The signature of low‐frequency oceanic forcing in the Atlantic Multidecadal Oscillation

The Atlantic Multidecadal Oscillation (AMO) significantly influences the climate of the surrounding continents and has previously been attributed to variations in the Atlantic Meridional Overturning Circulation. Recently, however, similar multidecadal variability was reported in climate models without ocean circulation variability. We analyze the relationship between turbulent heat fluxes and sea surface temperatures (SSTs) over the midlatitude North Atlantic in observations and coupled climate model simulations, both with and without ocean circulation variability. SST anomalies associated with the AMO are positively correlated with heat fluxes on decadal time scales in both observations and models with varying ocean circulation, whereas in models without ocean circulation variability the anomalies are negatively correlated when heat flux anomalies lead. These relationships are captured in a simple stochastic model and rely crucially on low‐frequency forcing of SST. The fully coupled models that better capture this signature more effectively reproduce the observed impact of the AMO on European summertime temperatures.


Introduction
The AMO has a demonstrable impact on the weather and climate in the continental regions surrounding the North Atlantic basin [Enfield et al., 2001;Folland et al., 1986;Sutton and Hodson, 2005;Knight et al., 2006] and is a crucial component in making skillful decadal climate forecasts [Keenlyside et al., 2008]. The AMO has been shown to be related to heat transport by the Atlantic Meridional Overturning Circulation (AMOC) in model experiments [Delworth et al., 1993;Knight et al., 2005;Latif et al., 2004;Delworth and Mann, 2000;Gastineau and Frankignoul, 2012;Ba et al., 2014], such that the North Atlantic warms when the AMOC speeds up and cools when the AMOC slows down, well reproducing observed multicentury proxy-based sea surface temperature (SST) variability [Delworth and Mann, 2000]. However, the observational record of AMOC is too short to directly link its variability to the AMO and alternative mechanisms have been identified as potential drivers of the AMO, questioning the role of AMOC. Recently, a mechanism invoking variability in the wind-driven ocean circulation in the region between the subtropical and subpolar gyres was shown to display good agreement with observations of SST and ocean heat content variability [McCarthy et al., 2015]. Alternatively, some studies have suggested that the variability of aerosol forcing on surface shortwave radiation could have generated the historical AMO variability [Mann and Emanuel, 2006;Booth et al., 2012]; however, this has been disputed [Zhang et al., 2013].
Recently, another alternative mechanism for driving the observed AMO variability has been proposed. Clement et al. [2015] compared the AMO characteristics in Coupled Model Intercomparison Project Phase 3 (CMIP3) preindustrial control simulations run with a 50 m slab mixed layer ocean model (hereafter "slab ocean" models), which do not permit variability in ocean heat transport, to the AMO characteristics in models coupled to an ocean general circulation model (hereafter "fully coupled" models) and observational SST data sets. The observed "horseshoe" pattern of SST variability associated with the AMO index-defined as the annually averaged, detrended SST anomaly over the North Atlantic basin-is remarkably similar in both slab ocean and fully coupled models (Figure 1). The weaker, tropical part of the AMO SST pattern has been linked to the wind-evaporation-SST feedback [Xie and Carton, 2004], which can be captured in slab ocean models. More recently, positive low cloud and dust feedbacks have been implicated for the tropical arm of the AMO [Yuan et al., 2016]. These mechanisms, however, are not effective in the extratropics, where the maximum amplitude of the SST pattern occurs. Since the AMO in the fully coupled and slab ocean models is seemingly indistinguishable, Clement et al. conclude that the AMO SST in midlatitudes must therefore be driven by large-scale atmospheric variability, which is essentially a white noise stochastic process on interannual time Annual SST anomalies (July through June) regressed onto AMO mid , calculated over the midlatitude North Atlantic (region outlined in blue), and the turbulent heat flux (THF) anomaly averaged over the 10 years prior to the year of the midlatitude AMO indices, in (a) observations (1880-2007); (b) ensemble mean of the CMIP5 preindustrial control simulations; (c) ensemble mean of the CMIP3 slab ocean control simulations. SST anomalies for AMO indices calculated over the whole North Atlantic (80 ∘ -0 ∘ W, 0 ∘ -60 ∘ N) are shown in the bottom left of each panel. THF anomalies are contoured at −0.5, 0, 0.5, 1 and 2 W m −2 , with negative contours dashed and the zero contour emboldened. Regions of negative THF are stippled. The THF averaged over the region outlined in blue is significantly positive (at the 90% level) in Figure 1a, is positive in more than 90% of the models in Figure 1b, and is negative in more than 90% of the models in Figure 1c.

10.1002/2016GL067925
scales [Woollings et al., 2014]. Here we investigate the source of the AMO, particularly in midlatitudes, in observations, fully coupled CMIP5, and slab ocean CMIP3 control simulations.

Gridded Observational Data Set
We use the sea surface temperatures (SSTs) from the Hadley Centre sea ice and sea surface temperature data set [Rayner et al., 2003] data set (from 1880 to 2014), the turbulent heat flux (THF) data set (provided over the region 20 ∘ -70 ∘ N in the North Atlantic) produced by Gulev et al. [2013] from the International Comprehensive Ocean-Atmosphere Data Set [Woodruff et al., 2011] (from 1880 to 2007), and the surface air temperatures over land from the Climate Research Unit Time Series [Harris et al., 2014[Harris et al., ] v. 3.23 (from 1901[Harris et al., to 2014. Annual anomalies are calculated by averaging from July to June.

Coupled Model Data
We analyze data from the final 127 years of the first member of each of the preindustrial control simulations (piControl) in the CMIP5 archive [Taylor et al., 2012], referred to as the fully coupled simulations (only analyzing 41 models that provided THF data). We also analyze data from the CMIP3 models [Meehl et al., 2007] coupled to a slab mixed layer ocean model with a prescribed ocean heat transport, referred to as the slab ocean models. We restrict our analysis of the slab ocean models to only the three models that provided at least 100 years of output, to give a relevant comparison to the observations and CMIP5 fully coupled models. Monthly mean values interpolated the model output on a 2.5×2.5 ∘ grid and removed the annual cycle from each model output before calculating the July to June averaged annual anomalies. The results presented here are essentially unchanged if January to December averaged annual anomalies are used instead.

Monte Carlo Significance Tests
For the regression and correlation calculations, 1000 surrogate indices were produced by taking the fourier transform of the original index and randomizing the phase, thus replicating the spectral properties of the original time series [Kaplan and Glass, 2012]. The equivalent regression and correlation statistics were then produced for each of the surrogate indices to give a measure of the significance of the observed relationship. For the difference plot in Figure 2, the 41 models were randomly stratified into 20 warm/cool models 1000 times to give a measure of the chance that the observed correlation difference could occur at random.

Relationship Between Turbulent Heat Flux and SST
In the absence of ocean circulation variability (i.e., Ekman currents, heat flux convergence, and entrainment), midlatitude SST anomalies are directly forced by turbulent (i.e., latent plus sensible) heat fluxes [Deser et al., 2010] (THFs). To focus on the midlatitude maximum in the AMO SST pattern, we define a midlatitude AMO index, AMO mid , over the region which exhibits the largest multidecadal variability in observations [Gulev et al., 2013]. AMO mid is defined as the area average of annual mean detrended SST anomalies over the region (60 ∘ -20 ∘ W, 40 ∘ --60 ∘ N). The results presented here are not sensitive to adjustments in the region used to define AMO mid within the midlatitudes but the results degrade when SST anomalies south of about 35 ∘ N are included, which is consistent with other mechanisms being important in generating the tropical part of the AMO pattern. AMO mid well captures the full AMO SST pattern in the northern part of the basin and even much of the tropical SST pattern in the observations (Figure 1). The AMO mid index and the AMO averaged over the whole North Atlantic are very closely correlated, with a correlation coefficient of 0.97.
To see the role of THFs in driving the AMO on decadal time scales, the THF anomalies (defined as positive upwards) were averaged over the preceding 10 years and regressed onto AMO mid (Figure 1). In observations, it has been shown that on decadal time scales the THF and SST anomalies are positively correlated in the midlatitude North Atlantic [Gulev et al., 2013] and here we see that the midlatitude THF is positive over the decade preceding a warm SST anomaly. In the fully coupled models the THF over the preceding decade is also positive, albeit weaker than in the observations. In the slab ocean models, however, a decade of negative midlatitude THF leads to a year with a warm SST anomaly, unlike in the observations or fully coupled models. The negative midlatitude THFs in the slab ocean models heat the ocean mixed layer and result in a warm AMO mid . In contrast, positive midlatitude THFs in the observations and fully coupled models cool the ocean mixed layer. Therefore, an additional mechanism that is most likely related to ocean circulation variability, which is not present in the slab ocean models, must be providing additional heating to the mixed layer in the midlatitude North Atlantic.  Figure 2b but for the 20 models with the coolest SAT anomaly regression. (d and e) The correlation between the long-term components of the THF and SST for the 20 warm and cool models, respectively, and (f ) the difference in correlation (i.e., warm models minus cold models). The stippling in Figure 2a indicates where the SAT regression is significant at the 90% level. The grey crosses in Figure 2f indicate where the difference between the correlations in the warm and cool are significant at the 90% level (calculated using a Monte Carlo resampling).
To further characterize the relationship between THFs and midlatitude SST anomalies, we now analyze lead-lag correlations at different time scales. We decompose AMO mid into AMO mid = AMO mid + AMO ′ mid , where the long-term component (AMO mid ) is calculated using a moving average (of varying length) and the short-term component (AMO ′ mid ) is the residual of AMO mid ; an equivalent separation is also performed on the THF (i.e., Q = Q + Q ′ ). It has previously been shown in observations that the long-term components of THF and midlatitude SST anomalies are positively correlated at zero lag [Gulev et al., 2013]. Interestingly, the observed long-term THF and SST anomalies are also positively correlated when either the THF or SST leads by up to a decade (Figures 3a and 3c). The short-term components, however, are negatively correlated at zero lag (Figures 3b and 3d), reflecting the relatively passive response of the midlatitude ocean to atmospheric forcing on interannual time scales [Gulev et al., 2013;Deser et al., 2010].
The ensemble mean of the correlation between the long-term THF and SST components in the fully coupled models is also positively correlated at zero lag (Figures 3a and 3e). The correlations are generally smaller than in the observations at all lags and time scales, but a significant majority of the fully coupled models capture the overall structure, showing strongly positive correlations when either the THF or SST leads by up to a decade. In the slab ocean models, however, the long-term components differ substantially from the observations and fully coupled models, depending critically on lag. When the THF leads, the correlation is negative at nearly all timescales, whereas when the SST leads, the correlation is positive at nearly all time scales. Therefore, when the THF leads in the slab ocean models, an extended period of negative THF warms the mixed layer and results in a warm SST anomaly. This warm SST anomaly is then damped by the atmosphere over time, resulting in positive THFs over the subsequent period. Similar long-term warm SST anomalies in the observations and fully coupled models tend to lag periods of positive THF, which act to cool the mixed layer, therefore something other than THF must be forcing the long-term SST anomalies. Interestingly, the fully coupled or slab ocean models are similarly unable to reproduce the negative correlation between the short-term THF and SST components at zero lag seen in the observations (Figures 3a, 3f, and 3h). The correlations were calculated using annual averages, indicating that the models may poorly represent the THF and SST variability on intra-annual time scales (similar correlations are seen if January to December averages are used). It is noteworthy that the largest spread in short-term correlations among the fully coupled models occurs at zero lag, suggesting some inconsistency between the models themselves (supporting information Figure S1). The stronger correlation between the short-term components in the slab ocean models, compared with the fully coupled models, may be related to the underestimation of mixed layer depth (50 m) in these models, such that there is greater SST response for the same turbulent heat flux anomaly.

Stochastic Model of Midlatitude AMO Variability
To further understand the relationships between THF and SST seen in the models and observations, we consider a simple stochastic climate model. Such models have previously proven very effective in capturing key features of midlatitude SST variability [Frankignoul and Hasselmann, 1977;Deser et al., 2003;Barsugli and Battisti, 1998;Bretherton and Battisti, 2000]. In our stochastic model the SST anomaly (T) follows where the total THF anomaly (Q) is composed of a damping term (with a constant timescale −1 = 4 years, to represent the persistence and/or reemergence of annual midlatitude SST anomalies) and a stochastic atmospheric forcing term (Q atmos = A hf dW, where A hf = 0.1 ∘ C yr −1 is a constant amplitude and dW is a Gaussian white noise process with unit variance). A periodic forcing term (F ocean = A lf sin , where A lf = 0.04 ∘ C yr −1 is a constant amplitude and lf = 60 years is the period) is added to mimic the presence of low-frequency variability in ocean heat transport. These values were chosen to approximately capture the variability of the observed AMO index in this region (see example time series in supporting information Figure 2). The stochastic model is run for 1000 ensemble members, each for 127 years to match the observations. To analyze the signature of ocean circulation variability, the model is also run without the low-frequency forcing term (i.e., F ocean = 0). Without the low-frequency forcing term, the variance of the SST in the stochastic model is reduced but this has no influence on the correlation statistics.
In the presence of low-frequency ocean forcing, the ensemble mean correlation between the long-term THF and SST components in the stochastic model is positive when either THF or SST leads by up to a decade (Figures 4a and 4c). This corresponds closely to the relationship between the long-term components of THF  Figures 3c and 3d the grey crosses indicate where the correlation is significant at the 90% level. In Figures 3e-3h, the dots indicate where the correlation has the same sign in more than 90% of the models. Correlations that are significant at the 90% level or have the same sign in more than 90% of the models are indicated by circles in Figures 3a and 3b. and SST in the observations and fully coupled models (Figures 3a, 3c, and 3e). Without low-frequency ocean forcing, the correlation between the long-term THF and SST components in the stochastic model is negative for all time scales when the THF leads but is positive when the SST leads (Figures 4b and 4d). This closely corresponds to the relationship between the long-term THF and SST components in the slab ocean models (Figures 3a and 3g). The correlation between the short-term components of THF and SST in the stochastic model is negative at zero lag and essentially identical both with and without low-frequency ocean forcing (Figures 4b, 4d, and 4f ), in agreement with the observed interannual correlation (Figures 3b and 3d). These results are insensitive to changes in the damping time scale −1 , providing it is sufficiently shorter than the timescale of the low-frequency forcing term. The simple stochastic model therefore highlights the importance of a low-frequency forcing term in reproducing the relationship between THF and SST seen in the observations and the fully coupled models, whereas the relationship between THF and SST seen in the slab ocean models is well captured by a model only forced with stochastic atmospheric forcing.

Importance of Low-Frequency Forcing in Fully Coupled Models
The AMO has an observed influence on the decadal variability of summertime surface air temperatures (SAT) over Europe as well as over the North Atlantic ocean [Sutton and Dong, 2012] (Figure 2a). To assess the importance of low-frequency ocean forcing on the decadal variability of surface temperatures the 11 year averaged AMO mid was regressed onto SAT in each of the 41 fully coupled models. We averaged the resulting SAT regression over a midlatitude North Atlantic/Europe region (black box in Figures 2a-2c) and stratified the models into groups of the 20 warmest and coolest SAT. The warmest models have a SAT pattern which is fairly similar to that seen in observations and is warmer than the coolest models over both the North Atlantic and Europe (Figures 2b and 2c). The warmest models exhibit large correlations between the long-term components of THF and SST when THF leads. Conversely, the coolest models exhibit a significantly weaker positive correlation when the THF leads (Figures 2f and 2g), indicating that these models tend to have a weaker low-frequency ocean forcing. In agreement with this, the slab ocean models also fail to capture the warming over Europe during positive AMO mid (supporting information Figure S3). Therefore, the models that best capture the observed response to AMO mid clearly exhibit a stronger signature of low-frequency ocean forcing (i.e., Figure 4). This implies that it is heat released by the ocean that leads to warming over Europe during the warm phase of the AMO.

Conclusions
While slab ocean models are able to produce SST patterns and statistics similar to those seen fully coupled models and observations, here we have shown that only fully coupled models are able to correctly reproduce the observed relationship between THF and SST in midlatitudes on decadal time scales. The slab ocean models respond passively to stochastic atmospheric forcing, whereas the fully coupled models and observations both exhibit positive correlations between THF and SST when either leads by up to a decade, which is shown to be a signature of low-frequency ocean forcing in a simple stochastic model. While we cannot make the link directly, by far the most plausible explanation is ocean circulation variability, which is not present in the slab ocean models. The source of the ocean circulation variability in the North Atlantic may be due to wind-driven circulation anomalies [McCarthy et al., 2015] or AMOC variability [Delworth et al., 1993;Knight et al., 2005;Latif et al., 2004;Delworth and Mann, 2000;Ba et al., 2014], but it is clear from our analysis that the observed AMO is not directly forced by stochastic atmospheric forcing in midlatitudes. Capturing the signature of low-frequency ocean forcing in fully coupled models is found to be crucially important in correctly representing the influence of AMO mid on summertime European temperatures, indicating that models that better represent low-frequency forcing of SST are more reliable for making decadal predictions.