Lecture 23: Tides and Sea Level...

Lecture23:TidesandSeaLevelChange

GEOS655TectonicGeodesyJeffFreymueller

TopicsToday

•  Tides•  TideGaugesandMeasurementofTidesandsealevelvariaEons– TidesurveysandEdalbenchmarksurveys– Long-termEdalrecords

•  Sealevelhistory•  TheSealevelequaEonandoceanfuncEon

TidesasaMeasureofChangingg•  Tidesarethemostobviouschangeingravity,causedbythe

aKracEonofthemoonandsun.–  SolidearthdeformsduetochangingEdalgravitaEonalpotenEal(solid

earth,de)–  OceanwaterflowsaroundduetochangingpotenEal(ocean,des)–  SolidearthdeformsduetochangingloadofoceanEdes(ocean,dal

loading)

•  Tidalbulgeistwo-sidedbecauseofearthrotaEon,andbecauseEarthisorbiEngaboutCMofEarth-Moonsystem

•  Tidalpoten,al(gravitaEonalpotenEal)varieswithposiEonofMoonandSunrelaEvetoEarth.

•  TidalvariaEonsgenerallydescribedasasumofharmonicterms.

TidalFricEon•  Earth’sEdalbulgegets

aheadofMoonposiEonbecauseofrotaEonofEarth–  TidalfricEonslowsEarth

rotaEonandincreasesorbitalradiusofMoon

–  Lengthofdayhasincreased~10%sinceDevonian,presentrateofchangeabout0.002sec/year

•  GeodeEcobservaEonsofchangeinlengthofdayreflectmostlyexchangeofangularmomentumbetweensolidearthandhydrosphere.

TidalPotenEal•  WecancomputetheEdal

potenEalatanypointontheEarth’ssurfacefrombasicphysics

b

r

R Ψ

€

UM = −GMm

b

UM = −GMm

r 1+R2

r2+ 2 R

rcosΨ

⎡

⎣ ⎢

⎤

⎦ ⎥

12

UM = −GMm

r1+

RrcosΨ+

R2

r232cos2Ψ−

12

⎛

⎝ ⎜

⎞

⎠ ⎟ +!

⎡

⎣ ⎢

⎤

⎦ ⎥

€

b2 = R2 + r2 − 2RrcosΨFrom the Law of Cosines:

TidalPotenEalTerms•  FirstorderapproximaEon:

distancetoMoonisconstant.

•  Firsttermisconstant•  Secondtermrelatestoorbit

ofEartharoundCMofEarth-Moonsystem

•  Thirdandfollowingtermsare,dalpoten,al.

•  We’lllookatthatthirdterminmoredetail.

€

UM (1) = −GMm

r

UM (2) = −GMmRr2

cosΨ

UM (3) = −GMm

rR2

r232cos2Ψ−

12

⎛

⎝ ⎜

⎞

⎠ ⎟ +!

⎡

⎣ ⎢

⎤

⎦ ⎥

RelaEonofΨtoLat-Long•  TheangleYismeasuredin

theplanedefinedbythevectorspandm,

•  Define(θ,φ)asasco-laEtude+logitudeofP

•  Define(θm,φm)asco-laEtude+longitudeofMoon(varies)

•  Longitudechangesby2πperday(non-rotaEngcoordinatesystem)

m

To Moon

P

Ψp

€

cosΨ = cosθ cosθm + sinθ sinθm cos ϕ −ϕm( )

€

123cos2Ψ−1( ) = =

3cos2θ −12

⎛

⎝ ⎜

⎞

⎠ ⎟ 3cos2θm −1

2⎛

⎝ ⎜

⎞

⎠ ⎟ +

+34sin2θ sin2θm cos2 ϕ −ϕm( )

+34sin2θ sin2θm cos ϕ −ϕm( )

Periodsoftheseterms•  Semi-diurnalEde

–  UndergoesacompletecycleeveryEme2(φ-φm)changesby2π,roughlytwiceaday

–  Amplitudevariesovercourseoflunarmonth

•  DiurnalEde–  UndergoesacompletecycleeveryEme(φ-φm)changesby2π,roughlyonceaday

–  Amplitudevariesovercourseoflunarmonth

•  FortnightlyEde–  Undergoesacompletecycletwiceperlunarmonth

•  PlushigherordertermsfromellipEcityofMoon’sorbit. €

3cos2θ −12

⎛

⎝ ⎜

⎞

⎠ ⎟ 3cos2θm −1

2⎛

⎝ ⎜

⎞

⎠ ⎟

€

34sin2θ sin2θm cos2 ϕ −ϕm( )

€

34sin2θ sin2θm cos ϕ −ϕm( )

SolarTides

•  SolarEdescomefromthesamecausesaslunarEdes.– Magnitude~0.42oflunarEdesduetoraEoofmassesandraEoofdistancescubed.

•  SolarEdesincludesemi-diurnalanddiurnal,butvarywithyearratherthanlunarmonth

•  SolarEdalcomponentsmaybeoutofphasewithlunarcomponents

TidalComponentsareNamed

•  OnlymajorEdalcomponentslistedhere•  LunarEdes

–  Semi-diurnalM2–  DiurnalK1,O1–  EllipEcalJ1,L1,K2,L2

•  SolarTides–  Semi-diurnalS2–  DiurnalP1–  EllipEcalR2,T2

•  SeehKp://en.wikipedia.org/wiki/Theory_of_Edes

TheM2EdeisverylargeinAlaskaduetoaresonanceintheGulfofAlaska

PredicEngTides•  TheperiodsoftheEdalharmoniccomponentsareknown.

•  TidescanbepredictedforwardinEmebyfifngamplitudesandphasesforeachharmoniccomponentbasedonsomedata.

•  Non-Edalcomponentsinclude:–  Stormsandstormsurges–  VariaEonsincurrents/salinity–  ElNiño/LaNiña–  PacificDecadalOscillaEonandotherbasin-scalevariaEons–  Someofthenon-Edalcomponentsrepeatseasonally

ExampleTideGaugeSite

Oldest continuous tide gauge site: Amsterdam, since 1700

13

Classical Float Gauge (from about 1832)

14

UK Float Gauge at Holyhead Float gauges are still important and can be made into digital gauges with the use of encoders

Example:KodiakTideStaEon

SampleTideData

AmonthofTideData

TidalHarmonicComponents•  TwentylargestharmoniccomponentsatKodiakIsland•  Const#NameAmplitudePhaseSpeed(=degrees/hour=360/period)•  -----------------------------------•  1M23.192308.128.9841042(=12.4hours)•  4K11.306288.615.0410686(=23.93hours)•  2S21.066341.430.0000000•  6O10.850273.013.9430356•  3N20.659284.228.4397295•  30P10.413284.414.9589314•  35K20.295332.830.0821373•  22SA0.256262.10.0410686(=1year)•  26Q10.154264.813.3986609•  11NU20.128284.228.5125831•  33L20.079321.029.5284789•  142N20.079258.927.8953548•  19J10.075297.915.5854433•  13MU20.072277.127.9682084•  24MF0.066165.21.0980331(=13.6days)•  27T20.062329.529.9589333•  20MM0.062191.70.5443747•  23MSF0.04951.51.0158958•  21SSA0.049151.70.0821373•  18M10.046293.214.4966939

TidalBenchmarkSurveys•  InaddiEontopermanentEde

gauges,therearemanyEdalbenchmarks,whichhavebeensurveyedrelaEvetoEdelevel.

•  GoodEdalbenchmarksurveysinclude2-3monthsoftemporaryEdegaugesurveystomeasuremajorEdalcomponents.

•  ShorterEdalbenchmarksurveysusenearbypermanentEdegaugesorevenEdetables.

SeaLevelMonitoring

•  EachcountryoperatesitsownEdegauges,datacoordinatedthroughinternaEonalorganizaEons–  PSMSL=PermanentServiceforMeanSeaLevel

•  UnderICSU•  ArchivesEdegaugedatafromalmost2000globalstaEons

–  GLOSS=GlobalseaLevelObservingSyStem•  UnderWMO•  ThemaincomponentofGLOSSisthe'GlobalCoreNetwork'(GCN)of290sealevelstaEonsaroundtheworldforlongtermclimatechangeandoceanographicsealevelmonitoring.

•  AlsoLong-termtrendsnetworkfedtoIPCC,etc.

http://www.pol.ac.uk/psmsl/programmes/gloss.info.html

Measuring Sea Level Changes

Tide Gauge (float)

Bottom Pressure Gauge

Altimeter System


Sea-Level Changes

Maldives Int. Airport

Different Time-Scales

•  Momentary changes due to tsunamis

•  Daily changes due to tides and surges

•  Seasonal changes

•  Interannual changes e.g. due to ENSO

•  Long term changes due to climate change

Causes of Sea Level Change

•  Local processes in river/coastal regimes

•  Ocean circulation changes

•  Regional and global climate changes

•  Geological processes

Past 100 years

•  Most records show evidence for

rising sea levels during the past

century

•  IPCC concluded that there has

been a global rise of

approximately 10-20 cm

during the past 100 years


Long Term Changes in Sea Level


Long Term Changes in Sea Level

Next 100 years

•  a rise between 9 and 88 cm

•  a central value of 48 cm

•  a rate of approx. 2.2 - 4.4

times that of the past

100 years

Projected sea level rise, IPCC 2001

PresentGLOSSCoreNetwork

AllPSMSLTideStaEons

PSMSLwith>40yearsrecords

Lower48SeaLevelTrends

AlaskaSeaLevelTrends

GlobalMeanSeaLevelNicholls and Cazenave (2011)

RegionalSeaLevelTrends1992-2009

Nicholls and Cazenave (2011)

AbsoluteSeaLevelVariaEon

•  MostofthevariaEoninthisfigureisoceanographic–redistribuEonofwater–  Thermalexpansionofsurfacewaters

–  ElNiño/LaNiña–  Otheroscillatoryshivsincurrents

•  Somelong-termtrendsareburiedinthisfigure

AddiEonofwatertoOceans•  MelEngglaciersarethemaincontributorofwatertotheoceans

•  ConEnentalwaterstorage(groundwater,reservoirs)hasbeenlargestsourceofuncertainty

•  AddiEonofwatertoreservoirshasreducedrateofsealevelrise(Chaoetal.,2008)

GlobalScaleVariaEons•  MeasureallmassredistribuEonusingdatafromtheNASAGRACEsatellitemission– Solve“sealevelequaEon”(FarrellandClark,1976)

Riva et al. (2010)

MeanSeaSurfacefrommulE-missionalEmetry

Sealevelvariability

SeasonalCycle

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LongTermSeaLevelChanges

•  Weknowfromgeologiststhatsealevelhaschangedovermany1000sofyearslargelyasaresultoftheexchangesofwaterbetweentheoceanandicecaps

•  SoweshouldnotbetoosurprisedifsealevelissEllchanging

Howiswaterredistributed?

•  Ifwaterisaddedtotheoceans(frommelEngglaciers,forexample),howisitdistributed?

•  Smallchanges–  Addedtopresentoceanareas,notland.DistribuEonofoceandescribedbyoceanfunc,on.

•  LargeChanges–  ForthemelEngoflargeamountsofice(GreenlandorAntarcEca),youhavetoaccountforthechangesinbathymetryofoceansduetoGIA,andalsothechangesinoceanareaassealevelrisesontocoastalplains.

OceanFuncEonwhite = 1; green = 0

4320K BP

4415K BP

4512K BP

46

9K BP

477K BP

48

TwoMainProblemswiththePresent‘Global’SeaLevelDataSet

•  Coverageisnotuniformaroundtheglobe.•  ‘SeaLevel’measurementsarerelaEvetolandlevel.Landlevelmaybechanging,too.

SOLUTION(to#2)èMeasureLandLevelsusingnewgeodeEctechniquessuchasGPSandAbsoluteGravity

49

Two Main Geodetic Tools for Measuring Land Level Changes

GPS Absolute Gravity

50

QuesEonsandAnswersQ. Has global sea level risen during the 20th

century ?

A. Yes. By 10-20 cm.

There are many references, see the IPCC Fourth Assessment Report for a review

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20th Century Sea Level Rise Estimates

Region, VLM Rate ± s.e. (mm/yr) Gornitz and Lebedeff (1987) Global, Geological 1.2 + 0.3 Peltier and Tushingham (1989, 1991) Global, ICE-3G/M1 2.4 + 0.9c Trupin and Wahr (1990) Global, ICE-3G/M1 1.7 + 0.13 Nakiboglu and Lambeck (1991) Global decomposition 1.2 + 0.4 Shennan and Woodworth (1992) NW Europe, Geological 1.0 + 0.15 Gornitz (1995)d NA E Coast, Geological 1.5 + 0.7c

Mitrovica and Davis (1995), Davis and Mitrovica (1996) Far field, PGR Model 1.4 + 0.4c Davis and Mitrovica (1996) NA E Coast, PGR Model 1.5 + 0.3c Peltier (1996) NA E Coast, ICE-4G/M2 1.9 + 0.6c Peltier and Jiang (1997) NA E Coast, Geological 2.0 + 0.6c Peltier and Jiang (1997) Global, ICE-4G/M2 1.8 + 0.6c Douglas (1997)d Global ICE-3G/M1 1.8 + 0.1 Lambeck et al. (1998) Fennoscandia, PGR Model 1.1 + 0.2 Woodworth et al. (1999) UK & N Sea, Geological 1.0 + 0.2 N.B. All these analyses use the same PSMSL data set

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QuesEonsandAnswersQ. Do we understand why it has risen?

A. Yes. (Or at least ‘more or less’)

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Whyhassealevelrisen?Main driver has been the

0.6 ºC global temperature change during the past century

but there have been many contributors to the sea level change.

See IPCC 4AR for a review.

55 Melting Low Latitude Glaciers (Alaska etc.)

56

-1.0 -0.5 0.5 1.0 1.5 2.0 0.0

0.0 1.0 -1.0

mm/year

2.0 mm/year

Thermal expansion

Glaciers Greenland (present)

Antarctica (present) Ice sheets (long term)

Permafrost Sedimentary deposits

TOTAL

OBSERVATIONS

Continental waters

20th Century Sea Level Rise - IPCC 2001

ProgressinUnderstandingBudget

•  IPCC2001underesEmatedseveralfactors–  Steric(thermalexpansion)–  ContribuEonfrommelEngglaciers.

•  RecentworkbySteveNerem(U.ofColorado)suggeststhatsealevelbudgetclosesfairlywell,andconsistentwithpresentalEmeterrateof>3mm/yr.

•  Chaoetal.(2008)esEmatedwaterstorageindamsandconcludedthatsealevelrateaveraged2.5mm/yrpost-WW2,parEallymaskedbyimpoundmentofwaterinreservoirs.

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QuesEonsandAnswersQ. Is the rate of rise increasing ?

A. Yes. On basis of study of long records spanning 18th to 20th centuries.

A. Not clear. On basis of 20th century tide gauge data alone.

A. Yes. On basis of altimeter and tide gauge from the 1990s.

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Sea level change contains an acceleration of sea level rise from the 19th to the 20th centuries probably due to climate change

PredictedGlobalAverageSeaLevel

VermeerandRahmstorf(2009)

IPCCAR4

IPCCAR4UnderesEmatesRise•  Presentobservedrateof

sealevelriseisattheupperenvelopeofIPCCpredicEons.

•  Why?–  IPCCAR4assumednoinputtosealevelfromglacierice.

–  Becausetheuncertaintyinthefutureresponseofglacierswaslarge

•  IPCCAR4esEmatesarealmostcertainlyalowerboundonfuturesealevelrise.

Allisonetal.(2009)



Pfefferetal.(2008)

IPCCAR4

Hayetal.(2015)ReconstrucEon

•  Reconstruct 20th century sea level change while attributing mass changes

•  Inverse problem including gravitationally self-consistent “fingerprints”

ExampleDataFits

Hay et al. (2015, Nature)

Results

Hay et al. (2015, Nature)

Church and

White (2011)

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Questions and Answers

Acceleration in the1990s? •  Look at altimetry

•  Look at tide gauge records.

•  Look at IPCC-type models. Answer: •  Yes

AlEmeterSeaLevelChange

http://sealevel.colorado.edu

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QuesEonsandanswersQ. How much might sea level rise in the 21st

century?

A. 9-88 cm with central value of 48 cm based on 35 emission scenarios and 7 AOGCMs (IPCC Third Report).



IPCCAR4

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QuesEonsandAnswersQ. How important will the 21st century changes be?

A. When MSL (or water depth) changes, and when also there are coupled changes in regional meteorology, there will be changes in storm surges, tides, waves and extreme water levels.

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It is important to keep in mind that these rising Sea Levels sooner or later lead to changes in Extreme Levels and often to local flooding. (This is not only a ‘Scientific’ exercise.)

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FloodsintheIrishSea2002

Douglas

Ramsey

"the worst in living memory"

Many £M’s damage in few hours

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Tuvalu Floods 2002

Typical coral island

Poor infrastructure

Erosion Plant damage

NewOrleans2005

Lecture 23: Tides and Sea Level...

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