Technological advances in the recent satellite altimeter missions of Jason-2, SARAL/AltiKa and CryoSat-2 have improved their signal-to-noise ratio, allowing us to observe finer-scale ocean processes with along-track data. Here, we analyse the noise levels and observable ocean scales in the northwestern Mediterranean Sea, using spectral analyses of along-track sea surface height from the three missions. Jason-2 has a higher mean noise level with strong seasonal variations, with higher noise in winter due to the rougher sea state. SARAL/AltiKa has the lowest noise, again with strong seasonal variations. CryoSat-2 is in synthetic aperture radar (SAR) mode in the Mediterranean Sea but with lower-resolution ocean corrections; its statistical noise level is moderate with little seasonal variation. These noise levels impact on the ocean scales we can observe. In winter, when the mixed layers are deepest and the submesoscale is energetic, all of the altimeter missions can observe wavelengths down to 40–50 km (individual feature diameters of 20–25 km). In summer when the submesoscales are weaker, SARAL can detect ocean scales down to 35 km wavelength, whereas the higher noise from Jason-2 and CryoSat-2 blocks the observation of scales less than 50–55 km wavelength.
This statistical analysis is completed by individual case studies, where filtered along-track altimeter data are compared with co-located glider and high-frequency (HF) radar data. The glider comparisons work well for larger ocean structures, but observations of the smaller, rapidly moving dynamics are difficult to co-locate in space and time (gliders cover 200 km in a few days, altimetry in 30 s). HF radar surface currents at Toulon measure the meandering Northern Current, and their good temporal sampling shows promising results in comparison to co-located SARAL altimetric currents. Techniques to separate the geostrophic component from the wind-driven ageostrophic flow need further development in this coastal band.
The ocean circulation in the northwestern Mediterranean Sea exhibits widespread mesoscale dynamics, with strongest values along the Northern Current which flows westwards along the French coast following the continental slope (Millot, 1999; Guihou et al., 2013). Observing the mesoscale variability is critical in this region since it plays a key role in the coupled ocean–atmospheric system that can lead to extreme precipitation events (Lebeaupin Brossier et al., 2015). Horizontal currents stirred by the mesoscales are important in the dispersion of pollutants and the monitoring of marine ecosystems. The vertical transport of heat, salt and nutrients is strongly driven by the smaller-scale dynamics, in the fronts and filaments surrounding these mesoscale eddies, and within the deep convection cells that form in the Gulf of Lyons in winter–spring (Herrmann et al., 2008).
Compared to other current systems at similar latitudes such as the Gulf Stream, the mesoscale variability in the northwestern Mediterranean Sea has a small Rossby radius of 5–15 km, varying seasonally with the stratification (Grilli and Pinardi, 1998). This makes the ocean dynamics of this region particularly difficult to observe and monitor. The surface mesoscale characteristics have been studied with satellite sea surface temperature (SST) and ocean colour data in clear-sky conditions (Robinson, 2010), but the mesoscale variability is often hidden in winter by clouds and in summer under the more homogenous warm surface layer. Numerical modelling studies are improving in resolution and in their internal physics to allow a better representation of the mesoscale variability (e.g. Herrmann et al., 2008), although these models need to be validated against observations.
In the global ocean, mapped satellite altimeter products have allowed unprecedented advances in understanding the mesoscale eddy variability and characteristics (Chelton et al., 2011). Altimetry measures sea surface height (SSH) that responds to mass and density changes over the entire water column, and as such, altimetry is the only satellite observation that can detect deep ocean changes. Deep-reaching mesoscale eddies can be tracked over many seasons or years (e.g. Morrow et al., 2004; Chelton et al., 2011), even if their surface signature disappears through air–sea interactions so that they become undetectable in satellite imagery. Although regional altimeter maps have been constructed with improved resolution and spatial scales adapted for the Mediterranean Sea (e.g. Pujol and Larnicol, 2005), the spacing between ground tracks still limits our ability to monitor scales less than 150 km wavelength (or 75 km diameter features) (Pascual et al., 2006). Thus we can only detect the larger mesoscale structures, missing most of the typical Rossby radius dynamics in the Mediterranean Sea.
Along-track altimeter data are able to detect finer scales than the mapped altimeter data, but the spatial scales we can resolve are still limited by the altimeter noise, the accuracy of the corrections and the processing methodology. However, over the last 5 years, there has been great progress in improving the quality of along-track satellite altimeter data for ocean studies. Of the three missions currently flying in the altimeter constellation, Jason-2 in Ku-band (launched in 2008) has benefitted from continually refined algorithms and corrections, and new waveform retrackers that allow more data points to be collected close to the coast and islands, and more stable performance with lower noise over the oceans (Dibarboure et al., 2011). SARAL/AltiKa (launched in 2013) was designed to have a smaller footprint and lower noise over all surfaces, due to the choice of antenna pattern, Ka-band frequency and its lower altitude (Verron et al., 2015). CryoSat-2 (launched in 2010) is primarily a cryosphere mission and not planned for ocean observations. Yet over the last years, considerable efforts have been made by the ESA SAMOSA project (Ray et al., 2015) and the CNES Cryosat-2 Processing Prototype (CPP) project (Boy et al., 2017) in collaboration with oceanographers to improve the waveform retracking over the ocean and provide adequate corrections for ocean observations. CryoSat-2 is in low-resolution mode over most of the global ocean but has synthetic aperture radar (SAR) mode observations available over a few regions, including the Mediterranean Sea, with improved along-track sampling down to 300 m and reduced noise. However, certain ocean corrections are less accurate than on Jason-2 or SARAL, including the radiometer correction and the mean sea surface estimate, since CryoSat-2 is on a geodetic orbit. These three altimeter missions with different technologies and data processing will provide an ideal data set to test the improved observational capabilities in the NW Mediterranean Sea.
Previous studies have analysed the altimetric capabilities in the NW Mediterranean Sea from conventional along-track data (Bouffard et al., 2008, 2011; Birol and Delebecque, 2014; Birol and Nino, 2015), including using seasonal averaging to reduce the noise for Jason but maintaining along-track resolution (Birol et al., 2010). Here we will take a different approach, in order to measure the altimetric signal-to-noise ratio statistically in the different seasons. We will calculate along-track sea level anomaly (SLA) spectra (e.g. Fu, 1983), which allows us to observe the SLA spectral energy at different wavelengths, and also the time-averaged spectral noise at small wavelengths. In terms of signal, the spectral energy of SLA is higher at longer wavelengths, and lower at small wavelengths, and geostrophic turbulence theory involves a cascade of energy from the larger to smaller scales, leading to a steep spectral slope in wavenumber space. When spectra are averaged (over different ground tracks in a region and/or over time along the same ground track), the random altimeter noise averages out to create a flat spectral noise floor in the 1 Hz data. This spectral noise level then defines our altimeter noise. The intersection of this noise floor with the spectral slope will define the limit of the observable wavelengths, where the signal-to-noise ratio is statistically greater than 1.
Following Xu and Fu (2012) we will remove the spectral noise from the spectra before calculating the spectral slope, to improve the slope estimate and have more precise observational limits. This technique has been applied to the global altimeter data sets, for Jason-1 by Xu and Fu (2012) and for Jason-2, SARAL and CryoSat-2 by Dufau et al. (2016). Their results showed considerable geographical variations in the spectral slope, noise levels and mesoscale resolution (Xu and Fu, 2012), and strong seasonal variations in the noise level and the mesoscale observing capabilities (Dufau et al., 2016). Neither study included the smaller Mediterranean Sea region, due to the limited spatial coverage in this regional sea. In our analysis, we will concentrate on tracks having at least 200 km length.
Altimetric data used in this study.
LRM: conventional low-resolution mode; SAR: synthetic aperture radar mode. First number corresponds to the total number of 200 km sections used in the regionally averaged spectra (Fig. 3); numbers in brackets correspond to the number of sections used in each seasonal average (Fig. 4).
These studies calculated their spectral slopes over a fixed “mesoscale” band from 70 to 250 km wavelength. The Mediterranean Sea, which is dominated by smaller dynamical structures, may have different spectral energy and spectral slopes in this band compared to open-ocean regions. The surface sea-state conditions are also dominated by short wind waves and less by long swell, which may impact on the radar altimeter's noise level. Both of these features will be considered in the first section of this paper. We aim to investigate the noise levels for the most recent altimeter missions, estimated from their spectral noise level in the Mediterranean Sea. We will revisit the appropriate filtering to be applied to remove the noise in different seasons. We will then consider what scales of ocean dynamics can be observed today in the Mediterranean Sea with along-track altimetry and investigate how much of the seasonal dynamical signal is observable above the seasonal noise.
In the second part of this paper, we will use a complementary approach and focus on the observation of individual features using a combination of altimetry and a limited number of glider sections and 2 years of high-frequency (HF) radar observations filtered at similar scales. We will examine whether the ocean scales observable with altimetry are also captured by the co-located in situ data. Glider–altimetry comparisons have been used for previous altimetry missions in the NW Mediterranean Sea (e.g. Bouffard et al., 2010) but not for the three most recent missions. For the glider comparison, we only have a limited number of historical co-located sections, and so gliders were deployed specifically along altimetric tracks for each of the three missions, under different mesoscale conditions. For the HF radar, we will use a HF radar site near Toulon, as part of the MOOSE observational array (Quentin et al., 2013), with an offshore extent of 25–75 km from the coast. We will discuss the strengths and limits of the different measurement systems' observation in the coastal band.
Distribution of altimeter tracks in the NW Mediterranean Sea showing
the different missions: the 10-day repeat Jason-2 mission in red, 35-day
repeat SARAL/AltiKa in green, and the 380-day repeat CryoSat-2 in grey. Only
sections greater than 200 km are included in the spectral analysis, and only
data more than 50 km from the coast are analysed to remove the increased
errors in the coastal zone. The distance from the coast is calculated using
the Stumpf database
(
Along-track SSH observations from the most recent altimetry missions (Jason-2, CryoSat-2 and SARAL/AltiKa) are analysed over the NW Mediterranean Sea (Fig. 1) and over different periods (Table 1). The data are made available from AVISO/CNES. Jason-2 is a conventional pulse-width limited altimeter operating in Ku-band (Lambin et al., 2010) and provides the longest time series: we use data over the 6.8-year period from July 2008 to February 2015. SARAL/AltiKa, with its 40 Hz Ka-band emitting frequency, its wider bandwidth, lower orbit, increased pulse repetitivity frequency and reduced antenna beamwidth, provides a smaller footprint and lower noise than the Ku-band altimeters (Verron et al., 2015). We use data from the nearly 2-year period from March 2013 to January 2015. CryoSat-2 is a synthetic interferometric altimeter (SIRAL) Ku-band instrument operating in three modes (low-resolution mode (LRM), synthetic aperture radar mode (SARM) and SAR interferometric mode). Only the SARM data are available over the Mediterranean Sea, and we use data from the CNES CryoSat-2 processing prototype (version 14) from CNES (Boy et al., 2017) over the 1-year period April 2013 to April 2014. For all three missions we will analyse the 1 Hz data only, which have a flat noise floor. Higher-frequency data (20 or 40 Hz) show a spectral bump at wavelengths less than 70 km, which does not allow us to estimate a stable noise floor (Dibarboure et al., 2011).
The choice to analyse different periods was dictated by the data availability and our desire to have longest possible time periods available for the seasonal analyses. The limited quantity of altimeter cycles considered during this period is compensated by the spatial averaging of available tracks in the NW Mediterranean Sea, which improves the statistical significance of our analysis.
Along-track SSH observations are maintained at their original observational
position and corrected for all instrumental, environmental and geophysical
corrections. Only the time variable part of the SSH is considered following
Stammer (1997), Le Traon et al. (2008) and Xu and Fu (2011, 2012). SLAs are calculated for all missions relative to their precise
along-track mean sea surface for Jason-2 and SARAL, both on a long-term
repeat track. CryoSat is on a geodetic orbit, and its SLAs are
calculated relative to a gridded mean sea surface (MSS_CLS2011,
A large number of gliders have been deployed in the NW Mediterranean Sea as
part of the MOOSE project (
Characteristics of the co-located glider and altimeter track sections.
Slocum gliders were used, diving at a 26
For comparison with the altimeter data, we need to obtain steric heights from the glider relative to 1000 m. For this, we calculate a single vertical profile at the central position for each of the diagonal dives (descending or ascending) and calculate steric heights from the density anomalies. Geostrophic velocities are also calculated relative to the 1000 m depth.
There is an additional “drift” speed that can be added to this geostrophic velocity, associated with the lateral heading correction used to keep the glider on track against a strong current. This drift correction represents the total current over the upper 1000 m and will include the barotropic currents close to the continental slope, some ageostrophic surface currents and a correction for the upper baroclinic flow. This correction was generally small in our region except near the continental slope, and we will clearly identify when this correction is used in the following study.
As part of the MOOSE observing system, a HF radar system has been installed
near Toulon (
The Toulon HF radar system uses two WERA radars that provide surface current
vectors over a region extending 80–100 km offshore, with a spatial
resolution of 3 km and an angular resolution of 2
Spectral analyses are performed on each of the three altimeter missions, with their tracks shown in Fig. 1. Only data more than 50 km from the coast are analysed to avoid the increased errors in the coastal zone. Each track and cycle is then selected along a common segment of 200 km. This segment length was chosen to allow a large number of altimeter segments in different regions in between the numerous islands and to be more than 50 km from the coast, to avoid the increased errors in the coastal altimeter data. This segment length is also long enough to well resolve the dominant scales (Rossby radius of 5–15 km). Missing data are a problem for a stable spectral analysis. If fewer than three consecutive 1 Hz points are missing (20 km), the data are linearly interpolated; if a larger gap is present the cycle is eliminated from the analysis. Tracks passing over large islands are thus eliminated (see Fig. 1). Wavenumber spectral analysis is then performed by Fourier transform on the ensemble of the remaining segments for each mission (see Table 1). The cycles are averaged in wavenumber space for the entire period and for each season.
An example of the power spectral density (PSD) of SLA averaged for all of the Jason-2 data in the NW Mediterranean Sea over the period 2008–2015 is shown as the black curve in Fig. 2. The PSD is high at longer wavelengths (> 300 km). There is a cascade of energy over the mesoscale range from 50 to 300 km, but the spectra become whiter at small wavelengths (i.e. less than 50 km), where the weaker ocean energy is hidden by the stronger instrument and geophysical noise.
Mean wavenumber spectra (power spectral density) for Jason-2 sea level anomalies, averaged over all tracks in the NW Mediterranean Sea > 50 km from the coast (black curve) for the period 2008 to 2015. The estimated noise level is shown as the horizontal black dashed line. The unbiased spectra (red curve) are obtained by subtracting this constant noise from the original spectra. The spectral slope (red dashed line) is calculated between 50 and 200 km wavelength. The intersection between these two curves occurs around 50 km wavelength for this case, which represents the mesoscale observational limit, above which the mean signal-to-noise ratio is > 1.
In the following seasonal analyses, the
Following the global studies made by Xu and Fu (2012) and Dufau et
al. (2016), we then subtract this statistically stable noise level from the
mean spectral curve, to obtain an unbiased spectral estimate corrected for
the noise (red solid line curve, Fig. 2). The
We define the
The
When a constant noise level is removed from each spectral PSD, the spectral
slopes line up surprisingly well, given the different space–time sampling of
the three missions over this 13-month period. The spectral slope is again around
The fact that the CryoSat-2 1 Hz data in SAR mode had a higher noise level than SARAL/AltiKa was unexpected. We verified that the CryoSat-2 20 Hz data were consistent with the 1 Hz averages, so this is not an averaging problem. The CryoSat-2 20 Hz SAR mode does exhibit a spectral hump for this region and time period that was not present in other regions with SAR data (Agulhas or tropical Pacific; S. Labroue, personal communication, 2016). This warrants further analysis of the particular surface roughness conditions occurring in the NW Mediterranean during this year, and further expertise in SAR processing for the Mediterranean conditions is needed. These results reinforce the very low noise level associated with the 40 Hz Ka-band SARAL data, averaged here to 1 Hz.
Seasonal spectra were also calculated from the longest time series possible,
i.e. over 6.5 years for Jason-2 data, over 22 months for SARAL/AltiKa, and
for the shorter 13-month period for CryoSat-2 (see Table 1). The spectral
noise floor levels for the seasonal analyses are shown in Fig. 4a. Note the
spectral units are in m
Figure 4b shows the observational limits for each altimeter mission by season. Clearly, the background noise is not the only limiting factor on the scales of mesoscale energy that we can observe. The SLA energy at low wavelengths also varies from one season to another. In winter, when the mixed layers are deepest and energetic deep convection cells occur in the NW Mediterranean Sea (e.g. Herrmann et al., 2008), all of the altimeter missions can observe wavelengths down to 40–50 km (individual features of 20–25 km). In summer when the submesoscales are weaker, SARAL can detect ocean scales down to 35 km wavelength, whereas the higher noise from Jason-2 and CryoSat-2 blocks the observation of scales less than 50–55 km. This characteristic was also noted in the global analysis of Dufau et al. (2016). Unfortunately in winter, when we would like to observe the smaller energetic submesoscales, all of the radar altimeters observe higher noise levels associated with the higher wind-wave field.
The previous section highlighted that the altimetric noise was effectively masking the smaller-scale SLA signals in the along-track data. The smallest scales observable with a signal-to-noise ratio greater than 1 will vary from one altimeter mission to another and seasonally. Statistically, we cannot observe structures less than 35–45 km wavelength with SARAL, or 50–60 km wavelength with the higher noise of Jason-2. However, individual energetic features may be revealed above the statistical noise. We will explore this with a series of co-located along-track altimeter–glider sections and compare the vertical structure observed by the gliders with their steric height and geostrophic velocities.
In this section, the filtering of the along-track altimetry data is based on the standard Loess filtering applied to the CTOH coastal processed data (Birol et al., 2010; Birol and Nino, 2015). For each glider–altimeter comparison, the first estimate of the along-track altimeter filtering scales was based on the seasonal spectral analysis results for each altimeter mission (see Sect. 3). Other cut-off frequencies around this seasonal statistical value were also tested. The filter which gave the best results in terms of glider–altimeter correlation coefficient and which had the lowest cut-off wavelength was then chosen. The altimeter filter values are given in Table 2.
One should bear in mind that the glider steric height and geostrophic
velocities (with or without their surface drift adjustment) will observe
different dynamics from the altimetric sea level and geostrophic velocity
anomalies. The steric height calculated from gliders represents the upper
ocean baroclinic component due to the density anomalies above 1000 m depth.
Altimetric SLAs include the full-depth baroclinic motions and the barotropic
component, and the barotropic flow may be quite active in the NW
Mediterranean Sea, in particular near the shelf break and slope (F. Lyard,
personal communication, 2016). When the glider “surface drift” is added to
the glider geostrophic currents relative to 1000 m, this may partially
correct for the missing barotropic component. Altimetry may also include
other SLA signals, such as from internal tides or internal waves, which
contribute as errors in the geostrophic velocity calculation (although tides
are small in the Mediterranean Sea). In addition, the altimetric SLAs have
the mean ocean circulation removed, whereas the gliders provide the total
upper ocean baroclinic flow. For consistency, the mean dynamic topography and
mean geostrophic velocities derived from Rio et al. (2014) are added to the
altimetric data for this comparison. The third main difference is the time
taken to make a section over 100 to 300 km. The altimeter makes a
“snapshot” of the section as it passes at 7 km s
One crucial point is that the gliders have their own noise and also measure HF ageostrophic ocean structures that will not be observable with altimetry. Figure 5 shows a vertical temperature section over the upper 200 m from the glider Milou along the SARAL altimeter track 57 from 27 October to 3 November 2014. Figure 5b shows the very small-scale signals in the upper ocean temperature structure along this 164 km long section. These may be associated with noise in the glider heading or from the processing steps, or from internal waves or rapid submesoscale structures. To remove these scales, we have applied a recursive Butterworth second-order along-track filter to the density data, before calculating the steric height or geostrophic anomalies, with a filter cut-off at 30 km wavelength, designed to retain the typical Rossby radius scales of 10–15 km in the NW Mediterranean Sea. This filtering step was recommended from previous glider studies (e.g. Durand et al., 2016). An example of the filter applied to the same temperature section is shown in Fig. 5c. Similar filtering is applied to the different glider sections presented below.
Ten glider sections are available, co-located with altimeter tracks (details given in Table 2). Here we present three glider track sections along different altimeter mission tracks.
The glider Campe followed a Jason-2 track 146 over a 300 km section from
42 to 39.5
The southbound section crosses a series of small reversing currents around
small SST structures of 30–50 km (Fig. 6a). The glider and along-track
Jason-2 data show cross-track currents in phase, although the Jason-2
amplitudes are stronger (correlation,
Three weeks later, the northbound section crosses a strong mesoscale eddy.
The three data sets present similar eastward currents across the mesoscale
eddy, and although the amplitude of the westward current near 42
Five-day series of satellite SST maps for the period 9–13 November.
The glider position is shown each day (in red), the SARAL–glider crossing
position on 12 November (in black), and the SARAL track passing on
12 November 2014. Daily SST fields at 0.02
Although a number of satellite underpasses were planned for SARAL, different deployment problems limited the number of successful intercomparisons (bad weather, gliders leaking, errors in estimating the satellite position, etc.). The longer sections did not necessarily cross any energetic features, and we eliminated sections where the currents were very weak. The short section presented here highlights another difficulty – comparing small-scale structures in a rapidly evolving field.
Figure 7a shows an example of the SARAL–glider comparison for the SARAL
track 388 and the glider Milou, which crossed a narrow, intense, westward
current around 42.75
If the glider and altimeter observations are overlaid on a daily time series
of satellite SST maps, the differences between these two observations becomes
clearer. Figure 8 shows the 5 days needed by the glider to complete this
77 km section to 1000 m depth and the evolving SST conditions during this
period. On the 9 November 2014, the glider was in the south and crossed a
cold eastward-moving filament. On 10 November, the glider is in weaker
conditions. On 11 November, the warmer westward-flowing current starts to
shift southward and on 12 November, when Jason-2 passed over, the warm
branch has extended south to 42.3
This example highlights the difficulty in comparing sections constructed from 5 days of glider data with the near-instantaneous coverage from the along-track altimetry data. These small-scale structures less than 50 km evolve quickly, and having observations that are not exactly co-located in space and time leads to large differences.
The third example concerns two gliders deployed at 1-day intervals along the
CryoSat-2 track 493, which passed on 27 April 2015. CryoSat-2 SAR data
are filtered at 35 km (see Sect. 3). Figure 9 shows that the two gliders and
the CryoSat-2 data detect well the westward-flowing Northern Current near
42.5
The along-track geostrophic currents (Fig. 9b) show that the two gliders,
separated by 1 day, observe the same features. However, the peaks in
westward flow, detected by the gliders at 42.6 and 42.1
In summary, the glider–altimeter comparisons reveal the difficulty in validating the along-track altimetry data with observations that are not exactly co-located in time and space. The relatively slow gliders are able to capture the slower-moving larger eddies, as seen in our example with Jason-2 and highlighted by previous studies (Bouffard et al., 2010). However, the real improvement in altimetric signal-to-noise levels expected with SARAL and CryoSat-2 are not revealed in these glider comparisons, mainly because at the time of these altimeter observations, rather weak signals were detected or the small-scale meanders were moving rapidly. In these cases, our observations approach the error levels of the two systems. Small offsets in the structure of the Northern Current could also be introduced by the removal of a mean sea surface from the CryoSat-2 data sets, which could induce errors on these small space scales (up to 80 km wavelength, Dufau et al., 2016). Although gliders can observe energetic small-scale structures in dedicated campaigns in the Mediterranean Sea (e.g. Bosse et al., 2015), the chance is small that these occur at the precise position and time when the gliders and altimeter tracks coincide. This comparison highlights the difficulty in setting up a validation campaign for altimetric observations of small-scale rapidly moving dynamics.
HF radar surface currents near Toulon for one date
(20 October 2013); direction with small arrows, current speed is in colour.
SARAL track 302 is marked in pink; 1 Hz cross-track geostrophic currents
from SARAL altimetry are in black; the HF radar total currents projected in
the altimetric cross-track direction are in red. The current scale of
0.3 m s
HF radar data provide an additional observation of the oceanic surface
currents. In comparison to the geostrophic component of the flow obtained
with altimetry and gliders, HF radars measure the total surface current, due
to balanced geostrophic and unbalanced ageostrophic currents (wind-driven,
inertial, tidal currents, etc.). The daily data set we used has been
processed to remove the HF tides and inertial currents, retaining
the geostrophic and wind-driven currents. Figure 10 shows an example of the
HF radar total currents for one date, 20 October 2013 near Toulon, with
the two coastal radar locations marked. The presence of the strong Northern
Current is clearly visible in the 2-D HF radar current vectors, with a
central jet only 10 km wide, the current spanning 20 km to its edges. This
is clearly below the statistical observability limits from the spectral
analysis of the three altimeter missions. The offshore extent of the HF radar
data is from 25 to 75 km from the coast, which extends into the coastal band
that was excluded from our spectral analysis, as it has frequently “noisy”
altimeter data and corrections. The small spatial coverage of the HF radar
means that no Jason-2 data cross this region, although we have one SARAL
track passing through the centre (Fig. 10) and a number of non-repeating
CryoSat-2 tracks. The angle of the SARAL track shown in Fig. 10 is such that
the cross-track geostrophic currents are mainly orientated in the principal
direction of the Northern Current. For this date (20 October 2013), the
amplitude of the HF radar currents, projected in the altimetric cross-track
direction (in red), is similar to the SARAL cross-track currents (in black),
reaching 0.7–0.8 m s
The advantage of the HF radar data set is its daily 2-D coverage at fine resolution, so we should not have the space–time offsets in the sampling of small-scale features that plagued the glider–altimeter comparisons. The disadvantage is that altimeter data in the last 10–50 km from the coast are noisy, and the ageostrophic wind-driven component of the HF radar surface currents can be strong here, in the region with strong mistral winds.
We have compared the observability of these near-shore currents with the finer-resolution SARAL altimeter time series, filtered at 35 km (see Sect. 3). SARAL data are available along this track every 35 days, and Fig. 11 shows the 18-month time series of cross-track surface velocities from the HF radar. The upper panel shows the full time series of HF radar currents projected perpendicular to the altimeter track; the middle panel shows the HF radar currents sampled at the same dates as the SARAL altimeter passes, and spatially sampled at 7 km as for the 1 Hz altimeter data. The bottom panel shows the SARAL 1 Hz geostrophic currents (mean and anomalies), filtered at 35 km. SARAL clearly detects more of the offshore return flow than the HF radar can but covers a similar data range as the HF radar to the coast. Along-track correlations of the HF radar and altimetric currents for this cross-track velocity component are between 0.7 and 0.9 for these 16 tracks, except for four dates, where the correlations drop below 0.5. The RMSE between the cross-track HF radar current amplitudes and the SARAL current amplitudes is shown in Fig. 12. Dates with low correlations (< 0.5) are marked with the vertical dashed line, and these have a higher RMSE. The RMSE is generally lower in the summer months when the wind is lower and increases in winter.
RMSE between the cross-track HF radar current amplitudes and the SARAL current amplitudes. Dates with low correlations (< 0.5) are marked with the vertical dashed line.
Wind forcing of the ageostrophic currents may explain part of the difference.
If we consider the daily time series of HF radar data (Fig. 11a) and extract
the outliers in cross-track velocity having > 1
The along-track altimeter spectral analysis allows us to estimate the mean dynamical scales that can be observed today with different altimeter technology and associated processing, and in different seasons. In winter, when the mixed layers are deepest and the submesoscale is energetic, all of the altimeter missions can observe wavelengths down to 40–50 km (individual feature diameters of 20–25 km). In summer when the submesoscales are weaker, SARAL can detect ocean scales down to 35 km wavelength, whereas the higher noise from Jason-2 and CryoSat-2 blocks the observation of scales less than 50–55 km wavelength.
This is a statistical view. There are limits in applying this too assiduously, especially as these statistics are calculated from relatively short records for SARAL, and only 13 months of reprocessed SAR data for CryoSat-2. We chose to analyse the longest time series possible for the seasonal calculations since the records are relatively short. However, entire years should be analysed to remove any sampling biases in these statistics. Given the long repeat time for CryoSat-2, we also measure different geographical regions in each season, which can introduce biases in our basin-scale averages. Interannual variations also occur in the dynamics in response to interannual atmospheric changes, which can lead to different deep convection events from one season to another (Adloff et al., 2015). Analysing a longer time series of SARAL and CryoSat data should improve the significance of these early results.
One application of this type of analysis is to improve the altimetric data post-processing to be adapted to the regional conditions. Today, along-track filtering is applied in a similar way to all altimeter missions to reduce the instrument and geophysical noise. Since consecutive altimeter points are laid down spatially, data are filtered spatially along the track to reduce this noise. Standard filtering in the AVISO along-track products DT2010 ranges from 55 km wavelength at high latitudes to around 250 km in the tropics (Dibarboure et al., 2011). The new AVISO products DT2014 apply lower along-track smoothing at 65 km wavelength, globally and for all missions (Pujol et al., 2016). This study suggests that the along-track filtering may be tuned in a regional study to be better adapted to the local dynamics and noise conditions. Thus in the NW Mediterranean Sea, filtering of Jason-2 data could vary seasonally from 50 km in winter to 60 km in autumn and spring (or a conservative 60 km year-round). SARAL could have a finer-scale along-track filtering applied, to retain wavelengths greater than 35 km in summer–autumn and 45 km in winter. A filter cutoff of 50 km year-round could be suitable for CryoSat-2. Knowing how this statistical signal-to-noise ratio varies from one mission to another, and seasonally, is very useful for regional applications, for local process studies or for data assimilation.
The in situ validation remains very limited in space and time and did not
allow us to confirm whether these smaller scales are realistic ocean
features. For the glider comparison with SARAL, small-scale structures were
detected by both systems, but their rapid movement prevented us from giving a
precise along-track co-location except for the short scales close to the
temporal crossing point. Indeed, for advective dynamics to be resolved
correctly, they should conform to the Friedrichs–Lewy condition,
i.e.
The SARAL intercomparison with the Toulon HF radar data was quite promising. Despite the apparent nearshore errors in the SARAL data, and the periods with strong wind-driven currents, the correlation between the SARAL geostrophic currents and HF radar total currents remained high. The position of the Toulon HF radar helps, as the observations are centred on the Northern Current, in a region where the current is strongly steered by bathymetry, and the geostrophic component is dominant. This example indicates that a strong coastal current, with a high signal-to-noise ratio, can be detected by satellite altimetry, even at 20 km from the coast. Improvements are still needed to reduce the altimetric errors in the nearshore region, and to compare the CryoSat-2 SAR current observations with the HF radar data. This good intercomparison suggests that HF radar data may be combined with altimetry to extend the observations (duration and offshore extent) of the Northern Current and its recirculation near Toulon.
Another potential way to cross-validate the feature scales observed by the different altimeter missions is to use the crossover points between different missions. Figure 1 shows that there are many crossover points during this analysis period, especially from CryoSat-2 on its long-repeat 369-day orbit and even from Jason-1, which moved into a long-repeat 406-day geodetic orbit from April 2012 to 1 July 2013. Our analyses of the small, fast-moving features in this paper indicate that we really need crossover measurements overlapping within 1–2 days to capture these fine-scale features. These multi-altimeter overlapping passes are also interesting for the missions on a similar inclination, since their overlapping sections can be quite long. For example, SARAL and CryoSat may have long overlapping sections with a time difference of less than 2 days (see Fig. 1). Similar long sections may be available from the Jason-1 geodetic mission and Jason-2. At present, we are developing the code to calculate the crossovers from multi-satellite passes and select the passes based on their time differences. This analysis will be performed as part of our ongoing work in this region.
For the future altimetric missions, finer spatial sampling and lower noise levels should continue, with Sentinel-3 in global SAR mode launched in early 2016, and SWOT providing 2-D interferometric SAR heights and images and an order of magnitude lower noise in 2021. Similar wavenumber spectral analysis techniques could be applied to estimate the noise levels and observable spatial scales with these new missions. This study illustrates that the difficulties in setting up an adequate in situ validation for the small-scale, rapidly evolving dynamics will remain a challenge to resolve in the future.
Altimeter data: the unfiltered along-track Jason-2 and SARAL altimeter SLA
data sets are available from the AVISO website
(
Glider data are available as part of the MOOSE project
(
HF radar data are also available as part of the MOOSE observing system
(
This work was carried out by Alice Carret as part of her master's programme. Rosemary Morrow supervised the work and prepared the manuscript with contributions from all co-authors. Guillaume Valladeau and Francois Boy provided co-supervision. Florence Birol and Fernando Nino provided support with the analysis. Celine Bachelier processed the glider data and Bruno Zakardjian the HF radar data.
The authors declare that they have no conflict of interest.
This work was funded by an OSTST CNES TOSCA grant. The glider and HF radar data were funded as part of the French MOOSE Mediterranean observing system programme, with additional financial support from CNES as part of the Comsom glider campaign. We gratefully acknowledge the constructive comments by two reviewers and the editor, which helped to improve the manuscript. Edited by: J. M. Huthnance Reviewed by: A. Sánchez Román and one anonymous referee