Investigating Atmospheric Responses to and Mechanisms Governing North Atlantic Sea Surface Temperatures over 10-Year Periods

Qinxue Gu aDepartment of Meteorology and Atmospheric Science, The Pennsylvania State University, University Park, Pennsylvania

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Melissa Gervais aDepartment of Meteorology and Atmospheric Science, The Pennsylvania State University, University Park, Pennsylvania
bThe Institute for Computational and Data Sciences, The Pennsylvania State University, University Park, Pennsylvania

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Elizabeth Maroon cDepartment of Atmospheric and Oceanic Sciences, University of Wisconsin–Madison, Madison, Wisconsin

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Who M. Kim dNational Center for Atmospheric Research, Boulder, Colorado

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Gokhan Danabasoglu dNational Center for Atmospheric Research, Boulder, Colorado

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Frederic Castruccio dNational Center for Atmospheric Research, Boulder, Colorado

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Abstract

North Atlantic sea surface temperature (SST) variability plays a critical role in modulating the climate system. However, characterizing patterns of North Atlantic SST variability and diagnosing the associated mechanisms is challenging because they involve coupled atmosphere–ocean interactions with complex spatiotemporal relationships. Here we address these challenges by applying a time-evolving self-organizing map approach to a long preindustrial coupled control simulation and identify a variety of 10-yr spatiotemporal evolutions of winter SST anomalies, including but not limited to those associated with the North Atlantic Oscillation–Atlantic multidecadal variability (NAO–AMV)-like interactions. To assess mechanisms and atmospheric responses associated with various SST spatiotemporal evolutions, composites of atmospheric and oceanic variables associated with these evolutions are investigated. Results show that transient-eddy activities and atmospheric circulation responses exist in almost all the evolutions that are closely correlated to the details of the SST pattern. In terms of the mechanisms responsible for generating various SST evolutions, composites of ocean heat budget terms demonstrate that contributions to upper-ocean temperature tendency from resolved ocean advection and surface heat fluxes rarely oppose each other over 10-yr periods in the subpolar North Atlantic. We further explore the potential for predictability for some of these 10-yr SST evolutions that start with similar states but end with different states. However, we find that these are associated with abrupt changes in atmospheric variability and are unlikely to be predictable. In summary, this study broadly investigates the atmospheric responses to and the mechanisms governing the North Atlantic SST evolutions over 10-yr periods.

Significance Statement

Climate variability in the North Atlantic Ocean has wide-ranging impacts on global and regional climate. However, the processes involved include interactions between the ocean and atmosphere that vary across both space and time, making it challenging to characterize and predict. Using a novel machine learning approach, this study identifies various time evolutions of North Atlantic sea surface temperature patterns over 10-yr periods. This includes evolutions with similar start states but different trajectories, which have important implications for predictability. Furthermore, we investigate the mechanisms responsible for these evolutions and how different sea surface temperature patterns affect atmospheric circulation through small-scale atmospheric disturbances. These new insights into the complex ocean–atmosphere interactions over time are critical for improving decadal prediction skill.

© 2023 American Meteorological Society. This published article is licensed under the terms of the default AMS reuse license. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Melissa Gervais, mmg62@psu.com

Abstract

North Atlantic sea surface temperature (SST) variability plays a critical role in modulating the climate system. However, characterizing patterns of North Atlantic SST variability and diagnosing the associated mechanisms is challenging because they involve coupled atmosphere–ocean interactions with complex spatiotemporal relationships. Here we address these challenges by applying a time-evolving self-organizing map approach to a long preindustrial coupled control simulation and identify a variety of 10-yr spatiotemporal evolutions of winter SST anomalies, including but not limited to those associated with the North Atlantic Oscillation–Atlantic multidecadal variability (NAO–AMV)-like interactions. To assess mechanisms and atmospheric responses associated with various SST spatiotemporal evolutions, composites of atmospheric and oceanic variables associated with these evolutions are investigated. Results show that transient-eddy activities and atmospheric circulation responses exist in almost all the evolutions that are closely correlated to the details of the SST pattern. In terms of the mechanisms responsible for generating various SST evolutions, composites of ocean heat budget terms demonstrate that contributions to upper-ocean temperature tendency from resolved ocean advection and surface heat fluxes rarely oppose each other over 10-yr periods in the subpolar North Atlantic. We further explore the potential for predictability for some of these 10-yr SST evolutions that start with similar states but end with different states. However, we find that these are associated with abrupt changes in atmospheric variability and are unlikely to be predictable. In summary, this study broadly investigates the atmospheric responses to and the mechanisms governing the North Atlantic SST evolutions over 10-yr periods.

Significance Statement

Climate variability in the North Atlantic Ocean has wide-ranging impacts on global and regional climate. However, the processes involved include interactions between the ocean and atmosphere that vary across both space and time, making it challenging to characterize and predict. Using a novel machine learning approach, this study identifies various time evolutions of North Atlantic sea surface temperature patterns over 10-yr periods. This includes evolutions with similar start states but different trajectories, which have important implications for predictability. Furthermore, we investigate the mechanisms responsible for these evolutions and how different sea surface temperature patterns affect atmospheric circulation through small-scale atmospheric disturbances. These new insights into the complex ocean–atmosphere interactions over time are critical for improving decadal prediction skill.

© 2023 American Meteorological Society. This published article is licensed under the terms of the default AMS reuse license. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Melissa Gervais, mmg62@psu.com

1. Introduction

Sea surface temperatures (SSTs) in the North Atlantic vary substantially on interannual to multidecadal time scales as has been shown in both observational (e.g., Bjerknes 1964; Tourre et al. 1999; Deser et al. 2010; Visbeck et al. 2001) and modeling (e.g., Delworth and Mann 2000; Danabasoglu et al. 2012; Kim et al. 2018) studies. This variability can either be driven by external forcing, such as anthropogenic greenhouse gas emissions or volcanic eruptions, or arise due to internal climate variability (e.g., Ting et al. 2014; Bellomo et al. 2018; Zhang et al. 2019). Perhaps the most well-known mode of oceanic variability is the Atlantic multidecadal variability (AMV), characterized by the basinwide warming or cooling of North Atlantic sea surface. The AMV has significant impacts on regional and global climate, influencing tropical cyclone activity (Klotzbach and Gray 2008), North American heat waves (Ruprich-Robert et al. 2018), Arctic sea ice (Zhang 2015), Asian monsoons (Lu et al. 2006), and precipitation around the globe (Enfield et al. 2001; McCabe et al. 2004; Sutton and Hodson 2005; Martin and Thorncroft 2014). Given these potential wide-ranging impacts of North Atlantic SST, it is important to identify the full range of its variability and the mechanisms responsible.

One key challenge in identifying the mechanisms responsible for such SST variability is the ability of both atmospheric forcing and internal ocean variability to play a key role. Using the AMV as an example, some studies emphasize the importance of ocean circulation and heat transport in driving the AMV (e.g., Zhang et al. 2016; Delworth et al. 2017; Zhang 2017), while others argue that the forcing comes primarily from the atmosphere (e.g., Clement et al. 2015; Cane et al. 2017) or is contributed from both air–sea fluxes and ocean dynamics (e.g., Yamamoto et al. 2020; Gu and Gervais 2022). Resolving this debate requires untangling the complex coupled processes involved.

Adding another layer of complexity is the potential role of feedbacks from atmosphere–ocean coupling as SST anomalies can in turn impact the atmospheric circulation. Although the response of the atmosphere to interannual SST anomalies in the midlatitudes is often viewed as negligible (Kushnir et al. 2002), atmospheric circulation responses associated with SST patterns from the AMV and the Atlantic meridional overturning circulation (AMOC) are shown in observations and modeling studies (Gastineau et al. 2013; Peings and Magnusdottir 2014; Gastineau and Frankignoul 2015; Peings and Magnusdottir 2016; Ruprich-Robert et al. 2017, 2018; Kim et al. 2020; Kwon et al. 2020; Gu and Gervais 2022). The impacts of meridional SST gradients on the North Atlantic atmospheric circulation through transient eddy feedbacks are also shown in idealized aquaplanet simulations with various SST distributions (Inatsu et al. 2003; Brayshaw et al. 2008), modeling studies with reduced AMOC (Brayshaw et al. 2009), and future climate projections of the so-called North Atlantic warming hole (Gervais et al. 2019). Because atmospheric transient eddy feedbacks are closely dependent on SST gradients, they can be difficult to capture if nuanced SST patterns are not clearly identified. Therefore, few studies have identified a full range of transient eddy activities in the North Atlantic Ocean.

Previous studies investigating North Atlantic SST variability on interannual-to-decadal time scales have primarily focused on the AMV (e.g., Clement et al. 2015; Zhang et al. 2019), tripole SST anomaly patterns typically associated with the North Atlantic Oscillation (NAO) (e.g., Fan and Schneider 2012; Schneider and Fan 2012), or SST patterns representing intermediate states in NAO–AMV interactions (e.g., Delworth et al. 2017; Peings and Magnusdottir 2016; Gu and Gervais 2022). Using a self-organizing map (SOM) method, Gu and Gervais (2021) identified additional SST patterns and a wider variety of transitions between patterns in the North Atlantic SST on decadal time scales in Community Earth System Model version 1 (CESM1). They showed that the most common transitions were from positive NAO-like to positive AMV-like to negative NAO-like to negative AMV-like and back to positive NAO-like states, consistent with previous results (e.g., Delworth et al. 2017; Peings and Magnusdottir 2016). Importantly, there are multiple common transitions that do not follow this trajectory and thus act to reduce predictability (Gu and Gervais 2021). Obtaining a better understanding of the dominant processes involved in generating these distinct evolutions would have important implications for reliable decadal prediction.

In this study, we seek to obtain a comprehensive understanding of the dominant North Atlantic SST evolutions and the coupled atmosphere–ocean processes that drive them. We utilize the Evolution-SOM method first introduced by Gu and Gervais (2022) to characterize variability in space and time simultaneously over 10-yr periods. This Evolution-SOM method allows us to capture SST evolutions with diverse trajectories, thus providing a more comprehensive characterization of spatiotemporal variability compared to conventional principal component analysis (PCA) or ordinary SOM methods. In this way, we are able to diagnose complex atmosphere–ocean coupled interactions associated with the diverse SST evolutions in the North Atlantic Ocean, including transient eddy feedbacks that are closely related to the details of meridional SST gradients. Key questions to be addressed in this study include the following: 1) How do various SST evolutions influence the atmosphere through transient eddy feedbacks? 2) What processes are more important for SST evolutions over 10-yr periods? 3) What drives SST evolutions with similar start states but different evolution trajectories?

2. Data and methods

a. Model simulation

This study utilizes the CESM1 1850 control simulation under constant preindustrial forcing conditions produced as part of the CESM1 Large Ensemble Project (CESM1-LE; Kay et al. 2015). The version of CESM1 used in this simulation is fully coupled and consists of the Community Atmosphere Model version 5 (CAM5), the Parallel Ocean Program version 2 (POP2), the Community Ice CodE Model version 4 (CICE4), and the Community Land Model version 4 (CLM4) component models, with nominal 1° horizontal resolution in all components. CESM1 is able to capture dominant modes of climate variability including the NAO (Deser et al. 2017; Athanasiadis et al. 2020) and AMV (Hahn et al. 2018; Hu et al. 2018), with similar interannual-to-decadal variability and weaker multidecadal variability compared to observations (Kim et al. 2018). A total of 1490 years of the preindustrial control simulation (model years 0405–1894) are used to characterize the internal variability in the North Atlantic after omitting the first 404 years to account for model spinup (Kay et al. 2015). With such a long time record and without the impact of external forcings, this simulation allows for the examination of the full range of internal variability in the model.

b. Evolution-SOM

SOM is a machine learning method that can classify high-dimensional datasets into a set of clusters (Kohonen 1982). The SOM method has been successfully utilized for a variety of applications in climate science, including describing atmospheric circulation (Hewitson and Crane 2002; Sheridan and Lee 2011; Gervais et al. 2016, 2020; Horvath et al. 2021), investigating teleconnection patterns (Reusch et al. 2007; Johnson et al. 2008; Li et al. 2015), characterizing climate variability (Morioka et al. 2010; Gu and Gervais 2021), and conducting climate predictions (Gu and Gervais 2021).

In the SOM method, a specified number of generalized patterns called SOM nodes are trained to approximate the input data’s distribution. For a well-trained SOM, these generalized SOM nodes are spatially organized and conserve topological order. Specifically, adjacent SOM nodes represent similar features, while distant ones represent different features. Unlike other classification methods such as k-means clustering (MacQueen 1967), SOM assumes that the input data distribution is a continuum. As a result, SOM nodes are trained to span the input data space rather than maximizing the difference between each other. This feature is suitable for characterizing variability of fields that change continuously such as sea level pressure (SLP) (e.g., Johnson et al. 2008) and SST (e.g., Gu and Gervais 2021). In addition, SOM can handle nonlinear behaviors and is not restricted by orthogonality and stationarity. This provides SOM with a benefit over PCA/empirical orthogonal function (EOF) methods, which are trained to maximize the variance and may merge together physically distinct patterns of variability (Reusch et al. 2005; Wills et al. 2017). In contrast, SOM can characterize physically relevant patterns (Johnson et al. 2008) and provides the ability to investigate the mechanisms and processes associated with these patterns.

To produce a SOM, the SOM size (i.e., the number and organization of SOM nodes) and other relevant parameters need to be specified. Each SOM node has the same size as an input data vector. After being initialized with random values, SOM nodes are trained by repeatedly being compared to input data vectors and then modified based on the SOM parameters. Here we use N to represent the number of steps each input data vector is compared to the nodes per training. Accordingly, for a training process, the total training steps L is the number of total input data vectors times N. At each training step n (which spans from 1 to L), an input data vector x(n) is compared to each SOM node mi(n), where i indicates the SOM node index and mi is the SOM node vector associated with node i. The Euclidean distance between x(n) and mi(n) is calculated for each SOM node, and the SOM node that has the minimum Euclidean distance is defined as the best match unit (BMU) c for this training step. SOM nodes are then updated toward this input data vector as follows:
mi(n+1)=mi(n)+α(n)hci(n)[x(n)mi(n)],
where mi(n + 1) is the data vector of SOM node i at training step n + 1 that is updated from mi(n), α(n) represents the learning rate parameter, and hci(n) represents the neighborhood function at training step n (Kohonen 2001). The learning rate parameter α(n) denotes the extent to which SOM nodes are modified at each training step. Here the inverse parameter is used that is defined as follows:
α(n)=α0/(1+100nL),
where α0 is the initial value for α that needs to be specified before training. Note that α(n) leads to larger updates at the beginning of each training and more subtle tuning near the end. The neighborhood function hci(n) determines the shape of the influence of input data vectors on SOM nodes. The Epanechikov function, calculated as follows, is applied here because it has been shown to outperform other neighborhood functions (Liu et al. 2006):
hci=max[0,1dci2σ(n)2].
In this equation, dci represents the distance between the BMU c and each SOM node i, and σ(n) denotes the radius of influence at training step n. Following this equation, hci is maximized when dci equals 0, indicating that the influence of each input vector on the nodes is maximized at its corresponding BMU in the neighborhood function. The influence of an input vector on SOM nodes decreases as dci increases, and the nodes outside the σ(n) remain unchanged. In this study we use a larger σ that impacts a wide array of nodes at the beginning and decreases its value with training time. The neighborhood function forms the topological order of SOM such that adjacent (distant) nodes are similar (different), which leads to the key difference between the SOM method and the k-means clustering.

The quality of the SOM is assessed using the Sammon map, quantization error (QE), and topographic error (TE). The Sammon map visualizes the Euclidean distance between nodes. A Sammon map is either flat, signifying a stable learning process, or folded over onto itself, indicating an unstable learning process (Jaye et al. 2019). The QE is the mean difference between the input data vectors and their corresponding BMU, measuring SOM nodes’ representativeness of the input data vectors. The TE assesses the topology organization of the map by computing the percentage of input data vectors whose second BMU (the second most similar node to the input data vector) is not adjacent to the BMU. Users can tune N, α, σ, and number of trainings to obtain a well-constructed SOM that has a flat Sammon map and a balance of low QE as well as TE. In general, well-constructed SOMs trained with the same input dataset have similar generalized patterns even with different parameters. Additional details of the SOM algorithm can be found in Kohonen (2001). The SOM Program Package (SOM_PAK) is available online (Kohonen et al. 1996; http://www.cis.hut.fi/research/som-research/). We increase the data capacity for the original SOM package following the method introduced in Gu and Gervais (2022).

The steps to train an Evolution-SOM are similar to those used to train an ordinary SOM as described above, with the difference in the creation of input data vectors. Figure 1 shows this difference in a schematic where each gray shape represents a spatial pattern in the input data. In the ordinary SOM (left part of Fig. 1), each input data vector is typically a spatial pattern for a single time step (e.g., X[I] that contains one gray shape). The resulting SOM patterns are therefore generalized patterns of spatial variability (blue shapes). In the Evolution-SOM utilized here (right part of Fig. 1), each input data vector consists of a specified number of consecutive spatial patterns (e.g., Y[J] that contains multiple gray shapes). Trained with numerous short “movies” instead of “pictures”, Evolution-SOM results in generalized evolutions of spatiotemporal variability (green shapes). That is, each node of the Evolution-SOM contains a generalized “movie” that has the same shape as an input data vector.

Fig. 1.
Fig. 1.

A schematic showing the difference between (left) an ordinary SOM and (right) an Evolution-SOM. Each gray shape represents a spatial pattern at a single time step in the input data. In the ordinary SOM, each input data vector is a spatial pattern at a single time step (e.g., X[I]), and the resulting SOM patterns are generalized patterns of spatial variability (blue shapes). In the Evolution-SOM, each input data vector contains a specified number of consecutive spatial patterns (e.g., Y[J]), and the resulting SOM patterns are generalized evolutions of spatiotemporal variability (green shapes).

Citation: Journal of Climate 36, 24; 10.1175/JCLI-D-23-0093.1

Normally, to capture an AMV-like low-frequency variability in the North Atlantic, low-pass time filtering or other methods to extract low-frequency variability are required (Peings and Magnusdottir 2016; Delworth et al. 2017; Kim et al. 2018; Wills et al. 2019; Gu and Gervais 2021). However, interannual signals can be blurred with the decadal time scale low-pass time filtering (e.g., Delworth et al. 2017). In contrast, the Evolution-SOM can capture both shorter and longer time scale processes over a specified evolution length without time filtering. Instead of isolating a specific time scale, the Evolution-SOM characterizes evolutions happening over a specific period (10 years in our study). In this way, the evolutions and associated mechanisms we identify in this study are more similar to what would be produced in a decadal prediction than the decadal variability identified by studies that apply time filtering to the data. We will show that both NAO-like and AMV-like SST states are present among the Evolution-SOM nodes constructed from unfiltered SST.

The evolution length, or the number of consecutive spatial patterns within each input data vector, depends on the time frame of variability one would like to characterize. In this study, we are interested in variability over 10-yr periods for two reasons. First, multiple climate fields show predictability on 1–10-yr time scales, as demonstrated by decadal prediction systems (e.g., Doblas-Reyes et al. 2013; Meehl et al. 2014; Yeager et al. 2018; Smith et al. 2019). Second, this time frame provides enough lead time for decision-making by policy makers in some sectors (e.g., Dunstone et al. 2022; Solaraju-Murali et al. 2022).

We employ the same 4 × 6 Evolution-SOM used in Gu and Gervais (2022) (Fig. 2 and Movie S1 in the online supplemental material) that is trained using all possible 10-yr time slices of North Atlantic December–February (DJF) SST anomalies within the retained 1490 years of the CESM1 simulation described in section 2a. For example, the first input data vector is 10 consecutive spatial patterns of North Atlantic DJF SST anomalies from model years 0405–0414, and the second one is 10 spatial patterns from model years 0406–0415. As such, we are not assuming that each 10-yr period is distinct in time and expect to see nodes that represent time shifts of typical evolutions. Furthermore, this allows for the use of all 10-yr SST evolutions available in the model simulation. We utilize DJF averaged SST because the reemergence of SST anomalies during winter results in prolonged memory and higher predictability (Alexander et al. 2001; Deser et al. 2003; Buckley et al. 2014; Buckley and Marshall 2016; Buckley et al. 2019; Zhang et al. 2019). The North Atlantic domain chosen is 20°–80°N, 90°W–40°E, which Gu and Gervais (2022) argue better captures the full-basin decadal variability. The DJF SST anomalies are produced by subtracting DJF climatology (computed over years 0405–1894) from the DJF SST for each year and location. Prior to training, we multiply the SST anomalies by the square root of the grid area to give each unit of surface area across the domain an equal weight (Johnson et al. 2008), and normalize the weighted anomalies along the time axis.

Fig. 2.
Fig. 2.

A three-dimensional representation of the 4 × 6 Evolution-SOM for 10-yr consecutive DJF SST anomalies (°C; shading) in the North Atlantic with year 1 in the foreground and subsequent years in the background. Nearby nodes are grouped as indicated by the green boxes (see the text for details). The entire SOM is shown in Movie S1 in years 1–10. The top-left corner of each subplot marks a two-index notation with the first (second) index representing the row (column) of the SOM node. The top-right corner of each subplot shows the frequency of occurrence of the corresponding node.

Citation: Journal of Climate 36, 24; 10.1175/JCLI-D-23-0093.1

We tested different sizes of SOMs to determine that the 4 × 6 Evolution-SOM is the smallest SOM able to span the data space. This Evolution-SOM is produced through two sets of trainings, the first designed to broadly identify and organize variability and the second designed to fine tune the SOM produced in the first training. For each set of training, the number of steps each input data vector is compared against the nodes (N) is 40. The initial learning rate parameters α0 are 0.1 and 0.01 and the radii of influence σ(n) are 5 and 2 for the first and second trainings respectively. With these tuning parameters, the Evolution-SOM has a flat Sammon map and a balance of small QE and TE (not shown). Sensitivity tests for SOM size and evolution length are shown in Gu and Gervais (2022); their results indicate that the SOM size and evolution length utilized here are suitable for our research purpose. After the two sets of training processes, each input data vector (10-yr evolution of SST anomalies) is assigned a final BMU that identifies the SOM node that is most similar to the corresponding input data vector. The frequency of each SOM node is then calculated as the percentage of input data vectors whose final BMU is the corresponding SOM node.

Composites of atmospheric and oceanic variables associated with the Evolution-SOM nodes enable us to investigate the processes associated with different 10-yr evolutions. Expanding upon Gu and Gervais (2022), who investigated composites for a single node, here we calculate the composites for all nodes to diagnose the mechanisms responsible for all twenty-four 10-yr evolutions. Lower-tropospheric meridional eddy heat transport at 850 hPa (υT850¯, where υ is the meridional wind and T is the air temperature), horizontal E-vector at 200 hPa (Eh200) and its divergence, and wind speed at 200 hPa (WSP200) are composited to diagnose the response of the atmosphere to the ocean through transient eddies following Hoskins et al. (1983). Note that υT¯ is calculated at 850 hPa because the heat flux by transient eddies maximizes at lower-tropospheric levels. It provides a measure of transient eddy growth through baroclinic processes and wave activity propagation. The term Eh200 approximates the momentum forcing of transient eddies to the mean flow, defined in Hoskins et al. (1983) as
Eh=(υ2u2¯,uυ¯),
where u is the zonal wind. To isolate baroclinic transient eddy activity, the daily mean wind and temperature fields used to calculate υT850¯ and Eh200 are high-pass filtered with an 8-day eighth-order Butterworth filter, as denoted by the prime symbol (′). Nine-point spatial smoothings are applied to the divergence of Eh200 to reduce noise. Other variables used for composites include SST, SLP, and ocean heat budget terms that are introduced in the following subsection.

c. Upper-ocean heat budget analysis

To quantify the processes contributing to the upper-ocean temperature tendency, we conduct an ocean heat budget analysis by decomposing the total temperature tendency in the upper 295 m following Yeager (2020) and Maroon et al. (2021):
1HDηθtdz=1HDη(uθ)dz+1HDη[(u*θ+K)]dz+QnetHρ0Cp,
where η is sea surface height, D is a fixed depth level (D = 295 m in this study), H = D + η, and dz is the thickness of each model layer for integration; θ is potential temperature and θ/t is thus the temperature tendency; u is the three-dimensional resolved ocean velocity; u* is the three-dimensional subgrid-scale velocity from the mesoscale (Gent and McWilliams 1990) and submesoscale (Fox-Kemper et al. 2011) parameterizations; K is the three-dimensional diffusive temperature flux; ∇ is the three-dimensional divergence symbol; Qnet includes the net air–sea heat flux and internal ocean heat flux due to ice formation, ρ0 is the ocean reference density (ρ0 = 1026 kg m−3), and Cp is the ocean heat capacity (Cp = 3996 J kg−1 °C−1). In the following discussion, the terms in the above equation are referred to as (from left to right) the total temperature tendency, the tendency contributed by resolved ocean advection (ADV), subgrid-scale processes (SUB), and net surface heat fluxes (SHF). The total temperature tendency is calculated as the sum of the three terms on the right-hand side because the actual temperature tendency term is not available in the simulation we use.

d. Pattern correlation

We measure the similarity between different spatial patterns for the composite atmospheric and oceanic variables with the anomaly correlation coefficient (ACC). ACC, a quantification of the spatial similarity between patterns, is one of the most widely used methods for spatial field prediction verification (Wilks 2011). The ACC of two composite spatial patterns is calculated as follows:
ACCg=1GwgPgQgg=1GwgPg2g=1GwgQg2,(1ACC1),
where Pg and Qg are the anomalies for each grid cell g with respect to their climatology for composite spatial patterns P and Q, respectively; wg is a weight of the horizontal area for each grid cell g; and G is the total number of grid cells within the domain.

To test whether the ACC between two spatial patterns of a composite field is significantly high or low, a null distribution of ACCs is created using a Monte Carlo method. We generate two new composite patterns, each comprising a number of spatial patterns randomly selected (without replacement) from winters in the model simulation. The number of spatial patterns used to create each new composite is equal to the number of spatial patterns associated with the corresponding original composite. The ACC between these two randomly formed composites is then calculated. By repeating this process 2000 times, a null distribution of ACC is created, and ACCs greater (smaller) than the 97.5th (2.5th) percentile are considered to be statistically significant.

3. Results

a. SST evolution

The full 4 × 6 Evolution-SOM (shown as an animation in Movie S1) characterizes spatiotemporal variability of winter SST anomalies in the North Atlantic over a 10-yr period. Each SOM node contains a generalized 10-yr evolution. The first time stamp (year 1) of the Evolution-SOM is shown in the foreground of Fig. 2, with years 2–10 following the gray arrows. The frequency of each SOM node is shown in the top-right corner of each subplot. Because nearby (faraway) SOM nodes show similar (different) spatiotemporal patterns, nearby nodes are grouped as indicated by the green boxes (Fig. 2) for discussion purposes. It is worth noting that nearby nodes, even when classified into different groups, can represent similar processes with varied timings.

Year 1 of the Evolution-SOM shows a variety of SST patterns in the North Atlantic across the different nodes (Fig. 2). Group 1 (G1) in the top left that includes nodes [1, 1], [1, 2], [2, 1], and [2, 2] has negative AMV-like patterns with large cold SST anomalies in the Subpolar North Atlantic (SPNA) and Greenland–Iceland–Norwegian (GIN) Seas, warm anomalies in the Northern Recirculation Gyre (NRG), and much weaker warm and cold anomalies in the subtropical North Atlantic (STNA) in year 1. G6 patterns, located in the lower-right corner, have generally opposite anomalies compared to the G1 nodes in year 1, showing quasi-monopolar warm SST anomalies over the North Atlantic. In the G4 nodes (lower-left corner), the spatial extent of the cold anomalies in the SPNA and GIN Seas is smaller than that in G1. Also, G4 has cold STNA anomalies while G1 has warm or near-neutral anomalies in the STNA. The overall year-1 patterns in G4 resemble intermediate states between negative AMV and NAO-like SST patterns (refer to Fig. 3 in Gu and Gervais 2021). Specifically, node [4, 2] is similar to the mid- and high-latitude anomalies typically associated with a negative NAO, while node [3, 1] is similar to a negative AMV pattern but with a less consistent monopolar pattern. The nodes in G5 resemble a negative NAO pattern in year 1 with large positive anomalies in the SPNA and negative anomalies in the STNA and GIN Seas of differing magnitudes. Most nodes in G2 and G3 resemble a positive NAO pattern (nodes [1, 5] and [1, 6]) and states that develop into or decay from a positive NAO pattern (nodes [1, 3], [1, 4], [2, 3], [2, 6]) in year 1, while nodes [2, 4] and [2, 5] have mostly small positive SST values over the domain in year 1.

Although some nodes have similar states in year 1 as described above, they may evolve differently as shown in Movie S1 (years 1–10 for all nodes) and Figs. 3 and 4 (years 2, 4, 6, 8, and 10 in G1 and G5 as examples). We will demonstrate that a considerable number of nodes show evolutions that are consistent with the dominant transition trajectory in the North Atlantic identified in Gu and Gervais (2021). That is from positive NAO-like to positive AMV-like to negative NAO-like to negative AMV-like to positive NAO-like states. Various nodes can represent different timing of this “cycle”. In addition, some nodes reveal other processes such as persistent AMV-like states, persistent NAO-like states, evolutions directly between positive and negative NAO-like states, and reversed NAO–AMV-like transition (e.g., weak AMV+-like to NAO+-like).

Fig. 3.
Fig. 3.

Years 2, 4, 6, 8, and 10 DJF SST anomalies (°C; shading) of the Evolution-SOM (Fig. 2) for G1 nodes including nodes [1, 1], [1, 2], [2, 1], and [2, 2].

Citation: Journal of Climate 36, 24; 10.1175/JCLI-D-23-0093.1

Fig. 4.
Fig. 4.

As in Fig. 3, but for G5 nodes including nodes [3, 3], [3, 4], [4, 3], and [4, 4].

Citation: Journal of Climate 36, 24; 10.1175/JCLI-D-23-0093.1

As shown in Fig. 3, while G1 nodes all start with negative AMV-like patterns, some nodes evolve toward positive NAO-like patterns (nodes [1, 1] and [1, 2], with the phase of node [1, 2] leading that of node [1, 1] by about 1 year) and some nodes maintain their year 1 patterns for multiple years (nodes [2, 1] and [2, 2]). Evolutions in nodes [1, 1] and [1, 2] are consistent with typical NAO–AMV interactions as summarized above. A similar behavior as in G1 is also seen in the G6 evolutions (Movie S1): nodes that start with similar positive AMV-like states end with different states. Specifically, nodes [3, 6] and [4, 6] evolve into negative NAO-like states that then persist for a long time, while nodes [3, 5] and [4, 5] have less persistent negative NAO-like patterns after evolving from the positive AMV-like patterns. An additional difference is that nodes [4, 5] and [4, 6] develop broader SPNA SST anomalies than nodes [3, 5] and [3, 6] during the evolution. The divergence of evolutions with similar start states has important implications for predictability. If we are able to understand the mechanisms driving those evolutions with similar start states but different evolution trajectories, we may help improve decadal prediction skill (see section 3d for further discussion of potential mechanisms).

Nodes that start with similar states but evolve to different states are present in all groups (Movie S1). For example, although they all start with intermediate states between negative NAO and AMV-like states, some nodes in G4 evolve to negative AMV-like phases (nodes [3, 1], [4, 1], and [4, 2], with differing timing), whereas the initial pattern in node [3, 2] persists throughout the 10-yr period. For G5 (the nodes that start with negative NAO-like patterns; Fig. 4), nodes [3, 3] and [4, 3] evolve to weak negative AMV-like patterns, while nodes [3, 4] and [4, 4] evolve to positive NAO-like states. These evolutions from negative to positive NAO over 10 years are different from the well-known NAO–AMV interactions that contain transition from negative NAO-like to negative AMV-like patterns. Three of the G3 nodes evolve from positive NAO-like patterns to positive AMV-like states (nodes [1, 5], [1, 6], and [2, 6], with differing timing), while the state in node [2, 5] is very persistent throughout 10 years. In G2, nodes [1, 3] and [1, 4] evolve from weak positive NAO-like states to positive AMV-like states. In comparison, node [2, 3] starts with a similar but weaker pattern compared to [1, 3] and [1, 4] and is much more persistent. Node [2, 4] evolves from weak warm anomalies in the North Atlantic to a weak positive NAO-like state. It starts with different states but ends with similar states compared to [2, 3], and has a reversed evolution as compared to node [1, 4] that is more frequently seen in typical NAO-AMV interactions.

In this section, we showed that nodes can start with similar patterns but end with different patterns or start with different patterns but end with similar patterns. These behaviors are consistent with the multitrajectory transition of North Atlantic SST revealed by Gu and Gervais (2021). With all these different evolutions identified, we can further investigate the mechanisms associated with them to obtain a more comprehensive understanding of spatiotemporal variability in the region.

b. Atmospheric responses to North Atlantic SST patterns

In this section, we broadly explore transient eddy forcing and atmospheric responses in the North Atlantic associated with all spatiotemporal SST evolutions. To diagnose the transient eddy forcing onto the mean flow, we conduct the E-vector analysis following Hoskins et al. (1983) for each of the twenty-four 10-yr evolutions. Figure 5 shows the composites of the variables associated with this analysis for selected nodes in year 1 as examples in order to demonstrate how transient eddy activities and jet streams are related to SST anomalies. Specifically, to measure the vertical transient eddy activity propagation, composites of the lower-troposphere meridional eddy heat transport anomalies at 850 hPa (υT850¯) are shown in the first column of Fig. 5 for year 1 of selected nodes and in Movie S2 for years 1–10 of all nodes, with composites of SST anomalies also presented in the same figure (contours) to display SST gradients. Composites of SST anomalies are similar to the SOM SST given in Fig. 2 as expected for a well-constructed SOM. Positive υT850¯ anomalies (reddish shading) denote eddies that tilt anomalously westward with height, which is a reflection of anomalous eddy growth through baroclinic processes and anomalously upward propagation of wave activity. To estimate the transient eddy momentum forcing of the zonal time-mean flow in the upper troposphere we show composites of the horizontal E-vector anomalies at 200 hPa (Eh200) (vectors) and spatially smoothed Eh200 divergence anomalies (shading) in the second column of Fig. 5 and in Movie S3. The term Eh200 provides an estimate of transient eddy momentum forcing of upper-troposphere zonal time-mean flow. Specifically, an anomalously divergent Eh200 (reddish shading) implies that transient eddies anomalously provide energy to the zonal mean flow and thus anomalously accelerate the zonal mean flow. Composites of WSP200 anomalies are shown in the third column of Fig. 5 and in Movie S4 to assess the anomalous upper-troposphere circulation response, with climatological WSP200 shown in purple contours. The same purple contours for WSP200 climatology are shown in the second column of Fig. 5 and Movie S3 to help readers intercompare the locations of anomalies of WSP200 and Eh200.

Fig. 5.
Fig. 5.

E-vector analysis result for selected nodes in year 1 including (a) [1, 5], (b) [4, 3], (c) [1, 2], (d) [2, 6], (e) [4, 6], and (f) [1, 1]. (left) Composite of winter meridional eddy heat flux at 850 hPa (υT850¯) anomalies (°C m s−1; shading with significant values at the 95% level in dots) and SST anomalies (°C; contours). SST contours are plotted every 0.1°C with solid purple (dashed green) contours for positive (negative) values and zero contour omitted. (center) Composite of anomalies of winter Eh200 (m2 s−2; arrows starting at 3 m2 s−2), spatially smoothed anomalies of Eh200 divergence (m s−2; shading with significant values at the 95% level in dots), and winter climatological WSP200 (m s−1; purple contours every 5 m s−1 starting from 30 m s−1). (right) Composite of winter WSP200 anomalies (m s−1; shading with significant values at the 95% level in dots) and winter climatology (m s−1; purple contours every 5 m s−1 starting from 30 m s−1). The entire composites for all nodes in years 1–10 are shown in Movies S2S4 for the variables in the left, center, and right columns, respectively.

Citation: Journal of Climate 36, 24; 10.1175/JCLI-D-23-0093.1

In general, we find that relationships between SST, transient-eddy activities, and jet streams exist in almost all evolutions, and these atmospheric responses depend on details of the SST anomalies. Specifically, larger meridional SST gradients induce larger surface baroclinicity, and thus lead to larger υT850¯, indicating anomalously upward propagating eddy activity. For example, node [1, 5] has anomalously colder SPNA and warmer STNA, leading to strongly enhanced meridional SST gradients between the SPNA and STNA in year 1 as shown by the density of SST contours at this location (Fig. 5a). These enhanced SST gradients are associated with anomalously upward propagating eddy activity at 50°–60°N as shown in the positive υT850¯ anomalies in Fig. 5a. Similarly, node [4, 3] has reduced eddy activity due to the decreased meridional SST gradient and surface baroclinicity (Fig. 5b). In general, downstream of large positive (negative) υT850¯ anomalies, there is anomalous divergence (convergence) of the Eh200 aloft as shown in the second column of Fig. 5 and Movie S3. Anomalously divergent Eh200 can provide energy to the mean flow, and thus leads to an enhanced poleward-shifted eddy-driven jet (e.g., node [1, 5] in year 1; Fig. 5a), while anomalously convergent Eh200 results in reduced and equatorward-shifted jets (e.g., node [4, 3]; Fig. 5b).

The locations of υT850¯, Eh200, and jet responses are sensitive to the locations of enhanced/reduced meridional SST gradients. For example, node [1, 2] in year 1 shows a negative AMV-like pattern with large negative SST anomalies extending from the SPNA to around 45°N, thereby intensifying the meridional SST gradient at 40°–50°N (Fig. 5c). This increased gradient leads to higher baroclinicity and larger υT850¯ at 40°–50°N. Notably, these regions of heightened conditions shift farther southwest compared to those seen in [1, 5] in year 1 (Fig. 5a vs Fig. 5c), aligning with the more southwestern displacement of the SST gradient increase. The corresponding location of Eh200 divergence and the enhanced jet lie farther southwest as well, consistent with the high-baroclinicity location.

The strengths of transient eddy activity are closely correlated to the magnitudes of meridional SST gradient. In addition to the strong anomalies of transient eddy activities and atmospheric responses corresponding to the large meridional SST gradient anomalies as described above, we notice that weaker anomalous divergence and convergence of Eh200 are often associated with weaker meridional SST gradient anomalies (e.g., node [2, 6] in year 1; Fig. 5d) or associated with meridional SST gradient anomalies with limited horizontal extent (e.g., node [4, 6] in year 1 in which the STNA cold anomalies have a limited horizontal extent; Fig. 5e), leading to weaker jet responses. Furthermore, with quasi-monopolar SST anomaly patterns (e.g., nodes [1, 1] in year 1; Fig. 5f), there are very small υT850¯ anomalies. Correspondingly, the anomalously divergent and convergent Eh200 zones have small magnitudes, leading to jets with quasi-climatological placement and strength.

Although we only discuss selected nodes as examples, these relationships among meridional SST gradients, transient eddy activities, and jet anomalies described above generally hold for each year in the 10-yr evolutions for all nodes (Movies S2–S4). Furthermore, the magnitudes of the υT850¯ and Eh200 anomalies associated with strong meridional SST gradient anomalies are on the order of 10% of their climatology (not shown). This implies that there is a robust atmospheric response to the ocean. However, this does not mean that the entirety of the jet anomalies is due to the response to SST anomalies. Here we use a fully coupled model that constrains our ability to separate atmospheric circulation patterns that force SST anomalies versus those that are a response to them. It is therefore possible that stochastic atmospheric variability plays a key role in producing an SST pattern and the transient eddy response provides a feedback onto the atmosphere.

c. What drives the SPNA upper-ocean temperature variability?

SST anomalies in the SPNA are important because they can induce 1) linear geopotential height responses through air–sea fluxes and 2) transient eddy forcing by impacting the meridional SST gradient coinciding with the North Atlantic storm track (Hoskins and Karoly 1981; Hendon and Hartmann 1982; Palmer and Zhaobo 1985; Ting and Peng 1995; Kushnir et al. 2002; Nakamura et al. 2004; Gervais et al. 2019). Therefore, they have implications for the sensible weather (Woollings et al. 2012; Lau and Ploshay 2013; Gervais et al. 2020) as well as the mean atmospheric circulation and North Atlantic jet (Nakamura et al. 2004; Brayshaw et al. 2009; Inatsu et al. 2003; Gervais et al. 2019). In addition, processes in the SPNA, identified as the dominant region of AMV (e.g., Wills et al. 2019), can influence North Atlantic climate through heat and salt transport (Grossmann and Klotzbach 2009; Moreno-Chamarro et al. 2017). Furthermore, the SPNA has been shown to be one of the regions with the highest predictability in initialized decadal predictions (e.g., Meehl et al. 2014; Boer et al. 2016; Yeager et al. 2018; Smith et al. 2019). Therefore, understanding the mechanisms driving the SPNA SST evolutions is of prime interest for society.

To examine the processes driving the winter SPNA upper-ocean temperature variability, which has similar interannual variability to the winter SPNA SST in all 24 evolutions (not shown), we apply a heat budget analysis to the upper 295 m SPNA [Eq. (5)]. The SPNA domain used here is shown in Fig. 6c, following the domain used in Yeager (2020). Figure 6a shows the composite temperature tendency anomalies in the winter upper 295 m SPNA temperature and the contributions from resolved ocean advection (ADV), surface heat fluxes (SHF), and subgrid-scale process (SUB) for the 10 years in each evolution node. Positive (negative) tendency anomalies indicate an anomalous increase (decrease) of winter SPNA upper-ocean temperature, or positive (negative) contributions to winter SPNA upper-ocean temperature due to the associated term. Significant composites at the 95% level using a Student’s t test are marked with dots.

Fig. 6.
Fig. 6.

(a) Composites of SPNA upper-295-m mean winter temperature tendency (gray lines), as well as the contributions from resolved ocean advection (ADV; violet lines), net surface heat fluxes (SHF; green lines), and subgrid-scale processes (SUB; orange lines) for the 10 years of evolution in all nodes. The shadings categorize the combined effects from ADV and SHF following the table in (b). Composite time steps with significant cooling (warming) from both SHF and ADV are shaded deep blue (red); time steps with significant cooling (warming) effect from ADV but insignificant effect from SHF are shaded light blue (pink) with hatching; time steps with significant cooling (warming) effect from SHF but insignificant effect from ADV are shaded light blue (pink) without hatching; time steps with significant opposite effects from SHF compared to ADV are shaded yellow; and time steps with insignificant effects from both SHF and ADV are shaded white. (b) The legend for the shading represents the combined effects from SHF and ADV as described in (a), with the frequency of each combined effects shown as a percentage. (c) The SPNA domain used is shown in blue shading.

Citation: Journal of Climate 36, 24; 10.1175/JCLI-D-23-0093.1

To quantitatively represent the contributions of different processes, we classify the individual effects of ADV and SHF into three categories as significant warming or cooling at the 95% level, or insignificant effect. Contributions from SUB are not discussed here because they typically have the opposite sign compared to the upper-ocean temperature tendency, acting as a damping mechanism for the effects from ADV and SHF. The ADV and SHF anomalies can have up to nine combined effects, shown in different color and shading combinations used to represent each category in Figs. 6a and 6b. We then calculate the percentage of composite winters associated with each category in all nodes as shown in Fig. 6b.

Surprisingly, the ADV and SHF anomalies have significant opposite effects during only 1 of the 240 composite time steps (24 nodes with 10 winters). In other words, when ADV significantly warms the SST, SHF rarely has a significant cooling effect on the SST, and vice versa. In contrast to the rarity of having opposite effects, the total frequency of ADV and SHF working collaboratively to force a positive (negative) tendency is 7% (9%). The collaborative effects of SHF and ADV appear in at least 1 year in the majority of 10-yr evolutions, as shown in the deeper blue and red bars in Fig. 6a. For example, collaborative effects appear when SST patterns are NAO-like (e.g., NAO+ in node [1, 6] years 1–2 and NAO− in node [4, 6] years 4–6) and AMV-like (e.g., AMV+ in node [2, 6] year 6 and AMV− in node [4, 1] years 8–9), as shown in Movie S1 and Fig. 6a. This combination may be attributed to the atmosphere circulation-related turbulent heat flux and Ekman transport associated with the wind stress that act in the same direction in the SPNA. Our study does not impose a specific time scale to the data, and instead focuses on the processes happening over the course of 10 years in a fully coupled model configuration. Therefore, our results are different from studies that identify the dominant role of oceanic processes with low-pass filtered data (e.g., Zhang et al. 2016; Delworth et al. 2017; Zhang 2017), as well as studies that emphasize the dominance of atmospheric variability with slab-ocean models or red noise models without oceanic damping (e.g., Clement et al. 2015; Cane et al. 2017) in driving the AMV.

For the largest amount of time, ADV acts on its own as seen in the 22% (20%) frequency when only ADV has significant warming (cooling) effect and SHF has an insignificant effect as shown in the light pink (light blue) shading with hatching in Figs. 6a and 6b. These times are not necessarily those with large temperature tendencies and so may not be associated with enhanced predictability. Nevertheless, it is still notable that we are able to identify the role of ADV with unsmoothed data with this methodology whereas previous studies (e.g., Zhang 2017; Yeager 2020) are only able to isolate the importance of ADV on decadal time scales using low-pass filtering.

In contrast, the percentage of time when SHF alone has a significant effect is only 10% (light blue and pink shading without hatching). It is notable that because SHF has a higher standard deviation, the anomalies need to have larger magnitude in order to be considered as significantly different from 0. For a large portion of the time, when there is a significant deviation in the temperature tendency, both SHF and ADV also significantly differ from zero.

d. Potential mechanisms driving evolutions with similar start states but different trajectories

As mentioned in section 3a, the Evolution-SOM captures evolutions that start with similar SST states but end with different SST states. Here we compare nodes [1, 1] and [2, 1] as an example to explore the potential mechanisms behind the differing trajectories. Composites of SST anomalies over years 1–7 within the 10-yr evolutions associated with nodes [1, 1] and [2, 1] are shown in Figs. 7a and 7b, respectively. Again, composites of SST anomalies are generally similar to their corresponding SOM SST patterns (Movie S1 and Fig. 3).

Fig. 7.
Fig. 7.

(a) Node [1, 1] composite of SST anomalies (°C; shading) from years 1–7. (b) As in (a), but for node [2, 1]. (c) Node [1, 1] composite of SLP anomalies (hPa; shading) from years 1–7. (d) As in (c), but for node [2, 1]. Significant shaded values at the 95% level are dotted. Panels with SST/SLP patterns that show a significant positive (negative) correlation between node [1, 1] and node [2, 1] are framed with a solid (dashed) black rectangle.

Citation: Journal of Climate 36, 24; 10.1175/JCLI-D-23-0093.1

Nodes [1, 1] and [2, 1] both start with quasi-monopolar SST anomalies resembling negative AMV-like patterns. However, node [1, 1] evolves to a positive NAO-like SST pattern with colder-than-normal SPNA and warmer-than-normal STNA (year 7), while node [2, 1] has different anomalies in the SPNA and STNA compared to [1, 1] in year 7 (Fig. 7). To quantitatively assess the similarity between spatial patterns associated with different nodes, we calculate the pattern correlation (ACC) for each year between nodes [1, 1] and [2, 1], within the domain of 20°–80°N, 90°W–40°E. The significance of the pattern correlation is tested using the method introduced in section 2d. Patterns that show a significant positive (negative) correlation are framed with solid (dashed) black rectangles (Fig. 7). According to this metric, nodes [1, 1] and [2, 1] display a significant positive correlation in years 1–5 and are insignificantly correlated afterward.

This divergence in the SST evolutions for nodes [1, 1] and [2, 1] is consistent with the change in the combined effects from the upper 295 m averaged SHF and ADV terms (Fig. 6). Both nodes have significant cooling driven by ADV at the beginning of the evolution, with additional cooling driven by SHF in node [1, 1] from years 2–5. In year 5, the abrupt change in the SHF term for node [2, 1] results in a significant warming effect and then both SHF and ADV lead to additional significant warming in year 6. On the contrary, in node [1, 1], the cooling in year 1 persists through year 7.

To further illustrate how atmospheric circulation differs in nodes [1, 1] and [2, 1], composite SLP anomalies associated with these two nodes for years 1–7 are shown in Figs. 7c and 7d. Nodes [1, 1] and [2, 1] both have a positive NAO-like dipole in years 2–3, with their SLP patterns showing a significant positive correlation (framed with a solid rectangle). However, beginning from year 5, the SLP pattern associated with node [2, 1] shifts to a negative NAO-like pattern, while node [1, 1] is still associated with a positive NAO-like pattern, leading to a significant negative pattern correlation in year 5 (framed with dashed rectangle). The abrupt change in the SLP pattern of node [2, 1] in year 5 can cause a reduction in surface westerlies over the SPNA, yielding a significant positive SHF anomaly, as shown in Fig. 6. In addition to the SHF, the negative NAO-like SLP pattern can also lead to anomalously northward Ekman transport through its impact on wind stress, which further contributes to a warming in the SPNA (e.g., Visbeck et al. 2003). These processes ultimately result in a reduced pattern correlation between the SST patterns of these two nodes after year 5.

It is valuable to investigate whether the divergence of SLP patterns in nodes [1, 1] and [2, 1] is predictable. Predictability in atmospheric circulation often comes from remote sources via teleconnections. Climate indices for El Niño–Southern Oscillation, Pacific decadal oscillation, and the Pacific–North American pattern display only minor differences in the years prior to the abrupt change in SLP correlation in nodes [1, 1] and [2, 1] (not shown). Therefore, teleconnections from the Pacific are likely not responsible for the divergence of SLP patterns in these two nodes. Similarly, we investigated the differences in Arctic sea ice in these two nodes to assess if forcing from sea ice could explain the divergence. Arctic sea ice anomalies in these two nodes are consistent with contemporaneous SST anomalies (not shown), implying that the sea ice anomalies are driven by similar processes to those driving the SST anomalies. These results suggest that the divergence of SST evolutions led by the abrupt SLP change may be attributed to stochastic atmospheric variability, which is likely unpredictable. Similar processes associated with stochastic atmospheric variability are seen in other pairs of SST evolutions that start with similar patterns but evolve to different patterns such as nodes [4, 5] and [4, 6], as well as nodes [3, 3] and [4, 4].

Although the stochastic atmospheric variability is likely the cause of the divergence of SST evolutions, transient eddy feedbacks may modulate how it impacts SST evolutions. For example, compared to node [2, 1], stronger transient eddy feedbacks in node [1, 1] may help sustain the meridional SST gradient and thus make the SST pattern more resistant to the stochastic forcing as demonstrated below. Specifically, node [1, 1] has cooling effects from both SHF and ADV in Years 2–4, while node [2, 1] only has a cooling effect from ADV, which may be associated with the subtle differences in the SLP patterns between nodes [1, 1] and [2, 1]. This additional heat loss through SHF leads to larger SST gradient between SPNA and STNA in node [1, 1], and thus can strengthen the transient eddy activities as shown clearly in υT850¯ and Eh200 anomalies in year 4 (Fig. S1). The enhanced jet in node [1, 1] associated with transient eddy activities would induce an equivalent barotropic geopotential height response, with strengthened low system to the north and strengthened high system to the south of the jet, similar to the condition as discussed by Gervais et al. (2019) associated with the North Atlantic warming hole. This response can amplify the original meridional SST gradient anomalies, resulting in a positive feedback [see Fig. 3c in Gu and Gervais (2022) for a schematic with a similar condition] and make the SST patterns less susceptible to stochastic forcings in node [1, 1] compared to node [2, 1]. However, because the climate system is fully coupled in this model simulation, we are not able to quantify the contribution from transient eddy feedbacks versus internal atmospheric variability to the divergence of SST evolutions.

4. Summary and discussion

We investigated the spatiotemporal internal variability in the North Atlantic SSTs, as well as the associated mechanisms and atmospheric responses by characterizing 10-yr evolutions in a long CESM1 preindustrial control simulation. The study uses the same Evolution-SOM as Gu and Gervais (2022) but extends their investigation of NAO–AMV-like interactions to all 10-yr evolutions of SST anomalies in the North Atlantic. Most previous studies investigating North Atlantic decadal variability focus on the AMV-related variability and NAO–AMV interactions. Here within this novel Evolution-SOM framework, we are able to identify a variety of 10-yr evolutions of SST anomalies, including those associated with the well-known NAO-AMV-like interaction, reversed NAO–AMV-like transition, persistent AMV-like and NAO-like states, and evolutions directly between opposite NAO-like phases.

By characterizing nuanced spatiotemporal SST evolutions, we are able to discern transient eddy activities and associated responses of atmospheric circulation that are closely dependent on the details of SST patterns. Previous studies (e.g., Kushnir et al. 2002) argue that unlike the interannual atmospheric variability in the tropics that is highly constrained by SST variability, the extratropical atmosphere is dominated by internal variability, and its SST-forced variability is relatively small including those through transient eddy forcing. In this study, however, by conducting composites that maintain the details of SST patterns including the meridional SST gradient, we find robust signals of atmospheric responses to the midlatitude SST through transient eddy forcing over 10-yr evolutions. Similar responses have been found previously in association with specific climate modes (e.g., Peings and Magnusdottir 2014, 2016) or future climate change (Gervais et al. 2019). The close dependence of the strengths and locations of atmospheric responses on the details of SST patterns over time indicates the usefulness of the Evolution-SOM methods for showing the details of different SST evolutions over 10 years without applying time filtering. This may have important implications for European and Mediterranean weather (e.g., Mahlstein et al. 2012; Davini et al. 2014).

Coupled atmosphere–ocean processes that shape the diverse 10-yr SST evolutions identified by Evolution-SOM were also investigated. Through a heat budget analysis, we revealed the noncompeting effects of resolved ocean advection and surface heat fluxes, the damping effect associated with subgrid-scale processes, and the importance of resolved ocean advection in driving the upper SPNA temperature. In addition, significant deviations in the upper SPNA SST tendency are often associated with collaborative effects from both the resolved ocean advection and surface heat fluxes. The collaborative effects identified here are different from previous studies that emphasize the preeminence of oceanic processes with low-pass filtered data (e.g., Zhang et al. 2016; Delworth et al. 2017; Zhang 2017) or the dominance of atmospheric variability using slab-ocean models or red noise models without oceanic damping (e.g., Clement et al. 2015; Cane et al. 2017) in driving the AMV. Our distinction lies in the focus on processes over 10 years without enforcing a specific time scale, using a fully coupled model configuration. This provides a unique perspective that aligns more closely with what would be produced in a typical decadal prediction (e.g., Yeager et al. 2018; Smith et al. 2019).

We further explored the potential mechanisms that can lead to evolutions with similar start states but different evolution trajectories. We found that abrupt changes in SLP and associated differences in surface heat fluxes lead to a divergence in SST evolution. Additional analysis of various teleconnections and Arctic sea ice show no evidence that this behavior can be attributed to predictable remote teleconnections. Therefore, this divergence of SST evolution is likely due to stochastic atmospheric variability that is not predictable at long leads. However, strengths of transient eddy feedbacks may alter the sustainability of SST patterns, and thus modulate how it responds to stochastic atmospheric variability.

We should note that the influence of different forcings in driving upper-ocean temperature anomalies may vary in models with different resolutions. The model in our study has a nominal 1° horizontal resolution with parameterized ocean-eddy effects. However, in Small et al. (2020), which used a CESM simulation with mesoscale ocean eddies resolved (∼0.1° horizontal resolution), 3D ocean heat advection is found to dominate upper 50 m heat content variability over much of the ocean, including the SPNA. Nevertheless, the large-scale features of ocean heat content budget in low-resolution models can be reproduced by spatially smoothing out the small-scale eddy motions in the high-resolution data as shown in Small et al. (2020), suggesting that the processes detected in our study fundamentally exist in CESM simulations regardless of resolution. Future work could apply the Evolution-SOM framework to high-resolution model outputs to determine how the climate variability in such simulations differs from that in coarser-resolution simulations. In addition, applying similar analyses to the Coupled Model Intercomparison Project phase 6 (CMIP6) preindustrial control simulations in the future could evaluate whether the mechanisms identified in our study maintain their validity across different models.

Acknowledgments.

We thank Stephen Yeager, Raymond G. Najjar, Jr., Laifang Li, and Andrew M. Carleton for insightful discussions and three anonymous reviewers for providing constructive feedback that improved this work. This work was supported by the Penn State College of Earth and Mineral Sciences “EMS Resubmit Research Grant” award. Pre-industrial control simulation data are made available by CESM Large Ensemble Community Project and supercomputing resources provided by NSF/CISL/Yellowstone. Computations for this research were conducted with the Pennsylvania State University Institute for Computational and Data Sciences (ICDS). This content is solely the responsibility of the authors and does not necessarily represent the views of the ICDS. Who Kim acknowledges support from NOAA OAR’s Climate Program Office through award NA20OAR4310408. The National Center for Atmospheric Research is a major facility sponsored by the National Science Foundation under Cooperative Agreement 1852977. Support for this research was also provided by the Office of the Vice Chancellor for Research and Graduate Education at the University of Wisconsin-Madison with funding from the Wisconsin Alumni Research Foundation.

Data availability statement.

The model simulation used in this study (CESM-LE; Kay et al. 2015) is available at https://www.cesm.ucar.edu/projects/community-projects/LENS/data-sets.html. The SOM Program Package (SOM_PAK; Kohonen et al. 1996) is available at http://www.cis.hut.fi/research/som-research/. Modifications of SOM_PAK to increase the data capacity are outlined in Gu and Gervais (2022).

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