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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

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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 [27,42–45].

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 (ωat−ϕa)+Asacos (ωsa t−ϕsa )+A18.61 cos (ω18.61 t−ϕ18.61)(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 (𝜔𝑡−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. (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

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 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.

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 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.

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

Remote Sens. 2021, 13, x FOR PEER REVIEW 8 of 24

2.2. Analysis of Vertical Crustal Movement Velocities Based on GNSS Data

Vertical crustal movements can be classified as relative 𝑣 or absolute 𝑣. Relative

vertical 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.

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.

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).

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:

ℎ(𝑡)=𝑣𝑡+ℎ+𝑐𝑠+𝑐𝑠+⋯+𝑐𝑠 (5)

where t-epoch, h(t)—height difference in epoch t; v—velocity between stations; h0—height

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 [63–67].

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=A∗Vup Vhald ;A=cosθasc sinθasc

cos∆αcosθdesc 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 Roscoﬀ 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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