remote sensing

Letter
First Evidence of Mesoscale Ocean Eddies Signature
in GNSS Reflectometry Measurements
Mostafa Hoseini 1,2, * , Milad Asgarimehr 2,3 , V alery Zavorotny 4 , Hossein Nahavandchi 1 ,
Chris Ruf 5 and Jens W ickert 2,3
1 Department of Civil and Environmental Engineering, Norwegian University of Sci ence and T echnology
NTNU, 7491 T rondheim, Norway
2 German Research Centr e for Geosciences GFZ, 14473 Potsdam, Germany
3 T echnische Universität Berlin, 10623 Berlin, Germany
4 Cooperative Institute for Research in Envir onmental Sciences, University of Colorado Boulder ,
Boulder , CO 80309, USA
5 Climate and Space Department, University of Michigan, Ann Arbor , MI 48109, USA
* Correspondence: [email protected]
Received: 28 November 2019; Accepted: 3 February 2020; Published: 6 February 2020
    
  

Abstract:
Feasibility of sensing mesoscale ocean eddies using spaceborne Global Navigation Satellite
Systems-Reflectometry (GNSS-R) measur ements is demonstrated for the first time. Measur ements of
Cyclone GNSS (CYGNSS) satellite missions over the eddies, documented in the A viso eddy trajectory
atlas, ar e studied. The investigation r eports on the evidence of normalized bistatic radar cr oss
section ( σ 0 ) responses over the center or the edges of the eddies. A statistical analysis using pr ofiles
over eddies in 2017 is carried out. The potential contributing factors leaving the signature in the
measur ements ar e discussed. The analysis of GNSS-R observations collocated with ancillary data
fr om the Eur opean Centr e for Medium-Range W eather For ecasts (ECMWF) Reanalysis-5 (ERA-5)
shows str ong inverse corr elations of
σ 0
with the sensible heat flux and surface str ess in certain
conditions.
Keywords: GNSS Reflectometry; Mesoscale ocean eddies; Bistatic Radar Cr oss Section; CYGNSS
1. Introduction
Mesoscale ocean eddies can drive atmospher e r esponse at mesoscales mainly through heat
fluxes [
1
] and they have a local influence on near -surface wind, cloud pr operties, and rainfall [
2
].
Analysis of mesoscale eddy-atmosphere interactions fr om general circulation models suggests
significant intermodel dif fer ences mainly stemming fr om two factors: surface wind strength and marine
atmospheric boundary layer adjustments to mesoscale heat flux anomalies [
3
]. Several Earth-observing
satellites have been aiding these models for decades with their data pr oducts.
Global Navigation Satellite System Reflectometry (GNSS-R) is a r elatively new Earth observation
technique for monitoring a large variety of geophysical parameters (see [
4
,
5
] for a review). This
technique exploits the GNSS signals of opportunity after being reflected fr om the Earth’s surface, both
over lands and oceans. The signals ar e inter cepted by low-cost, low-power and low-mass GNSS-R
r eceivers and ar e pr ocessed to extract geophysical information. These r eceivers onboard small low
Earth-orbiting satellites of fer cost-ef fective Earth observations with high coverage and unpr ecedented
sampling rate. Cyclone GNSS (CYGNSS) is the satellite constellation consisting of eight microsatellites
with the main science objective of ocean wind speed monitoring especially during hurricane events,
launched in December 2016 [ 6 ].
Ocean monitoring is one of the most mature spaceborne GNSS-R applications, with a pr oven
capability of surface wind measur ement [
7
–
9
]. Insignificant level of sensitivity to rain attenuation [
10
]
Remote Sens. 2020 , 12 , 542; doi:10.3390/rs12030542 www .mdpi.com/journal/remotesensing

Remote Sens. 2020 , 12 , 542 2 of 12
and cost-ef fective observation fr equency ar e the main advantageous characteristics motivating
r esear chers to develop new ideas for additional applications over oceans [
11
–
13
], and for the
development of futur e novel GNSS-R missions [ 14 , 15 ].
Remote sensing of oceanic featur es, e.g., eddies, based on high precision GNSS-R altimetric
measur ements, ar e being pursued. For instance, [
16
] deduced sea surface topography observations
fr om the GNSS-R phase measur ements onboar d the German High Altitude Long Range (HALO)
r esear ch air craft. In an air -borne GNSS-R study , the so-called “Eddy Experiment”, the capabilities
of the technique for ocean altimetry [
17
] and scatter ometry [
18
] wer e additionally demonstrated.
Nevertheless, the r esponse of the measur ements over mesoscale eddies is not yet characterized and
documented, despite the available lar ge datasets fr om r ecent GNSS-R satellite missions.
A high number of observations are pr ovided by CYGNSS offering a possibility to study the
feasibility of observing ocean eddies using GNSS-R measurements. This r esearch focuses on the
GNSS-R scatter ometric observations (rather than in an altimetry configuration) and tries to characterize
eddy signatur es in those measur ements for the first time. The data ar e empirically analyzed and the
signatur es and physical explanations ar e discussed. Following this intr oduction, Section 2 describes
the datasets and the method. The r esults are r eported and discussed in Section 3 . Finally , concluding
r emarks ar e given in Section 4 .
2. Data and Method
Four datasets ar e used for the analysis covering the period fr om March to December 2017.
The main dataset consists of the CYGNSS GNSS-R measur ements. The eight CYGNSS micr osatellites
ar e dispersed in 35
◦
inclined orbits with an altitude of
≈
520 km. The onboar d GNSS-R receivers ar e
equipped with distinct channels measuring up to four simultaneous GPS signals after r eflection from
the ocean surface [
19
]. The corresponding data ar e available at dif fer ent pr ocessing levels. Level 1
(L1) pr ovides a variety of parameters including the calibrated measur ements of bistatic radar cr oss
section (BRCS) as well as the Normalized BRCS (NBRCS)
σ 0
. The L1 data ar e further pr ocessed into
the 10 m r efer enced wind speed above the ocean surface at Level 2 (L2). For the analysis in this study ,
σ 0 pr oduct is extracted fr om the V ersion 2.1 (v2.1) dataset [ 20 , 21 ].
CYGNSS measur ements over the documented mesoscale eddies in A viso’s trajectory atlas version
2.0 ar e extracted. The atlas is a multi-mission altimetry-derived product with a daily temporal
r esolution [ 22 ]. Eddy characteristics, including the position and radius, spinning speed, and the type
(cyclonic/anticyclonic) ar e extracted fr om the atlas.
Near -surface ocean curr ent estimates fr om the Ocean Surface Curr ent Analysis Real-time dataset
(OSCAR) ar e also used in this study [
23
]. The ocean current data ar e provided with a spatial r esolution
of one-thir d degr ee. Nevertheless, they ar e spatially interpolated along the CYGNSS tracks. Due to
the five-day temporal r esolution of the OSCAR dataset, the tracks on those days, on which OSCAR
curr ent estimates ar e available, ar e collected for the analysis.
The analysis also uses ancillary data r etrieved fr om the Eur opean Centr e for Medium-Range
W eather For ecasts (ECMWF) Reanalysis-5 (ERA-5) product. The ERA5 is a global atmospheric
r eanalysis based on an ECMWF model assimilating observations fr om various sources including
satellite and gr ound-based measur ements [
24
]. The r etrieved parameters include surface wind-field,
Sea Surface T emperatur e (SST), Sensible Heat Flux (SHF), and turbulent surface stress field. These data
pr oducts of fer a possibility to discuss potential interactions of the geophysical parameters with the
GNSS-R
σ 0
. The r eanalysis measur ements are pr ovided hourly with a spatial resolution of 0.25
◦
. The
estimates ar e spatiotemporally interpolated along with the CYGNSS tacks being used in the study .
The eddy trajectory atlas detects an eddy as the outermost closed-contour of Sea Level Anomaly
(SLA) encompassing a single extremum [
22
]. The area enclosed by the contour of maximum
cir cum-average speed is consider ed as the eddy radius
R
. The CYGNSS tracks overpassing the
eddy with a maximum distance of 2
R
fr om the eddy center ar e collected and transformed into a local
coor dinate system (Figur e 1 ). The local coor dinate system has the origin at the center of the moving

Remote Sens. 2020 , 12 , 542 3 of 12
eddy with x- and y-axes oriented toward geographical east and north, respectively . Observations
marked with a poor quality flag in the CYGNSS dataset (L1, v2.1) and tracks with more than 10% data
loss ar e excluded fr om the collocated dataset.
The methodology of this study is based on the following steps. First, the signatures in the
CYGNSS
σ 0
ar e visually sought. The observed behavior in several cases can be the first evidence on
the possibility of an eddy-left signatur e in the GNSS-R measurements. This examination is followed by
statistical analyses to quantitatively characterize the signatures. W e investigate the collocated dataset
consisting of mor e than 2.7
×
10
5
NBRCS pr ofiles over
≈
6000 mesoscale eddies. The pr ofiles in the
along-track coor dinate system ar e normalized using the radius of each eddy and gridded between
− 1.1 × R to + 1.1 × R (Figur e 1 ).
Figure 1.
A sketch of the gridded GNSS-Reflectometry profile of Cyclone GNSS (CYGNSS) over an
eddy and the local coor dinate system with x- and y-axes oriented towar d east and north, respectively .
The visually observed behaviors of the
σ 0
pr ofiles show noticeable changes over the central
r egion or the edges of the eddies. These patterns ar e along with some linear and nonlinear changes
in dif fer ent scales. T o extract the main nonlinear anomalies over the center or at the edges of eddies
within the pr ofiles, linear and small scales fluctuations of
σ 0
should be filter ed out. W e apply Principal
Component Analysis (PCA) [
25
] to r educe the dimensionality of the dataset while preserving most of
the information within the
σ 0
pr ofiles. T o this end, a data matrix
X m × n
is formed using
n
pr ofiles, each
of which with
m
gridded observation points. The profiles ar e centered by subtracting the mean values.
Using Singular V alue Decomposition (SVD), the data matrix X can be written as:
X = U L V T (1)
wher e the columns of
U
and
V
ar e the left and right singular vectors, respectively .
L
is a diagonal
matrix with non-negative elements, the singular values
λ
. A proper gr oup of singular values and
corr esponding singular vectors is selected to r econstruct the data matrix. Columns of the reconstr ucted
matrix contain the filter ed
σ 0
pr ofiles. Assuming the set
I = { i
,
i +
1, ...,
k }
whose elements ar e the
indices of the selected gr oup, the r econstructed data matrix, ˆ
X is:
ˆ
X = X i + X i + 1 + ... + X k , X i = λ i U i V T
i (2)
wher e
U i
and
V i
ar e the left and right singular vectors associated with the singular value
λ i
. Columns
of the matrices
X i
r epr esent uncorr elated featur es of the
σ 0
pr ofiles. The quality of each principal
component (PC) can be measur ed by:
Λ i = λ i
∑ d
l = 1 λ l
(3)
wher e
Λ i
r epr esents the pr oportion of total variance explained by the principal component
i
. The
parameter d ( d ≤ m i n { m , n } ) is the number of non-zer o singular values.

Remote Sens. 2020 , 12 , 542 4 of 12
The investigation is followed seeking the conditions, in which the
σ 0
r esponse is mor e pronounced.
T o this end, the corr elation coefficient between
σ 0
and surface sensible heat flux is calculated at dif fer ent
wind speeds. Similarly , the corr elation coef ficient between
σ 0
and the mean turbulent surface str ess is
obtained in a range of angular dif fer ences between the CYGNSS observational track and the turbulent
surface str ess. The r esults are pr esented in the following section.
3. Results and Discussion
Generally , two pr ominent anomalies ar e observed in our investigation as r esponses of
σ 0
to the
pr esence of the eddies: one jump at the eddy center (single-jump behavior) or two jumps at the eddy
edges with a lower value at the center (double-jump behavior). Figur e 2 demonstrates the double- (a–c)
and single-jump (d–f) behaviors in dif fer ent exemplary cases. The sudden incr ease in
σ 0
is significant
enough to be easily discerned in the measur ements.
100
0 North
(km)
-100
(a) Lat: 24.41 ° , Lon: 140.88 ° ,
09-Jun-2017 11:55
0 -200
East(km)
100
0
NBRCS( 0)
200
300
100
North
(km)
0
(b) Lat: 34.63 ° , Lon: 290.57 ° ,
04-Jul-2017 12:25
0
East(km)
-200
10
-100
0 200
20
NBRCS( 0 )
30
40
100
North
(km)
0
(c) Lat: 33.05 ° , Lon: 137.87 ° ,
11-Jun-2017 08:10
0 -100
East(km)
NBRCS( 0 )
20
0
40
60
200
North
(km)
0
(d) Lat: 34.66 ° , Lon: 172.86 ° ,
30-Jun-2017 21:20
0
East(km)
-400
NBRCS( 0 )
20
0 -200
400
40
60
100
North
(km)
0
(e) Lat: -33.08 ° , Lon: 12.49 ° ,
01-Jun-2017 06:30
-100
0
East(km)
-400
50
0
NBRCS( 0 )
400
100
150
100
North
(km)
0
(f) Lat: 33.49 ° , Lon: 161.47 ° ,
09-Jul-2017 18:15
0
East(km)
-100
0
50
400
NBRCS( 0 )
100
150

Figure 2.
Exemplary cases of GNSS-Reflectometry
σ 0
double-jump (
a
–
c
) and single-jump
( d – f ) behaviors observed in Cyclone GNSS (CYGNSS) tracks.
Additional exemplary cases ar e shown along with the collocated ancillary data in Figur es 3 – 5 . In
Figur e 3 , clear fluctuations ar e r epeatedly demonstrated over the eddy edges (similar to Figure 2 a–c).
Once the track enters the eddy-affected ar ea,
σ 0
incr eases significantly and then dr ops quickly at the
center followed by another jump once the track leaves the eddy .

Remote Sens. 2020 , 12 , 542 5 of 12
Figure 3.
A track of Cyclone GNSS (CYGNSS) overpassing an eddy on 4 July 2017, 12:24. The top-left
panel displays sea surface temperatur e, surface wind (white arrows) and curr ent (blue cones). On the
top-right, instantaneous surface sensible heat flux (SHF) as well as surface str ess (blue arrows)
are visualized. The bottom panel pr ofiles CYGNSS
σ 0
along with the wind and curr ent velocity ,
instantaneous SHF and surface stress magnitudes.
Figure 4.
A track of Cyclone GNSS (CYGNSS) overpassing thr ee eddies on 4 June 2017, 08:11.
The top panel displays sea surface temperatur e, surface wind (white arr ows) and curr ent (blue cones).
In the middle, instantaneous surface sensible heat flux (SHF) as well as surface stress (blue arr ows)
are visualized. The bottom panel pr ofiles CYGNSS
σ 0
along with the wind and curr ent velocity ,
instantaneous SHF and surface stress magnitudes, r eferenced at the center of the middle eddy .

Remote Sens. 2020 , 12 , 542 6 of 12
Figur e 4 shows a CYGNSS track which is long enough to overpass thr ee cyclonic eddies. The
σ 0
behaves similarly to Figur es 2 a–c and 3 . The track does not cross the first eddy center . This causes
an incr ease in the value of
σ 0
when it passes the eddy outer lying ar ea. A remarkable fact is that
σ 0
r emains almost at the same level moving over the eddy edges and again drops to lower values once it
leaves the af fected r egion. Reaching the second eddy , the track sweeps also the ar eas close to the eddy
center and
σ 0
r esponds with a lower value at the center and two considerable incr eases at the edges.
The behavior of σ 0 is similar over the third eddy , however , the peaks stand at lower values.
Figur e 5 shows another CYGNSS track overpassing thr ee eddies. Similar to Figure 2 d–f,
σ 0
shows
a single peak at the center . The track enters the core r egion with a sudden incr ease in
σ 0
which again
dr ops to its initial level once the track moves of f the center . Similar behavior of
σ 0
is observed r eaching
the central r egion of the second and thir d eddies.
Figure 5.
A track of Cyclone GNSS (CYGNSS) overpassing thr ee eddies on 29 June 2017, 20:45. The
top panel displays sea surface temperatur e, surface wind (white arrows) and curr ent (blue cones).
In the middle, instantaneous surface sensible heat flux (SHF) as well as surface stress (blue arr ows)
are visualized. The bottom panel pr ofiles CYGNSS
σ 0
along with the wind and curr ent velocity ,
instantaneous SHF and surface stress magnitudes, r eferenced at the center of the second eddy .
Figur e 6 shows the PCA r esults where the first nine principal components of the dataset pr eserve
mor e than 95% of the statistical information in the dataset. The PCs r epr esent low to high-fluctuating
patterns within the pr ofiles. The first PC mainly r eflects the overall linear tr end of the
σ 0
pr ofile. The
other PCs captur e the r emaining non-linear variations of the pr ofiles over the eddies. W e reconstr uct
the pr ofiles using the eight components PC2-PC9 and calculate the corr elation coef ficient of each
r econstructed pr ofile with synthetic templates of the two observed patterns. Since the peaks over the
edges or at the center of the eddies could be slightly displaced fr om the exact expected location, we
consider up to ± 0.1 × R lag for the calculation of the correlation.
The analysis r eveals that about 12.7% (15.9%) of profiles demonstrate a corr elation coefficient of
0.7 or mor e with the single (double) peak template. W e also carried out the same statistical analysis

Remote Sens. 2020 , 12 , 542 7 of 12
over a new set of profiles collected r egardless of the pr esence of eddies. In a reverse appr oach, the
pr ofiles demonstrating a high corr elation with the templates (
≥
0.7) ar e investigated. About 45% of
these pr ofiles ar e either located on the eddies (accor ding to the A viso’s trajectory atlas) or show a high
corr elation ( ≥ 0.7) with the surface current.
Figure 6.
Principal components of the pr ofiles and the total variance of the data explained by each
principal component.
Results of the next statistical analysis over the collocated dataset r eveal a strong negative
corr elation of CYGNSS
σ 0
observations with both SHF and surface str ess under certain conditions.
Figur e 7 pr ovides insights into the favorable conditions, in which CYGNSS is more likely to sense
surface str ess and SHF over the eddies.
Figure 7.
Schematic repr esentation of surface stress change due to the interaction of an eastwar d
uniform wind with the surface current associated with an anticyclonic eddy (
a
), Correlation of the
σ 0
profiles of Cyclone GNSS (CYGNSS) with anomalies of instantaneous surface sensible heat flux at
differ ent wind speeds (
b
), the impact of dif ferent angular distances of the CYGNSS tracks with surface
stress vector on the corr elation between the σ 0 profiles and mean turbulent surface str ess ( c ).

Remote Sens. 2020 , 12 , 542 8 of 12
Figur e 7 a illustrates a simplified model of changing surface str ess due to the interaction between
the eddy surface curr ent and wind speed. In Figure 7 b, the behavior of
σ 0
is highly correlated with
SHF over the eddies at wind speeds between
≈
3 m/s and 7 m/s, wher e the values of the corr elation
coef ficients ar e mainly between
−
0.8 to
−
0.95. Accor ding to the theory , at high enough wind speed
(
≈ >
5 m/s), the surface parameter that contr ols the intensity of GNSS r eflections fr om the ocean
surface, or
σ 0
, is the low-pass mean square slope,
M S S L P
, of the ocean surface [
26
]. It is determined
by the part of the wave slope spectrum that r esides at wavenumbers smaller than
k ∗ = k c o s θ i nc /
3
wher e
θ i n c
is an incidence angle and
k
is the wavenumber
(
2
π / λ )
of the L-band GNSS signal [
27
].
The
σ 0
is inversely pr oportional to
M S S L P
. The lar gest contribution to the
M S S L P
originates fr om
the short-wave portion of the spectrum near
k ∗
. Fr om classic works of [
28
,
29
], it is known that
ther e ar e two main mechanisms af fecting that part of the wave spectrum: the varying wind surface
str ess and interaction of short waves with the curr ent gradients. At low enough wind speed, the
scattering of GNSS signals does not follow a pure quasi-specular scattering and ther e is a coherent
scattering component that tends the mechanism to a higher -order Bragg scattering, driven by Rayleigh
parameter [ 30 ]. Rayleigh parameter is pr oportional to waves at any wavenumbers. So, at this r egime
of wind speed, GNSS-R measur ements could be mor e sensitive to surface state, even to small-scale
r oughness modifications [
12
]. Figur e 7 c shows the impact associated with the angular dif fer ence of
CYGNSS tracks and surface str ess field dir ection. The direction of the CYGNSS track with r espect
to the surface str ess vector can incr ease the sensitivity of
σ 0
to surface stress anomalies within the
eddies. This means the GNSS-R measur ements are highly likely to sense the str ess field with a direction
against the moving GNSS-R specular points. It can be also seen that for the absolute angular distances
in the range of about 60 to 180 degr ees the wind stress would be mor e pronounced in the CYGNSS
measur ements.
Atmospheric boundary layer change associated with the eddy-induced SST anomalies r esults
in a varying wind field [
31
]. The modified local surface wind influenced by marine boundary layer
dynamics [
32
,
33
] can partially explain the GNSS-R
σ 0
patterns. The enhanced local wind over the
warm cor e of the eddy can lead to the abrupt change in the GNSS-R
σ 0
values. Since the improvement
in the weather and climate pr ojections r equir e detailed observations and understanding of warm
eddy-atmospher e interactions [
34
], this possible promising contribution by the GNSS-R technique
should be investigated.
The first cold-cor e eddy shown in Figur e 5 can cause a str ong dampening of wind intensity due to
downwar d transport of wind momentum, decelerating local surface wind. The sharp peak of GNSS-R
σ 0
r esides at the cor e r egion of the eddy wher e the SST has a lower value. This deceleration could also
happen when a tropical cyclone r eaches a strong cold-cor e eddy . Such eddies can broaden the eye
size of the storm during its passage and r educe its intensity [
35
]. For instance, an unforeseen rapid
weakening was demonstrated when the category 4 hurricane Kenneth passed over a cold-core eddy
on 19–20 September 2005 [ 36 ].
The discussed air-sea interactions over the eddies could explain the r esponse of GNSS-R
observations to SHF at the ocean-atmospher e interface thr ough the modified surface str ess. In Figure 3 ,
a local minimum of ERA5 surface str ess values takes place almost over the cor e r egion of the eddy .
The peaks of the str ess values appr oximately reside over the r otating current of the eddy . The impact
of the surface str ess on the pr ofile of CYGNSS
σ 0
is evident wher e sudden fluctuations ar e seen over
the edges and in the cor e. Lar ger SHF values with negative sign, i.e. upward dir ection of the flux, are
well synchr onized with two σ 0 minima at -150 and 150 km along with track coordinates.
In Figur e 4 , the most prominent change in the
σ 0
pr ofile can be seen over the middle eddy .
The possible signatur e of this eddy could be explained by a high value of stress appr oximately at
the eddy center wher e an incr ement of upwar d SHF is observed. The ERA5 could be subjected to
deficiencies in r esolving local sudden changes and It seems that it does not r eveal the same level of
details over the left eddy as those pr ovided by the CYGNSS measur ements. The behavior of
σ 0
over
the right eddy in this figur e can be described by the expected behavior of
σ 0
at very low wind speeds.

Remote Sens. 2020 , 12 , 542 9 of 12
Accor ding to [
37
], at very low wind speeds (< 2.5 m/s), the bistatic radar cross section is dir ectly
pr oportional to the r oughness (unlike the inverse corr elation at higher wind speeds). Therefor e, the
clear corr espondence between the magnitude of upwar d SHF and wind speed over this eddy closely
matches the similar pattern in σ 0 while the wind speed values are mainly below 2 m/s.
The surface curr ent associated with eddies is another factor that can affect surface str ess.
Considering surface str ess as a function of wind and ignoring the surface curr ent in the oceanic
numerical modeling, can result in the over estimation of the total energy input of wind to the ocean [
38
].
W ind stress ( τ ) can be calculated as [ 39 ]:
τ = ρ a C D ( W − U ) | W − U | (4)
wher e
ρ a
is the density of the air ,
C D
is the drag coeffi cient, and
W
and
U
ar e the wind and surface
curr ent, r espectively .
The behavior of
σ 0
in Figur e 5 can be partially attributed to the modified surface str ess at the
eddy curr ents. Eddy-induced curr ent can amplify or decrease the wind str ess (Figur e 7 a) or alter its
dir ection which can in turn change the level of
σ 0
sensitivity to surface str ess. Over the left eddy in
Figur e 5 , the similar dir ectional orientation of the CYGNSS track with respect to the surface str ess field
can lead to the weaker impact of str ess on the
σ 0
values (see Figur e 7 c). Interaction of eddy-induced
curr ent with surface str ess can incr ease the
σ 0
sensitivity over the edges r esulting in lower
σ 0
values.
Ther efor e, the vanishing curr ent at the core r egion would lead to the less pronounced impact of str ess
on
σ 0
. Although the stress field over the middle eddy is not as str ong, the angular differ ence of the
CYGNSS track with the stress field intensifies the impact. The str ong curr ent velocity on the edges
enhances the str ess on the left side and decr eases the stress on the right side of the eddy (see Figur e 7 a),
r esulting slightly higher
σ 0
values on the right edge compar ed to the left edge. The low magnitude of
SHF over this cold-cor e eddy together with almost zer o curr ent velocity at the center cause a sudden
peak in the
σ 0
value. The higher SHF magnitudes and str ess values between the two eddies keep the
σ 0 values at a lower level.
It is worth mentioning that concentrated biogenic films from natural life in the ocean can
potentially play a r ole in the power of r eflected GNSS-R signals. The turbulence associated with
the eddies brings the natural biogenic surfactants released fr om plankton and fishes to the surface,
wher e the concentration of the surfactant molecules can generate a surface tension. This phenomenon
could inhibit the development of Bragg waves [
40
]. Such ar eas ar e discerned as dark r egions in
the synthetic apertur e radar images since the signal is mainly forward scatter ed rather than being
backscatter ed. In a bistatic forwar d scattering configuration, the wide-enough smoothed r egions can
incr ease the power of GNSS signals after r eflection fr om the ocean. Therefor e, a dramatic increase in
σ 0
over these r egions can be expected. The characterization of biogenic surfactants’ r ole in the signal
forwar d scattering is r ecommended for futur e studies.
4. Conclusions
In this study , it is shown that spaceborne GNSS-R measurements can r espond to the existence of
eddies. Dif fer ent characteristics of eddies can impact the local wind as well as surface str ess which
can, in turn, affect GNSS-R measur ements. The normalized bistatic radar cross section (NBRCS)
exhibits a clear inverse corr elation with surface heat flux and surface str ess under certain conditions.
Nevertheless, characterization of the observed signatures r equires further study considering other
potential factors such as the ef fect of biogenic surfactants and the eddy-induced curr ents in the
surface str ess and ocean state. Many factors pr oduce NBRCS changes. The complexity of oceanic and
atmospheric mechanisms contr olling the GNSS scattering demands further sophisticated analyses in
futur e studies. Ther e are still open questions such as the conditions of occurr ences or the measurements
specific behaviors over cyclonic or anticyclonic eddies. This study initiates the development of the
novel GNSS-R technique for studying ocean mesoscale eddies, the feasibility of which has been
demonstrated for the first time.

Remote Sens. 2020 , 12 , 542 10 of 12
Author Contributions:
Conceptualization, M.H., H.N., M.A.; Data curation, M.H.; Formal analysis, M.H., M.A.,
V .Z. and C.R.; Funding acquisition, H.N.; Investigation, M.H. and M.A.; Methodology , M.H., M.A.; Software,
M.H.; Supervision, H.N. and J.W .; V alidation, M.H. and V .Z.; V isualization, M.H.; W riting–original draft, M.H.
and M.A.; W riting–review and editing, M.H., M.A., V .Z., H.N., C.R. and J.W . All authors have r ead and agreed to
the published version of the manuscript.
Funding:
This r esearch was funded by Norwegian University of Science and T echnology grant number 81771107.
Acknowledgments:
Authors would like to thank the teams in charge of CYGNSS, ECMWF , A viso and OSCAR
data products which made this study possible. All the data used in this study are publicly available and free
of charge at the associated r epositories. The CYGNSS and OSCAR datasets can be found at the NASA Physical
Oceanography Distributed Active Archive Center , PO.DAAC ( https://podaac.jpl.nasa.gov ). ERA5 dataset fr om
ECMWF can be downloaded from https://cds.climate.copernicus.eu and the A viso trajectory atlas is available on
https://www .aviso.altimetry .fr .
Conflicts of Interest: The authors declare no conflict of inter est.
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