2.1. GPS time series

The GPS data from the CRAC-ICE (Collaborative Research project into Antarctic Calving and ICeberg Evolution) November 2007 field program were collected by two receivers (Topcon GB1000 with PGA1 antennas), deployed to each side of the main western rift of Mertz Glacier Tongue with a 30 s sampling interval. The GPS receivers recorded data over 60 days, from 15 November 2007 to 15 January 2008.

The data from both GPS 4 and GPS 5 receivers have been processed using the GINS-PPP software developed by the Centre National d’Etudes Spatiales, France (Reference MartyMarty and others, 2012). This software allows the use of a Precise Point Positioning kinematic methodology and solves for ambiguities as integer values (Reference BlewittBlewitt, 2008). Such GPS data processing is usually achieved using a double-difference processing strategy. The new strategy provides an ideal way to process GPS data without the need for a reference or base station (i.e. relative positioning) and it still achieves a 2 cm accuracy (Reference Lescarmontier, Legresy, Coleman, Perosanz, Mayet and TestutLescarmontier and others, 2012).

The GPS positions were determined in Cartesian geocentric coordinates, in the ITRF2005 reference frame, taking into account the modeled solid earth and ocean tide loading displacements. Reference Lescarmontier, Legresy, Coleman, Perosanz, Mayet and TestutLescarmontier and others (2012) provide further details of the processing and the possible spurious signals remaining. We projected our solutions into a local orthogonal topocentric coordinate system (x, y, z) with the x axis defined as the along-tongue direction (defined as the velocity averaged over the whole observation period), y to the left, across the tongue, and z the local up direction (the local vertical, orthogonal to the x and y axes; Fig. 1). In the following we will use the terminology along-tongue for the x direction and across-tongue for the y direction.

2.2. Satellite images

We used imagery from Landsat 7 in panchromatic mode (15 m pixel size), SPOT 5 (Satellite Pour l’Observation de la Terre) in panchromatic mode (5 m pixel size), and European Remote-sensing Satellite (ERS-1 and ERS-2) synthetic aperture radar (SAR) images for both interferometric phase interpretation of the deformation and SAR amplitude images as a complement to the visible images. ERS images were processed with a 20 m pixel size. The images were then geo-referenced and projected onto the Universal Transverse Mercator (UTM) zone 55S map reference system using World Geodetic System 1984 (WGS84) ellipsoid parameters.

The images used are from different time periods and were selected to illustrate a specific feature or change in that feature. However, selection of a particular date for an image to best highlight the phenomenon under discussion is limited by the availability of images that are of suitable quality (e.g. cloud conditions in most of the MODIS images are overcast so the surface is obscured). Concerning the SAR images, only one set of images, comprised of four pairs from ERS-1 and ERS-2 sufficient to produce two double-difference interferograms, were available over the entire time period. SPOT 5 images were ordered specifically for our study, and so start later on.

2.3. Basal shear stress and sea surface slope based modeling

In the following, we determine the contributions from the different drivers of modulation of the ice tongue velocity. For this, we adapt a model developed by Reference GudmundssonGudmundsson (2007) that allows the basal shear stress to vary with the tide. We assume that all the variation in velocity on the floating tongue (as measured by our GPS), which we ascribe to tidal modulation, equates to the variation in velocity of the inflow from the grounded portion of the glacier. The difference between the velocity at the grounding zone and at our GPS station is the increase in velocity along the tongue due to longitudinal extension of the ice in the tongue. Measurements by feature tracking in satellite images show this additional velocity contribution is 0.55 m d⁻¹. The velocity variations across the grounding zone are thus transmitted to the floating part and to the rest of the ice tongue.

Reference GudmundssonGudmundsson (2007) implemented a model of ice-stream flow in which the basal shear stress was allowed to vary in conjunction with the tidal signal. With that model he was able to reproduce fortnightly variations in ice velocity of the type observed on Rutford Ice Stream. The two main assumptions used in that model are that:

• 1. within the ice, tidally induced stress perturbations are linearly related to tidal amplitude; and

• 2. deformation of till underlying the ice stream follows a nonlinear relationship between the shear stress and the rate of basal sliding velocity.

The basal sliding velocity is generally expected to be some function of basal shear stress (Reference ClarkeClarke, 1987; Reference Iverson, Hanson, Hooke and JanssonIverson and others, 1995; Reference TrufferTruffer, 1999; Reference Tulaczyk, Kamb and EngelhardtTulaczyk and others, 2000; Reference Fischer, Porter, Schuler, Evans and GudmundssonFischer and others, 2001; Reference TulaczykTulaczyk, 2006), and the results from Reference GudmundssonGudmundsson (2007) reinforce that assumption.

Our model follows the formulation of Reference GudmundssonGudmundsson (2007), in which the basal shear stress is defined as

where is the mean basal shear stress and the tidally driven variation is given by

where ρ _w is the density of sea water, g the gravitational acceleration, h(t) the height of the ocean tide varying with time, and K is a site-dependent modeling parameter.

We introduce an additional component corresponding to a gravitational force induced by the effect of sea-surface slope following Reference Makinson, King, Nicholls and GudmundssonMakinson and others (2012) and Mayet and the others Reference Mayet, Testut, Legresy, Lescarmontier and Lyard(2013), and we optimize the parameter values to picking match the situation on Mertz Glacier such that

where K_s is a constant, M is the mass of the ice tongue (here we estimate the volume using area from the imagery and thickness from radio-echo sounding to derive a value of 3200 Gt), α is the sea-surface slope in the along-tongue direction and S is the cross-sectional area at the grounding line on which the force is acting (here we take an approximation of S = 5600 m² as a simple geometric cross section based on our limited knowledge of ice thickness).

The basal shear stress can now be written, using Eqns (2) and (3), as

where K and K_s (constants) are the two site-dependent modeling parameters. In simple terms, the value of K_s is expected to equal that for K, but there is considerable uncertainty in the value of M, as well as the actual effective cross section S. As a consequence, these parameters will take different values. In addition, the influence of the tidal height is not simply exerted as the normal load at the base, but will be the integral of variations in drag over various parts of the base and sides of the tongue. In the following, we adjust K and K_s by a least-squares parameter optimization.

The basal sliding velocity u _b is written as

where C and m are modeling constants. This equation refers to Weertman’s sliding law (Reference PatersonPaterson, 1994). The total forward velocity is then assumed to be

where is the slip ratio, i.e. the ratio between the mean sliding velocity (u _b) and the mean forward deformational velocity (u _d). We adopt values for the sliding exponent of m = 3, and the basal sliding coefficient of C = 0.12 × 10⁻³ m d⁻¹ kPa^−m from Reference PatersonPaterson (1994), also determined as being the best-fitting values.

The main coefficients that remain to be determined are the slip ratio r, deduced from the ice surface slope, the mean surface velocity u _s, the coefficients K and K_s for the time-varying components of the basal shear stress, and the mean basal shear stress (Reference GudmundssonGudmundsson, 2007 for explanations). The optimal values found for the various parameters (following the procedure of Reference GudmundssonGudmundsson, 2007) are slip ratio r = 107, , K = 0.05 and K_s = 0.07. The values of K and K_s are similar, as expected before optimization. Sensitivity analysis and least-square optimizations are undertaken to fit the best parameter values, although no direct comparison with data from other ice streams is attempted.

3.1. Initiation of rifting

Two ice streams merge at about the grounding line to form Mertz Glacier Tongue. We refer to these as the west and south ice streams (Fig. 3). We derive their dimensions using SAR interferometry (Reference Legresy, Wendt, Tabacco, Remy and DietrichLegresy and others, 2004), shear limit as well as flowlines from a combination of repeated Envisat Advanced SAR images (red in Fig. 3). The southern ice stream is 10–15 km wide and the western stream is 13–14 km wide.

Fig. 3. Box 1 from Figure 1. SPOT 5 image of the grounding zone from 5 February 2008 with the location of the grounding line (green) and flowlines (red). The projection is in UTM with a 5 km grid spacing. The grounding line appears in green following the InSAR analysis of Poetzsch and others (2000). ©CNES 2008/Distribution Spot Image.

Figure 2 reveals surface features that exhibit different behaviors on the two ice streams. Transverse features oriented orthogonal to the ice velocity vector (y-direction, across-tongue) develop on both ice streams, upstream of the grounding line. The western ice stream bends left as it crosses the grounding line into Mertz Glacier Tongue and retains the orthogonal orientation of the features all the way to Mertz Glacier Tongue front. By contrast, for the southern stream, which bends to the right across the grounding line into Mertz Glacier Tongue, the features become rotated anticlockwise with respect to the flow vector (x, along-tongue) on the glacier tongue.

In Figure 4, we present the SAR amplitude image (Fig. 4a) and two different sets of double-differenced interferograms (Fig. 4b and c), zoomed on the part of Mertz Glacier Tongue where it exits the fjord. We observe a sequence of lateral rifts (appearing at the edge of the ice stream) in the southeast margin of Mertz Glacier Tongue, which form where the ice stream exits the fjord (H (hinge) zone in Fig. 4a). Reference MacGregor, Catania, Markowski and AndrewsMacGregor and others (2012) hypothesize that rifting as appearing in Figure 4 is favored at the margins, which are expected to be rheologically weaker (Reference Echelmeyer, Harrison, Larsen and MitchellEchelmeyer and others, 1994; Reference MacAyeal, Rignot and HulbeMacAyeal and others, 1998; Reference Khazendar, Rignot and LarourKhazendar and others, 2007) and to have numerous surface crevasses that may connect with basal crevasses, which form at the grounding line, to form margin rifts (Reference Catania, Conway, Raymond and ScambosCatania and others, 2006). The major eastern rift initiated in one of these margin rifts, and preferentially propagated along the transverse features that had initiated in the vicinity of the grounding zone. The major western rift developed in a similar fashion. Reference Legresy, Wendt, Tabacco, Remy and DietrichLegresy and others (2004), when investigating the flexure of Mertz Glacier Tongue, showed that the outer part of the ice tongue bends about the hinge zone (H in Fig. 4a) as a result of its flexure, and that this flexure is driven by the ocean circulation.

Fig. 4. Box 3 from Figure 1. Interferometric image from 1996 corresponding to the ERS SAR scenes of the stress zone on Mertz Glacier Tongue. (a) Amplitude and (b, c) phase. The projection is in UTM with a 2.5 km grid spacing. The images used to form these double-difference interferograms were acquired in April–May 1996. One fringe corresponds to 28 mm distance variation in the satellite line-of-sight (for details of the processing see Reference Legresy, Wendt, Tabacco, Remy and DietrichLegresy and others, 2004). The circle surrounds the hinge point (H) at the east of the glacier tongue. Arrows A, B and C point to the location of some of the crevasses at the site of the hinging point where the beam stress is maximum. Arrows D and E point to other crevasses forming on the eastern side of the ice tongue. SAR data ©European Space Agency 1996.

In Figure 4b, we observe dense fringe patterns along the margin of the glacier tongue associated with the vertical tidal motion, and a broad set of fringes on the outer tongue indicative of the horizontal rotation of that part of the tongue about zone H. In particular, we see fringe patterns over each of three transverse features (A, B, C in Fig. 4b) on the western ice stream, which reveal differential deformation within these features. The fringe pattern is equivalent to a relative displacement of the order of 2 cm in the satellite line-of-sight vector. Similarly in Figure 4c, the different combination of tidal intervals results in fewer fringes from tidal vertical motion and an absence of horizontal rotation fringes. There, we see different patterns of deformation within features A, B and C and, in addition, we see differential deformation of transverse features D and E from the southern ice stream. As the ice tongue advances ∼1 km a⁻¹ in this area, the transverse crevasses will be advected with the flow and new crevasses will initiate, forming the typical features visible on Mertz Glacier Tongue.

3.2. Evolution of the rifting area on Mertz Glacier Tongue since 1996

To follow the evolution of these rifts, we first derived the area of both rifts (Fig. 5), for the period 1996–2009, using ERS (first epoch in 1996) and Landsat 7 images. Several things can affect an individual measurement (e.g. sun orientation, shadowing effects, spatial resolution of the images, user interpretation). Measurements repeated a few times by two independent users obtained very similar results. We indicate the precision of our measurements as two pixels on each side of the rift, equating to ±30 m of rift width or ±0.5 km² of area, as represented by the vertical bars in Figure 5.

Fig. 5. Evolution of the rift surface area from 1996 to 2009 calculated from Landsat 7 and SAR images. The red line corresponds to the area of the eastern rift, the blue line to the area of the western rift (Fig. 1), the green lines are the sum of both rift areas, and a linear regression of the total area is plotted. Its intersection with the x axis indicates a starting date of major rift opening around 1992.

The evolution of the rift area comprises two main stages. Up to 2002, the eastern rift area increased as the rift widened, and lengthened as the tip propagated west. Then, during 2002, the western rift (blue lines in Fig. 5) started to open. From 2003, the eastern rift started closing while the western rift continued to develop. We estimate an effective total rift width as the sum of the two areas divided by the Mertz Glacier Tongue width, which amounts to ∼350 m from 2003 onwards. The linear fit of the sum over the entire period gives an opening rate of ∼0.91 km² a⁻¹ in area, 60 m a⁻¹ in width, or 16 cm d⁻¹, which is comparable with the western rift opening rate of 12 cm d⁻¹ measured by the GPS stations at one section across the rift in 2007–08. Extrapolating back to zero area gives an approximate start date for the eastern rift opening ∼1992. The 2002 initiation of the western rift is coincident with the impact of the C08 iceberg on Mertz Glacier Tongue (Reference MassomMassom and others, 2015). These two rifts can be defined as continuously active (C.C. Reference Walker, Bassis, Fricker and CzerwinskiWalker and others, 2013), as their evolution did not stop after their initiation and has not shown any dormant period.

3.3. Differential motion across the rift

In Figure 6, we present time series of the across-tongue component of the tidal current calculated from the TUGO-M barotropic model (with European Centre for Medium-Range Weather Forecasts (ECMWF) atmospheric forcing) (Reference Mayet, Testut, Legresy, Lescarmontier and LyardMayet and others, 2013), and of the across-tongue (y) component of positions measured at GPS 4 (black) and GPS 5 (red). Positive (negative) values of the across-tongue current correspond to westward (eastward) currents. Here we use the current as a proxy for the across-tongue components of the three forces associated with ocean circulation that act on the ice tongue (the pressure force, the drag force and the sea-surface slope-induced gravity force) as they all act in phase. Although the slope-induced force is not strictly linearly related to the current, it is qualitatively well represented by it (Reference Mayet, Testut, Legresy, Lescarmontier and LyardMayet and others, 2013).

Fig. 6. Time series of the mean velocity of (a) the TUGO modeled across-tongue current and (b) across-tongue position (black for GPS 4 (upstream), red for GPS 5 (downstream)), with the mean velocity of GPS 4 removed from both time series in order to show the 8 m opening of the rift over 60 days. We clearly see that positive (negative), across-tongue ocean forces correspond to a westward (eastward) displacement of the ice tongue. (c) Across-tongue position anomaly with mean velocity of GPS 4 removed from the GPS 4 time series (red for GPS 5) to show finer-scale across-tongue motion. Date format is dd/mm/yyyy.

The paths of GPS 4 and GPS 5 evolve into different directions over time. The mean velocity vector of GPS 5 is rotated 35° to the east of the mean velocity vector of GPS 4. This difference in direction is a consequence of the rift opening. Over 60 days, we measured a rift opening of 8 m (Fig. 6b) or a mean rate of 12 cm d⁻¹.

Station GPS 5 is located on the downstream, less constrained part of the ice tongue, and exhibits larger variability in the movement of this downstream part of Mertz Glacier Tongue. The time of the maximum in the tidal current matches the maximum displacement in GPS position. The greatest amplitudes of across-tongue movement occur during spring tides. The daily tidal modulation of the opening of the rift is ∼5 cm in amplitude, almost half the daily rate of opening. Considering these observations, we deduce that ocean currents are a major factor driving the rifting processes in the case of Mertz Glacier Tongue and we assume that rift propagation is continuous since its initiation (C.C. Reference Walker, Bassis, Fricker and CzerwinskiWalker and others, 2013).

We computed the changes in the relative vector between GPS 4 and GPS 5 as a function of time and resolved these changes into along-tongue and across-tongue components. We then subtract the mean trend from each component and filter out variations with periods 4 days to produce two time series of residuals (Fig. 7). The 4 day filter eliminates the daily-scale tidal variations. We note there is a systematic smooth variation with time in the residuals represented by the red curves. This smooth variation in rate is explained by a rotation of the downstream part of the tongue about a center 15.7 km from the midpoint of the vector as shown in Figure 2. Given this rotation, the expected pattern of residuals is shown as the red curve in Figure 7. The deviations of the filtered observations (black curve) from those for steady rotation (red curve) in Figure 7 indicate that this relative movement is not strictly a simple rotation and the center of the rotation may not be at a single point but may shift over time within the active rift area. In the longer term, the behavior of this part of the ice tongue is thought to be changing as the stresses evolve, as indicated by the earlier behavior of this ‘rifting system’. This showed us that the rift opening is not linear and the evolution of the stresses induced by its opening (implying the changing of the bending moment on the remaining ice tongue) influences the interaction of the ice tongue with the currents, and hence its effect on the rifting.

Fig. 7. Relative along-tongue and across-tongue displacements of the relative vector between GPS 4 and GPS 5 over 60 days. The black curves are filtered for periods shorter than 3 days with a linear filter, and in red appears the parabolic fit for the 60 days. The difference given relative to GPS 4 shows that, along-tongue, GPS 5 approaches GPS 4 and then comes back to its position. For the across-tongue movement, GPS 5 is located on the western side (negative) of GPS 4 and then moves to the eastern side (positive) of GPS 4. This movement is the result of a rotation of GPS 5 relative to GPS 4. Its center of rotation is calculated using the parabolic fit and is shown in Figure 2. Date format is dd/mm/yyyy.

Even if the rifting area was increasing over time and we anticipated that the tongue was going to calve, we would not be able to forecast the date of any calving event. In fact, the opening of the rifts is not linear, and unforeseen events (e.g. iceberg collisions) can completely change the balance of stresses on the ice tongue (Reference MassomMassom and others, 2015). This effect is not new and has been studied in the past (Reference Holdsworth and JacobsHoldsworth, 1985), but we still observe that the forces associated with tidal circulation are strong enough to open the rift through a bending moment on the ice tongue. They tend to increase its area and thus represent factors to take into account when investigating calving processes of ice tongues.

3.4. Impact of tides on the ice flow velocity: change in behavior

From the study of Reference Legresy, Wendt, Tabacco, Remy and DietrichLegresy and others (2004), we expected to see a modulation of the flow velocity dependent on the direction of the tidal current. However, the evolution of Mertz Glacier Tongue induced a change in this modulation. In this subsection, we investigate the effect of oceanic circulation on the rift opening, comparing the two sequences (before 2000 and after 2007) as well as the tidal modulation of the flow velocity using the Reference GudmundssonGudmundsson (2007)-based model.

Using our 60 day GPS time series, we computed the along-tongue ice speed by a simple linear fit on the positions within time windows of different lengths. We also computed various statistics of the velocity estimates using standard statistical tests, such as a Student’s t test. We find that using a time window wider than 30 min gives reliable estimates of the speed, which are significant at the 98% confidence interval. Calculating the linear fit over different time windows gives an idea of the part of the signal that is not related to the noise or to any kind of non-modeled signal (in that case, under 30 min sampling). Table 1 presents the velocity variability computed for the whole 60 day record, the associated 98% confidence interval, and the correlation with the model for different widths of the time window.

In Figure 8a, we see that the speeds computed from the measured GPS positions with a 4 hour window show a tidal pattern with daily peaks, together with a fortnightly modulation from the lunar–solar cycle, confirmed by a harmonic analysis. Figure 8b and c show a shorter time interval of the same time series over two 4 day intervals at spring tide and neap tide phase respectively. In addition, we display the speed computed with a 1 hour time window. At this short sub-tidal timescale, there is a clear and strong variability in the velocity, with positive and negative peaks occurring at any time over the series, whether during spring or neap tides. But there does appear to be a pattern in the association of peaks in the velocity and phases of the tides. In the spring tide phase, the greatest maxima occur during the ascending phases of the tides, and the maxima increase in value as the tide rises. During neap tide, the sub-tidal variability appears to be spread more evenly through the day, although there does appear to be a weak association of strongest maxima with the bottom of the tidal range. The peak-to-peak amplitude of velocity variations at sub-tidal scales can reach 1.5 m d⁻¹ or ∼50% of the average long-term velocity. Figure 8d shows the velocity recorded at GPS 4 (green) and GPS 5 (blue). The mean along-tongue velocity calculated for GPS 5 is slightly larger than for GPS 4 and is likely a consequence of the effect of longitudinal extension of the floating tongue together with the opening of the rift.

Fig. 8. (a) Along-tongue velocity (black) and sea-surface height measured at GPS 4 (red) over 60 days. (b, c) Along-tongue velocity and sea-surface height calculated from 1 hour (blue) and 4 hour time windows (black) for spring tides (b) and for neap tides (c) over 4 day intervals. (d) Comparison between GPS 4 (green) and GPS 5 (blue) along-tongue velocity.

Figure 9 shows the velocity in the along-tongue direction as measured at GPS 4 (upstream of the rift), the height measured at the same station, and the sea-surface slope (along-tongue), as calculated from the TUGO-M model (which incorporates the atmospheric pressure, wind and tides with ECMWF 3 hour forcing). We first notice that the sea-surface height measured in the area is characterized by a spring to neap cycle with a strong fortnightly period. The amplitude of the semidiurnal component varies over each period, with large semidiurnal amplitudes associated with the interval (neap to spring) corresponding to the increase in the fortnightly component, and small semidiurnal amplitudes corresponding to the decrease from spring to neap phase. Secondly, we see apparent daily and fortnightly variations of the ice velocity at GPS 4. The amplitude envelope of the along-tongue component is proportional to the envelope of the spring tide cycle. The mean velocity is 3.01 m d⁻¹ with a range of typical values from 2.95 up to 3.35 m d⁻¹. The correlation coefficient of the ice velocity with the sea-surface height is ∼0.6.

Fig. 9. (a) Sea-surface height anomaly; (b) sea-surface slope computed from TUGO-M; and (c) along-tongue velocity as recorded at GPS 4 (black) and along-tongue velocity modeled using the sea-surface height and slope (green) over 60 days.

The sea-surface slope signal has the same general characteristics as the sea-surface height signal. However, the phasing is significantly different, even though the variation of sea-surface height and the sea-surface slope are similar in character. The variations of surface elevation closely match those of the ice-shelf along-tongue displacement in both relative amplitude and phase, suggesting that tidally driven sea-surface height is the primary driver of along-tongue displacement. The maximum peak in ice velocity occurs 2.5 hours after the maximum peak in tidal elevation. On the other hand, the timing of the peak in sea-surface slope matches the peak of the semidiurnal tidal velocity.

The Reference Legresy, Wendt, Tabacco, Remy and DietrichLegresy and others’ (2004) study of ice velocity modulation on Mertz Glacier Tongue showed that the direction of tidal circulation and the effect of drag on the walls of the fjord were the main drivers of the flow modulation. The present study identifies a completely different behavior, where we find a small range of ice velocity variation, 1075–1225 m a⁻¹, in 2007, compared with the very large range of 700–2400 m a⁻¹ in 2000. The main change that has occurred over the 7 years between these dates is the opening of the rifts, which has modified the bending moment of the ice tongue, and disrupted transmission of the lateral load onto the walls of the fjord.

We now use our basal shear stress based model (Section 2.3) with a selection of scenarios to generate time series of along-tongue velocity values. We compare results from two of these scenarios (green and purple in Fig. 10) with our directly measured velocities (red in Fig. 10). We then discuss the effects involved in the modulation of the along-tongue velocity. For this analysis, we assume that the basal stress on the ice tongue is zero and, in particular, that there is no drag from the sides of the fjord on the floating part of the system within the fjord. Therefore velocity variations at any point downstream of the grounding line will be the same as those at the grounding line. Here we present results from GPS 4 (GPS 5 being the same).

Fig. 10. (a) Zoom-in of the modeled velocity (purple) from the sea-surface height only, and along-tongue velocity modeled using the sea-surface height and the slope (green) over 2 days. (b) Along-tongue velocity from GPS 4 observed (red).

The measured and modeled velocities are presented in Figure 10 as anomalies with respect to the long-term mean values. The comparison shows that despite the model simplicity, it reproduces fortnightly variations in velocity in considerable detail and gives a good fit to the amplitude of the variations. The model explains the main part of the velocity variation recorded by the GPS with a correlation coefficient of 0.69. The different drivers in the model, i.e. the sea-surface height and sea-surface slope, both derived from TUGO-M, contribute at different levels. With sea-surface height as the only driver, the model explains 43% of the variance, and the addition of the sea-surface slope explains a further 4% of the variance. The addition of atmospheric forcing through the contribution of pressure and wind does not make a significant difference to the computed velocities. In other words, the atmospheric forcing does not affect the velocities at the frequencies in the velocity time series where we observe the main variability. The tidal effects are thus the primary drivers. The modeled velocities shown for a short time interval in Figure 10 are derived using only the sea-surface height term (purple), and using both the sea-surface height and slope (green).