The impacts of oceanic deep temperature perturbations in the North Atlantic on decadal climate variability and predictability

Decadal climate predictability in the North Atlantic is largely related to ocean low frequency variability, whose sensitivity to initial conditions is not very well understood. Recently, three-dimensional oceanic temperature anomalies optimally perturbing the North Atlantic Mean Temperature (NAMT) have been computed via an optimization procedure using a linear adjoint to a realistic ocean general circulation model. The spatial pattern of the identified perturbations, localized in the North Atlantic, has the largest magnitude between 1000 and 4000 m depth. In the present study, the impacts of these perturbations on NAMT, on the Atlantic meridional overturning circulation (AMOC), and on climate in general are investigated in a global coupled model that uses the same ocean model as was used to compute the three-dimensional optimal perturbations. In the coupled model, these perturbations induce AMOC and NAMT anomalies peaking after 5 and 10 years, respectively, generally consistent with the ocean-only linear predictions. To further understand their impact, their magnitude was varied in a broad range. For initial perturbations with a magnitude comparable to the internal variability of the coupled model, the model response exhibits a strong signature in sea surface temperature and precipitation over North America and the Sahel region. The existence and impacts of these ocean perturbations have important implications for decadal prediction: they can be seen either as a source of predictability or uncertainty, depending on whether the current observing system can detect them or not. In fact, comparing the magnitude of the imposed perturbations with the uncertainty of available ocean observations such as Argo data or ocean state estimates suggests that only the largest perturbations used in this study could be detectable. This highlights the importance for decadal climate prediction of accurate ocean density initialisation in the North Atlantic at intermediate and greater depths.

response exhibits a strong signature in sea surface temperature (SST) and precipitation over North America and the Sahel region. The existence and impacts of these ocean perturbations have important implications for decadal prediction: they can be seen either as a source of predictability or uncertainty, depending on whether the current observing system can detect them or not. In fact, comparing the magnitude of the imposed perturbations with the uncertainty of available ocean observations such as Argo data or ocean state estimates suggests that the largest perturbations used in this study could be detectable. This highlights the importance for decadal climate prediction of accurate ocean density initialisation in the North Atlantic at intermediate and greater depths.
L482: create an under-or overdispersive Done. L925-928: No need for all those details after "linear model". Suggest replacing with "as described by …" Done.

Reviewer #3:
In my view, the authors have done very good job in addressing the constructive comments raised by the two previous reviewers.
What I am (still) puzzled with is that the perturbations have the largest magnitude below 1000m. I do not think that the authors make a convincing case, why this is dynamcially/physically reasonable; though I do understand that an explanation is beyond the scope here, but I think some brief speculations would be also good in the final part of the ms. I understand that other studies (e.g. Zanna et al) have found the same, and while I can follow their argument there, I am then wondering what we learn in addition here.
Our interpretation of this is that unlike surface anomalies, density anomalies induced in the deep ocean are able to persist over a sufficiently long time, maintaining meridional flow and amplifying the transient change of the AMOC (as discussed in Sévellec and Fedorov 2015). That explains the magnitude of the perturbations being greatest at depth. Zanna et al. is a very idealized study (flat bottom, rectangular basin, very idealized surface forcing), but they indeed found similar results possibly for the same physical reason. The fact that this mechanism holds in the fully coupled realistic climate model, albeit with a damping factor of the response of 3 is a new result.
We have added a brief discussion (l. 581-587) of this physical effect in the manuscript in the conclusion section.
Also, I feel that there is a mismacth between the ambitions/immediate relevance for initialized decadal predictions outlined at the end of the abstract and what is actually presented in the conclusions section. I would ask the authors to consider re-writing or extending this last part of the manuscript to make the overall context of this rather 'idealised' study clear.
We have added a short paragraph (l. 564-574) in the conclusion to insist that the potential teleconnections between the surface ocean and the atmosphere are still poorly represented in climate models, thereby limiting the applicability of the results for climate predictions. We have also added one sentence at the end of the paper to underline the fact that this study is idealized as compared to decadal predictions and that the exact link to decadal predictions is still to deepen.
basin. This propagation impacts the AMOC via thermal wind balance and basin-scale 132 variations of the zonal density gradient. There is evidence of a similar westward propagation 133 in the North Atlantic observations of sea-level height (e.g. Tulloch et al. 2009; Vianna and 134 Menezes 2013), subsurface temperature (Frankcombe et al. 2008), and SST (Feng and 135 Dijkstra 2014) with a comparable basin-crossing time (~10 years) as estimated by Sévellec 136 and Fedorov (2013b). It has been also identified in nearly 20 models of the CMIP5 database 137 (Muir and Fedorov 2016). In IPSL-CM5A-LR in particular, this oceanic mode exhibits 138 interaction with convective activity, sea ice, and atmospheric circulation (Ortega et al., 2015). 139 In the present analysis, climate response to the LOP is investigated in terms of changes 140 in NAMT, the AMOC strength, SST, and atmospheric temperature and precipitation. We use 141 ensemble experiments in order to extract the signal of the LOP response from the atmospheric 142 stochastic noise in a perfect model configuration, therefore avoiding pollution of the signal by 143 model drift, and model imperfections. The ensemble experiments, the coupled system and the 144 LOP are described in more detail in section 2. The response of the system to the oceanic 145 perturbations is then described in section 3, while implications for near-term climate 146 prediction are discussed in section 4. Finally concluding remarks are given in the last section. includes the sea ice model LIM2 (Fichefet and Maqueda 1997) and the biogeochemistry 160 model PISCES (Aumont and Bopp 2006). The coupling between the oceanic and atmospheric 161 components is achieved via OASIS3 (Valcke 2006). The reader is referred to the special issue noise is identical for all ensembles. As this perturbed SST field is only used when SST is 190 passed to the atmosphere during the integration first time step, this perturbation is considered 191 as an atmospheric-only perturbation. Germe et al. (2017) showed that this method is 192 equivalent to applying a random white noise to the whole oceanic temperature field. In 193 addition to this atmospheric perturbation, six ensembles utilize full-depth oceanic temperature 194 perturbations. The pattern of these perturbations corresponds to the LOP as computed by 195 Sévellec and Fedorov (2017) using the tangent linear forward and adjoint versions of the same 196 ocean model as in the coupled run. The six ensembles differ only by the magnitude and/or sign of the oceanic perturbation pattern as described below (see Table 1 for details). The 198 seventh ensemble, without any perturbation to the oceanic temperature field, is taken as a 199 benchmark to assess the impact of oceanic perturbations in the other ensembles and will be 200 further referred to as ATM.

Oceanic perturbation pattern 207
The specific pattern of the 3D global oceanic temperature field used to perturb the 208 oceanic initial state of each ensemble has been computed by Sévellec and Fedorov (2017) as However, the linearity of the response suggests that significant response could be identified 261 for weaker magnitudes by increasing the ensemble size and therefore the robustness of the 262 statistical test. The AMOC response to the LOP looks slightly asymmetric, being weaker for 263 negative (N10 and N20) than positive (P10 and p20) LOP. However, when taking into 264 account the confidence interval of the ensemble means, this asymmetry is not significant at and larger scale than its negative equivalent ensemble N20. This is in accordance with the 310 AMOC response identified in the previous section and is associated with stronger atmospheric 311 impacts as well (see other panels). A significant impact is found on the 2-meter air 312 temperature (T2M), over the ocean, but also over land in some areas (Figure 4, 2 nd row). 313 Apart from the eastern part of North America, the continental response to the positive and 314 negative LOP is not symmetric. For example, there is a significant response of T2M over the 315 Scandinavia for the P20 ensemble, which is not found significant for N20. A significant 316 impact is found over the western North Africa in N20, while it is found in the eastern North 317 Africa and Middle East regions in P20. These impacts on T2M persist throughout the year but 318 they are stronger in winter than in summer ( Figure 5). For P20, T2M pattern evolves slightly 319 with the forecasting year, but the warm anomaly in the North-Atlantic region persists 320 throughout the first 15 years of the forecasting period.  Despite these significant impacts on T2M and tropical precipitations, no significant 329 impact could be identified on the major modes of atmospheric variability over the North Atlantic sector, namely the North Atlantic Oscillation (NAO) and the East Atlantic Pattern 331 (not shown). The impact on the winter sea level pressure (SLP) pattern strongly varies with 332 the forecast range and a robust feature of the LOP impacts is difficult to identify at 333 interannual time scales (not shown). When averaging over the 5 to 10 forecast years, we find 334 a weak, but significant impact (Figure 4, 4 th row) over various regions of the North Atlantic. 335 Again, the pattern of the impact differs between the positive and negative LOP. In N20, the 336 pattern has a significant positive anomaly over the Arctic and non-significant negative 337 anomalies over the North Atlantic mid-latitudes, which may be interpreted as a negative As mentioned in section 2, the magnitudes of the LOP tested in this study sample a 361 large fraction of the NAMT index variability in CTL. This is highlighted in Figure 6a, where 362 the colour points, indicating the NAMT value for the different magnitudes of the LOP, are over-imposed on the grey shadings that represent respectively one, two, and three standard 364 deviations of NAMT interannual variability in CTL. We can see that P01 and P05 magnitudes 365 lie within one standard deviation of the variability from the mean state, which corresponds to 366 very frequent situations, while P20 and N20, on the other hand, rely within two and three 367 standard deviations, and therefore correspond to extreme, and relatively rare events. However, 368 the same analysis, repeated within 4 different oceanic layers (Figure 6b propagation mechanism. This suggests that the oceanic response to the LOP is not directly 392 due to its extreme integrated values but rather to its specifically located anomalies. 393

394
In summary, the LOPs exhibit a specific 3D pattern, with largest relative magnitudes 395 from intermediate to bottom depths, and a relatively weak perturbation at the surface, when 396 compared to the internal variability. Therefore, while occurrence of such anomalies is very frequent at the surface for all magnitudes that we have tested, their occurrences are extremely 398 rare in the intermediate and deeper ocean. In that respect, P20 and N20 could be seen as 399 extreme events within the North-Atlantic Ocean. If a perturbation resembling the LOP was to 400 be detected, one could suspect -although based on this single coupled model analysis -an 401 AMOC anomaly after 5 years, followed by a NAMT anomaly and possible impacts over land, 402 which bring valuable information to assess the North-Atlantic climate a few years ahead. This 403 raises the question about the ability of current monitoring systems to detect such anomalies. days (e.g. Hazeleger et al., 2013). We have estimated the magnitude of such perturbations in terms of NAMT using daily time series of the oceanic temperature in CTL. In practice, for 464 each daily oceanic temperature pattern we have computed the anomaly from the oceanic 465 temperature pattern occurring ten days before. Then, we compute the NAMT on these 466 anomaly fields and take its minimum and maximum values as the range of the initial 467 perturbations arising from this ensemble generation strategy. According to this analysis, the 468 perturbation of the oceanic state due to a 10-day lagged temperature anomaly field is much 469 larger in the surface layer (Figure 6b, yellow bar) than in the deeper layers where it remains 470 very close to zero, especially bellow 2000 m (Figure 6e, yellow bar). This is consistent with 471 the much stronger high frequency variability of the upper ocean. Therefore, the lagging 472 methodology is very unlikely to generate perturbation patterns that project onto the LOP, and 473 so to excite the subsurface variability mode.  atmospheric surface temperature, precipitations, and to a lesser degree SLP at 5-10-year 518 average forecast range. Even though our experimental design is idealized, these results have 519 strong implications in terms of decadal predictability of the climate. Indeed, they highlight 520 that anomalies in the deep ocean could have significant consequences for the upper ocean and 521 surface atmosphere on timescales from interannual to decadal. 522 The impact of LOP on the oceanic heat content is rather linear, whereas the response 523 of the SST and atmospheric variables are strongly asymmetric. Regarding the AMOC, its 524 response exhibits a weak asymmetry. Although not significant in our case, this asymmetry has 525 already been observed in the non-linear ocean forced model as a response to SSS optimal 526 perturbations (Sévellec et al., 2008). As explained in Sévellec et al. (2008), this asymmetry 527 may arise from the feedback of density anomalies on the vertical mixing. Indeed, a positive 528 density anomaly will enhance the vertical mixing and therefore the deep-water formation, 529 resulting in a stronger AMOC. On the other hand, a negative anomaly will reduce the vertical 530 mixing and the deep-water formation, resulting in a weaker AMOC. Depending on the 531 stratification before perturbation, the positive and negative perturbations will have a different 532 impact that may induce the asymmetry. Besides, even though we selected the initial state from 533 a neutral period regarding the NAMT and AMOC variability (cf. section 2), perfect neutrality 534 is elusive. Therefore, the asymmetry found in the response might result from the initial state 535 being closer to one sign version of the LOP than the other. Evaluating the impact of a peculiar 536 initial state on the AMOC response would require to test the LOP on several initial dates and 537 will be the object of future work. Likewise, even though an asymmetrical response of the 538 system to the LOP may arise from non-linear feedbacks or more generally from the non-linear perturbation for this circulation (cf. Sévellec and Fedorov 2015). 587 Our results also suggest that a climate prediction starting from an initial state 588 corresponding to an extreme event regarding the density anomaly in the deep North-Atlantic 589 would benefit from the initialization of the optimal structure determined in the ocean-only 590 model, therefore potentially increasing the prediction skill compared to the average skill in the 591   Where ( is the temperature in the grid cell i, and ( is the weight related to the volume of the 635 grid cell i. The computation of the error on this index is based on the propagation of 636 uncertainties as described in Taylor et al. (1997). As the local errors ( cannot be considered 637 as independent, these local uncertainties induce further uncertainties on the NAMT index: 638 This error is shown in figure Ia as gray shading. This error estimation considers all grid cells 640 as dependant and therefore gives an upper bound of the error that is likely to overestimate the 641 real uncertainty. 642 When considering the annual means, the same propagation of error could be used. 643 However, this is very likely to strongly overestimate this uncertainty as the resulting error is 644 found to be larger than the variability of the NAMT index ( Figure Ib: gray shading). In the 645 aim of giving more realistic error estimation, we have considered each realization as 646 independent for the computation of the annual mean. In that case, still following the 647 propagation of uncertainties described by Taylor et al. (1997), the error on the annual mean 648 NAMT can be written: 649 Where . is the number of values in a given year. This more restrictive estimation is 652 highlighted in Figure Ib in red shading. In that case, considering each time step as 653 independent in a given year is a strong assumption that is likely to give an underestimation of 654 the uncertainties. This highlights the complexity of assessing the uncertainty on a regional 655 mean temperature from in situ measurement and the large remaining uncertainty on this 656 estimation. As this paper is not dedicated to the estimation of in situ measurement errors we 657 use the red shading estimation in the main paper, which appears as a reasonable assumption.  10 5 --P20 20 10 --N10 -10 5 --N20 -20 10 --931