Relative sea-level rise and land subsidence in Oceania from tide gauge and satellite GPS

Abstract The relative and absolute sea-level patterns in the five LTT tide gauge stations of Oceania, Fremantle, and Sydney in Australia, Auckland, and Dunedin in New Zealand, and Honolulu in the Hawaii Islands, United States of America, are analyzed first based on tide gauge and GPS time series. The average relative rate of rise is +1.306 mm/yr., the average acceleration is +0.00490 mm/yr2, and the average absolute rate of rise is +0.125 mm/yr. This result is consistent with the result for Japan and the West Coast of the Americas. All the LTT tide gauges of the Pacific consistently show a small sea-level rise, with a significant contribution by subsidence, and negligible acceleration. This result is well-matched by the land increase, rather than shrinking, of the Pacific atolls’ islands recently highlighted by other researchers. Two case studies for locations where there are no LTT tide gauges are then provided. In Tuvalu, over the short time window 1977 to present, the relative rate of rise is +1.902 mm/yr., biased by low ESO water levels, and subsidence, but the absolute rate of rise is +0.157 mm/yr. In Adelaide, the relative rate of rise of the sea level is less than 2.3 mm/yr. with an overwhelming contribution by subsidence of 2.1 mm/yr. The thermosteric effect is thus less than 0.2 mm/yr. The sea-level acceleration is also small negative in Adelaide, −0.01936 mm/yr2.


Introduction
The sea levels are characterized by periodic oscillations, with di erent periodicities of hours, days, months [1], and decades [2] up to quasi-60 years. Along the coastline, these oscillations occur about a longer-term movement of rise or *Corresponding Author: Alberto Boretti, Department of Mechanical Engineering, College of Engineering, Prince Mohammad Bin Fahd University, Al Khobar, Saudi Arabia, E-mail: a.a.boretti@gmail.com fall dictated by land and sea components. The land component is not limited to global glacial isostatic adjustment (GIA) [3,4] or regional subsidence, for example for groundwater withdrawal [5,6] or other reasons, as explained in [7]. The sea component is similarly not limited to the thermosteric e ect [8] from the melting of ice on land and thermal expansion of ocean water as also explained in [7]. The relative sea level along the coast is well measured by tidal gauges, sometimes over periods of time often long enough to clear the longer-term trend of the sea levels periodic oscillations. Measurements of subsidence from satellite tracking of GPS domes nearby the tide gauges [9] permit to understand the sea component of the relative sealevel rise.
As relative sea-level trends oscillate with many periodicities, from hours to multi-decadal, up to quasi-60 years, only long-term-trend (LTT) tide gauges spanning more than 100 years without quality issues allow assessment of the rate of rise and the acceleration of the sea levels. The sea level oscillates with periodicities in the 60-year range, like other climate parameters [2,10,11]. Thus, more than 60 years of recording from the same tide gauge, without any major perturbation, are needed to compute a reliable rate of rise by linear tting [12][13][14]. More than 100 years are otherwise needed to compute a reliable acceleration by parabolic tting [15].
The measured monthly average mean sea levels (MSL) relative to the tide gauge instrument are given by the Permanent Service for Mean Seal Level (PSMSL, [16]). Di erent providers o er analyses of these data, (sealevel.info, [17]) and others.
The Global Positioning System (GPS) time series of antennas, originating from a constellation of satellites which is used for navigation and measurements of geodetic position, are given and analysed by di erent providers, such as Nevada Geodetic Lab (NGL, [18]), Jet Propulsion Laboratory (JPL, [19]), and Système d'Observation du Niveau des Eaux Littorales (SONEL, [20]). While the analysis of the sea level data is straightforward, the analysis of the GPS data is more troublesome, hence there is a need to use multiple providers, and compare the results of di erent analyses, to derive reliable values of the absolute vertical velocity of a GPS antenna. The GPS analysis by NGL is described in [21]. The GPS analysis by JPL is described by [22].
In very few cases the GPS antenna is co-located with the tide gauge, and precise leveling is ensured between the tide gauge instrument and the GPS antenna. In other cases, the absolute vertical velocity of the tide gauge instrument may di er from the absolute vertical velocity of the GPS antenna.
It is fairly agreed that the correction of the relative rate of rise of the sea level by the absolute velocity of a GPS antenna near the tide gauge returns the absolute rate of rise of the sea level [9]. The GPS correction is more accurate than the correction by a global glacial isostatic adjustment (GIA) model such as [3,4], that does not include any regional subsidence, human-induced as well as natural, or crustal movements [23]. The GPS method is discussed in [13] and [24].
Aim of the present contribution is to use measurements of relative sea levels from tide gauges, and measurements of subsidence from satellite tracking of GPS domes, to provide an up-to-date assessment of the relative and absolute sea-level rise, from actual observations, of Oceania, with cases study from Adelaide, South Australia, and Tuvalu.

Method
Two regressions are usually applied to the time series of the measured MSL to compute the relative sea-level rate of rise and acceleration. A linear regression: returns the sea level rate of rise v as the slope. A quadratic regression: returns the acceleration a as twice the second-order coefcient. Linear regression is also applied to the time series of the absolute vertical position of a GPS antenna located near the tide gauge installations to compute the absolute velocity w as the slope: The absolute rate of rise of the sea level u is then computed [9] as their sum: The analyses here proposed are from http://www. sealevel.info/, or originally developed in this manuscript by using MS O ce Excel linear and 2 nd order polynomial ttings of the raw data. While the actual procedure used to compute trend and acceleration is described in http://www.sealevel.info/, it must be mentioned that the tide gauge signal from long term trend tide gauges does not need to be cleared of noise or seasonal terms to compute reliable trend and accelerations, as this only a ects the con dence intervals or the R .
The pre-processing of http://www.sealevel.info/ is like the one adopted by NOAA [20]. If we apply MS O ce Excel linear and 2 nd order polynomial ttings to the raw data, we do not nd any practical di erence with the rate of rise and acceleration computed by http://www.sealevel.info/, that follows a slightly di erent procedure based on cleared data.
For a practical example, in the case of Brest, France, the slope in the analysis by http://www.sealevel.info/ is 0.997 mm/yr. vs. the 0.9984 mm/yr. of the simple linear tting of the raw data, for a di erence of 0.001 mm/yr. The acceleration in the analysis by http://www.sealevel. info/ is 0.01269 mm/yr vs. the 0.01264 mm/yr of the simple parabolic tting of the raw data, for a di erence of + .
mm/yr . The only di erence is the 95% con dence interval or the R of the estimation, which, however, are parameters of minimal value, only supplying a measure of the statistical accuracy of the tting. Both con dence interval and R do not help with cases, unfortunately common, where the record is unreliable, as it is for example with segmented records, where records originating from di erent ride gauges, of di erent sea and land contributions, often also misaligned each other, and with gaps between them, are coupled together to form a single record. One example of a composite record is Aden [21].
If the goal of the assessment is to compute the sea level rise by 2100, by taking as the present (2018) sea level rate of rise and acceleration 0.9984 mm/yr. and 0.01264 mm/yr , the constant acceleration sea level rise by 2100 is 124 mm. By taking as the present (2018) sea level rate of rise and acceleration 0.997 mm/yr. and 0.01269 mm/yr , the constant acceleration sea level rise by 2100 is also 124 mm. These di erences may be regarded as irrelevant.
For what concerns the absolute subsidence rates, we use here the results proposed by JPL. The results proposed by SONEL and NGL for the same domes are shown to give an idea of the uncertainty of the estimation, that, again, is not the statistical error of the tting, either con dence interval or R , but depends on the length of the time series, With reference to the above analysis by PSMSL, we prefer to use all the available data for every station to compute trends, and additionally, we compute accelerations. We also use stations neglected by PSMSL. Finally, we try to understand the subsidence contribution to the relative sea-level rise by looking at the subsidence rate of the nearby GPS domes.
Hence, we use for Fremantle, Australia all the data 1897 -2017, and for Sydney, Australia we coupled together with the data of the collocated tide gauges of Fort Denison 1 and 2 to produce a time series covering the time window 1886 to 2017. For Honolulu, US, we consider the data 1905 -2018. For New Zealand, in addition to Auckland 2, we also use the data of Dunedin, of time span 1900 -2017 and 73% completeness. Figure 2 presents the location of the GPS domes considered by JPL. This image is modi ed after [19]. JPL supplies the time rate of change of latitude, longitude, and elevation (height). The method is detailed in [22]. The data is obtained from eighty global GPS receivers. Precise GPS orbits and clocks are then computed in the NNR GPS reference frame. Transformation parameters are then computed from the NNR GPS frame to IGS14. Point positions for thousands of global GPS receivers are then computed in the NNR GPS reference frame. Phase ambiguities are resolved, and transformation parameters are applied to obtain the positions in IGS14. Finally, from the time series, after a search for breaks and removal of outliers, positions, velocities, breaks, and seasonal parameters are obtained.

. Fremantle
Fremantle is the best tide gauge of the Indian Ocean. MSL and GPS data are shown in Figure 3. From the MSL result at Fremantle, Australia, based on data from 1897/1 to 2016/12, it is v = + . ± . mm/yr., a = + . ± . mm/yr . Based on the GPS time series, according to SONEL, in PERT w = − . ± . mm/yr. Even larger subsidence is found by SONEL for the inland GPS dome of HIL1 (Hillarys), w = − . ± . mm/yr. According to JPL, in PERT w = − . ± . mm/yr., while JPL does not monitor HIL1.
Both PERT and HIL1 are far from the tide gauge. PSMSL and SONEL reported until recently PERT as the nearby GPS dome to consider for Fremantle. While this GPS dome is certainly far from the tide gauge, it was, however, the resulting negative absolute rate of rise for the single long-term-trend tide gauge of the Indian Ocean that dictated the removal of the absolute sea-level information of Fremantle from the SONEL and PSMSL databases [27]. As shown in Figure 4, from one day to the other, SONEL decided to drop the single station of the Indian Ocean (and similarly the single station of Japan) with a long-termtrend tide gauge record and a near GPS dome, without any explanation.
While the Fremantle tide gauge may be subjected to reduced subsidence vs. the GPS domes of PERT (or HIL1), certainly all the Perth basin is subjected to subsidence [28][29][30], and the sea levels are rising here mostly because the land is sinking.
mm/yr. If we take the JPL estimation of the subsidence rate for PERT as a reasonable estimation of the subsidence rate of the Fremantle tide gauge, then in Fremantle the relative rate of rise is v = + . mm/yr., the sea-level acceleration is a = + . mm/yr , and the absolute rate of rise is u = − . mm/yr.

. Sydney
Sydney is the best tide gauge of the South Paci c. MSL and GPS data are shown in Figure 5.
From the MSL result at Sydney, Fort Denison 1 and 2, Australia, based on data from 1897/1 to 2016/12, it is v = + .
± . mm/yr., a = + . ± . mm/yr . Figure 4: Absolute sea level rates of rise (relative sea-level rate of rise from tide gauge, absolute vertical land velocity from satellite GPS) in the world tide gauges with theoretically same data 1900 to 2013 before and after Fremantle was eliminated from the database of absolute sea level rises. Images modi ed from SONEL, [20]. The top is the "before" image, from [28]. The bottom, is the "after" image, downloaded 6 June 2018. Images modi ed after [27].
If we take the JPL estimation of the subsidence rate for SYDN as a reasonable estimation of the subsidence rate of the Sydney tide gauge, then in Sydney, v = + . mm/yr., a = + . mm/yr , and u = + . mm/yr.

. Auckland
Auckland is one of "Mitrovica's 23" tide stations with minimal vertical land motion, as well as one of "Holgate's best 9" tide gauge records. MSL and GPS data are shown in Fig  Based on the GPS time series, according to SONEL, in AUCK w = − . ± . mm/yr., while the domes of AUKT and TAKL have a signal not su ciently robust to compute a trend.
According to NGL, in AUCK w = − . ± . mm/yr., while in AUKT w = − . ± . mm/yr. and in TAKL w = − . ± . mm/yr. If we take the JPL estimation of the subsidence rate for AUCK as a reasonable estimation of the subsidence rate of the Auckland tide gauge, then in Auckland v = + . mm/yr., a = − . mm/yr , and u = + . mm/yr.

. Dunedin
Dunedin II is also one of "Mitrovica's 23" tide stations with minimal vertical land motion. MSL and GPS data are shown in Figure 7.
From the MSL result at Dunedin II, New Zealand, based on data from 1900/1 to 2015/12, it is v = + . ± .
± . mm/yr. mm/yr., in DUNT w = − . ± . mm/yr. and in OUS2 w = − . ± . mm/yr. If we take the JPL estimation of the subsidence rate for DUND as a reasonable estimation of the subsidence rate of the Dunedin tide gauge, then in Dunedin v = + . mm/yr., a = . mm/yr , and u = − . mm/yr.

. Honolulu
Honolulu is also one of "Mitrovica's 23" tide stations with minimal vertical land motion, as well as one of the "Holgate's best 9" tide gauge records. MSL and GPS data are shown in Figure 8.
From the MSL result at Honolulu, HI, USA, based on data from 1905/1 to 2018/3, it is v = + .
± . mm/yr . Based on the GPS time series, according to SONEL, w = − . ± . in the dome of HNLC, and w = − . ± . in the dome of ZHN1.
mm/yr. and in ZHN1 w = − . ± . mm/yr. If we take the JPL estimation of the subsidence rate for HNLC as a reasonable estimation of the subsidence rate of the Honolulu tide gauge, then in Honolulu, v = − + . mm/yr., a = − . mm/yr , and u = − . mm/yr.  Table 1 and Figure 9 present a summary of the tide gauge and GPS results for the LTT stations of Oceania. v is the relative rate of rise of the sea level, a the acceleration of the sea level, w the absolute vertical velocity of the tide gauge, u the absolute rate of rise of the sea level. The table also proposes as w the GIA vertical velocities VM2 from [4,24]. The GIA correction does not appear reasonable. GIA models are of little help here to understand the absolute sea level rises, suggesting on average an uplift velocity of wave = + . mm/yr. while the average subsidence rate from GPS is wave = − . mm/yr. The average relative rate of rise in the ve LTT stations of Oceania is vave = + . mm/yr., the average acceleration is aave = + . mm/yr. and the average absolute rate of rise is uave = + . mm/yr. The acceleration result is consistent with other global and regional estimations from LTT stations. [31,32] or [33] have pointed out that the sea levels at the LTT tide gauges are acceleration free.

Consistency of the result for Oceania with the global average
Over time windows long enough to clear the trend of the multidecadal oscillations, there is no sign of acceleration.
Authors of references [34,35] recently reported as the latest average acceleration of worldwide data sets is still remarkably close to zero. Comparable results of stable sea levels have been recently found in the LTT stations of Japan not notably a ected by crustal movement, namely Oshoro, Wajima, Hosojima and Tonoura [36].
Oshoro and Tonoura are neglected by PSMSL, which, however, includes Aburatsubo a ected by considerable crustal movement.
The stable sea levels of Japan are also acknowledged by the Japanese Meteorological O ce, [37], that openly states, "no clear long-term trend of rise is seen for the period from 1906 to 2017".
The minimal sea level rise since the beginning of the 20 th century shown by the Japanese Meteorological Ofce is the result of only the composite tide gauge record of Hamada, that is made of the long-term tide gauge of Tonoura, 1896 to 1984, of no sea-level rise, nor acceleration, plus the short-term tide gauge of Hamada II, 1984 to present, that is in an area of subsidence and experiences a large rate of rise [38].
In the 4 LTT tide stations of Japan not a ected by signi cant subsidence, Hosojima (data 1894 to 2018), Oshoro (data 1905 to 2018), Wajima (data 1894 to 2018), and Tonoura (data 1894 to 1984), the average sea level rate of rise is negligible, vave = + . mm/yr., and the average sea level acceleration is negative, aave = − . mm/yr [39]. The other LTT tide station of Japan, Aburatsubo (data 1894 to 2018), that is a ected by subsidence, has a positive sea level rate of rise, v = + . mm/yr., but still a negative acceleration, a = − . mm/yr [39].

Case study of Tuvalu
The fact that the Paci c sea levels are rising very slowly and not accelerating is also proposed by [41] discussing the increasing, rather than shrinking, emerged land of Paci c and Indian Ocean atolls islands. The emerged land area of many atoll islands in the Paci c (and the Indian Ocean) is consistently increasing, rather than decreasing [42][43][44].
To explain the increasing emerged land of the Paci c Ocean atolls islands, the case of Funafuti, Tuvalu is considered in detail. Since the average height of the islands is less than 2 m above sea level, Tuvalu is indeed particularly vulnerable to sea-level rise.
As previously mentioned, sea level may rise because the volume of water in the ocean is increasing (melting of ice on land and thermal expansion), as well as because the land is subsiding. It is well accepted that Paci c Atolls may be subjected to subsidence. Darwin's theory of Paci c atolls formation [45,46], assumes a subsiding volcano fringed by an upwards growing coral reef. While this theory may need extensions [47], land subsidence and growth of corals are key aspects to consider studying sea-level rise in the Paci c atolls.
Tuvalu has two tide gauges, the historical tide gauge of The presently operational tide gauge of FUNAFUTI B, part of the latest PSLM Project, has reports periodically provided in [50]. Despite the data are still updated regularly, there is no consolidated report since 2011 [51].
Sea level data has been recorded in Funafuti by one subsiding tide gauge from November 1977 to December 1999, and from another tide gauge from May 1993 to the present. The two tide gauge records are both too short to infer any proper trend for the rate of rise and acceleration. These two short tide gauge records cannot be coupled together because of the di erent sea and land contributions to the relative sea-level signal. The two nearest long-term tide gauges are Honolulu, at East, and Auckland, at West.
According to [44], the rate of rise of the sea level at the Funafuti tide gauge is + . mm/yr., a value that they also claim is twice the global average. However, [44] also measured a signi cant increment in land size that is di cult to reconcile with an intense sea level rise.
Similarly, [44] and [52] have shown that the land area of Tuvalu is increasing, rather than reducing. The increment of the land area is the e ect of the coral growth outpacing the sea-level rise of a weakly subsiding atoll.
The subsidence rate in Tuvalu may be assessed by using tide gauges and Global Positioning System (GPS) data. Three GPS antennas are in Funafuti, Tuvalu, close to the tide gauge. The time-series of monthly average mean sea level (MSL) relative to the tide gauge instrument are provided by PSMSL or the Australian Government Bureau of Meteorology (BOM, [53]). The time-series of GPS positions of antennas, together with their analyses, are provided by NGL, JPL, or SONEL). Figure 10a presents the location of the GPS antennas of TUVT, TUVA, and TUV1 in Funafuti. This image is modi ed after NGL. Figure 10b presents the location of the FUNAFUTI B tide gauge (SEAFRAME SENSOR) and of the benchmarks used for the leveling of the tide gauge. This image is modi ed after [54].
The GPS antenna of TUVA, at the airport, has the best coverage. This antenna is 2,544 m from the FUNAFUTI B tide gauge. The tide gauge is much closer to the TUVT GPS antenna which does not have enough coverage in the data sets considered. The principal benchmark is located close to the airport, where also the TUVA GPS antenna is located. The relative MSL of FUNAFUTI and FUNAFUTI B are compared over the period of overlapping to discover di erential subsidence. Linear tting of the di erence in MSL re-turns the di erence in subsidence rate. The precise levelling information of the FUNAFUTI B tide gauge referred to the datum at the airport is then used to determine the subsidence rates of both tide gauges versus the datum. The absolute GPS position of the antenna close to the datum is then used to compute the absolute subsidence rate by the linear tting. This procedure allows the assembly of the absolute and relative sea-level time series for Tuvalu spanning the time window 1977 to present, and compute then absolute and relative sea-level rates of rise.

. Relative sea level
The tide gauges of Tuvalu have been recently analyzed in [55]. Figure 11a presents the MSL recorded in FUNAFUTI. As acknowledged by the PSMSL, "Documentation added 2018-06-14. Data for 2000 and 2001 removed -this data was recorded by Australian National Tidal Centre's gauge (ID 1839) and was incorrectly attached to this site" the data of FUNAFUTI ends in Dec. 1999.
The linear and parabolic ttings of the data Nov. 1977 to Dec. 1999 suggest a rate of rise of + . mm/yr. and an apparent acceleration of + . mm/yr . The time window is too short to infer proper trends and accelerations [15,56].
John The lack of any sea-level-rise in Funafuti was also commented by [60].
As shown in [55], the small rate of rise of the historical tide gauge of FUNAFUTI was perfectly aligned with the his- The mean trend for all the tide gauge records that span more than 25 years, a minimum requirement to compute a trend, was + . mm/yr.
The historical data is forgotten since that year, with the observations from the new monitoring project started in 1993 replacing the observation from the historical stations. Figure 11b presents the MSL recorded in FUNAFUTI B. This tide gauge started recording in 1993, about the time of a low El Nino/Southern Oscillation (ENSO) water levels.
The linear and parabolic ttings of the data from May 1993 to Dec. 2017 suggest a rate of rise of + . mm/yr. and an apparent acceleration of − . mm/yr . The time window is too short to infer proper trends and accelerations. As rst noticed by [61], after the recovery from the low ENSO waters of 1998, since 1999, there is no sea-level rise at all. Figure 11c presents the analysis of the FUNAFUTI B tide gauge record with the starting date Jan. 1999, after the end of the low ENSO waters. The linear and parabolic t-tings suggest a rate of rise of + . mm/yr. and an apparent acceleration of + . mm/yr . The time window is too short to infer proper trends and accelerations. Figure 11d presents the delta MSL in between FUNA-FUTI and FUNAFUTI B. Apart from the initial data collected in the FUNAFUTI B tide gauge during the years 1993 and 1994, with sometimes also missing months, to show some initial trouble in the operation of the new tide gauge, since 1995 the di erence is increasing. Figure 12a presents the monthly maximum, mean and minimum sea level in FUNAFUTI. This graph was included in the 2006 news release on Tuvalu by The National Tidal Facility, Australia, [59], a link now broken. The gure shows the periodic drops in sea level during the ENSO events, but no rise. Figure 12b presents the monthly maximum, mean and minimum sea level in FUNAFUTI B. Apart from the initial troublesome measurements of 1993, the sea level is rising only because of the low ENSO waters of 1998. The monthly maximum mean and minimum sea-level are all characterized by a very weak rising trend. FUNAFUTI and FUNA-FUTI B are two di erent tide gauges, su ering di erent land and sea contributions to the relative sea-level signal recorded by the tide gauges. They should not be coupled together to infer any trend.
As suggested by [62], FUNAFUTI had initial sitespeci c subsidence larger than FUNAFUTI B responsible for a larger than the real apparent rate of rise in this tide gauge. The stable sea level of Tuvalu is also con rmed by [63].
Since 1995 the MSL of FUNAFUTI has been growing at a rate of 3.016 mm/yr. faster than the MSL of FUNAFUTI B. We may assume the FUNAFUTI tide gauge had an extra subsidence of 3.016 mm/yr. vs. the FUNAFUTI B tide gauge.
From the latest report of the PSLMP [51], we also know the FUNAFUTI B tide gauge is subsiding 0.1 mm/yr. vs. the primary benchmark close to the airport.
What is clear from Figures 11 and 12, is that sea levels have been rising in Tuvalu, as recorded by the tide gauges of FUNAFUTI and FUNAFUTI B, at an everything but dramatic rate, of the order of 1 mm/yr or less. The FUNAFUTI tide gauge was subjected to extra subsidence vs. the FUNA-FUTI B tide gauge, and this tide gauge is subjected to minimal subsidence vs. the primary benchmark. How much of the mm/yr. of relative sea-level rise is due to subsidence that may be determined by GPS positioning.
The data of Figures 11 and 12 do not supply any proper estimation of the rate of rise of the sea level, and even less of the sea-level acceleration, as the records, are too short. From the data of Figures 11 and 12, it may be only concluded that the sea levels have been rising truly little since 1979. There are however long-term trend tide gauges elsewhere in the Paci c. They are in Auckland and Honolulu. On average, the acceleration is small across the Paci c. There is no reason to expect anything di erent in Tuvalu.

. Subsidence
We may understand the contribution of land subsidence to the relative sea-level rise from the tide gauge signal by considering the time series of the GPS position of nearby antennas [9]. These data are, however, only recent.
According to NGL, the vertical velocity of the GPS antennas nearby the tide gauge of FUNAFUTI B, namely TUV1 and TUVA, are − . ± . mm/yr. and − . ± . mm/yr. respectively. The result for TUV1 is unreliable, based on very few data points. Opposite, the result for TUVA, Figure 13a, is based on 16 years of data. NGL has also the data for another station, TUVT, also su ering the lack of enough data.
For TUVA, even slightly larger subsidence of − . ± . mm/yr. is computed by SONEL, based on a slightly di erent analysis of the same data over a shorter time window, Figure 13b, while slightly smaller subsidence, − .
± . mm/yr. is computed by JPL, also because of slightly di erent analyses, Figure 13c.
The sea-level rise of Tuvalu is due to subsidence rather than the increasing volume of the ocean waters.
The relative sea level of Tuvalu is characterized by a mild rising, non-accelerating trend, mostly due to subsidence.

. Absolute sea level
The results shown in the prior sections may be used to compute a time series of absolute and relative sea-level since 1977. The FUNAFUTI tide gauge was subsiding at an extra rate of 3 mm/yr. The FUNAFUTI tide gauge result may thus be coupled to the FUNAFUTI B tide gauge result by shifting the FUNAFUTI MSL for the same value in December 1999, and then tilting the MSL for FUNAFUTI of 3.02 mm/yr., Figure 14a is the time window 1993 to 2000. There is a perfect agreement between the FUNAFUTI B and the FUNAFUTI shifted and tilted result apart from the very rst measurements collected in FUNAFUTI B that are unreliable. Figure 14b  lute sea-level record, obtained by considering the subsidence of FUNAFUTI B vs. the datum TUVABM, 0.1 mm/yr., plus the absolute subsidence of the TUVA GPS antenna, 1.645 mm/yr. from NGL. From the subsidence rates of Figures 12, 13 and 14, we may conclude that the thermosteric (absolute) sea level rate of rise may be less than 0.5 mm/yr. also in Tuvalu, + . mm/yr. to be precise.
The short FUNAFUTI tide gauge, which was subsiding at a rate of 3.1 mm/yr. vs the primary benchmark, suggests an apparent relative rate of rise of sea level of 0.43 mm/yr. The similarly short FUNAFUTI B tide gauge, that is minimally subsiding at a rate of 0.1 mm/yr. vs. the primary benchmark, suggests an apparent relative rate of rise of sea level of + . mm/yr. This latter result is biased by the extremely low ENSO waters of 1998. Since January 1999, the apparent rate of rise reduces to + . mm/yr. All the tide gauge records are too short to infer any proper trend. The composite tide gauge record of Funafuti shows a relative rate of rise of the sea level of 1.91 mm/yr. The TUVA GPS dome remarkably close to the primary benchmark shows a clear subsidence of 0.92 to 1.71 mm/yr. over the longer time window. The thermosteric (absolute) sea level rate of rise may thus be less than 0.5 mm/yr. also in Tuvalu. Tuvalu is growing in the area because the sea level is rising much less than what is thought. There are no signs in Tuvalu and nearby long-term tide gauges of signi cant sea-level rise exceeding the subsidence rate.

Case study of Adelaide
The historic tide gauge records of Port Adelaide Inner and Outer Harbor have been previously analyzed by [65]. Geological evidence shows that most of the signi cant rate of local sea-level rise is due to the localized, signi cant subsidence of the land, attributed to human activities associated with port development, reclamation of Holocene wetlands and groundwater extraction from deeper Tertiary aquifers. Three-quarters of the relative rate of rise of the sea level estimated at + . to + . mm/yr. is attributed by [65] to land subsidence. Authors of [65] computed an absolute rate of rise of the sea levels of + . mm/yr.
According to [66], "On the evidence, the Board is satis ed that sea level is presently rising at a rate of approximately 1.5 mm/yr. at most parts of the SA coast -the rate di ers at a few locations because of local land subsidence or uplift."  Figure 12: Monthly maximum, mean and minimum sea level in (a) FUNAFUTI, Image modi ed after http://www.john-daly.com/press/ press-02a.htm, and (b) FUNAFUTI B, Image modi ed after [51].
Port Pirie sea levels were previously analyzed by [67]. They found a long-term rate of sea-level fall attributed to isostatic up-warp of the coast. At Port Pirie, they found a relative sea-level trend of − . mm/yr. with neotectonics masking an absolute sea-level rise of + . mm/yr.
The sea level data are obtained from the PSMSL [16], as well as the National Tidal Centre, NTC, [68].
While the data should be the same, as discussed later, there are few remarkable di erences between the PSMSL and the NTC data sets.
The result of JPL is usually more reliable, but NGL covers a much larger number of GPS antennas, and usually more years of data, albeit sometimes also proposing subsidence rates computed by 1 year of data or even less that are everything but reliable. Figure 15 presents a picture with the location of the longest tide gauges of South Australia presently considered by PSMSL. The time window is from 1957 to 2016. The relative rate of rise of the sea level ranges from the + . mm/yr. of Victor Harbour, to the + . mm/yr. of Port Adelaide Outer Harbor. Figure 16 presents a picture of the location of the GPS antennas of South Australia presently considered by JPL. In Adelaide, JPL has ADE1 and ADE2, of vertical velocity − . and − . mm/yr. respectively. Then, the only     While the datum information is considered by PSMSL, only for the Port Adelaide Outer Harbor tide gauge record, it is otherwise interesting to consider the data for all the stations. Figure 17a presents all the metric data. The Port Adelaide Inner Harbor data suggest a rate of rise of 0.82 mm/yr. 1882 to 2012, but the alignment of the data collected in the 1800s may be suspicious. The Port Adelaide Outer Harbor data suggest a larger rate of rise + . mm/yr. 1940 to 2016, but this result may be an artifact of an initially larger subsidence rate. Figure 17b shows all the metric data from January 1940 to December 1990. The relative rate of rise is + . and + . mm/yr. for the perfectly consistent Port Adelaide Inner Harbor and Port Adelaide Inner II tide gauges, and it is a larger + . mm/yr. for the Port Adelaide Outer Harbor tide gauge. Hence, the Port Adelaide Outer Harbor tide gauge had at least initially extra subsidence for compaction or other causes. In Figure 17c there is the previous data all shifted for zero MSL December 1990. January 1941 to December 1945, the di erence between the Inner and Outer Harbor tide gauges reduces from 110 to 40 mm. Figure 17d shows the di erence between the MSL of the Inner and Outer Harbor tide gauges. The di erence is suspiciously high in the early-to-mid 1940s, as well as low in the late 1960s and early 1970s, to show datum issues in the two tide gauges.

. Relative and absolute sea level of Adelaide
While it appears to be di cult to couple together the two tide gauge records of Adelaide Inner and Outer Harbor to form a single tide gauge record as done in Sydney, where the nearby Fort Denison 1 and 2 tide gauge records have a very successful overlapping of 80 years (Sydney Fort Denison 1 has data 1886 -1993, Sydney Fort Denison 2 has data 1914 -2016), it is worth considering only the data since January 1943.
• With data since January 1940, for Adelaide, the relative sea-level rise is + . mm/yr., and the acceleration is − . mm/yr (Figure 18a). The image is from http://www.sealevel.info. • With data since January 1943, for Adelaide, the relative sea-level rise is + . mm/yr., and the acceleration is + . mm/yr ( Figure 18b). Also, this image is from http://www.sealevel.info. • The subsidence (ADE1 GPS dome as analyzed by JPL) is − . mm/yr. (Figure 18c).
Again, other GPS antennas of the area with less coverage, and therefore reduced reliability, that is even closer to the tide gauge location show smaller or larger subsidence. We use here JPL, rather than NGL, as the provider of the GPS data, because JPL has for this location a time series with more years of data. NGL has a shorter record of S021 suggesting a subsidence rate of − . mm/yr. based on data from 2000 to 2008.
• In Adelaide, the absolute rate of rise is about + . mm/yr., i.e. the e ect of global warming is small.
Authors of [65] computed an absolute rate of rise of the sea levels of 0.7 mm/yr. Figures 17 and 18 suggest the relative sea-level rate of rise is small, the subsidence contribution is large, and the absolute rate of rise of the sea levels is smaller.

. Relative sea levels of other medium-length tide gauges of South Australia
South Australia has other 3 tide gauges of about 60 years record length. The MSL data is from the NTC. As shown in Figure 19, the relative rate of rise is less than in Adelaide. • In Port Pirie, north of Adelaide, of 80 years length, the relative rate of rise of the sea levels is about 1 mm/yr. • In Port Lincoln, also North of Adelaide, of less than 60 years length, the relative rate of rise of the sea levels is about 1.9 mm/yr. • In Victor Harbor, South of Adelaide, also of less than 60 years, the relative rate of rise of the sea levels is about 1.4 mm/yr. This is the result of reduced subsidence. The Port Pirie tide gauge record shows a jump about 1997 that is not reproduced by the other tide gauges of Port Lincoln, Port Adelaide Inner and Outer Harbour, and Victor Harbour. This may be an artifact of a localized crustal movement or a movement of the tide gauge instrument.

Discussion
The proposed pattern is coherent with the other long-termtrend tide stations of the world. The global pattern is consistent with a small thermo-steric sea level rise with negligible acceleration, explained as a gentle recovery from the low temperatures of the Little Ice Age, that was caused by the record low solar activity of the Maunder and Spörer Minima [70] as well as volcanic activity and internal oscillations in the climate system [71]. The onset of the Little Ice Age occurred after the Medieval Warm Period, about 1350 [71]. It was the cause of the Vikings' decolonizing of the once green Greenland [72]. This cooling period ended about 1850 [73]. Since then, the sea levels are rising without any signi cant acceleration component. The e ect of global warming on the rate of rise of the sea level is thus much smaller than thought.

Conclusions
The relative sea-level measurements at the tide gauges, when collected over time windows long enough to clear a trend of the multidecadal oscillations, are the unsurpassed way to understand sea-level changes. The GPS positioning time series further help, understanding the contribution of subsidence to the relative sea-level signal. This latter result is less reliable.
The tide gauge and GPS measurements show a stable pattern across Oceania, of mild rising sea levels, with negligible accelerations, mostly explained by the sinking of the tide gauge instrument. In Fremantle, Sydney, Auckland, Dunedin, and Honolulu, the average relative rate of rise is + . mm/yr., the average acceleration is + . mm/yr., and the average absolute rate of rise is + . mm/yr. This pattern is consistent with the other long-term-trend tide stations of the Paci c.
This result is consistent with the land increase, rather than shrinking, of the Paci c atolls' islands recently highlighted by other researchers, here explained for the speci c case study of Tuvalu, where over the short time window 1977 to present, the relative rate of rise is + . mm/yr., biased by low ESO water levels and subsidence, but the average absolute rate of rise is + . mm/yr. The relative rate of rise of the sea level is less than 2.3 mm/yr. in Adelaide, with an overwhelming contribu-tion by subsidence. The thermosteric e ect is estimated to be around + . mm/yr. This result is perfectly aligned with the result for Sydney, and Fremantle. The sea-level acceleration is also negative in Adelaide.