Article

An Analysis of Vertical Crustal Movements along the European Coast from Satellite Altimetry, Tide Gauge, GNSS and Radar Interferometry

Abstract and Figures

The main aim of the article was to analyse the actual accuracy of determining the vertical movements of the Earth’s crust (VMEC) based on time series made of four measurement techniques: satellite altimetry (SA), tide gauges (TG), fixed GNSS stations and radar interferometry. A relatively new issue is the use of the persistent scatterer InSAR (PSInSAR) time series to determine VMEC. To compare the PSInSAR results with GNSS, an innovative procedure was developed: the workflow of determining the value of VMEC velocities in GNSS stations based on InSAR data. In our article, we have compiled 110 interferograms for ascending satellites and 111 interferograms for descending satellites along the European coast for each of the selected 27 GNSS stations, which is over 5000 interferograms. This allowed us to create time series of unprecedented time, very similar to the time resolution of time series from GNSS stations. As a result, we found that the obtained accuracies of the VMEC determined from the PSInSAR are similar to those obtained from the GNSS time series. We have shown that the VMEC around GNSS stations determined by other techniques are not the same.
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remote sensing
Article
An Analysis of Vertical Crustal Movements along the
European Coast from Satellite Altimetry, Tide Gauge,
GNSS and Radar Interferometry
Kamil Kowalczyk , Katarzyna Pajak * , Beata Wieczorek and Bartosz Naumowicz


Citation: Kowalczyk, K.; Pajak, K.;
Wieczorek, B.; Naumowicz, B.
An Analysis of Vertical Crustal
Movements along the European
Coast from Satellite Altimetry,
Tide Gauge, GNSS and Radar
Interferometry. Remote Sens. 2021,13,
2173. https://doi.org/10.3390/
rs13112173
Academic Editor: Sergey A. Lebedev
Received: 21 April 2021
Accepted: 31 May 2021
Published: 2 June 2021
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Copyright: © 2021 by the authors.
Licensee MDPI, Basel, Switzerland.
This article is an open access article
distributed under the terms and
conditions of the Creative Commons
Attribution (CC BY) license (https://
creativecommons.org/licenses/by/
4.0/).
Department of Geoinformation and Cartography, Institute of Geodesy and Civil Engineering,
University of Warmia and Mazury in Olsztyn, Oczapowskiego St. 2, 10-719 Olsztyn, Poland;
kamil.kowalczyk@uwm.edu.pl (K.K.); beata.zero@uwm.edu.pl (B.W.); bartosz.naumowicz@uwm.edu.pl (B.N.)
*Correspondence: katarzyna.pajak@uwm.edu.pl
Abstract:
The main aim of the article was to analyse the actual accuracy of determining the vertical
movements of the Earth’s crust (VMEC) based on time series made of four measurement techniques:
satellite altimetry (SA), tide gauges (TG), fixed GNSS stations and radar interferometry. A relatively
new issue is the use of the persistent scatterer InSAR (PSInSAR) time series to determine VMEC. To
compare the PSInSAR results with GNSS, an innovative procedure was developed: the workflow of
determining the value of VMEC velocities in GNSS stations based on InSAR data. In our article, we
have compiled 110 interferograms for ascending satellites and 111 interferograms for descending
satellites along the European coast for each of the selected 27 GNSS stations, which is over 5000
interferograms. This allowed us to create time series of unprecedented time, very similar to the time
resolution of time series from GNSS stations. As a result, we found that the obtained accuracies of the
VMEC determined from the PSInSAR are similar to those obtained from the GNSS time series. We
have shown that the VMEC around GNSS stations determined by other techniques are not the same.
Keywords: vertical crustal movements; satellite altimetry; tide gauge; GNSS; PSInSAR
1. Introduction
Vertical movements of the Earth’s crust are widely studied along the European coast,
which provides a reference for comparing the obtained results. The movements of the
Earth’s crust are significantly related to the maintenance and updating of coordinate sys-
tems, human activity, monitoring of flood hazards and changes in the mean sea level [
1
6
].
These movements are manifested by the horizontal and vertical displacement of tectonic
plates [
7
]. Vertical plate tectonics are more difficult to determine, and they have both natural
and sometimes anthropogenic causes [
8
]. Vertical movements of the earth’s crust are classi-
fied as relative or absolute (geocentric) movements, direct or indirect movements and point
or surface movements. They can be determined based on measurements involving vari-
ous techniques, including geometric levelling, global navigation satellite systems (GNSS),
Doppler orbitography and radiopositioning integrated by satellite (DORIS), satellite laser
ranging (SLR), synthetic aperture radar (SAR) and very long baseline interferometry (VLBI).
Vertical movements determined with the use of different techniques in the same area may
not be identical [
9
11
]. They may also differ for the same measuring technique [
12
]. These
differences can be attributed to environmental and anthropogenic factors, the types of
applied data [10] and the data compilation method.
Currently, vertical movements of the earth’s crust are most often determined as
absolute (geocentric) movements directly in permanent GNSS stations [
13
]. The density of
GNSS stations may vary for the different continents. Some stations are located on the coast
near tide gauge stations (TG) and colocated with them. Absolute vertical movements of
the Earth’s crust on the coast can be determined indirectly from satellite altimetry (SA) and
tide gauge (TG) data [13,14].
Remote Sens. 2021,13, 2173. https://doi.org/10.3390/rs13112173 https://www.mdpi.com/journal/remotesensing
Remote Sens. 2021,13, 2173 2 of 24
Tide gauges are widely used to detect sea level changes along European coasts.
Changes in sea level on the regional and global scale have been monitored with high
accuracy based on satellite altimetry (SA) data since 1993 [
15
]. Satellite altimetry observa-
tions provide information about absolute sea level within a geocentric reference frame. In
turn, TGs measure sea level relative to a land benchmark.
The difference between SA and TG observations is the geocentric vertical crust motion
at the TG site; therefore, both sea level measurements are combined to assess vertical
displacement at TG sites. In recent research, a combination of these measurements has
been used to estimate vertical crust movements [10,16,17].
Collaborative elaboration of results from different measurement techniques can be
done by interpolation or simultaneous data alignment. Both for the joint elaboration
of the results and their mutual verification, it is necessary to provide information on
the accuracy of the obtained vertical movements of the earth’s crust from individual
measurement techniques. This fact is often neglected in the literature, which may lead to
misinterpretation of the final results [
18
]. To obtain the accuracy at the assumed level for
each of the techniques, it is sought to determine the optimal conditions that should be met
by the time series. Therefore, for mareographic data, the series should be from several
dozen to several hundred years long with a monthly resolution. Similarly, requirements
are placed on the time series composed of altimetric data [
19
]. The areas were selected
so that the mareographic data was at least 50 years old and, in places, even up to several
hundred years. In the absence of such extensive series, the stations available with a shorter
time interval were adopted, as was the SA data in the longest possible time interval. This
allows the influence of the circulation of the moon’s nodes around the sun to be taken into
account, which many researchers have overlooked.
In this study, vertical crust movement was investigated based on the differences
between the time series of daily/monthly sea levels generated with the use of SA and TG
data in each selected TG station on the European sea coast. The change trends in mean sea
level were determined from TG observations and SA data in the European coastal zone.
Vertical crustal movements in nearby GNSS stations were also determined. GNSS time
series should contain data from at least 3 years of the measurement period [
20
] (optimally
it is 5 years) with daily resolution. GNSS data is at least 5 years old, and PPP compiled is
to be unaffected by GNSS network alignment.
An InSAR analysis was carried out in GNSS sites based on the data obtained from a
SAR-C sensor mounted on Sentinel-1A/B satellites for one frame of ascending orbits and
one frame of descending orbits. The persistent scatterer InSAR (PSI) method supported
the determination of deformation at coherent points on the ground over a long time
interval [
21
]. Displacement values were estimated by reducing error sources related to
temporal and geometrical decorrelation and atmospheric phase delay [
22
]. The following
issues were taken into account to reliably assess the identified persistent scatterer (PS)
points:
1.
The locations at which PS and GNSS data are measured do not coincide; therefore,
spatial interpolation is required [9];
2.
Sentinel-1 data are not synchronised spatially, which means that their start and end
times differ within each orbit.
Due to the different technical approach and the time-consuming nature of the cal-
culations, few studies indicate the optimal nature of the time series generated from the
PSInSAR data together with the actual accuracy assessment. Typically, these are series with
low time resolution (one interferogram per year, quarter or month) in a 1-, 2- or 3-year
time frame. Recently, the literature has shown a resolution of 290 interferograms over
5 years [18].
Our article uses an average of 110 interferograms for ascending satellites and 111
interferograms for descending satellites along the European coast for a selected 27 GNSS
stations, which gives over 5000 interferograms in a 3-year time interval, providing a time
resolution of nearly 1 week.
Remote Sens. 2021,13, 2173 3 of 24
To compare the PSInSAR results against GNSS, an innovative procedure was devel-
oped: the workflow of determining the value of vertical movement velocities in GNSS
stations based on InSAR data.
2. Materials and Methods
In this study, vertical movements of the earth’s crust along the European coast were
estimated using tide gauge (TG), satellite altimetry (SA), GNSS and satellite interferometric
synthetic aperture radar (InSAR) data (from Sentinel mission). Vertical movements were
determined in the locations shown in Figure 1.
Remote Sens. 2021, 13, x FOR PEER REVIEW 3 of 24
year time frame. Recently, the literature has shown a resolution of 290 interferograms over
5 years [18].
Our article uses an average of 110 interferograms for ascending satellites and 111
interferograms for descending satellites along the European coast for a selected 27 GNSS
stations, which gives over 5000 interferograms in a 3-year time interval, providing a time
resolution of nearly 1 week.
To compare the PSInSAR results against GNSS, an innovative procedure was
developed: the workflow of determining the value of vertical movement velocities in
GNSS stations based on InSAR data.
2. Materials and Methods
In this study, vertical movements of the earth’s crust along the European coast were
estimated using tide gauge (TG), satellite altimetry (SA), GNSS and satellite
interferometric synthetic aperture radar (InSAR) data (from Sentinel mission). Vertical
movements were determined in the locations shown in Figure 1.
Figure 1. The location of GNSS stations which were used to determine vertical crustal movements based on TG, SA and
InSAR data.
The obtained or created time series were decomposed. A linear trend and the trend
standard error were determined. The linear regression method and Fourier analysis were
used. Data were obtained from:
Tide gauge (TG): Permanent Service for Mean Sea Level (PSMSL) (1856–2018);
Institute of Meteorology and Water Management of the Polish National Research
Institute (1951–2017 and 1993–2017);
Satellite altimetry (SA): Copernicus Marine and Environment Monitoring Service
(CMEMS) (1993–2017);
Figure 1.
The location of GNSS stations which were used to determine vertical crustal movements based on TG, SA and
InSAR data.
The obtained or created time series were decomposed. A linear trend and the trend
standard error were determined. The linear regression method and Fourier analysis were
used. Data were obtained from:
Tide gauge (TG): Permanent Service for Mean Sea Level (PSMSL) (1856–2018);
Institute of Meteorology and Water Management of the Polish National Research
Institute (1951–2017 and 1993–2017);
Satellite altimetry (SA): Copernicus Marine and Environment Monitoring Service
(CMEMS) (1993–2017);
SAR data (SAR): SENTINEL-1A/B data from the Copernicus Open Access Hub as
part of the Copernicus mission (an initiative of the European Commission (EC) and
the European Space Agency (ESA)) (2015–2017);
GNSS: Nevada Geodetic Laboratory (NGL) (1999–2017); SONEL (1996–2018).
Remote Sens. 2021,13, 2173 4 of 24
The absolute vertical crustal movement is calculated with the use of the following
formula:
vh=vSA vT G (1)
where v
SA
—absolute change in sea level determined from altimetric data (referred to
an ellipsoid); v
h
—absolute vertical crustal movement (referred to an ellipsoid) and v
TG
relative change in mean sea level determined from TG observations.
The standard error in the determination of the absolute vertical movement of the
Earth’s crust is given by the below formula:
σvh=qσv2
SA +σv2
TG (2)
where
σvh
—the standard error of determination absolute vertical crustal movement;
σvSA
—the
standard error of determination change in sea level determined from altimetric data and
σvTG
—the standard error of determination relative change in mean sea level determined
from TG observations.
The calculated vertical movements of the Earth’s crust are verified against the values
determined in neighbouring points with the use of other techniques, and the values are
varied [
23
,
24
]. The basic prerequisite is the closest proximity of available TG [
25
,
26
]. The
relative movements v
R
between a GNSS station and a TG should be taken into account [
27
].
GNSS stations located on the coast provide the best neighbourhood. If GNSS stations
are not available, vertical movements are determined at the nearest alternative points
using SAR data. Deformations and deformation velocities are calculated based on SAR
data [
9
,
28
,
29
], and they should closely correspond to the velocities determined based on
GNSS station data.
Data from GNSS stations and TG form time series. SA and SAR data require additional
processing to form a time series. The time series for each data set differ in time resolution
(daily, several days, weekly, monthly), white and colour noise, a number of outliers and
discontinuities (gaps and jumps). The quality of velocity calculations depends on the
above factors, as well as the applied methods for eliminating or reducing the impact of
undesirable factors.
Several approaches are used to detect and determine the jump value (vertical shifts
in the data series) [
30
35
]. Jumping is caused by technical issues, human errors and en-
vironmental factors [
33
,
36
]. The determination of the vertical interval, which is regarded
as a jump, poses the main technical problem. The vertical interval is difficult to deter-
mine because the ranks are affected by environmental conditions, as well as outliers and
data gaps.
Several solutions for eliminating outliers have been proposed, and most of them are
based on the assumptions presented in the literature [
37
,
38
]. Outliers are also eliminated
by filling the gaps in the time series. Interpolation methods are used for this purpose [
39
].
Statistical and spectral methods are most commonly used to detect white and coloured
noise [
40
,
41
]. In most cases, only the main annual and semiannual periods of seasonality
are used, but considerably longer or shorter periods can also be applied due to the influence
of other factors [27,4245].
2.1. Analysis of Vertical Crustal Movement Velocities Based on SA and TG Data
Vertical crust movements in TG sites were estimated along the European coast based
on different time series for SA minus TG (Equation (1)). The time series for SA and TG data
describing changes in sea level were characterised by nearly identical behaviour. All the
time series had seasonal components (annual, semiannual and 18.61-year cycles related to
the relative movements of the Moon) and trend, which can be expressed as follows:
fF(t)=a+bt +Aacos (ωatϕa)+Asacos (ωsa tϕsa )+A18.61 cos (ω18.61 tϕ18.61)(3)
where f
F
(t) is a Fourier function; ais the bias; bis the trend; tis time; A
a
and A
sa
are the
annual and semiannual amplitudes, respectively;
ϕa
and
ϕsa
are the annual and semian-
Remote Sens. 2021,13, 2173 5 of 24
nual phase, respectively;
ωa
and
ωsa
are the annual and semiannual angular frequency,
respectively [
46
]; A
18.61
is the 18.61-year amplitude;
ϕ18.61
is the 18.61-year phase and
ω18.61
is the 18.61-year angular frequency.
The 18.61-year cycle is a lunar nodal cycle caused by the relative movements of the
Moon. This important precession of the Moon, namely the 18.61-year lunar nodal cycle,
causes tidal modulations over a range of interannual time scales. These modulations affect
the interpretation of TG data spanning several years, particularly when dealing with water
level extremes [
47
]. The least squares method was used to fit the time series of sea level
variations for every station, and annual and semiannual amplitudes and the long-term
trend in seasonal sea level variations were estimated.
TG measurements constitute long-time series of mean sea level data; they are obtained
from the Permanent Service for Mean Sea Level (PSMSL) [
48
] and provide primary evidence
for the rise in the globally averaged sea level. For this study, 27 TG stations on the European
coast (Figure 1) were selected from the PSMSL [
49
] and the Institute of Meteorology and
Water Management of the Polish National Research Institute. The TG data from the PSMSL
are the time series of monthly averages from the Revised Local Reference (RLR) data set,
and the 3 selected are presented in Figure 2. Data gaps in the time series were removed
with the interpolation method. This series should not contain outliers, effects of seasonality
or data discontinuities.
Remote Sens. 2021, 13, x FOR PEER REVIEW 5 of 24
the time series had seasonal components (annual, semiannual and 18.61-year cycles
related to the relative movements of the Moon) and trend, which can be expressed as
follows:
𝑓
(𝑡)=𝑎+𝑏𝑡+
𝐴
𝑐𝑜𝑠 (𝜔𝑡−𝜑
) +
𝐴
𝑐𝑜𝑠 (𝜔𝑡−𝜑
)+
𝐴
.𝑐𝑜𝑠 (𝜔.𝑡−𝜑.) (3)
where fF(t) is a Fourier function; a is the bias; b is the trend; t is time; Aa and Asa are the
annual and semiannual amplitudes, respectively; φa and φsa are the annual and
semiannual phase, respectively; ωa and ωsa are the annual and semiannual angular
frequency, respectively [46]; A18.61 is the 18.61-year amplitude; φ18.61 is the 18.61-year phase
and ω18.61 is the 18.61-year angular frequency.
The 18.61-year cycle is a lunar nodal cycle caused by the relative movements of the
Moon. This important precession of the Moon, namely the 18.61-year lunar nodal cycle,
causes tidal modulations over a range of interannual time scales. These modulations affect
the interpretation of TG data spanning several years, particularly when dealing with
water level extremes [47]. The least squares method was used to fit the time series of sea
level variations for every station, and annual and semiannual amplitudes and the long-
term trend in seasonal sea level variations were estimated.
TG measurements constitute long-time series of mean sea level data; they are
obtained from the Permanent Service for Mean Sea Level (PSMSL) [48] and provide
primary evidence for the rise in the globally averaged sea level. For this study, 27 TG
stations on the European coast (Figure 1) were selected from the PSMSL [49] and the
Institute of Meteorology and Water Management of the Polish National Research
Institute. The TG data from the PSMSL are the time series of monthly averages from the
Revised Local Reference (RLR) data set, and the 3 selected are presented in Figure 2. Data
gaps in the time series were removed with the interpolation method. This series should
not contain outliers, effects of seasonality or data discontinuities.
Figure 2. (ac) Time series of mean sea level anomalies based on TG data. (df) Time series of mean sea levels based on
SA data. The time series are displayed with arbitrary offsets for presentation purposes. The units are in centimetres.
Gridded daily sea level anomalies with a resolution of 0.25 × 0.25 degrees and the
time series for January 1993 to December 2017 from the Copernicus Marine and
Figure 2.
(
a
c
) Time series of mean sea level anomalies based on TG data. (
d
f
) Time series of mean sea levels based on SA
data. The time series are displayed with arbitrary offsets for presentation purposes. The units are in centimetres.
Gridded daily sea level anomalies with a resolution of 0.25
×
0.25 degrees and the
time series for January 1993 to December 2017 from the Copernicus Marine and Environ-
ment Monitoring Service (CMEMS) were used. The time series of altimetric data (one
series for each altimetric observation point) were obtained. This set combines data from
several altimetry missions. Altimetric measurements were corrected for atmospheric effects
(ionospheric delay and dry/wet tropospheric effects) and geophysical processes (solid,
ocean, pole tides, loading effect of ocean tides, sea state bias and the inverted barometer
response of the ocean). Detailed information on the introduced corrections can be found in
AVISO [50] and CMEMS [51].
Remote Sens. 2021,13, 2173 6 of 24
The differences in SA and TG data sets were investigated by correlation analysis. An
SA grid point that was highly correlated with TG data was selected. It is simultaneously
the closest SA grid to the TG data. The daily SA data were averaged to correspond with
monthly TG data. The mean value of the correlation coefficient was 0.93.
The two main goals of the time series analysis are to describe the character of the
analysed phenomenon based on a series of observations and to forecast future values.
These goals can be achieved if time series elements are identified and described. The
elements of a time series include a systematic component which can be described as a
trend (linear or not) and a seasonal component where the duration of seasonal fluctuations
can vary. Fluctuations can be regarded as a seasonality when their duration does not
exceed 1 year, but when the corresponding period is longer, an economic cycle and a
random component (noise) appear. These factors have to be identified in a formalised
forecasting method. Periodic phenomena are identified in a harmonic analysis where a
priori assumptions are not made. The harmonic analysis aims to decompose a time series
with the use of cyclic factors on sine and cosine functions related to a given wavelength.
Harmonic analyses are performed to determine the average value of the studied
phenomena. A trend was identified in the analysed data series; therefore, oscillations were
determined with the use of the following model [46]:
fH(t)=a+bt +
n/2
i=1aisin 2π
nit+βisin 2π
nit (4)
where f
H
(t) is a harmonic function; ais the bias; bis the trend; tis time and nis the number
of observations.
The amplitudes and phase shift were calculated for different harmonics. The annual,
semiannual and 18.61-year harmonics were calculated. The annual, semiannual and 18.61-
year harmonic functions for Sassnitz stations based on TG and SA time series are presented
in Figure 3.
Remote Sens. 2021, 13, x FOR PEER REVIEW 7 of 24
Figure 3. (a) Annual, semiannual and 18.61-year harmonics functions based on TG data for 19462017. (b) Annual,
semiannual and 18.61-year harmonics functions based on SA data for 19932017. (c) Annual, semiannual and 18.61-year
harmonics functions based on TG data for 19932017 in the Sassnitz station. The units are in centimetres.
Figure 4. (a) Annual, (b) semiannual and (c) 18.61-year amplitudes of the seasonal cycle based on SA and TG time series.
The correlation coefficients for amplitude were calculated based on SA and TG data (blue circles-dispersion plot; area
marked by red dashed lines-95% confidence interval of the regression line). The amplitude units are centimetres.
The correlation coefficient for annual variations from two independent observation
techniques was determined at 0.92. The mean annual amplitude was ±5.59 cm with an
estimation error of ±1.32 cm for TG data and ±6.17 cm for SA data with and estimation
error of ±1.44 cm. The mean semiannual amplitude was ±2.57 cm with an estimation error
of ±0.63 cm for TG data and ±1.79 cm for SA data with estimation error of ±0.42 cm. The
correlation coefficient for semiannual variations was 0.72, which is a satisfactory result,
but it was determined at only 0.34 for the 18.61-year cycle.
Figure 3.
(
a
) Annual, semiannual and 18.61-year harmonics functions based on TG data for 1946–2017. (
b
) Annual,
semiannual and 18.61-year harmonics functions based on SA data for 1993–2017. (
c
) Annual, semiannual and 18.61-year
harmonics functions based on TG data for 1993–2017 in the Sassnitz station. The units are in centimetres.
Remote Sens. 2021,13, 2173 7 of 24
All-time series had a seasonal amplitude (annual, semiannual and 18.61-year cycle),
and the correlations between the estimated amplitudes were calculated. The local sea
level can be monitored with the use of altimetry and TG data, which can also be used to
analyse the correlations between the variations in coastal sea level. The presented analysis
focused on annual, semiannual and 18.61-year sea levels for 1993–2017, and altimetry and
TG observations were compared on interannual timescales for validation purposes. SA and
TG observations were characterised by a good fit in terms of the annual cycle, semiannual
cycle and the 18.61-year cycle (Figure 4).
Remote Sens. 2021, 13, x FOR PEER REVIEW 7 of 24
Figure 3. (a) Annual, semiannual and 18.61-year harmonics functions based on TG data for 19462017. (b) Annual,
semiannual and 18.61-year harmonics functions based on SA data for 19932017. (c) Annual, semiannual and 18.61-year
harmonics functions based on TG data for 19932017 in the Sassnitz station. The units are in centimetres.
Figure 4. (a) Annual, (b) semiannual and (c) 18.61-year amplitudes of the seasonal cycle based on SA and TG time series.
The correlation coefficients for amplitude were calculated based on SA and TG data (blue circles-dispersion plot; area
marked by red dashed lines-95% confidence interval of the regression line). The amplitude units are centimetres.
The correlation coefficient for annual variations from two independent observation
techniques was determined at 0.92. The mean annual amplitude was ±5.59 cm with an
estimation error of ±1.32 cm for TG data and ±6.17 cm for SA data with and estimation
error of ±1.44 cm. The mean semiannual amplitude was ±2.57 cm with an estimation error
of ±0.63 cm for TG data and ±1.79 cm for SA data with estimation error of ±0.42 cm. The
correlation coefficient for semiannual variations was 0.72, which is a satisfactory result,
but it was determined at only 0.34 for the 18.61-year cycle.
Figure 4.
(
a
) Annual, (
b
) semiannual and (
c
) 18.61-year amplitudes of the seasonal cycle based on SA and TG time series.
The correlation coefficients for amplitude were calculated based on SA and TG data (blue circles-dispersion plot; area
marked by red dashed lines-95% confidence interval of the regression line). The amplitude units are centimetres.
The correlation coefficient for annual variations from two independent observation
techniques was determined at 0.92. The mean annual amplitude was
±
5.59 cm with an
estimation error of
±
1.32 cm for TG data and
±
6.17 cm for SA data with and estimation
error of
±
1.44 cm. The mean semiannual amplitude was
±
2.57 cm with an estimation error
of
±
0.63 cm for TG data and
±
1.79 cm for SA data with estimation error of
±
0.42 cm. The
correlation coefficient for semiannual variations was 0.72, which is a satisfactory result, but
it was determined at only 0.34 for the 18.61-year cycle.
2.2. Analysis of Vertical Crustal Movement Velocities Based on GNSS Data
Vertical crustal movements can be classified as relative v
r
or absolute v
h
. Relative ver-
tical crustal movements refer to any point (or surface) that is constant over time. Absolute
vertical crustal movements are referred to an ellipsoid [
52
], and they comprise relative
vertical crustal movements, average changes in sea level, eustatic movements and geoid
changes over time. Absolute crustal movements are geocentric crustal movements [
2
]
that are determined based on direct GNSS measurements as well as combined TG and
SA measurements [
13
]. The location of a GNSS station relative to the TG station and the
location of the point where changes in sea level were measured based on altimetric data
have to be determined to compare the results generated by different methods.
The GNSS is commonly used for geodetic measurements because it monitors land
movements with high precision [
53
,
54
]. This study analysed the measurements from a total
of 27 GNSS stations that are colocated with or positioned in the proximity of a TG station
on the European coast. The time series of vertical coordinates of 27 GNSS stations on the
European coast (Figure 1) were obtained from the Nevada Geodetic Laboratory (NGL) [
55
]
and SONEL (www.sonel.org, accessed on 12 December 2019). Time series from 3 selected
GNSS stations from a total of 27 stations are shown in Figure 5.
The time series covered a period of 4 to 17 years with daily time resolution. The
distance from the nearest TG ranged from 0.002 km to 16.069 km (Figure 6).
Remote Sens. 2021,13, 2173 8 of 24
Figure 5.
(
a
c
) The time series of 3 selected GNSS stations from a total of 27 stations. (
d
f
) The units are in centimetres.
The time series is in the line of sight (LOS) displacement (in mm) of two persistent scatterer points with an ascending and
descending track within GNSS stations. The time series are displayed with arbitrary offsets for presentation purposes.
Remote Sens. 2021, 13, x FOR PEER REVIEW 9 of 24
Figure 6. Distance between GNSS stations and the nearest TG (the longest distance between a TG station and a GNSS
station was 16.069 km, and the shortest distance between a TG station and a GNSS station was 0.002 km).
The data from the GNSS station form a daily time series covering several to more
than 10 years. All the time series feature data discontinuities, jumps and noise. According
to [13], the uncertainty of velocity calculations based on GNSS data ranges from 0.1
mm/year to 1.3 mm/year with a median of 0.21 mm/year. The time series of the
coordinates from the GNSS station were decomposed. Missing values were filled by
interpolation. Vertical shifts were defined with an algorithm developed for the needs of
this study [32]. The VSED algorithm filters the outlier series with the Grubbs method. It
defines and eliminates jumps and fits a trend line. The operations performed by the
algorithm are presented in Figure 7.
Figure 7. Steps of the VSED algorithm (KONE station): (a) Left and right moving averages are calculated according to
Equation (2) from [32]; (b) Left and right standard deviations are the square root of Equation (3) from [32]; (c) The output
function is Equation (4) from [32]; (d) The result of detection. The units on the y-axis are in metres. The units on the x-axis
are the number of observations.
Figure 6.
Distance between GNSS stations and the nearest TG (the longest distance between a TG station and a GNSS
station was 16.069 km, and the shortest distance between a TG station and a GNSS station was 0.002 km).
The data from the GNSS station form a daily time series covering several to more than
10 years. All the time series feature data discontinuities, jumps and noise. According to [
13
],
the uncertainty of velocity calculations based on GNSS data ranges from 0.1 mm/year to
Remote Sens. 2021,13, 2173 9 of 24
1.3 mm/year with a median of 0.21 mm/year. The time series of the coordinates from the
GNSS station were decomposed. Missing values were filled by interpolation. Vertical shifts
were defined with an algorithm developed for the needs of this study [
32
]. The VSED
algorithm filters the outlier series with the Grubbs method. It defines and eliminates jumps
and fits a trend line. The operations performed by the algorithm are presented in Figure 7.
Remote Sens. 2021, 13, x FOR PEER REVIEW 9 of 24
Figure 6. Distance between GNSS stations and the nearest TG (the longest distance between a TG station and a GNSS
station was 16.069 km, and the shortest distance between a TG station and a GNSS station was 0.002 km).
The data from the GNSS station form a daily time series covering several to more
than 10 years. All the time series feature data discontinuities, jumps and noise. According
to [13], the uncertainty of velocity calculations based on GNSS data ranges from 0.1
mm/year to 1.3 mm/year with a median of 0.21 mm/year. The time series of the
coordinates from the GNSS station were decomposed. Missing values were filled by
interpolation. Vertical shifts were defined with an algorithm developed for the needs of
this study [32]. The VSED algorithm filters the outlier series with the Grubbs method. It
defines and eliminates jumps and fits a trend line. The operations performed by the
algorithm are presented in Figure 7.
Figure 7. Steps of the VSED algorithm (KONE station): (a) Left and right moving averages are calculated according to
Equation (2) from [32]; (b) Left and right standard deviations are the square root of Equation (3) from [32]; (c) The output
function is Equation (4) from [32]; (d) The result of detection. The units on the y-axis are in metres. The units on the x-axis
are the number of observations.
Figure 7.
Steps of the VSED algorithm (KONE station): (
a
) Left and right moving averages are calculated according to
Equation (2) from [
32
]; (
b
) Left and right standard deviations are the square root of Equation (3) from [
32
]; (
c
) The output
function is Equation (4) from [
32
]; (
d
) The result of detection. The units on the y-axis are in metres. The units on the x-axis
are the number of observations.
The mathematical model used in this algorithm is a straight line with steps in differ-
ent epochs:
h(t)=vt +h0+c1s1+c2s2+. . . +cmsm(5)
where t-epoch, h(t)—height difference in epoch t;v—velocity between stations; h
0
—height
difference at epoch 0; c
1
,c
1
,
. . .
,c
m
—elements of the C matrix and s
1
,s
2
,
. . .
,s
m
magnitude of “jumps”.
The interval defining the “jump” was based on the standard deviation, which ranged
from
±
0.2 mm (values centred around the mean) to
±
0.7 mm (values scattered around the
mean). The number of jumps for the analysed GNSS stations, depending on the received
height determination error, is shown in Figure 8.
The number of jumps does not affect the accuracy of height determination for individ-
ual epochs in the time series of coordinates from the GNSS station.
Remote Sens. 2021,13, 2173 10 of 24
Remote Sens. 2021, 13, x FOR PEER REVIEW 10 of 24
The mathematical model used in this algorithm is a straight line with steps in
different epochs:
(𝑡)=𝑣𝑡++𝑐𝑠+𝑐𝑠+⋯+𝑐𝑠 (5)
where t-epoch, h(t)—height difference in epoch t; v—velocity between stations; h0height
difference at epoch 0; c1, c2,, cm—elements of the C matrix and s1, s2,, sm—magnitude
of “jumps”.
The interval defining the “jump” was based on the standard deviation, which ranged
from ±0.2 mm (values centred around the mean) to ±0.7 mm (values scattered around the
mean). The number of jumps for the analysed GNSS stations, depending on the received
height determination error, is shown in Figure 8.
Figure 8. The influence of height determination error 𝜎 on the number of jumps in the analysed time series of
coordinates from the GNSS station.
The number of jumps does not affect the accuracy of height determination for
individual epochs in the time series of coordinates from the GNSS station.
2.3. Analysis of the Vertical Movement Model Based on InSAR Data
The InSAR technique relies on interferometric comparison of SAR phase images to
determine relative surface motions from the millimetre to centimetre [56–58]. In contrast
to the pointwise information provided by GNSS, InSAR can provide a spatially dense
image of surface displacements. The InSAR technique based on time series analysis
(multitemporal InSAR, MTI) was used to achieve such a high level of accuracy and to
reduce the basic error related to temporal and geometrical decorrelation and atmospheric
phase delay. The course of deformation in the selected area was reconstructed with the
use of point methods based on the selection of pixels that maintain coherence in time
[21,59,60].
The interferometric phase in Equation (6) is the sum of contributions from several
factors, including the components to be extracted, and it specifies ground deformation in
the LOS (line of sight) direction in the time interval of the SAR image pair. The remaining
Figure 8.
The influence of height determination error
σH
on the number of jumps in the analysed time series of coordinates
from the GNSS station.
2.3. Analysis of the Vertical Movement Model Based on InSAR Data
The InSAR technique relies on interferometric comparison of SAR phase images to
determine relative surface motions from the millimetre to centimetre [
56
58
]. In contrast to
the pointwise information provided by GNSS, InSAR can provide a spatially dense image of
surface displacements. The InSAR technique based on time series analysis (multitemporal
InSAR, MTI) was used to achieve such a high level of accuracy and to reduce the basic
error related to temporal and geometrical decorrelation and atmospheric phase delay. The
course of deformation in the selected area was reconstructed with the use of point methods
based on the selection of pixels that maintain coherence in time [21,59,60].
The interferometric phase in Equation (6) is the sum of contributions from several
factors, including the components to be extracted, and it specifies ground deformation in
the LOS (line of sight) direction in the time interval of the SAR image pair. The remaining
factors relating to topography, atmosphere and orbit should be taken into account and
eliminated from the interferometric phase.
ϕint =ϕde f o +ϕatm +ϕorbit +ϕto po +ϕnoise (6)
where
ϕdefo
—LOS deformation,
ϕatm
—atmospheric delay,
ϕorbit
—orbit error,
ϕdopo
—DEM
error and ϕnoise—noise
The analysed GNSS stations are located in built-up areas along the European coast
(Figure 1). The method StaMPS (Stanford Method for Persistent Scatterers), based on
the PSI algorithm, was selected, and StaMPS software was used in this analysis. The
PSInSAR algorithm detects stable scatterers and extracts phase information for these
points. The StaMPS framework is a collection of spatial and temporal filtering routines
that can be used to estimate the phase components in Equation (6) by assuming a spectral
structure. More details are contained in [
60
]. The processed series of radar images (for
2015–2017) provided mean values of displacement velocities for persistent scatterers in
the LOS direction (
Figure 9
). On average, a calculated 110 interferograms for ascending
Remote Sens. 2021,13, 2173 11 of 24
and 111 interferograms for descending orbital passes were determined at each point of the
GNSS station.
Remote Sens. 2021, 13, x FOR PEER REVIEW 12 of 24
Figure 9. (a) Sentinel-1 (LOS) mean deformation velocity maps for 2015–2017 in the Sassnitz station for ascending, (b)
descending orbits. (c) In the Roscoff station for ascending, (d) and descending orbits. (e) In the Thessaloniki station for
ascending, (f) and descending orbits. Coloured dots represent the location of a PS, and the displacement rate measured at
each point is marked with an appropriate colour. Selected reference points (SASS, SAS2, ROTG, AUT1) are shown as green
squares. World Imagery data constitute the background.
Figure 9.
(
a
) Sentinel-1 (LOS) mean deformation velocity maps for 2015–2017 in the Sassnitz station for ascending, (
b
)
descending orbits. (
c
) In the Roscoff station for ascending, (
d
) and descending orbits. (
e
) In the Thessaloniki station for
ascending, (f) and descending orbits. Coloured dots represent the location of a PS, and the displacement rate measured at
each point is marked with an appropriate colour. Selected reference points (SASS, SAS2, ROTG, AUT1) are shown as green
squares. World Imagery data constitute the background.
Different objects make good permanent scatterers (PS), including buildings, lanterns
and fragments of various structures (bridges, fences, etc.). In areas without infrastructure,
Remote Sens. 2021,13, 2173 12 of 24
rock outcrops, hard unvegetated earth surfaces and boulders can be used as PS points.
However, the locations of PS points and GNSS stations do not coincide; the distances
between selected PS points and the GNSS station are shown in Figure 10. The longest
distance (of more than 300 m) was noted with the WLAD station, which is located on
port breakwaters. The distance between PS points and ROTG, SCOA, ACOR and TARI
stations, which are also located in the direct proximity of hydraulic structures, did not
exceed 64 m. The distance between the PS point and the SABL was determined to be 227.34
m because it is the only GNSS station surrounded by a forest with no permanent structures
in the vicinity.
Remote Sens. 2021, 13, x FOR PEER REVIEW 13 of 24
Figure 10. Distances between selected PS points from ascending and descending tracks and the GNSS station. PS targets
were ordered from the longest distance (334.28 m) from the WLAD station, and the shortest distance (0.98 m) from the
IJMU station.
The scheme in Figure 11 shows the workflow of determining the vertical movement
model based on InSAR data. In the scheme, in Step 4, groups of scatterers that exhibit
similar behaviour are analysed. Statistical procedures are used to evaluate their spatial
relationships and the consistency of estimated parameters in a given environment. During
processing, many points are rejected based on different quality criteria [70].
The spatial distribution of ascending and descending PS point targets, in addition to
the effect of temporal decorrelation, is highly related to the orientation of slopes and
correlates well with the terrain aspect [61,64,71]. The proposed approaches included
terrain aspect and interpolation performed in each range of time, both ascending and
descending targets to be the same range time. The nearest neighbour vector (NNV)
solution was used (according to the procedure http://gmt.soest.hawaii.edu, accessed on
10 January 2020). The PS points are not regularly spaced in space; the distances from their
nearest neighbour with opposite geometry are different. Therefore, the search radius was
determined based on the slope terrain analysis and the point density.
The locations of PS points and GNSS stations do not coincide; therefore, approaches
were adopted according to the diagram shown in Figure 11. In the first approach (Step 5),
the PS point was selected on the following assumptions:
1. The PS point is located on the same type of infrastructure or facility as the GNSS
station. Sufficient PS points should be available to detect outliers. Next, the height of
the PS points should be estimated to check whether the PS comes from the same
technical infrastructure object and not from the surface level;
2. Points should be selected from the area with the same slope. The point and slope
heights were derived from data based on Shuttle Radar Topography Mission Global
1 arc second (SRTMGL1);
3. PS point targets from ascending or descending tracks are located in the proximity of
a GNSS station, ~10 m.
Figure 10.
Distances between selected PS points from ascending and descending tracks and the GNSS station. PS targets
were ordered from the longest distance (334.28 m) from the WLAD station, and the shortest distance (0.98 m) from the
IJMU station.
The three-dimensional motion was only partly captured in the calculated rate of
change in the LOS direction [
61
]. Therefore, the components of vertical movement had
to be determined from SAR observations in the LOS. Radar satellites acquire image data
of the same area on ascending (south to north) and descending (north to south) orbital
passes. An LOS velocity V
los
is composed of the 3D velocity components V
EW
(East–West),
V
NS
(North–South) and V
up
(Up-Down)
.
The LOS displacements can be mathematically
transformed to V
EW
and V
up
components if available at the same location for all analysed
tracks and within the same time period. The V
NS
displacements are small due to the polar
orbit of all SAR satellites and the side-looking image geometry [
62
]. Various approaches to
determining 3D surface motion from InSAR data are discussed in publications [6367].
The PSI deformation value should be predicted at the location of the GNSS stations.
Every location is different, and complex deformation phenomena may occur; however,
an assessment of each station is possible [
68
]. In this article, vertical motion in GNSS
stations was calculated based on various view geometries and viewing angles. During data
postprocessing, ascending and descending PSI measurements were paired to calculate the
vertical component for each PS point using Equation (7) [69]:
hVasc
los Vdesc
los i=AVup Vhald ;A=cosθasc sinθasc
cosαcosθdesc sinθdesc (7)
where V
los
—deformation along the LOS, V
up
—vertical deformation,
Vhald
—projection of
horizontal deformation in descending azimuth look direction,
θ
—incident angle and
α
satellite heading difference between ascending and descending mode [22].
Remote Sens. 2021,13, 2173 13 of 24
The scheme in Figure 11 shows the workflow of determining the vertical movement
model based on InSAR data. In the scheme, in Step 4, groups of scatterers that exhibit
similar behaviour are analysed. Statistical procedures are used to evaluate their spatial
relationships and the consistency of estimated parameters in a given environment. During
processing, many points are rejected based on different quality criteria [70].
Remote Sens. 2021, 13, x FOR PEER REVIEW 14 of 24
Figure 11. Workflow scheme of determining the value of vertical movement velocities in GNSS stations based on InSAR
data.
The PS points that met the criteria listed above were 25% of the points (6 stations)
(Figure 10). In the second approach (Step 6), the following was adopted:
There are no PS points directly (condition 3 from the first attempt);
Points were selected in a surrounding area with a radius of 500 m;
Eliminate outliers;
Displacements behave linearly in time within a radius of 500 m of the GNSS station.
Then, the NNV was calculated, and the spatial interpolation was performed, taking
into account the geostatistical properties of displacements in each measurement epoch.
The PSI results were spatially interpolated by the Kriging method. PS point targets from
ascending and descending tracks were interpolated separately. Based on a review of the
literature [9,72], the ordinary Kriging method with a spherical, exponential and Gaussian
semivariogram model were applied to the PSI vector data [61].
3. Results
Vertical crust movements in TG stations were estimated from different time series of
TG data (Figure 12a) and SA data (Figure 12b) using robust linear regression [73]. Each
Figure 11.
Workflow scheme of determining the value of vertical movement velocities in GNSS stations based on InSAR data.
The spatial distribution of ascending and descending PS point targets, in addition
to the effect of temporal decorrelation, is highly related to the orientation of slopes and
correlates well with the terrain aspect [
61
,
64
,
71
]. The proposed approaches included terrain
aspect and interpolation performed in each range of time, both ascending and descending
targets to be the same range time. The nearest neighbour vector (NNV) solution was used
(according to the procedure http://gmt.soest.hawaii.edu, accessed on 10 January 2020).
The PS points are not regularly spaced in space; the distances from their nearest neighbour
with opposite geometry are different. Therefore, the search radius was determined based
on the slope terrain analysis and the point density.
Remote Sens. 2021,13, 2173 14 of 24
The locations of PS points and GNSS stations do not coincide; therefore, approaches
were adopted according to the diagram shown in Figure 11. In the first approach (Step 5),
the PS point was selected on the following assumptions:
1.
The PS point is located on the same type of infrastructure or facility as the GNSS
station. Sufficient PS points should be available to detect outliers. Next, the height
of the PS points should be estimated to check whether the PS comes from the same
technical infrastructure object and not from the surface level;
2.
Points should be selected from the area with the same slope. The point and slope
heights were derived from data based on Shuttle Radar Topography Mission Global 1
arc second (SRTMGL1);
3.
PS point targets from ascending or descending tracks are located in the proximity of a
GNSS station, ~10 m.
The PS points that met the criteria listed above were 25% of the points (6 stations)
(Figure 10). In the second approach (Step 6), the following was adopted:
There are no PS points directly (condition 3 from the first attempt);
Points were selected in a surrounding area with a radius of 500 m;
Eliminate outliers;
Displacements behave linearly in time within a radius of 500 m of the GNSS station.
Then, the NNV was calculated, and the spatial interpolation was performed, taking
into account the geostatistical properties of displacements in each measurement epoch.
The PSI results were spatially interpolated by the Kriging method. PS point targets from
ascending and descending tracks were interpolated separately. Based on a review of the
literature [
9
,
72
], the ordinary Kriging method with a spherical, exponential and Gaussian
semivariogram model were applied to the PSI vector data [61].
3. Results
Vertical crust movements in TG stations were estimated from different time series of
TG data (Figure 12a) and SA data (Figure 12b) using robust linear regression [
73
]. Each
difference in the time series of SA and coastal TG data was analysed by considering a linear
trend and an annual, semiannual and 18.61-year cycle.
Remote Sens. 2021, 13, x FOR PEER REVIEW 15 of 24
difference in the time series of SA and coastal TG data was analysed by considering a
linear trend and an annual, semiannual and 18.61-year cycle.
Figure 12. (a) Map of the linear trend in coastal stations estimated from different time series of TG data (TG data from the
beginning of data to 2018). (b) Map of the linear trend in coastal stations estimated from different time series of SA data
(SA data from 1993 to 2017); the units on both pictures are in mm/year. The linear trend standard errors are visualized by
black circles. Positive values of the linear trend are visualized by a red arrow. Negative values of the linear trend are
visualized by a blue arrow.
The results of the analysis were used to calculate linear trends in vertical crust
movement on the TG sites along the European coast based on SA data minus TG data and
at GNSS time series (GNSS stations closest to TG stations were considered). The velocity
in coastal stations, estimated from the different time series of SA data minus TG data from
the beginning of data to 2018, is shown in Figure 13a. The velocity in coastal stations,
estimated from the different time series of SA data minus TG data from 1993–2018, is
shown in Figure 13b.
Figure 13. (a) Map of vertical crust movements in coastal stations estimated from different time series of SA data minus
TG data (from the beginning of data to 2018). (b) Map of vertical crust movements in coastal stations estimated from
different time series of SA data minus TG data (1993–2017); the units on both pictures are in mm/year. The linear trend
standard errors are visualized by black circles. Positive values of the linear trend are visualized by a red arrow. Negative
values of the linear trend are visualized by a blue arrow.
Figure 12.
(
a
) Map of the linear trend in coastal stations estimated from different time series of TG data (TG data from the
beginning of data to 2018). (
b
) Map of the linear trend in coastal stations estimated from different time series of SA data (SA
data from 1993 to 2017); the units on both pictures are in mm/year. The linear trend standard errors are visualized by black
circles. Positive values of the linear trend are visualized by a red arrow. Negative values of the linear trend are visualized by
a blue arrow.
Remote Sens. 2021,13, 2173 15 of 24
The results of the analysis were used to calculate linear trends in vertical crust move-
ment on the TG sites along the European coast based on SA data minus TG data and at
GNSS time series (GNSS stations closest to TG stations were considered). The velocity in
coastal stations, estimated from the different time series of SA data minus TG data from
the beginning of data to 2018, is shown in Figure 13a. The velocity in coastal stations,
estimated from the different time series of SA data minus TG data from 1993–2018, is
shown in Figure 13b.
Remote Sens. 2021, 13, x FOR PEER REVIEW 15 of 24
difference in the time series of SA and coastal TG data was analysed by considering a
linear trend and an annual, semiannual and 18.61-year cycle.
Figure 12. (a) Map of the linear trend in coastal stations estimated from different time series of TG data (TG data from the
beginning of data to 2018). (b) Map of the linear trend in coastal stations estimated from different time series of SA data
(SA data from 1993 to 2017); the units on both pictures are in mm/year. The linear trend standard errors are visualized by
black circles. Positive values of the linear trend are visualized by a red arrow. Negative values of the linear trend are
visualized by a blue arrow.
The results of the analysis were used to calculate linear trends in vertical crust
movement on the TG sites along the European coast based on SA data minus TG data and
at GNSS time series (GNSS stations closest to TG stations were considered). The velocity
in coastal stations, estimated from the different time series of SA data minus TG data from
the beginning of data to 2018, is shown in Figure 13a. The velocity in coastal stations,
estimated from the different time series of SA data minus TG data from 1993–2018, is
shown in Figure 13b.
Figure 13. (a) Map of vertical crust movements in coastal stations estimated from different time series of SA data minus
TG data (from the beginning of data to 2018). (b) Map of vertical crust movements in coastal stations estimated from
different time series of SA data minus TG data (1993–2017); the units on both pictures are in mm/year. The linear trend
standard errors are visualized by black circles. Positive values of the linear trend are visualized by a red arrow. Negative
values of the linear trend are visualized by a blue arrow.
Figure 13.
(
a
) Map of vertical crust movements in coastal stations estimated from different time series of SA data minus TG
data (from the beginning of data to 2018). (
b
) Map of vertical crust movements in coastal stations estimated from different
time series of SA data minus TG data (1993–2017); the units on both pictures are in mm/year. The linear trend standard
errors are visualized by black circles. Positive values of the linear trend are visualized by a red arrow. Negative values of
the linear trend are visualized by a blue arrow.
In the TG dataset, trend changes in the European coastal zone ranged from
1.75
±
1.59 mm/year (Tarifa2 station in Spain) to +5.26
±
0.19 mm/year (Borkum station in
Germany).
In the SA dataset, trend changes in the European coastal zone ranged from +0.87
±
0.08 mm/year (Ibiza station in Spain) to +4.48
±
0.08 mm/year (Gdansk station in Poland).
The mean trend for all stations was determined at +2.92
±
0.08 mm/year based on SA data
in a different period (1993 to 2017). A comparison of both data sets revealed the highest
trend values in the northern European coastal zone (Germany and Poland) and the lowest
trend values in the southern European coastal zone (Spain).
The differences in the trend values calculated based on TG and SA data were greatest
in the Tarifa2 station (+4.24
±
1.59 mm/year) and smallest in the Roscoff station (+0.44
±
0.08 mm/year).
Velocities in GNSS stations ranged from nearly 0 mm/year (TERS, SABL, CANT, TARI)
to
3 mm/year (ACOR, SCOA). The trend standard error ranged from nearly 0 mm/year
(SASS, WARN, TERS, SABL, CANT, LAMP) to ±2.0 mm/year (SCOA).
Vertical crust movement values were estimated based on multitime SAR data series,
and they ranged from
2.24
±
0.39 mm/year (IJMU) to +2.88
±
0.30 mm/year (TGBF). The
mean minimum standard error was
±
0.20 mm/year (GESR), and the maximum standard
error was
±
0.49 mm/year (SAS2). The greatest changes in velocity were observed in
the coastal zone of Northwestern Europe. The mean velocity values in the stations in
France, Belgium, the Netherlands and Germany were negative in the range of
2.24
±
0.39 mm/year (IJMU) to
0.14
±
0.46 mm/year (SMTG). The highest positive values
were noted in TGBF (Germany) at +2.88
±
0.30 mm/year and TERS (Netherlands) at
+0.27
±
0.40 mm/year. The stations in the Baltic Sea zone in Northern Europe moved
Remote Sens. 2021,13, 2173 16 of 24
with mean positive velocities: +0.65
±
0.45 mm/year in SWIN, +0.19
±
0.48 mm/year in
WLAD, +0.21
±
0.20 mm/year in GESR and +0.07
±
0.40 mm/year in WARN. Stations on
Rügen island in Germany moved with mean negative velocities: +0.66
±
0.49 mm/year in
SAS2 and +0.53
±
0.33 mm/year in SASS. The stations in Southern Europe (Spain) were
characterised by positive velocities in the range of +0.06
±
0.22 mm/year (CANT) to +0.47
±
0.39 mm/year (SCOA). Negative velocity was observed only in the ACOR station (
0.35
±
0.35 mm/year). A map of vertical crust movements in coastal stations estimated from
different time series of GNSS and PSInSAR data is presented in Figure 14.
Remote Sens. 2021, 13, x FOR PEER REVIEW 16 of 24
In the TG dataset, trend changes in the European coastal zone ranged from 1.75 ±
1.59 mm/year (Tarifa2 station in Spain) to +5.26 ± 0.19 mm/year (Borkum station in
Germany).
In the SA dataset, trend changes in the European coastal zone ranged from +0.87 ±
0.08 mm/year (Ibiza station in Spain) to +4.48 ± 0.08 mm/year (Gdansk station in Poland).
The mean trend for all stations was determined at +2.92 ± 0.08 mm/year based on SA data
in a different period (1993 to 2017). A comparison of both data sets revealed the highest
trend values in the northern European coastal zone (Germany and Poland) and the lowest
trend values in the southern European coastal zone (Spain).
The differences in the trend values calculated based on TG and SA data were greatest
in the Tarifa2 station (+4.24 ± 1.59 mm/year) and smallest in the Roscoff station (+0.44 ±
0.08 mm/year).
Velocities in GNSS stations ranged from nearly 0 mm/year (TERS, SABL, CANT,
TARI) to 3 mm/year (ACOR, SCOA). The trend standard error ranged from nearly 0
mm/year (SASS, WARN, TERS, SABL, CANT, LAMP) to ± 2.0 mm/year (SCOA).
Vertical crust movement values were estimated based on multitime SAR data series,
and they ranged from 2.24 ± 0.39 mm/year (IJMU) to +2.88 ± 0.30 mm/year (TGBF). The
mean minimum standard error was ±0.20 mm/year (GESR), and the maximum standard
error was ± 0.49 mm/year (SAS2). The greatest changes in velocity were observed in the
coastal zone of Northwestern Europe. The mean velocity values in the stations in France,
Belgium, the Netherlands and Germany were negative in the range of 2.24 ± 0.39
mm/year (IJMU) to 0.14 ± 0.46 mm/year (SMTG). The highest positive values were noted
in TGBF (Germany) at +2.88 ± 0.30 mm/year and TERS (Netherlands) at +0.27 ± 0.40
mm/year. The stations in the Baltic Sea zone in Northern Europe moved with mean
positive velocities: +0.65 ± 0.45 mm/year in SWIN, +0.19 ± 0.48 mm/year in WLAD, +0.21 ±
0.20 mm/year in GESR and +0.07 ± 0.40 mm/year in WARN. Stations on Rügen island in
Germany moved with mean negative velocities: +0.66 ± 0.49 mm/year in SAS2 and +0.53 ±
0.33 mm/year in SASS. The stations in Southern Europe (Spain) were characterised by
positive velocities in the range of +0.06 ± 0.22 mm/year (CANT) to +0.47 ± 0.39 mm/year
(SCOA). Negative velocity was observed only in the ACOR station (0.35 ± 0.35 mm/year).
A map of vertical crust movements in coastal stations estimated from different time series
of GNSS and PSInSAR data is presented in Figure 14.
Figure 14. (a) Map of vertical crust movement in coastal stations estimated from different time series of GNSS data. GNSS
data were acquired from 27 GNSS stations which are colocated with or positioned in the proximity of a TG station on the
European coast. (b) Map of vertical motion based on multitime SAR data series for 2015–2017; the units on both pictures
are in mm/year. The linear trend standard errors are visualized by black circles. Positive values of the linear trend are
visualized by a red arrow. Negative values of the linear trend are visualized by a blue arrow.
Figure 14.
(
a
) Map of vertical crust movement in coastal stations estimated from different time series of GNSS data. GNSS
data were acquired from 27 GNSS stations which are colocated with or positioned in the proximity of a TG station on the
European coast. (
b
) Map of vertical motion based on multitime SAR data series for 2015–2017; the units on both pictures
are in mm/year. The linear trend standard errors are visualized by black circles. Positive values of the linear trend are
visualized by a red arrow. Negative values of the linear trend are visualized by a blue arrow.
The estimates of vertical crust movements obtained from GNSS stations and the
combination of SA data minus TG data were compared in 27 sites along the European coast
where both types of measurements were available.
The movement of the Earth’s crust determined from the combination of TG and SA
data ranged from
2.31
±
0.21 mm/year (Borkum, Fischerbalje) to + 2.54
±
0.06 mm/year
(Kolobrzeg, Gedser). The mean standard error was
±
0.13 mm/year (TG data from the
beginning of data to 2018) and
±
0.47 mm/year (TG data for 1993–2017). The greatest
standard error values were noted in Les Sables D’Olonne (
±
0.29 mm/year—TG to 2018)
and TARIFA 2 (±1.59 mm/year—TG since 1993) (Figure 15).
The greatest differences in vertical movement calculated based on PSI data and GNSS
data were noted in TGBF, SCOA, COUD, SAS2 and SASS stations. Differences were also
observed in ACOR, IJMU, SABL and TERS stations. The vertical component of interpolated
PS points was calculated according to Equation (7). The values obtained in GNSS stations
and interpolated PS points are shown in Figure 16.
Remote Sens. 2021,13, 2173 17 of 24
Remote Sens. 2021, 13, x FOR PEER REVIEW 17 of 24
The estimates of vertical crust movements obtained from GNSS stations and the
combination of SA data minus TG data were compared in 27 sites along the European
coast where both types of measurements were available.
The movement of the Earth’s crust determined from the combination of TG and SA
data ranged from 2.31 ± 0.21 mm/year (Borkum, Fischerbalje) to + 2.54 ± 0.06 mm/year
(Kolobrzeg, Gedser). The mean standard error was ±0.13 mm/year (TG data from the
beginning of data to 2018) and ±0.47 mm/year (TG data for 1993–2017). The greatest
standard error values were noted in Les Sables D’Olonne (±0.29 mm/year—TG to 2018)
and TARIFA 2 (±1.59 mm/year—TG since 1993) (Figure 15).
Figure 15. Vertical crust movements in TG sites along the European coast based on SA and TG data and the corresponding
GNSS.
The greatest differences in vertical movement calculated based on PSI data and GNSS
data were noted in TGBF, SCOA, COUD, SAS2 and SASS stations. Differences were also
observed in ACOR, IJMU, SABL and TERS stations. The vertical component of
interpolated PS points was calculated according to Equation (7). The values obtained in
GNSS stations and interpolated PS points are shown in Figure 16.
Figure 15.
Vertical crust movements in TG sites along the European coast based on SA and TG data and the correspond-
ing GNSS.
Remote Sens. 2021, 13, x FOR PEER REVIEW 18 of 24
Figure 16. Vertical crust movements in TG sites along the European coast derived from PSInSAR data and the
corresponding GNSS data.
4. Discussion
The obtained results present vertical deformations in the proximity of selected GNSS
stations located on the European coast along with an assessment of the actual accuracy.
Differences were observed in the rate of changes in average sea level determined
based on TG data (long-term observations) along the European coast. The greatest
changes were observed in tide gauges in the Mediterranean area. The rate of changes in
the mean sea level increased to the south (positive values), and a decrease was observed
in only two tide gauge stations (Tarifa2 station in Spain and Concarneau station in France).
The mean changes in sea level along the European coast, determined based on
satellite altimetry data, increased towards the north. All changes in sea level were positive.
To validate the presented calculations, the velocity determined on selected stations
were compared with SONEL measurements based on TG data. Based on TG data and SA
data for 1993–2011, 1993–2014 and 1993–2015 time periods, nine European coastal stations
were chosen (Sassnitz, Warnemunde 2, Borkum (Fisherbalje), West-Terschelling,
Ijmuiden, Les Sables D’Olonne, Santander III, La Coruna III and Thessaloniki stations).
SONEL velocity measurements (mm/year) were based on SA (Aviso Global MSLA heights
in delayed time) and TG (PSMSL demeaned TG time series) [74]. The results are shown in
Figure 17.
Figure 16.
Vertical crust movements in TG sites along the European coast derived from PSInSAR data and the corresponding
GNSS data.
4. Discussion
The obtained results present vertical deformations in the proximity of selected GNSS
stations located on the European coast along with an assessment of the actual accuracy.
Remote Sens. 2021,13, 2173 18 of 24
Differences were observed in the rate of changes in average sea level determined
based on TG data (long-term observations) along the European coast. The greatest changes
were observed in tide gauges in the Mediterranean area. The rate of changes in the mean
sea level increased to the south (positive values), and a decrease was observed in only two
tide gauge stations (Tarifa2 station in Spain and Concarneau station in France).
The mean changes in sea level along the European coast, determined based on satellite
altimetry data, increased towards the north. All changes in sea level were positive.
To validate the presented calculations, the velocity determined on selected stations
were compared with SONEL measurements based on TG data. Based on TG data and
SA data for 1993–2011, 1993–2014 and 1993–2015 time periods, nine European coastal
stations were chosen (Sassnitz, Warnemunde 2, Borkum (Fisherbalje), West-Terschelling,
Ijmuiden, Les Sables D’Olonne, Santander III, La Coruna III and Thessaloniki stations).
SONEL velocity measurements (mm/year) were based on SA (Aviso Global MSLA heights
in delayed time) and TG (PSMSL demeaned TG time series) [
74
]. The results are shown in
Figure 17.
Remote Sens. 2021, 13, x FOR PEER REVIEW 19 of 24
Figure 17. A comparison of the velocity estimated in nine European coastal zone stations and SONEL stations based on
TG and SA time series.
The comparison produced relatively satisfactory results. The greatest difference
between the values calculated in this study and those determined in the SONEL network
based on the TG time series was noted in the Borkum station. This discrepancy could be
attributed to differences in the analysed time periods (1993–2011 in the SONEL network,
1993–2017 in this study).
Differences were observed in the vertical movements of the Earth’s crust determined
from GNSS data (Figure 14a). The greatest negative vertical movements were observed in
ACOR and SCOA stations. The greatest standard errors in velocity determination were
noted in SAS2, ILDX and SCOA stations.
In real data time series, an accuracy of 0.1 mm per year can be achieved over a 100-
year observation period. In time series without seasonal variations, an accuracy of 0.1 mm
per year requires an observation period of 49 years [19]. To achieve an accuracy of 0.5
mm/year, a minimum observation period of 3 years is needed [20]. The above assumptions
do not apply to AUT1, ILDX and SCOA stations. The calculated standard error values
differ from the predicted values, which indicates that the time series is disrupted (the
changes in coordinate values proceed in a disordered manner, and their cause is
unknown). According to [13], the uncertainty of velocity determinations based on GNSS
data ranges from 0.1 mm/year to 1.3 mm/year with a median of 0.21 mm/year. Both higher
and lower accuracy values were obtained in this study. The velocity calculated in this
study based on GNSS data differs from that calculated by the analytical centres in ULR,
NGL and JPL (Table 1). The greatest differences were noted in IJMU, COUD, SMTG,
SCOA, TARI, IBIZ and AUT1. Considerable differences were also observed in standard
error values. These discrepancies indicate that the method of calculating and interpreting
vertical shifts in time series (jumps) has a significant impact on the final result.
The results obtained during our research of vertical movement velocity on the coasts
of Poland, Denmark and Germany was verified on the basis of the article [75]. Differences
in values may be connected with the different length of the time series and chosen time
periods.
The trends in mean sea level were determined by [76] based on TG data for the coastal
areas in France (Dunkerque, Roscoff, Saint-Malo, Concarneau, Les Sables D’Olonne, Saint
Jean De Luz, Sete and other locations that were not analysed in this study). Relative sea
level trends and vertical land movements were determined for 1993–2018. The vertical
land movements estimated in the cited study are consistent with the presented findings
for the Saint-Malo station (0.63 ± 0.55 mm/year in the cited study; 0.68 ± 0.30 mm/year
in this study), Concarneau station (0.46 ± 0.42 mm/year and 0.46 ± 0.24 mm/year,
respectively), Les Sables D’Olonne station (0.05 ± 0.37 mm/year and 0.08 ± 0.07 mm/year,
respectively), Sete station (0.87 ± 0.43 mm/year and 0.83 ± 0.13 mm/year, respectively)
and Rosco station (1.28 ± 0.43 mm/year and 1.67 ± 0.26 mm/year, respectively).
Figure 17.
A comparison of the velocity estimated in nine European coastal zone stations and SONEL stations based on TG
and SA time series.
The comparison produced relatively satisfactory results. The greatest difference
between the values calculated in this study and those determined in the SONEL network
based on the TG time series was noted in the Borkum station. This discrepancy could be
attributed to differences in the analysed time periods (1993–2011 in the SONEL network,
1993–2017 in this study).
Differences were observed in the vertical movements of the Earth’s crust determined
from GNSS data (Figure 14a). The greatest negative vertical movements were observed in
ACOR and SCOA stations. The greatest standard errors in velocity determination were
noted in SAS2, ILDX and SCOA stations.
In real data time series, an accuracy of 0.1 mm per year can be achieved over a 100-
year observation period. In time series without seasonal variations, an accuracy of 0.1
mm per year requires an observation period of 49 years [
19
]. To achieve an accuracy
of 0.5 mm/year, a minimum observation period of 3 years is needed [
20
]. The above
assumptions do not apply to AUT1, ILDX and SCOA stations. The calculated standard error
values differ from the predicted values, which indicates that the time series is disrupted (the
changes in coordinate values proceed in a disordered manner, and their cause is unknown).
According to [
13
], the uncertainty of velocity determinations based on GNSS data ranges
from 0.1 mm/year to 1.3 mm/year with a median of 0.21 mm/year. Both higher and lower
accuracy values were obtained in this study. The velocity calculated in this study based
on GNSS data differs from that calculated by the analytical centres in ULR, NGL and JPL
(Table 1). The greatest differences were noted in IJMU, COUD, SMTG, SCOA, TARI, IBIZ
and AUT1. Considerable differences were also observed in standard error values. These
Remote Sens. 2021,13, 2173 19 of 24
discrepancies indicate that the method of calculating and interpreting vertical shifts in time
series (jumps) has a significant impact on the final result.
Table 1.
Velocities of crust movement calculated in this study are based on GNSS data and SONEL network data calculated
by three analytical centres (ULR, NGL, JPL).
Analysis Centre
Time Span [Year]
ULR NGL JPL In Work
Reference Frame,
Ellipsoid
ITRF08,
GRS80
ITRF14,
GRS80
ITRF14,
GRS80
ITRF08,
GRS80
Reference Epoch 2004.4973 2012.386 2020.0001 2004.4973
GNSS STATION
Velocity ±
Standard Error
[mm/Year]
Velocity ±
Standard Error
[mm/Year]
Velocity ±
Standard Error
[mm/Year]
Velocity ±
Standard Error
[mm/Year]
SASS 11 0.83 ±0.55 0.65 ±0.64 0.63 ±0.39 0.60 ±0.06
SAS2 2 - 0.62 ±1.56 - 0.67 ±0.76
WARN 11 0.66 ±0.59 0.22 ±0.65 0.34 ±0.36 0.72 ±0.06
TERS 17 0.18 ±0.22 0.63 ±0.42 - 0.02 ±0.04
IJMU 9 0.51 ±0.34 1.33 ±0.57 - 0.42 ±0.08
COUD 6 0.18 ±0.65 0.92 ±0.58 - 0.45 ±0.26
SMTG 4 0.63 ±0.47 1.78 ±0.59 - 0.68 ±0.30
ROTG 4 1.28 ±0.33 1.92 ±0.55 - 1.67 ±0.22
KONE 6 0.46 ±0.32 0.78 ±0.48 - 0.46 ±0.24
SABL 11 0.05 ±0.24 0.46 ±0.58 - 0.08 ±0.07
ILDX 7 Not robust 1.21 ±0.63 0.96 ±0.40 1.52 ±0.52
SCOA 8 2.69 ±0.28 1.63 ±0.59 3.06 ±0.46 3.20 ±1.92
CANT 13 0.03 ±0.17 0.70 ±0.48 0.78 ±0.58 0.18 ±0.05
ACOR 13 2.20 ±0.54 2.49 ±0.40 2.21 ±0.22 3.32 ±0.23
TARI 4 0.20 ±0.59 2.09 ±1.05 - 0.09 ±0.40
IBIZ 9 2.36 ±0.18 1.39 ±0.51 - 1.02 ±0.21
SETE 6 0.85 ±0.27 1.25 ±0.56 - 0.83 ±0.13
AJAC 13 0.40 ±0.14 0.56 ±0.46 0.04 ±0.38 0.30 ±0.11
LAMP 14 0.35 ±0.28 0.22 ±0.48 0.19 ±0.41 0.25 ±0.05
AUT1 8 1.20 ±0.31 1.92 ±0.50 - 0.77 ±0.32
TGBF 4 0.75 ±0.79 0.52 ±0.64 - 0.96 ±0.30
GESR 10 0.63 ±0.66 0.22 ±0.58 0.63 ±0.39 0.44 ±0.17
DUB2 8 - 1.94 ±0.89 - 1.49 ±0.01
PORE 9 - 1.51 ±1.03 1.03 ±0.70 0.92 ±0.02
The results obtained during our research of vertical movement velocity on the coasts
of Poland, Denmark and Germany was verified on the basis of the article [
75
]. Differences
in values may be connected with the different length of the time series and chosen time
periods.
The trends in mean sea level were determined by [
76
] based on TG data for the coastal
areas in France (Dunkerque, Roscoff, Saint-Malo, Concarneau, Les Sables D’Olonne, Saint
Jean De Luz, Sete and other locations that were not analysed in this study). Relative sea
level trends and vertical land movements were determined for 1993–2018. The vertical
land movements estimated in the cited study are consistent with the presented findings for
the Saint-Malo station (
0.63
±
0.55 mm/year in the cited study;
0.68
±
0.30 mm/year in
Remote Sens. 2021,13, 2173 20 of 24
this study), Concarneau station (
0.46
±
0.42 mm/year and
0.46
±
0.24 mm/year, respec-
tively), Les Sables D’Olonne station (
0.05
±
0.37 mm/year and
0.08
±
0.07 mm/year,
respectively), Sete station (
0.87
±
0.43 mm/year and
0.83
±
0.13 mm/year, respectively)
and Roscoff station (
1.28
±
0.43 mm/year and
1.67
±
0.26 mm/year, respectively).
Differences were observed only in the Dunkerque station (
0.18
±
0.71 in the cited study,
+0.45 ±0.26 mm/year in this study).
The values of crust movement determined with the use of Equation (1) are shown
in Figure 13a,b. Crust movements were well above zero in 12 tide gauges (based on data
for 1993–2017). Tide gauges were below zero in Lampedusa and Sassnitz, which could
be attributed to a greater decrease in average water levels calculated based on TG data
rather than SA data. According to [
13
], the uncertainty of velocity determinations based on
GNSS data is three to four times lower on average in comparison with combined satellite
radar altimetry minus TG data which ranges from 0.3 mm/year to 3.0 mm/year, with a
median of 0.80 mm/year. The uncertainty of trends for time series of daily SA data ranges
from 0.04 mm/year to 0.09 mm/year, and it is higher when monthly data are used (around
0.40 mm/year). The uncertainty of trends based on the entire TG time series (monthly data)
ranges from 0.03 mm/year (time series covering approximately 200 years) to 1.59 mm/year
(time series covering approximately 20 years).
The adopted method for verifying the velocity of GNSS stations was based on radar
interferometry data generated with the use of the PSI approach. The results indicate that
the velocities calculated in selected stations (TGBF, COUD, SCOA, TERS, SAS2 and SASS)
based on SAR data differ in sign relative to the values calculated based on GNSS data.
As shown in Figure 14a,b, the velocities calculated based on GNSS and SAR data differ
in stations located on the North Sea and the Bay of Biscay. A considerable difference
was observed in the SCOA station (
3.67 mm/year) where the standard error of velocity
determination reached
±
0.39 mm/year in the PSI method and
±
1.92 mm/year in the
calculations based on GNSS data. A large discrepancy was also noted in the ACOR station
(
2.97 mm/year), where the standard error reached
±
0.35 mm/year in the PSI approach
and
±
0.23 mm/year in the calculations based on GNSS data. In the TGBF station, the
difference in the velocity was +3.84 mm/year with a standard error of
±
0.30 mm/year
in the PSI method and
±
0.30 mm/year in the calculations based on GNSS data. On the
other hand, the velocities calculated based on GNSS and SAR data are more similar in
stations located on the Baltic Sea and the Mediterranean. The smallest difference was
observed in the SWIN and LAMP stations. In the SWIN station, the difference in the
velocity was +0.07 mm/year with a standard error of
±
0.45 mm/year in the PSI method
and
±
0.18 mm/year in the calculations based on GNSS data. In the LAMP station, the
difference in the velocity was
0.10 mm/year with a standard error of
±
0.35 mm/year
in the PSI approach and
±
0.05 mm/year in the calculations based on GNSS data. The
remaining velocity values resulted from the calculation of relative displacements in the PSI
method as well as from differences in the analysed data sets and time periods.
5. Conclusions
TG and SA data were used to determine variations in sea level in the coastal zone. The
results point to considerable differences in sea level trends, and they indicate that local and
regional processes influence TG time series The results presented in the study point to land
subsidence in the south and southwest along the European coast. These observations were
confirmed by the data from permanent GNSS stations and InSAR systems. The InSAR
technology helps with the determination of the vertical movements of the Earth’s crust
(deformation) in the areas surrounding GNSS stations.
Different measurement techniques have different real accuracies in determining the
vertical movements of the earth’s crust. The standard error from the combination of TG and
SA data ranged from
±
0.06 mm/year to
±
0.21 mm/year at a long-time resolution and from
±
0.31 mm/year to
±
1.59 mm/year at a short-time resolution. The use of an unprecedented
number of PSInSAR datasets allowed the estimation of a new level of accuracy in the
Remote Sens. 2021,13, 2173 21 of 24
range of
±
0.20 mm/year to
±
0.49 mm/yy. The accuracy of the vertical movements of the
Earth’s crust from GNSS data ranged from
±
0.04 mm/year to
±
1.92 mm/year. Comparing
the PSInSAR results required the development of a new procedure: the workflow of
determining the value of vertical movement velocities in GNSS stations based on InSAR
data.
Author Contributions:
K.K. conception; K.K., K.P. and B.W. methodology; B.N. validation, K.K., K.P.
and B.W. writing—original draft preparation; B.N. writing—review and editing. All authors have
read and agreed to the published version of the manuscript.
Funding: This research received no external funding.
Institutional Review Board Statement: Not applicable.
Informed Consent Statement: Not applicable.
Data Availability Statement:
The tide gauge data is provided by PSMSL (http://www.psmsl.org/
data/obtaining/ (accessed on 12 December 2019)) and from the Institute of Meteorology and Water
Management of the Polish National Research Institute. The gridded sea level anomalies product is
provided by CMEMS (Copernicus Marine and Environment Monitoring Service—https://marine.
copernicus.eu/; http://doi.org/10.17616/R31NJMU4; data for 1993–2017 (accessed on 15 May 2020)).
The GNSS data are available from SONEL (https://www.sonel.org (accessed on 15 January 2020))
and the NGL (Nevada Geodetic Laboratory—http://geodesy.unr.edu/ (accessed on 12 December
2019)). SENTINEL-1A/B data comes from the Copernicus Open Access Hub as part of the Copernicus
mission (https://scihub.copernicus.eu/dhus/#/home, accessed on 08 April 2020); (an initiative of the
European Commission (EC) and the European Space Agency (ESA); https://search.asf.alaska.edu/#/,
accessed on 16 March 2020).
Acknowledgments:
All the respectable reviewers and editors are acknowledged for their fruitful
comments and suggestions concerning the paper.
Conflicts of Interest: The authors declare no conflict of interest.
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... In coastal interferometric synthetic aperture radar (InSAR) deformation measurements, the ground tidal displacements along the LOS direction can reach 2~4 decimeters, and it usually reaches centimetres in a single-frame differential InSAR (DInSAR) interferogram with a spatial range of 100~250 km [1]. Currently, the tidal effects are generally ignored in InSAR deformation measurements, while a best-fitting ramp is applied to remove the spatial residual large-scale errors in differential interferograms [2][3][4]. The traditional bilinear ramp fitting method can eliminate tidal displacements in most instances, such as inland areas or small-range DInSAR measurements because the magnitude of the ocean tidal loading (OTL) displacement within the SAR image is minor and the spatial variations of the solid earth tide (SET) displacements tend to be linear ramps. ...
... where f LSSV M is the least squares support vector machine (LSSVM) based on the polynomial kernel function [26], b 0 is a constant deviation, and Phasor Model m,n is the phasor of the m tidal constituents of the OTL model at the location of n GPS sites with the order from large to small, and the tidal constituents displacements of any tide loading point p in the range of the GPS reference sites network can be predicted. In coastal areas with a high site density of GPS networks, the expression of the site location and the constituents can be determined based on the Formula (4). ...
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A long-strip differential interferometric synthetic aperture radar (DInSAR) measurement based on multi-frame image mosaicking is currently the realizable approach to measure large-scale ground deformation. As the spatial range of the mosaicked images increases, the nonlinear variation of ground ocean tidal loading (OTL) displacements is more significant, and using plane fitting to remove the large-scale errors will produce large tidal displacement residuals in a region with a complex coastline. To conveniently evaluate the ground tidal effect on mosaic DInSAR interferograms along the west coast of the U.S., a three-dimensional ground OTL displacements grid is generated by integrating tidal constituents’ estimation of the GPS reference station network and global/regional ocean tidal models. Meanwhile, a solid earth tide (SET) model based on IERS conventions is used to estimate the high-precision SET displacements. Experimental results show that the OTL and SET in a long-strip interferogram can reach 77.5 mm, which corresponds to a 19.3% displacement component. Furthermore, the traditional bilinear ramp fitting methods will cause 7.2~20.3 mm residual tidal displacement in the mosaicked interferograms, and the integrated tidal constituents displacements calculation method can accurately eliminate the tendency of tidal displacement in the long-strip interferograms.
... The vertical movements of the Earth's crust from the data of TG and SA is calculated by the below formula [24]: ...
... The InSAR-based ground motion service uses active corner reflectors -transponders -as a central unit of the new method. In such a way, we can tie InSAR motions with velocities from GNSS if the transponders are located in the vicinity of the GNSS station or TG [24]. In summary, with a sufficiently long-time span reaching from 5 to 12 years, we were able to obtain reliable estimates for the vertical ground motion at the TG sites along the Adriatic Sea coasts. ...
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Tide gauge observations provide sea level relative to the Earth’s crust, while satellite altimetry measures sea level variations relative to the centre of the Earth’s mass. Local vertical land motion can be a significant contribution to the measured sea level change.Satellite altimetry was traditionally used to study the open ocean, but this technology is now being used over inland seas too.The difference of both observations can be used to estimate vertical crustal movement velocities along the sea coast. In this paper, vertical crustal movement velocities were investigated at tide gauge sites along the Adriatic Sea coast by analyzing differences between Tide Gauge (TG) and Satellite Altimetry (SA) observations. Furthermore, the estimated vertical motion rates were compared with those from nearby GNSS measurements.The study determines the practical relationships between these vertical crustal movements and those determined from unrelated data acquired from the neighbouring GNSS stations. The results show general consistence with the present geodynamics in the Adriatic Sea coastal zone.
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Vertical crustal movements can be calculated on the basis of Global Navigation Satellite Systems (GNSS) permanent stations positioning results (the absolute motion) as well as on vectors between the stations (the relative motion). The time series, which are created in both cases, include, apart from the information about height, measurement noise, and they are burdened with the influence of factors that are sometimes difficult to identify. These factors make momentary or long-term changes in height. The times of sudden changes in height (jumps) can be difficult to identify and estimate. In order to calculate the velocity of vertical movements, each of the jumps should be identified. It means that both the epoch of each jump and its value must be estimated. The authors of this article developed an algorithm that supports the process of creating the models of vertical crustal movements from GNSS data. The algorithm determines the epoch of a jump and estimates the velocity of vertical movements. The aim of the article is to verify the algorithm on the basis of height changes in adjacent stations of polish national CORS network ASG-EUPOS and to set proper algorithm parameters. The results received on the basis of the algorithm were evaluated and verified using four possible methods: visual evaluation, testing the algorithm using adjacent input parameter values, information in .log files and analysis of the loop misclosure. The results indicate that the algorithm functions properly and is useful in the creation of vertical crustal movement models from GNSS data.
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GNSS can provide a temporally dense set of geodetic coordinate observations in three dimensions at a small number of discrete measurement points on the ground. Compare this to the Interferometric Synthetic Aperture Radar (InSAR) technique which gives a spatially dense set of geodetic observations of ground surface movement in the viewing geometry of the satellite platform, but with a temporal sampling limited to the orbital revisit of the satellite. Using both of these methods together can leverage the advantages of each to derive more accurate, validated surface displacement estimates with both high temporal and spatial resolution. In this paper, the properties of both techniques are discussed with a view to combined usage for future Australian datums. Differential GNSS processing is applied to data observed at a local geodetic network in the Sydney region as well as time series InSAR analysis of Radarsat-2 data. Surface displacements resulting from the two techniques are compared and validated at 21 geodetic monitoring sites equipped with GNSS and radar corner reflectors (CRs). The resulting GNSS/InSAR displacement time series agree at the level of 5 to 10 mm. This case study shows that the co-located GNSS/CR sites are well suited to compare and combine GNSS and InSAR measurements. An investigation of potential multipath effects introduced by the CRs attached directly to GNSS monumentation found that daily site coordinates are affected at a level below 0.1 mm. The GNSS/CR sites may hence serve as a local tie for future incorporation of InSAR into national datums.
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In this paper, seasonal sea level variations have been determined at five locations in the Baltic Sea from satellite altimetry for the period 1993–2015. The results were compared to tide gauge water level data. Annual and semi-annual amplitudes have been investigated for both sea level anomalies and tide gauge water level. It was found that the two independent observations of sea level variations along the Polish coast are in good agreement both in terms of their annual and semi-annual amplitudes and their annual and semi-annual phases. The annual cycles in the sea level variations measured by altimetry and tide gauge reach maximum values at approximately the same month (November/December). Moreover, this article shows the differences between the annual and semi-annual amplitudes and phases in the sea level anomalies and water level data within the same time frame. The difference in the annual amplitudes between the satellite altimetry and the tide gauge results is between 0.33 cm and 1.53 cm. The maximum differences in the annual cycle of the sea level changes were found at the Swinoujscie station. The correlations between the original series and the calculated curves were determined, and the relationship between the amplitudes and the phases were investigated. The correlation between the annual variations observed from the two independent observation techniques is 0.92. To analyse the dynamics of the change in sea level, the linear trend was estimated from the satellite altimetry and tide gauge time series both in the original time series of the data and in the time series in which seasonal variations were removed. In addition, we calculated the estimated errors of regression and how many years’ worth of data are needed to obtain an accuracy of 0.1 mm per year. The estimated errors of regression showed that to get an accuracy of 0.1 mm per year, we need 100 years of data.