[1]Charles-Antoine Guérin

[1]MIO, Univ Toulon, CNRS, AMU, IRD, Toulon,France 2]M2C, Normandie Univ.,
UNICAEN, UNIROUEN, CNRS, Caen, France 3]SOCIB, Balearic Islands Coastal
Observing and Forecasting System, Palma, Spain

# High-Frequency Radar observation of strong and sheared currents: the
Alderney race paradigm

Dylan Dumas<EMAIL_ADDRESS>Anne-Claire Bennis  anne-
<EMAIL_ADDRESS><EMAIL_ADDRESS>Guiomar Lopez<EMAIL_ADDRESS>Laurent Benoit<EMAIL_ADDRESS>*  [  [

###### Abstract

The Alderney Race has been identified as a future site for the development of
tidal energy, due to its bidirectional strong current reaching 5 m/s during
spring tides. This hydrodynamics is very difficult to measure by in situ or
remote sensing means. High-frequency coastal radars can provide a synoptic and
near-real-time view of such a complex circulation, but the classical
processing algorithms are not adapted to the extreme situation of strongly
sheared currents. We propose an improved high-resolution direction-finding
technique for the azimuthal processing of such radar data. It uses phased-
array systems and combines the advantages of the usual beam-forming technique
to eliminate many problems related to the distortion of Doppler spectra by
extreme currents. The method is evaluated with a unique data set of radar
measurements at two radar frequencies (13 and 24.5 MHz) and three spatial
resolutions (200, 750, and 1500 m). The radar-based surface currents are
analyzed in the light of a high-resolution numerical model and also compared
with in situ measurements. While high azimuthal resolution can be achieved in
this way, it is shown that the typical range resolutions of 750 and 1500 m are
insufficient to account for the strong spatial variations of the surface
current at some specific times and locations.

###### keywords:

Tidal hydrodynamics, Coastal High-Frequency Radar, Signal processing
technique, Direction Finding, Beam Forming, Numerical modeling

##  1 Introduction

Changes in the Earth’s climate due to anthropogenic effects are increasingly
present and becoming more frequent. To mitigate these changes, some groups of
countries, such as the EU, have agreed on the common goal of carbon
neutrality. The development of marine renewable energy including tidal energy
is a promising way to achieve this goal. Researchers have studied the complex
hydrodynamics of the Alderney Race (France) since it is the most promising
tidal site in Western Europe, with a maximum potential of $5.1\hskip
2.0pt\mathrm{GW}$ due to extreme tidal currents reaching $5\hskip
2.0pt\mathrm{m.s^{-1}}$ [e.g. 6].

Instrumentation of the Alderney Race with classical in situ instruments such
as current meters, wave buoys, or pressure gauges is a challenging task due to
the high exposure of these devices to damage and loss. In addition to this
maintenance issue, another limitation is the punctual nature of the
measurements, which is useful but not sufficient for the tidal industry. An
alternative is the use of land-based High-Frequency radar (HFR), which can
provide a synoptic view of surface currents and sea state. As is well known
since the pioneering experiment of [10], the dominant electromagnetic sea echo
measured by HFR is due to the so-called Bragg wave, whose wavelength is half
the radar wavelength. As a result, the backscattered ocean Doppler spectrum
has two main peaks, called Bragg lines, at a predictable frequency, and the
HFR radial surface current velocity is obtained by subtracting the observed
position of the Bragg line from its theoretical position [37]. HFR can thus
provide near real-time measurements of the surface layer current over a region
typically extending a few tens of kilometers from shore, with a spatial
resolution on the order of a few $\mathrm{km^{2}}$, depending on the operating
frequency. The physics and technology behind HFR have reached a mature state.
(see e.g. [33, 27, 32] for recent reviews) and these instruments give
satisfactory estimates, with known limitations and accuracy, of the surface
currents in the vast majority of situations. However, the non-standard case of
very intense currents undergoing strong horizontal and vertical shears such as
those found in the Alderney Race falls outside of the applicability domain of
standard radar signal processing methods and requires dedicated treatments.

[25, 26] analyzed the hydrodynamics of the Alderney race using the first HFR
datasets from two radar stations implemented at the Cape of La Hague in 2017,
operating at $13.5\hskip 2.0pt\mathrm{MHz}$ and $24.5\hskip 2.0pt\mathrm{MHz}$
(more details on the HFR facilities are given in section 2.2). The HFR surface
velocity was compared with the surface velocity computed by a three-
dimensional fully coupled wave-current model. Very good results were obtained,
with RMSE (Root Mean Square Error) less than $0.4\hskip
2.0pt\mathrm{m.s^{-1}}$ and $0.6\hskip 2.0pt\mathrm{m.s^{-1}}$ during spring
and neap tides, respectively. The correlation coefficients are greater than
$0.95$ over the entire HF region. They found maximum errors in shallow areas
with high mean current values ($1.25\hskip 2.0pt\mathrm{m.s^{-1}}$ and
$2.7\hskip 2.0pt\mathrm{m.s^{-1}}$ during neap and spring tides,
respectively).

In the literature, HF measurements and processing algorithms for strong
currents (i.e., with a mean velocity above, say, $2\hskip
2.0pt\mathrm{m.s^{-1}}$) are rarely documented and, to the best of our
knowledge, are limited to studies in the Bali Strait (Indonesia) and the
Fromveur Strait (France). In the case of the Bali Strait, the tidal velocity
can reach a maximum of $2.97\hskip 2.0pt\mathrm{m.s^{-1}}$ and $2.17\hskip
2.0pt\mathrm{m.s^{-1}}$ during ebb and flood, respectively. Data from two HFRs
operating at $26.275\hskip 2.0pt\mathrm{MHz}$ were tested against ADCP
(Acoustic Doppler Current Profiler) data from [13]. Good agreement was found
between the two datasets with a correlation coefficient of $0.813$ and an RMSE
of $0.22\hskip 2.0pt\mathrm{m.s^{-1}}$ for the meridional velocity. In
contrast, the HFR zonal velocity was found to be very different from the ADCP
zonal velocity, with a correlation coefficient of $0.235$ and an RMSE of
$0.402\hskip 2.0pt\mathrm{m.s^{-1}}$. The authors attributed this inaccuracy
to the smaller magnitude of the zonal component and the unfavorable
configuration of the HFR stations. Surface current monitoring in the Fromveur
Strait (France) using a pair of HFRs has revealed a maximum tidal current of
about $3.8\hskip 2.0pt\mathrm{m.s^{-1}}$ [36]. [38, 39] found a correlation
coefficient of about $0.82$ and a zero phase lag between the HFR surface
velocity and the ADCP depth-averaged velocity. They concluded that the HFR
surface velocity is $15-20\%$ higher than the ADCP depth-averaged velocity,
which is in agreement with [30]. In contrast, Fig. 6 and Fig. 10 of [38, 39]
show a significant underestimation (by more than $1\hskip
2.0pt\mathrm{m.s^{-1}}$) of the absolute velocity, as shown in Fig. 4 of [26]
for the Alderney race. The conflicting results of these studies suggest that
the measurement of very strong and rapidly changing currents with HFR is not
yet fully reliable and requires some improvements in the processing
algorithms. They also raise fundamental questions about the relevant spatial
and temporal resolution needed to observe such sheared currents.

In this study, we present radar processing methods adapted to the case of
intense surface currents, whose velocity can be even higher than the Bragg
wave velocity. This situation requires high-resolution azimuthal processing,
which can only be achieved by Beam Forming (BF) processing using a large
phased-array (16 antennas) or by high-performance Direction Finding (DF)
processing. However, when strong currents are combined with a strong sea
state, the latter approach fails due to the difficulty of identifying the
first-order Bragg region in the omnidirectional Doppler spectra. We propose an
adaptation of the DF method to solve this problem. For this purpose, we resort
to several techniques recently proposed for phased-array radars in [12] and
complement them with a preconditioning of the first-order Bragg range with a
preliminary BF. This new method, which we call "hybrid BF-DF", is applied to
the HF data of the Alderney Race, and its performance is evaluated using the
results of a three-dimensional numerical model and a comparison with a
classical BF processing with a large number of receiving antennas.

While previous studies using the same HFR stations [25, 26] dealt only with
typical range resolutions of 1500 m and 750 m at 13 and 24.5 MHz,
respectively, in this study we present an original data set acquired during
one week at the very high spatial resolution of 200 m for the higher transmit
frequency (24.5 MHz). The addition of this exceptional data set allows us to
evaluate the impact of spatial resolution on the detection of first-order
Bragg peaks and surface current mapping. We show that at some specific
locations and times of the tidal cycle, a very fine spatial resolution is
required to account for horizontal current shear, which can be misleading when
averaged over a coarser radar cell.

The paper is organized as follows. The study site and the HFR facilities are
described in section 2. The radar signal processing methods and the improved
algorithms are presented in section 3. Various results and performances of the
HFR measurements in the light of numerical model outputs and in situ
measurements are shown and discussed in Section 4, together with a discussion
of the influence of spatial resolution. Conclusions are presented in section
5.

##  2 Site description

###  2.1 The Alderney race

The study site, Alderney Race, is located in the English Channel, which
separates France from the United Kingdom. The English Channel is an
epicontinental sea with a maximum depth of about $200\hskip 2.0pt\mathrm{m}$
[11]. The hydrodynamics are mainly driven by semi-diurnal tides, which produce
two ebb and two flood tides each day, with a maximum tidal range of $14\hskip
2.0pt\mathrm{m}$ in the Mont-Saint-Michel Bay during very large spring tides
[9]. Surface waves and wind also influence the hydrodynamics of the English
Channel, especially during storms and near the coast [e.g. 23]. The tidal
current in the English Channel can also modify the surface winds and cause
tidal winds [31].  The Alderney Race is located in the western part of the
English Channel near the Cotentin Peninsula between the Cape of La Hague and
the island of Alderney (Fig. 1). Due to the Venturi effect, the Alderney Race
is the site of the strongest current in the English Channel. The strong
current generates numerous whitecaps, which cover the surface of the race with
a constant white coat. The maximum current velocity is about $5\hskip
2.0pt\mathrm{m.s^{-1}}$ and can reach $7\hskip 2.0pt\mathrm{m.s^{-1}}$ under
special conditions [15]. The current is horizontally and vertically sheared by
ocean turbulence and surface wave effects (e.g. [29],[26],[4]). The tidal
current moves northeast and southwest during high and low tide, respectively.
The flood current is more intense than the ebb current, resulting in a tidal
asymmetry of $3\%$ in calm conditions and up to $13\%$ in storm conditions
[4]. Swell, most of the time coming from the Atlantic Ocean, and wind waves
propagate over the Alderney Race [40]. They are refracted, shoaled and
dissipated by the current [2]. The seafloor of the Alderney Race is complex
with various morphological features (e.g. submarine cliffs, tidal dunes) and
uneven with a wide range of roughness types from coarse sands to rocky blocks
of $1\hskip 2.0pt\mathrm{m}$ lengthscale [14]. Strong tidal currents interact
with these bottom features and generate highly energetic three-dimensional
turbulence structures that are ejected from the bottom to the surface, as
shown by [15] and simulated by [8, 3], for example. Turbulent structures are
visible at the surface of a ship in calm conditions and appear to have a
length scale of about $15-20$ m.

###  2.2 HF radar facilities

In December 2017, the University of Caen-Normandy deployed two phased-array HF
radars (WERA: wave radar), originally developed by [16], at the Cape of La
Hague, located $5\hskip 2.0pt\mathrm{km}$ from each other in Goury and
Jobourg, respectively (Fig. 1). Each system consists of a 16-element linear
receive array, an 8-element square transmit array, and radar electronics.
These monostatic radars operate alternately at two different frequencies,
$13.5\hskip 2.0pt\mathrm{MHz}$ and $24.5\hskip 2.0pt\mathrm{MHz}$, thanks to a
4-element transmit array for $24.5\hskip 2.0pt\mathrm{MHz}$ and a 4-element
transmit array for $13.5\hskip 2.0pt\mathrm{MHz}$, while the 16-element
receive array is the same for both transmit frequencies. Four sets of
measurements per hour are recorded alternately, two sets of $17\hskip
2.0pt\mathrm{min}$ at $13.5\hskip 2.0pt\mathrm{MHz}$ and two sets of $12\hskip
2.0pt\mathrm{min}$ at $24.5\hskip 2.0pt\mathrm{MHz}$, allowing an estimation
of the surface current with a temporal resolution of about $30\hskip
2.0pt\mathrm{min}$. Given the available frequency bandwidth, the range
resolution is $1500\hskip 2.0pt\mathrm{m}$ and $750\hskip 2.0pt\mathrm{m}$ at
$13.5\hskip 2.0pt\mathrm{MHz}$ and $24.5\hskip 2.0pt\mathrm{MHz}$,
respectively. In addition, a temporary allocation of a large frequency
bandwidth around $24.5\hskip 2.0pt\mathrm{MHz}$ allowed testing of a high-
resolution mode for one week at a range resolution of $200\hskip
2.0pt\mathrm{m}$. The theoretical angular resolution based on the length of
the array is about $14^{\circ}$ at $13.5\hskip 2.0pt\mathrm{MHz}$ and
$7^{\circ}$ at $24.5\hskip 2.0pt\mathrm{MHz}$.The main characteristics of the
HF radars are summarized in table 1.

Table 1:  Overview of the radar characteristics (bandwidth frequency, range, angular and time resolutions, measurement duration) according to the transmission frequency ($13.5\hskip 2.0pt\mathrm{MHz}$ and $24.5\hskip 2.0pt\mathrm{MHz}$). | $\mathbf{13.5}\hskip 2.0pt\mathrm{MHz}$ | $\mathbf{24.5}\hskip 2.0pt\mathrm{MHz}$
---|---|---
Bandwidth ($\mathrm{kHz}$) | 100 | 200
Range resolution ($\mathrm{m}$) | 1500 | 750 or 200
Angular resolution (∘) | 14 | 7
Time resolution ($\mathrm{min}$) | 30 | 30
Duration ($\mathrm{min}$) | 17 | 12
Bragg wavelength $\lambda_{B}$ ($\mathrm{m}$) | 11.11 | 6.12
Bragg frequency $f_{B}$ ($\mathrm{Hz}$) | 0.37 | 0.50
Critical current $U_{c}$ ($\mathrm{m/s}$) | 4.17 | 3.09
Figure 1: Locations of the two HF radar sites: Goury-WERA and Jobourg-WERA and
their spatial coverage (blue patterns) with the common region (white/gray
contours) [19].

##  3 Radar processing

The conversion of antenna voltage into surface current maps involves a complex
chain of signal processing common to the various types of HF radar. We will
briefly recall what is necessary for the following, and refer to e.g. [17] for
a more detailed description of radar principles. Range gating of the
backscattered signal is achieved using standard frequency-modulated continuous
wave technology with a chirped transmit waveform. The different range cells of
the radar signal are obtained by a simple Fast Fourier Transform (FFT) over
the fast time within each transmission cycle. The theoretical range resolution
is related to the single frequency band $B$ by the simple relationship $\Delta
R=c/2B$, where $c$ is the speed of light. This allows in principle a
resolution of 750 m in the low-resolution mode ($B=200$ kHz) or a resolution
of 200 m in the high-resolution mode ($B=750$ kHz). However, the application
of a tapered window to prevent secondary lobes in the fast time FFT (which
would introduce mutual coupling between the different ranges) reduces the
actual range resolution, which is about 2 times coarser. Complex
omnidirectional Doppler spectra for each antenna are further obtained with an
FFT on slow time (i.e., at the chirp rate) for each range cell. The final step
is azimuthal discrimination, which requires combining the complex
omnidirectional spectra over the antenna array. The most common azimuthal
processing method for linear receive arrays is beamforming (BF), which
proceeds by delaying and summing the complex antenna signals and can steer the
beam continuously in any direction of a half-space. By applying BF to the
complex omnidirectional Doppler spectra, azimuthally resolved Doppler spectra
(hereafter referred to as directional Doppler spectra) can be obtained for any
radar cell. We recall that the directional Doppler spectra are composed of 2
sharp peaks located at plus and minus the Bragg frequency
$f_{B}=\sqrt{g/(2\pi\lambda_{B})}$ predicted by the first-order Bragg theory
[1]. In the presence of a radial current ($U_{r}$), these peaks are translated
by an additional Doppler shift: $\Delta f=U_{r}/\lambda_{B}$. The principle of
HFR current estimation is based on the accurate measurement of this extra
Doppler shift. It is well known that angular resolution is limited by the size
of the array and degrades at large distances. The alternative to BF is the
Direction Finding (DF) approach, which is generally used for compact arrays.
In the DF technique, each frequency ray of the First-Order Bragg Region (FOBR)
in the omnidirectional Doppler spectrum (corresponding to a given value of the
radial surface current) is assigned to an azimuthal direction using the MUSIC
algorithm [5, 35]. The main idea behind this algorithm is that the vector
obtained from the complex antenna gains on the receive array in the direction
of a source belongs to the signal subspace (that is, the complementary of the
null subspace associated with the zero eigenvalue) of the covariance matrix of
the antenna signals. By steering in all possible directions, such an
eigenvector can be found by minimizing its projection on the null subspace or,
which is equivalent, by maximizing its inverse projection, which is called the
MUSIC factor. There is no well-defined criterion for the angular resolution of
the MUSIC method, which can be arbitrarily fine depending on the signal-to-
noise ratio. Although DF was originally designed for compact arrays, it has
proven to be very valuable for phased-arrays as well. Recently, [12] developed
an ensemble of techniques to improve both the accuracy and coverage of surface
current maps obtained from DF processing of arrays. The results were validated
with drifter measurements and shown to outperform BF for 8- and 12-antenna
receiver arrays. The main novelty of these techniques is the use of so-called
“antenna grouping”, which consists in applying a DF search algorithm to a
large number of sub-arrays, thereby increasing the radar coverage. In
addition, an automatic and real-time antenna calibration procedure has been
developed in the bistatic configuration, where the remote transmitter is used
as an external source to adjust the antenna gains. This last possibility is
not available in the monostatic case relevant to this study. Nevertheless, the
antenna grouping technique allows to perform a single, manual calibration by
systematically searching for the phase corrections that minimize the map
rotations between different 3-antenna groups.

Figure 2: Example of a Range-Doppler map obtained with the Jobourg station at
24.5 MHz (750 m resolution mode) in the presence of very strong surface
currents. The right Bragg line overlaps the region of negative Doppler shift
and the zero-Doppler line (red dashed line) is no longer relevant to identify
the “positive side” or “negative side” of the Bragg regions. A more
appropriate separation criterion is obtained with the solid blue line, which
is the median of the 2 lines.

###  3.1 Direction Finding for very strong currents

A key step for the successful application of the DF technique is the correct
identification of the FOBR, which is the only relevant frequency interval for
the evaluation of the radial surface currents. The classical technique is
based on a “null-finding” criterion, which amounts to searching for the local
minima at both ends of the positive and negative main peaks (see e.g. [34] for
a recent review), a procedure that requires some parameter tuning and is
subject to error. Improved techniques have been developed based on image
processing methods [22] that reduce the number of parameters to calibrate and
increase the success rate of detection. Another family of techniques proceeds
with a statistical approach by making a preliminary estimate of the radial
current distribution in a coarsely defined FOBR (with fixed bounds imposed by
the maximum possible current) and setting a first-order bound as a quantile of
the distribution [12]. The bounds are then dynamically adjusted at each
observation cycle. However, the presence of very strong currents raises
several issues in the DF processing of Doppler spectra that even these
improved techniques cannot handle. In the case of an extremely large current,
the shifted Bragg frequency peak may “cross” the zero Doppler line and thus
undergo a sign change that makes its identification with the reference Bragg
peaks ambiguous. This is illustrated in Figure 2, which shows an azimuthally
resolved (i.e. “beam-formed”) range-Doppler map obtained with BF at the
Jobourg station. As can be seen, the extreme variations of the currents in the
first 20 km lead to a very unusual shape of the Bragg lines; the right Bragg
line, which usually corresponds to a positive Doppler shift, clearly overlaps
the region of negative frequencies. The corresponding critical value for the
radial surface current is $U_{r}=\lambda_{B}f_{B}$, which is $4.17$ m/s at
$13.5$ MHz and $3.09$ m/s at $24.5$ MHz. These values are generally never
reached, except in some very specific locations such as the Alderney Race,
where the tidal current can reach such extremely large magnitudes. In the
omnidirectional Doppler spectrum, where the contributions from all azimuthal
directions are mixed, the occurrence of such phenomena can lead to errors in
the identification of the Bragg region, as some Bragg lines may be attributed
to the “wrong” side of the spectrum. A second problem associated with strong
currents is the overlap of the first- and second-order regions for the
omnidirectional Doppler spectrum, due to the extreme variation of the first-
order Bragg peaks with direction. These two problems are illustrated in
figures 3 and 4, which compare the omnidirectional Doppler spectrum of the
Jobourg station with the azimuthally resolved Doppler spectra using BF in two
different directions on two different days. It appears that the second order
peaks of the latter fall within the main broad peak of the former (Figure 3)
and that the “positive” first order directional Doppler peak lies on the
negative side of the frequencies (Figure 4). Therefore, the identification of
the FOBR is problematic and flawed, with errors resulting from misinterpreted
second-order contributions. Note that this last problem is specific to DF
processing and does not affect BF processing. Therefore, in the case of a
phased-array radar, we can take advantage of the BF processing to improve the
selection of the FOBR.

Figure 3: Doppler spectra obtained on October 6, 17:20 UTC, 2018 at the
Jobourg station (24.5 MHz, 750 m resolution mode) for a range of 10 km. The
omnidirectional spectrum (blue line) is compared with the azimuthally resolved
spectra at 40${}^{\circ}\mathrm{N}$ CCW (red line) and
100${}^{\circ}\mathrm{N}$ CCW (yellow line). As seen, the second-order peaks
of the directional spectra fall inside the main broad peaks of the
omnidirectional spectrum, so these second-order contributions can be mistaken
with first-order Bragg lines in the DF process. Figure 4: Same as Figure 3 on
October 10, 2018, 07:20 UTC at a range of 4.7 km. The radial current in
direction 34${}^{\circ}\mathrm{N}$ CCW is so strong that the “positive” Bragg
peak crosses the zero frequency, making the identification of the Bragg
frequencies ambiguous.

The main idea is to perform a preliminary identification of both sides of the
FOBR using directional Doppler spectra. For each range and steering direction,
the FOBR can be unambiguously identified within a frequency interval whose
width depends on the frequency resolution (hence the integration time), the
azimuthal resolution (hence the length of the receive array), and the
variation of the radial surface current in the local angular sector. By
sweeping across all steering directions and concatenating the FOBR of each
directional Doppler spectrum, we can reconstruct the FOBR of the
omnidirectional spectrum without second-order artifacts. The method is
illustrated in Figure 5, which shows the omnidirectional range Doppler map
(top) in a situation where both the large currents and the important second-
order contribution make it difficult to identify the FOBR with a simple
contour detection method. The middle panel shows the selected FOBR, while the
bottom panel shows the same using the concatenation of FOBRs obtained with
directional Doppler spectra. Although the FOBR selected with a contour
criterion is visually intuitive, it is flawed with extra Doppler rays around
10 km (due to misinterpreted second-order or RFI contributions) and misses the
strong negative shifts around 5 km due to very strong horizontal current
shear.

Figure 5: Example of range-Doppler map (top panel) for the omnidirectional
Doppler spectrum recorded at Jobourg (24.5 MHz, 750 m resolution) in a day
with strong waves and currents. The middle panel shows the selected FOBR with
a classical contour detection of the omnidirectional spectrum. The bottom
panel shows the FOBR obtained by concatenating the FOBR of directional Doppler
spectra.

While concatenating the FOBR of directional Doppler spectra, we create a table
of correspondence between a given Bragg line and the associated steering
direction and side of the spectrum (left or right). This helps to improve the
DF processing by allowing a posteriori control of the Direction of Arrival
(DA). Each DA found with the MUSIC algorithm for a given Bragg line in the
omnidirectional spectrum is checked to be consistent with the corresponding
steering direction(s) found with the BF. This allows the elimination of
parasitic DA corresponding to Radio Frequency Interference (RFI), ships, or
second-order contributions. From now on, we will refer to the DF processing
that uses a preliminary BF processing for the selection of the FOBR and a
posteriori verification of the DA as the “Hybrid BF/DF” method (which should
not be confused with another hybridization developed by ACTIMAR called HYDDOA
(cf. patent: FR 1562550).).

a)

b)

c)

d)

Figure 6: Radial current maps obtained at the Jobourg station (24.5 MHz, 200 m
resolution) on November 14, 03:00, 2020, with different azimuthal processing
with the 16-antenna receive array: a) BF b) DF with FOBR selection obtained
with dynamical intervals; c) DF with FOBR obtained by contour selection; d) DF
with FOBR selection obtained with BF ("hybrid BF/DF").

a)

b)

c)

d)

Figure 7: Same as Figure 6 for the Goury station.

Figures 6 and 7 show an example of hourly radial maps obtained at the Jobourg
and Goury stations using either the classical BF processing or the DF
processing with the 3 FOBR selection methods mentioned above (dynamic bounds,
contour selection by null detection, or concatenation of the domains obtained
with BF). The antenna grouping and noise reduction methods developed in [12]
were applied to the DF processing. As expected, BF produces a smoother and
cleaner map but suffers from angular smearing in the far field and at the edge
of the radar coverage where the azimuthal resolution deteriorates. The DF maps
are better resolved and show finer spatial structures. However, DF based on
dynamic FOBR search interval or contour selection is plagued by isolated spots
in the central region of the map as well as spurious structures in the
southern part of the map. These artifacts are the remnants of second-order
Doppler peaks that have resisted the application of noise removal techniques
developed by [12], due to the overlap between the first and second-order
regions in the omnidirectional Doppler spectrum. These artifacts are
completely removed by the hybrid BF/DF method. Additionally, this method
extends the range and coverage, especially around Alderney Island

Note that the radar coverage obtained with BF is greater at the Jobourg
station, while it is similar to that of the Goury station when DF processing
is used. This is due to a higher transmitted power at the Jobourg station,
which is also affected by a higher level of electromagnetic interference. This
is caused by a stronger coupling between the transmitting and receiving
antennas (which are closer together) and, in the case of high wind speeds, by
gust-induced mechanical vibrations in the antenna arrays, which are fixed to
the ground by textile fiber ropes.

##  4 Results and performances

###  4.1 Performance assessment using a 3D numerical model

The validation of HFR measurements is known to be a difficult task, as it is
usually based on in situ measurements that are spatially sparse and have
different integration depths and horizontal resolutions. In the absence of a
dedicated in situ field campaign, a surrogate means of validation is
comparison with numerical models. Even if they cannot be considered as ground
truth, they at least have the advantage of providing spatial maps that allow
an overall qualitative comparison (as opposed to a pointwise quantitative
comparison with in situ instruments). We have used the hydrodynamic model,
CROCO [21], coupled two ways to the spectral wave model, WAVEWATCH-III [42].
This coupled model can compute wave-current interactions in three dimensions
using the vortex force formalism of [28]. Wave effects on the current are
simulated as well as changes in the wave field due to surface currents and sea
level. Both models use the same horizontal grids, for which a nesting
technique allows the use of three different horizontal resolutions: $600\hskip
2.0pt\mathrm{m}$, $120\hskip 2.0pt\mathrm{m}$, and $30\hskip 2.0pt\mathrm{m}$.
CROCO, which runs in three-dimensional mode, also has a vertical
discretization based on a following-terrain coordinate $\sigma$ that ranges
from $-1$ at the bottom to $0$ at the surface and extends over $20$ levels.
The coupled model is forced at its open boundaries by the CST France Atlas
[24] with 114 tidal constituents for tidal dynamics and by two-dimensional
wave spectra from the HOMERE numerical wave database for sea state dynamics
[e.g. 7]. At the surface and for both models, wind stress is applied at a
spatial resolution of $24.5\hskip 2.0pt\mathrm{km}$ from the ERA5 database
[20]. The exchange between CROCO and WAVEWATCH-III is managed by the automatic
coupler OASIS [41]. The numerical configuration used here is based on that of
[2, 4] and [26]; which have already been tested on in situ and HF radar data.
The coupled model was run from November 13-19, 2020, a period that covers one
week of HFR measurements in high spatial resolution mode (200 m range
resolution) and also corresponds to a period of spring tides and strong wind
waves during which high surface currents were observed.

The model surface currents obtained in the first child grid at a horizontal
resolution of $120$ meters were projected onto the Goury and Jobourg radials
for ease of comparison. For a more quantitative evaluation, we decided to
focus on the hourly radial current time series observed by HFR in the high-
resolution mode (24.5 MHz and 200 m range resolution) at a few strategic
locations representative of the site specificity. The selected points, labeled
from P1 to P15, are shown in Figure 8 together with the bathymetry of the
site. They are representative of the different situations that can occur in
the radar domain for the surface current: mid-range positions with a weak
Jobourg radial (P01-P03, P08, P10-P11), near-range positions with a strong
Jobourg radial (P04-P07), far-range in deeper water (P09, P12), and far-range
around the island of Alderney. The HFR-based hourly currents were calculated
using both the BF and hybrid BF/DF processing. To evaluate the two HFR radials
separately, the surface current vectors calculated with the CROCO model were
projected along the two radial directions as seen from the Goury and Jobourg
stations. To quantify the amplitude of variation of the radials, we define a
suitable statistical index $A$ as the mean difference (during the time
considered) between the maximum and minimum value of the current during all
tidal cycles:

$A=\langle(U_{r})_{max}-(U_{r})_{min}\rangle$ (1)

The discrepancy between the model and HFR based radials has been quantified,
on the one hand, by their RMS difference ($\sigma_{BF}$ and $\sigma_{DF}$) and
their Pearson correlation coefficient ($\rho_{BF}$ and $\rho_{DF}$) and, on
the other hand, by their difference in amplitude $A$. These statistical
indicators are given in tables 2 and 3 for the radial velocities measured at
the Jobourg and Goury stations. This table shows that the agreement between
the model and the radar measurements, or between the two types of radar
processing (BF or DF), is generally very good, except for a few locations. For
the Jobourg station and using the BF method, $\sigma_{BF}$ varies between
$0.13\hskip 2.0pt\mathrm{m.s^{-1}}$ and $0.74\hskip 2.0pt\mathrm{m.s^{-1}}$
with a mean $\sigma_{BF}$ around $0.37\hskip 2.0pt\mathrm{m.s^{-1}}$. Close
values are found using the DF method with a $\sigma_{DF}$ between $0.16\hskip
2.0pt\mathrm{m.s^{-1}}$ and $0.76\hskip 2.0pt\mathrm{m.s^{-1}}$ and a mean
$\sigma_{DF}$ around $0.35\hskip 2.0pt\mathrm{m.s^{-1}}$. Maximum values for
$\sigma_{DF}$ and $\sigma_{BF}$ are observed in P14, which is at the limit of
spatial coverage as shown in Fig. 12. These values remain weak relative to the
magnitude of the flow for this period. The same behavior is observed for the
Goury station, with a $\sigma_{DF}$ in [$0.17\hskip 2.0pt\mathrm{m.s^{-1}}$ ;
$0.88\hskip 2.0pt\mathrm{m.s^{-1}}$] and a $\sigma_{BF}$ in [$0.17\hskip
2.0pt\mathrm{m.s^{-1}}$ ; $0.86\hskip 2.0pt\mathrm{m.s^{-1}}$]. The mean
values of $\sigma_{BF}$ and $\sigma_{DF}$ are around $0.38\hskip
2.0pt\mathrm{m.s^{-1}}$ and $0.4\hskip 2.0pt\mathrm{m.s^{-1}}$, respectively.
As for the Jobourg station, the maximum values of $\sigma$ were found at point
P13, located near the island of Alderney at the limit of the HFR spatial
coverage. The overall agreement between model and radar measurements is good
at Jobourg with 8 out of 15 values of $\rho_{BF}$ and $\rho_{DF}$ greater than
or equal to $0.95$ and very good at Goury with 11 out of 15 values greater
than or equal to $0.95$. These values are consistent with the previous
analysis by [26] using the standard BF method and the fully coupled 3D model,
MARS-WAVEWATCH-III, by [2, 4]. In this study, the RMSE was calculated by
spatio-temporal averaging over the radar coverage at different tidal cycles
and was found to range from $0.18\hskip 2.0pt\mathrm{m.s^{-1}}$ to $0.60\hskip
2.0pt\mathrm{m.s^{-1}}$. In tables 2 and 3 we have highlighted in blue the
points with the best agreement (P4 and P10, with less than 10% in the
statistical parameters) and in red those with the maximum discrepancy (P1, P5,
P7, and P9, with more than 20% difference in the statistical parameters) for
the 2 radar stations simultaneously. Since these last four locations are
within the limits of spatial coverage, this larger discrepancy is not due to
outliers in the HFR estimate. [26] pointed out that the lowest comparison
values occur in shallow areas with a strong bathymetric gradient. The impact
of these steep gradients is confirmed at locations P1, P5, and P7, in the
vicinity of which the induced heterogeneity of radial velocities may not be
well captured by the model, which uses a horizontal resolution of 120 meters.

Examples of the corresponding time series are shown in figures 9, 10, and 11,
together with the simultaneous value of the significant wave height obtained
with the numerical model at the same location. Although the low-resolution
wind forcing of the ERA5 reanalysis may lead to an imperfect estimate of the
significant wave height, which is also affected by the surface current and sea
surface height, it is sufficient to provide the trend and magnitude of the
latter. The model and the HFR radial velocity are in better agreement for the
Goury radial velocity than for the Jobourg station. This can be attributed to
the aforementioned practical limitations of the antenna receiving array at
Jobourg (section 3.1), namely a higher level of noise in the radar signal and
a greater sensitivity of the antennas to wind gusts, which can induce
mechanical vibrations in the antenna arrays. This could explain some of the
discrepancies when the significant wave height exceeds $2\hskip
2.0pt\mathrm{m}$. Finally, the discrepancies may be related to the turbulence
modeling in the numerical model.

The model radial velocities show smoother variations than observed with the
radar. This may be due to the use of the LES Smagorinsky turbulence model for
horizontal mixing and the RANS-GLS turbulence model for vertical mixing, which
are known to smooth the flow compared to other types of turbulence models such
as the $\alpha$ model [3].

Figure 12 shows two different tidal events on November 15, where the flow
velocity is most intense. For these two events, the DF method can produce i) a
gap-free map thanks to the [12] group antenna method, and ii) a velocity field
showing significant horizontal shear, which is traditionally difficult to
measure and extract from HFR data. The region of intense velocities is less
extensive than in the numerical simulations but follows bathymetric contours
as previously reported in the literature. Note the reduction in radar coverage
at the ebb. This corresponds to a stronger sea state around this time (as seen
from the evolution of the significant wave height), which can significantly
degrade the working range of the radar [18].

Table 2:  Amplitude of variation (obtained as the mean difference between the
maximum and the minimum over a tidal cycle) of the radial current estimated at
the Jobourg station with the CROCO model ($A_{m}$); the HFR-based BF
estimation ($A_{BF}$); the HFR-based DF estimation ($A_{DF}$). RMS difference
and Pearson correlation coefficient between the CROCO model and the HFR-based
radial currents estimated with BF ($\sigma_{BF}$)and $\rho_{BF}$) and DF
($\sigma_{DF}$ and $\rho_{DF}$), respectively. All values are given in m/s.
The model amplitudes that have a discrepancy larger than 20% (respectively,
smaller than 10%) have been highlighted in red (respectively, blue). The RMS
differences that are smaller than 10% of the model amplitude and the
correlation coefficients that are larger than 0.95 have been highlighted in
blue.

| $A_{m}$ | $A_{BF}$ | $A_{DF}$ | $\sigma_{BF}$ | $\sigma_{DF}$ | $\rho_{BF}$ | $\rho_{DF}$
---|---|---|---|---|---|---|---
P1 | 1.81 | 1.11 | 1.29 | 0.34 | 0.33 | 0.95 | 0.92
P2 | 0.79 | 0.84 | 0.94 | 0.13 | 0.16 | 0.89 | 0.85
P3 | 1.03 | 1.04 | 1.02 | 0.20 | 0.20 | 0.86 | 0.86
P4 | 6.17 | 5.52 | 5.49 | 0.50 | 0.49 | 0.99 | 0.99
P5 | 7.28 | 6.71 | 6.68 | 0.66 | 0.58 | 0.99 | 0.99
P6 | 6.57 | 6.87 | 6.89 | 0.48 | 0.42 | 0.99 | 0.99
P7 | 4.54 | 3.72 | 4.10 | 0.46 | 0.38 | 0.99 | 0.99
P8 | 2.67 | 2.25 | 2.25 | 0.28 | 0.27 | 0.99 | 0.99
P9 | 1.73 | 1.26 | 1.37 | 0.25 | 0.21 | 0.95 | 0.95
P10 | 2.00 | 2.06 | 2.20 | 0.22 | 0.20 | 0.96 | 0.97
P11 | 0.77 | 1.13 | 0.96 | 0.18 | 0.20 | 0.81 | 0.77
P12 | 1.28 | 1.12 | 1.02 | 0.28 | 0.26 | 0.65 | 0.68
P13 | 3.28 | 3.46 | 3.51 | 0.47 | 0.48 | 0.94 | 0.94
P14 | 3.29 | 3.47 | 3.45 | 0.74 | 0.76 | 0.82 | 0.81
P15 | 3.58 | 3.12 | 3.27 | 0.45 | 0.41 | 0.95 | 0.95

Table 3:  Same as Table 3 for the Goury station. | $A_{m}$ | $A_{BF}$ | $A_{DF}$ | $\sigma_{BF}$ | $\sigma_{DF}$ | $\rho_{BF}$ | $\rho_{DF}$
---|---|---|---|---|---|---|---
P1 | 2.72 | 3.55 | 3.66 | 0.28 | 0.34 | 0.98 | 0.97
P2 | 5.13 | 4.80 | 4.99 | 0.44 | 0.42 | 0.99 | 0.98
P3 | 4.77 | 4.12 | 3.95 | 0.48 | 0.54 | 0.99 | 0.99
P4 | 2.59 | 2.91 | 2.91 | 0.18 | 0.25 | 0.99 | 0.98
P5 | 2.14 | 2.45 | 2.62 | 0.17 | 0.23 | 0.98 | 0.98
P6 | 2.99 | 2.31 | 2.46 | 0.49 | 0.46 | 0.99 | 0.99
P7 | 2.02 | 2.30 | 2.48 | 0.22 | 0.22 | 0.97 | 0.97
P8 | 4.68 | 4.71 | 4.09 | 0.35 | 0.36 | 0.99 | 0.99
P9 | 0.54 | 0.85 | 0.72 | 0.19 | 0.17 | 0.69 | 0.65
P10 | 4.19 | 3.78 | 4.03 | 0.32 | 0.31 | 0.99 | 0.99
P11 | 4.54 | 4.32 | 4.54 | 0.37 | 0.35 | 0.99 | 0.98
P12 | 2.08 | 2.06 | 1.98 | 0.21 | 0.21 | 0.95 | 0.96
P13 | 4.91 | 4.40 | 4.64 | 0.86 | 0.88 | 0.87 | 0.88
P14 | 4.12 | 1.60 | 2.22 | 0.72 | 0.84 | 0.92 | 0.91
P15 | 4.18 | 1.58 | 1.94 | 0.49 | 0.42 | 0.90 | 0.94
Figure 8: Location of the points P1 to P15 for the evaluation of the HFR-based
time series of radial currents. The ADCP location is marked with a cross. The
bathymetric depth is superimposed in color scale. Figure 9: High-resolution
Radial currents obtained at location P4 from HFR measurements (24.5 MHz, 200 m
resolution mode) with DF (blue solid lines) and BF (black solid lines). A
comparison is given with the radial current inferred from the CROCO-WAVEWATCH-
III model (gray solid lines for the significant wave height and red dashed
lines for the radial velocity) Figure 10: Same as Figure 9 for the radial
currents obtained at location P5.  Figure 11: Same as Figure 9 for the radial
currents obtained at location P7.

Figure 12: Magnitude of the total current (color scale) with superimposed
bathymetric contours (gray scale) and velocity vectors (black arrows). Results
are obtained from the CROCO model (left panel) and the HFR measurements in the
high-resolution 200 m mode (right panel) using DF method for flood (first row)
and ebb (second row) flow.

###  4.2 Performance assessment using in situ measurements

Another way to assess the HFR current is by comparison with Acoustic Doppler
Current Profiler (ADCP) measurements. A bottom-mounted ADCP was installed in
2017 and maintained for one year to measure the vertical profile of the
current at a depth of 30 to 40 $\mathrm{m}$ near point P10 at position
-2.0296∘E and 49.6808∘N. It measures the three components of flow velocity
from the bottom to the surface every meter (which is the bin size) after the
blanking zone [15]. The measurement cell located 2 meters below the water
surface, taking into account the tidal variations, was used to make a relevant
comparison with the HFR measurement and to avoid spurious reflections from the
sea surface echo contaminating the closest bin to the surface. The ADCP
measurements are updated every 10 minutes, with an observation time of 20
minutes, which is comparable to the integration time required for the HFR
observations (12 minutes). Since ADCP velocities were not available during the
HFR period, another period with ADCP in the field and similar tidal conditions
was chosen for comparison. Thus, HFR data from November 13 to 18, 2020 were
tested against ADCP data from November 3 to 8, 2017. The two periods differ
only in the sea state, which was less energetic in November 2017. The entire
ADCP period is covered by the equivalent HFR cycle, except for two days of
missing data (Fig. 13).

A very good agreement with the ADCP data is observed with the two radar signal
processing methods (BF and DF), which give similar surface velocities. The
RMSE and Pearson correlation coefficients are found to be 0.27 m/s and 0.96
with BF, while they are equal to 0.26 m/s and 0.97 with DF. The largest
discrepancy is observed for the maximum values of the absolute velocity, which
is known to be the most difficult to estimate with HFR radar processing
algorithms, especially for the ebb current [26]. These differences are also
explained by the different spatial scales involved in the two types of
measurements, namely the size of the integration cells for HFR and ADCP data
(about a kilometer versus a few meters) and the effective sensing depth (2 m
below the sea surface for ADCP, about 30 cm for radar). Finally, the pointwise
nature of the ADCP at a specific geographic position may account for some
local effects that are not present in the HFR data. Despite these structural
differences, the agreement between the two types of measurements remains
remarkably good, with an RMSE of less than 10% of the typical amplitude.

Figure 13: Magnitude of the total current measured by the ADCP at 2 m below
the surface (blue solid line) and the high-resolution HFR measurement (24.5
MHz, 200 m range resolution) using BF (yellow solid line) and using DF (red
solid line).

###  4.3 The influence of range resolution

As seen above, the strong horizontal shear of the surface flow at some
locations requires a high spatial resolution in both range and azimuth to be
captured by the HFR measurement. The dual frequency capability (13 MHz and
24.5 MHz) of the HFR network as well as the dual resolution mode at the 24.5
MHz frequency (750 m or 200 m) provide the opportunity to test this effect.
The first observation is the narrowness of the first-order Bragg peaks in the
high-resolution radar data. Figure 14 shows three Doppler energy spectra at
200 m range resolution in adjacent cells near point P5. Superimposed is the
average of these spectra, which in principle represents the Doppler spectrum
that would be recorded in a low-resolution 1500 m cell. As can be seen from
these plots, the low-resolution first-order Bragg peak (1500 m) is much
broader than its high-resolution counterpart (200 m) and presents several
maxima that can be misleading when applying azimuthal processing. DF and BF
can therefore select different values for the peak frequency, resulting in
different surface velocities. This suggests that the shearing and meandering
of the surface current in the Alderney Race has a characteristic scale that is
much smaller than the typical radar resolution of 1500 m and can only be
captured in the high-resolution mode of 200 m, where the broadening of the
Doppler peak is less pronounced, if not absent. This opens the way to
characterize the horizontal shear by assessing the relevant length scale of
each meander through its representation in the Doppler spectrum.

Figure 14: Doppler spectra obtained at the Jobourg station in the high-
resolution mode (24.5 MHz, 200 m range resolution) at the range cells 24,27
and 30 in the vicinity of P5 (red, blue, and yellow thin lines, respectively).
The thick magenta line shows the Doppler spectrum obtained by averaging the
high-resolution spectra between the range cells 24 and 30 to simulate the
effect of a coarser resolution of about 1500 m. The dashed vertical lines mark
the position of the first-order peaks that would be estimated in each case,
showing the important variation of radial current inside the same low-
resolution cell.

Another experiment is to compare the surface current radial maps obtained
almost simultaneously at the 2 alternate radar frequencies. Figure 15 shows
successive radial maps (with a 20 min time delay) obtained with the Jobourg
station at 13 MHz and 24.5 MHz using the 2 types of azimuthal processing (BF
or hybrid BF/DF). Note that the available range resolution is coarser at 13
MHz (1500 m) than at 24.5 MHz (750 m). To make them comparable, we have
modified the tapering window used for range gating at 13 MHz to increase the
effective resolution (at the cost of increased secondary lobes) and bring it
closer to the range resolution obtained at 24.5 MHz with the Blackman tapering
window. This allows us to isolate the effect of azimuthal resolution alone.
Since the same receive antenna array is used at both radar frequencies, the
theoretical azimuthal resolution obtained at 13 MHz is about twice as coarse
as the azimuthal resolution obtained at 24.5 MHz ($14^{\circ}$ versus
$7^{\circ}$). This can be seen quite clearly in Figure 15a), where the fine
structures of high current intensity near the coast are smeared when observed
at 13 MHz, whereas they are well rendered at 24.5 MHz. Note that the DF
processing (in its improved hybrid version) provides a better description of
the sharp fronts that are visible around the spot of the most intense current,
regardless of the radar frequency. This shows that with a smaller phased-array
(here equivalent to 8 antennas), the DF processing method remains high-
performing and can advantageously replace a longer antenna array (16
antennas).

Figure 15: Quasi-simultaneous radial maps obtained at the Jobourg station with
different radar frequencies and different azimuthal processing: a) 13 MHz BF;
b) 13 MHz DF; c) 24.5 MHz BF d) 24.5 MHz DF. The effective range resolution at
the two radar frequencies is about 1500 m.

##  5 Conclusion

Strong and sheared currents such as those encountered in the Alderney Race are
challenging to measure with HFR. Capturing their spatial heterogeneity
requires spatial resolution, which can only be achieved with a wide frequency
bandwidth and a large number of antennas. Second, the large Doppler shifts
caused by the surface current can cause the Bragg lines to cross the zero
Doppler axis, making their identification ambiguous. Finally, in the presence
of strong waves and currents, the first- and second-order spectra can overlap
in the omnidirectional Doppler spectrum, causing the DF approach to fail. We
have addressed these issues in this paper. An improved hybrid DF based on BF
preconditioning is proposed that eliminates the first/second order ambiguity
and, as a by-product, also eliminates the RFI and extends the radar coverage.
A systematic comparison was made with the classical BF processing available
for a phased-array radar system. At the highest operating frequency (24.5
MHz), the 16 antenna array provides an azimuthal resolution of the order of 7
degrees at the beam center, which is sufficient to detect fine flow structures
in the near and medium range.

The improved DF method was evaluated with the classical BF and the HFR
measurements were tested against a numerical model (CROCO) at several sites
with different bathymetry and against in situ measurements, namely an ADCP
time series.

In the light of these comparisons, the 16 antenna BF and the DF processing
were found to be generally very close and both very consistent with models and
ADCP. However, there are a few specific locations with complex and shallow
bathymetry where the spatial variations of the current can be very sharp in
both space and time, especially during ebb and flow. In this case, the time
series of the HFR-based currents show structured asymmetric patterns that the
model cannot reproduce, and peaky extrema that have a larger amplitude when
estimated with the DF processing. We took advantage of an exceptional permit
to operate the HFR in a very high spatial resolution mode (200 m) to observe
the surface at a very fine scale and to investigate the limits of coarser
resolution (750 or 1500 m) in the context of strong and sheared currents. The
Doppler spectra measured at high resolution show first-order Bragg lines that
are better defined (i.e. thinner) than at low resolution, where they show
broader and more fragmented peaks (Fig. 14), which can lead to ambiguous
estimates of the radial current depending on the technique used. Finally, HFR
measurements at 13 and 24.5 MHz were compared, where the theoretical azimuthal
resolution using BF processing varies by a factor of two. While BF processing
is inaccurate at the lowest radar frequency, the improved DF technique
performs equally well in both situations.

AcknowledgementsThe HF radars were bought by Caen University as a part of the
‘Manche 2021’ project, co-funded by the EU and the Conseil Régional de
Normandie, throughout the FEDER-FSE operational programme 2014–2020. The
numerical results benefited from CRIANN computing resources. The authors also
express their gratitude to L. Perez and M. Boutet for their technical
assistance and L. Furgerot for providing the in situ data acquired in the
framework of HYD2M project funded by the Agence Française pour la Recherche
(ANR-10-IEED-0006-07). Declarations Ethical Approval Not applicable Funding
Not applicable

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CMS-CR-2023/285 December 4, 2023

Four top quark production searches and cross section measurements at the LHC

Niels Van den Bossche

Ghent University, Ghent, Belgium

on behalf of the ATLAS & CMS Collaborations

> Four top quark production is a rare standard model process that has been
> observed for the first time in proton-proton collisions at $\sqrt{s}=13$ TeV
> at the CERN LHC by both the ATLAS and CMS Collaborations. Both observations
> were made in the same-sign dilepton and multilepton final states of the
> process and are presented in this contribution. In addition, another
> measurement of four top production by the CMS Collaboration using the all
> hadronic, one lepton and opposite-sign dilepton final states is presented.
> This is the first result to take a direct look at the all hadronic final
> state.

> PRESENTED AT
>
>
>
>
> 16th International Workshop on Top Quark Physics
> 24–29 September, 2023

††footnotetext: Copyright 2023 CERN for the benefit of the ATLAS and CMS
collaborations. Reproduction of this article or parts of it is allowed as
specified in the CC-BY-4.0 license.

##  1 Introduction

Four top quark production is a rare process with a cross section predicted by
the standard model (SM) of $13.4^{+1.0}_{-1.8}$ fb at $\sqrt{s}=13$ TeV [1].
Despite the low cross section, the process can serve as an important probe to
new physics, as new massive bosons can dramatically enhance the production
cross section. In addition, it can serve as a probe of the top-Higgs Yukawa
coupling, complementary to other measurements of this SM parameter.

In this contribution, three results by the ATLAS and CMS Collaborations [2, 3]
are presented. The first is a search for four top production by the CMS
Collaboration targetting the zero ($0\ell$), one ($1\ell$) and two opposite-
sign lepton ($2\ell$OS) final states [4]. Two other results, one from each
collaboration, present the observation of this rare process [5, 6]. These
observations were achieved using the two same-sign ($2\ell$SS), three
($3\ell$) and four lepton ($4\ell$) final states.

##  2 The $0\ell$, $1\ell$ and $2\ell$OS final states

The CMS Collaboration performed a search for four top production in $0\ell$,
$1\ell$ and $2\ell$OS events [4]. These three final states combined have a
large branching fraction of 87%, but the sensitivity is limited by the
background from t$\bar{\text{t}}$ with additional (b) jets and QCD multijet
production. To reduce these contributions, top taggers are used, targetting
both boosted and resolved top quark signatures. The signal and control region
definitions differ in each final state, but are generally defined by a large
number of (b tagged) jets and the existence of tagged top quark candidates.

Figure 1: The BDT score in the zero lepton (also referred to as all-hadronic)
final state. Signal regions like this are used to extract the four top cross
section [4].

Regions enriched in four top events are created using BDTs in the zero and one
lepton final states and used in the template fit. In the two opposite-sign
lepton final state, the scalar sum of the transverse momentum of all jets is
used as the discriminating variable between signal and background. The cross
section is extracted with a template fit to the signal and control regions,
with one of the $0\ell$ signal regions shown in Figure 1. The measured cross
section is $36\pm 7\text{(stat)}^{+10}_{-8}\text{(syst)}$ fb and evidence for
four top production is obtained with an observed statistical significance over
background of $3.9$ standard deviations. The result is combined with an older
CMS measurement in the $2\ell$SS, $3\ell$ and $4\ell$ final states [8],
leading to a measured cross section of $17\pm 4\text{(stat)}\pm
3\text{(syst)}$ fb.

##  3 The $2\ell$SS, $3\ell$ and $4\ell$ final states

Four top quark production was observed in the $2\ell$SS, $3\ell$ and $4\ell$
final states by the ATLAS and CMS Collaborations [5, 6]. The results are a
reanalysis of the Run 2 datasets in these final states and supersede the
previous results published by both collaborations [7, 8]. The observations are
made possible thanks to many improvements in reconstruction techniques, object
identification such as b tagging, and analysis methods.

Compared to the previously discussed final states, the branching fraction is
significantly smaller, at only 13%, but the background is drastically reduced
as well and made up of a mix of reducible and irreducible processes. One of
the most important backgrounds are events, mainly t$\bar{\text{t}}$, with
additional nonprompt leptons, which are leptons originating from semileptonic
b decays or photon conversions in the detector material. The rate of these
events is in both results reduced by employing a per-lepton BDT, trained to
identify prompt leptons. A much smaller irreducible background comes from
events with charge misidentified electrons. In the ATLAS result, a per-
electron BDT is also applied to reduce the misidentification rate, while in
the CMS result, three charge measurements are required to give the same result
for each electron. The majority of the reducible background is made up of
t$\bar{\text{t}}$W, t$\bar{\text{t}}$Z and t$\bar{\text{t}}$H production.

### ATLAS result

The nonprompt background is split in 4 different contributions, predicted from
MC simulations and normalized in four dedicated control regions. In addition,
a lot of care is taken on the t$\bar{\text{t}}$W background. The main
contribution is predicted with next-to-leading order (NLO) QCD MC and additive
weights to consider the fully electroweak contributions. Since it is known
that the NLO term first order in QCD and third order in electroweak has a
large contribution to the cross section, a dedicated sample is simulated and
used. Lastly, the number of jets distribution is corrected using jet scaling
regimes, where a ratio is defined based on the number of events in
neighbouring bins in the number of jets distribution. This ratio is expected
to be equal to a constant at a large number of additional jets on top of the
hard process, and proportional to $1/(1+n)$, with $n$ the number of additional
jets, for low values of n. In practice, these two regimes flow over into one
another. Four control regions are defined to extract the parameters associated
with these jet scaling regimes, as well as two normalization factors, one for
t$\bar{\text{t}}$W+ and one for t$\bar{\text{t}}$W- events. The result of the
corrections to the t$\bar{\text{t}}$W modelling are compared to data using a
number of jets distribution using bins of the number of events with two
positive leptons minus the number of events with two negative leptons, for
which the result is shown in the left panel of Figure 2.

Figure 2: (left) Using the charge asymmetry in t$\bar{\text{t}}$W events, the
modelling of the process as a function of the number of jets is checked after
the corrections with the jet scaling regimes [5]. (right) The GNN output score
in the signal region, used to extract the cross section of four top production
[5].

In summary, a total of eight control regions are introduced. To extract four
top production, a single signal region is used, covering all considered final
states, with a high requirement on the number of jets, b tagged jets and the
scalar sum of the transverse momenta of the jets and leptons in an event. The
signal is separated from the background processes by using a graph neural
network (GNN) and the signal strength is extracted with a template fit to the
GNN score distribution in the signal region, as shown in Figure 2, as well as
one template per control region. This leads to a measured cross section of
$22.5^{+4.7}_{-4.3}\text{(stat)}^{+4.6}_{-3.4}\text{(syst)}$ fb and an
observation of the process with a statistical significance of 6.1 standard
deviations.

### CMS result

The nonprompt background is predicted using a tight-to-loose ratio method,
where the contribution in the signal and control regions is predicted from
sidebands in data, defined by loose-but-not-tight leptons (where the signal
and control regions are defined using tight leptons).

The t$\bar{\text{t}}$W background is predicted using NLO QCD MC with the
normalization free floating in the fit. Two dedicated control regions in the
same-sign dilepton final state are introduced, as well as using a the output
of a multiclass BDT in the signal region, which is trained to separate
t$\bar{\text{t}}$W production from other background processes.

Dedicated signal regions are used for each of the analyzed four top final
states. Since the background composition changes between these final states,
three control regions are introduced for $3\ell$ and $4\ell$ events to ensure
a correct modelling of the background. Two of these regions are introduced for
the $3\ell$ final state, one with a looser requirement on the number of (b
tagged) jets, and one requiring an opposite-sign same-flavour lepton pair with
an invariant mass close to that of the Z boson. In the $4\ell$ final state, a
similar control region to the last one is used. These two control regions
allow to float the normalization of the t$\bar{\text{t}}$Z background in the
fit, and also allow to check the contributions of WZ and ZZ production with
additional (b) jets.

Figure 3: (Left) An example of a signal region used in the fit to extract the
four top cross section. The BDT score of the four top class is used to
maximize the sensitivity [6]. (Right) Combination of the two same-sign
dilepton control regions used in the analysis, designed to extract the
t$\bar{\text{t}}$W cross section and verify the nonprompt modelling. The
signal region BDT is used to separate the t$\bar{\text{t}}$W and nonprompt
contributions [6].

The signal regions are defined by a high number of (b tagged) jets and the
scalar sum of the transverse momenta of all jets. Two multiclass BDTs are
trained, one for the same-sign dilepton and one for a combination of the three
and four lepton final states. Three classes are defined for each BDT: a signal
class, a t$\bar{\text{t}}$ class, trained with a combination of events with
nonprompt and charge misidentified leptons, and a t$\bar{\text{t}}$X class,
trained on a combination of t$\bar{\text{t}}$W, t$\bar{\text{t}}$Z and
t$\bar{\text{t}}$H. The signal regions are split in these three classes
according to the BDT output and the same-sign dilepton signal region is
further split in electron-electron, electron-muon and muon-muon events. The
cross section is extracted with a template fit to a combination of signal and
control regions, with an example of these fitting regions for the signal and
control regions shown in Figure 3. The measured cross section is
$17.7^{+3.7}_{-3.5}\text{(stat)}^{+2.3}_{-1.9}\text{(syst)}$ fb, and the
process is observed with a statistical significance of 5.6 standard
deviations.

##  4 Summary

The most recent searches and measurements for four top quark production
performed in various final states by the ATLAS and CMS Collaborations are
presented. The process has been observed for the first time at both
experiments but the statistical uncertainty is still the limiting component.
The results all report a higher than expected cross section, but still agree
with the standard model of particle physics within less than 1.8 standard
deviations.

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