*Coastal Sea Level Trends from a Joint Use of Satellite Radar Altimetry, GPS and Tide… DOI: http://dx.doi.org/10.5772/intechopen.98243*

principally the Permanent Service for Mean Sea Level (PSMSL) [61], the Venice Tide Forecast and Early Warning Center (Centro Previsioni e Segnalazioni Maree, CPSM) of Venice Municipality, the Istituto Superiore per la Protezione e la Ricerca Ambientale (Italian Institute for Environmental Protection and Research (ISPRA)) and the Institute of Marine Sciences of the National Research Council of Italy (CNR-ISMAR).

**Figure 2** shows the position of the TGs on the map of the Adriatic Sea region. Some of the TG records have been formed by collating partial records from different sources. Such TGs are marked by an asterisk. The individual positions of the TGs with respect to the twelve closest nodes of the.

C3S altimetry grid are shown in **Figure 3**: note that some of the grid nodes are represented over land. This is an artifact of the gridding procedure that partially extrapolates over land the SLA field [36].

VEPTF is the shortest record in the set, as it started sea level recordings only in 1974. Nonetheless, its length is almost double that of the altimetry era, and abundantly double the period of the lunar nodal tide. To treat evenly all the TG records, we consider in situ sea level data from 1974 up to 2018 for all the TGs.

Plots of the in situ, as well as of the altimetry sea level anomaly monthly means observed at the six locations in the Adriatic Sea are reported in **Figure 4**: the seasonal and tidal signals have been removed from both the in situ and the altimetry datasets. The altimetry grid node associated to the TG time series has been chosen as the one whose time series has the higher correlation coefficient with the sea level time series of the TG, among the twelve grid nodes closest to the latter. All the sea level trend errors have been calculated considering serial correlation and are given with a 95% confidence interval.

The altimetry dataset used to represent sea level anomaly in **Figure 4** is C3S. The in situ and the remotely sensed sea level records are in good agreement, as the lowest Pearson's correlation coefficient between altimetry and TG sea level time series is 0.82 at the Rovinj station, while all the others reach values larger than 0.91.

However, in some period a marked difference between in situ and altimetry SLA are seen, as for example in VENEZIA during 2012–2019 (TG sea level higher than altimetry), which is also confirmed by the nearby TG of VEPTF and seems to interest in a lesser extent also TRIESTE and DUBROVNIK, and for ROVINJ in

#### **Figure 2.**

*Positions of six tide gauges in Adriatic Sea. Color bar indicates length of available time series of sea level at tide gauges; shortest time series is about 50 years.*

*u*\_ *<sup>i</sup>* ¼ *g*\_*<sup>i</sup>* � *s*\_*<sup>i</sup>* ¼ *g*\_*<sup>i</sup>* � *g*\_*<sup>i</sup>* þ *g*\_*<sup>i</sup>* � *s*\_*<sup>i</sup>* ¼ *g*\_

1.All the time series have a linear trend in every period in which they are

2.The absolute sea level rates observed by satellite altimetry in its era can be extended backward in time to cover the timespan of the associated TG relative

While the first assumption can be easily verified by visual inspection or with more precise statistical methods, as the goodness-of-fit R<sup>2</sup> test [59], the second assumption, needed to permit the third change of variable in Eq. (12), can be more difficult to assess. In general, the linearity of a TG's RSLR trend can partly corroborate the validity of the second assumption, as the probability that two different, non-linear trends of the local ASLR and VLM perfectly combine by chance, to give

The method of derivation of VLM described in the previous section will now be applied to a real case. To this end we have chosen the Adriatic Sea for its complexity and for the interest in this area. Indeed, several historical heritage cities and commercial/productive sites lie in the coastal area of the region, not to mention the number of people leaving along the Adriatic Sea coast, which at the end of last century was already higher than 3.5 million [60]. First, we will derive the VLM values in the Adriatic Sea using the classical LIPWC technique. After that, the LIPWC method will be applied to the same data using the change of variable

The TG in the Adriatic Sea for which long time series of monthly sea level are available are few. **Table 1** reports their name, position, and data availability. The records of the TGs have been formed in some case from different sources,

51.45″ 12°20<sup>0</sup>

51.29″ 12°30<sup>0</sup>

50.00″ 13°45<sup>0</sup>

01.18″ 13°37<sup>0</sup>

23.88″ 16°26<sup>0</sup>

28.40″ 18°03<sup>0</sup>

*Principal characteristics of tide gauges considered in Adriatic Sea. Some of the tide gauge records have been formed by collating partial records from different sources. Such situation is marked by an asterisk after the tide*

**Long (° E)** **Data (%)**

**Time Span (Years)**

13.39″ 97 1872–2018 147

29.69″ 100 1974–<sup>2018</sup> <sup>45</sup>

33.90″ 89 1875–2018 145

44.86″ 99 1955–<sup>2018</sup> <sup>64</sup>

18.44″ 100 1952–<sup>2018</sup> <sup>67</sup>

38.84″ 99 1956–<sup>2018</sup> <sup>63</sup>

**Record Length (Years)**

presented in Eq. (12), and the results of the two strategies compared.

**(° N)**

sea level changes. For it to work two assumptions are necessary:

*Geodetic Sciences - Theory, Applications and Recent Developments*

considered.

sea level time series.

an overall linear trend, is obviously low.

**Location TG Name Lat**

Venice VENEZIA \* 45°25<sup>0</sup>

Venice off-shore VEPTF 45°18<sup>0</sup>

Trieste TRIESTE \* 45°38<sup>0</sup>

Rovinj ROVINJ 45°05<sup>0</sup>

Split SPLIT \* 43°30<sup>0</sup>

Dubrovnik DUBROVNIK 42°39<sup>0</sup>

**Table 1.**

*gauge name.*

**104**

**7. Case-study of Venice and Adriatic Sea**

In other words, we overcome the limitation of equal ASLR at all TGs by removing from both, the TG time series and the altimetry time series associated with the TG, a linear trend equal to that measured by the altimeter. Such change of variables (COV) does not alter the statistical properties of the TG and altimetry time series but eliminates any difference in relative sea level changes due to different absolute

0 *<sup>i</sup>* � *s*\_ 0 *i* *:* (12)

sources of information are available from local and national public agencies: in this study we used for the VENEZIA TG station also data acquired and processed by ISPRA at the PSAL tide gauge [64], which provides a relevant part of the VENEZIA sea level record. **Table 2** reports the vertical velocities registered at five of the six tide gauges considered in this study, with their time span and the values provided by one or more centers for the same TG by one or more GPS stations nearby.

— 1.46 0.09

**ISPRA (mm y<sup>1</sup> ) Span (yr)**

2010–2015

**Distance from TG (Km)**

— 6.97 0.25 0.52

— < 4.00 0.10 0.64

— — 16.62 1.51 1.03

— — 4.15 1.83 0.70

**Pooled Mean (mm y<sup>1</sup> )**

2014–2020

2003–2020

2011–2021

2004–2012

2000–2020

0.01 1.59 0.65

*Plots of the sea level anomalies registered by tide gauges (1974–2018, in blue) and observed by the satellite*

*Coastal Sea Level Trends from a Joint Use of Satellite Radar Altimetry, GPS and Tide…*

*DOI: http://dx.doi.org/10.5772/intechopen.98243*

**Figure 4.**

**GPS station**

PSAL VENEZIA

TRIE TRIESTE

PORE ROVINJ

SPLT SPLIT

**Table 2.**

**107**

DUBR+DUB2 DUBROVNIK

*altimetry (1993–2018, C3S dataset, in orange).*

**NGL (mm y<sup>1</sup> ) Span (yr)**

1.70 0.80 2014–2020

0.52 0.45 2003–2020

1.51 1.03 2011–2021

0.45 0.68 2004–2012

1.83 0.70 2000–2020

**SONEL (mm y<sup>1</sup> ) Span (yr)**

0.20 0.26 2003–2013

0.25 0.34 2004–2012

*Geocentric surface vertical velocities at three locations in the Adriatic Sea from GPS stations.*

#### **Figure 3.**

*Geographical location of the six tide gauges and position of the twelve nearest grid points of C3S altimetry SLA. Tide gauges are marked by black squares. Altimetry grid nodes are red dots. Blue triangle marks the grid node with best correlation match. Also shown (green circle) the lowest root mean square difference of the TG and altimetry monthly time series.*

2014–2015 (TG sea level lower than altimetry), and also SPLIT in 2002–2005 (TG higher than altimetry). On the other hand, common patterns are identified in all the records throughout the observation period.

Global positioning system (GPS) observations are synergistically included in our analysis. Several sources of GPS data, at different elaboration levels, are currently available online for geocentric surface velocity data and trends from continuous GPS (CGPS) stations at selected locations, in particular near TGs: Système d'Observation du Niveau des Eaux Littorales (SONEL)/Université La Rochelle (ULR) [62], Nevada Geodetic Laboratory (NGL, University of Nevada) [63]. Other *Coastal Sea Level Trends from a Joint Use of Satellite Radar Altimetry, GPS and Tide… DOI: http://dx.doi.org/10.5772/intechopen.98243*

#### **Figure 4.**

*Plots of the sea level anomalies registered by tide gauges (1974–2018, in blue) and observed by the satellite altimetry (1993–2018, C3S dataset, in orange).*

sources of information are available from local and national public agencies: in this study we used for the VENEZIA TG station also data acquired and processed by ISPRA at the PSAL tide gauge [64], which provides a relevant part of the VENEZIA sea level record. **Table 2** reports the vertical velocities registered at five of the six tide gauges considered in this study, with their time span and the values provided by one or more centers for the same TG by one or more GPS stations nearby.


#### **Table 2.**

*Geocentric surface vertical velocities at three locations in the Adriatic Sea from GPS stations.*

2014–2015 (TG sea level lower than altimetry), and also SPLIT in 2002–2005 (TG higher than altimetry). On the other hand, common patterns are identified in all the

*Geographical location of the six tide gauges and position of the twelve nearest grid points of C3S altimetry SLA. Tide gauges are marked by black squares. Altimetry grid nodes are red dots. Blue triangle marks the grid node with best correlation match. Also shown (green circle) the lowest root mean square difference of the TG and*

Global positioning system (GPS) observations are synergistically included in our analysis. Several sources of GPS data, at different elaboration levels, are currently available online for geocentric surface velocity data and trends from continuous GPS (CGPS) stations at selected locations, in particular near TGs: Système d'Observation du Niveau des Eaux Littorales (SONEL)/Université La Rochelle (ULR) [62], Nevada Geodetic Laboratory (NGL, University of Nevada) [63]. Other

records throughout the observation period.

*Geodetic Sciences - Theory, Applications and Recent Developments*

**Figure 3.**

**106**

*altimetry monthly time series.*

PSAL is almost co-located with the VENEZIA PUNTA DELLA SALUTE TG. For SPLIT, data from the CGPS station of SPLT were acquired. It is worth mentioning that SPLT is, with PSAL in VENEZIA, among the few CGPS co-located with TGs in the Adriatic Sea. The TRIE CGPS station is the nearest to the TRIESTE TG, but 6.9 km far from it, over a hill north-west of Trieste: for this reason, TRIE CGPS station cannot be considered co-located with the TRIESTE TG. Neither can the PORE CGPS station for ROVNIJ be considered as such, and the DUBR and DUB2 CGPS stations in DUBROVNIK: PORE is located 16 km north of Rovinj along the coast, while DUBR and DUB2 are located 4 km away and 400 m in height.

field applicable to the Adriatic area is not constant, potentially revealing that different processes could be at the base of the observed crustal motions. From the other side, such numbers reveal also that the VLM is an essential parameter in sea level studies conducted mainly from tide gauge data. Thus, every methodology able to estimate the VLM at the TG is of extreme interest to correct the RSL observed at the TGs themselves, in particular where no geodetic measurements are available to

*Coastal Sea Level Trends from a Joint Use of Satellite Radar Altimetry, GPS and Tide…*

To conclude this section about the classical approach to VLM estimate from sea level data, we report a comparison of the two gridded altimetry datasets: C3S and SLCCI. To provide a fair comparison, both datasets have been limited to the same common period of temporal coverage: 1993–2015. The results of the classical

Column 4 of **Table 4** reports the RSLR, which is common to both ways to calculate VLM, the classical and the LIPWC.. In columns 2 and 3, differences can be seen in the ASLR measured by C3S and SLCCI: the most notable refers to TRIESTE, which appears to observe an ASLR of 4.51 mm y�<sup>1</sup> in the C3S dataset, and 3.42 mm

difference in ASLR for TRIESTE is reflected in the final VLM rate. Regardless the marked difference for TRIESTE, the other rates appear in good agreement between

So far, we have shown the results of the classical approach to VLM determination from altimetry and tide gauge. From now on we present and analyze the results of the linear inverse problem with constraints, in the modified version which exploit a change of variable to disentangle the contribution of the ASLR from the system. To do so we examine only the results relative to the C3S dataset, for three reasons: first of all, the final results do not differ much between the two datasets; second, the C3S gridded product has an enhanced resolution in the Mediterranean Sea, and an appropriate regional processing; third, the C3S dataset has a time span longer than SLCCI, and most important, it is intended to be continuously updated in the future. VLM results derived with the LIPWC-COV approach are shown in **Table 5**, together with the values of the ASLR and RSLR values used for the calculation, and the VLM

The difference between the results obtained in the classical approach and the LIPWC-COV approach is evident; while the classical approach range of VLMs is

0.93]. This is to the result of the introduction of the constraints in Eq. (7), which enter the linear system, propagating the structure and values of the relative vertical motion between the TGs in the solution. The effect of the constraints is best seen in

VENEZIA 4.16 � 1.71 4.47 � 2.07 6.08 � 2.08 �1.93 � 0.79 �1.61 � 0.91 VEPTF 4.17 � 1.73 4.47 � 2.07 6.44 � 2.07 �2.27 � 0.81 �1.97 � 0.93 TRIESTE 4.51 � 1.84 3.42 � 1.78 4.49 � 1.98 0.02 � 0.71 �1.07 � 0.74 ROVINJ 4.09 � 1.85 4.37 � 1.86 1.91 � 2.04 2.18 � 1.17 2.46 � 1.04 SPLIT 4.44 � 1.57 4.15 � 1.48 4.15 � 1.87 0.29 � 0.70 0.00 � 0.76 DUBROVNIK 4.01 � 1.42 3.98 � 1.45 4.67 � 1.70 �0.66 � 0.62 �0.69 � 0.70

*g*\_ **SLCCI (mm y**�**<sup>1</sup> )**

*VLM estimates from in situ RSL and remotely observed C3S and SLCCI ASL 1993-2015.*

, that provided by LIPWC-COV is almost half as wide: [�1.41

ð Þ *g*\_ � *s*\_ **C3S (mm y**�**<sup>1</sup> )**

ð Þ *g*\_ � *s*\_ **SLCCI (mm y**�**<sup>1</sup> )**

*s*\_ **(mm y**�**<sup>1</sup> )** . The

y�<sup>1</sup> in the SLCCI dataset: these numbers differ by more than 1 mm y�<sup>1</sup>

the two datasets, even if in general C3S supplies lower errors.

derived with the classical approach for ease of comparison.

estimate the VLM.

[�2.12 2.30] mm y�<sup>1</sup>

**Location** *g*\_ **C3S**

**Table 4.**

**109**

**(mm y**�**<sup>1</sup> )**

approach to VLM estimate are given in **Table 4**.

*DOI: http://dx.doi.org/10.5772/intechopen.98243*

With the data described so far, the VLM can be derived with the classical method, i.e. subtracting the TG RSLR from the ASLR observed by altimetry at the associated grid point. This approach, described in [43], allows to estimate the VLM separately at each location for which RSL and ASL records are available. The error associated to these estimates is drastically reduced when the linear trend of VLM is calculated by differencing the time series of the ASL and RSL, instead of combining the two errors of ASLR and RSLR as they were two independent measurements. From here on, all the errors on the sea level change rate are calculated according to this convention. The results of such approach are shown in **Table 3**: in column 1 appear the TG locations, in column 2 the ASLR derived by altimetry, in column 3 the RSLR derived by the TG, and in column 4 the VLM (*u*\_ *<sup>i</sup>* ¼ *g*\_*<sup>i</sup>* � *s*\_*i*) derived by differencing the time series of ASL and RSL monthly time series.

First of all we note that the error of the VLM estimates in the fourth column, obtained as standard error of the trend of the differenced time series (ASL-RSL) are much lower than that provided by the error propagation formula for the difference of the trend estimates of two statistically-independent time series, as in this case the error propagation formula would provide *σgs* ¼ ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi *σ*2 *<sup>g</sup>* þ *σ*<sup>2</sup> *<sup>s</sup>* <sup>2</sup> q , and in the VENEZIA case, for example, it would determine a standard error of 2.26 mm y�<sup>1</sup> instead of the 0.65 mm y�<sup>1</sup> resulting by calculating the trend and the standard deviation of the differentiated time series.

A second aspect worth to note is the independence of each VLM determination from all the others. That means if one of the VLM estimates is affected by large errors or relies on data of bad quality (RSL and/or ASL), it does not influence the evaluation of the others.

The third observation about the numbers reported in **Table 3** is that while the ASLR is almost constant at all sites of the Adriatic Sea considered in this study, the RSLR observed at the TGs are much more varied, determining VLM estimates going from �2.12 to +2.30 mm y�<sup>1</sup> . From one side, this means that the vertical velocity


#### **Table 3.**

*Results of calculations using C3S altimetry dataset (1993–2018). Column 1 reports the TG location; columns 2 and 3 the absolute and relative sea level rates in the altimetry era; column 4 the VLM calculated with the classical approach (ALT-TG). All data are in mm y*�*<sup>1</sup> .*

*Coastal Sea Level Trends from a Joint Use of Satellite Radar Altimetry, GPS and Tide… DOI: http://dx.doi.org/10.5772/intechopen.98243*

field applicable to the Adriatic area is not constant, potentially revealing that different processes could be at the base of the observed crustal motions. From the other side, such numbers reveal also that the VLM is an essential parameter in sea level studies conducted mainly from tide gauge data. Thus, every methodology able to estimate the VLM at the TG is of extreme interest to correct the RSL observed at the TGs themselves, in particular where no geodetic measurements are available to estimate the VLM.

To conclude this section about the classical approach to VLM estimate from sea level data, we report a comparison of the two gridded altimetry datasets: C3S and SLCCI. To provide a fair comparison, both datasets have been limited to the same common period of temporal coverage: 1993–2015. The results of the classical approach to VLM estimate are given in **Table 4**.

Column 4 of **Table 4** reports the RSLR, which is common to both ways to calculate VLM, the classical and the LIPWC.. In columns 2 and 3, differences can be seen in the ASLR measured by C3S and SLCCI: the most notable refers to TRIESTE, which appears to observe an ASLR of 4.51 mm y�<sup>1</sup> in the C3S dataset, and 3.42 mm y�<sup>1</sup> in the SLCCI dataset: these numbers differ by more than 1 mm y�<sup>1</sup> . The difference in ASLR for TRIESTE is reflected in the final VLM rate. Regardless the marked difference for TRIESTE, the other rates appear in good agreement between the two datasets, even if in general C3S supplies lower errors.

So far, we have shown the results of the classical approach to VLM determination from altimetry and tide gauge. From now on we present and analyze the results of the linear inverse problem with constraints, in the modified version which exploit a change of variable to disentangle the contribution of the ASLR from the system. To do so we examine only the results relative to the C3S dataset, for three reasons: first of all, the final results do not differ much between the two datasets; second, the C3S gridded product has an enhanced resolution in the Mediterranean Sea, and an appropriate regional processing; third, the C3S dataset has a time span longer than SLCCI, and most important, it is intended to be continuously updated in the future. VLM results derived with the LIPWC-COV approach are shown in **Table 5**, together with the values of the ASLR and RSLR values used for the calculation, and the VLM derived with the classical approach for ease of comparison.

The difference between the results obtained in the classical approach and the LIPWC-COV approach is evident; while the classical approach range of VLMs is [�2.12 2.30] mm y�<sup>1</sup> , that provided by LIPWC-COV is almost half as wide: [�1.41 0.93]. This is to the result of the introduction of the constraints in Eq. (7), which enter the linear system, propagating the structure and values of the relative vertical motion between the TGs in the solution. The effect of the constraints is best seen in


#### **Table 4.**

*VLM estimates from in situ RSL and remotely observed C3S and SLCCI ASL 1993-2015.*

PSAL is almost co-located with the VENEZIA PUNTA DELLA SALUTE TG. For SPLIT, data from the CGPS station of SPLT were acquired. It is worth mentioning that SPLT is, with PSAL in VENEZIA, among the few CGPS co-located with TGs in the Adriatic Sea. The TRIE CGPS station is the nearest to the TRIESTE TG, but 6.9 km far from it, over a hill north-west of Trieste: for this reason, TRIE CGPS station cannot be considered co-located with the TRIESTE TG. Neither can the PORE CGPS station for ROVNIJ be considered as such, and the DUBR and DUB2 CGPS stations in DUBROVNIK: PORE is located 16 km north of Rovinj along the coast, while DUBR and DUB2 are located 4 km away and 400 m in height. With the data described so far, the VLM can be derived with the classical method, i.e. subtracting the TG RSLR from the ASLR observed by altimetry at the associated grid point. This approach, described in [43], allows to estimate the VLM separately at each location for which RSL and ASL records are available. The error associated to these estimates is drastically reduced when the linear trend of VLM is calculated by differencing the time series of the ASL and RSL, instead of combining the two errors of ASLR and RSLR as they were two independent measurements. From here on, all the errors on the sea level change rate are calculated according to this convention. The results of such approach are shown in **Table 3**: in column 1 appear the TG locations, in column 2 the ASLR derived by altimetry, in column 3 the RSLR derived by the TG, and in column 4 the VLM (*u*\_ *<sup>i</sup>* ¼ *g*\_*<sup>i</sup>* � *s*\_*i*) derived by

*Geodetic Sciences - Theory, Applications and Recent Developments*

differencing the time series of ASL and RSL monthly time series.

**(mm y**�**<sup>1</sup> )**

error propagation formula would provide *σgs* ¼

differentiated time series.

evaluation of the others.

from �2.12 to +2.30 mm y�<sup>1</sup>

**Table 3.**

**108**

**Location** *g*\_

*classical approach (ALT-TG). All data are in mm y*�*<sup>1</sup>*

First of all we note that the error of the VLM estimates in the fourth column, obtained as standard error of the trend of the differenced time series (ASL-RSL) are much lower than that provided by the error propagation formula for the difference of the trend estimates of two statistically-independent time series, as in this case the

case, for example, it would determine a standard error of 2.26 mm y�<sup>1</sup> instead of the 0.65 mm y�<sup>1</sup> resulting by calculating the trend and the standard deviation of the

A second aspect worth to note is the independence of each VLM determination from all the others. That means if one of the VLM estimates is affected by large errors or relies on data of bad quality (RSL and/or ASL), it does not influence the

The third observation about the numbers reported in **Table 3** is that while the ASLR is almost constant at all sites of the Adriatic Sea considered in this study, the RSLR observed at the TGs are much more varied, determining VLM estimates going

VENEZIA 3.36 � 1.45 5.15 � 1.73 �1.79 � 0.65 VEPTF 3.38 � 1.46 5.50 � 1.73 �2.12 � 0.67 TRIESTE 3.75 � 1.58 3.56 � 1.66 0.18 � 0.60 ROVINJ 3.33 � 1.58 1.03 � 1.85 2.30 � 1.06 SPLIT 3.60 � 1.36 2.92 � 1.65 0.68 � 0.63 DUBROVNIK 3.34 � 1.22 3.79 � 1.48 �0.45 � 0.55

*Results of calculations using C3S altimetry dataset (1993–2018). Column 1 reports the TG location; columns 2 and 3 the absolute and relative sea level rates in the altimetry era; column 4 the VLM calculated with the*

*.*

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi *σ*2 *<sup>g</sup>* þ *σ*<sup>2</sup> *<sup>s</sup>* <sup>2</sup> q

. From one side, this means that the vertical velocity

*s*\_ **(mm y**�**<sup>1</sup> )** , and in the VENEZIA

ð Þ *g*\_ � *s*\_ **(mm y**�**<sup>1</sup> )**


were attained by a different methodology in calculating the rates of absolute and relative sea level change rates and their formal errors. Moreover, in the years following 2010 the VLM rates at the five common TG locations have remained substantially unmodified with respect to the Wöppelmann and Marcos' results. As a final step regarding VLM, we have calculated the root mean square difference (RMSD) of the VLM calculated with GPS and those calculated with the classical and the new (LIPWC-COV) approaches and found that the second one is lower: Classic

*Coastal Sea Level Trends from a Joint Use of Satellite Radar Altimetry, GPS and Tide…*

; LIPWC-COV approach: 1.34 mm y<sup>1</sup>

The discrepancy observed between this study and that of Wöppelmann and Marcos can largely be ascribed to the different periods covered by the altimetry datasets (C3S and SLCCI datasets cover time periods respectively 44% and 23% longer than the study of Wöppelmann and Marcos). Other factors that may contribute to explain the difference between the results of the two studies are the processing of the altimetry data and the inclusion of the VEPTF TG in this study. The rates of absolute sea level change at the TGs, calculated as the sum of relative sea level change and VLMs derived in this study with the LIPWC-COV approach,

for the whole period covered by the TG record, are reported in **Table 6**.

2.33–2.71, with a sample mean of 2.43 mm y<sup>1</sup>

(1974–2018) are shown in **Figure 6**.

**Table 6.**

**111**

*approach. All data are in mm y<sup>1</sup>*

The uncertainty of the sample mean (last row of **Table 6**) was obtained as standard error of the sample mean, considering the rates as random and independent variables. The absolute sea level change rates vary in a very narrow interval,

is much lower than the precision of each individual determination of SL change rate at the TGs. As pointed out by Wöppelmann and Marcos [50], such a low dispersion is unlikely to be determined from estimates of independent random variables: it is instead the evidence of the high performance of LIPWC method for determining accurate VLM rates from TG and altimetry differenced time series. The ASLR rates calculated by altimetry in 1993–2018 and through the LIPWC-COV technique

Clearly, the ASLR values calculated for the longer period are smaller than those

calculated in the shorter one, but the modulation of the rate from TG to TG is apparently reflected in the LIPWC-COV approach. As already noted, the errors associated to the ASLR rates derived in the LIPWC-COV are also smaller, thanks to the introduction of the constraints on the relative vertical land motion between paired TGs. The mean value of the ASLR calculated for the Adriatic Sea with the LIPWC-COV approach, is in general agreement with both regional studies on the Mediterranean Sea (0.7 0.2 mm y<sup>1</sup> (1945–2000) [65]; 1.60 0.35 mm y<sup>1</sup> (1992–2010) [50]; 2.44 0.5 mm y<sup>1</sup> (1993–2012) [66]; 2.87 0.33 mm y<sup>1</sup> (1992–2016) [67]),

**Location** \_

*.*

VENEZIA 2.33 0.83 VEPTF 2.37 0.86 TRIESTE 2.71 0.75 ROVINJ 2.29 0.80 SPLIT 2.57 0.74 DUBROVNIK 2.28 0.74 Pooled mean 2.43 0.80 Sample mean 2.43 0.18

*ASLR from TG records over whole period 1974–2018, corrected for VLM estimated with the LIPWC-COV*

.

. The standard deviation of the sample

*ζ***-***VLMLIPWC-COV*

approach: 1.84 mm y<sup>1</sup>

*DOI: http://dx.doi.org/10.5772/intechopen.98243*

**Table 5.**

*VLM results using C3S altimetry dataset (1993–2018). Location in column 1; ASLR in column 2; RSLR in the altimetry era (1993-2018) in column 3; RSLR 1974-2018 in column 4; VLM calculated with the classical approach in column 5, as in column 4 of Table 3, and with the LIPWC-COV in column 6. Columns 7 reports the VLM values directly detected by the GPS stations associated with three TGs.*

**Figure 5**, where the plot of the LIPWC-COV solution follows the general form of the classical solution, but with a reduced spread.

In **Figure 5** are reported also the VLM values measured by the CGPS stations of PSAL (VENEZIA), TRIE (TRIESTE) and SPLT (SPLIT), and the values of VLM estimated by Wöppelmann and Marcos [50] with the LIPWC technique without the change of variable.

In the classical approach, as there is no optimization of errors as in the LIPWC technique, we see a wide spread of the VLM values. This is particularly evident for ROVINJ TG, whose ð Þ *<sup>g</sup>*\_ � *<sup>s</sup>*\_ estimates reach more than 2 mm y�<sup>1</sup> , while the LIPWC-COV approach calculates it as less than 1 mm y�<sup>1</sup> . The LIPWC solution proposed by Wöppelmann and Marcos [50] presents much lower standard errors than LIPWC-COV solution described in this study. We presume that such low standard errors

#### **Figure 5.**

*Scatterplots of VLM values derived with the classical* ð Þ g\_ � s\_ *and the LIPWC-COV approaches using the C3S altimetry dataset (period 1993–2018). GPS estimates (in black) are also reported. Results from the study of Wöppelmann and Marcos (W&M) for the period 1992–2010 are shown in green for comparison. The zero level is drawn in black. (adapted from [58]).*
