A dynamically based method for estimating the Atlantic meridional overturning circulation at 26°N from satellite altimetry

. The large-scale system of ocean currents that transport warm waters in the upper 1000 m northward and return deeper cooler waters southward is known as the Atlantic meridional overturning circulation (AMOC). Variations in the AMOC have significant repercussions for the climate system, hence there is a need for long-term 10 monitoring of AMOC fluctuations. Currently the longest record of continuous directly measured AMOC changes is from the RAPID-MOCHA-WBTS programme, initiated in 2004. The RAPID programme, and other mooring programmes, have revolutionised our understanding of large-scale circulation, however, by design they are constrained to measurements at a single latitude and cannot tell us anything pre-2004. Near-global coverage of surface ocean data from satellite altimetry is available since the launch of TOPEX/Poseidon satellite in 1992 and has been shown to provide reliable estimates of surface ocean transports on interannual time scales including previous studies that have investigated empirical correlations between sea surface height variability and the overturning circulation. Here we show a direct calculation of ocean circulation from satellite altimetry of the upper mid-ocean transport (UMO), the Gulf Stream transport through the Florida Straits (GS), and the AMOC using 20 a dynamically based method that combines geostrophy with a time mean of the vertical structure of the flow from the 26°N RAPID moorings. The satellite-based transport captures 56%, 49%, and 69% of the UMO, GS, and AMOC transport variability, respectively, from the 26°N RAPID array on interannual (18-month) time scales. Further investigation into the vertical structure of the horizontal velocity shows that the first baroclinic mode accounts for 83% of the interior geostrophic variability, the barotropic mode accounts for 82%, and the combined 25 barotropic and first baroclinic mode account for 98% of the variability. Finally, the methods developed here are used to reconstruct the UMO and the AMOC for the time period pre-dating RAPID, 1993 to 2003. The effective implementation of satellite-based method for monitoring the AMOC at 26°N lays down the starting point for monitoring large-scale circulation at all latitudes.

the vertical structure of the horizontal flow to develop a satellite-based MOC transport on interannual time scales.
In contrast to earlier efforts by Hirschi et al. (2009) and Kanzow et al. (2009), the longer records now available at RAPID enable us to test the methods for longer timescales (interannual, rather than sub-annual), and we find that the 110 skill is generally higher at interannual timescales than at shorter timescales. Unlike Frajka-Williams (2015), this method now uses geostrophy (east minus west differences in sea level anomaly) rather than finding the point location where the sea level anomaly has the strongest correlation with the transport variability. This change in the method is a prerequisite to developing similar methods at other latitudes as it reduces (though does not entirely eliminate) the requirement for in situ data to 'train' the method. In addition, while Szuts et al. (2012) and Clement et 115 al. (2014) found that multiple modes are required to explain the variance in the western boundary profiles, we show that on interannual timescales, the contributions from higher modes are reduced and the first mode explains a majority of the variance. In the following section (2), a brief overview of data and methods used here are presented.
Then an evaluation of the satellite data and parameters from the RAPID moorings follows in section 3. Rossby wave theory and an in-depth analysis of horizontal velocity normal modes from RAPID mooring data is shown in section 120 4. Sections 5 and 6 investigate construction of the upper mid-ocean, the Gulf Stream, and the AMOC transports from satellite altimetry. Finally, summary and conclusions are given in section 7.
The third component, , is the sum of the western boundary wedge transport ( ), the hypsometric mass compensation ( ), and the internal geostrophic transport ( ) over the top 1100 m. is the northward 185 transport measured between the Abaco Island continental shelf and the WB2 mooring. functions to compensate so that the net meridional flow is zero, and is the internal geostrophic [southward] transport.
Through geostrophic balance, the meridional mass transport is proportional to the integrated pressure difference between the eastern ( ) and western ( ) basin endpoints such that: where f is the Coriolis parameter, 0 is reference density, and is the reference level at -4740 m.. Pressure at z = -h is then related to sea level displacement and the vertical profile of density as follows: where g is gravitational acceleration and is satellite SLA.

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Satellite altimetry measures the surface geostrophic velocity, but surface geostrophic velocity does not give us information about the vertical structure of the horizontal velocity, thus time-varying geostrophic flow is combined with the first mode of horizontal velocity to obtain (section 4 and 5). The is estimated using satellite altimetry and linear regression (section 5). The is constructed by adding the satellite-derived and with the obtained from ERA5 wind stress as per Eq.
(2) (sections 5 and 6). In the following sections, the 205 relationship between satellite and vertical structure of the flow from the moorings is used to develop a new method for estimating AMOC transport.

Evaluation of the satellite and mooring data
The CMEMS absolute dynamic topography (ADT) is computed as the sum of SLA and mean dynamic topography (MDT). The MDT is a mean estimate of SSH above the geoid over the given reference period 1993 to 2013 (Rio et 210 al., 2018; further details on this data product here: https://www.aviso.altimetry.fr/en/data/products/auxiliaryproducts/mdt.html). The ADT shows characteristics of the mean state North Atlantic with negative ADT marking the subpolar gyre in the north (>= 48°N; Fig. 1a) and positive ADT delimiting the subtropical gyre, largely occupying the region between 15°N and 40°N (<40°N; Fig. 1a). Key features are observed at 36°N, where positive wheeling jet, eventually feeding into the North Atlantic Current on its path northward. The negative ADT around the region of the Grand Banks (48°N) is representative of the equatorward flowing Labrador Current that supplies the Slope Sea just north of the Gulf Stream (e.g. Petrie and Drinkwater, 1993;Frantantoni and Pickart, 2007) influencing its position (Pena-Molino and Joyce, 2008;Sanchez-Franks et al., 2016). The Labrador Current is also part of the surface flowing limb of the AMOC. The apparent bipolar structure over the North Atlantic is similar to 220 the EOF mode 1 of the North Atlantic, characterized by Zhang (2008) as the AMOC fingerprint. The standard deviation of the ADT shows most of the variability is contained within the region of the Gulf Stream after it separates from Cape Hatteras (Fig. 1b). This variability is due to the large latitudinal shifts in the Gulf Stream position following changes in the North Atlantic Oscillation (e.g. Sanchez-Franks et al., 2014;Sanchez-Franks et al., 2015;Perez-Hernandez andJoyce, 2014, Bisagni et al., 2017;Taylor and Stephens, 1998). Further details of 225 AMOC are reviewed in Zhang et al., (2019).
In the region of the RAPID 26°N mooring array ( Fig. 1a,b), the time-varying ADT at western and eastern points show substantially higher mean and fluctuations in the western boundary (0.73 m root mean square (RMS)) compared to the eastern boundary (0.21 m RMS) over the 2004 to 2018 period (Fig. 1c). Variability from the cross-230 basin pressure gradient is largely driven by the variability along the western boundary on lower frequency (periods longer than a year) timescales (Frajka-Williams, 2015).

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The RAPID programme estimates geostrophic transport from the difference between the basinwide eastern and western endpoint pressure fluctuations (Eq. 3). Correspondingly, to construct a estimate from satellite altimetry, the time-varying east-west SLA difference (∆ ) is compared at each gridpoint with the RAPID . applied. In general correlations are highest in the western part of the basin in the 26-30°N latitudinal band, and in the east for roughly the same latitudes between 25-35°W (Fig. 2a). It is interesting to note that the correlations along the RAPID line are lower than those found at higher latitudes 27-30°N. This could be due to an improvement in the 245 signal to noise ratio further north.
The correlation map illustrates the optimal choice of longitude and latitude coordinates for max correlation of ∆ with RAPID , r = 0.74 (statistically significant at 95% level), where the eastern SLA gridpoint is located at 27.875°N and 13.125°W and the western SLA gridpoint is located at 27.875°N and 74.375°W (Fig 2a). The east and 250 west dynamic height measurements from the moorings make up the interior geostrophic component of the RAPID (section 2.2); however, the also includes contribution from the Antilles Current. For the satellite data to account for as much of the upper mid ocean transport variability as possible, it is advantageous to use satellite endpoints as shown in Fig. 2a to calculate ∆ , which here appears to better reflects the changes in the meridional mass transport. This is consistent with other studies which have similarly found higher agreement between RAPID 255 transport and satellite variability north of 26°N (e.g. Frajka-Williams, 2015). Further, sensitivity of the correlation between RAPID and ∆ to the choice of filter was tested for 6 month intervals at 6 month, 12 months and 24 months, in addition to the 18 month Gaussian filter (Fig. S1). The pattern of correlations between RAPID and ∆ across the subtropical North Atlantic remained generally consistent between the four different choices of filter (as described above for the 18 month filter), where correlations decreased (for eastern SLA 260 gridpoint located at 27.875°N and 13.125°W and the western SLA gridpoint located at 27. 875°N and 74.375°W) and were lowest at r = 0.48 (statistically significant at 95% level) using 6 month filtering, increasing to r = 0.67 using 12 month filtering, and r = 0.79 when using the 24-month filter, contrasted with r = 0.74 when using the 18month filter.

Variability in the vertical
In order to determine how well the SLA can estimate the upper 1000 m circulation, it is useful to assess to what depth the variability from SLA captures sub-surface variability. Thus SLA is compared to the dynamic height (Eq. 1) at every depth from the surface to 1100 dbar from the RAPID moorings in the western and eastern boundary. Fig.   270 2b shows the correlation (r values) between SLA west and east gridpoints (as indicated in previous section) and dynamic height from the RAPID moorings: West, WB3 and EB. In this section only, the respective RAPID mooring dynamic height has been referenced at the surface to SLA (hereafter ) to get correlation value of 1 at the surface which decreases with depth to assess to what depth surface variability is coherent. In the western boundary, SLA at 27.875°N and 74.375°W is compared with both WB3 and West, and the correlation in the top 1100 dbar is found to 275 be everywhere greater than r = 0.79 (r = 0.79; statistically significant at 95% level). SLA has a higher correlation with at mooring West, compared to WB3, maintaining a statistically significant correlation coefficient above r = 0.88 (statistically significant at 95% level) in the top 1100 dbar. Correlation between SLA and WB3 decreases more abruptly at around 300 dbar. In the eastern boundary, correlation between SLA at 27.875°N and 13.125°W and at EB is similarly high throughout the top 1100 dbar of the ocean, albeit weaker compared with the western boundary 280 mooring, with correlations from r = 1 at the surface decreasing to r = 0.77 (statistically significant at 95% level) at a depth of 1100 dbar (Fig. 2b). These results suggest that the variability observed at the sea surface is a good measure and coherent with variability to at least a depth of 1100 dbar. This is in agreement with Clement et al. (2014) who showed that isopycnal displacements at the RAPID western mooring locations agree well with satellite data.
Specifically, Clement et al. (2014) did a similar analysis using profiles of isopycnal displacements, instead of 285 dynamic height, from the moorings and satellite. They found statistically significant correlation (r = 0.5 -0.6) between WB3 and WB2 with SSHA, respectively, in the upper 1000 m over 2004 to 2011. They did not analyse moorings in the eastern boundary. Given that here we have referenced the dynamic height to SLA at the surface, as well as a longer time period and different filtering, the discrepancies between our studies are reasonable.
For completeness, the SLA is also compared to dynamic height anomaly thickness for the 0-1100 dbar layer ( Fig.   290 S2). The dynamic thickness is calculated from the difference in dynamic height (referenced to 4820 dbar) at 0 and 1100 dbar and gives a measure of the shear between those levels (independent from choice of reference level). In both the western and eastern basin, the dynamic height thickness anomaly has a standard deviation smaller (0.30 m 2 s -2 at WB3 and 0.07 m 2 s -2 at East) than the SLA multiplied by gravitational acceleration (0.70 m 2 s -2 in the west and 0.14 m 2 s -2 in the east). This result suggests that the baroclinic structure in the upper 1100 dbar is not overwhelming 295 the SLA signal, and the SLA can be used for transport estimates in the upper 1100 dbar.

Westward propagation
Wind stress and density fluctuations dominate AMOC variability on seasonal and sub-annual time scales (Hirschi et 300 al., 2007). Wind-driven variability may also play a role on interannual time scales, for example during the winter of 2009/2010, anomalous wind-driven Ekman transport contributed to interannual AMOC fluctuations (Zhao and Johns, 2014;Evans et al., 2017). However, density variability in the upper 1000 m has also been identified as a leading driver of the AMOC on interannual time scales (Hirschi et al., 2007). This density variability is associated with isopycnal perturbations that travel westward as long Rossby waves (Hirschi et al., 2007;Hirschi et al., 2009).

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The Rossby waves impact the upper mid-ocean component of the AMOC transport through their effect on the eastwest density structure of the basin (Hirschi et al., 2007;Cabanes et al., 2008;Hirschi et al., 2009).
The changes in the upper 1000 m of the density field from westward propagation are visible as a sea surface signal and have been shown to be captured by satellite altimetry. Altimeters are most likely to reflect the first baroclinic 310 mode, and by association motion of the main thermocline, due to the nature of baroclinic modes which is surface intensified (Wunsch, 1997).  Kanzow et al., 2009 (their Fig. 5). The speed of these westward propagating anomalies is typically similar to 320 baroclinic Rossby wave phase speed (Gill, 1982;Hirschi et al., 2007;Killworth & Blundell, 2003).

Modal decomposition
Sea surface signals observed by satellite altimetry reflect changes in the top (1000 m) stratified ocean. Though 325 satellite altimetry can measure surface geostrophic velocities, it cannot be used to infer the vertical structure of the flow. To understand the contribution of the flow's vertical structure to the meridional mass transport, and how that impacts satellite-derived transport, pressure modes derived from RAPID mooring data are examined.
The vertical structure of the flow is assessed using normal mode decomposition, assuming a flat bottomed and 330 motionless ocean (Gill, 1982), using data from the RAPID moorings at the western (West, WB3) and eastern (EB) boundary. The normal mode decomposition for the given mode number n = 0,1,2…is determined from the Sturm-Liouville Eq.: Where ( ) is the Brunt-Vaisala frequency and 2 is the phase/modal speed of the waves. The boundary conditions are defined as = 0 at = 0, − .

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The buoyancy frequency (N) is estimated from temperature and salinity profiles at moorings West, WB3, and EB, which are converted into density profiles, ( ), and averaged over the 2004 to 2018 time period: 345 Normalisation is then computed to satisfy Kronecker delta, , (rendering the resulting normal modes dimensionless) such that:

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Where is 4820 dbar, the bottom reference depth of the moorings.
The buoyancy frequency and the pressure modes, (as per Eq. 5 and 6), are estimated at West, WB3 and EB (Fig.   4). The stratification profile is characteristic of buoyancy profiles in the North Atlantic (e.g. Szuts et al., 2012;Clement et al., 2014): in the west, the buoyancy frequency shows a sharp maximum at 80 dbar and a second maxima 355 around 600 to 800 dbar before decreasing to background stratification levels around 1100 dbar. These two peaks indicate strong stratification linked to the seasonal and main pycnocline (Siegel et al., 1999). Moving eastward across the basin, at WB3, the upper stratification decreases and the peak deepens to 100 dbar, the second peak also deepens and has slightly lower stratification than at mooring West. The stratification minima apparent in West and WB3 at 300-400 dbar is indicative of 18°C water (i.e. subtropical mode water), characteristic of the western 360 subtropical North Atlantic. On the other side of the basin, in the eastern boundary, the stratification at EB is decreased though the subsurface maximum remains at 100 dbar. Figure 4 also shows the first four pressure modes at West and WB3 and EB. Mode 0 is here representative of the barotropic mode, while modes 1 to 3 are the first 3 baroclinic modes. The first mode shows a zero crossing roughly 365 between 1000-1100 dbar in the western boundary (West and WB3), which deepens to 1500 dbar by the time it reaches the eastern boundary (EB). In general, western moorings show shallower zero crossings and more complex structure, reflective of the peaks in stratification in the west, compared to the eastern mooring which has a deeper zero crossing and smoother structure. The vertical structure of the horizontal velocity shown here is consistent with the characteristic shape of known modes in the western North Atlantic (at this latitude) (e.g. Gill, 1982;Szuts et al. 370 2012, their Fig. 6.14c and 2, respectively). The shape of the first baroclinic mode in the surface to its first zero crossing (1100-1500 dbar) will be key in informing the satellite-derived estimates of transport, as altimetry has been shown to capture the upper 1000 m intensified structure of the flow (away from the boundaries by 45 km), reflective of the first baroclinic normal mode (Wunsch 1997;Szuts et al., 2012). The zeroeth mode, i.e. the barotropic mode, is important in the deeper ocean (> 1000 m), which is less stratified (Wunsch, 1997;Kanzow et al., 2008). However, 375 below the upper 1000 m, changes in the deeper transport are not captured by satellite altimetry (Kanzow et al., 2008).
In the following sections, in-depth analysis of the normal modes from moorings and their relationship with satellite altimetry is explored.

Modal amplitude and variability
To understand the importance of each mode to the total variability observed in dynamic height anomaly, (Eq. 1, referenced to 4820 dbar), measured by the RAPID moorings, the modal amplitude is analysed and used to construct 385 time varying from the normal modes. The amplitudes of the modes, , are estimated by integrating the product of the normal mode, , and such that: where n = 0,1,2,3…is the mode number and H is the reference pressure 4820 dbar. Because satellite altimetry has been shown to reflect fluctuations associated with the amplitude first baroclinic mode (Hirschi et al., 2009;Wunsch & Stammer, 1997), the amplitude for the first mode, c1, can also be written in terms of SLA, , such that: Where 1 ( = 0) is the surface value of the first mode, and s is a scale factor equal to 0.25, needed to adjust to the correct magnitude. SLA does not account for baroclinic shear in the upper 1100 m of the water column: if we integrated the SLA over the upper 1100 m to obtain geostrophic transport, the SLA would overestimate the transport magnitude compared to dynamic height (e.g. S3). For this reason, it is necessary to combine the SLA with the 400 vertical structure of the first baroclinic mode; however, a comparison between the dynamic height from the RAPID moorings and the SLA indicate further correction/scaling could be needed. Thus a scale factor is determined empirically by examining the signal from at the surface (z = 0) at moorings West and EB against . The modal amplitude (Eq. 9) can also be combined with the pressure modes (Eq. 6) to reconstruct as follows:  (Fig. 7 a,b). The difference between and * at West suggests that although the reconstruction generally captures intensified structure in the upper 1000 dbar, it underestimates the magnitude of and does not capture any of the signal below 1000 dbar (Fig. 7c). These differences may be due to 445 the fact that the reconstruction uses only the first baroclinic mode, reflective of changes in the main thermocline, and thus has oversimplified structure in the upper layer of the ocean compared to the at West. Further, the baroclinic structure, in general, is more likely to reflect changes in the stratified upper ocean to roughly 1000 m, while in the deeper less stratified ocean, barotropic motion is more important (Kanzow et al., 2008). In the eastern boundary, * is reconstructed using the first baroclinic mode at EB (Fig. 7d), similar to pressure perturbation analysis as per Szuts The contribution of the barotropic mode (mode 0) and higher baroclinic modes (modes 1 and 2) to * is examined in 455 Figure 8. The inclusion of barotropic mode and higher baroclinic modes in * shows substantially improved patterns of the variability in the upper 1000 dbar, with reduced differences at every pressure level (Fig. 8) compared to * using only mode 1 (Fig. 7). To assess whether the inclusion of the barotropic and higher baroclinic modes makes a meaningful contribution to the upper ocean transport, transports from the * reconstruction using the normal modes and the at West and EB are presented in the following section.

Transport anomalies from West and EB moorings
Transport anomalies at West and EB are estimated using , * and respectively, with the aim of understanding the contribution of the normal modes to variability and implications for satellite-based transport. Kanzow et al.

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(2010), Chidichimo et al. (2010) and Szuts et al. (2012) set the precedent for estimating transport from a single mooring (as opposed to a horizontal gradient) to separate the contribution of the western and eastern components of the basinwide geostrophic transport. Therefore, transport from at West or EB (as indicated) is defined as:

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The mode-reconstructed * transport is calculated using the modes (Eq. 6) and modal amplitude (Eq. 9) such that:

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If the amplitude of the first mode is taken to correspond to (i.e. ̂ ; Eq. 10), then the satellite-based transport can be constructed using the vertical structure from the first baroclinic mode 1 in the following manner: 480 A comparison of the and the reconstructed transports shows that accounts for 83% of the variability of (r = 0.91, statistically significant at 95% level) at West and 90% of the variance of (r = 0.95, statistically significant at 99% level) at EB, where is reconstructed using only the first mode ( Fig. 9 a,d). Including the second baroclinic mode as well as the first in the reconstructed transport, , shows some improvement in the correlation with at West (r= 0.98, statistically significant at 99%) and slight decrease at EB ( 500 r= 0.94, statistically significant at 99%), though the amplitude of still underestimates ( Fig. 9 b,e). The addition of the barotropic mode to the first baroclinic mode in noticeably improves the amplitude of and correlation with at West (r = 0.99) and EB (r = 0.999) (Fig. 9 c,f). Analysis of the barotropic component shows that it accounts for 86% and 63%, respectively, in the total variability at West and EB (Fig. S4) and could explain some of the discrepancies in the satellite-based estimates, as satellite altimetry only captures baroclinic variability. The 505 second baroclinic mode is shown to account for 18% and 0.34% (not statistically significant) of variance at West and EB moorings (Fig. S4).
The basinwide geostrophic transport can be constructed for and * respectively, by integrating the eastwest difference such that Eq. (12) and (13) Where subscripts E and W denote east (EB) and west (West), respectively. ∆ and ∆ have a correlation of r = 515 0.91 (significant at 99% level) when ∆ is constructed using only mode 1 (Fig. 9g). The correlation between ∆ and ∆ increases to r = 0.97, when ∆ is constructed using modes 1 and 2, and to r = 0.99 when ∆ is constructed using modes 0 and 1 (Fig. 9h,i). These results suggest that the time-averaged first baroclinic mode accounts for most of the interior geostrophic transport variability; while the barotropic mode accounts for 82% of the variability, and the combined barotropic and first baroclinic mode accounts for 98% (Fig. S4). The barotropic mode is reflective of 520 changes in the deeper less stratified ocean.

Construction of the GS, the UMO and AMOC transports
The Gulf Stream within the Florida Straits has a mean of 31.2 Sv and is balanced by the UMO and Ekman transports, mean of -18 and 3.74 Sv, respectively, to yield the total mean AMOC transport of 17 Sv (McCarthy et al., 2015). The Gulf Stream time series is based on a submarine telephone cable that has been recording data 525 between the Bahamas and Florida at 27°N since 1982 (Baringer and Larsen, 2001). Principles of geostrophy have been previously used to provide alternative mechanisms for estimating the cable-based using satellite altimetry (Volkov et al., 2020) and pressure gauges (Meinen et al., 2020).
Here, the east-west difference in (∆ ) in the western end of the basin (i.e. west of 77°W) is compared with the 530 submarine cable data (Baringer and Larsen, 2001). Maximum correlation between from the cable data and the satellite ∆ (r = 0.70, statistically significant at 95% level) is found when using located at 27.625°N and 77.125°W, and located at 27.625°N and 80.125°W (Fig. S5)

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Here, linear regression is used against the cable-based to obtain the regression coefficients (a, b) needed to produce a final estimate for satellite-based GS transport: * ( ) = ∆ + ,  (Fig. 10a,b).
The satellite-based, * , is constructed by combining the satellite-based mode amplitude, ̂ (Eq.10) with the first baroclinic mode F1(z) (Eq. 6) as follows: Where subscripts E and W denote east (for at 27.875°N and 13.125°W and at EB) and west (for is 27. Previously, satellite-derived estimates of the and the have been compared with the RAPID 26°N array, and constructed for the 1993 to 2013 period in Frajka-Williams (2015; hereafter EFW15). EFW15 found that SLA could be used to obtain a proxy for mass overturning transport. The statistical relationship between the RAPID 610 and the SLA on low frequency (18 month) timescales provided the main method for estimating the EFW15 . The EFW15 was estimated by adding the same estimates of (ERA5 reanalysis) and (submarine cable) used by RAPID to the . Here it is fitting to compare the EFW15 method with the method derived in sections 4 and 5, which relies on altimetric data and geostrophic balance, and therefore gives a methodologically consistent (satellite only) method that incorporates climatological stratification and has the potential to be applied to 615 other latitudes. This is in contrast with EFW15 which was a statistically based method that assumes the existence of in situ observations. Further work is needed to determine the origins of the scale factor required to balance the transports, whether due to sampling issues or uncertainties in satellite sea level anomaly near the boundaries.
Additionally, the RAPID is compared with a third separate estimated from GloSea5, a global ocean and ice reanalysis product (Blockley et al., 2014;Jackson et al., 2016;MacLachlan et al., 2015;Jackson et al., 2019).

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GloSea5 uses the ocean model NEMO (Nucleus for European Modelling of the Ocean) that has a ¼° surface resolution and assimilates in observational data including satellite (Megann et al., 2014). impacts (Zhang et al., 2019), it is now more important than ever to find long term and cost-effective replacements/backup systems that can monitor changes in the AMOC.
One previous effort to use satellite altimetry as a proxy for AMOC variability, led by EFW15, relied on a statistical 675 relationship between the RAPID and the SLA on low frequency (18 month) timescales to estimate the .

The EFW15
was estimated by adding the same estimates of (ERA5 reanalysis) and (submarine cable) used by RAPID to the . Their method successfully recovered ~85% of the and 92% of the on interannual time scales. Earlier studies used more dynamically based methods and combined SLA with the vertical structure of horizontal flow from mooring data and found that the SLA had little skill at capturing the upper mid-680 ocean transport (e.g. Hirschi et al., 2009;Kanzow et al., 2009;Szuts et al., 2012). The goal of this study was to similarly use satellite altimetry as a proxy for AMOC variability and re-evaluate dynamics-based methods (e.g. Hirschi et al., 2009;Kanzow et al., 2009;Szuts et al., 2012) for using satellite altimetry to estimate the as well as the components of the AMOC, which could eventually be used at other latitudes. Thus, using principles of geostrophy and normal mode decomposition a method for constructing the upper mid-ocean transport, * , and by extension the * , at 26°N from satellite altimetry on low frequency (18 months) time scales was devised here by combining the first baroclinic mode, derived from time-averaged density profiles from the RAPID moorings, with SLA to reproduce the * and * transports. Using this new method, we find that 56% of RAPID variability could be captured and 69% of the RAPID variability on interannual (18 month) time scales.
Sensitivity testing using different filtering windows decreases variance captured by * and * , respectively, to 690 18% of and 50% of the when using 6 month Gaussian smoothing; 45% of and 66% of the when using 12 month Gaussian smoothing; and an increase to 62% of and 72% of the when using 24 month Gaussian smoothing. The component of was also reproduced separately using the satellite altimetry; we found that it captures 49% of the GS variability via the Florida Straits as measured from the telephone cable (Meinen et al., 2010)  Because the altimetry has no knowledge of vertical shear, estimating transport over the upper 1000 m using only satellite altimetry results in an overestimation of the transport's magnitude (Fig. S3). Thus, normal mode 705 decomposition was investigated using the RAPID moorings to answer 2 questions: a) How much does the vertical structure of the flow contribute to the upper-mid ocean transport ( ) variability, and b) can the pressure modes be combined with the satellite to provide an improved way of estimating mass overturning transport. In the first instance, we find that the first baroclinic mode accounts for 83% of the observed interior geostrophic transport variability, the barotropic mode accounts for 82% of the variability, and the combined barotropic and first baroclinic 710 mode account for 98% of the total variability. In the second instance, we find that combining the satellite altimetry with the vertical structure (from the 1 st baroclinic mode) improves the magnitude of values for the altimetry-based transport. However, a scale factor is still needed to further correct the values to capture the magnitude of the .
We posit the need for a scale factor is the result of the satellite altimetry not capturing the full signal observed by the moorings, because of proximity of moorings to land, where variability is also influenced by coastal processes baroclinic mode) does not improve the amount of variance captured by the satellite-based * compared to RAPID variability, and using time-varying pressure modes (instead of time-averaged) do not necessarily improve correlation between the RAPID and the satellite-derived * . Further discrepancies between satellite-based transport and RAPID transport may be due to the barotropic component, which the satellite-based method does not 720 account for.
To summarise, principles of geostrophy can be used with satellite altimetry to effectively capture upper mid-ocean and GS transport, and by extension, AMOC transport. The vertical structure of the flow (from the moorings) does not improve the amount of variability the satellite-based method captures; however, the analysis of the normal mode 725 decomposition yields insight into the governing modes of variability associated with the on interannual timescales, and the limits this places on any satellite-based transport method. While this method progresses attempts at a dynamically robust method for estimating AMOC transport using satellite altimetry, which can also be used to recreate the AMOC the start of the satellite time period, pre-dating RAPID, the method is still not independent from the mooring array and without improved understanding of the scale factor, further investigation is needed to produce 730 an altimetry-based method for the AMOC that can be used at other latitudes.