Causes of the 2015 North Atlantic cold anomaly in the ECCOv4 state estimates

. The subpolar North Atlantic is an important part of the global ocean and climate system, with SST variability in the region inﬂuencing the climate of Europe and North America. While the majority of the global ocean exhibited higher than average surface temperatures in 2015, the subpolar North Atlantic experienced record low temperatures. This interannual cold anomaly is thought to have been driven by surface forcing, but detailed questions remain about how the anomaly was created and maintained. To better quantify and understand the processes responsible for the cold anomaly, we computed mixed 5 layer temperature budgets in two releases of the ECCO Version 4 global ocean state estimate. These state estimates have been brought into consistency with a large suite of observations without using artiﬁcial sources or sinks of heat, making them ideal for temperature budget studies. We found that strong surface forcing drove approximately 75% of the initial anomalies in the cooling of the mixed layer in December 2013, after which the cold anomaly was sequestered beneath the mixed layer. Reemergence of the cold anomaly during the summer/autumn of 2014 was primarily the result of a strong temperature gradient 10 across the base of the mixed layer, with vertical diffusion accounting for approximately 70% of the re-emergence. Weaker surface warming of the mixed layer during the summer of 2015 enhanced the anomaly, causing a temperature minimum. Spatial patterns in the budgets also show large differences between the north and south of the anomaly region, with particularly strong initial surface cooling in the south related to the positive phase of the East Atlantic Pattern. It is important to note that this interannual cold anomaly, which is thought to be primarily driven by surface forcing, is distinct from the multi-decadal 15 North Atlantic "warming hole", which is thought to be primarily driven by changes in advection. coast, positive (warm) anomalies are only present during the summer, so do not strongly affect the 2015 annual average.

used in ECCOv4-r4 in comparison to ECCOv4-r3 (ECCO Consortium et al., 2021, see Table 2). We use the two releases to 90 show that the results are insensitive to the changes in model setup; the differences between them do not influence the ability to reproduce the 2015 cold anomaly within the model, nor do they affect the conclusions on the drivers of the cold anomaly.
However, a detailed analysis of how the model differences lead to differences in the representation of the cold anomaly is outside the scope of this paper. 95 We compute mixed layer temperature budgets for the North Atlantic using a well-established analysis method (e.g. Frankignoul, 1985;Peter et al., 2006;Dong et al., 2007), as described in Equation 1 below. We define the mixed layer depth (MLD), h m , as the depth at which potential density is 0.03 kg m −3 greater than that of the surface cell. The net rate of change in the average mixed layer temperature, T m , is attributed to surface heat fluxes, horizontal advection, entrainment of water from beneath the mixed layer, vertical and horizontal diffusion, and lateral induction, which describes the horizontal transport of water through 100 the base of a sloped mixed layer:

Mixed layer temperature budget
(1) Q net is the net heat flux into the surface ocean, and ρ 0 and c p are constants denoting reference density and specific heat capacity. The decay of incoming shortwave radiation within the top depth cells is represented by the function q (Chakraborty and Campin, 2013). u m is the lateral ocean velocity averaged over the mixed layer, and ∆T is the difference between the 105 average temperature of the mixed layer and that of the model depth cell immediately below. The entrainment velocity is defined as the rate of change in MLD, but this is set to zero for a shallowing mixed layer, since detrainment does not alter the properties of the remaining water in the mixed layer.
In output advection and diffusion terms following the steps set out by Piecuch (2017). The budget terms for each cell within the mixed layer were then averaged at each timestep to replicate the terms of the approximated mixed layer budget. The surface heat flux term of the budget is computed in the same way for each method, however the fully closed budget does not include the entrainment or lateral induction terms and so does not factor in the changing depth of the mixed layer. The results of these closed budgets are shown in the Appendix.

The 2015 cold anomaly in the state estimates
The 2015 cold anomaly is present in the SST of both state estimates (Fig. 2). As in the observations, the SST anomalies are most strongly negative when only the summer of 2015 is considered, but a clear cold anomaly is also seen when the anomalies are averaged over the whole year. The state estimates capture the overall pattern of the 2015 cold anomaly, especially within the box focused on throughout this study, although there are some spatial differences. In ECCOv4-r3, negative SST anomalies 140 occur throughout the box in the 2015 average (Fig. 2a), with slight positive anomalies further to the northeast and southwest, agreeing with observations. When averaged over summer only (Fig. 2b), the differences from the observations are clearer, with negative anomalies across the region but with a centre towards the north of the box rather than the southwest. In ECCOv4-r4, the negative anomaly in the 2015 average is similar to that of observations within the box (Fig. 2c), except for slight positive anomalies along the southern coast of Greenland. Positive anomalies also occur in the Labrador Sea when the SST anomaly 145 is averaged over the whole of 2015. However, in both the models and observations, the sign of the anomalies in this region is strongly dependent on the period over which the subtracted climatology is calculated. The positive anomalies in ECCOv4-r4  averaged over the cold blob region, for ECCOv4-r3 (red) and ECCOv4-r4 (blue). The shaded area marks the time period from when the initial cold anomaly begins to emerge to when the anomaly once again becomes positive.
are driven by warming from January to April, but when only summer is considered, the anomalies in this region are much closer to the observations (Fig. 2d).
In this work, we focus only on the anomalies within the box shown. Because the anomaly has no regular shape, and to 150 remove the effect of the warm anomalies along the Greenland coast in ECCOv4-r4 that are not seen in observations, we define the cold blob region as the area within the selected control volume with an average 2015 SST anomaly below zero. The results of the mixed layer temperature budgets are insensitive to the inclusion of these areas. When the SST anomaly is averaged over this region, the R 2 values between the time series of anomalies in HadISST1 observations and the state estimates are 0.92 for ECCOv4-r3 and 0.94 for ECCOv4-r4, for the period 1992-2015. 155 We focus on the cold anomaly within the mixed layer. The time series of the mixed layer temperature anomalies averaged over the cold blob region is therefore shown for each state estimate in Fig. 3. The 2015 cold anomaly is clear in the mixed layer temperature as the most negative anomalies over the time series, and there is little difference between the two state estimates (R 2 = 0.96). Negative temperature anomalies first appear in November 2013, decreasing to -0.9°C in April 2014, before switching to positive anomalies from July to September 2014. The anomalies then become negative again and decrease strongly, reaching 160 a minimum of -1.4°C in ECCOv4-r3 and -1.6°C in ECCOv4-r4 in August 2015. The linear trend in the anomalies in mixed layer temperature from the start of the cooling (December 2013) to the peak cold anomaly (August 2015) is -0.40°C yr −1 in ECCOv4-r3, and -0.48°C yr −1 in ECCOv4-r4. The anomalies then remain predominantly negative throughout 2016 and 2017.
The linear trend in the anomalies from the peak of the anomaly until the end of the ECCOv4-r4 time series (December 2017) is 0.56°C yr −1 .

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There are clear signatures of re-emergence in the vertical structure of the temperature anomalies and the MLD (Fig. 4).
The anomaly begins in the winter of 2013/14, and reaches a minimum within the shallow summer 2015 mixed layer. During 2013, weak warm temperature anomalies extend through the water column, before cold anomalies develop in the winter of 2013/14, extending throughout the deep winter mixed layer. The following summer, the mixed layer shallows and the negative anomalies are sequestered beneath, where they continue to decrease slowly. During this time, the mixed layer temperature 170 instead experiences positive (warm) anomalies, as seen within the average mixed layer temperature in Fig. 3. In October 2014, the mixed layer starts to deepen again and the cold anomaly re-emerges within the mixed layer. Further cooling occurs during the summer of 2015, with the minimum temperature occurring in each model within the shallow summer mixed layer.
Following the minimum, the cold anomaly is sustained through 2016 at a lesser magnitude (past the end of the ECCOv4-r3 time series), and is again sequestered below the mixed layer during the summer when very small anomalies are seen within the 175 shallow mixed layer. In general, both the warm anomalies prior to the formation of the cold anomaly, and the cold anomaly itself, are more intense in ECCOv4-r4. However, there is still very little difference between the two models when the average temperature of the mixed layer is considered (Fig. 3). At its deepest, the cold anomaly extends from the surface to depths of at least 500 m. During the formation of the cold anomaly, the depth of the winter mixed layer within the cold blob region

Processes driving seasonal temperature variability in the cold blob region
To determine the processes controlling temperature variability within the cold blob region, the average seasonal cycle of the mixed layer temperature budget was calculated (Fig. 5). This approach to computing the mixed layer temperature budget takes 185 into account the spatio-temporal variability in MLD, but due to the low temporal resolution of the model data and the various assumptions made in the method, there is a residual between the actual temperature tendency of the mixed layer and the sum of the budget terms driving that tendency. The warming of the mixed layer during summer is slightly overestimated (i.e. the sum of the temperature budget terms is greater than the actual temperature tendency within the model) and the cooling during winter is also overestimated, however the majority of the seasonal temperature variability is captured by the budget in each model.

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The horizontal diffusion and lateral induction terms are not shown as they have a negligible effect on temperature variability in the cold blob region.
The average seasonal cycle in temperature tendency within the region is dominated by the surface heat flux, which drives a warming of the mixed layer from April to August and a cooling of the mixed layer from September to March. The maximum seasonal warming due to surface forcing occurs in July (3.4°C month −1 in ECCOv4-r3, 3.1°C month −1 in ECCOv4-r4) and the maximum cooling occurs in November (-1.7°C month −1 in ECCOv4-r3, -1.6°C month −1 in ECCOv4-r4). Vertical diffusion is the second most important term, driving a cooling of the mixed layer from approximately May to September, with the maximum cooling occurring from July to August (-0.8°C month −1 in ECCOv4-r3, -1.0°C month −1 in ECCOv4-r4). This seasonal variability in diffusive cooling is driven by the seasonality in the temperature difference between the mixed layer and thermocline, with a greater difference when the mixed layer is shallow in summer. This relationship is further discussed in 200 section 3.4.
No vertical entrainment occurs from December to July due to the shallowing mixed layer, but entrainment cools the mixed layer from August to October/November, as the mixed layer deepens and entrains colder water from below. In each model, the maximum mixed layer cooling via entrainment occurs in September, when the rate of deepening of the mixed layer is highest. The impact of entrainment is small, causing a maximum cooling of -0.2°C month −1 in both models. Advection is 205 also low throughout the year; in ECCOv4-r3, a slight advective cooling of the mixed layer occurs from January to March with a maximum of -0.2°C month −1 , but is negligible through the rest of the year, and in ECCOv4-r4 advection is always close to zero. While there are some differences between the model results, the dominant processes of the mixed layer temperature budget show very similar seasonal cycles. and meridional advection. Approximately 75% of the anomalous initial cooling of the mixed layer is therefore due to surface forcing, while the remaining 25% is predominantly a result of horizontal advection.

Processes driving the 2015 cold anomaly
Following the initial cooling, anomalies in each of the main temperature budget terms are then low until April 2014, when higher than average surface warming drives overall positive anomalies in the temperature tendency from April to June (Fig. 6).
Since the mixed layer is shallow over this period, while the surface warming acts to increase the average temperature of the 225 mixed layer, it has a relatively small effect on the heat content of the water column. The warming of the mixed layer is also suppressed by strong vertical diffusion, driven by the high temperature difference between the mixed layer and thermocline ( Fig. 7c). The temperature difference is greatest during summer when the mixed layer is shallow and heated by strong surface  The re-emergence of the cold anomaly is also enabled by the deepening of the mixed layer, which results in the entrainment 235 of colder water from below. The mixed layer cooling via entrainment in the ECCO models is small, with anomalies peaking during August at -0.1°C month −1 in both models. The depth of the mixed layer is not particularly anomalous during the winter of 2014 (Fig. 7b), especially in comparison to the following two years, and the timings of the minima in entrainment anomalies do not always correspond to anomalies in MLD. It is therefore the large temperature difference between the mixed layer and thermocline that drives the re-emergence of the cold anomaly, primarily through vertical diffusion, with the cooling where positive values signify that the mixed layer is warmer than the thermocline, and the associated vertical diffusion term of the mixed layer budget (°C yr −1 ; red). Note, the seasonal cycle has not been removed from either term in c).
of the mixed layer enhanced by entrainment during the autumn of 2014. The process of the re-emergence following the strong cooling of December 2013 is illustrated in Fig. 8   for ECCOv4-r4, however very similar results for ECCOv4-r3 can be found in the Appendix (Fig. A2-A4). In general, the magnitude of the anomalies in the temperature budget terms is reduced in the north due to a meridional gradient in winter MLD, with deeper mixed layers in the north of the region.
The surface-driven cooling that drives the initial cold anomaly is much stronger in the south, with two clear peaks in October and December 2013 (Fig. 9b). The strongest surface-driven cooling of -1.0°C month −1 occurs in December, compared to 265 -0.3°C month −1 in the north. This is a result of the stronger surface ocean heat loss (Fig. 10a,b) and because the mixed layer is generally shallower in the south, so smaller anomalies in net heat flux are required to impact the average mixed layer temperature. A second earlier minimum in surface-driven cooling of the mixed layer is also clear in the south in October 2013, due to a a higher than average heat flux out of the surface ocean (Fig. 10b). In the north, 85% of the total cooling anomalies during December 2013 is a result of surface forcing, while the remaining 15% is due to advection. In the south, the effect of  advection is greater, driving approximately 30% of the initial cooling anomalies in December 2013, while the remaining 70% is due to surface forcing.
In the summer of 2014, the surface-driven warming is stronger in the south, but leads to a much greater temperature gradient across the base of the mixed layer than in the north (Fig. 10e,f), and subsequent stronger diffusive cooling of the mixed layer.
The maximum diffusion in the south occurs in August 2014, reaching -0.6°C month −1 , while the maximum in the north reaches 275 only -0.3°C month −1 . This diffusive cooling is followed by stronger negative tendency anomalies in the north in September 2014, caused by a combination of surface fluxes, advection, entrainment and diffusion (Fig. 9a). The most negative anomalies are in the surface flux term, reaching -0.3°C month −1 , and are caused by negative anomalies in the heat flux into the ocean, which are not seen in the south (Fig. 10a,b). Anomalies in entrainment at this time are due to the continued strong temperature gradient across the base of the mixed layer, rather than anomalies in the MLD (Fig. 10e). Despite the anomalies generally 280 being of a lower magnitude in the north, the strongest entrainment is a similar level to that in the south (Fig. 9), meaning that entrainment plays a greater role in the re-emergence of the cold anomaly in the north. Entrainment drives a mixed layer cooling also of -0.1°C month −1 in August 2014 in the south, before driving a further cooling of -0.1°C month −1 a month later in the north. While the temperature gradient at the mixed layer base is weaker in the north, anomalies in the MLD are much larger (Fig. 10c,d), leading to entrainment of a similar magnitude in both regions. In the north, anomalies in processes driving 285 re-emergence from June 2014 to February 2015 are approximately 60% a result of vertical diffusion, and 40% entrainment. In the south, where the impact of entrainment is lesser, the re-emergence over this period is a result of approximately 80% vertical diffusion and 20% entrainment.
In January 2015, strong surface heat loss in the north of the cold blob region (Fig. 10a) is not replicated in the surface flux term of the mixed layer budget, due to concurrent large anomalies in MLD. While surface forcing still drives a cooling of the 290 mixed layer in January 2015, anomalies in the term are slightly positive as greater surface heat loss would be required to affect the temperature tendency of the greater volume of water in the mixed layer. The weakened surface-driven warming (negative anomalies) in the summer of 2015 leads in the north with a peak of -0.6°C month −1 in May, followed by a peak in the south of -1.0°C month −1 in July (Fig. 9). In both cases, the negative anomalies are due to weak negative anomalies in the net heat flux (Fig. 10a,b) into a shallow summer mixed layer. In both the north and the south, the anomalies lead to the strongest SST 295 anomalies in the summer of 2015 (Fig. 11). Anomalies in the surface warming of the mixed layer are positive from January to July 2016 in the north of the cold blob region, acting to diminish the cold anomaly. Positive anomalies in the surface flux term in the south also reach a similar magnitude, but oscillate between positive and negative. The processes driving the cold anomaly in the north and south of the cold blob region are illustrated in Fig. 11. 3.6 Drivers of the surface-driven cooling of the mixed layer 300 While multiple processes are important for the evolution of the 2015 cold anomaly, the anomaly would not have developed without the initial strong surface cooling in December 2013. Since there are clear differences in the magnitude of the heat flux out of the ocean in the north and south of the cold blob region during this period (Fig. 10a,b), the spatial distribution of anomalies in that heat flux is shown in Fig. 12a. To further understand the reasons for those spatial patterns, the simultaneous anomalies in the zonal and meridional components of the surface wind stress are also shown (Fig. 12c,e) as well as the 305 anomalies in MLD (Fig. 12g).
While the negative anomalies in the surface heat flux extend across the majority of the subpolar North Atlantic in December 2013, the most negative anomalies occur in the cold blob region south of 54°N, and to the northwest in the Labrador Sea ( Fig. 12a). Averaged over the entire cold blob region, the heat flux out of the surface in December 2013 is approximately 45% greater than the climatological mean. At the same time, the usual westerly winds over the subpolar gyre are much stronger in 310 the southern half of the North Atlantic and in the Labrador Sea (Fig. 12c), matching the patterns of negative anomalies in the

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Strong surface forcing in the winter of 2014/15 has also previously been observed, linked to the positive state of the NAO (Yeager et al., 2016;Josey et al., 2018). However this was not seen in the anomalies of the mixed layer temperature budget, in  either the north or the south of the cold blob region (Fig. 9). Strong negative anomalies in the net surface flux into the ocean were present in January 2015 and the spatial distribution of these anomalies is shown in Fig. 12b. There are clear negative anomalies in the north which have a similar spatial pattern to positive anomalies in the zonal wind stress (Fig. 12d). At the 325 same time, anomalies in the meridional wind stress are slightly positive across the majority of the cold blob region (Fig. 12f).
Anomalies in the MLD in January 2015 (Fig. 12h) explain why the increased surface heat loss does not result in negative anomalies in the mixed layer temperature: the mixed layer is anomalously deep in the north of the cold blob region, so stronger surface forcing is required to affect the average temperature of the larger volume of water in the mixed layer. Therefore, while the mixed layer is cooling during January 2015, that cooling is no greater than the climatological average. Since the strong 330 surface forcing extends to the east of the box defining the cold blob region (Fig. 12a,b), the mixed layer budget was repeated  (Marshall et al., 2001). Positive NAO conditions have previously been shown to result in a particularly strong increase in the westerly winds in the Irminger Sea due to the interaction between the large scale flow and the Greenland topography (Doyle and Shapiro, 1999;Moore, 2003), as seen in the spatial distribution of zonal wind stress anomalies in While the deepening mixed layer did result in the entrainment of colder water from below, we found that this entrainment of colder water was not enough to explain the re-emergence of the cold SST anomaly. Instead, vertical diffusion dominated, while 365 entrainment was still important but had a weaker influence. The re-emergence, via anomalies in both vertical diffusion and entrainment, appears to have been largely a result of the strong temperature gradient across the base of the mixed layer, which was particularly high in the summer/autumn of 2014 due to summer surface warming. The relative importance of entrainment was greater in the north of the cold blob region, where deeper winter mixed layers resulted in larger entrainment velocities in the autumn, though it was still a secondary process in comparison to the influence of vertical diffusion.
Since the mixed layer budgets were approximated and the diffusivity values chosen in order to reduce the error in the budgets, there is some error in the magnitude of the vertical diffusion term. However, the closed mixed layer temperature budget shows similar levels of diffusive cooling during the summer/autumn of 2014 (Fig. A1), giving further confidence in our results. Our chosen method of computing the budgets allows us to directly relate the levels of entrainment and vertical diffusion to changes in MLD and temperature, in order to describe the process of the re-emergence of the cold anomaly in greater detail. Since advection played a minor role in comparison to surface forcing in driving the cooling that caused the cold anomaly to develop, particularly in the south of the region, we can conclude that the 2015 cold anomaly was largely the result of vertical processes, i.e. surface forcing, vertical diffusion, and entrainment. The dynamics of the 2015 cold anomaly could therefore 390 likely be represented by a one-dimensional model, albeit with a slightly underestimated magnitude.

Increased convection during the cold anomaly
During the 2015 cold anomaly, the depth of the winter mixed layer in the cold blob region increased, reaching a maximum depth during the winter/spring of 2015. At the same time, the mixed layer in the region was undergoing a longer term freshening (Holliday et al., 2020), which is also present in the ECCOv4 state estimates (Fig. 13). The freshening indicates that the 395 interannual deepening of the winter mixed layer was the result of stronger temperature-driven convection, while changes in salinity instead acted to stratify the mixed layer. The subsequent increased production of Subpolar Mode Water following the enhanced convection has also been suggested to have exacerbated the freshening via its impact on the velocity of the North Atlantic Current (Holliday et al., 2020). The timing of the fresh anomalies in ECCOv4 support this theory, with the strongest fresh anomalies occurring in the aftermath of the peak cold anomaly and the enhanced convection.

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Average winter mixed layers are deeper in the north of the North Atlantic in comparison to further south. The MLD anomalies relative to the climatology were also much deeper in the north of the cold blob region over the evolution of the cold anomaly.
MLDs were especially deep in the winter of 2015, explaining the stronger influence of entrainment in the north. The increased convection also had subsequent effects on the other terms of the temperature budget, with the differences in the depth of the mixed layers between the northern and southern regions leading to differences in how the mixed layer was impacted by 405 anomalies in the overlying atmospheric conditions. This shows the importance of considering the spatial patterns in the drivers of this and similar cold anomalies in the North Atlantic, particularly the meridional differences in forcing.

Mixed layer budgets in ECCO
Following the methods of previous studies (Frankignoul, 1985;Peter et al., 2006;Dong et al., 2007), we chose to approximate the mixed layer temperature budgets using monthly mean values, as opposed to values from each model timestep. Because our 410 chosen method uses a certain set of well-understood assumptions, including the concepts of entrainment and lateral induction, it provides unique insights into the evolution of the mixed layer that would be unclear or unavailable in a closed-budget representation. This may sound counter-intuitive, since closed budgets are desirable in a large number of applications. The advantage comes from the fact that entrainment and lateral induction represent the average effect of how the temporally-varying mixed layer interacts with its environment over a chosen time period, in our case one month, in a way that is not captured by 415 following the mixed layer at each timestep. The view of the mixed layer produced by this method should be considered as one among many, as different views will complement each other and help us build a more complete understanding of mixed layer evolution. That being said, for validation purposes, we did compare the similarities between the anomalies in our mixed layer budgets and those in the fully closed budgets, and we found them to be similar (See Appendix). Note the non-uniform spacing of the vertical axes.
The two ECCOv4 state estimates used here are relatively coarse in terms of their horizontal resolution. Unresolved processes 420 are represented by mixing and bolus transport schemes whose parameters have been optimized by the 4D-VAR process, partially offsetting the limitations of the coarse model resolution. In particular, (Forget et al., 2015b, Fig. 4) showed that optimizing the spatially-varying mixing coefficients in ECCOv4 greatly improved the representation of its water mass properties.

Conclusions
In this work, we used the ECCOv4 state estimate to analyze the causes of the 2015 North Atlantic cold anomaly. The anomaly 425 was primarily driven by strong surface forcing; specifically, anomalous winds were responsible for the majority of the initial cooling in the winter of 2013/14. This cooling was strongest in the south of the anomaly region, related to the strongly positive EAP. The re-emergence of the cold anomaly the following winter was primarily driven by vertical diffusion due to a strong temperature gradient across the base of the mixed layer, while entrainment over the same period was relatively weak. Although anomaly region was not reflected in the mixed layer temperature, as deeper winter mixed layers masked the impact of surface cooling on temperature. Advection played a minor role in the evolution of the cold anomaly, however more work on the processes occurring beneath the mixed layer would be useful for determining whether advection was the cause of the continued cooling of the sequestered cold anomaly. Further work investigating the cold anomaly in higher resolution models would also be a welcome addition to the literature.

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and is described by Rayner et al. (2003) .  where positive values signify that the mixed layer is warmer than the thermocline, and the associated vertical diffusion term of the mixed layer budget (°C yr −1 ; red). Note, the seasonal cycle has not been removed from either term in c).