1. Introduction
Sea level rise is one of the most important threats caused by climate change on coastal areas. Despite the uneven distribution of tidegauges with long time series, global mean sea level has been reconstructed during the twentieth and twenty first centuries by means of Reduced Space Optimal Interpolation [
1,
2,
3,
4,
5] and Optimal Statistical Interpolation [
6]. These works and the recent use of altimetry data have revealed that global mean sea level increased at a rate of 1.7 mm/yr [1.3 to 2.2 mm/yr] from 1901 to 2018, and this rate has accelerated to 3.7 mm/yr [3.2 to 4.2 mm/yr] for the period 20062018 [
7,
8]. The main causes of sea level rise were the ocean warming and the melting of glaciers, and of Greenland and Antarctica Ice Sheets, [
9,
10,
11]. However, changes in the global mean sea level could not be representative of local or regional ones [
8,
12], and the assessment of such changes is of paramount importance for establishing adaptation strategies [
13].
Changes in local mean sealevel can be decomposed into a mass component (manometric sealevel change) and a density component (steric sealevel change) [
14,
15]. The latter can be further decomposed into thermosteric and halosteric sealevel changes. Although the halosteric contribution is considered to be negligible on a global scale [
14,
16], it could have a great importance on a local or regional one [
17], and in concentration basins such as the Mediterranean Sea [
15,
18,
19]. The mass component of sea level can be inferred subtracting the steric contribution to the observed sea level, or recently, since the launch of the GRACE mission in 2002, from gravimetry measurements. Nevertheless, the gravimetry data have a coarse resolution of 300 km [
20] and therefore cannot be used for local or even regional studies. For instance, in the case of the Mediterranean Sea, [
19] found that these data could be used to infer the mass component for the whole Mediterranean Sea, but were not suitable for smaller spatial scales.
The main goal of this work is to analyse the longterm trends of relative sea level change (RSLC) on a local scale in the north, west and south Atlantic coasts of the Iberian Peninsula, the Canary Islands, and the Spanish Mediterranean coasts, including the Balearic Islands. Long time series from tidegauges are used for the analysis of the period 19482019, and both, tidegauge data, and altimetry data (in this case relative to the reference ellipsoid; geocentric sealevel change, [
14]) are compared for the more recent period 19932019. Previous works have corrected the observed sea level for the atmospheric forcing by means of barotropic 2D models forced by realistic pressure and wind fields [
21,
22,
23,
24]. The thermosteric and halosteric contributions to RSLC have been calculated from vertical profiles of temperature and salinity compiled in different data bases or from reanalysis projects [
15,
25,
26]. In this work we follow a different approach, already used in [
27]. Monthly time series of atmospheric pressure, zonal and meridional components of the wind, and thermosteric and halosteric contributions were calculated from different databases. Then a multiple linear regression was used to determine which factors contributed to the sea level variability and to estimate their contributions to the observed sea level trends.
Section 2 describes the data used and the methodology applied.
Section 3 presents the results, and finally a discussion and summary of the main results are presented in section 4.
4. Discussion and Conclusions
The atmospheric correction by means of the linear regression model yields the expected results for the pressure and the alongshore component of the wind, in those cases where the coast has a clear orientation. Assuming that the sea reaches the equilibrium state after a change of pressure
ΔP, the response of sea level should be:
The mean surface density in the area of study ranges between 1025.9 kg/m
^{3} at the Canary Islands, and 1027.1 kg/m
^{3} at the northernmost tide gauges of the Mediterranean Sea. According to these values, the relation between the sea level variations and those of the atmospheric pressure should be between 9.94 and 9.95 mm/mbar, that can be rounded to 10 mm/mbar and which is the wellknown inverse barometer effect (see for instance [
14]). Taking into account the uncertainty of the coefficients calculated in the linear regression, most of such coefficients are not different from the theoretical value (column #3 in
Table 3 and
Table 4).
It is more difficult to predict quantitatively the response of sea level to the wind variability. Nevertheless, our results show a qualitative agreement with the expected upwelling and downwelling processes along the northern and southern coasts of the Iberian Peninsula, as well as on its Atlantic coast. Westerly (positive) and northerly (negative) winds induce upwelling (decrease of sea level) on the southern and Atlantic coasts respectively. Therefore, the coefficients of the linear regression were negative in the first case and positive in the second one (see columns #4 and #5 in
Table 4 and
Table 4). In the northern coast of the Iberian Peninsula, westerly winds were responsible for downwelling (increase of sea level), yielding a positive value for the coefficient of the
U component of the wind at Santander. The numerical values for these coefficients showed that the sea level change for m/s of variation of the wind is comparable to the effect of sea level change for each mbar of pressure.
The atmospheric contribution to the sealevel change is frequently estimated by means of 2D barotropic circulation models [
21,
22,
23,
24]. The final validation of these results is usually done calculating the variance reduction of the tidegauge time series, or calculating the correlation coefficients between observed sea level and that predicted by the 2D barotropic models. [
23] found a correlation ranging between 0.6 and 0.7 depending on the tide gauge considered, and [
42] found correlations as high as 0.8. If the linear model was applied, considering only the atmospheric forcing, the multiple correlation coefficients ranged between 0.49 and 0.78, with the only exception of Arrecife, where it was 0.37. In any case, the statistical model used in this work should be only considered as a complementary approach to the numerical modeling, as the response of sealevel to the atmospheric forcing could be far from linear in some cases, depending on the topography and geometry of the coast. The explanation of the coefficients of the thermosteric and halosteric contributions to sea level presents more difficulties. The sea level variability can be decomposed into a mass and a steric contribution. The latter can be divided into thermosteric and halosteric ones. This decomposition can be expressed by means of equation (6) (see [
15] for a detailed discussion of this expression and the interpretation of the different terms of it):
δm is the mass in a water column of area δA. The first term in the right hand side of equation (6) is the change in sea level produced by the change of mass per unit of area. The second and third terms are the thermosteric and halosteric contributions as defined in (1.2) and (1.3). Let us consider that we know the monthly change of sea level at any tide gauge or position where altimetry data are available. If we also know the change that the temperature and salinity have experienced along the water column for the same location and month, we could calculate their contributions to the observed sea level variability. In other words, according to equation (6), the coefficients that relate the thermosteric and halosteric terms and the observed sea level should be 1. If we wanted to calculate the mass component of the sea level variability we should simply subtract both contributions from the sea level change. However, the coefficients for these two predictors were always below 1 in the linear regression. Furthermore, in some cases the forward stepwise regression model did not select some of these predictors for explaining the variance of sea level. This simply indicates that, in those cases, the time series of thermosteric and halosteric contributions were not significantly correlated with the observed sea level. As explained in the results section, this cannot be attributed to the possible colinearity of the thermosteric and halosteric sealevel changes. Nor it can be attributed to the data base used, as similar results were obtained using the NCAR/UCAR Research Data Archive and the RADMED project data. Therefore there are two possible explanations for this result.
First, the temperature and salinity data used for determining the steric contribution for each tide gauge or altimetry grid point, corresponded to a large area of 1º x 1º. This large area does not necessarily represent the local conditions of the tide gauges. If the steric component of sea level was spatially homogeneous, it would not be a problem to use this large geographical area of 1º x 1º in our calculations. On the contrary, we cannot be sure that the same kind of seaatmosphere interaction occurs in coastal and opensea waters, and the 1:1 relationship would not hold necessarily. We should be careful interpreting this result. It does not mean that the equation (6) is not right, or that equations (1.2) and (1.3) do not represent the steric contributions to the sea level variability. It would simply mean that the available time series of temperature and salinity profiles, represent the real conditions at the open sea, but they are not representative of the local changes occurring at the costal tide gauges.
This explanation has another problem. The altimetry sea level also corresponds to an opensea area similar to that representative of the temperature and salinity profiles used for the calculation of the steric contribution. Neither in this case the η_{T} and η_{H} predictors were significantly correlated with the altimetry sealevel in all the locations, and in those cases when these predictors were selected by the linear model, the coefficients were also lower than 1, as in the case of tidegauge data.
A second explanation is that the available temperature and salinity data do not yield reliable estimations of the steric contributions, neither for the opensea areas, nor for the coastal ones. This problem has already been evidenced by [
19] for the case of the Mediterranean Sea. These authors pointed out that the different available data bases did not allow obtaining consistent estimations of the steric component of the sea level and of the mass of salt contribution. As a consequence of this, consistent estimations of the contribution of the mass of freshwater could not be obtained. This problem arises from the scarcity of temperature and salinity data along the water column which makes very difficult to calculate the monthly, interannual and long term variability of the heat and salt content in the upper layer of the sea, where there is a very large natural variability [
45,
46]. [
47] subsampled the results from a numerical model at the same times and locations where real temperature and salinity profiles were available. These authors interpolated the subsampled data onto a regular 3D grid on a monthly basis. Linear trends estimated from these interpolated data were not able to capture the real longterm variability of the simulated data, evidencing the limitations of the present gridded climatologies.
Taking into account all the problems related to the scarcity of data, we considered that the monthly thermosteric and halosteric contributions calculated in the present work could not be the real ones, but still could have a certain correlation with them. Once again the coefficients relating the observed sea level to the thermosteric and halosteric contributions would not be 1 and we could not subtract directly such contributions to calculate the addition of mass.
Either the first explanation is true, or the second one, the degree of correlation between the observed sea level and the available steric contributions was determined by the time series themselves, and the stepwise correlation analysis. In those cases in which there was a significant correlation, the coefficients that related the observed sea level to
η_{T} and
η_{H} and the linear trends calculated for these predictors were used to estimate the thermosteric and halosteric contributions to the linear trends of sea level. In such cases, the salinity profiles were also used to estimate the contribution of the mass of salt. Notice that as expression (1.3) is not directly used to estimate the contribution of the halosteric component, it would not be consistent to use equation (1.4) for the calculation of the mass of salt. If (1.4) is divided by (1.3), and neglecting the variability of
β along the water column compared to the changes in
ΔS, the ratio of both contributions would be
being
ρ_{0} and
β_{0} some average or reference values. Therefore, the mass of salt contribution was estimated as the halosteric contribution multiplied by the factor (7). It could also be argued that the term (1.4) could have been included as another predictor in the linear model and the mass of salt could have been estimated directly by the linear regression. In such case the two predictors given by equations (1.3) and (1.4) would be proportional and the resulting system of equations would be illconditioned.
In those cases in which none of
η_{T} and
η_{H} were significantly correlated with the sea level, those predictors were not used to estimate the mass contribution of sea level. We have to emphasize that this does not mean that there is no steric contribution to the observed sea level, nor contribution of the mass of salt. It simply means that the available time series of steric contribution do not resemble the real ones and therefore cannot be used for this purpose.
Figure 4A (period 19482019) and
4C (period 19932019) show the mass contribution of sea level, once corrected for the atmospheric forcing. This contribution includes the addition of freshwater and salt.
Figure 4B and
4D show the contribution of the mass of salt (red triangles) and the contribution of the mass of freshwater. In those figures corresponding to the 19932019 period, both the tide gauge (black lines) and the altimetry (blue lines) analyses have been included.
Considering the long period 19482019, only tide gauge data were available. Gibraltar sea level trend was negative (see column #2 in
Table 1) and so was the contribution of mass addition and freshwater (
Figure 4A and B). This is not a reliable result and indicates that some sort of leveling or any other problem affected to this tide gauge during this period. For this reason, this tide gauge will be excluded in the following discussion. The sea level, averaged for the whole area, (corrected for the effect of GIA) increased at a rate of 1.58 ± 0.19 mm/yr. This result is coincident with the trend observed for Global Mean Sea Level (GMSL) from 1901 to 2018, which is 1.7 mm/yr [
7,
8]. During this period, the atmospheric pressure had a positive trend in all the tide gauges analysed which induced a decrease of the sea level. However, the behavior of the thermosteric and halosteric contributions and that of the addition of mass of salt had different values for the different geographical areas analyzed. Averaging the results for the Atlantic coast of the Iberian Peninsula (northern and western coasts), the RSLC was 2.05 ± 0.21 mm/yr. It was observed a warming and salting of the water column which produced positive and negative trends for the thermosteric and halosteric sealevel changes. Nevertheless, there was no significant correlation between these terms and the observed RSLC. Hence, the thermosteric, halosteric and mass of salt terms did not contribute significantly to the RSLC and the addition of mass and that of freshwater were the same and larger than the observed RSLC (2.3 ± 0.4 mm/yr).
This is an unrealistic result. The water column has warmed during the period 19482019 (see column #6 in
Table 1). Although the halosteric term had a negative trend that could partially counterbalance the thermosteric one, it is also associated to a positive contribution of the term of mass of salt. Therefore, the warming of the oceans, that have absorbed the 90 % of the heat stored by the Earth Climate System [
48], should have contributed to the RSLC as observed on a global scale [
9]. The lack of correlation between our
η_{T},
η_{H} time series and the RSL do not allow us to use them for the calculation of their contribution to the sea level trends. It could be argued that the available thermosteric and halosteric time series are not able to reproduce the monthly and interannual variability of sea level, but they still could capture its longterm variability. In that case, we could simply subtract the thermosteric and halosteric trends to the sea level trend to obtain that of the mass component. This would be equivalent to accept that the coefficients relating
η_{T} and
η_{H} to sea level are lower than 1 for the monthly and interannual time scales, but they are equal to 1 for the long time scales. Similarly, the mass of salt could be directly subtracted to the mass component to assess the change of mass of freshwater. When these calculations were carried out, the results were unrealistic, with negative freshwater contributions in some cases.
In the case of the Canary Islands, for this period of time (19482019) the RSL increased at a rate of 1.09 ± 0.14 mm/yr, with a mass contribution of 1.3 ± 0.3 mm/yr. Once again the analysis of the steric and salt contributions did not yield significant results. Finally, in the case of the southern Atlantic Iberian coast and that of the Mediterranean Sea, the sea level trend was 1.35 ± 0.18 mm/yr, which is similar to that obtained for the Western Mediterranean by [
6] (1.2 ± 0.14 mm/yr). The thermosteric and the mass of salt contributions were positive and the halosteric one was negative yielding contributions of 1.6 ± 0.4, 0.15 ± 0.05 and 1.5 ± 0.4 mm/yr for the mass, mass of salt and mass of freshwater contributions respectively. These results are more in agreement with other works that estimate that the addition of fresh water on a global scale is higher than 1 mm/yr [
49] or 1.31 mm/yr [
9]. Nevertheless, it should be taken into account that these latter estimations correspond to the 1990s decade and the first decade of the present century, whilst our results are calculated for a longer period of time.
The discussion above suggests that the available temperature and salinity data are not suitable for the analysis of the monthly, interannual, and longterm variability of the steric and mass of salt components of sea level. This would support those results in [
19,
47]. [
46] also showed that the available temperature and salinity data collected in the Mediterranean Sea during the second half of the twentieth century and the first decades of the twenty first one, could not capture the longterm trends of these variables at the upper layer of the sea, because of the scarcity of data combined with the large natural variability of this layer. Despite the data scarcity problem, it should be considered that these tide gauges are not provided with GNSS receivers. As no altimetry data are available for comparison during this period, other problems such as vertical land movements, or changes in the location of the instruments, that have not been properly documented, could not be discarded.
Both tide gauges and altimetry data are available for the period 19932019. The comparison of these results shows that trends estimated from altimetry data are quite homogeneous (see
Table 5 and
Table 6 and blue lines in
Figure 4). When averaging for the whole area of study, the RSL increased at a rate of 2.8 ± 0.3 mm/yr with mass, salt and freshwater contributions of 2.8 ± 0.5, 0.10 ± 0.09, and 2.7 ± 0.6 mm/yr. The results obtained from the analysis of tide gauge data are much more variable reflecting possible local effects or even errors in the instrumentation. However, these effects are canceled when the results are averaged, and the trends estimated for RSL, mass, salt, and freshwater contributions are similar to those calculated from altimetry data: 2.5 ± 0.7, 2.7 ± 1.1, 0.25 ± 0.25 and 2.5 ± 1.4 mm/yr respectively.
During this recent period there are no contributions from the atmospheric forcing. Although these variables were significantly correlated with the observed sea level (
Table 4), the atmospheric pressure did not show any longterm trend, whereas the
U and
V components of the wind increased in some cases and decreased in others. The agreement between the altimetry and tide gauge results confirm the acceleration of the sea level trends during recent decades, but once again the observed sea level was not significantly correlated to the thermosteric and halosteric components in most of the cases. Consequently, the linear model is not able to estimate the steric contribution, nor it can estimate the mass, salt, and freshwater ones. Nevertheless, it is worth considering the particular case of L'Estartit. It is well known that the WMED has undergone a warming process along the twentieth century which has accelerated during the beginning of the twenty first one. Therefore, the thermosteric component should contribute not only to the monthly and interannual variability of the sea level variability, but also to its longterm trend (see column #6 in table 6), as observed on a global scale [
7,
8,
9]. On the other hand, this sea has also suffered an intense salinity increase [
18,
46,
50] and there should be a negative contribution of the halosteric component and a positive one of the mass of salt (column #7 in table 6 and
Figure 4D). In this case all the predictors, both those representing the atmospheric forcing (
P, U, V) and the thermosteric and halosteric components, contributed to the observed sea level variability (see
Table 4 and
Table 6). Furthermore, the linear model has a multiple correlation coefficient of 0.88, which means that the model is able to explain the 77 % of the sea level variance. Hence, we can be confident that the different contributions to the longterm trends of the sea level are accurately estimated. These results indicate that the sea level increased at L'Estartit at a rate of 2.7 ± 0.8 mm/yr since 1993. The atmospheric forcing is significantly correlated with the RSL and explains part of the monthly and interannual variability, but as these variables did not experience any longterm trend during the period 19932019, they did not contribute to the sea level linear trend. The thermosteric and halosteric contributions were positive and negative, as expected, and the resulting mass addition had a positive trend of 3.3 ± 1.9 mm/yr. The mass of salt contribution was 1.9 ± 1.0 mm/yr and the freshwater contribution was 1.4 ± 2.9 mm/yr for the tidegauge data, and 1.3 ± 2.0 for the altimetry ones. The large uncertainty in the latter component arises from the formula for the expansion of errors. As the trend for the mass of freshwater is derived from the subtraction of the mass of salt from the mass component, its uncertainty is the sum of both errors. However, the obtained value is close to those recently reported, based on the melting of glaciers and Greenland and Antarctic ice sheets [
9,
49] who estimated this contribution as 1.31 mm/yr. Furthermore, in the case of L'Estartit, the estimations of the sea level linear trends, and its different components, are almost the same when calculated from tide gauge or altimetry data. Our hypothesis is that the good behavior of the statistical model for L'Estartit arises from the quality of the data. First, the tide gauge started operating in recent decades (1990) with no location changes or any other known problem. Beside this, its location is very close to an area very intensively sampled by different monitoring programs [
51], and has received considerable attention because of its proximity to the area of formation of Western Mediterranean Deep Water.
In summary, averaging for all the tide gauges, it can be stated that the sea level increased at a rate of 1.58 ± 0.19 mm/yr from 1948 to 2019. The large dispersion of these results, based on the analysis of tidegauge data, makes it difficult to estimate differences between the three large geographical areas analyzed: Atlantic Iberian Peninsula, Canary Islands, and Southern Peninsula and Spanish Mediterranean Sea. The trends of sea level accelerated during the period 19932019. The results for the three areas and both for tidegauge and altimetry data are very similar (indistinguishable within the uncertainty level) and range from 2.3 ± 0.8 to 3.0 ± 0.3 mm/yr. The available data do not allow us to estimate the thermosteric and halosteric contributions in a reliable way, and therefore the mass and salt components cannot be estimated. According to previous works, this seems to be the result of the data scarcity. On the contrary, the results from L'Estartit, which is located in a well sampled area, allowed us to estimate the positive and negative contributions of the thermosteric and halosteric components of sea level, and the mass of salt. The mass of freshwater at this location increased at a rate of 1.4 ± 2.9 mm/yr for tide gauge data, and 1.3 ± 2.0 mm/yr for the altimetry data, in agreement with recent observations derived from glacier ice melting. These results evidence once more the importance of the monitoring systems of the oceans for estimating the different contributions to the present sea level rise.
Figure 1.
Black dots show the position of tidegauges with long time series, used for their analysis. Black circles show those tidegauges with short time series that are not suitable for the analysis of longterm trends, but were used for filling or extending the long time series.
Figure 1.
Black dots show the position of tidegauges with long time series, used for their analysis. Black circles show those tidegauges with short time series that are not suitable for the analysis of longterm trends, but were used for filling or extending the long time series.
Figure 2.
Time series of sea level anomalies for the northern and western coasts of the Iberian Peninsula, and the Canary Islands. Black lines show the time series of sea level anomalies and red lines show the regression on the predictors selected by the stepwise forward linear regression. Each row corresponds to a different location: Santander (A, B, C), Vigo (D, E, F), A Coruña (G, H, I), Leixoes (J, K, L), Cascais (M, N, O), Arrecife (P, Q, R), Las Palmas (S, T) and Tenerife (U, V, W). The left, central and right columns correspond to the tide gauge data for the period 19482019, tide gauge data for the period 19932019, and altimetry data for the period 19932019 respectively. Linear trends corrected for GIA have been inserted.
Figure 2.
Time series of sea level anomalies for the northern and western coasts of the Iberian Peninsula, and the Canary Islands. Black lines show the time series of sea level anomalies and red lines show the regression on the predictors selected by the stepwise forward linear regression. Each row corresponds to a different location: Santander (A, B, C), Vigo (D, E, F), A Coruña (G, H, I), Leixoes (J, K, L), Cascais (M, N, O), Arrecife (P, Q, R), Las Palmas (S, T) and Tenerife (U, V, W). The left, central and right columns correspond to the tide gauge data for the period 19482019, tide gauge data for the period 19932019, and altimetry data for the period 19932019 respectively. Linear trends corrected for GIA have been inserted.
Figure 3.
Time series of sea level anomalies for the southern Atlantic coast of the Iberian Peninsula, and the Spanish Mediterranean coast (including the Balearic Islands). Black lines show the time series of sea level anomalies and red lines show the regression on the predictors selected by the stepwise forward linear regression. Each row corresponds to a different location: Cádiz (A, B, C), Tarifa (D, E, F), Algeciras (G, H, I), Ceuta (J, K, L), Málaga (M, N, O), Alicante (P, Q, R), L’Estartit (S, T) and Palma (U, V). The left, central and right columns correspond to the tide gauge data for the period 19482019, tide gauge data for the period 19932019, and altimetry data for the period 19932019 respectively. Linear trends corrected for GIA have been inserted.
Figure 3.
Time series of sea level anomalies for the southern Atlantic coast of the Iberian Peninsula, and the Spanish Mediterranean coast (including the Balearic Islands). Black lines show the time series of sea level anomalies and red lines show the regression on the predictors selected by the stepwise forward linear regression. Each row corresponds to a different location: Cádiz (A, B, C), Tarifa (D, E, F), Algeciras (G, H, I), Ceuta (J, K, L), Málaga (M, N, O), Alicante (P, Q, R), L’Estartit (S, T) and Palma (U, V). The left, central and right columns correspond to the tide gauge data for the period 19482019, tide gauge data for the period 19932019, and altimetry data for the period 19932019 respectively. Linear trends corrected for GIA have been inserted.
Figure 4.
Figure 4A shows the contribution to the sea level linear trends of the addition of mass (black lines).
Figure 4B shows the contribution to the sea level linear trends of the addition of freshwater (black line) and the mass of salt (red triangles). Both
Figure 4A and
4B correspond to the period 19482019 and the 17 tide gauges analyzed. Shaded areas and red vertical bars are the 95 % confidence intervals.
Figure 4C, and
Figure 4D, show similar results for the period 19932019. In these cases, black lines correspond to the analysis of the 17 tide gauges, and the blue lines to the analysis of the altimetry data from the 17 grid points closest to the tide gauges. In all the cases the xaxis shows the initial of the tide gauges: Santander (S), Vigo (V), A Coruña (A), Leixoes (L), Cascais (C), Arrecife (Ar), Las Palmas (LP), Tenerife (Te), Cádiz (C), Tarifa (T), Algeciras (Al), Gibraltar (G), Ceuta (C), Málaga (M), Alicante (Ali), L’Estartir (Le) and Palma (P).
Figure 4.
Figure 4A shows the contribution to the sea level linear trends of the addition of mass (black lines).
Figure 4B shows the contribution to the sea level linear trends of the addition of freshwater (black line) and the mass of salt (red triangles). Both
Figure 4A and
4B correspond to the period 19482019 and the 17 tide gauges analyzed. Shaded areas and red vertical bars are the 95 % confidence intervals.
Figure 4C, and
Figure 4D, show similar results for the period 19932019. In these cases, black lines correspond to the analysis of the 17 tide gauges, and the blue lines to the analysis of the altimetry data from the 17 grid points closest to the tide gauges. In all the cases the xaxis shows the initial of the tide gauges: Santander (S), Vigo (V), A Coruña (A), Leixoes (L), Cascais (C), Arrecife (Ar), Las Palmas (LP), Tenerife (Te), Cádiz (C), Tarifa (T), Algeciras (Al), Gibraltar (G), Ceuta (C), Málaga (M), Alicante (Ali), L’Estartir (Le) and Palma (P).
Table 1.
Linear trends for the period 19482019. Column #1 indicates the location and the relative sea level contribution by GIA obtained from the PSMSL [
33,
34,
35]. Column #2 presents sea level trends for tide gauge data. Columns #3 through #7 show those significant trends for the atmospheric pressure,
U component of the wind,
V component of the wind, thermosteric, and halosteric contributions of sea level. Linear trends for sea level at column #2 are corrected for the effect of GIA.
Table 1.
Linear trends for the period 19482019. Column #1 indicates the location and the relative sea level contribution by GIA obtained from the PSMSL [
33,
34,
35]. Column #2 presents sea level trends for tide gauge data. Columns #3 through #7 show those significant trends for the atmospheric pressure,
U component of the wind,
V component of the wind, thermosteric, and halosteric contributions of sea level. Linear trends for sea level at column #2 are corrected for the effect of GIA.
Period 
Linear trends (b ± 95 % CI). Tide gauges. 
19482019 
Sea Level b 
Pressure b_{P}

Uwind b_{U}

Vwind b_{V}

Thermost. b_{T}

Halost. b_{H}

Location (GIA) 
mm/yr 
dbar/yr 
ms^{1}/yr 
ms^{1}/yr 
mm/yr 
mm/yr 
Santander (0.11) 
2.08 ± 0.21 
0.02 ± 0.01 
0.01 ± 0.01 
0.01 ± 0.00 
0.62 ± 0.10 
0.36 ± 0.15 
Vigo (0.12) 
2.66 ± 0.24 
0.02 ± 0.01 


1.72 ± 0.16 
1.41 ± 0.18 
A Coruña (0.0) 
2.29 ± 0.22 
0.02 ± 0.01 


1.18 ± 0.14 
0.78 ± 0.17 
Leixoes (0.2) 
1.61 ± 0.20 
0.02 ± 0.01 


1.78 ± 0.17 
1.41 ± 0.19 
Cascais (0.07) 
1.62 ± 0.19 
0.02 ± 0.01 


1.98 ± 0.20 
1.26 ± 0.24 
Arrecife (0.01) 
0.59 ± 0.16 
0.02 ± 0.01 

0.01 ± 0.01 
0.96 ± 0.15 

Las Palmas (0.05) 






Tenerife (0.09) 
1.59 ± 0.12 
0.02 ± 0.01 

0.02 ± 0.00 
1.19 ± 0.12 
0.32 ± 0.13 
Cádiz (0.18) 
2.62 ± 0.21 
0.02 ± 0.01 
0.01 ± 0.01 

1.43 ± 0.12 
1.16 ± 0.25 
Tarifa (0.18) 
1.38 ± 0.21 
0.02 ± 0.01 


1.48 ± 1.13 
1.21 ± 0.25 
Algeciras (0.19) 
1.00 ± 0.14 
0.02 ± 0.01 


1.48 ± 0.13 
1.21 ± 0.25 
Gibraltar (0.19) 
0.18 ± 0.16 
0.02 ± 0.01 


1.48 ± 0.13 
1.21 ± 0.25 
Ceuta (0.18) 
0.89 ± 0.15 
0.02 ± 0.01 


1.48 ± 0.13 
1.21 ± 0.25 
Málaga (0.23) 
1.40 ± 0.19 
0.02 ± 0.01 

0.01 ± 0.00 
1.53 ± 0.13 
1.51 ± 0.24 
Alicante (0.05) 
0.82 ± 0.17 
0.02 ± 0.01 

0.01 ± 0.00 
1.44 ± 0.09 
1.91 ± 0.15 
L’Estartit (0.06) 






Palma (0.25) 






Table 2.
Linear trends for the period 19932019. Column #1 indicates the location. Column #2 presents two values. The upper one is for sea level trends estimated from tide gauge data, and the lower one from altimetry data. Columns #3 through #7 show those significant trends for the atmospheric pressure, U component of the wind, V component of the wind, thermosteric, and halosteric contributions of sea level. Linear trends for sea level from tide gauges at column #2 are corrected for the effect of GIA.
Table 2.
Linear trends for the period 19932019. Column #1 indicates the location. Column #2 presents two values. The upper one is for sea level trends estimated from tide gauge data, and the lower one from altimetry data. Columns #3 through #7 show those significant trends for the atmospheric pressure, U component of the wind, V component of the wind, thermosteric, and halosteric contributions of sea level. Linear trends for sea level from tide gauges at column #2 are corrected for the effect of GIA.
Period 
Linear trends (b ± 95% CI) Tide gauges and altimetry. 
19932019 
Sea level b 
Pressureb_{P}

Uwind b_{U}

Vwind b_{V}

Thermost. b_{T}

Halost. b_{H}

Location 
mm/yr 
dbar/yr 
ms^{1}/yr 
ms^{1}/yr 
mm/yr 
mm/yr 
Santander Tide Gauge Altimetry 
2.0 ± 0.8 2.56± 0.25 

0.02 ± 0.02 
0.02 ± 0.02 

1.5 ± 0.7 
Vigo Tide gauge Altimetry 
1.4 ± 0.9 2.9± 0.3 



0.9 ± 0.8 

A Coruña Tide Gauge Altimetry 
3.0 ± 0.9 2.69 ± 0.25 



1.1 ± 0.6 
0.7 ± 0.7 
Leixoes Tide gauge Altimetry 
1.3 ± 0.8 3.07± 0.25 

0.02 ± 0.02 
0.03 ± 0.02 

1.0 ± 0.9 
Cascais Tide gauge Altimetry 
3.8 ± 0.5 2.8± 0.3 


0.05 ± 0.03 


Arrecife Tide gauge Altimetry 
1.4 ± 0.5 3.0 ± 0.3 

0.03 ± 0.02 
0.03 ± 0.02 

1.0 ± 0.6 
Las Palmas Tide gauge Altimetry 
3.3 ± 0.5 2.9 ± 0.3 

0.02 ± 0.02 
0.02 ± 0.02 
0.8 ± 0.5 

Tenerife Tide gauge Altimetry 
3.4± 0.8 3.1± 0.3 

0.02 ± 0.02 
0.02 ± 0.02 
1.5 ± 0.5 

Cádiz Tide gauge Altimetry 
1.3 ± 0.9 3.2± 0.3 


0.03 ± 0.02 
0.7 ± 0.6 
2.8 ± 1.1 
Tarifa Tide gauge Altimetry 
4.7 ± 0.7 2.5± 0.3 



2.4 ± 0.7 
1.5 ± 1.2 
Algeciras Tide gauge Altimetry 
2.3 ± 0.6 2.4± 0.4 



2.4 ± 0.7 
1.5 ± 1.2 
Gibraltar Tide gauge Altimetry 
4.7 ± 0.6 2.4± 0.4 



2.4 ± 0.7 
1.5 ± 1.2 
Ceuta Tide gauge Altimetry 
1.9 ± 0.6 2.4± 0.4 



2.4 ± 0.7 
1.5 ± 1.2 
Málaga Tide gauge Altimetry 
3.7 ± 0.7 4.1± 0.4 

0.03 ± 0.03 

2.4 ± 0.7 

Alicante Tide gauge Altimetry 
2.0 ± 0.8 3.0± 0.3 



2.9 ± 0.4 
4.2 ± 0.6 
L’Estartit Tide gauge Altimetry 
2.7 ± 0.8 2.7 ± 0.3 



2.9 ± 0.3 
6.2 ± 0.4 
Palma* Tide gauge Altimetry 
2.0 ± 1.1 1.8 ± 0.5 



3.7 ± 0.5 
5.9 ± 0.5 
Table 3.
Coefficients of the linear model expressed by means of equation (4). These results correspond to the tide gauge data for the period 19482019. Only the coefficients corresponding to the predictors selected by the stepwise forward regression are presented. The multiple correlation coefficient, R, is also included.
Table 3.
Coefficients of the linear model expressed by means of equation (4). These results correspond to the tide gauge data for the period 19482019. Only the coefficients corresponding to the predictors selected by the stepwise forward regression are presented. The multiple correlation coefficient, R, is also included.
Period 
Coefficients of the linear model for sea level from Tide gauges 
19482019 
Time b 
Pressure b_{1}

Uwind b_{2}

Vwind b_{3}

Thermost. b_{4}

Halost. b_{5}

R 
Location 
mm/yr 
mm/mbar 
mm/ms^{1}

mm/ms^{1}




Santander

2.08 ± 0.21 
9.4 ± 0.9 
8.2 ± 2.1 
14.9± 2.3 


0.85 
Vigo

2.66 ± 0.24 
11.6 ± 1.1 
11.31 ± 2.3 
20.2 ± 2.4 


0.85 
A Coruña

2.29 ± 0.22 
9.9 ± 1.0 
5.4 ± 2.2 
18.1 ± 2.3 


0.84 
Leixoes

1.61 ± 0.20 
8.2± 1.0 

21.1± 2.1 
0.10± 0.05 

0.81 
Cascais

1.62 ± 0.19 
11.3±1.0 
5.1 ± 1.4 
4.0 ± 1.2 

0.07 ± 0.04 
0.84 
Arrecife

0.59 ± 0.16 
9.6 ± 1.8 



0.11 ± 0.07 
0.46 
Las Palmas








Tenerife

1.59 ± 0.12 
12.1 ± 1.3 


0.14 ± 0.07 
0.07 ± 0.06 
0.83 
Cádiz

2.62 ± 0.21 
12.1 ± 1.8 
10.0 ± 2.5 
6± 3 


0.75 
Tarifa

1.38 ± 0.21 
12.7 ±2.0 
7.9± 2.1 
15 ±7 
0.22 ± 0.11 
0.22 ± 0.05 
0.64 
Algeciras

1.00 ± 0.14 
11.8± 1.2 
6.9 ± 1.3 
13 ± 4 

0.09 ± 0.03 
0.72 
Gibraltar

0.18 ± 0.16 
10.7± 1.5 
6.2 ± 1.7 
18± 5 
0.22 ± 0.08 
0.17 ± 0.04 
0.62 
Ceuta

0.89 ± 0.15 
12.7± 1.3 

13±5 
0.13 ± 0.06 

0.70 
Málaga

1.40 ± 0.19 
14.1± 1.3 
11.7± 1.8 

0.10 ± 0.09 
0.17 ± 0.05 
0.71 
Alicante

0.82 ± 0.17 
13.6 ± 1.0 
6.2 ± 1.8 
7±3 


0.76 
L’Estartit








Palma








Table 4.
Coefficients of the linear model expressed by means of equation (4). These results correspond to both the tide gauge and altimetry data for the period 19932019. Only the coefficients corresponding to the predictors selected by the stepwise forward regression are presented.
Table 4.
Coefficients of the linear model expressed by means of equation (4). These results correspond to both the tide gauge and altimetry data for the period 19932019. Only the coefficients corresponding to the predictors selected by the stepwise forward regression are presented.
Period 
Coefficients ± 95% CI of the linear model for sea level from Tide gauges and altimetry 
19932019 
Time b 
Pressure b_{1}

Uwind b_{2}

Vwind b_{3}

Thermost. b_{4}

Halost. b_{5}

R 
Location 
mm/yr 
mm/mbar 
mm/ms^{1}

mm/ms^{1}




Santander Tide gauge Altimetry 
2.0 ± 0.8 2.56 ± 0.25 
10.0 ± 0.9 1.3 ± 0.6 
10.2 ± 2.0 2.4 ± 1.3 
11.7 ± 2.5 6.4 ± 1.6 
0.19 ± 0.11 0.19 ± 0.07 
0.10 ± 0.07 0.09 ± 0.05 
0.92 0.83 
Vigo Tide gauge Altimetry 
1.4 ± 0.9 2.9 ± 0.3 
11.6 ± 1.4

9 ± 3 4.8 ± 1.4 
18 ± 3 6.1 ± 1.4 
0.27 ± 0.15 0.13 ± 0.07 
0.19 ± 0.13 0.10 ± 0.06 
0.83 0.81 
A Coruña Tide gauge Altimetry 
3.0 ± 0.9 2.69 ± 0.25 
9.3 ± 1.6 0.8 ± 0.6 
4 ± 3 1.4 ± 1.3 
18 ± 4 5.2 ± 1.4 
0.27 ± 0.19 0.12 ± 0.07 
0.18 ± 0.17 0.08 ± 0.06 
0.79 0.82 
Leixoes Tide gauge Altimetry 
1.3 ± 0.8 3.07 ± 0.25 
8.3 ± 1.4 1.2 ± 0.7 

21 ± 3 5.7 ± 1.4 
0.12 ± 0.06 
0.08 ± 0.05 
0.83 0.84 
Cascais Tide gauge Altimetry 
3.8 ± 0.5 2.8 ± 0.3 
8.7 ± 1.0 
5.8 ± 1.4 3.1 ± 1.1 
4.6 ± 1.3 4.6 ± 1.0 


0.89 0.80 
Arrecife Tide gauge Altimetry 
1.4 ± 0.5 3.0 ± 0.3 
7.7 ± 2.1


3.8 ± 2.4 
0.19 ± 0.08 
0.13 ± 0.08 
0.60 0.78 
Las Palmas Tide gauge Altimetry 
3.3 ± 0.5 2.9 ± 0.3 
9.7 ± 1.8 

4.2 ± 2.2 
0.26 ± 0.09 0.18 ± 0.08 
0.13 ± 0.08 0.11 ± 0.07 
0.85 0.78 
Tenerife Tide gauge Altimetry 
3.7 ± 0.5 3.1 ± 0.3 
12 ± 2 3.6 ± 1.8 

3.5 ± 2.2 
0.21 ± 0.12 0.25 ± 0.09 
0.10 ± 0.10 0.15 ± 0.08 
0.79 0.78 
Cádiz Tide gauge Altimetry 
1.3 ± 0.9 3.2 ± 0.3 
9.9 ± 2.5 
8 ± 3 3.4 ± 1.2 
11 ± 5 7.0 ± 1.5 
0.09 ± 0.06 
0.13 ± 0.08 0.04 ± 0.03 
0.63 0.83 
Tarifa Tide gauge Altimetry 
4.7 ± 0.7 2.5 ± 0.3 
12.2 ± 1.7

7.3 ± 1.7 2.6 ± 1.1 
25 ± 6 18 ± 3 

0.04 ± 0.04 
0.89 0.77 
Algeciras Tide gauge Altimetry 
2.3 ± 0.6 2.4 ± 0.4 
10.5 ± 1.6 1.5 ± 1.5 
5.5 ± 1.6 3.4 ± 1.5 
22 ± 6 16 ± 5 

0.08 ± 0.03 
0.83 0.68 
Gibraltar Tide gauge Altimetry 
4.7 ± 0.6 2.4 ± 0.4 
10.8 ± 2.0 1.5 ± 1.5 
7.2 ± 2.0 3.4 ± 1.5 
23 ± 7 16 ± 5 


0.84 0.68 
Ceuta Tide gauge Altimetry 
1.9 ± 0.6 2.4 ± 0.4 
12.1 ± 1.6

1.9 ± 1.5 
18 ± 6 20 ± 5 
0.08 ± 0.06 

0.81 0.66 
Málaga Tide gauge Altimetry 
3.7 ± 0.7 4.1 ± 0.4 
12.1 ± 1.8

12.3 ± 2.1 4.4 ± 1.6 
8 ± 5 13 ± 4 
0.06 ± 0.06 
0.15 ± 0.04 
0.84 0.79 
Alicante Tide gauge Altimetry 
2.0 ± 0.8 3.0 ± 0.3 
10.3 ± 1.6 3.0 ± 1.1 
3.1 ± 1.8 
5.4 ± 3.0 


0.63 0.77 
L’Estartit Tide gauge Altimetry 
2.7 ± 0.8 2.7 ± 0.3 
13.5 ± 1.0 2.9 ± 0.7 
8 ± 3

4.2 ± 2.1 3.3 ± 1.3 
0.27 ± 0.14 0.3 ± 0.1 
0.22 ± 0.12 0.25 ± 0.09 
0.88 0.79 
Palma Tide gauge Altimetry 
2.0 ± 1.1 2.0 ± 1.1 
9.7 ± 2.0 2.3 ± 1.1 

6 ± 3 
0.34 ± 0.14 
0.28 ± 0.23 
0.58 0.58 
Table 5.
Contribution of the different factors to the observed trends of sea level from tide gauge data and the period 19482019.
Table 5.
Contribution of the different factors to the observed trends of sea level from tide gauge data and the period 19482019.
Period 
Contributions to Sea Level trends from tide gauges. 
19482019 
Mass add. 
Pressure 
Uwind 
Vwind 
Thermost. 
Halost. 
Location 
mm/yr 
mm/yr 
mm/yr 
mm/yr 
mm/yr 
mm/yr 
Santander

2.1 ± 0.4 
0.20 ± 0.10 
0.05 ± 0.04 
0.10 ± 0.07 


Vigo

2.9 ± 0.4

0.22 ± 0.13 




A Coruña

2.5 ± 0.3 
0.18 ± 0.11 




Leixoes

2.0 ± 0.4 
0.18 ± 0.08 


0.18 ± 0.10 

Cascais

1.9 ± 0.4 
0.22 ± 0.11 


0.08 ± 0.09 
0.09 ± 0.05 
Arrecife

0.82 ± 0.23 
0.22 ± 0.07 




Las Palmas







Tenerife

1.7 ± 0.3 
0.20 ± 0.07 


0.17 ± 0.08 
0.02 ± 0.02 
Cádiz

2.8 ± 0.4 
0.23 ± 0.11 
0.06 ± 0.06 



Tarifa

1.6 ± 0.5 
0.27 ± 0.10 


0.33 ± 0.16 
0.27 ± 0.09 
Algeciras

1.4 ± 0.3 
0.25 ± 0.08 



0.11 ± 0.04 
Gibraltar

0.1 ± 0.4 
0.22 ± 0.08 


0.32 ± 0.12 
0.20 ± 0.07 
Ceuta

1.0 ± 0.3 
0.26 ± 0.09 


0.19 ± 0.09 

Málaga

1.8 ± 0.5 
0.29 ± 0.12 


0.16 ± 0.13 
0.26 ± 0.08 
Alicante

1.1 ± 0.3 
0.25 ± 0.13 

0.04 ± 0.03 


L’Estartit







Palma







Table 6.
Contribution of the different factors to the observed trends of sea level from tide gauge and altimetry data and the period 19932019.
Table 6.
Contribution of the different factors to the observed trends of sea level from tide gauge and altimetry data and the period 19932019.
Period 
Contributions to Sea Level trends from tide gauges and altimetry. 
19932019 
Mass add. 
Pressure 
Uwind 
Vwind 
Thermost. 
Halost. 
Location 
mm/yr 
mm/yr 
mm/yr 
mm/yr 
mm/yr 
mm/yr 
Santander Tide gauge Altimetry 
2.3 ± 1.4 2.6 ± 0.5 

0.22 ±.0.22 0.05 ± 0.06 
0.24 ± 0.21 0.13 ± 0.12 

0.16 ± 0.13 0.14 ± 0.09 
Vigo Tide gauge Altimetry 
1.2 ± 1.1 2.8 ± 0.4 



0.24 ± 0.24 0.12 ± 0.12 

A Coruña Tide gauge Altimetry 
2.6 ± 1.4 2.5 ± 0.4 



0.3 ± 0.3 0.14 ± 0.11 
0.14 ± 0.18 0.06 ± 0.07 
Leixoes Tide gauge Altimetry 
2.0 ± 1.2 3.2 ± 0.5 


0.7 ± 0.4 0.19 ± 0.12 

0.08 ± 0.09 
Cascais Tide gauge Altimetry 
4.0 ± 0.6 3.0 ± 0.4 


0.21 ± 0.15 0.21 ± 0.14 


Arrecife Tide gauge Altimetry 
1.5 ± 0.6 2.9 ± 0.4 


0.10 ± 0.11 

0.12 ± 0.11 
Las Palmas Tide gauge Altimetry 
3.0 ± 0.7 2.8 ± 0.4 


0.09 ± 0.09 
0.21 ± 0.16 0.14 ± 0.11 

Tenerife Tide gauge Altimetry 
3.3 ± 0.8 2.8 ± 0.6 


0.07 ± 0.08 
0.32 ± 0.21 0.38 ± 0.18 

Cádiz Tide gauge Altimetry 
2.1 ± 1.5 3.3 ± 0.6 


0.4 ± 0.3 0.24 ± 0.14 
0.10 ± 0.14 0.06 ± 0.07 
0.4 ± 0.3 0.11 ± 0.10 
Tarifa Tide gauge Altimetry 
4.6 ± 0.7 2.5 ± 0.3 




0.06 ± 0.07 
Algeciras Tide gauge Altimetry 
2.1 ± 0.7 2.4 ± 0.4 




0.12 ± 0.11 
Gibraltar Tide gauge Altimetry 
4.7 ± 0.6 2.4 ± 0.4 





Ceuta Tide gauge Altimetry

1.7 ± 0.7 2.4 ± 0.4 



0.19 ± 0.15 

Málaga Tide gauge Altimetry 
4.1 ± 1.0 4.1 ± 0.7 

0.4 ± 0.3 0.13 ± 0.12 

0.14 ± 0.15 

Alicante Tide gauge Altimetry 
2.0 ± 0.8 3.0 ± 0.3 





L’Estartit Tide gauge Altimetry 
3.3 ± 1.9 3.4 ± 1.2 



0.8 ± 0.4 0.8 ± 0.3 
1.4 ± 0.7 1.5 ± 0.6 
Palma Tide gauge Altimetry 
3.7 ± 2.5 0.7 ± 1.2 



1.3 ± 0.6 
1.6 ± 1.4 