Using Sea Level to Determine the Strength, Structure and Variability of the Cape Horn Current

The Cape Horn Current (CHC) is one of the components of the Antarctic Circumpolar Current system that enables it to fulfill its crucial role as a conduit between ocean basins. Despite this, to‐date there have been very few measurements of CHC strength and none continuous in time or space. Here, we use a combination of ocean models, one free‐running and one data‐assimilating, and satellite altimetry (1993–2021) to estimate the time‐dependent strength of the CHC at 10 transects along its length. We find the time‐mean CHC transport increases from 0.4 ± 0.5 Sv near 49°S to 5.3 ± 2.2 Sv at Cape Horn, with peak‐to‐peak interannual fluctuations of 0.8–3.4 Sv. Although, theoretically, increased run‐off from a wasting Patagonian Ice‐field would strengthen its flow, the CHC appears quite stable over the last 29 years, with little evidence of a coherent, long‐term increase or decrease in the strength of the current.


Introduction
By connecting the Pacific, Atlantic and Indian Oceans, the Antarctic Circumpolar Current (ACC) system is a crucial element of the global ocean's circulation and Earth's climate system (e.g., Brady et al., 2021;J. Marshall & Speer, 2012;Rintoul, 2018;Watson et al., 2014).Relative to the other major currents, the structure of the ACC is complex, consisting of a system of discrete fronts, jets and flows that vary in strength, orientation and meridional separation (Kim & Orsi, 2014;Rintoul et al., 2001).As it is fed from waters leaking from the ACC downstream of the East Pacific Rise (Chaigneau & Pizarro, 2005), and returns these waters in a modified form to the ACC as it passes through Drake Passage (Acha et al., 2004;Garzón et al., 2016;Strub et al., 2013), the Cape Horn Current (CHC) can be considered a component of the overall ACC system (Lamy et al., 2015;Wu et al., 2019).Moreover, it is a component that acts as an inter-basin conduit, drawing relatively cold and fresh Subantarctic Surface Water from the South Pacific, and injecting it into the South Atlantic.Here it modifies the hydrodynamic and nutrient properties of the Patagonian Shelf (Antezana, 1999;Bianchi, 2005;Combes & Matano, 2018;Giussi et al., 2016;Guinder et al., 2020), one of the most productive and economically important fisheries in the Southern Hemisphere, before feeding into the Malvinas Current (Frey et al., 2021;Palma et al., 2021Palma et al., ). et al., 2011Palma et al., , 2012Palma et al., , 2013;;Tarakanov & Gritsenko, 2018).However, an unambiguous identification of the CHC in the Drake Passage is challenging and these values are not necessarily representative of the CHC in its entirety.
Given the challenges of measuring the strength of the CHC directly along its length, here we develop a method that uses a combination of ocean modeling and satellite altimetry to estimate the strength of the CHC and how it is changing over time.The method implicitly assumes geostrophic balance.However, since only the surface flow can only be obtained directly from the sea level gradient, Δh (e.g., Alvera-Azcárate et al., 2009), we derive an empirical relationship between Δh and the depth-integrated volume transport as has been done, for example, for the Florida Current (Maul et al., 1985;Volkov et al., 2020).For the CHC, however, due to a dearth of additional observations, our empirical relationship is based on two numerical ocean models.In Section 2, the modeling and altimetry data and associated methods are described.Estimates of the CHC transport are provided in Section 3. Finally, a concluding discussion is given in Section 4.

Model and Reanalysis Data
Our analysis depends on two ocean models.The first is the global, eddy-resolving, free-running ORCA0083-N06 version of the Nucleus for European Modeling of the Ocean (NEMO) ocean model run at the National Oceanography Center, Southampton.ORCA0083-N06, hereafter referred to as NEMO, has a nominal horizontal resolution of 1/12° and 75 vertical levels.The run covers the period 1958-2015 and is forced by the Drakkar Surface Forcing data set version 4.1 (Brodeau et al., 2010).For further details see Marzocchi et al. (2015).The second, Ocean Reanalysis System 5 (ORAS5), is a data-assimilating (sea surface temperature, sea-ice concentration, in-situ temperature and salinity, and sea level anomalies) version of NEMO, forced by ERA-Interim atmospheric reanalysis (Zuo et al., 2019).Ocean Reanalysis System 5 has the same number of vertical levels as NEMO, but has a lower horizontal resolution (1/4°) and covers the shorter period 1975 to 2014.From both models we use monthly mean sea surface height and velocity fields.
To characterize the CHC transport, and establish a relationship with sea level, we focus on 10 transects (Figure 1b).Each transect extends from the shelf to approximately 200 km off-shore and is orientated such that the flow is approximately normal to the section.The first transect crosses the CHC zonally at 49°S, 76°W and the tenth crosses the CHC meridionally at 57°S, 68°S.The total distance spanned by the sections is around 1,100 km giving an averaged interval between each transect of 123 km.
To determine the transport for each cell on a transect we first compute the velocity normal to the transect, with positive flow to the south (or east for transect 10), according to U n = u cos(π/2 − ϕ) − v cos(ϕ), where u and v are the zonal and meridional velocities at the center of the cell, respectively, and ϕ is the angle of the transect relative the equator.The transport is then obtained by multiplying the normal velocity by the area of the face through which it flows.For the zonal transects (1-3) and meridional transect (10), this is the area of the zonal or meridional face of the cell, whereas for the diagonal transects (4-9) it is the area of the diagonal cross-section through the cell.These are then summed vertically from the surface to 400 m, the maximum depth of the CHC suggested by the time-mean transport sections (Figure S1 in Supporting Information S1), excluding negative (e.g., equatorward) values, which are largely due to the equatorward-flowing side of the predominantly anti-cyclonic eddies crossing the off-shore CHC boundary, to obtain the total poleward/eastward transport at each grid point along a transect.
To calculate representative CHC transport timeseries, T i (t), for each transect i = 1, …, 10, the depth summed transports (Figure S2 in Supporting Information S1) were further integrated between the CHC lateral boundaries (blue lines in Figure S2 in Supporting Information S1) which, for transects 1-8, correspond to the time-mean transport minima either side of the peak transport in NEMO.For transects 9 and 10, where the influence of the ACC makes determination of the CHC boundaries more difficult, we use the transect 8 limits, which correspond to inflection points in the normal surface current speed (see Figures S4i and S4j in Supporting Information S1).As the transport minima are not always as well-defined as in NEMO, we also use the NEMO limits for ORAS5.Because we also wish to have a single set of limits for computing the sea level difference timeseries,  Δℎ() = ℎ   − ℎ    , we again use the NEMO limits, but with the boundary between the on-shore, h on , and off-shore, h off , sea level timeseries lying midway between the NEMO and ORAS5 time-mean transport peaks.

Altimetry Data
To provide a range of transport estimates, we use three altimetry products: (a) the two-satellite (two-sat) SSH product produced and distributed by the Copernicus Climate Change Service (C3S), the stability of which makes it suitable for studying long-term change (Taburet et al., 2019); (b) the all-satellite sea level anomaly (SLA) maps (all-sat), disseminated by the Copernicus Marine Environment Monitoring Service (CMEMS), which sacrifices some stability for improved spatial resolution (Pujol et al., 2016); (c) the JPL SLA timeseries produced as part of the Multi-Mission Ocean Altimeter Data used in Research Environments (MEaSUREs) Program (Beckley et al., 2017).Since the latter two are missing the time-mean sea level, we add the CLS18 mean dynamic topography (MDT; also distributed by CMEMS).All three data sets have a horizontal resolution of 0.25° × 0.25°, but we interpolated onto the NEMO grid to facilitate the calculation of the SSH difference timeseries as described above.
Finally, an analysis of the formal mapping errors on the CLS22 MDT and two-sat SLA's confirm that altimetry errors are small (<12%) in comparison to the sea level differences we use in this study.

The Time-Mean Cape Horn Current
The time-mean CHC in NEMO follows the 500 m isobath poleward along the western South American Coast from 48°S to 56°S (Figure 1a).In its formative stage, the CHC is relatively weak and diffuse before emerging near 51°S as a more intense and narrowly focused current.From this point, the CHC gradually increases in strength and, to some extent, width, before merging with an un-named eastward flowing frontal current (which can also be seen in the altimetry data; see Figure S3 in Supporting Information S1) somewhere between transects 8 and 9, and then the Sub-Antarctic Front (SAF; Kim & Orsi, 2014) of the ACC between transects 9 and 10.Associated with the current is an across-slope SSH gradient, with SSH increasing toward the coast (Figure 1b).1c) before rising to a peak within 20 km of the 500 m isobath and then declining less smoothly.Where the decline is smooth (e.g., transect 4), we can estimate the width of the CHC to be around 60 km.For transects 9-10, where the CHC merges with the SAF, the combined current widens to approximately 140 km, and becomes asymmetric with respect to the 500 m isobath, with a similar extent of 40 km toward the coast, but extending to approximately 100 km offshore (Figures S4i and S4j in Supporting Information S1).Confirming the impression from Figure 1a, peak current speeds generally increase from north to south.For the first three transects, the peak speeds are similar at 8-12 cm s −1 (Table 1).The peak speed increases to 24 cm s −1 for transect 4, and then to 28-33 cm s −1 for transects 5-9.Finally, for transect 10, where the CHC fully merges with the SAF, the peak velocity nearly doubles to 56 cm s −1 .
The CHC is also visible in ORAS5 (Figure 1d), and there is a similar marked increase in the current strength near 51°S, as seen in NEMO.However, compared to NEMO, the CHC is not as sharply defined and appears weaker to the north of 53°S, while appearing stronger to the south of this latitude.These differences are also reflected in the SSH from ORAS5 where, although the overall pattern is similar, the on-off shore gradients are not as sharp as they are in NEMO and the gradient is weaker (stronger) in the northerly (southerly) portion of the domain.There is also a marked difference, clear in the SSH maps (Figures 1b and 1e), in the path of the ACC and where it merges with the CHC.In contrast to NEMO, where the CHC merges with the SAF gradually between transects 8 and 10, in ORAS5 there is a sharp northward deflection of the SAF near 72°W such that it merges with the CHC earlier.In this respect, ORAS5 compares less favorably than NEMO with altimetry (Figure S3 in Supporting Information S1).
These differences are seen clearly in the normal surface current speeds in ORAS5 (Figure 1f).As for NEMO, peak current speeds generally increase from north to south.Although the peaks are not as clearly defined as in NEMO, for most transects, current speeds do increase from the open ocean toward the coast and reach a local maximum close to the 500 m isobath.If the core of the CHC is defined as the local maximum within 20 km of the isobath, we find similar maximum current speeds for transects 1-3 and 6-7, but lower peak speeds at transects 4-5 and 8 (Table 1).However, reflecting the more angular path taken by the ACC in ORAS5, the peak speeds for transects 9 and 10 are much greater than for NEMO.

Cape Horn Current Transports
Unlike the peak surface velocity, NEMO's time-mean CHC transport-calculated from CHC transport timeseries, T i (t) (Figure S5 in Supporting Information S1)-remains relatively constant between transects 1-8, with a minimum of 0.73 Sv at transect 3, a maximum of 1.68 Sv at transect 8 and a mean transport of 1.25 Sv across the eight transects (Table 1).The transport fluctuations are also of a similar magnitude, with a mean standard deviation (s.d.) of 0.76 Sv and, for interannual variability, a mean peak-to-peak range of 1.65 Sv.Reflecting the merging of the CHC with the SAF as Cape Horn is approached, for transect 9, the transport increases to 3.5 ± 1.5 Sv and then to 6.7 ± 3.1 Sv for transect 10, with peak-to-peak interannual fluctuations of 3.6 and 7.1 Sv, respectively.
For transects 1-8, the CHC time-mean transports in ORAS5 are slightly higher than those in NEMO, ranging from 1.0 to 1.3 Sv for transects 1-3, to 1.4-2.1 Sv for transects 4-8 (Table 1).However, the variability at all transects, as reflected in the standard deviations of the unfiltered monthly mean timeseries and the T max−min ranges of the filtered interannual timeseries (except transects 1 and 3), is weaker.For transects 9 and 10, where the CHC is joined by the SAF, the ORAS5 mean volume transport is 7.1 and 17.9 Sv, around two and three times the NEMO transports, respectively.

Relationship With Sea Level
The close relationship between T i and Δh i shown in Figure 2, suggests that it should be possible to use the latter to calculate the former.Table 1 confirms this to be the case.For transects 1-8, regression coefficients between T i and Δh i (unfiltered) range from 0.16 to 0.24 Sv cm −1 , with a mean of 0.19 Sv cm −1 , in NEMO, and from 0.22 to 0.40 Sv cm −1 , with a mean of 0.26 Sv cm −1 , in ORAS5.The higher ORAS5 values reflect weaker sea level gradients in the lower resolution model.Multiplying Δh i by the regression coefficients yields a set of reconstructed transport timeseries,  T .For transects 1-8, the skill of these transport reconstructions (defined as the variance in the original unfiltered transport timeseries accounted for by the reconstruction) ranges from 77% (3) to 86% (4) for NEMO and 69% (2) to 87% (7) for ORAS5, with mean values of 80% and 76% for NEMO and ORAS5 (Table 1).
Of course, regression coefficients and skill scores only refer to the time-variable component of the timeseries.It is clear from Figure 2 (and Figures S6 and S7 in Supporting Information S1), however, that T i and  T also agree in terms of their mean values, showing the relationship implied by the regression coefficients also holds for the mean part of the fields.This is confirmed by the close agreement between the regression coefficients and  ∕Δℎ , the ratio of the mean transport and the mean SSH difference for each transect (Table 1).This is as expected given the two quantities are related through geostrophy.
Sea level can also be used to reconstruct transport timeseries at transects 9 and 10 where the CHC gains in strength by merging with the northern branch of the SAF.This is true for both models despite the ORAS5 transport being stronger than in NEMO, especially for transect 10 (for the reasons discussed above).For transect 9, the regression coefficients are 0.33 and 0.42 Sv cm −1 for NEMO and ORAS5, respectively, somewhat larger than for transects 1-8 and the skills are 89% (NEMO) and 98% (ORAS5).For transect 10, the regression coefficients increase still further to 0.53 (NEMO) and 0.67 (ORAS5) Sv cm −1 .Here the skill scores are the highest of all the sections, with near-perfect values of 97% (NEMO) and 99% (ORAS5).

Reconstructed Transports From Altimetry
The strong relationship between T i and Δh i seen in the models suggests that we can derive the actual CHC transport from observed SSH.To do this we compute Δh i using three altimetry products and scale these timeseries by the mean of NEMO and ORAS5 regression coefficients at each transect (Figure 3).For all transects, the reconstructed volume transports,  T , from all three products are in close agreement, with the time-mean transports,  T , over period of 1993-2021 (computed from the three individual transport estimates) increasing from 0.42 to 0.98 Sv at transects 1-3, to 1.35-2.46Sv at transects 4-8, and finally to 4.12 (5.31) Sv at transect 9 (10) (Table 1).
Focusing on the two-sat product, whose stability makes it most suited to detecting long-term climate signals (Taburet et al., 2019), there does not appear to be a consistent decline or increase in the strength of the CHC over the altimetry period (1993-2021) (Table 1).Four transects (1, 2, 4, 8) show a weak increase in strength and the rest show a weak decrease.However, none of the trends are significantly different from zero at the 95% level.While a similar picture of a stable CHC emerges from the all-sat product, the JPL reconstruction tells a somewhat different story.In this case, all transects show a decline in CHC strength, with this decline being significantly different from zero at six transects.The largest decline of 0.21 Sv decade −1 (approximately 6% of the mean strength) is found at transect 9.In contrast, according to the all-sat and two-sat products, the strongest trend of −0.19 Sv decade −1 is found at transect 10, but this is not statistically different from zero at the 95% level (Table S1 in Supporting Information S1).Therefore, the declining trends seen in the JPL product cannot be considered robust and the evidence points toward a stable CHC over the altimetry period.

Concluding Discussion
In conclusion, two ocean models, one free-running and one data-assimilating, despite some differences in their representation of the CHC, both show a strong relationship between the strength of the CHC and the SSH gradient Although the agreement between the NEMO (1/12 of a degree) and ORAS5 (  1 4 of a degree) ocean models gives us some confidence that the latter resolution, which is also the resolution of the altimetry products, is sufficient to resolve most, if not all, of the CHC transport, we cannot rule out an additional component of the flow for which even the resolution of NEMO is too coarse to capture.This issue should be investigated in future studies.
Given that El Niño-Southern Oscillation (ENSO) events generate coastally-trapped waves that propagate as SSH anomalies down the Pacific coast of South America (Strub & James, 2002), one might expect ENSO to impact the strength of the CHC.Inline with this expectation, for the strong 1997-1998 El Niño both models show elevated transport at transects 1-4 (Figure S5 in Supporting Information S1).However, this only occurs for isolated months and so leaves little trace at interannual timescales (Figure 2).Moreover, there is no obvious consistent pattern for across ENSO events.Nor does there seem to be a clear relationship with the Southern Annular Mode (SAM).This is in contrast to (Guihou et al., 2020) who reported that the negative phase of the SAM strengthened meridional winds and thereby the CHC.However, this may be because they focused on just the upper 200 m which is more strongly influenced by the wind.As for the trend, it is likely the interannual variability arises through a combination of mechanisms and drivers, and ENSO-SAM interactions (R. L. Fogt & Bromwich, 2006;R. Fogt et al., 2011), the relative contributions of which likely vary with latitude.
Although a full examination of the dynamics of the CHC is beyond the scope of this study, the across-slope SSH gradient is, in part, due to the relative freshness of the coastal water resulting from continental run-off (Acha et al., 2004;Dávila et al., 2002;Thiel et al., 2007).It might therefore be expected that the CHC may increase in strength as global warming increases melting of the Patagonian ice-field (Bravo et al., 2021).However, over the altimetry period, the CHC is stable, with no transects showing a statistically significant (at the 95% level) trend across at least two of the altimetry products.The JPL product suggests a more coherent pattern of CHC slowdown, but this should be treated with caution given it is not replicated in the other two products.Of course, the naive 10.1029/2023GL105033 9 of 10 picture painted above may be confounded by other factors such as changes in coastal precipitation (Almazroui et al., 2021) or wind forcing (Montini et al., 2019), both of which could be related to long term changes in the SAM (Gillett et al., 2006;G. J. Marshall, 2003), or other atmospheric changes.Certainly, more work and a longer observational record are required to fully elucidate the consequences of climate change on the CHC.

Figure 1 .
Figure 1.(a) The time-mean (1958-2015) vertical-averaged (0-400 m) current speeds in NEMO.(b) As in (a) but for the SSH.Transects are marked in white and the 500 m isobath is shown dashed.(c) The time-mean surface current speeds normal to the first eight transects, with an offset of 5n cm s −1 , where n is the transect number, added to each curve, and distance is given relative to the 500 m isobath (see Figure S4 in Supporting Information S1 for transects 9 and 10).(d-f) As in (a-c) but for the Ocean Reanalysis System 5 reanalysis averaged from 1975 to 2014.

Figure 1c (
Figure1c(transects 1-8) and FigureS4(all transects) in Supporting Information S1 show the time-mean surface current speed in NEMO normal to the 10 transects.Moving along each transect from the open ocean toward the coast, NEMO current speeds reach a local minimum 30-60 km from the 500 m isobath (corresponding to 0 km on the x-axis of Figure1c) before rising to a peak within 20 km of the 500 m isobath and then declining less smoothly.Where the decline is smooth (e.g., transect 4), we can estimate the width of the CHC to be around 60 km.For transects 9-10, where the CHC merges with the SAF, the combined current widens to approximately 140 km, and becomes asymmetric with respect to the 500 m isobath, with a similar extent of 40 km toward the coast, but extending to approximately 100 km offshore (FiguresS4i and S4jin Supporting Information S1).Confirming the impression from Figure1a, peak current speeds generally increase from north to south.For the first three transects, the peak speeds are similar at 8-12 cm s −1 (Table1).The peak speed increases to 24 cm s −1 for transect 4, and then to 28-33 cm s −1 for transects 5-9.Finally, for transect 10, where the CHC fully merges with the SAF, the peak velocity nearly doubles to 56 cm s −1 .
properties of the altimetry-based CHC reconstructions (with values the mean of the three individual altimetry products).Finally, CHC linear trends over 1993-2021 based on the two-sat altimetry product, with 95% confidence intervals, are reported.

Figure 2 .
Figure 2. (a-j) The Cape Horn Current transport in NEMO at the 10 transects shown in Figure 1b (black).Also shown are the sea level gradient timeseries (blue) and reconstructed transport timeseries (green).(k-t) As for (a-j) but for Ocean Reanalysis System 5. A 1-year low-pass filter has been applied to all timeseries.Corresponding unfiltered timeseries are shown in Figures S6 and S7 in Supporting Information S1.

Figure 3 .
Figure 3. Timeseries of Cape Horn Current transport at the 10 transects shown in Figure 1b using the two-sat (orange), all-sat (green), and JPL (pink) sea level products.A 1-year low-pass filter has been applied to all timeseries.
Skill measures the agreement between the original and reconstructed transport timeseries.Values are shown for NEMO and ORAS5 (in parenthesis).

Table 1
The Strength of the Cape Horn Current and Its Relationship With Sea Level, Where T is the Unfiltered Transport Standard Deviation, T max−min is the Interannual Transport Range, corr(T, Δh) and β are the Correlation and Regression Coefficients Between the Transport, T, and Across-Slope Sea Level Gradient, Δh