Meridional heat transport due to mesoscale / submesoscale eddies 

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Volume change estimate due to SSH variability

We examined both the seasonal variability and interannual variability of the SSH volume, in order to compare its order of magnitude with the horizontal geostrophic volume transport convergence over the EDW formation region. During a typical seasonal cycle (for example in 2002 in Figure 2-5), the SSH volume peak-to-peak variablity is about: 2:3 1012m3 􀀀 1:7 1012m3 = 0:6 1012m3 = 0:02 Svy Given the area of EDWformation region is 4:321012m2, the SSH seasonal variability averaged over the EDW formation region is: 0:6 1012m3=(4:32 1012m2) 0:125m.
This seasonal variability is due to the thermosteric component of the SSH. During the period of 2002-2015, the change of volume is about: 2:3 1012m3 􀀀 1:8 1012m3 = 0:5 1012m3 = 0:016 Svy The SSH associated volume in the EDW formation region roughly increased by 0:016 Svy over 14 years. This translates into an annual trend of : 0:5 1012m3=14yr 0:036 1012m3 yr􀀀1 = 1:1 10􀀀3 Sv That is, on average over the domain, a change of SSH of: 0:036 1012(m3 yr􀀀1)=(4:32 1012m2) 0:008myr􀀀1.
To summarize, the volume rates of change due to SSH, both in the seasonal cycle and on a decadal scale, are much less in order of magnitude, than the horizontal volume uxes at the boundaries or than the vertical volume ux at 800m in depth.
This inferiority of SSH’s role in volume rate of change holds regardness of its subcomponents due to thermal expansion, or due to dynamic factors.

Closing the heat budget: inverse model approach

The direct calculation of the budget from dierent data sources led to unbalanced volume and heat budget in the domain of study. To ensure that volume and heat are conserved over the domain, we developed an inverse model. The inverse problem serves to solve the problem of inverting a Fredhold integral equation of the rst kind. (Jackson, 1979). y() = Z b a x()K(; )d + e(). where a and b are x contants. x() is an unknown function, that often describes the internal » properties, for example, the velocity eld, that needs to be corrected. K(; ) is a known Kernel function, which, in the linear case, is a prescribed eld (temperature, density, or salinity) , y() is an observed function, which often describes the measured external » properties. e() is a random error function. In the linear space, after discretization in and , Equation 2.12 is rewritten in the form of Y(X) = AX.

To identify EDW

The EDW, on a T/S diagram (Figure 2-13 a and b) is identied as the nearly homogeneous water mass around 18oC in temperature and 36:0 􀀀 36:7psu in salinity (Speer and Forget, 2013). To identify the EDW there are dierent criteria (Forget et al., 2011). The EDW was to the rst order selected as the water with temperature between 17􀀀19oC , a common and rough criteria to identify EDW also used by Worthington 1976, Kwon and Riser 2004, Maze et al. 2009, Forget et al. 2011 etc. Moreover, a stratication criteria is often added to address the homogeneity of the EDW. Kwon and Riser (2004) used vertical temperature gradient @T=@z < 0:006oC m􀀀1, and Forget et al. (2011) examined the EDW volume using two potential vorticity criteria: PV < 1:5 10􀀀10m􀀀1s􀀀1 and PV < 2:0 10􀀀11m􀀀1s􀀀1.

Temperature criteria

We used the 17-19 degree layer to obtain a primary estimate of EDW volume time series. Figure 2-14(a) shows the climatological EDW thickness for the 1966-2017 period. The thickness reaches more than 300m along the equatorward ank of the Gulf Stream Extension, with a monthly standard deviation reaching 80m slightly to the north of climatological mean maximum. Figure 2-14(b) shows the typical seasonal cycle of EDW volume. We see from April to October, a rapid and then steady erosion of the EDW volume mainly driven by mixing with the seasonal pycnocline (Billheimer and Talley, 2016b). From November to March, the EDW volume increases, reaching the largest volume in March. The EDW seasonal formation is primarily driven by surface water mass transformations related to winter time buoyancy loss (Forget et al., 2011; Maze and Marshall, 2011). The seasonal cycle amplitude is 1:55 1014m3, a value that is in line with Forget et al. (2011) estimate. The interannual variability amplitude is 5:0 1014m3, a value that is remarkably larger than the seasonal cycle. Again, our estimate is in line with the bibliography (Kwon and Riser, 2004; Levine et al., 2011).
Figure 2-14 shows the thickness standard deviation pattern, that is mainly associated with the seasonal ventilation of the mode water through the mixed layer seasonal variability (not shown). Indeed, our maximum standard deviation region corresponds to the EDW formation region, as described by Maze et al. (2009) for instance. Note that we used the seasonal maximum area between 17oC􀀀19oC as the EDW seasonal maximum outcropping region (referred to as outcropping region).

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Ventilated EDW volume

The mixed layer is an ocean surface layer in direct contact with the atmosphere, stirred by turbulence, homogenizing temperature and other properties within some range of depths. Surface ocean cooling and salinization, associated with negative surface buoyancy ux, sensible heat loss, or latent heat loss due to surface evaporation, increase surface water density, leading convective motion within the mixed layer. The depth of this nearly homogeneous layer, namely the mixed layer depth (MLD), generally is about 50􀀀100m with large global spatial variation. In northern North Atlantic region, the MLD can exceed 1000 m. In subtropical region, along the equatorward ank of western boundary current, the MLD can reach 300􀀀500m, which allows the formation of volumnous pycnostad. Note that below the mixed layer, temperature and salinity change rapidly with depth, in the summer time, forming the seasonal pycnocline.
We examined the winter ventilated EDW volume, not including the EDW that is trapped under the mixed layer. We selected the winter surface EDW outcropping regions, with sea surface density ranging from 26:2􀀀26:6 kgm􀀀3, and integrating this outcrop down to the mixed layer depth. The mixed layer depth is evaluated using the second criteria developed by de Boyer Montégut et al. (2004), as the depth of the sea water denser than that of 10-meter by 0:02kg=m3.

Table of contents :

1 INTRODUCTION 
1.1 North Atlantic subtropical stratication
1.1.1 EDW subduction and obduction
1.1.1.1 Subduction at southern ank of EDW bulk
1.1.1.2 Subduction estimates
1.1.2 Air-sea heat uxes
1.1.3 Geostrophic heat advection
1.1.4 Ekman current
1.1.5 Mesoscale eddies at the Gulf Stream northern ank
1.1.6 Mesoscale/submesoscale eddies at the southern ank
1.2 Air-sea coupling near Gulf Stream
1.2.1 Impact by NAO
1.2.2 Feedback to NAO
1.3 Preconditioning
2 Data and Method 
2.1 Datasets
2.2 Domain of study
2.3 Heat budget calculation
2.3.1 Equations
2.3.2 Terms
2.3.3 Geostrophic current
2.3.4 Ekman current
2.3.5 Volume change estimate due to SSH variability
2.3.6 Closing the heat budget: inverse model approach
2.3.6.1 Our model
2.3.6.2 Stochastic inversion
2.3.6.3 Validation
2.4 Gulf Stream positioning
2.5 To identify EDW
2.5.1 Temperature criteria
2.5.2 Density-stratication criteria
2.5.2.1 Ventilated EDW volume
2.6 Interannual time scales
2.6.1 Signal decomposition
2.6.2 Time ltering
2.7 Denition of extremes
2.8 Buoyancy Budget
2.8.1 Fixed-domain buoyancy content anomaly BCASep
2.8.2 Relative September buoyancy content anomaly
2.9 Weather Regimes
3 Heat Budget 
3.1 Abstract
3.2 Introduction
3.3 Direct Results
3.3.1 Periods with and without OHC extremes
3.3.2 Interannual Variability
3.3.3 Major contributing factors to OHC variability
3.3.4 Frequency component of OHC and its major contributing factors
3.3.5 OHC explained variance
3.3.6 Recirculation gyre
3.3.7 Gulf Stream positioning
3.3.8 Air-sea heat uxes
3.3.9 OHC extreme occurrences
3.4 Discussion
3.4.1 AMOC: the 1990s sudden increase and 2009-2010 slowdown .
3.4.1.1 Two periods of OHC extreme absence
3.4.2 Meridional heat transport due to mesoscale / submesoscale eddies
3.4.3 Interannual band-pass lter
3.5 Summary
4 Eighteen Degree Water extreme formation years 
4.1 Abstract
4.2 Introduction
4.2.1 Extreme years in EDW freshly ventilated volume
4.2.2 Ekman current
4.2.3 EDW subduction and obduction
4.2.4 EDW formation volume
4.3 Results
4.3.1 Extreme occurrences over a multi-decadal period
4.3.2 EDW renewal spatial distribution
4.3.3 Interannual variability of EDW ventilated volume
4.3.4 OHC of the September-March period
4.3.5 Air-sea heat ux
4.3.6 Ekman eects
4.3.7 NAO
4.3.8 Preconditioning
4.3.9 A brief summary of the direct results
4.4 Discussion
4.4.1 Ventilated Volume and Subducted Volume
4.4.2 Wind-driven Heaving
4.4.3 EDW outcropping volume
4.4.4 Annual maximum outcropping area
4.4.5 Geostrophic transport at 30oN
4.4.6 Uncertainty of geostrophic transport at 30oN
4.4.7 EDW convection due to the Ekman term
4.4.7.1 OHC and EDW volume
4.5 Summary
5 Conclusions and Future Work 
5.1 Conclusions
5.2 Future Work
A Weather conditions and Weather regimes 
A.1 Introduction
A.2 Results
A.2.1 Impact of NAO through Ekman heat divergence
A.2.1.1 Atmospheric states
A.2.1.2 Weather conditions
A.2.2 Winter storm watch
A.2.2.1 Strong EDW formation years: 2005, 2010, and 2013 .
A.2.2.2 Weak EDW formation years: 2008, 2012, 2014, and 2015
A.2.2.3 Intermediate EDW formation years: 2011 and 2018 .
A.2.2.4 Surface wind stress curl
A.2.3 Impact of Atlantic Ridge/Blocking through Air-sea heat uxes
A.2.3.1 10m surface wind speed
A.2.3.2 Air-sea surface heat uxes
A.2.3.3 EDW volume composites
A.2.3.4 Impact of NAO through Gulf Stream
A.3 Discussion
A.3.1 Wind stress curl
A.3.2 Zero-year lag impact
A.3.3 Lagged correlation
A.4 Summary
B Buoyancy Budget 
B.1 A hybrid buoyancy model
B.1.1 Results
B.2 Fixed-domain BCASep
B.2.1 Role of preconditioning for extreme years
B.3 Discussion
B.3.1 Seasonal cycle
B.3.2 Interannual variability
B.3.3 BCA
Sep v.s. xed-domain BCASep
C Eective Resolution 
C.1 Signal smoothing: Gaussian kernel optimization
D Heat budget climatology and seasonal cycle
D.1 Climatology
D.2 Seasonal cycle
E Heat budget error estimates 
E.1 2002-2019 time series
E.2 Interannual variabilities

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