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![Page 1: Lecture 23: Tides and Sea Level Changegps.alaska.edu/jeff/Classes/GEOS655/Lecture23_tides_sealevel.pdf · Lecture 23: Tides and Sea Level Change ... • 21 SSA 0.049 151.7 0.0821373](https://reader031.fdocuments.net/reader031/viewer/2022030415/5aa1b41b7f8b9ab4208c0e82/html5/thumbnails/1.jpg)
Lecture23:TidesandSeaLevelChange
GEOS655TectonicGeodesyJeffFreymueller
![Page 2: Lecture 23: Tides and Sea Level Changegps.alaska.edu/jeff/Classes/GEOS655/Lecture23_tides_sealevel.pdf · Lecture 23: Tides and Sea Level Change ... • 21 SSA 0.049 151.7 0.0821373](https://reader031.fdocuments.net/reader031/viewer/2022030415/5aa1b41b7f8b9ab4208c0e82/html5/thumbnails/2.jpg)
TopicsToday
• Tides• TideGaugesandMeasurementofTidesandsealevelvariaEons– TidesurveysandEdalbenchmarksurveys– Long-termEdalrecords
• Sealevelhistory• TheSealevelequaEonandoceanfuncEon
![Page 3: Lecture 23: Tides and Sea Level Changegps.alaska.edu/jeff/Classes/GEOS655/Lecture23_tides_sealevel.pdf · Lecture 23: Tides and Sea Level Change ... • 21 SSA 0.049 151.7 0.0821373](https://reader031.fdocuments.net/reader031/viewer/2022030415/5aa1b41b7f8b9ab4208c0e82/html5/thumbnails/3.jpg)
TidesasaMeasureofChangingg• Tidesarethemostobviouschangeingravity,causedbythe
aKracEonofthemoonandsun.– SolidearthdeformsduetochangingEdalgravitaEonalpotenEal(solid
earth,de)– OceanwaterflowsaroundduetochangingpotenEal(ocean,des)– SolidearthdeformsduetochangingloadofoceanEdes(ocean,dal
loading)
• Tidalbulgeistwo-sidedbecauseofearthrotaEon,andbecauseEarthisorbiEngaboutCMofEarth-Moonsystem
• Tidalpoten,al(gravitaEonalpotenEal)varieswithposiEonofMoonandSunrelaEvetoEarth.
• TidalvariaEonsgenerallydescribedasasumofharmonicterms.
![Page 4: Lecture 23: Tides and Sea Level Changegps.alaska.edu/jeff/Classes/GEOS655/Lecture23_tides_sealevel.pdf · Lecture 23: Tides and Sea Level Change ... • 21 SSA 0.049 151.7 0.0821373](https://reader031.fdocuments.net/reader031/viewer/2022030415/5aa1b41b7f8b9ab4208c0e82/html5/thumbnails/4.jpg)
TidalFricEon• Earth’sEdalbulgegets
aheadofMoonposiEonbecauseofrotaEonofEarth– TidalfricEonslowsEarth
rotaEonandincreasesorbitalradiusofMoon
– Lengthofdayhasincreased~10%sinceDevonian,presentrateofchangeabout0.002sec/year
• GeodeEcobservaEonsofchangeinlengthofdayreflectmostlyexchangeofangularmomentumbetweensolidearthandhydrosphere.
![Page 5: Lecture 23: Tides and Sea Level Changegps.alaska.edu/jeff/Classes/GEOS655/Lecture23_tides_sealevel.pdf · Lecture 23: Tides and Sea Level Change ... • 21 SSA 0.049 151.7 0.0821373](https://reader031.fdocuments.net/reader031/viewer/2022030415/5aa1b41b7f8b9ab4208c0e82/html5/thumbnails/5.jpg)
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:
![Page 6: Lecture 23: Tides and Sea Level Changegps.alaska.edu/jeff/Classes/GEOS655/Lecture23_tides_sealevel.pdf · Lecture 23: Tides and Sea Level Change ... • 21 SSA 0.049 151.7 0.0821373](https://reader031.fdocuments.net/reader031/viewer/2022030415/5aa1b41b7f8b9ab4208c0e82/html5/thumbnails/6.jpg)
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
⎛
⎝ ⎜
⎞
⎠ ⎟ +!
⎡
⎣ ⎢
⎤
⎦ ⎥
![Page 7: Lecture 23: Tides and Sea Level Changegps.alaska.edu/jeff/Classes/GEOS655/Lecture23_tides_sealevel.pdf · Lecture 23: Tides and Sea Level Change ... • 21 SSA 0.049 151.7 0.0821373](https://reader031.fdocuments.net/reader031/viewer/2022030415/5aa1b41b7f8b9ab4208c0e82/html5/thumbnails/7.jpg)
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( )
![Page 8: Lecture 23: Tides and Sea Level Changegps.alaska.edu/jeff/Classes/GEOS655/Lecture23_tides_sealevel.pdf · Lecture 23: Tides and Sea Level Change ... • 21 SSA 0.049 151.7 0.0821373](https://reader031.fdocuments.net/reader031/viewer/2022030415/5aa1b41b7f8b9ab4208c0e82/html5/thumbnails/8.jpg)
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( )
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SolarTides
• SolarEdescomefromthesamecausesaslunarEdes.– Magnitude~0.42oflunarEdesduetoraEoofmassesandraEoofdistancescubed.
• SolarEdesincludesemi-diurnalanddiurnal,butvarywithyearratherthanlunarmonth
• SolarEdalcomponentsmaybeoutofphasewithlunarcomponents
![Page 10: Lecture 23: Tides and Sea Level Changegps.alaska.edu/jeff/Classes/GEOS655/Lecture23_tides_sealevel.pdf · Lecture 23: Tides and Sea Level Change ... • 21 SSA 0.049 151.7 0.0821373](https://reader031.fdocuments.net/reader031/viewer/2022030415/5aa1b41b7f8b9ab4208c0e82/html5/thumbnails/10.jpg)
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
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PredicEngTides• TheperiodsoftheEdalharmoniccomponentsareknown.
• TidescanbepredictedforwardinEmebyfifngamplitudesandphasesforeachharmoniccomponentbasedonsomedata.
• Non-Edalcomponentsinclude:– Stormsandstormsurges– VariaEonsincurrents/salinity– ElNiño/LaNiña– PacificDecadalOscillaEonandotherbasin-scalevariaEons– Someofthenon-Edalcomponentsrepeatseasonally
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ExampleTideGaugeSite
Oldest continuous tide gauge site: Amsterdam, since 1700
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13
Classical Float Gauge (from about 1832)
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14
UK Float Gauge at Holyhead Float gauges are still important and can be made into digital gauges with the use of encoders
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Example:KodiakTideStaEon
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SampleTideData
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AmonthofTideData
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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
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TidalBenchmarkSurveys• InaddiEontopermanentEde
gauges,therearemanyEdalbenchmarks,whichhavebeensurveyedrelaEvetoEdelevel.
• GoodEdalbenchmarksurveysinclude2-3monthsoftemporaryEdegaugesurveystomeasuremajorEdalcomponents.
• ShorterEdalbenchmarksurveysusenearbypermanentEdegaugesorevenEdetables.
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SeaLevelMonitoring
• EachcountryoperatesitsownEdegauges,datacoordinatedthroughinternaEonalorganizaEons– PSMSL=PermanentServiceforMeanSeaLevel
• UnderICSU• ArchivesEdegaugedatafromalmost2000globalstaEons
– GLOSS=GlobalseaLevelObservingSyStem• UnderWMO• ThemaincomponentofGLOSSisthe'GlobalCoreNetwork'(GCN)of290sealevelstaEonsaroundtheworldforlongtermclimatechangeandoceanographicsealevelmonitoring.
• AlsoLong-termtrendsnetworkfedtoIPCC,etc.
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http://www.pol.ac.uk/psmsl/programmes/gloss.info.html
Measuring Sea Level Changes
Tide Gauge (float)
Bottom Pressure Gauge
Altimeter System
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http://www.pol.ac.uk/psmsl/programmes/gloss.info.html
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
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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
http://www.pol.ac.uk/psmsl/programmes/gloss.info.html
Long Term Changes in Sea Level
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http://www.pol.ac.uk/psmsl/programmes/gloss.info.html
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
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PresentGLOSSCoreNetwork
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AllPSMSLTideStaEons
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PSMSLwith>40yearsrecords
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Lower48SeaLevelTrends
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AlaskaSeaLevelTrends
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GlobalMeanSeaLevelNicholls and Cazenave (2011)
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RegionalSeaLevelTrends1992-2009
Nicholls and Cazenave (2011)
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AbsoluteSeaLevelVariaEon
• MostofthevariaEoninthisfigureisoceanographic–redistribuEonofwater– Thermalexpansionofsurfacewaters
– ElNiño/LaNiña– Otheroscillatoryshivsincurrents
• Somelong-termtrendsareburiedinthisfigure
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AddiEonofwatertoOceans• MelEngglaciersarethemaincontributorofwatertotheoceans
• ConEnentalwaterstorage(groundwater,reservoirs)hasbeenlargestsourceofuncertainty
• AddiEonofwatertoreservoirshasreducedrateofsealevelrise(Chaoetal.,2008)
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GlobalScaleVariaEons• MeasureallmassredistribuEonusingdatafromtheNASAGRACEsatellitemission– Solve“sealevelequaEon”(FarrellandClark,1976)
Riva et al. (2010)
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MeanSeaSurfacefrommulE-missionalEmetry
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Sealevelvariability
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SeasonalCycle
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LongTermSeaLevelChanges
• Weknowfromgeologiststhatsealevelhaschangedovermany1000sofyearslargelyasaresultoftheexchangesofwaterbetweentheoceanandicecaps
• SoweshouldnotbetoosurprisedifsealevelissEllchanging
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Howiswaterredistributed?
• Ifwaterisaddedtotheoceans(frommelEngglaciers,forexample),howisitdistributed?
• Smallchanges– Addedtopresentoceanareas,notland.DistribuEonofoceandescribedbyoceanfunc,on.
• LargeChanges– ForthemelEngoflargeamountsofice(GreenlandorAntarcEca),youhavetoaccountforthechangesinbathymetryofoceansduetoGIA,andalsothechangesinoceanareaassealevelrisesontocoastalplains.
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OceanFuncEonwhite = 1; green = 0
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4320K BP
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4415K BP
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4512K BP
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9K BP
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477K BP
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TwoMainProblemswiththePresent‘Global’SeaLevelDataSet
• Coverageisnotuniformaroundtheglobe.• ‘SeaLevel’measurementsarerelaEvetolandlevel.Landlevelmaybechanging,too.
SOLUTION(to#2)èMeasureLandLevelsusingnewgeodeEctechniquessuchasGPSandAbsoluteGravity
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Two Main Geodetic Tools for Measuring Land Level Changes
GPS Absolute Gravity
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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.
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55 Melting Low Latitude Glaciers (Alaska etc.)
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-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
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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
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PredictedGlobalAverageSeaLevel
VermeerandRahmstorf(2009)
IPCCAR4
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IPCCAR4UnderesEmatesRise• Presentobservedrateof
sealevelriseisattheupperenvelopeofIPCCpredicEons.
• Why?– IPCCAR4assumednoinputtosealevelfromglacierice.
– Becausetheuncertaintyinthefutureresponseofglacierswaslarge
• IPCCAR4esEmatesarealmostcertainlyalowerboundonfuturesealevelrise.
Allisonetal.(2009)
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PredictedGlobalAverageSeaLevel
VermeerandRahmstorf(2009)
Pfefferetal.(2008)
IPCCAR4
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Hayetal.(2015)ReconstrucEon
• Reconstruct 20th century sea level change while attributing mass changes
• Inverse problem including gravitationally self-consistent “fingerprints”
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ExampleDataFits
Hay et al. (2015, Nature)
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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
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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).
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PredictedGlobalAverageSeaLevel
VermeerandRahmstorf(2009)
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
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NewOrleans2005
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NewOrleans2005