Absolute and relative sea-level rise in the New York City area by measurements from tide gauges and satellite global positioning system

Alberto Boretti

College of Engineering,Prince Mohammad Bin Fahd University,Al Khobar,Saudi Arabia

Abstract The absolute and relative rates of rise of the sea level are computed for the New York City area by coupling global positioning system records of the position of fixed domes nearby tide gauges,with the tide gauges’ records.Two tide gauges are considered,one long-term trend,more reliable,The Battery,in lower Manhattan,and one shorter,less reliable,Sandy Hook,in New Jersey.The relative rates of rise of the sea level are +2.851 and +4.076 mm/yr.The subsidence rates are -2.151 and -3.076 mm/yr.The absolute rates of rise of the sea level are +0.7 and +1.0 mm/yr.The relative sea-level acceleration,reliable only in The Battery,is about + 0.008 mm/yr².This acceleration is about the same as the world average long-term trend tide gauge,as well as the average long-term trend tide gauge of the East Coast of North America.The absolute rate of rise of the sea level by 2050 in the lower Manhattan area will be likely less than 30 mm,and the absolute rate of rise of the sea level by 2100 likely less than 80 mm.The relative rate of rise of the sea level by 2050 in the Manhattan area will be likely 85 mm,and the relative rate of rise of the sea level by 2100 likely 228 mm,because of the overwhelming subsidence contribution.

Keywords:Wetland Vertical Development;Elevation Capital;Thermo-Steric Sea-Level Rise;Land Subsidence;Tidal Marsh Sustainability;Global Positioning System.

Subject Classification

18:Coastal Engineering;42:Geology;62:Ocean;63:Ocean Engineering;70:Physics;78:Signal Processing

1.Introduction

According to [ 1 ],as global temperatures increase,the ocean and atmosphere of the Northeast are becoming warmer.Thus,they project the sea levels in the New York City area to rise one to two feet by mid-century,and by as much as six feet by the end of the century.This will raise the base water level such that flooding due to high tides and extreme storms will reach further inland.Additionally,they say a warmer ocean is likely to generate extreme weather of greater intensity,likely leading to more frequent or more intense hurricanes.While the lack of any sign that global warming has caused an increase in the frequency or intensity of hurricanes is discussed elsewhere [2]the present contribution discusses the absolute and relative rates of rise of the sea levels for the specific area.

As 1 foot is 304.8 millimeters,the claimed one to two feet by mid-century,translate in about 10.16 to 20.32 mm/yr.of the average rate of sea-level rise in the next 30 years(ratio of sea-level rise by the number of years).The six feet by the end of the century translate into an average rate of about 22.86 mm/yr.(ratio of sea-level rise by number of years).The real-world rates of rise of the sea levels are on average much smaller than that,much less than 0.3 mm/yr.in the naïve average of all the long term trend tide gauges of the world (see for example the stations of www.psmsl.org/ products/ trends/ trends.txt with more than 100 years of recording).Furthermore,these rates of rise have not been subjected to any acceleration over the last century.

Although the climate models predict that rising CO2levels should cause an accelerated sea-level rise,the sea level measurements show that,thus far,there has been no detectable acceleration in the rate of sea-level rise.Refs.[ 3,4,5,16–20,22,28–61 ]are in between the many papers which have reported the lack of acceleration in the rate of sea-level rise.It has been shown already that worldwide the relative sea levels are rising and falling depending on the location but on the average rise only slowly and not accelerating.Here we analyze the absolute and relative rates of rise of the sea levels for the specific area considered by Princeton Environmental Institute [1],plus the bigger picture of all the long term trend(LTT) tide gauges along the East Coast of North America.

GPS monitoring of fixed domes,coupled to relative sealevel measurements from tide gauges,permits to assess the sea and land contributions to relative sea-level rate of rise (SLR).The technique is applied to understand the sea level pattern of Jamaica Bay,NY,USA.The relative sea level is rising mostly because the land is sinking,with a rate of rise very weakly accelerating,as the sea levels mostly oscillate about a constant longer-term trend.Land subsidence and changes in tidal hydrodynamics play a much larger role than thermosteric sea level rise in marsh loss in Jamaica Bay,New York.

Cahoon et al.[6]recently presented an evaluation of the relationship among marsh elevation,and the rates of marsh surface elevation change and relative sea-level rise in marshes located in Jamaica Bay,New York.They pointed out that coastal wetlands maintain a steady-state in response to the local conditions in which they develop (i.e.,local sea-level trend,sediment supply,hydrology,soil nutrient concentrations).If local conditions change,however,such as sea-level rise accelerates,or local sediment supply and hydrology are altered by human actions,or soil nutrient enrichment occurs,then the system is no longer in steady-state as the accumulation of sediment and organic matter changes,which impacts the ability of the wetland to maintain a consistent elevation within the vegetation growth range.Understanding this relationship is key to assessing wetland stability.

The tidal dynamics and tidal ranges across Jamaica Bay,which influence the degree of flooding of the marsh surface,are provided by Swanson and Wilson [7]who based their analyses on the Sandy Hook tide gauge.Understanding the relationship between marsh elevation and tidal flooding depths is crucial to the analyses conducted by Cahoon et al.[6].Swanson and Wilson [7]identified relative sea-level rise as a possible factor contributing to marsh loss in Jamaica Bay,New York.However,increases in tidal ranges in Jamaica Bay was also the result of natural and engineering modifications that occurred in the bay during the first half of the twentieth century.According to Swanson and Wilson [7],the increases in the elevations of high tides are the same order of the increases in regional sea level since the early 1900s.Marsh inundation in the bay is thus larger than before and larger than adjacent bays.

An evaluation of whether or not the relative sea-level rise at New York City is accelerating,and which are the sea (thermosteric sea level rise and other effects,including changes of circulation) and land (glacial isostatic adjustment and other effects,including groundwater withdrawal-induced subsidence) contributions to this acceleration,constitutes an important addition to the study.This evaluation is here performed.Specific for Manhattan,worth to mention is also the load by tall buildings contributing to subsidence.Groundwater withdrawal-induced subsidence is otherwise a common problem along the east coast of the United States.

The sea and land level change components of the relative change in sea level at Battery Park in lower Manhattan,New York City,as well as Sandy Hook,New Jersey,are well described by the time series of the relative sea-level from tide gauges,and the GPS position of domes nearby the tide gauges.GPS monitoring is resulting in extremely helpful in many fields,including computations of subsidence rates [ 8,9 ].

2.Method

The work is based on the analysis of time series of relative sea-level rise from tide gauges,and the position of GPS domes from satellite tracking.The relative rates of rise of the sea levels (SLR,r) and the subsidence rates (LSR) are computed by the linear fitting.The accelerations of the sea levels(SLA,r) are computed by the parabolic fitting.The absolute rates of rise the sea levels (SLR,a) are the sum of SLR,r,and LSR [ 10,11 ].

Regarding the error,the monthly average mean sea levels can be measured with an accuracy of the order of the millimeter.The relative rate of rise of the sea levels is obtained by the linear fitting of the MSL time series {ti,MSLi},i=1,…N with the time expressed in years,integers,and decimals.In a long term trend tide gauge of length more than 100 years,N is above 1,200.In absence of quality issues in the measurements,such as change of instrument,change of location of the instrument,missing measurements,it is well accepted that the relative rates of rise of the sea levels can be computed with an accuracy up to 0.01 mm/yr.(see for exampletidesandcurrents.noaa.gov/sltrends/,www.psmsl.org/products/trends,www.sealevel.info).In case of accelerations,it is similarly accepted that the relative accelerations of the sea levels can be computed with an accuracy of up to 0.0001 mm/yr2(see for example www.sealevel.info).Uncertainties or ± 95 confidence intervals typically came with the evaluations (see for exampletidesandcurrents.noaa.gov/sltrends /,www.psmsl.org/ products/ trends,www.sealevel.info).It is worth to mention that a constant acceleration of 0.0001 mm/yr2applied to a rate of rise of 1 mm/yr.translates in a total sea-level rise of 100.5 mm by one century.1 mm/yr.is an overestimation of the rate of rise of the sea levels in the most of the long term trend tide gauges of the world,(see in www.psmsl.org/ products/ trends/ trends.txt the long term trend tide gauges only).Conversely,a constant acceleration of 0.001 mm/yr2applied to the same rate of rise of 1 mm/yr.translates in a total sea-level rise of 105 mm by one century,and a constant acceleration of 0.01 mm/yr2applied to the same rate of rise of 1 mm/yr.translates in a total sea-level rise of 150 mm by one century.

It is necessary to apply a constant acceleration of 0.1 mm/yr2to the same rate of rise of 1 mm/yr.to produce a total sea-level rise of 600 mm by one century,that is a number we should start to worry about.By assuming the subsidence rate is about constant in every location (but it is not)and the relative acceleration only representing the thermossteric effects,small accelerations of the order 0.01 and less demonstrate thermos-steric sea level rises are everything but dramatic.

3.Thermosteric Sea-Level Rise and land subsidence in New York

It is well-known that the land in New York is sinking due to global and local phenomena.The global glacial isostatic adjustment [ 12,13 ]is one of the reasons the land is moving vertically.More localized phenomena such as groundwater withdrawal are also known to produce even stronger subsidence [15].

Estimations of SLR,r is misleading if performed by using short records,being the sea levels characterized by oscillations of periodicities quasi-60 years [ 21,14 ].This gives the false impression of accelerations and decelerations when there are only oscillations about the same trend line.

SLR,a is computed by correcting SLR,r measured by a tide gauge instrument by the absolute vertical motion of the instrument LSR [ 10,11 ].

The tide gauge of the Battery,New York,is the closest to Jamaica Bay,New York.It is one of the longest in the world and has a very close GPS antenna to compute SLR,a.The tide gauge of Sandy Hook,New Jersey,is shorter,of length insufficient to compute a realistic acceleration,and with a not that close,nearby GPS antenna.Both tide gauges are needed to understand the land and sea components of the SLR,r for the area.

Fig.1 a shows the location of Jamaica Bay and the tide gauges of The Battery,New York,and Sandy Hook,New Jersey.Image reproduced modified after www.psmsl.org.The three locations may have different SLR,r,because of the different sea and land components.The sea component is not limited to the thermosteric sea level rise,but also includes other factors such as changes in circulation.The land component is not limited to global glacial isostatic and regional subsidence from groundwater withdrawal.

In the Battery,New York there is one of the world’s longest tide gauge records.With date range 1856/1 to 2018/3,SLR,r is 2.849 ± 0.087 mm/yr.and SLA,r is 0.00849 ± 0.00388 mm/yr ² (Fig.1.b,image from www.sealevel.info).Remarkably close to the tide gauge (49 meters) there is the GPS antenna of NYBP.With data from 2009.3087 to 2019.2608,the GPS dome has (IGS08 reference frame) -14.978 ± 0.263 mm/yr.east velocity,4.533 ± 0.266 mm/yr.north velocity and -2.151 ± 0.975 mm/yr.up velocity,i.e.LSR (Fig.1.c,image from geodesy.unr.edu).This LSR supplies SLR,a of about 2.849-2.151=0.698 mm/yr.subjected to a small acceleration.The small acceleration is a common feature of the long-term trend tide gauges of the United States and the rest of the world [ 3,–5,16–20 ].

In Sandy Hook,with date range 1932/11 to 2017/12,SLR,r is 4.070 ± 0.207 mm/yr.and the (apparent) SLA,r is 0.00634± 0.01883 mm/yr ² (Fig.1.d,image from www.sealevel.info).The nearby GPS station of SHK5 is 553 meters apart.With data from 1996.0301 to 2019.2608,the GPS dome has (IGS08 reference frame) -11.868 ±0.168 east velocity,6.008 ±0.159 north velocity,and -2.541 ± 0.493 up velocity,i.e.LSR(Fig.1.e,image from geodesy.unr.edu).This LSR supplies an SLR,a of about 4.070-2.541=1.529 mm/yr.that is more than double the absolute rate of rise of the Battery,NY.Alternative to the analysis of geodesy.unr.edu,sideshow.jpl.nasa.gov proposes for the nearby GPS station of SHK1,same 553 meters apart from the tide gauge,now dismissed,a much larger subsidence rate 1996 to 2006.The SHK1 GPS dome has(IGS08 reference frame) -10.691 ± 0.353 east velocity,5.320± 0.432 north velocity,and -3.076 ± 1.453 up velocity,i.e.LSR (Fig.1.f,image from sideshow.jpl.nasa.gov).This LSR supplies an SLR,a of about 4.070-3.076=0.994 mm/yr.that is closer to the SLR,a of the Battery,NY.

Comparison of Figs.5 and 6 indicates the uncertainties in assessing the LSR,which are much larger than assessing the SLR,r or the SLA,r.By using the same data,different breakpoint alignments,automatic or manual,provide quite different results.

Regarding Sandy Hook,New Jersey,if with date range 2002/1 to 2015/12 the SLR,r is 6.325 ± 3.456 mm/yr.,then with date range 2004/1 to 2017/12 the SLR,r is reduced at 3.744 ± 3.267 mm/yr.This does not mean the sea level is decelerating,only that it makes no sense to compute SLR,r with 13 years short records.

4.Relative sea level along the East Coast of North America

The nonlinear absolute and relative sea-level patterns in the 33 long-term-trend (LTT) tide gauges of the East Coast of North America,from tide gauge records and GPS positioning,have been recently examined in [22].Table1 presents a summary of sea-level rise and subsidence results.u is the relative sea-level rise,w is the absolute vertical velocity at the GPS antenna nearby the tide gauge,and v=u + w is the absolute sea-level rise.The table is reproduced modified from [22].Fig.2 presents a map with the relative sealevel rise trends in the locations with more than 80 years of data in the PSMSL database,with the East Coast of North America in evidence.Also,this map is reproduced modified from [22],which used modified the map produced by www.psmsl.org.

The PSMSL map only shows Halifax and Trois-Rivieres in Canada,then the US stations between Portland and Key West.Galveston,that in the Gulf of Mexico,and not strictly speaking East Coast of North America is also shown.Galveston is located in a well-known area of extreme subsidence for oil and groundwater extraction.

Figure 1.(a) Location of Jamaica Bay and the tide gauges of The Battery,New York,and Sandy Hook,New Jersey.Image reproduced modified after www.psmsl.org.(b) the monthly average mean sea levels in the Battery,NY (image reproduce modified from www.sealevel.info).On the right is the atmospheric CO 2 concentration,represented by the green line.(c) land velocity about The Battery,New York tide gauge location,GPS antenna of NYBP.(image from geodesy.unr.edu).(d) the monthly average mean sea levels in the Sandy Hook,NJ (image reproduced modified from www.sealevel.info).On the right is the atmospheric CO 2 concentration,represented by the green line.(e) land velocity about the Sandy Hook tide gauge location,GPS antenna of SHK5.(image from geodesy.unr.edu).(f) land velocity about the Sandy Hook tide gauge location,GPS antenna of SHK1.(image from sideshow.jpl.nasa.gov).

Figure 1.Continued

In the 33 LTT stations along the East Coast of North America,the average relative rate of rise is 2.22 mm/yr.subjected to a small,positive acceleration of + 0.0027 mm/yr2.The average relative rate of rise of the 11 stations in Canada is 0.61 mm/yr.subjected to a negative acceleration of -0.0133 mm/yr2while the average relative rate of rise of the 22 stations of the US is 3.02 mm/yr.subjected to a positive acceleration of 0.0108 mm/yr2.Excessive groundwater withdrawal-induced subsidence is much stronger for the East coast of the United States than Canada [ 15,23–27 ].This is likely responsible for most of the difference.

The acceleration result is consistent with other global and regional estimations from LTT stations such as [3–5].The LTT stations of the East Coast of North America have acceleration values on average positive,but of the order of the nanometers per year squared,similarly to the other data sets.This result is perfectly consistent with the many papers whichhave reported the lack of acceleration in the rate of the sealevel rise [ 3–5,16–20,22,28–61 ].

Table1 Summary of sea-level rise and subsidence results.u is the relative sea-level rise,w is the absolute vertical velocity at the GNSS antenna nearby the tide gauge,and v=u + w is the absolute sea-level rise.Tablereproduced modified from [22].

5.Conclusions

•The relative sea-level rate of rise (SLR),from tide gauge records,is -2.851 mm/yr.at Battery Park and it is -4.076 mm/yr.in the shorter tide gauge record of Sandy Hook.The relative sea-level acceleration is about + 0.008 mm/yr ²in Battery Park.

•The most likely subsidence from GPS time series is about-2.151 mm/yr.at Battery Park and it is -3.076 mm/yr.in Sandy Hook.

•The most likely absolute SLR is therefore about 0.7 mm/yr.in Battery Park and it is 1.0 mm/yr.in Sandy Hook.

•Thus,in the New York City area,the likely absolute SLR is about 0.7 to 1.0 mm/yr.,the likely relative sea-level acceleration is about + 0.008 mm/yr ²,the likely subsidence is about -2.151 to -3.076 mm/yr.,and the likely relative SLR is about -2.851 to -4.076 mm/yr.

•As the relative SLR,that is the result of the land and sea components,has negligible acceleration in the long-termtrend tide gauge at Battery Park,this is an indication that both land subsidence,and absolute sea-level rise,have been stable over the period of observation.

•This result is confirmed by the 32 other long term trend stations along the East Coast of North America in addition to Battery Park.The average relative rate of rise is 2.22 mm/yr.subjected to a small,positive acceleration of+ 0.0027 mm/yr2.

•Differentiating in between Canadian and US stations,the average relative rate of rise of the 11 stations in Canada is 0.61 mm/yr.subjected to a negative acceleration of -0.0133 mm/yr2while the average relative rate of rise of the 22 stations of the US is 3.02 mm/yr.subjected to a positive acceleration of 0.0108 mm/yr2.

Figure 2.Locations of the tide gauges with more than 80 years of data in the PSMSL database.Image reproduced modified after www.psmsl.org.Northern-most station is Trois Riviere,Southern-most station is Key West.Image reproduce modified after [22].

•Excessive groundwater withdrawal-induced subsidence that is much stronger for the East coast of the US than Canada,is likely responsible for most of the difference,with different circulations patterns and other phenomena accounting for the rest.•It may be concluded that the absolute SLR by 2050 in the Manhattan area will be likely 30 mm,and the SLR by 2100 likely 80 mm.The relative SLR by 2050 in the Manhattan area will be likely 85 mm,and the SLR by 2100 likely 228 mm,for the overwhelming subsidence contribution.

•Ocean and coastal management should be based on proven sea level data and not on speculations by unvalidated models.

Funding

The author received no funding

Declaration of Competing Interest

The author has no conflict of interest to declare.