1. Introduction
The climate of the next few decades, particularly on regional scales, will depend on natural climate variations in addition to anthropogenic forcing (e.g., Hawkins and Sutton 2009; Corti et al. 2015; DelSole 2017). Therefore, unlike centennial climate predictions, in which the climate state is largely a response to anthropogenic forcing, decadal climate predictions require an accurate specification of the initial climate state and an adequate representation of natural variability in addition to knowledge of external forcings. Given the inherently chaotic nature of the atmosphere, prospects for decadal climate prediction lie in the interaction of the atmosphere with slower parts of the climate system: the ocean, the cryosphere, and the geosphere. The impact of ocean initialization on decadal climate predictions, termed “initial-value predictability,” has been intensely studied over recent years; in particular phases 5 and 6 of the Coupled Model Intercomparison Project (CMIP5 and CMIP6) include decadal prediction experiments, which were performed using numerous participating models (Doblas-Reyes et al. 2013; Meehl et al. 2014; Boer et al. 2016; Eyring et al. 2016).
The two main approaches for studying initial-value predictability are 1) initialized predictions and 2) statistical measures of predictability. In initialized predictions, such as the CMIP5/CMIP6 decadal prediction experiments, a coupled model initialized with ocean observations is used to produce an ensemble of forecasts. Improvements in predictability are inferred by comparing the skill of the ocean initialized forecasts with the skill from uninitialized forecasts. In the initialized forecasts, predictive skill can arise from both ocean initial conditions and external forcing. In the absence of an initialized ocean, the skill comes entirely from external forcing. Note that the skill of a forecast relative to some reference (e.g., persistence or uninitialized simulations) is a quantity evaluated at a specific lead time. The predictability time scale is a metric of the time period over which a forecast has skill.
Initialized predictions suggest that the Atlantic is a region of enhanced predictability for sea surface temperature (SST; Smith et al. 2007; Keenlyside et al. 2008; Pohlmann et al. 2009; van Oldenborgh et al. 2012; Karspeck et al. 2015; Årthun et al. 2017) and upper-ocean heat content (UOHC; Yeager et al. 2012; Hermanson et al. 2014). Using decadal prediction experiments with the Community Climate System Model version 4 (CCSM4), Karspeck et al. (2015) show that the North Atlantic is the only region where ocean initialization leads to a statistically significant increase in skill of SST forecasts (at lead times of both 2–5 and 6–9 years) compared to an uninitialized model; a similar result was found by Doblas-Reyes et al. (2013) using the multimodel mean of CMIP5 models. A number of studies have suggested that predictability of North Atlantic SSTs and UOHC is related to variations in the Atlantic meridional overturning circulation (AMOC; Keenlyside et al. 2008; Pohlmann et al. 2009; Matei et al. 2012; Yeager et al. 2012; Hermanson et al. 2014). However, as detailed in Karspeck et al. (2015), successful decadal prediction in the North Atlantic may not rely on prediction of the AMOC, but rather on adequate initialization of the temperature and salinity fields (and hence geostrophic currents, including the AMOC).
Initialized predictions have also been used to show that the recent changes in UOHC in the subpolar gyre are predictable (Yeager et al. 2012; Hermanson et al. 2014). Some studies have suggested that these decadal changes in subpolar UOHC are related to variations in the AMOC (Robson et al. 2016) while others have focused on the importance of changes in the gyre circulation related to the overlying winds (e.g., Bersch 2002; Häkkinen and Rhines 2004; Sarafanov et al. 2008; Häkkinen et al. 2011; Piecuch et al. 2017), including shifts in the Gulf Stream path (Nigam et al. 2018; Ruiz-Barradas et al. 2018).
Statistical measures of initial value predictability can be estimated from long control runs of climate models with time-invariant external conditions (Branstator et al. 2012; DelSole et al. 2013; DelSole 2017).1 Since these methods do not require model experiments, these techniques facilitate the comparison of predictability properties among multiple models. Branstator et al. (2012) estimate initial value predictability for UOHC (defined as average temperature over the upper 300 m) in six atmosphere–ocean general circulation models; they find that there are large regional variations in predictability time scales in the North Atlantic, and the locations of highest predictability are different for each model. Predictability time scales in the subpolar North Atlantic range from less than 3 years to more than 15 years, while time scales in the subtropical North Atlantic range from less than 2 years to 10 years.
DelSole et al. (2013) use a similar multivariate regression model trained on climate model simulations, but they apply the model to observations (with external forcing removed) as well. They find that the North Atlantic basin is the region where the regression model has the highest skill for predicting SST, with significant skill for up to 6 years for both observations and the ensemble mean of preindustrial and twentieth-century simulations. However, the skill varies considerably with ensemble member: one ensemble member has no skill at any lead time and another has skill for up to 10 years. The spread in skill is primarily due to model differences, consistent with the results of Branstator et al. (2012).
While most predictability studies are based on models, a few studies have made statistical predictions based purely on observations (Alexander et al. 2008; Zanna 2012; Ho et al. 2013; Newman 2013; Huddart et al. 2017). One method for estimating observed predictability time scales for SST is to use a linear inverse model (LIM) derived from SST observations. Predictability for decadal SST variations from LIMs is generally 3–4 years over most of the North Atlantic domain, with predictability generally being larger in subpolar regions (Zanna et al. 2012; Newman 2013; Huddart et al. 2017). Furthermore, the skill of LIMs is in many cases found to be comparable to that of initialized models, suggesting that predictions from a LIM are a useful benchmark for interannual to decadal SST predictions (Newman 2013; Huddart et al. 2017). Similar results regarding predictability in the Atlantic basin have been found using other statistical methods, such as autoregressive models and constructed analog models (Ho et al. 2013). Statistical models can also be used to help understand dynamics behind predictability. For example, statistical models demonstrate that in the Atlantic basin coupling between the tropics and extratropics plays only a small role in setting predictability time scales (Huddart et al. 2017), in contrast to the Pacific basin where coupling between the tropics and extratropics plays a much larger role (Newman 2007; Alexander et al. 2008; Newman et al. 2016; Dias et al. 2019).
In this paper, we estimate predictability time scales of Atlantic SST and UOHC purely from ocean observations. A central question in this paper is whether spatial variations in predictability time scales can be explained by spatial variations in the ocean mixed layer depth (MLD). According to the null hypothesis of SST variability, the ocean mixed layer integrates stochastic atmospheric forcing, resulting in a red SST spectrum with a dominant time scale directly proportional to the MLD (Frankignoul and Hasselmann 1977). In this framework, the fact that the North Atlantic has longer predictability time scales than other basins may simply be explained by the deep MLDs in the North Atlantic. We consider a linear dependence of predictability time scales with MLD to be a simple null hypothesis to explain spatial variations in predictability time scales; we will evaluate this null hypothesis in our study.
In section 2 we introduce the diagnostics and datasets that we will use for SST and UOHC and define a measure of the decorrelation time scale, which we use to quantify predictability of SST and UOHC. We compute decorrelation time scales for UOHC and wintertime SST in section 3 and compare them quantitatively in section 4. In section 5, we determine to what extent spatial variations in decorrelation time scales can be explained by spatial variations in the wintertime climatological MLD. In section 6 we determine to what extent decaying versus oscillatory variations play a role in setting decorrelation time scales for UOHC and wintertime SST. Finally, in section 7 we conclude and discuss how our results relate to prior studies.
2. Methods
In this section we describe the diagnostics that we will use for SST and UOHC. Then, we introduce a measure of the decorrelation time scale, which we use to quantify predictability of SST and UOHC.
a. Diagnostics for SST and upper-ocean heat content
Although SST is the ocean variable that most directly interacts with the atmosphere, predictability time scales for SST may underestimate ocean memory. SST memory is lost in the summertime due to the formation of the seasonal thermocline. In winter when the mixed layers deepen, anomalies isolated beneath the seasonal thermocline can become entrained in the mixed layer. This process, often referred to as the “reemergence mechanism” (Alexander and Deser 1995), can lead to enhanced predictability for wintertime SSTs (Namias and Born 1970; de Coëtlogon and Frankignoul 2003; Deser et al. 2003).
Our analysis of predictability of SST and H will utilize six different gridded observational products. As our analysis requires long time series for SST and H, and data products have substantial uncertainties, which are generally larger for earlier periods, we choose several data products to help understand the uncertainty. [See Kennedy (2014) for a review of uncertainty in SST data products and Boyer et al. (2016) for a review of uncertainty in ocean temperature products.] We use monthly SST from Extended Reconstructed SST version 5 (ERSST v5; Smith et al. 2008), Hadley Center SST (HadISST; Rayner et al. 2003), and COBE SST2 (Hirahara et al. 2014). We calculate H from monthly fields of gridded temperature from Ishii (Ishii et al. 2006), EN4.2.1 (Good et al. 2013), and the ocean temperature data product from Cheng (Cheng et al. 2017). All analyses will be restricted from 1945 to present, and the specific periods used for each product are listed in Tables 1 and 2. Our results are unchanged if we instead restrict all products to the period of 1945–2012, which is common to all data products.
Sensitivity of the decorrelation time scale T2 to method and data product. Each of the three data products for H is listed along the top row and left column, leading to a matrix comparing the data products. Shown is a comparison of T2 for 
The wintertime climatological MLD D is an important parameter in our study, but the MLD is a diagnostic that cannot directly be measured. We use three different estimates of D, two based on the gridded data products (Ishii and EN42) and one from the Argo MLD climatology of Holte et al. (2017), henceforth Argo MLD. In all cases the MLD is based on a threshold method in which the MLD is given by the depth at which the density exceeds a near-surface reference density by an amount 
The wintertime (January–March) climatological MLD D from (a) Ishii, (b) EN4.2.1, and (c) the Argo MLD climatology (Holte et al. 2017). In all cases the MLD is based on a threshold method in which the MLD is given by the depth at which the density exceeds the density at a near-surface reference depth 
Citation: Journal of Climate 32, 10; 10.1175/JCLI-D-18-0509.1
In all cases D is very deep in the Labrador Sea, Irminger Sea, and Iceland basin; relatively deep south of the Gulf Stream; and quite shallow elsewhere (Fig. 1). In the Labrador and Irminger Seas, D is significantly larger for Ishii and EN4 (maximum about 1500 m; Figs. 1a,b) than for the Argo MLD product (maximum around 1000 m; Fig. 1c), which is consistent with the fact that a variable density threshold results in a smaller density criteria and therefore shallower MLDs in cold regions. The value of D in the Argo MLD product (Fig. 1c) is also more patchy, which is the result of calculating MLD directly from in situ profiles rather than from a highly smoothed monthly temperature field (as in Ishii and EN4).
Gridded temperature fields and D are used to calculate H according to Eq. (1). For Ishii and EN4, D is based on the MLD calculated from the respective gridded product (e.g., Fig. 1a for Ishii and Fig. 1b for EN4); for Cheng we use D based on the Argo MLD climatology (Fig. 1c). Both annual average values of H, henceforth 
Previous work using an ocean state estimate demonstrates that SST and H are highly correlated on interannual time scales (Buckley et al. 2014). We now show that a close correspondence between wintertime SST and H is also seen in the Ishii gridded product. The Ishii product is chosen for this analysis since Ishii includes COBE SST2 observations, leading to a consistent product that can be used to compare SST and H. Figure 2 shows the squared correlation (at each grid point) between 
Squared correlation at each grid point between 
Citation: Journal of Climate 32, 10; 10.1175/JCLI-D-18-0509.1
b. Measure of predictability time scales
In this paper, T2 will be interpreted as a lower bound on the predictability time scale. This interpretation is motivated by the fact that autocorrelations out to lag T2 tend to be significant, and therefore a linear regression model can make skillful predictions at least as long as T2. It is a lower bound because it is based purely on the local autocorrelation function. Including additional predictors, such as nonlocal SST or variations in the AMOC, may improve skill (and thus correspond to longer predictability time scales). For instance, a LIM that captures covariability between multiple spatial patterns may have more skill at individual points than a regression model fitted to data at each point. Thus, our diagnostic T2 is best understood as a lower bound on predictability, one which may be a useful benchmark against which to evaluate dynamical models or more sophisticated statistical measures of predictability [such a comparison is made in the framework of atmospheric predictability in Schubert et al. (1992)]. For these reasons, we henceforth refer to T2 as the decorrelation time scale.
If we know the exact value of our autocorrelation function, we can integrate over all lags to find T2, but for a finite length time series we can only calculate the sample autocorrelation function. For a sufficiently long time series, we can instead integrate from lag 
3. Decorrelation time scales for upper-ocean heat content and SST
In this section we calculate decorrelation time scales for H and wintertime SST based on gridded observational products. Decorrelation time scales for 
The decorrelation time scale T2 (colors) for 
Citation: Journal of Climate 32, 10; 10.1175/JCLI-D-18-0509.1
The black dots in Fig. 3 and Fig. S1 show grid points where the decorrelation time scale is not significantly different from white noise on interannual time scales (see the appendix for details). In these regions there is no interannual predictability, although there may be predictability on shorter time scales (which could be examined by looking at monthly H anomalies). One can see that the interannual predictability of H is mostly restricted to the extratropics. Therefore, for the rest of our analysis we will consider only the extratropical North Atlantic (ETNA; north of 20°N).
Results shown in Fig. 3 and Fig. S1 are from yearly averages for H (
Now we present results showing the decorrelation time scales for 
The decorrelation time scale T2 for 
Citation: Journal of Climate 32, 10; 10.1175/JCLI-D-18-0509.1
The results from the three different data products are quite consistent. If we regrid all estimates for T2 onto a common 1° grid and compute linear fits for all points in the ETNA between the various data products, we find R2 values between 0.60 and 0.79 and slopes between 0.5 and 2.0 (see Table 2). The deviation of the slopes from one is due to COBE SST2 having significantly larger decorrelation time scales than the other two products.
4. Comparing decorrelation time scales for upper-ocean heat content and SST
We now explore the relationship between decorrelation time scales for SST and H using the Ishii data product. To present results that are most comparable, wintertime values are used for both SST and H, but recall that decorrelation time scales for 
A comparison of the decorrelation time scale T2 for 
Citation: Journal of Climate 32, 10; 10.1175/JCLI-D-18-0509.1
Now we explore the points where the linear relationship between T2 for 
Figure 5b shows the spatial distribution of the outliers from the linear fit. All of the outliers are in the subpolar gyre, and the outliers where T2 is larger for 
Although differences between decorrelation time scales for 
- Large spatial gradients in MLDs: Regions of deep convection are characterized by weak vertical gradients and deep MLDs, but there are strong lateral gradients in properties. These lateral gradients are baroclinically unstable, leading to a rapid growth of baroclinic eddies that act to restratify the near-surface layer (Send and Marshall 1995; Jones and Marshall 1997; Marshall and Schott 1999; Frajka-Williams et al. 2014). The input of buoyant waters from boundary currents adjacent to regions of deep convection is also important in this restratification process (Straneo 2006; Schmidt and Send 2007). Time scales for restratification in the Labrador Sea are thought to be rapid (from weeks to months). While air–sea heat fluxes are quite large over the Labrador Sea and may play a role in restratification, near surface restratification occurs more rapidly than can be accounted for by air–sea heat fluxes alone, indicating the importance of lateral mixing (Send and Marshall 1995; Jones and Marshall 1997). Wintertime SST anomalies are rapidly destroyed by restratification, but since the restratification is restricted to the near-surface layers (top few hundred meters at most), anomalies in
- Large temporal variability in MLD: Figure 2 shows that low correlations between
5. Can mixed layer depth variations explain spatial variations in decorrelation time scales?
In this section we explore our null hypothesis that spatial variations in decorrelation time scales are related to variations in the wintertime climatological MLD D. We first consider the linear relationship between the decorrelation time scale for H and D and then consider the relationship between the decorrelation time scale for wintertime SST and D. Then, we use the slopes of the linear relationships to estimate the damping parameter.
a. Relationship between decorrelation time scale for H and D
Figures 6a–c show scatterplots between D and T2 for all points in the ETNA based on 
How decorrelation time scales for H are related to D: (left) Scatterplots comparing the decorrelation time scale T2 for 
Citation: Journal of Climate 32, 10; 10.1175/JCLI-D-18-0509.1
Sensitivity of relationship between T2 for H and D to the MLD product used: (a),(b) As in Figs. 6a and 6b and (c),(d) as in Figs. 6d and 6e, but D is from the Argo MLD climatology (Holte et al. 2017). This value of D is used for both the values of D in the scatterplot and in the calculation of H according to Eq. (1).
Citation: Journal of Climate 32, 10; 10.1175/JCLI-D-18-0509.1
In calculating the linear fits, all points in the ETNA are included, regardless of whether or not the values of T2 can be distinguished from white noise on interannual time scales (dash-dotted gray lines in Figs. 6a–c, 7a, and 7b show values of T2 above which T2 can be distinguished from white noise on interannual time scales). All points are included since points where D is shallow and there is no interannual predictability are part of the observed relationship between T2 and D; in fact, if there were places with large D where there was no interannual predictability, these points would not match the expectation from the null hypothesis and would require explanation.
Now we explore the points that do not follow the scaling of T2 with D. The green (black) points in Figs. 6a–c, 7a, and 7b indicate outliers that are more than two standard deviations above (below) the best-fit line. There are significantly more outliers above the line than below the line, indicating that there are more points with higher than expected predictability than lower than expected predictability. Figures 6d–f show the spatial distribution of the outliers; the spatial distribution of the outliers is quite similar when the calculations for Ishii and EN4 are repeated using D from the Argo MLD climatology (Figs. 7c,d). The outliers are mostly confined to the subpolar gyre, except for a few points with higher than expected predictability in the slope waters west of the Gulf Stream. Points with higher than expected predictability are almost all confined to shallow bathymetry: the North American continental shelf, the Grand Banks, and the Reykjanes Ridge, a concurrence that needs further investigation, particularly in the context of previous work suggesting that interactions of ocean currents with bathymetry are an important process in generating upper ocean temperature variability (e.g., Nigam et al. 2018). There are very few points with lower than expected predictability, and their locations are not robust between the different data products, so it is somewhat difficult to determine their origin. There does seem to be some tendency for points with lower than expected predictability to occur in regions with large spatial and temporal gradients in D. This may be due to rapid restratification as a result of lateral mixing by eddies, which is expected to lead to decorrelation time scales shorter than those predicted by local values of D (Send and Marshall 1995; Jones and Marshall 1997; Marshall and Schott 1999; Frajka-Williams et al. 2014).
b. Relationship between decorrelation time scale for wintertime SST and D
We now consider the relationship between variations in D and T2 for wintertime SST; in considering this relationship we use D based on the Argo MLD climatology for all three SST data products. Figures 8a–c show a scatterplot between D and T2 for 
- Predictability time scales for H are expected to be proportional to D according to stochastic climate models (e.g., Frankignoul and Hasselmann 1977; Deser et al. 2003; de Coëtlogon and Frankignoul 2003), but there is not the same expectation for SST, which is also influenced by surface processes, as discussed in section 4.
- SST is a noisier field than H, as depth averaging acts as a low-pass filter (see section 4). Additionally, for H we are able to further suppress noise by averaging over a year rather than just averaging over the wintertime months.
- For the fit between T2 and D for the SST analysis, we use D from the Argo MLD climatology, which is relatively patchy. Our analysis with Ishii and EN4 shows that the portion of the variance of T2 explained by D decreases somewhat when D from the Argo MLD product is used compared to the smoother values of D based on the gridded data products (cf. Figs. 6a,b and 7a,b).
- In the Labrador Sea, predictability for
How decorrelation time scales for wintertime SST are related to D: (left) Scatterplots comparing the decorrelation time scale T2 for 
Citation: Journal of Climate 32, 10; 10.1175/JCLI-D-18-0509.1
Now we explore the points that do not follow the scaling of decorrelation time scale with D. The green (black) points in Figs. 8a–c indicate outliers that are more than two standard deviations above (below) the best fit line. There are significantly more outliers above the line than below the line, indicating that there are more points with higher than expected predictability than lower than expected predictability. Figures 8d–f show the spatial distribution of the outliers. The outliers almost all have higher than expected predictability and are located in the region with large decorrelation time scales south of Greenland. There is a small region of points with lower than expected predictability in the Labrador Sea, consistent with the fact that while D is deep and decorrelation time scales for 
c. The damping parameter
Expressing the slope in the units of α is not intended to suggest that calculating α based on the fits between T2 and D is an accurate method for calculating the damping parameter; instead the goal is merely to express m in units that are familiar to the reader. Namely, the canonical value of the damping by air–sea heat fluxes derived by Frankignoul et al. (1998) is αa = 20 W m−2 K−1, although values are somewhat higher in the subpolar gyre and vary seasonally (values are larger in the wintertime). Differences between our calculations and that of Frankignoul et al. (1998) include:
- Frankignoul et al. (1998) estimate only atmospheric damping αa, whereas we calculate the total damping rate by the atmosphere and ocean. Some studies suggest that oceanic damping is as large or larger than atmospheric damping (Hall and Manabe 1997), which explains why our calculated values of α are generally larger than 20 W m−2 K−1.
- Our value of α depends linearly on the chosen value of D. We chose D as the wintertime climatological MLD, a quantity that is quite large in the subpolar gyre, which also contributes to our relatively large values of α.
- Frankignoul et al. (1998) consider damping of monthly SST anomalies, whereas we consider wintertime SST and H. As a result of the formation of the seasonal thermocline,
6. Are there oscillatory variations in SST or upper-ocean heat content?
The value of T2 measures the decorrelation time scale of SST/H, but it does not distinguish between different types of variability that may be leading to the measured value of T2. For example, does T2 simply indicate damping with an e-folding time scale given by T2 or does oscillatory behavior play a role? The goal of this section is to determine the extent to which decaying versus oscillatory behavior of the autocorrelation function is important in setting decorrelation time scales for 
Scatterplots for the AR2 coefficients, 
Citation: Journal of Climate 32, 10; 10.1175/JCLI-D-18-0509.1
7. Conclusions
In this work, a lower bound for predictability time scales for SST and UOHC is estimated purely from ocean observations, and the degree to which spatial variations in the MLD can explain predictability time scales is quantified. Two diagnostics are used for SST/UOHC: wintertime SST and the temperature averaged over the layer from the surface to the wintertime climatological MLD (integral denoted as H); both diagnostics quantify the ocean memory on interannual time scales and are designed to minimize the effects of seasonal variations, specifically the loss of SST memory in the summertime due to the formation of the seasonal thermocline. Gridded observational products are used to estimate predictability for wintertime SST and H in the North Atlantic using a measure of the decorrelation time scale based on the local autocorrelation function (DelSole 2001). Decorrelation time scales for both wintertime SST and H are longest in the subpolar gyre, with maximum decorrelation time scales of 4–6 years. Decorrelation time scales for wintertime SST and H are generally similar, except in regions with very deep mixed layers, such as the Labrador Sea, where time scales for H are much larger. Oscillatory variations are found to play little role in setting predictability time scales for wintertime SST and H; instead decorrelation time scales are controlled mainly by the decay rate of anomalies.
Our decorrelation time scales are generally similar to predictability time scales calculated from observations using other statistical techniques, such as linear inverse models (LIMs). Predictability for decadal SST variations from LIMs is generally 3–4 years over most of the North Atlantic domain, with predictability generally being larger in subpolar regions (Zanna et al. 2012; Newman 2013; Huddart et al. 2017). The similarity of our results to those from LIMs suggests that our consideration of a predictability measure based on the local autocorrelation (e.g., the decorrelation time scale) is likely not a significant limitation in the Atlantic basin. This is further supported by results from LIMs that suggest nonlocal SST variability has little influence on SST predictions in a given region of the Atlantic (Huddart et al. 2017). Our conclusion that oscillatory variations play little role in predictability of wintertime SST and H is supported by results from statistical models that suggest predictability in the Atlantic, while higher than most other basins, only slightly exceeds that of a persistence forecast (DelSole et al. 2013).
While our results generally agree with other studies on the magnitude of predictability time scales in the North Atlantic, there are some differences in the detailed spatial patterns. For example, Zanna et al. (2012) find that forecast skill compared to climatology is quite low in the subpolar region south of Greenland, but we find that this region has relatively high values of T2 (greater than 2 years). This result may be due to the analysis of wintertime SST (in our study) versus annual-average SST [in Zanna et al. (2012)], the different time periods studied [Zanna et al. (2012) start analysis in 1870 whereas we start in 1945], or the truncation of the SST variability using empirical orthogonal functions in the LIM. The spatial patterns of predictability time scales for SST in Huddart et al. (2017) are more similar to ours, but this study uses decadal filtering to construct the LIM, so results are not directly comparable to our study. It would be interesting to create a LIM to predict wintertime SST or wintertime/annual average H (with no additional filtering) and see how these results compare to our decorrelation time scales.
Spatial variations in the wintertime climatological MLD explain 51%–74% of the regional variations in decorrelation time scales for UOHC and 26%–40% of the regional variations in decorrelation time scales for SST in the extratropical North Atlantic. These results suggest that to leading order decorrelation time scales for H are determined by the thermal memory of the ocean. Interestingly, decorrelation time scales for UOHC that are significantly larger than expected based on the local mixed layer depth tend to be located in regions with shallow bathymetry. Decorrelation time scales for wintertime SST have a weaker relationship with the MLD, as a result of both noise and surface processes. In particular, in the Labrador Sea, decorrelation time scales for wintertime SST are much shorter than expected from the local MLD.
The suggestion that a large portion of the spatial variations in predictability time scales can be explained by variations in the wintertime climatological MLD raises the question of whether SST and UOHC variability in the ocean can simply be explained by stochastic atmospheric forcing. Addressing this question is the subject of ongoing work. The fact that the damping parameter calculated from our decorrelation time scales is significantly larger than the canonical atmospheric damping parameter (e.g., Frankignoul et al. 1998) suggests that oceanic damping is important, as found by Hall and Manabe (1997) and argued by Zhang (2017). Where dynamical oceanic process (e.g., ocean currents) are important in creating SST and UOHC anomalies remains to be explored in detail, but both our results and other studies suggest oceanic processes are more important in the subpolar gyre (e.g., Buckley et al. 2014, 2015; Karspeck et al. 2015; Robson et al. 2014; Menary et al. 2015; O’Reilly et al. 2016; Delworth et al. 2017; Piecuch et al. 2017; Zhang 2017).
Our observationally based results do not indicate the same degree of variation in the magnitude and spatial patterns of predictability time scales that are typically seen in CMIP5 models. Whether this is due to model deficiencies or may be related to the limited sampling period of ocean observations is currently not clear. Our results suggest that the predictability diagnostics that have been used for CMIP5 models, particularly temperature averaged over depth layers that are constant in space [e.g., top 300 m used in Branstator et al. (2012)] may not be the best measures of ocean memory. Calculating predictability time scales for wintertime SST and H for CMIP5/CMIP6 control integrations and historical runs is a subject of ongoing study.
One of the most significant caveats of our study is that we only have about 70 years of observations and remove a quadratic function (in time) from our data prior to analysis. Therefore, we can only resolve variations up to decadal time scales. If longer variations play a substantial role in ocean predictability, then our results are surely an underestimate of ocean predictability.
We thank Laure Zanna, Sumat Nigam, and one anonymous reviewer for insightful comments. MB was funded by the NOAA ESS Program (NA16OAR4310167) and NASA Physical Oceanography Program (NNX17AH49G). TD was supported by the National Oceanic and Atmospheric Administration (NA16OAR4310175, NA14OAR4310160), National Science Foundation (AGS-1338427), and National Aeronautics and Space Administration (NNX14AM19G). MSL gratefully acknowledges NOAA support from Grant NA16OAR4310168, and LL acknowledges NSF support from Grant NSF-OCE-12-59102.
APPENDIX
Determining the Level of T2 That Can Be Distinguished from White Noise on Interannual Time Scales
In our analysis, we use yearly time resolution observations (wintertime average SST and yearly and wintertime average H), and thus we are only able to measure interannual predictability. The point of this appendix is to evaluate what value of T2 is required in order to demonstrate statistically significant interannual predictability. From a theoretical perspective, the minimum value of T2 is one, and this value will occur when the autocorrelation decreases to zero at a lag of one year. However, due to finite sampling it is possible to get larger values of T2 even for white noise time series, which have no interannual predictability. Thus, we generate probability distribution functions for T2 based on white noise input (for time series of SST and H) and compute thresholds for T2. Where T2 calculated from the data exceeds the threshold from white noise, we conclude that there is interannual predictability. Where T2 does not exceed the threshold, the variability cannot be distinguished from white noise on interannual time scales.
We first generate a time series of white noise with the same length as the number of years of the observational dataset of SST or H. The specific lengths of the time series of SST and H for each product are given in Tables 1 and 2, but in all cases the time series are about 70 years. Then, to be consistent with the approach taken for the analysis of the data, a quadratic function (in time) is removed from the time series and AR fits are computed (using AR order of 2). We repeat this experiment 10 000 times in order to get distributions for the AR parameters resulting from white noise. Figure A1a shows a histogram of the AR2 coefficients, 
Histograms of AR parameters and T2 for white noise (with the same length of the observational time series). Distributions come from 10 000 repetitions (see the appendix). (a) The AR2 coefficients, 
Citation: Journal of Climate 32, 10; 10.1175/JCLI-D-18-0509.1
REFERENCES
Alexander, M. A., and C. Deser, 1995: A mechanism for the recurrence of wintertime midlatitude SST anomalies. J. Phys. Oceanogr., 25, 122–137, https://doi.org/10.1175/1520-0485(1995)025<0122:AMFTRO>2.0.CO;2.
Alexander, M. A., L. Matrosova, C. Penland, J. D. Scott, and P. Chang, 2008: Forecasting Pacific SSTs: Linear inverse model predictions of the PDO. J. Climate, 21, 385–402, https://doi.org/10.1175/2007JCLI1849.1.
Argo, 2019: Argo float data and metadata from Global Data Assembly Centre (Argo GDAC). SEANOE, accessed 2019, https://doi.org/10.17882/42182.
Årthun, M., T. Eldevik, E. Viste, H. Drange, T. Furevik, H. L. Johnson, and N. S. Keenlyside, 2017: Skillful prediction of northern climate provided by the ocean. Nat. Commun., 8, 16152, https://doi.org/10.1038/ncomms16152.
Bersch, M., 2002: North Atlantic Oscillation–induced changes of the upper layer circulation in the northern North Atlantic Ocean. J. Geophys. Res., 107, 3156, https://doi.org/10.1029/2001JC000901.
Boer, G. J., and Coauthors, 2016: The Decadal Climate Prediction Project (DCPP) contribution to CMIP6. Geosci. Model Dev., 9, 3751–3777, https://doi.org/10.5194/gmd-9-3751-2016.
Boyer, T., and Coauthors, 2016: Sensitivity of global upper-ocean heat content estimates to mapping methods, XBT bias corrections, and baseline climatologies. J. Climate, 29, 4817–4842, https://doi.org/10.1175/JCLI-D-15-0801.1.
Branstator, G., H. Teng, G. A. Meehl, M. Kimoto, J. R. Knight, M. Latif, and A. Rosati, 2012: Systematic estimates of initial-value decadal predictability for six AOGCMs. J. Climate, 25, 1827–1846, https://doi.org/10.1175/JCLI-D-11-00227.1.
Buckley, M. W., R. M. Ponte, G. Forget, and P. Heimbach, 2014: Low-frequency SST and upper-ocean heat content variability in the North Atlantic. J. Climate, 27, 4996–5018, https://doi.org/10.1175/JCLI-D-13-00316.1.
Buckley, M. W., R. M. Ponte, G. Forget, and P. Heimbach, 2015: Determining the origins of advective heat transport convergence variability in the North Atlantic. J. Climate, 28, 3943–3956, https://doi.org/10.1175/JCLI-D-14-00579.1.
Cheng, L., K. E. Trenberth, J. Fasullo, T. Boyer, J. Abraham, and J. Zhu, 2017: Improved estimates of ocean heat content from 1960 to 2015. Sci. Adv., 3, e1601545, https://doi.org/10.1126/sciadv.1601545.
Corti, S., and Coauthors, 2015: Impact of initial conditions versus external forcing in decadal climate predictions: A sensitivity experiment. J. Climate, 28, 4454–4470, https://doi.org/10.1175/JCLI-D-14-00671.1.
de Coëtlogon, G., and C. Frankignoul, 2003: The persistence of winter sea surface temperature in the North Atlantic. J. Climate, 16, 1364–1377, https://doi.org/10.1175/1520-0442-16.9.1364.
DelSole, T., 2001: Optimally persistent patterns in time-varying fields. J. Atmos. Sci., 58, 1341–1356, https://doi.org/10.1175/1520-0469(2001)058<1341:OPPITV>2.0.CO;2.
DelSole, T., 2017: Decadal prediction of temperature: Achievements and future prospects. Curr. Climate Change Rep., 3, 99–111, https://doi.org/10.1007/s40641-017-0066-x.
DelSole, T., and M. K. Tippett, 2018: Predictability in a changing climate. Climate Dyn., 51, 531–545, https://doi.org/10.1007/s00382-017-3939-8.
DelSole, T., L. Jia, and M. K. Tippett, 2013: Decadal prediction of observed and simulated sea surface temperatures. Geophys. Res. Lett., 40, 2773–2778, https://doi.org/10.1002/grl.50185.
Delworth, T. L., F. Zeng, L. Zhang, R. Zhang, G. A. Vecchi, and X. Yang, 2017: The central role of ocean dynamics in connecting the North Atlantic Oscillation to the extratropical component of the Atlantic multidecadal oscillation. J. Climate, 30, 3789–3805, https://doi.org/10.1175/JCLI-D-16-0358.1.
Deser, C., M. A. Alexander, and M. S. Timlin, 2003: Understanding the persistence of sea surface temperature anomalies in midlatitudes. J. Climate, 16, 57–72, https://doi.org/10.1175/1520-0442(2003)016<0057:UTPOSS>2.0.CO;2.
Dias, D. F., A. Subramanian, L. Zanna, and A. J. Miller, 2019: Remote and local influences in forecasting Pacific SST: A linear inverse model and a multimodel ensemble study. Climate Dyn., 52, 3183–3201, https://doi.org/10.1007/s00382-018-4323-z.
Doblas-Reyes, F. J., and Coauthors, 2013: Initialized near-term regional climate change prediction. Nat. Commun., 4, 1715, https://doi.org/10.1038/ncomms2704.
Eyring, V., S. Bony, G. A. Meehl, C. A. Senior, B. Stevens, R. J. Stouffer, and K. E. Taylor, 2016: Overview of the Coupled Model Intercomparison Project phase 6 (CMIP6) experimental design and organization. Geosci. Model Dev., 9, 1937–1958, https://doi.org/10.5194/gmd-9-1937-2016.
Frajka-Williams, E., P. B. Rhines, and C. C. Eriksen, 2014: Horizontal stratification during deep convection in the Labrador Sea. J. Phys. Oceanogr., 44, 220–228, https://doi.org/10.1175/JPO-D-13-069.1.
Frankignoul, C., and K. Hasselmann, 1977: Stochastic climate models, Part II: Application to sea-surface temperature anomalies and thermocline variability. Tellus, 29, 289–305, https://doi.org/10.3402/tellusa.v29i4.11362.
Frankignoul, C., and E. Kestenare, 2002: The surface heat flux feedback. Part I: Estimates from observations in the Atlantic and the North Pacific. Climate Dyn., 19, 633–647, https://doi.org/10.1007/s00382-002-0252-x.
Frankignoul, C., A. Czaja, and B. L’Heveder, 1998: Air–sea feedback in the North Atlantic and surface boundary conditions for ocean models. J. Climate, 11, 2310–2324, https://doi.org/10.1175/1520-0442(1998)011<2310:ASFITN>2.0.CO;2.
Good, S. A., M. J. Martin, and N. A. Rayner, 2013: EN4: Quality controlled ocean temperature and salinity profiles and monthly objective analyses with uncertainty estimates. J. Geophys. Res. Oceans, 118, 6704–6716, https://doi.org/10.1002/2013JC009067.
Häkkinen, S., and P. B. Rhines, 2004: Decline of subpolar North Atlantic circulation during the 1990s. Science, 304, 555–559, https://doi.org/10.1126/science.1094917.
Häkkinen, S., P. B. Rhines, and D. L. Worthen, 2011: Atmospheric blocking and Atlantic multidecadal ocean variability. Science, 334, 655–659, https://doi.org/10.1126/science.1205683.
Hall, A., and S. Manabe, 1997: Can local linear stochastic theory explain sea surface temperature and salinity variability? Climate Dyn., 13, 167–180, https://doi.org/10.1007/s003820050158.
Hawkins, E., and R. Sutton, 2009: Decadal predictability of the Atlantic Ocean in a coupled GCM: Forecast skill and optimal perturbations using linear inverse modeling. J. Climate, 22, 3960–3978, https://doi.org/10.1175/2009JCLI2720.1.
Hermanson, L., R. Eade, N. H. Robinson, N. J. Dunstone, M. B. Andrews, J. R. Knight, A. A. Scaife, and D. M. Smith, 2014: Forecast cooling of the Atlantic subpolar gyre and associated impacts. Geophys. Res. Lett., 41, 5167–5174, https://doi.org/10.1002/2014GL060420.
Hirahara, S., M. Ishii, and Y. Fukuda, 2014: Centennial-scale sea surface temperature analysis and its uncertainty. J. Climate, 27, 57–75, https://doi.org/10.1175/JCLI-D-12-00837.1.
Ho, C. K., E. Hawkins, L. Shaffrey, and F. M. Underwood, 2013: Statistical decadal predictions for sea surface temperatures: A benchmark for dynamical GCM predictions. Climate Dyn., 41, 917–935, https://doi.org/10.1007/s00382-012-1531-9.
Holte, J., L. D. Talley, J. Gilson, and D. Roemmich, 2017: An Argo mixed layer climatology and database. Geophys. Res. Lett., 44, 5618–5626, https://doi.org/10.1002/2017GL073426.
Huddart, B., A. Subramanian, L. Zanna, and T. Palmer, 2017: Seasonal and decadal forecasts of Atlantic sea surface temperatures using a linear inverse model. Climate Dyn., 49, 1833–1845, https://doi.org/10.1007/s00382-016-3375-1.
Ishii, M., M. Kimoto, K. Sakamoto, and S.-I. Iwasaki, 2006: Steric sea level changes estimated from historical ocean subsurface temperature and salinity analyses. J. Oceanogr., 62, 155–170, https://doi.org/10.1007/s10872-006-0041-y.
Jones, H., and J. Marshall, 1997: Restratification after deep convection. J. Phys. Oceanogr., 27, 2276–2287, https://doi.org/10.1175/1520-0485(1997)027<2276:RADC>2.0.CO;2.
Karspeck, A., S. Yeager, G. Danabasoglu, and H. Teng, 2015: An evaluation of experimental decadal predictions using CCSM4. Climate Dyn., 44, 907–923, https://doi.org/10.1007/s00382-014-2212-7.
Keenlyside, N., M. Latif, J. Jungclaus, L. Kornblueh, and E. Roeckner, 2008: Advancing decadal-scale climate prediction in the North Atlantic sector. Nature, 453, 84–88, https://doi.org/10.1038/nature06921.
Kennedy, J. J., 2014: A review of uncertainty in in situ measurements and data sets of sea surface temperature. Rev. Geophys., 52, 1–32, https://doi.org/10.1002/2013RG000434.
Marshall, J., and F. Schott, 1999: Open-ocean convection: Observations, theory, and models. Rev. Geophys., 37, 1–64, https://doi.org/10.1029/98RG02739.
Matei, D., H. Pohlmann, J. Jungclaus, W. Müller, H. Haak, and J. Marotzke, 2012: Two tales of initializing decadal climate prediction experiments with the ECHAM5/MPI-OM model. J. Climate, 25, 8502–8523, https://doi.org/10.1175/JCLI-D-11-00633.1.
Meehl, G. A., and Coauthors, 2014: Decadal climate prediction: An update from the trenches. Bull. Amer. Meteor. Soc., 95, 243–267, https://doi.org/10.1175/BAMS-D-12-00241.1.
Menary, M. B., D. L. R. Hodson, J. I. Robson, R. T. Sutton, and R. A. Wood, 2015: A mechanism of internal decadal Atlantic Ocean variability in a high-resolution coupled climate model. J. Climate, 28, 7764–7785, https://doi.org/10.1175/JCLI-D-15-0106.1.
Namias, J., and R. M. Born, 1970: Temporal coherence in North Pacific sea-surface temperature patterns. J. Geophys. Res., 75, 5952–5955, https://doi.org/10.1029/JC075i030p05952.
Newman, M., 2007: Interannual to decadal predictability of tropical and North Pacific sea surface temperatures. J. Climate, 20, 2333–2356, https://doi.org/10.1175/JCLI4165.1.
Newman, M., 2013: An empirical benchmark for decadal forecasts of global surface temperature anomalies. J. Climate, 26, 5260–5269, https://doi.org/10.1175/JCLI-D-12-00590.1.
Newman, M., and Coauthors, 2016: The Pacific decadal oscillation, revisited. J. Climate, 29, 4399–4427, https://doi.org/10.1175/JCLI-D-15-0508.1.
Nigam, S., A. Ruiz-Barradas, and L. Chafik, 2018: Gulf Stream excursions and sectional detachments generate the decadal pulses in the Atlantic multidecadal oscillation. J. Climate, 31, 2853–2870, https://doi.org/10.1175/JCLI-D-17-0010.1.
O’Reilly, C. H., M. Huber, T. Woollings, and L. Zanna, 2016: The signature of low-frequency oceanic forcing in the Atlantic multidecadal oscillation. Geophys. Res. Lett., 43, 2810–2818, https://doi.org/10.1002/2016GL067925.
Piecuch, C. G., R. M. Ponte, C. M. Little, M. W. Buckley, and I. Fukumori, 2017: Mechanisms underlying recent decadal changes in subpolar North Atlantic Ocean heat content. J. Geophys. Res. Oceans, 122, 7181–7197, https://doi.org/10.1002/2017JC012845.
Pohlmann, H., J. H. Jungclaus, A. Köhl, D. Stammer, and J. Marotzke, 2009: Initializing decadal climate predictions with the GECCO oceanic synthesis: Effects on the North Atlantic. J. Climate, 22, 3926–3938, https://doi.org/10.1175/2009JCLI2535.1.
Rayner, N. A., D. E. Parker, E. B. Horton, C. K. Folland, L. V. Alexander, D. P. Rowell, E. C. Kent, and A. Kaplan, 2003: Global analyses of sea surface temperature, sea ice, and night marine air temperature since the late nineteenth century. J. Geophys. Res., 108, 4407, https://doi.org/10.1029/2002JD002670.
Robson, J., R. Sutton, and D. Smith, 2014: Decadal predictions of the cooling and freshening of the North Atlantic in the 1960s and the role of ocean circulation. Climate Dyn., 42, 2353–2365, https://doi.org/10.1007/s00382-014-2115-7.
Robson, J., P. Ortega, and R. Sutton, 2016: A reversal of climatic trends in the North Atlantic since 2005. Nat. Geosci., 9, 513–517, https://doi.org/10.1038/ngeo2727.
Ruiz-Barradas, A., L. Chafik, S. Nigam, and S. Häkkinen, 2018: Recent subsurface North Atlantic cooling trend in context of Atlantic decadal-to-multidecadal variability. Tellus, 70A, 1–19, https://doi.org/10.1080/16000870.2018.1481688.
Sarafanov, A., A. Falina, A. Sokov, and A. Demidov, 2008: Intense warming and salinification of intermediate waters of southern origin in the eastern subpolar North Atlantic in the 1990s to mid-2000s. J. Geophys. Res. Oceans, 113, C12022, https://doi.org/10.1029/2008JC004975.
Schmidt, S., and U. Send, 2007: Origin and composition of seasonal Labrador Sea freshwater. J. Phys. Oceanogr., 37, 1445–1454, https://doi.org/10.1175/JPO3065.1.
Schubert, S. D., M. J. Suarez, and J.-K. Schemm, 1992: Persistence and predictability in a perfect model. J. Atmos. Sci., 49, 256–269, https://doi.org/10.1175/1520-0469(1992)049<0256:PAPIAP>2.0.CO;2.
Send, U., and J. Marshall, 1995: Integral effects of deep convection. J. Phys. Oceanogr., 25, 855–872, https://doi.org/10.1175/1520-0485(1995)025<0855:IEODC>2.0.CO;2.
Smith, D. M., S. Cusack, A. W. Colman, C. K. Folland, G. R. Harris, and J. M. Murphy, 2007: Improved surface temperature prediction for the coming decade from a global climate model. Science, 317, 796–799, https://doi.org/10.1126/science.1139540.
Smith, T. M., R. W. Reynolds, T. C. Peterson, and J. Lawrimore, 2008: Improvements to NOAA’s historical merged land–ocean surface temperature analysis (1880–2006). J. Climate, 21, 2283–2296, https://doi.org/10.1175/2007JCLI2100.1.
Straneo, F., 2006: Heat and freshwater transport through the central Labrador Sea. J. Phys. Oceanogr., 36, 606–628, https://doi.org/10.1175/JPO2875.1.
Toyoda, T., and Coauthors, 2015: Intercomparison and validation of the mixed layer depth fields of global ocean syntheses. Climate Dyn., 49, 753–773, https://doi.org/10.1007/s00382-015-2637-7.
van Oldenborgh, G. J., F. J. Doblas-Reyes, B. Wouters, and W. Hazeleger, 2012: Decadal prediction skill in a multi-model ensemble. Climate Dyn., 38, 1263–1280, https://doi.org/10.1007/s00382-012-1313-4.
von Storch, H., and F. W. Zwiers, 2002: Statistical Analysis in Climate Research. Cambridge University Press, 484 pp.
Yeager, S., A. Karspeck, G. Danabasoglu, J. Tribbia, and H. Teng, 2012: A decadal prediction case study: Late twentieth-century North Atlantic Ocean heat content. J. Climate, 25, 5173–5189, https://doi.org/10.1175/JCLI-D-11-00595.1.
Zanna, L., 2012: Forecast skill and predictability of observed Atlantic sea surface temperatures. J. Climate, 25, 5047–5056, https://doi.org/10.1175/JCLI-D-11-00539.1.
Zanna, L., P. Heimbach, A. Moore, and E. Tziperman, 2012: Upper ocean singular vectors of the North Atlantic climate with implications for linear predictability and variability. Quart. J. Roy. Meteor. Soc., 138, 500–513, https://doi.org/10.1002/qj.937.
Zhang, R., 2017: On the persistence and coherence of subpolar sea surface temperature and salinity anomalies associated with the Atlantic multidecadal variability. Geophys. Res. Lett., 44, 7865–7875, https://doi.org/10.1002/2017GL074342.
DelSole and Tippett (2018) propose a generalized framework for predictability valid when there are variations in external forcing.
As the Cheng product does not include salinity, we cannot calculate potential density from this product and thus cannot calculate MLDs.
