Abstract Mechanisms of the internally generated decadal-to-multidecadal. variability of SST in the Atlantic Ocean in a coupled GCM

Transcription

1 Clim Dyn DOI /s Mechanisms of internally generated decadal to multidecadal variability of SST in the Atlantic Ocean in a coupled GCM Hua Chen 1 Edwin K. Schneider 2,3 Zhiwei Wu 1 Received: 21 July 2014 / Accepted: 16 May 2015 Springer-Verlag Berlin Heidelberg 2015 Abstract Mechanisms of the internally generated decadal-to-multidecadal variability of SST in the Atlantic Ocean are investigated in a long control simulation of the Community Climate System Model version 3 with constant external forcing. The interactive ensemble (IE) coupling strategy, with an ensemble of atmospheric GCMs (AGCM) coupled to an ocean model, a sea-ice model and a land model, is used to diagnose the roles of various processes in the coupled GCM (CGCM). The noise components of heat flux, wind stress and fresh water flux of the control simulation, determined from the CGCM surface fluxes by subtracting the SST-forced surface fluxes, estimated as the ensemble mean of AGCM simulations, are applied at the ocean surface of the IE in different regions and in different combinations. The IE simulations demonstrate that the climate variability in the control simulation is predominantly forced by noise. The local noise forcing is found to be responsible for the SST variability in the Atlantic Ocean, with noise heat flux and noise wind stress playing a critical role. The control run Atlantic multidecadal variability Electronic supplementary material The online version of this article (doi: /s ) contains supplementary material, which is available to authorized users. * Hua Chen chen@mail.iges.org Earth System Modeling Center and Key Laboratory of Meteorological Disaster of Ministry of Education, Nanjing University of Information Science and Technology, Nanjing , China Department of Atmospheric Oceanic and Earth Sciences, George Mason University, Fairfax, VA, USA Center for Ocean Land Atmosphere Studies, Institute of Global Environment and Society, Fairfax, VA, USA (AMV) index is decomposed into interannual, decadal and multidecadal modes based on the ensemble empirical mode decomposition. The AMV multidecadal mode, a combination of 50- and 100-year modes, is examined in detail. The North Atlantic Oscillation (NAO) pattern in the atmosphere, dominated by the noise component, forces the multidecadal mode through noise heat flux and noise wind stress. The noise wind stress forcing on the multidecadal mode is associated with ocean dynamics, including gyre adjustment and the Atlantic Meridional Overturning Circulation (AMOC). The AMV decadal mode is also found to be related to noise NAO forcing. The associated ocean dynamics are connected with both noise heat flux and noise wind stress, but the AMOC related to the decadal mode is more likely to be forced by noise heat flux. For both multidecadal and decadal modes, the atmospheric response to SST, including the SST-forced heat flux and SST-forced wind stress, acts as a damping. Keywords Atlantic multidecadal variability Interactive ensemble Internal atmospheric noise 1 Introduction There are generally two kinds of mechanisms explaining the low frequency climate variability: external forcing and internal dynamics. External forcing refers to the solar radiation (e.g., Lean et al. 1995), aerosols from volcanic eruption (e.g., Robock and Mao 1992), and greenhouse gas changes (e.g., Houghton et al. 1990). With only climatological external forcing, the low frequency SST variability (with time scale more than a month) can still exist, due to the response to the intrinsic atmospheric and oceanic variability that would exist in the absence of time varying

2 H. Chen et al. boundary forcing (referred to as the internal atmospheric noise and internal oceanic noise thereafter; Hasselmann 1976; Barsugli and Battisti 1998; Schneider and Fan 2007), or due to atmosphere ocean coupled feedbacks not involving noise forcing (El Niño-Southern Oscillation, ENSO, Zebiak and Cane1987; Pacific Decadal Variability, Latif and Barnett 1994). The SST response to the internal atmospheric noise can involve ocean dynamics including the gyre circulations, ocean wave dynamics, and the meridional overturning circulation, as well as stable coupled atmosphere ocean feedbacks (Delworth and Greatbatch 2000; Marshall et al. 2001; Frankcombe et al. 2010; Fan and Schneider 2012; Schneider and Fan 2012). Multidecadal SST variability associated with the Atlantic Meridional Overturning Circulation (AMOC) has also been attributed to both unstable coupled atmosphere ocean feedbacks and intrinsic ocean variability (see Delworth et al and Liu 2012 for literature reviews). Unstable feedbacks are strong enough to lead to variability without an outside source of excitation (such as stochastic forcing), and therefore must be positive. Stable feedbacks can be positive or negative, but are not strong enough to lead to variability without an outside source of excitation. This distinction was possibly first made with regard to ENSO by Blanke et al. (1997), who speculated that ENSO irregularity indicated that ENSO was neutral or stable, as this irregularity would not occur in their simple model without stochastic forcing. In the North Atlantic, two major modes of low frequency variability of SST exist, an interannual and decadal time scale mode with a spatial tripole-like distribution and an interdecadal time scale mode with a single-signed spatial distribution. The tripole mode, with three distinct centers in the subpolar, western subtropical and tropical North Atlantic, appears to be related to the North Atlantic Oscillation (NAO) in the atmosphere (e.g., Marshall et al. 2001; Czaja and Marshall 2001; Fan and Schneider 2012). The target of the current study is the interdecadal singlesigned SST structure in the North and equatorial Atlantic Ocean (e.g., Deser and Blackmon 1993; Delworth et al. 2007), which is referred to as the Atlantic Multidecadal Variability (AMV, also known as Atlantic Multidecadal Oscillation) pattern. A full cycle of the AMV is around years and perhaps even longer from both observations and model studies (e.g., Kushnir 1994; Delworth and Mann 2000). The AMV has significant climate associations with the African Sahel rainfall, Atlantic hurricane and North American and European summer climate in observations and model simulations (Knight et al. 2006). Delworth and Greatbatch (2000) found that AMV could be a damped oscillatory ocean mode forced by the stochastic surface heat flux. Delworth and Mann (2000) and Tanimoto and Xie (2002), among others, pointed out that the AMV might be the northern hemisphere component of what is most simply described as a dipole mode encompassing the whole Atlantic with sign changing across the Intertropical Convergence Zone. Visbeck et al. (2003) noted that AMV could be closely related to variability with tripole-like SST distribution. Based on observation data, Dima and Lohmann (2007) suggested that AMV depended on the atmosphere ocean sea ice interactions, in which the atmospheric response of sea level pressure (SLP) to the SST anomalies in the North Atlantic could affect the sea ice export and fresh water flux in the subpolar North Atlantic. The AMV has also been related to other important modes in other oceans, such as the Pacific Decadal Variability (d Orgeville and Peltier 2007; Zhang and Delworth 2007). Liu (2012) reviewed the dynamics of interdecadal variability in both Pacific and Atlantic oceans, where stochastic forcing was considered as the major driving mechanism for almost all interdecadal variability whereas the ocean atmosphere feedback played a minor role. The simulated AMOC demonstrates significant multidecadal variability, with its period ranging from to 21 years in various climate models (e.g., Delworth et al. 1993; Timmermann et al. 1998; Dai et al. 2005; Dong and Sutton 2005). The mechanisms of the multidecadal variability of the AMOC have been explored in many studies, such as the atmospheric surface flux forcing (Delworth and Greatbatch 2000; Kuhlbrodt et al. 2007), the convective activity in the deep-water formation regions and freshwater export from the Arctic to the convection sites (Jungclaus et al. 2005), the stochastic wind curl forcing and Labrador Sea convection (Tulloch and Marshall 2012), the surface fluxes associated with stochastic changes in the NAO (Kwon and Frankignoul 2012), and the positive density anomalies at the Labrador Sea deep water formation site (Danabasoglu 2008; Danabasoglu et al. 2012). The AMOC has been associated with the AMV in many studies. Delworth et al. (1993) showed an AMV-like SST pattern derived from the AMOC index defined as the maximum of the annual-mean meridional overturning streamfunction in the northern hemisphere. Deser and Blackmon (1993) and Kushnir (1994) isolated a monopole SST pattern with a multidecadal time scale in observations, and suggested that it might be governed by a basin-wide dynamical interaction that involves the AMOC. Huang et al. (2011) found an association between a horseshoe-shape AMV-like SST pattern and an AMOC 30-year oscillation in a simulation with the Climate Forecast System model. The interactive ensemble (IE) coupling strategy was introduced to coupled GCMs (CGCM) by Kirtman and Shukla (2002). The IE_CGCM configuration used here consists of an ensemble of six atmospheric GCMs (AGCM) coupled to a single ocean model, a single sea-ice model and a single land model. The ensemble mean of the six-member AGCM ensemble, forced with the same SST from the

3 Mechanisms of internally generated decadal-to-multidecadal variability of SST in the Atlantic ocean model, is considered as the SST-forced signal. The internal atmospheric noise is independent in each of the AGCM ensemble members. Thus, the ensemble averaging in the IE filters out the internal atmospheric noise surface fluxes that go into the ocean. An essential property of the IE is that it then eliminates the SST variability resulting from stable feedbacks. IE simulations demonstrate for several CGCMs (e.g., Kirtman and Shukla 2002; Kirtman et al. 2005, 2009, 2011; Lopez et al. 2013) that ENSO-type oscillations occur when the stochastic forcing is removed, showing that these are unstable oscillations. However, the ENSO variability in the CGCM has different properties, such as spatial structure, from that in the IE_CGCM. Thus, the stochastic forcing is also important for ENSO, and it is difficult to classify the CGCM ENSO as either stable or unstable. Since the IE_CGCM filters out the atmospheric noise, a specified realization of the noise surface flux can be applied to force the IE_CGCM at the sea surface and will produce deterministic results for the SST variability in regions where the coupled feedbacks are stable. Schneider and Fan (2007) proposed a null hypothesis that all surface temperature climate variability is forced by noise generated internally in the atmosphere or ocean, extending the Hasselmann (1976) mechanism to include atmosphere and ocean dynamics, as well as stable coupled feedbacks. Using the noise-forced IE_CGCM, they demonstrated that the SST variability in a CGCM simulation was primarily forced by atmospheric noise, except in the tropical Pacific and some regions of the high latitude oceans. Fan and Schneider (2012) applied the noise-forced IE method to a CGCM, where the noise surface fluxes were obtained from reanalysis, extending the approach of Seager et al. (2000). They found that the observed year-by-year evolution of the wintertime tripole pattern in North Atlantic, with a period of 11 years, was recovered, consistent with Seager et al. (2000). Additional IE simulations demonstrated that the observed tripole variability in the latter half of the twentieth century was forced primarily by the local noise surface heat flux, with the proviso that the results have substantial uncertainty due to model dependence. The mechanisms of the observed SST variability with longer time scales were not analyzed. In the present study, we present an analysis of the mechanisms of a multidecadal mode and a decadal mode of SST variability in the North Atlantic in a long control simulation of CGCM. The analysis and results are novel in that the response of the coupled system to the atmospheric noise surface flux forcing, including the ocean s dynamical response to this forcing and the coupled response to the atmospheric feedbacks to the time varying SST, are calculated explicitly. This approach provides a bridge between the simplest mechanistic models and the complex CGCM, and is particularly useful when the variability is primarily forced by internal atmospheric noise, as turns out to be the case here. To understand the low-frequency AMV, it is important to isolate atmospheric noise forcing from other mechanisms, such as the coupled feedback, the gyre circulations, the AMOC and so on. On top of all this, the external forcing could play a role in the observed AMV, a mechanism that is beyond the scope of the current study. In the following, Sect. 2 describes the models and experiments. Section 3 presents the results from model simulations and introduces the decomposition of the AMV index into several modes with different time scales. The mechanisms of the multidecadal mode of AMV are investigated in Sect. 4 and a discussion on the decadal mode of AMV is presented in Sect. 5. Section 6 contains the summary and discussions. 2 Models and experiments The CGCM used in the study is the Community Climate System Model version 3 (CCSM3; Collins et al. 2006a), the same as in Chen et al. (2013). It couples the atmosphere, ocean, land and sea-ice models through a flux coupler without flux correction. We perform experiments using the T42_gx1v3 version, with a spectral atmosphere truncated at total wavenumber 42 and 26 levels in the vertical, and nominal 1 horizontal resolution in the ocean and sea-ice models. The interactive ensemble (IE) CGCM (IE_CGCM) and experimental design are described in the following. 2.1 IE_CGCM The IE version of CCSM3 was described in Kirtman et al. (2009, 2011). The IE_CGCM is composed of an ensemble of six AGCMs coupled to a single oceanic GCM (OGCM), a single sea-ice model and a single land model. Each AGCM ensemble member has the same boundary conditions, as provided by the ocean, land and sea-ice models, but at the beginning of a simulation, each has different initial conditions. As the IE evolves, each AGCM experiences the same SST predicted by the OGCM, thus they have the same SST-forced signal. The OGCM, on the other hand, experiences the ensemble mean of the surface fluxes from six AGCMs. In this way, the IE coupling strategy reduces greatly the internal atmospheric noise (referred to as noise in the rest of the paper), but at a substantial increase in computational expense. The ensemble mean of the sixmember AGCM ensemble reduces the noise variance by a factor of six, approximately 83 %, and is considered as the SST-forced component, although for the six-member AGCM ensemble the residual noise is not truly negligible. To investigate the mechanisms of the multidecadal variability, noise surface fluxes are added to the ocean of the IE_CGCM as a specified surface forcing. The total surface

4 H. Chen et al. Table 1 Experiments Experiments Description Integration period Purpose CGCM 300-year CGCM control run with constant 1990 external forcing IE_G_all IE_CGCM forced by full noise surface fluxes in global oceans IE_no_noise IE_CGCM without noise surface fluxes forcing the ocean IE_ATL_all IE_CGCM forced by full noise surface fluxes restricted in the Atlantic Ocean only (40 S 65 N, 100 W 20 E) IE_ATL_ws IE_CGCM forced by noise wind stress in the Atlantic Ocean only IE_ATL_hf IE_CGCM forced by noise heat flux in the Atlantic Ocean only IE_ATL_fwf IE_CGCM forced by noise fresh water flux in the Atlantic Ocean only 12/01/ /01/1011 Synthetic observations to analyze 01/01/ /01/0840 To demonstrate the role of noise in the SST variability in the CGCM To focus on the role of local noise forcing To isolate the role of specific type of noise in the SST variability fluxes over ocean in the IE are then composed of the specified noise plus the atmospheric feedback to the SST as given by the ensemble mean of the atmospheres in the IE. Due to software constraints in this version of the IE, the land and sea ice in IE_CGCM are forced with the ensemble mean atmospheric conditions (i.e. temperature, wind, precipitation) rather than the ensemble mean surface fluxes, a feature that leads to rather large mean biases over land and sea ice (Kirtman et al. 2011). Since the atmosphere and ocean are coupled once a day, the daily noise surface fluxes are calculated and added once a day to the ensemble mean surface fluxes from the six-member AGCM ensemble to force the ocean model. If the internal atmospheric noise is the primary forcing of the low frequency SST variability, then the noise forced IE_CGCM should reproduce the CGCM control simulation SST (Schneider and Fan 2007). Note that there is no feedback between the noise surface fluxes and evolving ocean state in the IE experiments. The climatology of the noise surface fluxes were removed, which would make the long term mean zero as well as topof-the-atmosphere contribution. 2.2 Experiments This study is based on perfect model and perfect data experiments, where all simulations are carried out in the model world. Table 1 lists the experiments carried out in this study. The CGCM simulation was integrated for 300 years with constant 1990 external forcing. Each of the six IE_CGCM experiments was integrated for 100 years, with the atmospheric noise specified in different regions and in different types. Here is some explanation of the spin-up behavior of our experiments. The control simulation was a branch run, with each model component initialized from the restart files of a previous reference case CCSM3 T42 NoOMP which was an existing long simulation integrated from model year 0001 at Rosenstiel School of Marine and Atmospheric and Science by Dr. Ben Kirtman. Our integration was a restart from model date 12/01/0710 to minimize spin-up in the reference case data for both the atmospheric and oceanic variables. The spin-up time (i.e., initial transients feature) was not obviously found in the control simulation, yet the first 13 months of the model output were excluded from analysis. A 300-year monthly dataset from Jan 0712 to Dec 1011 were analyzed for the control simulation. Before carrying out the IE_CGCM experiments described here, we had performed a substantial number of IE experiments with this model, and found that the spinup time for the IE_CGCM SST was about years. We integrated each of the IE_CGCM experiments in Table 1 for 100 years, starting from 01/01/0741. The spin-up was found to be short for IE_CGCM experiments IE_G_all and IE_ATL_fwf, but there was apparently a year spinup for IE_ATL_all, IE_ATL_hf and IE_ATL_ws (Fig. S1 in the Supplemental Material). Therefore, the first 30 years of the IE_CGCM output from all experiments are not included in the results presented here, and the last 70 years from Jan 0771 to Dec 0840 are utilized in the following analyses. 2.3 Determination of internal atmospheric noise The determination of the internal atmospheric noise, which was added to the ocean of IE_CGCM, was described in Chen et al. (2013), and is briefly reviewed here. An ensemble of six AGCM simulations was made using the standalone CAM3 (Collins et al. 2006b), the same AGCM as in the CCSM3 and at the same resolution, with each ensemble

5 Mechanisms of internally generated decadal-to-multidecadal variability of SST in the Atlantic Fig. 1 Signal-to-noise standard deviation ratio (SNR) in the coupled GCM of a surface heat flux, b zonal wind stress, c meridional wind stress, and d fresh water flux. Land grids are masked member forced by the same time-varying SST from the CGCM simulation, but started from different initial conditions. The SST-forced surface fluxes were estimated as the ensemble mean of AGCM simulations, and the noise in the surface fluxes was determined as a residual of the CGCM surface fluxes after subtracting the SST-forced part. The noise was found for the net surface heat flux (sum of the absorbed solar flux, net longwave radiation, sensible and latent heat flux; due to an oversight, the latent heat of melting for snowfall was not included), absorbed solar flux, wind stress, and fresh water flux. These fluxes are then added to the ensemble mean fluxes obtained from IE_CGCM. Chen et al. (2013) and Chen and Schneider (2014) found that noise variances, and also the SST-forced responses, were indistinguishable between the CGCM and the AGCM forced by the SST from the CGCM. These results support the contentions that the noise that is diagnosed as described above and used as forcing approximates the true noise, and that the IE is an appropriate tool for the investigation. Figure 1 shows the signal-to-noise standard deviation ratio (SNR) for the net surface heat flux, wind stress and fresh water flux. It is seen that the SST-forced components dominate over the tropical oceans, while noise dominates over the extratropical oceans. Compared with wind stress and fresh water flux (Fig. 1b d), the SNR of heat flux (Fig. 1a) is larger in mid-and-high-latitude North Atlantic and along the Kuroshio extension, indicating that the noise heat flux and SST-forced heat flux are both important in these regions. 3 Results from model simulations This section describes the results from the CGCM and IE_CGCM simulations. The monthly mean data, with the annual cycle and linear trend removed, are analyzed. The global mean top-of-the-atmosphere net heat flux is near zero in the CGCM control simulation and IE experiments. 3.1 SST variability Kirtman et al. (2009) found that the IE_CGCM had a systematic impact on the mean SST, which was largest in the Northern Hemisphere high latitudes but very small in the tropics and Southern Hemisphere. The current study

6 H. Chen et al. Fig. 2 Left column (a, c): local correlation of the monthly SST anomalies in the coupled GCM (CGCM) with a IE_G_all and c IE_no_noise. Values that are significant at 5 % level using t test are shaded. Right column (b, d): standard deviation ratio of the monthly SST anomalies b between IE_G_all and CGCM, and d between IE_ no_noise and CGCM. Values between 0.9 and 1.1 are not plotted. The land and sea-ice-covered regions are masked employs the same IE_CGCM as Kirtman et al. (2009), but focuses on the SST variability. The monthly SST anomalies (SSTA) in the CGCM are highly correlated with those in IE_G_all, except in the equatorial western Pacific and high latitude North Atlantic (Fig. 2a). Additionally, the standard deviation ratio of the SST variability between the CGCM and IE_G_all is close to one (Fig. 2b). Thus, the noise forced IE_CGCM can reproduce much of the SST variability in the CGCM over a large portion of the global oceans, indicating that noise is responsible for the SST variability in these oceans. As noted in Schneider and Fan (2007), if the SST variability is entirely locally forced by the atmospheric noise, the expected correlation for the noise forced IE and the CGCM is 0.82 rather than 1 due to the residual noise in the AGCM ensemble mean. The possible reasons for correlations smaller than 0.82 in Fig. 2a may be that the SST in these regions is not forced by noise (e.g., ENSO) or that the effect of internal oceanic noise (e.g., Kirtman et al. 2006) is not taken into account. In contrast, the SSTA in the IE_no_noise are very weakly and insignificantly correlated with the CGCM (Fig. 2c), and only a small fraction of the SST variance of the CGCM is captured (Fig. 2d), with % in the North Pacific and high-latitude North Atlantic and % in other oceans, except for % in the equatorial Pacific. This is consistent with the SST variability in most of the global oceans in the CGCM being primarily noise forced. In the region where the SST variability is entirely forced by the atmospheric noise, the variance ratio of the no-noise IE-CGCM to the CGCM is expected to be 0.17, because of the finite size of the AGCM ensemble in the IE (Wu et al. 2004). The larger ratio in the equatorial Pacific implies that the model ENSO is not forced primarily by the internal atmospheric noise, in agreement with Kirtman et al. (2009). The IE results indicate that the SST variability outside of the tropics is mostly forced by the atmospheric noise. Although the IE_CGCM is not perfect, it can then be useful to diagnose the mechanisms of the SST variability as we can specify different types of noise forcing in different oceanic regions in the IE_CGCM to identify the respective roles of the noise forcing and coupled dynamics in the SST variability. Although the noise is not predictable, its

7 Mechanisms of internally generated decadal-to-multidecadal variability of SST in the Atlantic influence can be diagnosed after the fact from the essentially deterministic and reproducible runs of the IE. Figure 3 displays the correlations and standard deviation ratios of the SSTA between the CGCM and IE simulations with noise restricted in the Atlantic Ocean only. The Atlantic SST variability is captured in IE_ATL_all (Fig. 3a, b), and teleconnections from the Atlantic to other oceans are not strong. The noise heat flux and noise wind stress play an important role in the SST variability in the Atlantic Ocean (Fig. 3c f), while the noise fresh water flux has negligible impact on the SST variability (Fig. 3g, h). 3.2 AMV The AMV index in the current study is defined as the annual mean SST averaged over North Atlantic (0 60 N, 80 0 W), in the same region as in Trenberth and Shea (2006). The time-means and variances of the AMV indices are listed in Table 2. It is found that the simulated climatological mean AMV in the CGCM is 19.3 C, while time means in the IE_CGCMs are reduced by C. The variances in IE_G_all are the same as in the CGCM, but are smaller in IE_ATL_all/ws/hf/fwf. In particular, the variability in IE_ATL_ws and IE_ATL_fwf is greatly reduced compared to the CGCM and other IE_CGCM experiments. The 300-year AMV index in the CGCM demonstrates large variability of different time scales (solid curve in Fig. 4a), with spectral peaks at 100, 12 and 6 years that are significant at 10 % confidence level (Fig. 5a). There is a decreasing trend of AMV in all IE experiments between years 0771 and 0840 (Fig. 4b), consistent with the CGCM during the same period which appears to be related to the multidecadal variability. Furthermore, the detrended AMV index in the CGCM is significantly correlated at 5 % level with those in IE_G_all, IE_ATL_all and IE_ATL_hf during the overlapping years, but is insignificantly correlated with those in IE_ATL_ws and IE_ATL_fwf (Table 2). This is consistent with Delworth and Greatbatch (2000) that the AMV was forced by the stochastic surface heat flux. Thus, the global noise forcing (IE_G_all) and local noise forcing (IE_ATL_all) can simulate the temporal variability of AMV in the CGCM to a large degree, with the noise heat flux playing a dominant role. We cannot conclude from this that the noise wind stress and noise fresh water flux are not important. In fact, it will be seen below that the noise wind stress plays an important role in the structure of the AMV. The simultaneous regression of SSTA in the CGCM onto the CGCM AMV index (Fig. 6a) displays a monopole pattern in the North Atlantic. The monopole AMV pattern is not uniform but has a horseshoe shape. The positive anomalies are large along the Gulf Stream after it separates from North America (referred to thereafter as the North Atlantic Current, NAC) and are also large in the eastern North Atlantic and southwestward extension, but are small in the western part of the subtropical gyre. The AMV spatial pattern in the CGCM resembles the observed pattern as shown in Trenberth and Shea (2006) and Delworth et al. (2007). The IE_G_all simulates a similar SST pattern to the CGCM, but with smaller magnitude than the CGCM (figure not shown). Therefore, the IE_CGCM is appropriate for diagnosing the mechanisms of AMV of the CGCM. The IE experiments forced with different types of noise surface fluxes restricted in the Atlantic Ocean help to decompose the roles of various local mechanisms that produce the AMV. Similar to IE_G_all, the AMV pattern in IE_ATL_all (Fig. 6b) is also strongly correlated with the CGCM (the spatial correlation coefficient being 0.69), suggesting that AMV is primarily forced by the local noise. The magnitude of regression in IE_ATL_all is smaller than the CGCM. The AMV pattern is captured along NAC in IE_ATL_ws (Fig. 6c), while it is captured in the eastern North Atlantic and southwestward extension in IE_ATL_hf (Fig. 6d), but nowhere in IE_ATL_fwf (Fig. 6e). Thus, both the noise heat flux and noise wind stress are responsible for generating the AMV pattern. Figure 6f, which is the sum of Fig. 6c, d, is more similar to Fig. 6a than either of them, suggesting that the forcings from noise heat flux and noise wind stress combine in a linear fashion. 3.3 Decomposition of the AMV index Using the ensemble empirical mode decomposition (EEMD, Wu and Huang 2009), the AMV index is decomposed into a relatively small collection of empirically determined intrinsic mode functions based on the local characteristic time scales of the data. The period of each EEMD mode is a mean period that is determined by counting the number of peaks (i.e., local maxima). The AMV index in the CGCM after EEMD includes two interannual modes (not shown), a decadal mode (approximately 12-year period, Fig. 7b), three multidecadal modes (25-, 50- and 100-year periods, Fig. 7c e), and a nonlinear trend that is very small (dashed curve in Fig. 7a). These six modes explains 97 % of the undecomposed AMV variance, with the interannual modes accounting for 50 %, the 12-year mode accounting for 16 %, the 25-year mode accounting for 9 %, the 50-year mode accounting for 15 %, and the 100-year mode accounting for 7 %. It indicates that the CCSM3, with constant external forcing, is able to generate substantial SST variability on decadal-to-multidecadal time scales. In the following sections, we will focus on several AMV modes from EEMD, rather than the undecomposed AMV, because the modes with different time scales are mixed together in the undecomposed AMV. Each mode from EEMD is related to an SST pattern (Fig. 8b g) that is not

8 H. Chen et al. (g) (h) Fig. 3 Left column (a, c, e, g): local correlation of the monthly SST anomalies between the coupled GCM (CGCM) and a IE_ATL_all, c IE_ATL_hf, e IE_ATL_ws, and g IE_ATL_fwf. Values that are significant at 5 % level using t test are shaded. Right column (b, d, f, h): standard deviation ratio of the monthly SST anomalies b between IE_ ATL_all and CGCM, d between IE_ATL_hf and CGCM, f between IE_ATL_ws and CGCM, h between IE_ATL_fwf and CGCM. Values between 0.9 and 1.1 are not plotted. The land and sea-ice-covered regions are masked. The area within thick solid lines in a is the region where the atmospheric weather noise surface fluxes are added to the Atlantic Ocean in the ocean model in IE_ATL_all/hf/ws/fwf

9 Mechanisms of internally generated decadal-to-multidecadal variability of SST in the Atlantic Table 2 Time mean, variance and correlation of AMV indices Model Period Time mean ( C) * Significant at 5 % level Variance ( C 2 ) Correlation with CGCM CGCM IE_G_all * IE_ATL_all * IE_ATL_ws IE_ATL_hf * IE_ATL_fwf the total variance of the AMV. The reasons for combining these two modes into a single mode for analysis are that the SST patterns associated with these two are similar and that the spectral peak at 100 years is significant at 10 % level (Fig. 5a), justifying the significance of the combined multidecadal mode. It is not surprising that the multidecadal mode has two significant peaks, one at 50 years and the other at 100 years (figure not shown). In Sect. 5, we briefly discuss the AMV decadal mode (i.e., 12-year mode), which is also significantly different from red noise (Fig. 5a). 4 Mechanisms of the AMV multidecadal mode The analysis of the IE_CGCM experiments, allows us to examine the respective role of the different types of noise forcing in the AMV. The regressions of oceanic and atmospheric fields onto the CGCM AMV multidecadal mode isolate the structures of the multidecadal variability for these fields. In this section, the lagged regressions onto the AMV multidecadal mode, from the AMV lagging by 30 years Fig. 4 a Time evolution of the Atlantic Multidecadal Variability (AMV) index in the coupled GCM (solid curve) and IE_G_all (dotted curve). The climatological mean values of two indices are shown as thin lines. b Time evolution of the AMV index in IE_G_all (solid curve), IE_ATL_all (long dashed curve), IE_ATL_ws (short dashed curve), IE_ATL_hf (long and short dashed curve) and IE_ATL_fwf (dotted curve). Unit: C the same as Fig. 8a, indicating that forcings and oceanic processes that determine the time scale might be different. The sum (Fig. 8h) best resembles the regression onto the undecomposed AMV index (Fig. 8a), compared to any single mode. It suggests that each single mode from EEMD should be critical for constituting the AMV pattern as it is. In Sect. 4, we concentrate on the AMV multidecadal mode for analysis, which is a combination of the 50-year mode and 100-year mode, accounting for 22 % of Fig. 5 Spectrum of a the annual mean Atlantic Multidecadal Variability (AMV) index and b the Atlantic Meridional Overturning Circulation (AMOC) index in the coupled GCM (black curves). The red solid curves are corresponding red noise spectrum, and the red dashed curves are 10 % confidence upper limit of red noise spectrum. The y-axis is power. The x-axis is frequency, unit: cycles per year

10 H. Chen et al. Fig. 6 Simultaneous regressions of SST anomalies onto the standardized Atlantic Multidecadal Variability (AMV) index in the coupled GCM (CGCM), where the SSTA is from the a CGCM, b IE_ATL_ (i.e., 30 years prior to an AMV maximum) to AMV leading by 20 years (i.e., 20 years after an AMV maximum), are displayed to examine the evolution of the oceanic and all, c IE_ATL_ws, d IE_ATL_hf, e IE_ATL_fwf, and f sum of and. Unit: C per standard deviation of AMV. The regions that are significant at 5 % level using t test are dotted atmospheric fields prior to and after the maximum AMV mode. Since the purpose is to diagnose the mechanisms of the multidecadal mode in the CGCM, the time series of this

11 Mechanisms of internally generated decadal-to-multidecadal variability of SST in the Atlantic mode from the CGCM control simulation is employed in the lagged regressions for all experiments. For the CGCM, the mode is from years 0712 to 1011 and is standardized before regressions. For the IE_CGCM experiments, the part between years 0771 and 0840 directly from the standardized index is used in the lagged regressions. 4.1 SST pattern Fig. 7 The Atlantic Multidecadal Variability (AMV) index and ensemble empirical mode decomposition (EEMD) modes in the 300- year coupled GCM simulation. a AMV index (solid curve) and nonlinear trend (dashed curve), b EEMD mode with period of 12 years, c EEMD mode with period of 25 years, d EEMD mode with period of 50 years, and e EEMD mode with period of 100 years Figure 9 shows the evolution the SSTA in the CGCM associated with the AMV multidecadal mode using lagged regressions. The SSTA pattern (Fig. 9d) shows large positive anomalies along the NAC at N, but much smaller positive anomalies in the eastern North Atlantic and southwestward extension than the regression onto the full AMV index (Fig. 8a). Hence, the multidecadal mode structure emphasizes the NAC part of the spatial pattern of the unfiltered AMV. Prior to an AMV maximum, the positive SSTA is small and narrow in latitudinal extent along the NAC and eastern North Atlantic, which strengthens and extends with increased lagged time (Fig. 9a c). After the maximum AMV, the positive SSTA weakens along the NAC (Fig. 9e, f) and will change to a negative phase (figure not shown). The regression patterns of the SSTA in IE_G_all and IE_ATL_all onto the AMV mode are very similar with the CGCM (figures not shown). In IE_ATL_ws, noise wind stress is the only noise forcing applied to the ocean model. At lag 0 year (Fig. 10d), large positive SSTA are reproduced along NAC, demonstrating an important role of noise wind stress. Compared to the CGCM, the SSTA from IE_ATL_ws is relatively small in the eastern North Atlantic and southwestward extension, and even opposite in sign to the south of NAC and near the western coast of North Africa, implying that other forcings besides noise wind stress are important in those places. In IE_ATL_hf, noise heat flux is the only noise forcing applied to the ocean model. At lag 0 year, the positive SSTA are simulated in the eastern North Atlantic and southwestward extension (Fig. 11d), demonstrating the dominant role of noise heat flux in these regions. But the SSTA is negative along NAC, opposite to the CGCM. The regressions are very small in the IE_ATL_fwf (figure not shown), where the noise fresh water flux is the only noise forcing applied to the ocean model, indicating that noise fresh water flux plays a negligible role in forcing the multidecadal mode. Therefore, both the noise heat flux and noise wind stress force the AMV multidecadal mode, with noise wind stress forcing along NAC and noise heat flux forcing in the eastern North Atlantic and southwestward extension. Both contribute jointly to the SST pattern of the AMV multidecadal mode. 4.2 The NAO Marshall et al. (2001) pointed out that the SST tripole mode in the North Atlantic was related to NAO. Here we also find an important association of the NAO with the AMV multidecadal mode. The lagged regression pattern of noise component of SLP in the CGCM onto the AMV multidecadal mode (Fig. 12) resembles that of the undecomposed SLP (figure not shown) in both structure and magnitude, indicating that the noise component of SLP is dominant.

12 H. Chen et al. (g) (h) Fig. 8 Simultaneous regressions of SST anomalies in the coupled GCM (CGCM) onto the a Atlantic Multidecadal Variability (AMV) index, b AMV 3-year mode, c AMV 6-year mode, d AMV 12-year mode, e AMV 25-year mode, f AMV 50-year mode, g AMV 100-year mode, and h sum of b + c + d + e + f + g. Unit: C per standard deviation of AMV. The regions that are significant at 5 % level using t test are dotted in a g The SLP pattern associated with the multidecadal mode is NAO-like, a north south dipole of SLP anomalies with the northern center over Iceland and southern Greenland and the southern center spanning the mid-latitude North Atlantic and western Europe. The positive phase of the NAO leads the AMV maximum (Fig. 12a c), which then weakens (Fig. 12e, f) and gradually changes to a negative NAO phase (figure not shown). the pressure gradient increases between subpolar and mid-latitude regions, enhancing the climatological westerlies in between and thus resulting in more turbulent heat flux out of ocean (i.e., negative heat flux anomalies). In the meantime, the anomalous easterlies to the south of the center of positive SLP weaken the climatological westerlies, resulting in less turbulent heat flux out of ocean (i.e., positive heat flux anomalies). The regression of noise heat flux onto the AMV mode is displayed in Fig. 13. A comparison of Fig. 13 with Fig. 12 shows that the sign of the noise heat flux is consistent with NAO forcing as stated above, though their centers 4.3 Role of noise heat flux The noise NAO forcing is associated with the noise heat flux. In the positive phase of NAO (Fig. 12a d), 13

13 Mechanisms of internally generated decadal-to-multidecadal variability of SST in the Atlantic Fig. 9 Lagged regressions of SST anomalies in the coupled GCM (CGCM) onto the CGCM Atlantic Multidecadal Variability (AMV) multidecadal mode. From a to f: Lag = 30, 20, 10, 0, +10 and +20 years. Negative years indicate AMV lagging and positive years do not agree. Prior to an AMV maximum (Fig. 13a c), the noise heat flux is negative (upward) at N and is positive (downward) to the south of 40 N. After the indicate AMV leading. Unit: C per standard deviation of AMV multidecadal mode. The regions that are significant at 5 % level using t test are dotted AMV maximum, the magnitude of the noise heat flux weakens (Fig. 13e, f) and changes to opposite signs (figure not shown).

14 H. Chen et al. Fig. 10 Same as Fig. 9, but for SST anomalies in IE_ATL_ws Though the noise heat flux pattern seems to roughly agree with the CGCM SST pattern in the North Atlantic (Fig. 9), the centers of anomalies do not. Besides, the noise heat flux pattern is not consistent with the SST pattern in IE_ATL_hf (Fig. 11). This is indicative of other processes contributing to the SST pattern, such as the oceanic

15 Mechanisms of internally generated decadal-to-multidecadal variability of SST in the Atlantic Fig. 11 Same as Fig. 9, but for SST anomalies in IE_ATL_hf

16 H. Chen et al. Fig. 12 Lagged regressions of the noise component of SLP in the coupled GCM onto the Atlantic Multidecadal Variability (AMV) multidecadal mode. From a to f: Lag = 30, 20, 10, 0, +10 and +20 years. Negative years indicate AMV lagging and positive years indicate AMV leading. Unit: Pa per standard deviation of AMV multidecadal mode. The regions that are significant at 5 % level using t test are dotted

17 Mechanisms of internally generated decadal-to-multidecadal variability of SST in the Atlantic Fig. 13 Lagged regressions of the noise heat flux in the coupled GCM onto the Atlantic Multidecadal Variability (AMV) multidecadal mode. From a to f: Lag = 30, 20, 10, 0, +10 and +20 years. Positive (negative) values indicate downward into (upward out of) the ocean. Negative years indicate AMV lagging and positive years indicate AMV leading. Unit: W/m 2 per standard deviation of AMV multidecadal mode. The regions that are significant at 5 % level using t test are dotted

18 H. Chen et al. dynamic or thermodynamic response to the atmospheric feedback. 4.4 Role of noise wind stress On the other hand, the noise NAO forcing is also associated with the noise wind stress (Fig. 14), with lower-thannormal SLP corresponding to cyclonic wind (i.e., positive curl) and higher-than-normal SLP corresponding to anticyclonic wind (i.e., negative curl). Noise wind stress forces the AMV multidecadal mode through ocean dynamics Ocean gyres As Ekman transport is to the right of the wind stress in the Northern Hemisphere, positive (or negative) wind stress curl produces Ekman transport divergence (or convergence), resulting in negative (or positive) sea surface height (SSH) anomalies (figure not shown). In a barotropic ocean, the pattern of the SSH anomalies should resemble that of the barotropic streamfunction (BSF). Figure 15 shows lagged regressions of BSF in the CGCM onto the AMV multidecadal mode, where the BSF zero curve from climatology separates the climatological subtropical and subpolar gyres and represents the location of the climatological NAC. The most outstanding feature preceding the maximum AMV is the gyre close to and straddling the BSF zero curve (called the intergyre gyre by Marshall et al. 2001), representing a northward displacement of the subtropical gyre across the BSF zero curve in this phase. As the SST meridional gradient is very large close to the climatological boundary between the subtropical and subpolar gyres (Fig. S2 in the Supplemental Material), there are large SSTA associated with the northward displacement of the subtropical gyre, contributing to the large SSTA on the border of the subtropical and subpolar gyres (i.e., along the NAC) in Figs. 9 and 10. After the maximum AMV, the anomalous intergyre gyre moves to even higher latitude (Fig. 15e, f). At a later time, an anomalous negative gyre moves northward across the BSF zero curve (figure not shown), resulting in decrease of the SSTA along the NAC and eventually an opposite phase of AMV. In IE_ATL_ws, the BSF regression related to the multidecadal mode also displays an anomalous positive gyre straddling the BSF zero curve prior to the maximum AMV (figure not shown), contributing to large SSTA along the NAC (Fig. 10). However, this feature could not be found in IE_ATL_hf, suggesting that noise wind stress plays a dominant part in the SST through ocean gyres. In summary, the negative wind stress curl and related positive SSH anomalies at midlatitude are connected with a northward displacement of the subtropical gyre, which leads to large SSTA along the NAC. This is consistent with some studies on the adjustment of ocean gyre circulations to the wind stress forcing (Frankignoul et al. 1997; Miller et al. 1998; Deser et al. 1999; Schneider et al. 2002; Kwon et al. 2010). This mechanism could explain how the SST pattern in the CGCM and IE_ATL_ws is forced by the noise wind stress at mid-and-high latitude North Atlantic. 4.5 AMOC In order to understand the association of the AMOC with the AMV multidecadal mode, we first examine the AMOC index, defined as the maximum of the annual-mean meridional overturning streamfunction from 20 S and 65 N from ocean surface to bottom. The time-means and variances of the AMOC indices in all experiments are listed in Table 3. It is found that the simulated climatological mean AMOC streamfunction in the CGCM has a maximum value of 18.9 Sverdrup (Sv, or 10 6 m 3 s 1 ), consistent with 18.5 Sv at 26.5 N from the Rapid Climate Change-Meridional Overturning Circulation and Heatflux Array program (Cunningham et al. 2007). Compared to the CGCM, time means in the IE_CGCM experiments are reduced by Sv. The variances in IE_G_all and IE_ATL_all are larger than that in the CGCM, but are smaller in IE_ATL_ws, IE_ATL_hf and IE_ATL_fwf. In particular, the variability of AMOC in IE_ATL_fwf is greatly reduced compared to the CGCM and other IE_CGCM experiments. Thus, both the noise heat flux and noise wind stress play a critical role in the AMOC variability in CCSM3, while the noise fresh water flux has negligible role. Furthermore, the detrended AMOC index in the CGCM is significantly correlated at 5 % level with those in IE_G_all, IE_ATL_all and IE_ATL_ws during the overlapping years, but is not strongly correlated with those in IE_ATL_hf and IE_ATL_fwf (Table 3). We can conclude that the AMOC is strongly forced by the atmospheric noise, and primarily the wind stress noise. This is consistent with Tulloch and Marshall (2012) that the AMOC was forced by the stochastic wind stress curl. The 300-year AMOC index in the CGCM shows variability from decadal-multidecadal to centennial time scales (Fig. S3a in the Supplemental Material), with spectral peaks significant at 90 and 9 years (Fig. 5b). Much stronger 25-year AMOC variability was found by Danabasoglu (2008), using the same CGCM as here, but with a higher resolution (T85) atmosphere. However, the prominent quasi-oscillatory AMOC variability was not present through the whole simulation, and was suppressed for the final ~200 years of a ~700 year simulation (their Fig. 1a). The AMOC anomalies in the CGCM associated with the AMV multidecadal mode have a single cell in the upper 3.5 km (Fig. 16). Prior to an AMV maximum, anomalous deep convection (sinking) occurs at N, with maximum of the streamfunction at 45 N at the depth of

19 Mechanisms of internally generated decadal-to-multidecadal variability of SST in the Atlantic Fig. 14 Lagged regressions of the noise wind stress (vectors) and noise wind stress curl (shadings) in the coupled GCM onto the Atlantic Multidecadal Variability (AMV) multidecadal mode. From a to f: Lag = 30, 20, 10, 0, +10 and +20 years. Positive (negative) shading indicates cyclonic (anticyclonic) wind stress. Negative years indicate AMV lagging and positive years indicate AMV leading. Unit of wind stress curl: N/m per standard deviation of AMV multidecadal mode. The displayed vectors are significant at 5 % level using t test

20 H. Chen et al. Fig. 15 Lagged regressions of barotropic streamfunction (BSF) in the coupled GCM onto the Atlantic Multidecadal Variability (AMV) multidecadal mode. From a to f: Lag = 30, 20, 10, 0, +10 and +20 years. Negative years indicate AMV lagging and positive years indicate AMV leading. The thick solid curve is BSF zero curve from climatology. Unit: Sv per standard deviation of AMV multidecadal mode. The regions that are significant at 5 % level using t test are dotted

21 Mechanisms of internally generated decadal-to-multidecadal variability of SST in the Atlantic Table 3 Time mean, variance and correlation of AMOC indices Model Period Time mean (Sv) * Significant at 5 % level Variance (Sv 2 ) Correlation with CGCM CGCM IE_G_all * IE_ATL_all * IE_ATL_ws * IE_ATL_hf IE_ATL_fwf km, constituting a positive anomalous AMOC. The cell strengthens and extends southward (Fig. 16b, c), and reaches maximum between lag 10 year and lag 2 year. It then weakens and gradually changes sign to a negative cell of AMOC (Fig. 16d f). Similar features are found in IE runs (except IE_ATL_fwf), but the cell centers are shallower than in the CGCM (figures not shown). Therefore, the AMOC, forced by noise heat flux and noise wind stress, contributes to a positive phase of the AMV multidecadal mode. The surface buoyancy fluxes cannot drive the AMOC alone, but they are necessary for the existence of AMOC and are critically important for the deep water formation (DWF) (Kuhlbrodt et al. 2007). The Labrador Sea is the DWF site related to the decadal AMOC variability in the CCSM3 (Danabasoglu 2008). The mixed layer depth (MLD) can be regarded as an identifier of the deep convection and is found to correspond well with AMOC variability (Fig. 17). As stated earlier, for positive NAO forcing, the positive noise wind stress curl at subpolar ocean produces Ekman transport divergence and thus upward Ekman pumping, which cools the upper ocean at subpolar region and could be detected from Fig. 10. The noise heat flux prior to an AMV maximum is negative at subpolar region, especially in the Labrador Sea (Fig. 13a c), suggestive of large amount of heat out of the ocean and thus cooling of the upper ocean. However, the SST pattern (Fig. 11) and the MLD pattern (figure not shown) forced by the noise heat flux do not correspond with the pattern of noise heat flux (Fig. 13). The discrepancy could come from the surface salinity anomalies that are likely to play an important role in this region, which requires further investigation. It is possible that the AMOC acts as a delayed negative feedback if the AMOC heat flux is strongly influencing the AMV SST, as we can see from Fig. 17d f that the AMV warming shuts off convection. The decreased AMOC will then lead to decreasing AMV. However, it is also possible that the AMOC is responding passively to the noise. We are not yet able to distinguish which regime the AMV variability is in. 4.6 Role of the SST forced response of the atmosphere We have shown that the noise component of SLP related to the AMV multidecadal mode, which dominates over the SST-forced SLP component, is NAO-like and forces the multidecadal mode. The SST-forced component of SLP in the CGCM, estimated from the ensemble mean of six AGCMs simulations forced by the CGCM SST, demonstrates a very weak NAO-like pattern approximately opposite in sign to the noise counterpart (figure not shown). This suggests that the SST-forced response of the atmosphere acts as damping of the AMV multidecadal mode. Note that the noise and SST-forced patterns of SLP do not oppose each other at each grid point as would be expected for a damping, nor is the amplitude of the SST forced pattern proportional to the amplitude of the multidecadal mode SSTA. These properties need further investigation. Similarly, the SST-forced components of heat flux and wind stress, relevant to the SST-forced component of SLP, also serve as damping or negative feedback to the SST pattern. 5 Discussion on the AMV decadal mode In this section, the lagged regressions of the oceanic and atmospheric fields onto the AMV decadal mode, from the AMV lagging by 6 years (i.e., 6 years prior to an AMV maximum) to AMV leading by 4 years (i.e., 4 years after an AMV maximum), are displayed. 5.1 SST pattern Figure 18 shows the evolution the SSTA in the CGCM associated with the AMV decadal mode. At lag 0 year, the SSTA pattern (Fig. 18d) shows large positive anomalies in the subpolar North Atlantic and much smaller anomalies to the south of 40 N. At 6 years prior to an AMV maximum (Fig. 18a), the SSTA pattern is opposite in sign to that at lag 0 year. Thus, the decadal mode structure emphasizes the subpolar part of the spatial pattern of the unfiltered AMV. The regression patterns of the SSTA in IE_G_all and IE_ATL_all onto the AMV decadal mode are similar to the CGCM (figures not shown). In IE_ATL_ws (Fig. 19), at lag 0 year, large positive SSTA are reproduced along the western part of NAC, which is much larger in magnitude than the CGCM; while large negative SSTA in the subpolar North Atlantic are found to be opposite in sign to the CGCM. In IE_ATL_hf (Fig. 20), at lag 0 year, large positive SSTA are simulated in the subpolar North Atlantic, consistent with the CGCM, but the simulated negative SSTA along the western part of NAC is opposite in sign to the CGCM. This demonstrates that the role the noise