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\begin{document}

\title{New Global Mean Dynamic Topography CNES-CLS-22 Combining Drifters,
Hydrological Profiles and High Frequency Radar Data~}



\author[1]{Solène Jousset}%
\author[1]{Sandrine Mulet}%
\author[1]{Eric Greiner}%
\author[2]{John Wilkin}%
\author[3]{Lien Vidar}%
\author[2]{Gérald Dibarboure}%
\author[4]{Nicolas Picot}%
\affil[1]{CLS, Ramonville Saint Agne, 31250, France}%
\affil[2]{Affiliation not available}%
\affil[3]{Institute of Marine Research, Bergen, Norway}%
\affil[4]{CNES, Ramonville Saint Agne, 31520, France}%


\vspace{-1em}



  
  \date{May 24, 2024}


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\textbf{Abstract.} The mean dynamic topography (MDT) is a key reference
surface for altimetry. It is needed for the calculation of the ocean
absolute dynamic topography, and under the geostrophic approximation,
the estimation of surface currents. CNES-CLS mean dynamic topography
(MDT) solutions are calculated by merging information from altimeter
data, GRACE, and GOCE gravity field and oceanographic in situ
measurements (drifting buoy velocities, High Frequency radar velocities,
hydrological profiles). The objective of this paper is to present the
newly updated CNES-CLS22 MDT. The main improvement of this new
CNES-CLS22 MDT over the previous CNES-CLS18 MDT is in the Arctic, with
better coverage, no artifacts and a more realistic solution. This is due
to the use of a new first guess estimated with the CNES-CLS22 MSS and
the GOCO06s geoid to which optimal filtering has been applied, as well
as Lagrangian filtering at the coast to reduce the intensity of normal
currents at the coast. Improvements also include updating the drifting
buoy and T/S profile databases, as well as processing to obtain
synthetic mean geostrophic velocities and synthetic mean heights. In
addition, a new data type, HF radar data, was processed to extract
physical content consistent with MDT in the Mid Atlantic Bight region.
The study of this region in particular has shown the improvements of the
CNES-CLS22 MDT, but that there is still work to be done to obtain a more
physical solution over the continental shelf. The CNES-CLS22 MDT has
been evaluated against independent height and velocity data in
comparison with the previous version, the CNES-CLS18. The new solution
presents slightly better results, although not identical in all regions
of the globe.

\section*{1 Introduction}

{\label{introduction}}

Since the early days of altimetry, estimating absolute dynamic
topography (ADT) accurately has been an issue (Rio 2010). The absence of
an accurate geoid at spatial scales corresponding to the spatial
resolution of altimetry data along tracks, i.e. 7km at 1Hz and 300m at
20Hz, does allow to reconstruct absolute dynamic topography accurately.
So most scientific studies of the ocean have used the temporally
variable part of sea level relative to the mean over a reference period:
the sea level anomaly (SLA). And this has improved our knowledge of the
dynamics of mesoscale structures. However, many scientific and
operational activities require accurate absolute sea level. For the
study of eddy-mean interactions, a positive sea level anomaly can be due
to different processes such as anticyclonic eddies, the strengthening of
a quasi-permanent anticyclonic eddy, the weakening of a cyclonic eddy,
or the displacement of a current or eddy (Rio et al. 2007; Pegliasco et
al. 2020). Pegliasco et al. (2020) shows that it is more appropriate to
use absolute dynamic topography rather than SLA to track eddies. For the
correct assimilation of altimetry data into models, Hamon et al. (2019)
have highlighted the need for an accurate MDT as well as its associated
error. Finally, absolute dynamic topography provides access to
geostrophic currents, useful data for monitoring ocean currents, and
different application as maritime security, ocean pollution.

Furthermore, with the arrival of new swath observations from the SWOT
(Surface Water and Ocean Topography) satellite launched in December 2022
(Fu et al. 2012), which provides sea level observations over swaths 120
km wide with a resolution of 2 km, an accurate MDT at a spatially finer
resolution and defined close to the coast is needed.

To access the absolute dynamic topography, it is necessary to estimate
an accurate Mean Dynamic Topography (MDT ; ADT = MDT + SLA). Since the
launch of the ESA GOCE satellite (Gravity and Ocean Circulation
Experiment; Pail et al. 2011), the Earth's geoid has been measured with
centimetric accuracy at a spatial resolution of 100km. In addition, the
accumulation of altimetry data, improved processing and, in recent
years, the special processing applied to leads (fractures in ice) have
led to an improvement in the Mean Sea Surface (MSS) and its estimation
over ice-covered areas such as the Artic Ocean (Schaeffer et al. 2023).
The ''geodetic'' approach (Bingham et al. 2008), which consists of
estimating the MDT by subtracting the geoid from the MSS, then applying
a reliable filter, provides accurate solutions for spatial scales
greater than 100km. To estimate spatial scales shorter than 100km, it is
necessary to add information to these scales. A first method is to use
altimetry data to add finer scales to the geoid. These geoids are called
combined geoids, Eigen6c4 (F\selectlanguage{ngerman}örste et al. 2014) and XGM2019e (Zingerle et
al. 2020) are examples. From these combined geoids, it is possible to
estimate a geodetic MDT such as MDT DTU22 (Knudsen et al. 2022). Another
approach is to use a large-scale satellite-only geodetic MDT and add the
small scales from in-situ ocean data (temperature and salinity profiles,
velocities estimated from drifting buoys or High Frequency radars).
These in situ data need to be processed to extract only the physical
content corresponding to the MDT. This approach is used to estimate the
various CNES-CLS MDTs (Rio and Hernandez 2004; Rio et al. 2011; Rio et
al. 2014; Mulet et al. 2021) and in this study.

This paper presents the new CNES-CLS22 Mean Dynamic Topography (MDT)
solution. Improvement has been made possible by the recent availability
of updated time series of drifter and in situ temperature and salinity
profiles data, improved MSS and geoid model. The method is reminded in
section 2, while data used in the computation and validation are
presented in section 3. The new CNES-CLS22 MDT is described and
validated in section 4. Conclusions and discussion are provided in
section 5.

\section*{2 Method}

{\label{method}}

The method used to estimate the new CNES-CLS2022 MDT follows the same
approach than the one detailed in Rio and Hernandez (2004), Rio et al.
(2007, 2011 and 2014a), and Mulet et al. (2021). It is a three-step
approach reminded and summarized below:

The first step is to compute a first guess MDT from the filtered
difference between the MSS and the geoid model: a geodetic MDT. The
effective resolution of this resulting field depends on the noise level
of the raw differences between the MSS and the geoid height; it is
around 125km (Bruinsma et al. 2014).

The second step is to compute synthetic estimates of the MDT and
associated mean geostrophic velocities from in-situ data. The drifter
data and High Frequency (HF) radar data are processed to keep only the
geostrophic component. For the dynamic heights estimated from the T/S
profiles, they are processed to add the missing components: the
barotropic component and the deep baroclinic component. Temporal
variability is removed from the dynamic heights and velocities, by
subtracting the altimeter sea level anomalies and the associated
geostrophic velocity anomalies respectively. Since the altimeter sea
level anomalies referenced to the 1993-2012 reference period, the
processed in-situ dynamic heights and velocities are then also
referenced to the 1993-2012 period, and this allows the use of in-situ
observations over a longer period than the reference period (Rio and
Hernandez 2004). The processed dynamic heights are averaged by 1/4°
boxes to obtain the synthetic mean heights and the processed velocities
are averaged by 1/8° boxes to obtain the synthetic mean velocities.
Velocities from HF radar are averaged per cell (6X6km resolution). Note
that this version of the MDT uses only Mid Atlantic Bight HF radar data.

Finally, the third step consists in improving the large-scale MDT (from
step 1) from the synthetic data (from step 2) through a multivariate
objective analysis whose formulation was first introduced in
oceanography by Bretherton et al. (1976). This analysis takes as input
the a-priori knowledge of the MDT variance and zonal and meridional
correlation scales.

\subsection*{2.1 Computation of first guess and comparison with previous
first
guess}

{\label{computation-of-first-guess-and-comparison-with-previous-first-guess}}

The raw difference between the CNES-CL22 MSS and GOCO06s geoid height is
filtered using the optimal filter fully described in Rio et al. (2011).
For the MDT CNES-CLS22 computation, this step has been improved with the
application of additional Lagrangian filter along the coast to avoid
streamline going into land.

The geostrophic velocities associated with the first guess calculated
from the raw differences between the CNES-CL22 MSS and GOCO06s geoid
height optimaly filtered are compared with the drifter velocities
(section 3); the drifter velocities have been processed to obtain a
physical content comparable with the geostrophic velocities. Similarly,
the geostrophic velocities associated with the first guess of the
CNES-CLS18 MDT have been compared with the drifter velocities. Figure 1
shows the improvement (blue color) or degradation (red color) of the RMS
of the differences with the drifter velocities of the CNES-CLS22 first
guess compared with the CNES-CLS18 first guess, in current amplitude (a)
and current direction (b). Figure 1 (a) shows that current amplitude is
strongly enhanced near the coast, almost everywhere. In the open ocean,
the differences between the two first guesses in comparison to drifters
are minimal, except south of 45°S, particularly in the Indian Ocean,
where there are degradation boxes for first guess 2022. For this
comparison, Lagrangian filtering at the coast has not yet been applied.
This improvement at the coast in the amplitude of the geostrophic
currents associated with the first guess compared with the drifters is
linked to the use of the new CNES-CLS22 MSS and the new GOCO06s geoid.
As for the current direction shown in Figure 1 (b), there is no clear
improvement or deterioration in the new first guess compared with the
old one.\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image1/image1}

\end{center}
\end{figure}

Figure 1: Comparison of the RMS of the differences (a) in current
modulus and (b) in direction, of the independent drifting buoy
velocities and the altimeter geostrophic velocities obtained using MDT
solutions first guess of the CNES-CLS22 (unfiltered at the coast with
the Lagrangian filter) and the first guess of the CNES-CLS18, in percent
:

\(\mathbf{\%}\mathbf{\text{RMSD}}\mathbf{\,=}\frac{\mathbf{\text{RMS}}\left(\mathbf{U}_{\mathbf{\text{MDT}}_{\mathbf{FG22}}}\right)\mathbf{-}\mathbf{\text{RMS}}\left(\mathbf{U}_{\mathbf{\text{MDT}}_{\mathbf{FG18}}}\mathbf{-}\mathbf{U}_{\mathbf{d}}\right)}{\mathbf{\text{RMS}}\left(\mathbf{U}_{\mathbf{\text{MD}}\mathbf{T}_{\mathbf{FG18}}}\mathbf{-}\mathbf{U}_{\mathbf{d}}\right)}\mathbf{\,}\). These statistics are calculated in boxes of 5* by
5*. Only boxes with more than 100 measurement points and more than 10
different drifters are shown. The bluish colors denote improvement while
reddish colors stand for degradation.

\subsection*{2.2 Computation of the synthetic mean
heights}

{\label{computation-of-the-synthetic-mean-heights}}

The aim of estimating synthetic mean heights is to use temperature and
salinity profiles to calculate a mean height whose physical content is
the same as the MDT. Temperature and salinity profiles are used to
calculate density variations in the water column and to estimate a
dynamic height (between the profile's reference depth and the surface)
representing the baroclinic component of the dynamic circulation. Here
we use reference depths of 200, 400, 900, 1200 and 1900m, with each
dynamic height calculated according to one of these reference depths,
the deepest accessible according to the maximum depth of the T/S
profile. The dynamic heights thus estimated do not have the same
physical content as the Altimeter Sea Level Anomalies (SLA), as the SLA
is also influenced by baroclinic processes between the reference depth
and the bottom, as well as by barotropic processes not measured by
change in temperature and salinity (Rio et al. 2014b). To obtain average
heights over the reference period, we need to remove the temporal
variability (of the SLA) from the instantaneous dynamic heights; we
therefore need to remove the temporal variability by subtracting the
part of the SLA corresponding to the baroclinic process from the surface
to the reference depth. Then add the missing components: the barotropic
signal and the baroclinic signal from the reference depth of the profile
to the bottom. The method for these two steps is the same as the one
fully described in Rio et al. (2011) and also used in Rio et al. (2014a)
and in Mulet et al. (2021).

In particular, the missing quantity, the average contribution of deep
baroclinic and barotropic processes, is estimated as the difference
between the climatology of dynamic heights relative to the given
reference depth, the same as the T/S profile and the first estimate of
the CNES-CLS MDT22. For each reference depth considered in this study
(200, 400, 900, 1200 and 1900m), a climatology is calculated from the
same CORA database (section 3) to remain consistent, this time using the
maximum number of profiles possible, i.e. for the reference depth 200m,
using all profiles deeper than 200m. These climatologies are then
filtered at the same spatial scale as the first guess, i.e. 125km.

The optimal analysis to estimate the CNES-CLS22 MDT is performed on the
anomalies with respect to the first guess, so we remove the first guess
from the synthetic fields before the optimal analysis and then add this
first guess to the result to obtain the final MDT. In this
remove-restore framework, the estimation of mean synthetic heights is
equivalent to considering only the small scales of synthetic dynamic
heights relative to reference depth. Figure 2 shows these fine scales of
synthetic mean heights (all reference depths averaged by 1/8\selectlanguage{ngerman}° by 1/8°
boxes). The signal is intense in the large western boundary currents and
in the Antarctic Circumpolar Current (ACC), with anomalies of over +/-10
cm. These mean synthetic heights will tend to accelerate these large
currents.

Finally, the synthetic mean heights are averaged in 1/8\selectlanguage{english}* boxes. The
associated errors are computed as described in Rio et al. (2011). These
errors are high in areas of high oceanic variability: western boundary
currents, the ACC; and near the poles, where there are few data or less
confidence in processing. Overall, the error is less than 2cm in the
rest of the ocean. As in the Rio et al. (2014b) study, the error
associated with these mean synthetic heights does not take into account
the first-guess error and is therefore certainly underestimated.\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image2/image2}

\end{center}
\end{figure}

Figure 2: Fine scales of synthetic mean heights, all reference depths
averaged by 1/8\selectlanguage{ngerman}° by 1/8° boxes in cm, equivalent to mean synthetic
heights minus first guess (input to optimal analysis).

\subsection*{2.3 Computation of the synthetic mean
velocities}

{\label{computation-of-the-synthetic-mean-velocities}}

The objective of this estimation is to process the velocities estimated
from drifters (section 3) and surface Argo float drifts to obtain the
physical content of the geostrophic currents associated with the MDT.
This is achieved by removing from the drifter velocities the
ageostrophic components of the current, as well as the temporal
variability of the geostrophic component of the velocities:

\begin{equation}
U_{\text{synth}}=U_{\text{drifter}}-U_{\text{Ekman}}-U_{\text{Stokes}}-U_{\text{inertial}}-U_{\text{tidal}}-U_{ageo-hf}-U_{\text{slippage}}-U_{\text{alti}}^{{}^{\prime}}\nonumber \\
 \end{equation}

First, wind-driven currents (\(U_{\text{Ekman}}\)) is removed from the
drifter velocity, as well as the wind slippage (\(U_{\text{slippage}}\)),
which is the direct effect of wind on undrogued drifters.
\(U_{\text{Ekman}}\) is taken from the Copernicus-Globcurrent product
(MULTIOBS\_GLO\_PHY\_REP\_015\_004,
\emph{\url{https://data.marine.copernicus.eu/product/MULTIOBS\_GLO\_PHY\_REP\_015\_004/description}})
while wind slippage correction (\(U_{\text{slippage}}\)) is available in the
CMEMS INSITU\_GLO\_PHY\_UV\_DISCRETE\_MY\_013\_044 product
(\emph{\url{https://data.marine.copernicus.eu/product/INSITU\_GLO\_PHY\_UV\_DISCRETE\_MY\_013\_044/description}}).
These products are consistent as they use same upstreams for
computation: ERA5 wind and wind stress (section 3), and Mixed Layer
Depth as a proxy to the Ekman layer thickness (from CMEMS ARMOR3D:
MULTIOBS\_GLO\_PHY\_TSUV\_3D\_MYNRT\_015\_012,
\emph{\url{https://data.marine.copernicus.eu/product/MULTIOBS\_GLO\_PHY\_TSUV\_3D\_MYNRT\_015\_012/description}}).
Then the temporal variability of the geostrophic component of velocities
(\(U_{\text{alti}}^{{}^{\prime}}\)) is removed. Next, the tide, inertial oscillations
and residual ageostrophic signal (as U\textsubscript{stokes}) are
removed by high-frequency filtering. Finally, the mean synthetic
velocities obtained are averaged in boxes 1/8\selectlanguage{ngerman}° by 1/8°.

This method, the estimation of the wind-driven component of the current
and slippage, and the filtering applied are fully described in Mulet et
al. (2021, section 5) and build on previous work by Rio and Hernandez
(2004), Rio et al. (2007, 2011 and 2014a).

For this new MDT, we are also using velocities data estimated from High
Frequency radars located in the Mid Atlantic Bight area, on the East
Coast of the USA, from Cape Hatteras to Cape Cod. In the same way as for
drifter data, the aim is to process these velocities to obtain synthetic
velocities with the physical content of geostrophic MDT velocities. We
used the cleaned, detited, high-frequency signal-filtered and mean
currents over the period 2006-2016, processed by Rutgers University
(Roarty et al. 2020). Then the mean wind-driven currents over the same
period (\(U_{\text{Ekman}}\) taken from the Copernicus-Globcurrent product
MULTIOBS\_GLO\_PHY\_REP\_015\_004) were removed and finally these mean
currents were re-referenced to the 1993-2012 reference period.

Figure 3 shows these mean synthetic velocities estimated from (a)
drifters (at 1/8° resolution) and (b) HF radar data, over the Mid
Atlantic Bight area off New Jersey and Delaware (USA). The figure also
shows the 100m and 2000m isobaths that mark the limit of the continental
shelf. The average synthetic velocities estimated by drifters are much
noisier, with more intense currents, than those estimated from HF
radars. However, both maps show a recirculation current to the
south-east at the 100m isobath. The drifters (Figure 3 a) show this
current as narrow and intense (15 to 20 cm/s), whereas the HF radars
(Figure 3 b) show a broad current of between 5 and 10 cm/s. Very close
to the coast, velocities are generally low (below 5 cm/s), but currents
can be perpendicular to the coast (e.g. Figure 3 b at 74.5°, 75° and
75.5°W). Between 74.9° and 75°W, the outflow of the Delaware River could
explain these cross-shore currents.

These differences can be explained by the very different sampling of the
two types of data:

- HF radar: at least 50\% of data every hour over 10 years

- Drifters (1 or 2 drifters per box near the coast).

Moreover, it is likely that drifters tend to converge at the center of
the current due to convergence and subduction, resulting in a sampling
bias in favor of a narrow jet.\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image3/image3}

\end{center}
\end{figure}

Figure 3: Synthetic mean velocities in the Mid Atlantic Bight region off
New Jersey and Delaware, estimated (a) from drifting buoy (at 1/8\selectlanguage{ngerman}°) and
(b) from HF radar data. Black lines represent 100m and 2000m isobaths.

\subsection*{2.4 Multivariate objective
analysis}

{\label{multivariate-objective-analysis}}

The third step of this method is multivariate objective analysis as in
Rio and Hernandez (2004), Rio et al. (2007, 2011 and 2014a) and in Mulet
et al. (2021), which uses the synthetic mean geostrophic velocities and
synthetic mean heights to improve the first guess, in particular to
improve the fine scales, to obtain the CNES-CLS22 MDT. This optimal
analysis requires the a priori MDT variance and the a priori zonal and
meridional spatial correlation scales of the estimated field. The same
statistical a priori as for Rio et al. (2014a) and Mulet et al. (2021)
are used here. In the equatorial band, as the geostrophic approximation
is no longer valid, only mean synthetic height observations are used for
MDT estimation, and for current estimation, only mean synthetic
velocities observations are used for inversion.

\section*{3 Data}

{\label{data}}

The CNES-CLS22 MDT is calculated from a combination of altimeter and
space gravity data, in situ measurements and model winds. The method
allows us to estimate the mean over the 1993-2012 reference period, but
is not limited to observations from this period. For each in situ
observation, we remove the altimetric variability referenced to the
1993-2012, thus obtaining an estimate of the mean dynamic topography
corresponding to the reference period. The following datasets are used:

-- \emph{MSS.} The CNES-CLS22 MSS derived for the 1993-- 2012 reference
time period by Schaeffer et al. (2023) is used.

-- \emph{Geoid model.} The satellite-only geoid model GOCO06s (Kvas et
al. 2021) is used with the CNES-CLS22 MSS in the computation of the MDT
first guess.

-- \emph{Altimeter sea level anomalies (SLAs).} The DUACS-2021 (Taburet
et al. 2022) multimission gridded sea level and derived geostrophic
velocity anomaly products distributed by the Sea Level Thematic Assembly
Center (SL-TAC) from the CMEMS altimeter are used.

-- \emph{Dynamic heights.} These are calculated from temperature and
salinity (T/S) profiles from CTD and ARGO from CMEMS CORA Release
November 2022 (period 1993-2020, Szekely et al. 2023), processed by the
In Situ Thematic Assembly Center (INS-TAC) of the Copernicus Marine
Environment and Monitoring Service (CMEMS). In order to carry out a
cross-validation of the new CNES-CLS22 MDT with the latest CNES-CLS18
MDT (Mulet et al. 2021), about 5\% of the T/S profiles which will not be
used for the calculation of the MDT, is kept. These 5\% of the T/S
profiles are randomly selected since 2017, in order to have a set of
validation data that is independent of the new MDT but also of the
CNES-CLS18 MDT.

-- \emph{In situ velocities.} Two types of in situ drifting buoy
velocities are used, the 6-hourly SVP-type drifter distributed by the
Surface Drifter Data Assembly Center (SD-DAC; Lumpkin and Johnson 2013)
and the Argo floats surface velocities from the regularly updated
YOMAHA07 dataset for the period 1997--2021 (Lebedev et al. 2007).
SVP-type drifters consist of a spherical buoy with a drogue attached in
order to minimize the direct wind slippage and follow the ocean currents
at a nominal 15 m depth. When the drogue gets lost, the drifter is then
advected by the surface currents and the direct action of the wind. In
this study both the 15 m drogued and the surface undrogued drifter
velocities over the 1993-- 2021, period are considered for the MDT
calculation. 10\% of the AOML drifters dataset are randomly selected
after 2017 and kept for validation of the results (independent data from
CNES-CLS22 and CNES-CLS18). This new CNES-CLS22 MDT also uses velocity
data estimated from HF radars located in the Mid Atlantic Bight area,
East coast of the US from Cape Hatteras to Cape Cod. We used the
cleaned, detited, high-frequency signal-filtered and mean currents over
the period 2006-2016 (processed by Rutgers University, Roarty et al.
2020).

-- \emph{Wind data.} Wind stress data are needed for the calculation of
the wind-driven velocities (Sect. 2.3) that is used to remove part of
the ageostrophic component from drifter velocities. We use the 3-hourly,
80 km resolution wind stress fields from ERA5 (Hersbach et al. 2018) for
the period 1993--2021.

\section*{4 Results}

{\label{results}}

\subsection*{4.1 High-resolution CNES-CLS2022 MDT and associated
currents}

{\label{high-resolution-cnes-cls2022-mdt-and-associated-currents}}

The CNES-CLS22 MDT obtained is shown on Figure 4 (a) and the amplitude
of the associated geostrophic currents is displayed in Figure 4 (b).
Compared with the first guess, the CNES-CLS22 MDT contains more small
scales, gradients are tighter and currents are accelerated. Figure 5
also shows a zoom of this new CNES-CLS22 MDT (a) and the amplitude of
the associated geostrophic currents (b) over the Artic zone, as well as
a zoom of the CNES-CLS18 MDT (c) and the amplitude of the associated
currents (d). Firstly, we note that the CNES-CLS22 MDT covers the Artic
zone, which was not the case before. This is due to the improved
coverage of the CNES-CLS22 MSS used to estimate the first guess of this
new MDT. Artifacts present on the CNES-CLS18 MDT have disappeared from
the new version, for example around 110-120°E. Moreover, Beaufort gyre
is better resolved and Pan Arctic transport is visible. On the other
hand, the Beaufort Gyre tends to ''spread out'' over the Canadian
Archipelago, which is not physical. In this area of the Canadian
Archipelago, the CNES-CLS22 MSS is slightly weaker (Schaeffer et al.
2023), which probably explains the poor physical representation of the
CNES-CLS22 MDT. Furthermore, the reliability of MDT is lower in areas
where observations are rare or absent, so results must be interpreted
with caution in these areas; in the European Arctic, the Kara Sea is an
example of such sparsely observed areas.\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image4/image4}

\end{center}
\end{figure}

Figure 4: (a) The CNES-CLS22 MDT (cm) and (b) and the amplitude of the
geostrophic currents associated with this MDT (cm/s).\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image5/image5}

\end{center}
\end{figure}

Figure 5: Zoom in on the Artic zone of (a) the CNES-CLS22 MDT (in cm),
(b) the amplitude of the associated geostrophic currents (in cm/s), (c)
the CNES-CLS18 MDT (in cm) and (d) the amplitude of the geostrophic
currents associated with the CNES-CLS18 MDT (in cm/s).

To look at the energy content of MDT, different MDT solutions were
compared through a spectral analysis: the first guess (called
FirstGuess22), the previous CNES-CLS13 MDT, the previous CNES-CLS18 MDT
(Mulet et al. 2021), the DTUUH22 MDT (Knudsen et al. 2022), the new
CNES-CLS22 MDT and the Glorys12 numerical model MDT (1/12\selectlanguage{ngerman}° numerical
model from Mercator-Ocean and distributed within CMEMS: product
GLOBAL\_REANALYSIS\_PHY\_001\_030,\emph{https://resources.marine.copernicus.eu/?option=com\_csw\&view=details\&product\_id=GLOBAL\_REANALYSIS\_PHY\_001\_030}).

Figure 6 shows spectral analysis for a 10° box in the Antarctic
Circumpolar Current area, between 38°E and 48°E and between 44°S and
54°S. In this zone, the CNES-CLS22 MDT (in black) has significantly more
energy than the first guess (noted FirstGuess22, in dashed blue) on
scales from 600 km to the smallest, and it is the in-situ data that
increase the energy on these scales. The three CNES-CLS MDTs (13 in
yellow, 18 in red and 22 in black) follow the energy level and descent
of the GLORYS12 model (in green), up to 100km for the CNES-CLS13 MDT,
and up to around 60km for the CNES-CLS18 (small offset on the energy
level with GLORYS12, but same decrease slope) and the CNES-CLS22 MDT. At
the smallest scales, there is still an energy decay towards the smallest
scales, but this is less marked than at scales above 60km, probably due
to the noise that must be starting to affect these scales. For the
CNES-CLS22 MDT, residual scales below 60km, below 30km and below 15km
were observed (figures not shown). The MDT fields and associated
geostrophic currents show coherent physical structures, but the more we
look at the smaller scales the more noise becomes visible; the residual
scales below 15km are noisy. Figure 6 also shows the spectrum of the
DTUUH22 MDT (in dashed pink), whose energy curve decays more rapidly
than GLORYS12 below 300km scales, reaching a plateau around 60-70km, at
which scales the noise should start to affect the structures, and then
decays more slowly.\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image6/image6}

\end{center}
\end{figure}

Figure 6: Spectral Power Density obtained for different MDT solutions in
a 10\selectlanguage{ngerman}°x10° box in the Antarctic Circumpolar Current area for the
meridional current, between 38°E and 48°E and between 44°S and 54°S.

\subsection*{4.2 Validation}

{\label{validation}}

The validation of the CNES-CLS22 MDT is carried out using different
approaches. First, this solution is evaluated qualitatively by region
(the European Arctic and the Mid Atlantic Bight), then it is evaluated
quantitatively with independent drifter data and then with independent
height data estimated from T/S profiles.

\subsubsection*{4.2.1 Qualitative
validation}

{\label{qualitative-validation}}

4.2.1.1 The European Arctic

{\label{the-european-arctic}}

As seen previously, the CNES-CLS22 MDT provides better coverage of the
Arctic region and corrects various CNES-CLS18 artifacts. In this
section, we take a closer look at the European Arctic region, and in
particular the Yermak Plateau area where the Fram Strait branch of the
Atlantic Water flow to the Arctic enters the Polar Basin (fig. 7a), and
the St. Anna Trough in the northern Kara Sea which is the main gateway
for the Barents Sea branch of the Atlantic Water flow to the Polar Basin
(e.g., Schauer et al., 2002, Rudels, 2015; Fig. 7d). We are looking at
different solutions for these two areas. For the zoom on the Yermak
Plateau, the new CNES-CLS22 MDT solution is shown in Fig. 7a with the
bathymetric and geographic elements cited in this section, the
CNES-CLS18 MDT solution is shown in Fig. 7b and in 7c the DTUUH2022
solution is shown. For the zoom on the St Anna Through, the CNES-CLS22
MDT solution is shown in Fig. 7d with the geographical elements
mentioned, the CNES-CLS18 solution is shown in Fig. 7e and the DTUUH2022
solution in Fig. 7f. A first observation is that the DTUUH2022 solution
is smoother than the two CNES-CLS solutions on these two zones.\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image7/image7}

\end{center}
\end{figure}

Figure 7: (a) CNES-CLS22 MDT, (b) CNES-CLS18 MDT and (c) DTUUH22 MDT in
Yermak Plateau area. The white line represents the 1000m isobath and the
black line the 200m isobath. Figure 7a shows the bathymetric and
geographical features: the Yermak Plateau and Svalbard Archipelago. (d)
CNES-CLS22 MDT, (e) CNES-CLS18 MDT and (f) DTUUH22 MDT in St Anna
Through area. The white line represents the 1000m isobath and the black
line the 200m isobath. Figure 7d shows the geographical features: the St
Anna Through, the Franz Josef Land Archipelago, the Novaya Zemlya (NZ),
the Barrents Sea (BS) and the Kara Sea (KS).

In the Yermak Plateau area, where the Fram Strait branch of the Atlantic
Water inflow enters the Polar Basin, the CNES-CLS22 MDT shows better
alignment of the flow with the bathymetry both for the Svalbard branch
crossing the plateau and the Yermak branch going around the plateau (see
Fig. 1 in Meyer et al. 2017), compared with the CNES-CLS18 MDT and
DTUUH22 MDT.

The CNES-CLS22 MDT also shows some improvements in the St. Anna Trough
where the Barents Sea branch of the Atlantic Water flow to the Arctic
exits the Barents Sea and enters the Polar Basin. Here, the CNES-CLS22
MDT better aligns with the bathymetry in the northeastern Barents Sea
and northern Kara Sea compared with the CNES-CLS18 MDT and DTUUH22 MDT.
Moreover, several more detailed differences also better align with
features of the flow reported in the literature. The main flow from the
Barents Sea is clearly aligned along the bathymetry in the southern part
of the trough between the Novaya Zemlya and Franz Josef Land
archipelagos (Schauer et al. 2002; Lien and Trofimov 2013), and there is
a clear indication of cyclonic circulation of the Fram Strait branch
within the same trough (Gammelsr\selectlanguage{ngerman}ød et al. 2009; Lien and Trofimov 2013).
There is also indication of a continuous Novaya Zemlya Coastal Current
along the northern tip of Novaya Zemlya (Lien and Trofimov 2013), which
is not clearly seen in the CNES-CLS18 MDT and DTUUH22 MDT. Further north
in the St. Anna Trough the CNES-CLS22 MDT shows better alignment of the
flow with the bathymetry (e.g., Dmitrenko et al. 2015) compared with the
smoother DTUUH22 MDT, in addition to more distinct features not seen in
the CNES-CLS18 MDT or DTUUH22 MDT. At 81N, there is an indication of a
cyclonic eddy previously identified by hydrographic observations, likely
caused by the Fram Strait branch entering the St. Anna Trough (Osadchiev
et al. 2022). Moreover, a bathymetric feature to the east of the Franz
Josef Land archipelago likely affects the southward flowing part of the
Fram Strait branch and causes an anti-cyclonic flow as shown in the
CNES-CLS22 MDT.

4.2.1.2 Mid Atlantic Bight

{\label{mid-atlantic-bight}}

As seen in section 2.3, the CNES-CLS22 MDT integrates synthetic
geostrophic velocities estimated from high-frequency radar velocities in
the Mid Atlantic Bight area on the east coast of the USA between Cape
Cod and Cape Hatteras. In this section, the CNES-CLS22 MDT is looked at
more precisely in the Mid Atlantic Bight, a region just north of the
Gulf Stream with recirculation on the slope and circulation on the
continental shelf shown in Fig. 8 (b).

Fig. 8 shows the contours of the CNES-CLS22 MDT (d) in comparison with
the CNES-CLS18 MDT (c) and a ROMS model MDT (a). The ROMS model MDT
(Fig. 8 (a)) is an average from the ROMS model used in a climatological
diagnostic configuration to calculate a kinematically (coastline and
bathymetry) and dynamically (ROMS nonlinear model physics) consistent
circulation constrained by mean observations of the ocean state and
forced by mean surface fluxes and river inflows (details given in Wilkin
et al. 2022).

Lentz (2008) and Zhang et al. (2011) have advanced arguments as to the
magnitude of the along-shelf sea level gradient in the Mid Atlantic
Bight necessary to complete a momentum balance. We expect gentle
southwestward flow throughout the Mid Atlantic Bight, and certain
recirculation features in the Gulf of Maine and Georges Bank that are
clearly evident in the ROMS MDT (Fig. 8 (a)). The across-shelf sea level
gradient is consistent with observed southwestward mean currents.
Furthermore, the known pattern of geostrophic coastal currents requires
that the MDT contours be largely parallel to the coast, which is the
case with the ROMS MDT and not always the case with the CNES-CLS18 (Fig.
8 (c)) and 22 (Fig. 8 (d)) MDTs.\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image8/image8}

\end{center}
\end{figure}

Figure 8: (a) ROMS model MDT contours, (b) Mid Atlantic Bight
circulation, (c) CNES-CLS18 MDT contours and (d) CNES-CLS22 MDT
contours.

CNES-CLS18 MDT (Fig. 8 (c)) shows a slightly more organized circulation
on the shelf, although contours on the inner shelf are noisy. Coastal
currents in the Gulf of Maine emerge: Coastal currents on the Scotian
Shelf or in the Gulf of Maine are present but weak. In addition, there
are still MDT contours cutting the coast, and sea-level slope inversions
along the shelf.

The CNES-CLS22 MDT (Fig. 8 (d)) is also noisy on the continental shelf,
and there are still contours cutting the coast (associated with low
geostrophic velocities). Coastal currents on the Scotian Shelf are more
organized, but there still flows into the coast of central New Jersey.
So CNES-CLS22 MDT is a significant improvement, but that there is still
a way to go to bring MDT to the coast on broad shelves.

\subsubsection*{4.2.2 Quantitative validation with independent T/S
profiles}

{\label{quantitative-validation-with-independent-ts-profiles}}

The CNES-CLS22 and CNES-CLS18 MDTs are compared with independent data.
Around 5\% of the T/S profiles dataset are randomly selected from 2017
and kept for validation (independent data for CNES-CLS22 and CNES-CLS18
MDTs). The dynamic height estimated from T/S profiles (from a reference
depth) characterizes a baroclinic component of the dynamic circulation.
Whereas altimetry measures a height that is also influenced by
baroclinic processes occurring from the reference depth to the bottom of
the water column, and by barotropic processes. For validation purposes,
we choose to keep only the deepest profiles (with a reference depth of
1900m), thus reducing the number of deep baroclinic processes not taken
into account; this leaves us with a validation set of 2\% of the
database.

As a first step, we compare the CNES-CLS18 and CNES-CLS22 MDTs against
these independent dynamic heights, by looking at the correlation of the
ADT (SLA+MDT considered) and the independent dynamic heights (figures
not shown). Correlations are calculated in boxes of 5\selectlanguage{ngerman}° by 5° (with at
least 20 data) and are high, mostly between 0.8 and 1 for both MDTs, and
it is difficult to differentiate between them.

Secondly, Figure 9 (a) shows the mean bias per 5°X5° box between the ADT
estimated from the CNES-CLS22 MDT and the independent dynamic heights.
This global mean bias is 1.30 m, with spatial variations in the
Norwegian Sea and to the south near Antarctica (equivalent for
CNES-CLS18, not shown) and mainly represents the barotropic component
not observed by the dynamic heights. This is why it is removed from the
estimate of mean synthetic heights for the calculation of the MDT and
the following validation diagnosis on Fig. 9 (b) shows a comparison
between the variances of the differences (not considering the bias)
between the different ADTs and the dynamic heights, in percent. In blue
(in red), the variance of differences is reduced (increased) using
CNES-CLS22 compared with CNES-CLS18.

Globally, we see an improvement in CNES-CLS22 MDT compared with
CNES-CLS18, but this is not true in all regions. South of the Atlantic
and the Indian Ocean (as far south as Australia), the variance of
differences is reduced for CNES-CLS22 by more than 10\% for many boxes
(even if boxes of strong reduction are juxtaposed with boxes of
increased variance of differences). Areas of degradation are
concentrated in the north-western Atlantic, particularly south of
Greenland, in the very north of the Pacific (along the Gulf of Alaska to
the Fox Islands, and close to Russia) and in the south of the Pacific,
where there are degradations of over 10\% (also juxtaposed with
improvement boxes).\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image9/image9}

\end{center}
\end{figure}

Figure 9: (a) shows the bias in centimetres between the dynamic heights
estimated from the independent T/S profiles and the ADT calculated from
the CNES-CLS2 MDT. And (b) shows the reduction/increase in variance of
the differences between independent dynamic heights and ADT (from
CNES-CLS18 and CNES-CLS22) in percent. In blue (in red), the variance of
differences is reduced (increased) using CNES-CLS22 compared with
CNES-CLS18. All these statistics are calculated in 5\selectlanguage{ngerman}°X5° boxes, and only
boxes with at least 20 data are kept.

\subsubsection*{4.2.3 Quantitative validation with independent
drifters}

{\label{quantitative-validation-with-independent-drifters}}

The CNES-CLS18 and CNES-CLS22 solutions are compared with independent
velocity data. 10\% of the AOML drifters dataset are randomly selected
and kept for validation (independent data). These drifters are not
evenly distributed across the oceans. There are few drifters close to
Antarctica (south of about 50°S), at the equator and in Artic. In
addition, the Atlantic is slightly better sampled than the other basins,
and in particular than the North Indian.

To compare to the MDTs, we remove the wind-driven current (Ekman current
and wind slippage for undrogued drifters) from total drifters current
and then data are filtered at inertia frequency (if inertia frequency is
between 1 and 5 days, otherwise take a minimum of 1 day and a maximum of
5 days) to remove the tide and inertial waves. The objective is to keep
only the geostrophic signal. As the geostrophy hypothesis is no longer
valid at the equator, we exclude drifters between 5°S and 5°N at the
equator.

Absolute dynamic topography values were calculated by adding the CMEMS
gridded SLA to the new CNES-CLS22 MDT. Associated geostrophic current
were then derived and interpolated along the drifter trajectories. Bias
and Root Mean Square differences (RMSD) between the obtained geostrophic
velocities with CNES-CLS22 and CNES-CLS18 and the drifter derived
geostrophic velocities were calculated spatially by 5°X5° boxes. All
these statistics are calculated with at least two different drifters and
with at least 100 measurement points.

Comparisons of bias (a) in current modulus (in m/s) and (b) in direction
(in degrees) are shown on Figure 10. In blue (in red), there is a
decrease (increase) in bias for geostrophic currents derived from the
ADT estimated with the CNES-CLS22 MDT. Globally, there is a decrease in
bias in current modulus (Figure 10 a) using the new solution, with a
greater decrease in bias in areas of strong currents: Gulf Stream,
Kuroshio, Agulhas Current and Antarctic Circumpolar Current. The areas
of degradation are South Greenland and South Kerguelen. For the
directional bias (Figure 10 b), the contribution of the new solution is
more mixed, as the direction of geostrophic currents derived from the
ADT using the CNES-CLS18 is better in the South between the Kerguelens
and southern Australia. These remain areas with fewer validation
drifters.\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image10/image10}

\end{center}
\end{figure}

Figure 10: Comparison of bias (a) in current modulus and (b) in current
direction independent drifting buoy velocities and the altimeter
geostrophic velocities obtained using different MDT solutions. In blue
(in red), the bias is reduced (increased) using CNES-CLS22 compared with
CNES-CLS18.\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image11/image11}

\end{center}
\end{figure}

Figure 11: Comparison of the RMS of the differences (a) in current
modulus and (b) in direction, of the independent drifting buoy
velocities and the altimeter geostrophic velocities obtained using MDT
solutions CNES-CLS22 and CNES-CLS18, in percent :\(\mathbf{\%}\mathbf{\text{RMSD}}\mathbf{\,=}\frac{\mathbf{\text{RMS}}\left(\mathbf{U}_{\mathbf{\text{ADT}}\mathbf{22}}\right)\mathbf{-}\mathbf{\text{RMS}}\left(\mathbf{U}_{\mathbf{\text{ADT}}\mathbf{18}}\mathbf{-}\mathbf{U}_{\mathbf{d}}\right)}{\mathbf{\text{RMS}}\left(\mathbf{U}_{\mathbf{\text{ADT}}\mathbf{18}}\mathbf{-}\mathbf{U}_{\mathbf{d}}\right)}\mathbf{\,}\). In
blue (in red), the bias is reduced (increased) using CNES-CLS22 compared
with CNES-CLS18. All these statistics are calculated in 5\selectlanguage{ngerman}°X5° boxes, and
only boxes with at least 2 drifters difters differents and at least 100
measurement points, are kept.

Comparisons of RMS of the differences (a) in current modulus and (b) in
direction, of the independent drifting buoy velocities and the altimeter
geostrophic velocities obtained using MDT solutions CNES-CLS22 and
CNES-CLS18, in percent, are shown are shown on Figure 11. In blue (in
red), the RMSD is reduced (increased) using CNES-CLS22 compared with
CNES-CLS18. In terms of current amplitude (Figure 11 a), the majority of
boxes show an improvement of between 0 and 2.5\% for the CNES-CLS22
solution, with in particular a greater improvement at Kuroshio and in
the Caribbean Sea. Areas of degradation in current amplitude RMS are the
area around Kerguélen in the ACC and along the southeast coast of
Greenland. Comparison of the RMS of differences in current direction
(Figure 11 b) shows a more mixed result with degradation boxes compared
to the CNES-CLS18 solution: in the ACC in the South Pacific. It can also
be noted that some boxes show an improvement in the RMS of differences
for the CNES-CLS22 solution in current amplitude but not in direction,
and vice versa; this is the case for some boxes south of the Kerguélen
Islands and at the extreme south of the Pacific. The areas around the
Kerguélen Islands, in the South Pacific between -140°E and -120°E, and
around the Fox Islands in the extreme North Pacific remain areas of
degradation in RMS of the differences in modulus and current direction
for the new solution compared with the previous one. On the other hand,
the Kuroshio, the North Atlantic and the Labrador Sea, as well as the
Indian Ocean are areas where the RMS of the differences for the new
CNES-CLS22 solution has improved compared to the CNES-CLS18 solution.

Globally, the two solutions CNES-CLS22 and CNES-CLS18 remain close with
these drifter comparisons, as shown in the following Table 1, which
summarizes the drifter comparison statistics over the whole area up to
70°N. Both solutions have a difference RMS of between 10.5 and 11 cm/s
for U and V components and current modulus, and a difference RMS of
around 34° in direction. The comparison of the two solutions favours the
new one, but by less than 1\%. It should also be noted that the
comparison between the first guess and the CNES-CLS22 MDT shows an
improvement in U and V of around 5\% in the RMS of differences, and an
improvement of around 6\% in current amplitude and 2\% in direction,
which is expected.\selectlanguage{english}
\begin{longtable}[]{@{}lllll@{}}
\toprule
RMS(differences) & U {[}cm/s{]} & V {[}cm/s{]} & M {[}cm/s{]} & D
{[}\selectlanguage{ngerman}°{]}\tabularnewline
\midrule
\endhead
CNES-CLS22 MDT & 10,57 & 10,62 & 10,79 & 34,24\tabularnewline
CNES-CLS18 MDT & 10,59 & 10,63 & 10,83 & 34,26\tabularnewline
CNES-CLS22 MDT first guess & 11,11 & 11,17 & 11,47 &
35,05\tabularnewline
\% 22 vs 18 & -0,2\% & -0,1\% & -0,4\% & -0,1\%\tabularnewline
\% 22 vs 22 first guess & -4,9\% & -4,9\% & -5,9\% &
-2,3\%\tabularnewline
\bottomrule
\end{longtable}

Table 1: RMS of the differences for the zonal component U, the
meridional component V, the current modulus and the direction of the
current, of the independent drifting buoy velocities and the altimeter
geostrophic velocities obtained using MDT solutions CNES-CLS22,
CNES-CLS18 and the CNES-CLS22 first guess. The last two lines show the
reduction/increase in RMS of the differences between two solutions:
CNES-CLS22 versus CNES-CLS18 and CNES-CLS22 versus CNES-CLS22 first
guess, in percent (a negative percentage is a decrease in the RMS of the
differences). These statistics were generated using all available
drifters up to 70\selectlanguage{ngerman}°N.

Given the small number of independent drifters in Arctic, this area is
treated separately. Table 2 summarizes the RMS of the differences
between the geostrophic currents derived from drifters (degraded
treatment) and the geostrophic currents derived from ADTs calculated
with the CNES-CLS22, CNES-CLS18 and background CNES-CLS22 solutions. The
last two lines show in percent the reduction in RMS of the differences
between CNES-CLS22 and CNES-CLS18 MDT and its first guess. In the zonal
and meridional components of the current, the new solution reduces the
RMS of the differences compared with the drifters by 19\% and 12\%
respectively. This improvement translates into a clear improvement in
direction of 9\%, which reduces the RMS of the differences from around
56° to 50°; but the RMS of the differences in current amplitude remains
very slightly better for CNEs-CLS18. Note that, as the coverage is not
quite identical, there are more points taken into account for CNES-CLS22
than for CNES-CLS18.\selectlanguage{english}
\begin{longtable}[]{@{}lllll@{}}
\toprule
\textbf{RMS(differences)} & \textbf{U {[}cm/s{]}} & \textbf{V
{[}cm/s{]}} & \textbf{Modulus {[}cm/s{]}} & \selectlanguage{ngerman}\textbf{Direction
{[}°{]}}\tabularnewline
\midrule
\endhead
\textbf{CNES-CLS22 MDT} & 7,95 & 8,12 & 9,61 & 50,43\tabularnewline
\textbf{CNES-CLS18 MDT} & 9,86 & 9,23 & 9,58 & 55,88\tabularnewline
\textbf{CNES-CLS22 MDT first guess} & 7,97 & 8,26 & 10,02 &
51,77\tabularnewline
\textbf{\% 22 vs 18} & -19,4\% & -12,0\% & 0,4\% & -9,8\%\tabularnewline
\textbf{\% 22 vs 22 first guess} & -0,2\% & -1,7\% & -4,1\% &
-2,6\%\tabularnewline
\bottomrule
\end{longtable}

Table 2: RMS of the differences for the zonal component U, the
meridional component V, the current modulus and the direction of the
current, of the independent drifting buoy velocities and the altimeter
geostrophic velocities obtained using MDT solutions CNES-CLS22,
CNES-CLS18 and the CNES-CLS22 first guess. The last two lines show the
reduction/increase in RMS of the differences between two solutions:
CNES-CLS22 versus CNES-CLS18 and CNES-CLS22 versus CNES-CLS22 first
guess, in percent (a negative percentage is a decrease in the RMS of the
differences). These statistics are based on the Artic zone north of
80\selectlanguage{ngerman}°N. As the CNES-CLS18 MDT has a smaller coverage, the number of points
used is slightly different for this solution than for the others.

\section*{5 Conclusions}

{\label{conclusions}}

The main improvement of this new CNES-CLS22 MDT over the previous
CNES-CLS18 MDT is in the Arctic, with better coverage, no artifacts and
a more realistic solution. Globally, the new CNES-CLS22 solution is
close to the CNES-CLS18 solution, both have better resolution of small
scales than previous CNES-CLS MDTs but are potentially polluted by noise
at very short scales. The CNES-CLS22 MDT has been evaluated against
independent height and velocity data in comparison with the previous
version, the CNES-CLS18. The new solution presents slightly better
results, although not identical in all regions of the globe. In
particular, the results are better in the Antarctic Circumpolar Current
in terms of height, better off Japan and particularly in the Arctic in
terms of geostrophic velocities. For geostrophic currents, those of the
new CNES-CLS22 MDT in the Antarctic Circumpolar Current are slightly
worse than those of the CNES-CLS18 in comparison with drifters.

Improvements to this new MDT include a new first-guess with the
CNES-CLS22 MSS and the GOCO06s geoid to which optimal filtering has been
applied, as well as Lagrangian filtering at the coast to reduce the
intensity of normal currents at the coast, drifting buoy and T/S profile
databases have been updated, as have updated processing to obtain
synthetic mean geostrophic velocities and synthetic mean heights. In
addition, a new type of data, HF radar data, was processed to extract
physical content consistent with MDT in the Mid Atlantic Bight region.
The study of this region in particular, showed the improvements of
CNES-CLS22 MDT, but that there is still work to be done to obtain a more
physical solution on the continental shelf. Indeed, on these continental
shelves in general, the first guess is not always good because it's
close to the coast and today we only process T/S profiles with a depth
greater than 200m; we therefore lack data on these shelves. HF radar
data can provide some velocities information, as there are few drifting
buoy data in these coastal regions, but processing is difficult, as
complex and non-negligible ageostrophic currents have to be removed. In
the case of the Mid Atlantic Bight, these HF radar data do not allow us
to obtain a MDT with a geostrophic flow not crossing the coastline.

Thanks to the new first-guess and in particular the new CNES-CLS22 MSS,
the Arctic area is covered in this MDT and the artifacts of CNES-CLS18
have disappeared. Looking more specifically at the European Arctic
region, the new CNES-CLS22 solution presents structures in agreement
with the literature in the Yermak Plateau area and in the St Anna
Through region.

With the arrival of new swath observations from the SWOT (Surface Water
and Ocean Topography) satellite launched in December 2022 (Fu et al.
2012), the continuous improvement of MDT accuracy and resolution is
necessary. The inclusion of new coastal data, such as HF radar and SAR
data, and shallower T/S profiles not currently taken into account,
requires a clear separation of geostrophic and ageostrophic processes,
and access to physical content consistent with MDT. These treatments
call for new methods in order to best process continental shelf areas
with varied oceanographic phenomena.

\section*{Data availability}

{\label{data-availability}}

The CNES-CLS22 MDT is available on AVISO+
\emph{\url{https://www.aviso.altimetry.fr/en/data/products/auxiliary-products/mdt/mdt-global-cnes-cls.html}}

\section*{Competing interests}

{\label{competing-interests}}

The authors declare that they have no conflict of interest.

\section*{Acknowledgements}

{\label{acknowledgements}}

We thank the beta users for their valuable feedback, and Laurent Berino
for his comments on the Artic region.

\section*{References}

{\label{references}}

Bingham, Rory J., Keith Haines, and Chris W. Hughes. 2008. ``Calculating
the Ocean's Mean Dynamic Topography from a Mean Sea Surface and a
Geoid.'' \emph{Journal of Atmospheric and Oceanic Technology} 25 (10):
1808--22.

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