Sea Level Rise and Land Subsidence Contributions to the Signals from the Tide Gauges of China

1 Introduction

The tide gauges measure the sea level relative to the instruments. The vertical motion of subsidence of the tide gauge is often larger than the sea level rise. The periodic oscillations of the sea levels may suggest much larger or much smaller than legitimate sea level rises if improperly accounted. It is therefore important to develop a proper mathematical framework to compute a rate of rise for the relative sea level depurated of the oscillations, and then to separate the land subsidence component from the long term component due to the thermal expansion of the oceans and the mass addition from melting of ices [1–5], i.e. the global warming component.

The implication for policy makers and environmental managers of the global warming component is what makes small differences extremely relevant. If on a worldwide basis, the tide gauge signals do not show significant acceleration components, as it has been shown in [1–5], then, locally, coastal planning may proceed on the basis of proven local results without any accountancy of sea level rise scenarios computed by models [21]. Conversely, if some acceleration will appear, then the use in local coastal planning of modelled global sea level rises linked to emission scenarios as [22] could become realistic and worth considering.

2 Sea level data

The world tide gauges measure the local relative sea level that is oscillating with many periodicities. Because of the oscillatory behaviour, with important periodicities up to a quasi-60 years, more than 60 years of data recorded without major gaps and in absence of perturbing events are needed to infer the local relative rate of rise of the sea level and the time rate of change of this parameter representing the sea level acceleration [1, 2].

A tide gauge then does not measure the absolute sea level but only the value relative to the tide gauge position. Because of the general subsidence or uplift for an area, and the additional likely subsidence at the tide gauge, the vertical velocity of the tide gauge may be in module even larger than the module of the relative rate of rise of sea levels [3, 4] and often of subsidence.

3 Tide gauge analysis

As proposed in [1–5], the analysis of the tide gauge results is made by using a simle statistic. Traditonally the relative rates of rise are computed through the linear fitting:

applied to a distribution of measured points {x_i, y_i}i=1, ..., n where y_i is the monthly average relative mean sea level at the time x_i. In this equation, SLR is the relative rate of rise, a⁺ the intercept and y⁺ the fitted value at the time x.

The residuals:

are the error for the mostly periodical oscillations, noise, fitting inaccuracies, and eventually the influence of global warming. If detectable, global warming would produce a departure from the linear trend, i..e. global warming is detectable through an increment of the relative rate of rise when new data are added.

The relative rate of rise SLR_j,k is computed over the time window (x_k-x_j) by linearly fitting the data {x_i, y_i}i=j, ..., k through the formula:

where x̅ and .y̅ are the sample means. Usually j=1 is the oldest record, and k=n is the latest record, and SLR_1,n is the latest estimation of the relative rate of rise. The use of equation 3 with j variable and k=n permit to compute different sea level velocities simulating the effect of tide gauge recording started at different times x_j. The use of equation 3 with j=1 and k variable permit to compute the sea level velocities at any time x_k. This gives an estimation of the acceleration:

The relative sea level acceleration oscillates and it may be positive or negative simply as a result of the sea level oscillations rather than global warming or cooling. It is therefore important to consider many tide gauges of significant lengths to infer reasonable conclusions.

By introducing a fitting with a line and multiple sines having the expression:

where y^* is the fitted relative sea level and the time x, SLR^* is the relative rate of rise and a^* is the intercept, while A_i, x_c,i, w_i are the amplitudes, phases and periods of the oscillations. The residual

is now the error for noise, fitting inaccuracies, periodic oscillations not exactly sinusoidal, periodic oscillations that are not included or eventually the influence of global warming (if detectable) that would produce a departure from the linear trend.

The study of the equation 6 is a further method to detect sea level acceleration (or deceleration). Also relevant is the comparison of the time series SLR_1,k(x_k) or SLA_k(x_k) computed from the measured data {x_i, y_i}i=1, ..., k or the fitted data {x_i, yi⋆}i=1, ..., k where yi⋆=y⋆(xi) from equation 5. Very close behaviour of measured and fitted distributions are an indication the influence of global warming is negligible.

4 Naïve averaging of worldwide tide gauges

PSMSL [6] proposes in their latest “Table of Relative Mean Sea Level Secular Trends derived from PSMSL RLR Data” update 14-Feb-2014 the relative rates of rise computed for 2133 tide gauges of variable record length (maximum 183, minimum 21, average 56.5 years) with the more recent, shortest tide gauges collected mostly in areas of subsidence and geographical coverage still non uniform.

The use in different times of different populations of tide gauges of different length, different rates of subsidence or uplift, and different parameters of the oscillations is what permits the false claim the sea level have been accelerating over the last decades when actually all the long term tide gauges of the world have been on average acceleration free.

The average rate of rise of the 2133 tide gauges is 1.04 ± 0.45 mm/year. However, this number has very little significance.

By using the relative rates of rises computed by linear fitting of all the tide gauge data in the 170 tide gauges of PSMSL having length more than 60 years at the present time [5], the average relative sea level velocity of the worldwide tide gauges of enough length to infer a trend is better assessed at 0.25± 0.19 mm/year [3, 4]. The additional information to consider is then that these 170 tide gauges are on average acceleration free and on average subjected to subsidence more than uplift.

By using the GPS velocities of nearby GPS domes computed by JPL [8] or SONEL [7] applying equation 1 to the GPS position time series, unfortunately requesting many realignments, the worldwide average tide gauge is more likely subject to subsidence rather than uplift, so the worldwide average absolute rate of rise is very likely even smaller [3, 4].

The rates of rise of the long term tide gauges may increase or decrease from one update to other suggesting local positive or negative accelerations. However, this is simply the result of the oscillations and on average the changes are negligible [3, 4]. Nevertheless, rather than computing inaccurate absolute sea level rates of rise it makes more sense to compute the more reliable relative sea level accelerations.

If the relative rates of rise do not increase, why there should be a positive global mean sea level rate of rise? Mass addition by melting of ice and thermal expansion by warming of waters at the rates computed by the climate models should translate in significant accelerations of the rate of rise of sea levels. If this does not occur, it means that the computed effects of ice melting and thermal expansion are overrated.

If we want to study the changes in the rate of rise of sea levels over the satellite altimeter era, we do not have to consider all the 170 tide gauges of PSMSL having length more than 60 years at the present time [5], but only those that were already satisfying this requirement 20 years ago.

The tide gauges of PSMSL having length more than 80 years at the present time are 100, and the average rate of rise for them is 0.24 ± 0.15 mm/year. For these 100 tide gauges, the rate of rise has been moving up and down over the last 20 years without any sign of globally positive or negative accelerations.

The cases of San Diego, Seattle, San Francisco, Sydney, Freemantle and many other specific tide gauges has been already shown elsewhere [1–5]. The case of the composite record of Hong Kong North Point and Quarry Bay will be shown here after.

5 The tide gauges of China

China does not have many tide gauges of enough quality and length to infer proper trends. In the PSMSL sea level survey [5], the tide gauges listed are QINHUANGDAO, DALIAN, XIAMEN, ZHAPO, KANMEN, CHN plus NORTH POINT, TAI PO KAU and TOLO HARBOUR in HKG and MACAU in MAC. None of these tide gauges satisfy the minimum length and completeness requirement.

The relative sea level rates of rise are proposed in Table 1, together with record length, year start and year end. The table also present the results of QUARRY BAY that despite a short record may be coupled to NORTH POINT to form the only record of good quality and length and this composite record labelled later NPQB.

Further details of the different relative sea level records considered in the Table are presented below:

1. QINHUANGDAO (PSMSL Station ID 614, Latitude 39.9, Longitude 119.6) has time span of data 1950– 1994 and completeness (%) 99. Date of last update is 24 Jul 1995 and the apparent relative rate of rise computed in [6] is 0.04mm/year.

2. DALIAN (PSMSL Station ID 723, Latitude 38.866667, Longitude 121.683333) has time span of data 1954– 2013 and completeness (%) 79/81 (RLR vs. metric data [9]). Date of last update is 05 Mar 2014 and the apparent relative rate of rise computed in [6] is 2.13mm/year.

3. XIAMEN (PSMSL Station ID 727, Latitude 24.45, Longitude 118.066667) has time span of data 1954–2004 and completeness (%) 99. Date of last update is 05 Nov 2007 and the apparent relative rate of rise computed in [6] is 1.1mm/year.

4. ZHAPO (PSMSL Station ID 933, Latitude 21.583333, Longitude 111.816667) has time span of data 1959– 2013 and completeness (%) 99. Date of last update is 05 Mar 2014 and the apparent relative rate of rise computed in [6] is 2.22mm/year.

5. KANMEN (PSMSL Station ID 934, Latitude 28.083333, Longitude 121.283333) has Time span of data 1959– 2013 and completeness (%) 99. Date of last update is 05 Mar 2014 and the apparent relative rate of rise computed in [6] is 1.97mm/year.

6. MACAU (PSMSL Station ID 269, Latitude 22.2, Longitude 113.55) has Time span of data 1925–1985 and Completeness (%) 97. Date of last update is 06 Sep 1990 and the apparent relative rate of rise computed in [6] is 0.25mm/year.

7. TAI PO KAU, TOLO HARBOUR (PSMSL Station ID 1034, Latitude 22.4425, Longitude 114.183889) has a Time span of data 1963–2013 and Completeness (%) 94. Date of last update is 15 Jul 2014 and the apparent relative rate of rise computed in [6] is 3mm/year.

8. NORTH POINT (PSMSL Station ID 333, Latitude 22.3, Longitude 114.2) has time span of data 1929–1985 and completeness (%) 64. Date of last update is 01 Jan 1980 and the apparent relative rate of rise computed in [6] is -1.23mm/year.

9. QUARRY BAY (PSMSL Station ID 1674, Latitude 22.291111, Longitude 114.213333) has Time span of data 1986–2013 and Completeness (%) 100. Date of last update is 15 Jul 2014 and the apparent relative rate of rise is computed here as 3.22mm/year.

From the data above, not a single tide gauge has enough data to compute a realistic relative sea level rise trend, and considering the phasing of the multi-decadal oscillations for the Western Pacific (for example in Sydney) that are shifted vs. the phasing of the multi-decadal oscillations for the Eastern Pacific (for example San Diego), the apparent rates of rise of the short records up to the present time are very likely overrating the actual relative rate of rise of the sea level.

6 Subsidence at the tide gauges of China

A tide gauge measures the sea level relative to the instrument. If the instrument is sinking, the sea level is oscillating about a rising trend and vice versa.

It is very well known that China generally suffers of land subsidence, and the tide gauge installations may suffer of additional subsidence vs. the inland [13–20]. The subsidence of China is partially natural, however in many cases man made and not certainly through the carbon dioxide emission. Land subsidence in China occurs for geological conditions, as the thick soft sediments with high compressibility and for dynamic conditions, as groundwater overdraft and engineering construction [20]. The rapid expansion and development of industrialization and urbanization are important factors for land subsidence [20].

How much of the measured relative rate of rise originates from subsidence at the tide gauge is difficult to say, because there is no estimation from SONEL [7] and JPL [8] of the vertical velocities of GPS domes nearby the tide gauges of Table 1, and obviously no monitoring of the relative motion of the tide gauge vs. the GPS domes.

We do know China is affected by land subsidence, we do know coastal tide gauges may suffer extra subsidence vs. inland objects, we do not know how much the tide gauges are subsiding.

Table 1 presents therefore relative rates of rise that also wrongly account for the quasi-60 years multi-decadal oscillation component and that may suffer of unassessed subsidence.

Opposite to CHINA and MACAU, for HONG KONG there are alternative estimations of the GPS dome velocities [10] and information about the levelling of the tide gauge.

According to [10], the estimated ITRF2005 velocity and the uncertainty for the HKSC dome nearby the NORTH POINT and QUARRY BAY tide gauges is 0.02 ± 0.36 mm/year. The computation of [10] is certainly even less reliable than the computations of [7] and [8] for other sites still suffering ± 1–2 mm/year uncertainties.

The best opportunity to compute one realistic rate of rise of sea levels is to couple the NORTH POINT and QUARRY BAY results.

Hourly tidal records are available from the North Point tide gauge station for the period 1954 to 1985 [11]. The station was built on reclaimed land and the tide gauge was installed on a sea wall. Monitoring of land settlement was carried out and the height of the tide gauge benchmark was measured by precise levelling, a land surveying technique based on trigonometric calculations, against the Hong Kong survey benchmark to an accuracy of about 4 millimetres. In view of settlement of the sea wall and revaluation of the tide gauge benchmark, the gauge was reset in 1954, 1956 and 1958.

The rate of settlement was about 6 millimetres per year in the 1950s and decreased to about 2 millimetres per year in the 1980s. At the nearby Quarry Bay tide gauge station the rate of settlement was about 6 millimetres per year in the 1980s and decreased to about 2 millimetres per year about 2000.

In contrast to NPQB, other tide gauge stations were not built on reclaimed land. Regular settlement measurements for these stations have been carried out since December 1991. The measurements showed that the tide gauge benchmarks fluctuated within a vertical range of about 2 to 10 millimetres and no significant trends were observed.

7 The NPQB tide gauge

Even if the most part of the analyses for NORTH POINT and NPQB including the one of [5] consider the first measured point in 1950, measurements were actually collected also from May 1929 to April 1930, with a two decades of interruption until January 1950.

The average relative rate of rise January 1950 to December 2012 is 1.09 mm/year.

The average rate of rise since May 1929 is 1.37 mm/year.

These results are obtained by fitting the available measured data with the gaps from missing data in the record.

It can make sense to fill the gaps in the long NPQB tide gauge record to compute the most likely sea level oscillations for the specific area.

The major issue in combining the NORTH POINT and QUARRY BAY tide gauges is posed by the unaccounted differential subsidence the QUARRY BAY tide gauge may have, that could bias the sea level velocity towards higher values.

Figure 1 presents the NPQB tide gauge result. a) is the measured MSL with gaps and fitting with a line and sines. b) is the measured MSL with gaps filled and fitting with a line and sines. c) is the same of b) with zoom on the last two decades. d) is the residual of the fitting with a line and sines. e) is the present rate of rise of sea level by using different record length. f) is the time history of the rate of rise from all the data up to a specific time. g) is the same of f) with zoom on the last two decades. h) is the acceleration over the last two decades computed as time rate of change of the velocity in g).

Fig. 1

NPQB tide gauge result: a) measured MSL with gaps and fitting with a line and sines; b) measured MSL with gaps filled and fitting with a line and sines; c) same of b) with zoom on the last two decades; d) residual of the fitting with a line and sines; e) present rate of rise of sea level by using different record length; f) time history of the rate of rise from all the data up to a specific time; g) same of f) with zoom on the last two decades; h) acceleration over the last two decades computed as time rate of change of the velocity in g).

The MSL behaviour is well described by oscillations with monthly, annual, inter-annual and multi decadal sinusoidal periodicities.

If an oscillation is not exactly sinusoidal, a longer periodicity oscillation may be approximated by different sinusoidal oscillations of same and reduced periodicities.

The most relevant sinusoidal periodicities are the six months, annual, quasi-20 years, quasi-30 years and quasi- 60 years.

Due to the multi-decadal oscillations, records starting about 1980 return apparent rate of rise four times the legitimate value, while records starting about 1960 return 2 times the legitimate value.

The NPQB tide gauge has similarities with the Sydney and San Diego tide gauges analysed in [1–5]. The NPQB tide gauge is obviously much closer to the Sydney tide gauge that has the quasi-60 years’ oscillation shifted vs. San Diego.

Over the time span of the satellite altimeter computation, on the other coast of the Pacific, for example San Diego, the relative rate of rise of sea level has been increasing from 1993 to 1999 and it is decreasing since 1999. In Sydney, on the same coast of the Pacific but in the southern rather than the Northern hemisphere, the relative rate of rise of sea level has been flat until 1999 and it is then increasing slowly.

This is not the result of global warming or global cooling but only of the phases, amplitudes and periods of the oscillations and the record length in any specific location.

For SYDNEY and SAN DIEGO, the absolute velocity of the GPS domes nearby the tide gauges (from [7, 8]) suggest a subsidence rate about the relative rate of rise of the tide gauge, i.e. it is not the sea level to rise but very likely the tide gauge to move down.

8 Discussion

As pointed by Mörner [12], sea level is rising at a small rate or it is probably not rising at all.

A simple linear analysis applied to the world tide gauges show oscillations and not accelerations of the relative sea levels over the last two decades. The average relative rate of rise of the sea level in the tide gauges of enough quality and length all over the world is about +0.25 mm/year.

GPS-based computations of the absolute vertical velocity GPS domes close to the tide gauge still suffer of inaccuracies of ± 1–2 mm/year much larger than the module of the worldwide average relative rate of rise [3, 4]. The above relative rate of rise is very likely mostly the result of subsidence more than uplift at the tide gauge, but an absolute sea level rise cannot be computed with accuracy from GPS and tide gauges.

The satellite global mean sea level (GMSL) rated +3.2 mm/year by climate model-like corrections of flat and noisy satellite altimeter signals has same lack of value than all the other never validated climate model prediction. Therefore, the study of the acceleration patterns in the relative sea level records of enough quality and length is a superior criterion vs. the study of the absolute sea levels to infer the effects of the carbon dioxide emission.

The satellite altimeter record had been interfered with to show sea level rising, because the raw data from the satellites showed no increase in global sea level at all. The raw data from the TOPEX/POSEIDON sea-level satellites which operated from 1993-2000 shows after exclusion of the effects of the El Nińo Southern Oscillation of 1997/1998 a sea-level trend of zero.

The GRACE gravitational-anomaly satellites able to measure ocean mass show that sea level fell slightly from 2002-2007. Without climate model like “corrections”, there would be no Global Mean Sea Level rated as +3.2 mm/year, in sharp contrast with the tide gauge direct measurements [3, 4].

The GMSL absolute rate of rise of 3.2 mm/year is incompatible with the +0.25 mm/year relative rate of rise of the average worldwide tide gauge that is free of acceleration over the same time window 1993 to present of the GMSL computation. If there is no acceleration in the worldwide tide gauges of the world of enough length and quality since 1993, it is impossible that the GMSL is not only +3.2 mm/year but also a number different from zero.

In key sites, as the Maldives, the Laccadives, Tuvalu, India, Bangladesh, French Guyana, Venice, Cuxhaven, Korsřr, Saint Paul Island, Qatar, and others where sea level rise could have an immediate impact, sea level is not rising at all, further supporting the tide gauge result.

9 Conclusions

In the specific of China, the significant subsidence of the land is what is the most likely responsible for the rising seas. The relative sea levels are not accelerating, consistently with the worldwide average. This subsidence is the result of natural and anthropogenic factors. The anthropogenic factors include petroleum production, production of natural gas, geothermal development, ground water exploitation, load of heavy constructions as high rise buildings, dewatering. By tackling the anthropogenic carbon dioxide emission, this does not change the anthropogenic subsidence.