability described here seems to belong to the second category, where the stochastic forcing, exhibiting nearly white-noise character, is provided by heat flux variability linked to the NAO. However, ocean–atmosphere coupling over the southern Greenland area is key to enhancing the level of multidecadal variability, especially in SST, and extending the variability to longer time scales.
This study supports previous studies (e.g., Delworth et al. 2017; Sun et al. 2018; Zhang et al. 2019), suggesting that the ocean circulation is crucial in the generation of the multidecadal variability in the NA region. However, climate models simulate a wide range of multidecadal variability with varying spatial patterns, time scales, and mechanisms. Since instrumental observations are limited, in the ocean and in the atmosphere, it is not possible to verify by data the existence of a multidecadal eigenmode in the NA sector and its underling mechanism as simulated by the KCM, specifically the three-way interaction between the SPG, AMOC, and atmosphere.
Acknowledgments
This work was supported by a Ph.D. scholarship funded jointly by the China Scholarship Council (CSC). Support from the InterDec Project (Grant Agreement 01LP1609B) and the project RACE (Grant Agreement 03F0651B) funded by the German Ministry of Education and Research (BMBF) is acknowledged. We thank to Dr. Taewook Park at Korea Polar Research Institute for conducting the model experiments and providing the data. We thank the three anonymous reviewers for their valuable comments on our manuscript.
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