1. Introduction
The North Atlantic undergoes variations in sea surface temperature (SST) on multidecadal time scales (e.g., Kerr 2000; Frankcombe et al. 2008; Chylek et al. 2011; Vianna and Menezes 2013), with impacts on the climate of adjacent land areas (e.g., Enfield et al. 2001; Knight et al. 2006; Msadek and Frankignoul 2009; Sutton and Dong 2012; Sutton et al. 2018) and beyond (Lu et al. 2006; Zhang and Delworth 2006). These SST variations are widely referred to as Atlantic multidecadal variability (AMV).
A variety of mechanisms have been proposed to drive AMV, including external forcing by anthropogenic aerosols (Booth et al. 2012), and/or volcanoes (Otterå et al. 2010; Swingedouw et al. 2017), atmospheric forcing (Clement et al. 2015), internal oceanic variability (Sévellec and Fedorov 2013; Gastineau et al. 2018), and coupled ocean–atmosphere modes of variability involving the Atlantic meridional overturning circulation (AMOC; Knight et al. 2005; Ortega et al. 2015). Atmospheric feedbacks are also likely to play a crucial role in setting the AMV pattern (Xie 2009). There is as yet little consensus on the precise mechanism as AMV simulation varies from model to model in both phenomenology and driving processes (Drews and Greatbatch 2017; Muir and Fedorov 2017; Sévellec and Sinha 2018; Sutton et al. 2018).
Observational studies are hindered by the relatively short instrumental record that captures only one or two AMV cycles and lacks information on other variables such as the AMOC. Recent studies have instead utilized AMOC proxies; for example, McCarthy et al. (2015) use a sea level–based indirect proxy of the AMOC to demonstrate a link between the AMOC, OHC in the top 500 m, and AMV from the 1920s to the 2000s.
The link between AMOC and upper ocean OHC is well established in modeling studies (Robson et al. 2012; Zhang 2008; Zhang and Zhang 2015). There is a strong correlation between subtropical AMOC and meridional heat transport (MHT) found in models (Sévellec and Huck 2015; Moat et al. 2016) and observations (Johns et al. 2011). Grist et al. (2010) found, in a model based analysis for 1958–2002, that the subpolar gyre OHC anomaly was more strongly correlated with the ocean heat transport convergence (r = 0.75) than with surface fluxes (r = 0.5). Similarly, Robson et al. (2014, 2018) and Hodson et al. (2014) found the AMOC and its associated ocean heat transport was the dominant process in the 1990s warming and the 1960s cooling of the subpolar gyre. Likewise, Williams et al. (Williams et al. 2014; R. Williams et al. 2015), using a model that was strongly relaxed to observed temperature and salinity, attributed decadal changes in subpolar gyre OHC to changes in the AMOC.
Whatever the detailed mechanisms and drivers of the AMV, it seems likely that horizontal ocean heat transport convergence and surface fluxes of heat will both play important roles. However the key relationship between changes in oceanic heat transport, OHC, and SST is not well understood, particularly on multidecadal time scales, which is the focus of this paper.
A number of studies have attempted to identify fingerprints of changing AMOC directly on the SST, thus bypassing the need to examine OHC. However, the results from climate models are variable (Roberts et al. 2013; Zhang 2008) and although there is now evidence of a similar pattern associated with the limited duration observational record (Smeed et al. 2018), without a verified mechanism it is difficult to be confident in these fingerprints.
A more rigorous approach was adopted by Buckley et al. (2014) where interannual heat content was evaluated over the depth of the monthly maximum climatological mixed layer (i.e., the portion of the upper ocean in contact with the atmosphere). Using the ECCO state estimate for the period 1992–2010 they estimate that 70% of the variability in mixed layer heat content is explained by local forcing (i.e., air sea heat fluxes and Ekman convergence) and only 30% due to advection over large parts of the North Atlantic. Their use of the monthly maximum mixed layer was an improvement over previous studies which employ a spatially constant depth horizon. However, because of the length of the simulation they were unable to address multidecadal time scales.
The Buckley et al. (2014) approach was extended to the global domain by Roberts et al. (2017), who used a similar theoretical framework, including a spatially variable maximum mixed layer depth (MLD) to differentiate the near-surface layer in contact with the atmosphere from the rest of the ocean. Unlike Buckley et al. (2014) they used observationally based gridded OHC products and surface fluxes from atmospheric reanalyses with a Kalman filter–based method to obtain an estimated heat budget with error bounds for both the mixed layer and the rest of the ocean, evaluating ocean heat transport convergence as a residual. Their results indicated that on interannual time scales there are extensive regions (equator and western boundary currents and the Antarctic Circumpolar Current) where ocean heat transport convergence dominates the OHC variability of the mixed layer and over large parts of the rest of the ocean both ocean heat transport convergence and surface heat fluxes are important. This contrasts with the full-depth OHC, which on these time scales is dominated by ocean heat transport convergence.
In this paper we consider temperature changes in the mixed layer, taking account of its time-varying depth using the SST evolution equation described by Stevenson and Niiler (1983), paying particular attention to the diffusive flux at the base of the mixed layer.
We address the following questions using a state-of-the-art coupled climate model that we demonstrate has realistic Atlantic multidecadal variability:
What controls the multidecadal evolution of full depth OHC in the subpolar North Atlantic? What are the respective roles of ocean surface fluxes versus internal ocean processes? Is there a difference between the deep convection regions to the west and the region farther east that is more influenced by the North Atlantic Current?
What controls the multidecadal evolution of SST in the subpolar North Atlantic? Are the respective roles of surface fluxes and internal ocean processes similar and if not how do they differ?
What is the relationship between changes in the deep (sub mixed layer) OHC and SST? How and why are the forcing terms different?
How do both deep OHC and SST depend on the AMOC?
We focus on the subpolar North Atlantic (SPNA) as the AMV spatial pattern is strongly concentrated in this region (e.g., Sutton et al. 2018). In contrast, subtropical AMV is thought to be caused by relatively rapid (months to a few years) adjustment of the subtropical ocean to changes in the subpolar gyre via boundary waves (Johnson and Marshall 2002), or by atmospheric feedbacks to SPNA variability (Sutton et al. 2018).
The paper is organized as follows. We use a rigorous theoretical framework for comparing OHC and SST variability in section 2. Details of the model configurations and methodology are given in section 3. The results are presented in section 4 and conclusions in section 5.
2. Theory
a. Full depth ocean heat content
Equations (1) and (2) could equally be evaluated over different depth horizons if H(λ, φ) in Eq. (1) is replaced by a fixed depth taking bottom topography into account. We examine the sensitivity of our results to choice of depth horizon in section 4e.
b. Sea surface temperature
Neglecting horizontal diffusion, changes in the ocean temperature averaged over the mixed layer, Ta, at any given location can be caused either by heating/cooling at the air–sea interface, QNET, or by horizontal advection, vertical advection/diffusion of heat, and entrainment/detrainment of fluid into or out of the mixed layer.
Once ∂ξ/∂t and QNET/h have been calculated, RML/h and RML can be evaluated as a residual from observations (with associated observational uncertainty), or exactly from a heat-conserving climate model.
c. Anomaly formulation
The first term on the RHS of Eq. (10) represents “external” forcing of the SST by surface fluxes, while the second term represents trends due to “internal” processes in the ocean. These are analogous to
d. Parameterization of diffusive vertical heat flux
3. Model description and analysis procedure
a. HadGEM3-GC2 coupled climate model
We analyze output from a 300-yr preindustrial control simulation HadGEM3-GC2 (K. Williams et al. 2015), a high-resolution version of the Met Office HadGEM3 climate model, including ocean, atmosphere, sea ice, and land surface components. The ocean configuration is the Global Ocean version 5.0 (Megann et al. 2014) of the v3.4 NEMO model (Madec 2008), which uses the ORCA025 tripolar grid (~0.25° horizontal resolution) and 75 vertical levels. The sea ice component, also on the ORCA025 grid, is version 4.1 of the Los Alamos Sea Ice Model (CICE; Hunke and Lipscomb 2010), which includes five sea ice thickness categories and has improved representation of Arctic sea ice concentration with respect to previous configurations (Rae et al. 2015).
The atmosphere component is the Global Atmosphere version 6.0 of the Met Office Unified Model (UM; Walters et al. 2011), with a horizontal resolution of N216 (~60 km at midlatitudes) and 85 levels in the vertical. The land surface model is the Global Land version 6.0 of the Joint U.K. Land Environment Simulator (JULES; Best et al. 2011), which shares the same grid as the atmospheric component.
This control simulation has been employed in many studies to examine a variety of climate system processes. For example, the model has been used to examine mechanisms of decadal variability in the Labrador Sea (Ortega et al. 2017), predictions of the winter NAO (Scaife et al. 2014; Dunstone et al. 2016), and climatic trends in the North Atlantic (Robson et al. 2016).
b. Analysis procedure
Equations (1)–(12) were evaluated from the GC2 climate model simulation (K. Williams et al. 2015) using monthly mean potential temperature, MLD (defined as the depth at which the potential density referenced to the surface differs from the surface density by 0.01 kg m−3), and mean net surface heat flux.
For each model year we take each month and calculate the average tendency terms for SST and OHC for the 1-yr period from that month to the same month in the next year (January 2294–January 2295, February 2294–February 2295, … , December 2294–December 2295). We then calculate the mean of these 12 averaged tendency terms to obtain a consolidated tendency term representative of the entire year. With this approach an exact heat budget for the annual mean OHC or SST anomaly is obtained. A constant value of ρ0CP = 4.1 × 106 J m−3 K−1 was used throughout.
All variables are filtered to retain periods of 10 years and longer using an 11-point Parzen filter for annual means, or a 121-point filter for monthly means (Press 1986). The results were essentially the same using a running mean filter.
4. Results
a. Mean OHC and SST tendency terms
Over long time scales, the mean OHC tendency is very small and surface fluxes balance advection as in Eq. (6), hence it is sufficient to examine just one of these latter terms in order to understand the mean state. The HadGEM3-GC2 300-yr mean QNET is shown in Fig. 1a. The net heat flux term shows cooling in the Gulf Stream region and SPNA (north of a line connecting Florida with the Bay of Biscay) and warming in the subtropics (south of this line). The cooling is considerably weaker in the central SPNA, and there is a strong region of warming on the shelf region of the Grand Banks. The warming in the subtropics is enhanced toward the shelf-slope regions bordering Africa and South America. Equation (6) indicates that advection has a mean pattern opposite to the surface heat flux term with cooling in the subtropics and warming in the subpolar regions.
(a) HadGEM3-GC2 control simulation 300-yr mean full depth OHC tendency component due to net surface heat flux (W m−2). (b) As in (a), but for SST tendency (K month−1). A negative surface net heat flux indicates a loss of heat from ocean to atmosphere. (c) Seasonal MLD variation (m) during model year 2295 at 55.4°N, 24.8°W. Horizontal lines represent depth horizons of 100 m, 200 m, and the maximum MLD of 482.5 m at this location. (d) QNET (blue) and accumulated QNET (red) (W m−2) at 55.4°N, 24.8°W. (e) QNET/h (blue) and accumulated QNET/h (red) (W m−3) at 55.4°N, 24.8°W.
Citation: Journal of Climate 32, 18; 10.1175/JCLI-D-18-0709.1
Thus, as expected, the model shows warming in the subtropics and cooling in the subpolar regions due to differential radiative heating. The ocean circulation (mainly the AMOC in the North Atlantic) redistributes the excess heat in the tropics toward the pole.
The HadGEM3-GC2 300-yr mean SST tendency due to surface fluxes in the North Atlantic, the first term in Eq. (8), is shown in Fig. 1b. Surface fluxes introduce a warming SST tendency everywhere with the exception of the western boundary regions and some small isolated regions in the tropics, and the Greenland and Labrador Seas. In the Gulf Stream Extension, North Atlantic Current, and subpolar gyre regions the sign is opposite to the effect of surface heat fluxes on the OHC (cf. Fig. 1a). Also the pattern is different, with maximum values over the Grand Banks shelf region, in the subtropical gyre, and in the western subpolar region. The prevailing positive tendencies occur because of the MLD factor h in the denominator of the QNET/ρ0CPh term in Eq. (8), which weights the annual mean toward the summer months when the MLD is shallowest and the ocean experiences heat gain from surface fluxes. Advection-diffusion-entrainment opposes the warming effect of surface fluxes and hence is negative in most locations.
The result that in most of the North Atlantic north of 30°N, surface fluxes impose a negative trend on the annual mean full depth heat content while also imposing a positive trend on the annual mean SST is somewhat counterintuitive and bears further explanation. As an illustration, Fig. 1c displays the MLD over the model year 2295 at 55°N, 28°W. In January, the MLD is 300 m. It deepens to a maximum of 400 m in February before shallowing over spring (March–May) to a minimum of about 20 m in June. Over summer (June–August) the mixed layer remains very shallow but during the autumn it deepens, reaching in excess of 100 m in December. For comparison the maximum winter MLD over the 300-yr simulation (482.5 m) is shown as a solid line. Also marked are the 100- and 200-m depth levels. Evidently, use of a temporally fixed depth to characterize the mixed layer (e.g., Buckley et al. 2014; Roberts et al. 2017), while mathematically simpler, is problematic. Heat content in such a fixed layer is not simply related to SST in any season.
Surface heat flux, QNET, for each month of the year is plotted in Fig. 1d (blue). There is strong (turbulent) heat loss from ocean to atmosphere between January and March and again between October and December. In summer, between May and August, the ocean gains heat due to increased insolation. At this example location, the seasonal variation of the net surface heat flux is ±200 W m−2.
The red line in Fig. 1d represents the accumulated net surface heat flux (i.e., the accumulated sum of the values plotted in blue). The accumulated heat flux remains negative over the whole year, indicating that winter heat loss strongly outweighs summer heat gain. Hence in the annual mean, surface heat flux tends to reduce OHC and a negative value is found in Fig. 1a at this location.
The surface flux–related forcing term for SST, QNET/h, is plotted in red in Fig. 1e. The high values of h in winter, spring and autumn compared to summer (up to 20 times higher) result in much smaller values of QNET/h in these seasons so the accumulated value of QNET/h (red) is strongly positive from May to the end of the year and a positive value is found in the corresponding location in Fig. 1b.
b. Simulated AMV variability
A common hypothesis for the observed temporal AMV variability is heat redistribution by the AMOC. While changes in the AMOC and associated changes in horizontal heat transport divergence can potentially affect full depth OHC, whether and by what mechanism changes in full-depth OHC are translated to changes in SST are not clear. In this section, we first examine the relationship between the AMOC and AMV in the HadGEM2-GC2 simulation, then use our theoretical framework to obtain insights into the mechanisms.
Figure 2a shows the AMV index calculated from annual mean model output, together with the AMOC anomaly at 26°N (Fig. 2b), and 50°N (Fig. 2c), with respect to its long-term mean, low-pass filtered with a cutoff period of 10 yr. The AMV index shows multidecadal variability reminiscent of the observations and the time scale of the variability (~50 yr) is within the range estimated from observations and multimodel studies (20–70 yr). There are four large AMOC excursions in the simulation period (Figs. 2b,c) and these are matched with large AMV fluctuations. The spatial pattern associated with the AMV (regression coefficient of the linear correlation of SST with the AMV index) is shown in Fig. 2d. The pattern approximately matches that obtained from observations (e.g., Sutton et al. 2018; see also Kushnir 1994) but the region of low regression in the western subtropics (between Florida and Cape Hatteras) is larger than that seen in observations and in addition the Greenland Sea shows the opposite sign regression coefficient. However, the HadGEM3-GC2 control simulation has fixed atmospheric aerosol and CO2 concentrations, whereas the real-world AMV may be influenced by changing concentrations of anthropogenic aerosols or greenhouse gases. Hence, even if the model was perfect, we might not expect or demand exact agreement. On the other hand, the current generation of climate models shows a range of AMV time scales and spatial patterns, hence some of the results presented in this study may be model dependent and it will be important to compare them across a range of models in future.
(a) The HadGEM3-GC2 AMV index time series, and AMOC anomalies (both 10-yr low pass filtered) at (b) 26°N and (c) 50°N. (d) SST pattern associated with the AMV, represented by the regression slope between AMV index and 10-yr low pass filtered SST anomalies at each grid point over 300 model years. Dots indicate values that are significant at the 95% level.
Citation: Journal of Climate 32, 18; 10.1175/JCLI-D-18-0709.1
Correlation analysis shows a lagged relationship between AMOC and AMV with a maximum correlation coefficient of 0.56 (26°N) and 0.52 (50°N) with the AMOC leading by ~5 and ~9 years (Fig. 3a). The thicker black and red lines indicate significance at the 95% level. Both time series were detrended and autocorrelations were considered in determining the degrees of freedom for significance testing (Emery and Thomson 1997). Although significant correlations are found, they do not account for all the AMV variance and many other processes could contribute to the AMV variability including subpolar gyre variability independent of the AMOC, atmospheric teleconnections from the tropics, and variability of the Northern Hemisphere cryosphere including sea ice and snow cover.
(a) Lagged correlation between the AMOC anomaly (Sv) and the AMV (both 10-yr low pass filtered) indicating that the AMV lags the AMOC at 26°N (black) and 50°N (red). Thick lines indicate correlations are significant at the 95% level. Also shown is the AMOC anomaly at (b) 26°N and (c) 50°N. Events spanning a full AMOC cycle are indicated by letters A–D. Colors represent four different phases of the AMOC in each event: phase 1 (red), phase 2 (blue), phase 3 (cyan), and phase 4 (magenta).
Citation: Journal of Climate 32, 18; 10.1175/JCLI-D-18-0709.1
The time series of the AMOC at 26°N (Fig. 3b) and 50°N (Fig. 3c) are divided into events (labeled A to D) where each event spans a full AMOC cycle. We subdivide each event into four phases corresponding to decreasing and increasing AMOC during periods of negative and positive AMOC anomalies respectively. Thus, each event has a full cycle of the AMOC during which the AMOC anomaly reduces to a minimum (phase 1; red), increases from the minimum to zero (phase 2; blue), increases to a maximum value (phase 3; cyan), and then decreases to zero (phase 4; magenta). The year numbers of these events (based on the AMOC excursions, not the matching AMV excursions) are listed in Tables 1 and 2. The duration of the events varies between 12 and 65 years and individual phases vary from 3 to 26 years.
Time periods of major AMOC events at 26°N and their phases in the HadGEM3-GC2 control simulation. The duration in years of each event is in parentheses. The events are shown in Fig. 3b.
Time periods of major AMOC events at 50°N and their phases in the HadGEM3-GC2 control simulation. The duration in years of each event is in parentheses. The events are shown in Fig. 3c.
In the next section, we will investigate the processes controlling the OHC and SST trends in the different phases of the AMOC cycle. We will concentrate on SST and OHC changes during the four events, focusing both on the full time series, and on a composite of all four events.
c. OHC trends during different phases of the AMOC
Figures 4a–d shows OHC trend composites based on the AMOC at 26°N (upper panels) in the North Atlantic for each phase in turn of a composite of all four events A–D (annual mean trends averaged over the duration of each phase of all four events; Table 1 lists the model years included in each phase). During phase 1 (AMOC anomaly < 0 and reducing) there is a negative heat content trend in the SPNA coupled with increasing OHC in the subtropical gyre (STG) and in the Nordic seas (Fig. 4a). There is a dipole pattern in the intergyre region (Cape Hatteras to the Bay of Biscay) with positive trends in the west and negative in the east. In phases 2–4 we see positive OHC trends spreading first into the eastern and northern SPNA (Fig. 4b) and later into the western SPNA (Figs. 4c,d). Negative trends appear in the western part of the intergyre region in phase 2, but there is a return to positive trends in phases 3 and 4. The STG (south of 40°N) shows somewhat complicated behavior, with mainly positive trends in phases 1 and 4, and opposite signed north–south dipoles in phases 2 and 3. The Nordic seas as a whole vary coherently, with OHC increasing in phases 1 and 4, and decreasing in phases 2 and 3. The OHC trend composites based on the AMOC at 50°N (Figs. 4e–h) show strong similarity with those based on the AMOC at 26°N. Phase 1 at 26°N (Fig. 4a) and at 50°N (Fig. 4e) look very similar, for example, as do phases 2–4. Of particular note is the fact that in the SPNA, in phase 4, when the AMOC is reducing, the OHC shows a warming tendency.
Composites of (a)–(d) net OHC tendency (W m−2) on AMOC phase at 26°N, phases 1–4. (e)–(h) As in (a)–(d), but at 50°N. (i)–(l) Net SST tendency (K month−1) on AMOC phase at 26°N, phases 1–4. (m)–(p) As in (i)–(l), but for 50°N. The timings and durations of the phases and events are shown in Figs. 3b and 3c. Thick black lines define the western and eastern SPNA used in this analysis.
Citation: Journal of Climate 32, 18; 10.1175/JCLI-D-18-0709.1
The SST trend composites based on the AMOC at 26°N show some similarities to the corresponding OHC composites in the SPNA, intergyre, and STG regions, but also substantial differences (cf. Figs. 4a–d with Figs. 4i–l). For example, in phase 3 the patterns are broadly similar with extensive warming over the whole SPNA and the eastern SPNA (Figs. 4c,k), whereas in phase 4 the western SPNA has strongly increasing OHC (Fig. 4d) but the SST is weakly increasing (Fig. 4l). In contrast to the OHC trends, the peak SST warming occurs in phases 2 and 3, not in phase 4. In the SPNA, SST trend composites based on the AMOC at 50°N show a phase lag compared to those based on the AMOC at 26°N. Phases 2, 3, and 4 of the 50°N-based composites (Figs. 4n–p) are very similar to phases 1, 2, and 3 respectively of the 26°N-based composites (Figs. 4i–k). The SST phases at 26°N bear some similarity to the observation based normalized SST trends presented in Fig. 2 of Caesar et al. (2018). The sequence established for the composite event is essentially seen in the individual events (not shown).
Figure 5 shows the two terms,
Composites of (a)–(d)
Citation: Journal of Climate 32, 18; 10.1175/JCLI-D-18-0709.1
In phases 1 and 2, the advection anomaly term,
d. SST trends during different phases of the AMOC
We now examine the contributions to the net SST tendency shown in Figs. 4i–p, focusing on the advection-diffusion-entrainment related term [RML/ρ0CPh]*. From Eq. (9) we plot [RML/ρ0CPh]* for each phase in Figs. 6a–d. The term shows interesting spatial structure particularly around the Labrador and Irminger Seas (areas of deep convection in the model; Ortega et al. 2017). The Gulf Stream and its extension in particular shows systematic changes in sign and magnitude with a warming signal in phases 1 and 4 and a cooling signal in phases 2 and 3 reminiscent of the advection term in the OHC equation (Figs. 5e–h) The surface flux related term [QNET/ρ0CPh]* (not shown) is essentially similar in pattern, but of negative amplitude. These two terms are much larger than the net tendency, which is the residual between two very large and opposing terms, hence this decomposition yields little insight into the relative role of each term.
Composites on each phase 1–4 of the AMOC at 26°N. (a)–(d)
Citation: Journal of Climate 32, 18; 10.1175/JCLI-D-18-0709.1
Turning to the anomaly formulation in Eq. (10) we now plot
Finally we turn to Eq. (12) and evaluate
e. Eastern and western subpolar North Atlantic
There is a tendency for both OHC and SST to show different responses in the western compared to the eastern SPNA (see Fig. 4 for region definitions). For example, for the composites based on the AMOC at 26°N (Fig. 4), in phase 1 there is a more negative OHC tendency in the eastern SPNA than in the western SPNA; in phase 2 the tendencies are of opposite sign; and in phase 3 there is a stronger positive tendency in the eastern SPNA than the west. Accordingly, we investigate the spatially averaged response in each region separately.
OHC and SST spatially averaged over the eastern and western SPNA and the AMOC at 26° and 50°N are plotted in Fig. 7. Both regions show a lagged relationship between the AMOC at both latitudes (black, magenta; Fig. 7c) and the OHC (red; Figs. 7a,b). At 26°N the AMOC leads western SPNA OHC by 15 years and at 50°N by 18 years (see Table 3). The corresponding lead times for the eastern SPNA are 10 and 12 years. This is consistent with our earlier finding that OHC tendencies tend to propagate anticlockwise around the SPNA (Fig. 4). The SST (blue, Fig. 7) is also related to the AMOC, but the lag is smaller compared to the OHC (5 and 7 years at 26° and 50°N respectively) and it does not vary between the eastern and western SPNA.
Full-depth OHC (red) and SST (blue) anomalies in (a) western and (b) eastern SPNA. (c) AMOC anomalies at 26°N (black) and AMOC at 50°N (magenta). All variables are 10-yr low-pass filtered.
Citation: Journal of Climate 32, 18; 10.1175/JCLI-D-18-0709.1
Correlation coefficients for lagged regressions between the AMOC and OHC, SST and associated terms for the eastern and western SPNA. The maximum correlation (r), and the lag at which the maximum occurs (years) is shown (−AMOC leads, +AMOC lags).
To explore the possibility that the OHC variability may depend on the depth horizon over which it is evaluated, we evaluate the OHC [Eq. (1)] from the surface to depth horizons of 100, 200, 500, and 1000 m and the full ocean depth [Fig. 8; for this figure (only) we use monthly data in order to accurately characterize the lags between different depth horizons]. In both eastern and western SPNA (Figs. 8a,b), the variability of the OHC is qualitatively similar no matter which depth horizon is employed: correlations of the OHC at 1000 m with the OHC at shallower depths yields r2 values between 0.63 (100 m) to 0.94 (500 m) in the west and 0.83 (100 m) to 0.93 east (500 m). However, the variability for deeper depth horizons lags with respect to shallower ones (Figs. 8c,d); this is particularly marked in the western SPNA where the correlation also drops more rapidly with depth. Nevertheless, a robust result is that SST leads heat content, irrespective of the depth horizon to which it is evaluated (Figs. 8c,d). This is quantified in Table 4, which shows the maximum correlation, and the lag at which the maximum occurs, of each heat content evaluation with the SST. In the western SPNA, the lag narrows from 45 months for full depth to only 3 months for 100-m depth, but a lag always remains. In the east, the SST and the OHC become almost simultaneous for depths shallower than 200 m and the correlation becomes very close to unity. In summary, for depth horizons greater than 200 m the maximum correlation between OHC and SST never reaches unity and a substantial lag (1.5 to 3.5 yr) occurs.
Variation in OHC anomaly (J m−2) evaluated from the surface to various depths (100, 200, 500, and 1000 m; full depth) and their relationship with SST anomaly in (a) western and (b) eastern SPNA. SST has been scaled and offset for comparison with the OHC. (c),(d) Correlation coefficients between OHC and SST for depths between 100 and 1000 m, and lags between −20 and 20 yr. Negative lag indicates SST leading OHC. All variables are 10-yr low-pass filtered.
Citation: Journal of Climate 32, 18; 10.1175/JCLI-D-18-0709.1
Correlation coefficients for lagged regressions between the OHC and SST for the eastern and western SPNA shown in Fig. 8. The maximum correlation (r), and the lag at which the maximum occurs (in months) is shown.
f. Balance between surface fluxes and advection
1) OHC
Having discussed the variation in OHC we now examine the processes controlling its rate of change via Eq. (7). Figures 9a and 9b show
Terms in the OHC Eq. (2):
Citation: Journal of Climate 32, 18; 10.1175/JCLI-D-18-0709.1
The term with the larger absolute magnitude will drive the sign of the OHC tendency. If the other term is of opposite sign then it will act as a brake whereas if it is of the same sign then the two terms act in concert. For example in year 2240 the absolute magnitude of the surface heat flux (
In Fig. 9a the surface flux term often leads advection by a few years, r = 0.5 at 6.5 years, implying that in the western SPNA surface fluxes control the evolution of the full-depth OHC. However, QNET and RFD are significantly anticorrelated and correlated respectively with the AMOC at 26°N with the AMOC leading or simultaneous (Table 3). This implies that it is the AMOC that is the main driver of the heat content. Further support for this conclusion will be given in section 4f, which considers the time evolution of a composite AMOC cycle.
In the eastern SPNA, the opposite pattern occurs (Fig. 9b). First, the decadal variability of advection (RFD in blue), 6.1 W m−2, is much larger in magnitude than that of surface fluxes, 3.9 W m−2, unlike the western SPNA where the variability is of roughly equal amplitude (both ~4.3 W m−2). In addition, advection tends to lead surface fluxes by a few years, r = 0.3 at 11 years (disregarding a peak at 2.5 years, which is statistically insignificant), suggesting that advection is the controlling process in this region. Once again, the AMOC is significantly related to both terms (Table 3).
2) SST
Moving on to the processes controlling the SST, we have already noted that in order to make progress we need to use Eq. (12) with a parameterized heat flux (Q−h) at the base of the mixed layer. This is further illustrated by Fig. 10a, which shows the relative contributions of surface fluxes
Terms in the SST Eqs. (9)–(12):
Citation: Journal of Climate 32, 18; 10.1175/JCLI-D-18-0709.1
Using Eq. (10), we again find a very high degree of compensation between the surface flux and advection terms (Figs. 10c,d), although now the surface flux–related term for the SST,
Finally we parameterize the diffusive heat flux Eqs. (11) and (12) at the base of the mixed layer. The simple parameterization results in a separation of the surface heat flux and advection-entrainment term (Figs. 10e,f). This decomposition allows us to draw similar conclusions for the SST as we drew for the OHC, namely that in the western SPNA both surface heat flux and advection-diffusion-entrainment play major roles in setting the net SST tendency. By contrast in the eastern SPNA, the advection-entrainment term is the clear driver of SST variations on decadal time scales.
3) Relationship between OHC and SST tendency terms
A strong relationship emerges between the rates of change of full depth OHC (∂OHC/∂t) and rates of change of SST (∂SST/∂t) (Fig. 11a). Maximum positive correlations are found at lags of 18 months (west) and 3 months (east). As well as these positive correlations, negative correlations are found when the ∂OHC/∂t leads ∂SST/∂t by 63 months (west) and 67 months (east).
Correlation coefficient between processes in the western (black) and eastern (red) SPNA at different lags. Thick lines indicate regressions of 95% significance. All variables are 10-yr low-pass filtered. (a)
Citation: Journal of Climate 32, 18; 10.1175/JCLI-D-18-0709.1
As mentioned in the previous subsection, the adjusted surface flux–related term for the SST,
By parameterizing the heat flux at the base of the mixed layer, we obtain strong lagged correlations of the advection-entrainment term,
g. Drivers of net tendencies in OHC and SST
We obtain further insights into the controls on SST and OHC variation by forming a composite AMOC anomaly cycle based on all four individual events. To do this we take each phase in turn and assign identical timings for the start and end points of the phase. Thus for phase 1 the start year of each event is set to time zero and the end year is set to 2π. For example, phase 3 of event C spans years 2275–88, including 14 years, whereas event D spans 2385–95 for phase 1, a total of 11 years. Thus both 2275 and 2385 are assigned a time of π and 2288 and 2395 are assigned a time of 3π/2 and all intermediate values are interpolated onto a regular grid with spacing π/50. In this way all four events and all four phases can be stretched onto a common timeframe and averaged to form a composite AMOC anomaly at 26°N and associated anomalies of SST (ξ*) and OHC (
SST anomaly, ξ*, and full-depth OHC anomaly,
Citation: Journal of Climate 32, 18; 10.1175/JCLI-D-18-0709.1
Going further, we can form composites of all the quantities in Eqs. (9)–(12). Figure 12c shows composites of the rate of change of heat content
The SST tendency behaves in a broadly similar way [Figs. 12e and 12f, where the net tendency, ∂ξ*/∂t, is in light blue, the surface flux–related term,
The OHC advection term follows the AMOC according to expectations but surface fluxes release the extra heat input to the atmosphere when the AMOC is rising but the AMOC anomaly is still negative (i.e., in phase 2 of the composite event). It is only when the AMOC anomaly becomes positive that the heat content begins to rise. When the AMOC is falling in phase 4, advection falls too, but OHC increases because the opposing contribution of surface fluxes falls faster. A period of decreasing OHC follows when surface fluxes begin to rise at about the time that the AMOC is halfway between its peak and zero (particularly marked in the western SPNA).
As already noted, the net SST tendency in Fig. 12e leads the AMOC anomaly at 26°N in the western SPNA. Since the advection-entrainment term also lags the SST tendency, but the surface flux term leads all three, this suggests that surface fluxes in the western SPNA are at least partly responsible for the large AMOC variations seen in the model. But the surface fluxes are partially set by the AMOC through its (eventual) control of the SST (via subtropics and the eastern SPNA) emphasizing the coupled nature of the AMOC variability.
h. Drivers of OHC and SST variations
In this section we summarize the driving terms which characterize the AMOC cycle (Fig. 13). Recalling from section 4e that the term with the larger absolute magnitude [either surface flux related or advection (-entrainment) related] drives the sign of the OHC tendency. If the other term is of opposite sign then it will act as a brake; if it is of the same sign then the two terms act in concert. In Fig. 13a the net OHC tendency for the composite AMOC event is shown in black. We then divide the cycle into regimes depending on which term is dominant (i.e., either |RFD| > |QNET| or more rarely |QNET| > |RFD|). For each regime the corresponding terms are averaged over the duration of the regime and a constant value plotted in order to quantitatively depict the interplay between the forcing terms during each regime. These regimes do not in general line up with the AMOC phases (p1–p4); for example, midway between phase 1 at φ ~ π/4 to partway through phase 3 (φ ~ 1.1π) advection (blue) is the driving term with an average value of approximately −3.0 W m−2 and it is opposed by surface fluxes (red) with an average value of approximately +1.0 W m−2. In the subsequent regime, for a brief period surface fluxes dominate as the advection term transitions from negative to positive values as does the net tendency itself. From here to the peak net tendency (φ ~ 1.2π to φ ~ 1.4π) the two terms act in concert after which surface fluxes transition to negative values. Advection remains the dominant term in this regime, but receives substantial opposition from surface fluxes.
(a) Net OHC tendency (black) in the western SPNA for the composite AMOC event. Average surface flux (red) and advection (blue) for heat budget regimes. (b) As in (a), but for the eastern SPNA. (c) Net SST tendency (black) in the western SPNA for the composite AMOC event. Average surface heat flux (red) and advection (blue) terms for SST equation regimes. (d) As in (c), but for the eastern SPNA.
Citation: Journal of Climate 32, 18; 10.1175/JCLI-D-18-0709.1
The situation in the eastern SPNA (Fig. 13b) is similar, but the cycle is shifted to earlier times with respect to the west. As with the west, there is a shift from negative to positive forcing by advection halfway along the period when the net tendency increases (φ ~ 0.9π) and a shift from positive to negative surface flux forcing close to the time of peak net tendency (φ ~ 1.3π). In addition, there is an extended regime where surface fluxes are the dominant term (φ ~ 1.7π to φ ~ 2.0π) which is not seen in the west. Despite this, advection is clearly the dominant term over most of the cycle for both eastern (66% of the time) and western SPNA (88% of the time). The equivalent plots for the SST are shown in Figs. 13c and 13d. These are quite similar to the OHC plots, especially for the eastern SPNA, but it is noteworthy that surface fluxes play a more important role especially in the west, where there is a long period from φ ~ 0.6π to φ ~ 1.4π during which surface fluxes dominate, albeit sometimes narrowly. In both east and west, surface fluxes dominate from φ ~ 1.7π to φ ~ 2.0π. Overall advection dominates only 53% of the time in the western SPNA and 61% of the time in the eastern SPNA. Unlike the composite terms in Figs. 12e and 12f the results shown in Figs. 13c and 13d are not very sensitive to whether or not we use the unadjusted [Eq. (10)] or adjusted tendency terms [Eq. (12)].
5. Conclusions
We have developed a novel combined approach to the mixed layer and full-depth ocean heat budgets and used it to investigate sea surface temperature (SST) and ocean heat content (OHC) variability on decadal to multidecadal time scales in the subpolar North Atlantic (SPNA), the main center of action of the Atlantic multidecadal variability (AMV). Our analysis has employed a state-of-the-art coupled climate model, HadGEM3-GC2, in which the simulated AMV index and spatial pattern is very similar to observed estimates. The new elements of the approach are development of an equation for evolution of anomalous SST and a parameterization of the diffusive heat flux at the base of the mixed layer.
The results of our analysis show that both OHC and SST tendencies are the result of a competition between two terms representing the effects of surface fluxes and advection for OHC (advection-entrainment for SST). These terms have different forms in the OHC and SST equations, because additional terms related to entrainment appear in the SST equation but not in the OHC equation. Hence, the relationship between OHC and SST becomes an investigation into how and why the surface fluxes and advection-related terms differ between the OHC and SST equations.
The main conclusions are listed below:
Anomalies in the OHC tendency propagate around the SPNA on decadal time scales with a clear relationship to the phase of the AMOC.
In the SPNA, AMOC anomalies lead SST anomalies, which in turn lead OHC anomalies. This result does not depend on the depth used for calculation of OHC and is common to both eastern and western SPNA.
OHC variations in the SPNA on decadal time scales are largely dominated by AMOC variability because it controls variability of advection which is shown to be the dominant term in the OHC budget. Surface heat fluxes modulate the OHC variability, particularly as OHC peaks and declines. Surface heat flux plays a larger role in SST variability.
The advection term covaries with the AMOC in the eastern SPNA but lags the AMOC in the western SPNA, leading to the anticlockwise propagation of OHC anomalies around the SPNA.
The lag between OHC and SST is traced to differences between the advection term for OHC and the advection-entrainment term for SST. The latter leads the former particularly in the western SPNA.
In the western SPNA, surface fluxes and SST appear to precede and cause AMOC changes, whereas in the east AMOC changes cause the changes in SST and surface fluxes.
The main implication of our study is that deep OHC changes are not associated with immediate changes in SST in HadGEM3-GC2; indeed, changes in SST precede OHC deep changes. There is also a very clear difference in the dominant process between the eastern and western SPNA. In the former region, advection is dominant, whereas in the latter surface fluxes dominate. While our study confirms the important role of the AMOC in the decadal variability of the North Atlantic SST, this role cannot be simplified as an increasing AMOC leading to increasing heat content leading to increasing SST, which is a common assumption underlying numerous studies of contemporary and paleo variability of the North Atlantic (e.g., Chen and Tung 2018). For example, in this study using HadGEM3-GC2 the SPNA OHC rarely immediately increases as AMOC increases (phase 2 in Fig. 12), because the advection term must first switch sign from negative to positive (Figs. 13a,b). On the other hand the SST can and does begin rising quite soon after the AMOC starts increasing, because the surface flux term is already driving an increasing SST at this time and reduced opposition to this term from advection reinforces this trend.
In the western SPNA in particular it seems that surface fluxes drive both the subsequent evolution of the advection-entrainment term, and ultimately the AMOC. The detailed mechanism by which surface fluxes can influence the advection still need to be determined, but may be related to the projection of short (seasonal to interannual) time scale correlations between MLD and temperature onto the decadal time scale [see appendix A, Eq. (A9)].
The diagnostic framework developed here is eminently suitable for use with observations and multimodel ensembles. For observations, however, great care must be taken in analysis of errors as rates of change of both OHC and SST consist of a fine balance (i.e., a small residual) between large competing terms of opposite sign. In addition, decadal-scale observational analysis would require high-quality mixed layer depth observations that are still not available globally. Finally, we note that the new framework can be usefully applied to the CMIP6 model ensemble in order to establish the robustness of the results, and to reveal individual model deficiencies that could help usefully constrain climate change projections.
Acknowledgments
This research was funded by the NERC ACSIS Programme (Grant NE/N018044/1), the NERC funded RAPID AMOC programme at 26°N, the DYNAMOC project (NE/M005097/1), the SMURPHS project (NE/N005686/1 and NE/N005767/1), and funding from the European Union Horizon 2020 research and innovation programme BLUE-ACTION (Grant 727852). The coupled climate model data are available from the Met Office Managed Archive Storage System (MASS). Analysis codes are available from the corresponding author on request.
APPENDIX A
Derivation of SST Anomaly Equation
APPENDIX B
Optimal Value for Diffusive Heat Flux Fraction λ
As explained in section 4d we obtain an optimal value for λ by ensuring that the resulting mixed layer advection entrainment term
(a) Maximum correlation coefficient r between
Citation: Journal of Climate 32, 18; 10.1175/JCLI-D-18-0709.1
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