Shen Kuo Lecture-Forbes-IAGA-2017-for pdf - CCARccar.colorado.edu/.../ShenKuoLecture-Forbes-IAGA-2017.pdf · Vertical Wave Coupling and Space Weather in the Atmospheres of Earth and

9/3/17 ShenKuo Lecture,IAPSO-IAMAS-IAGAJointAssembly,CapeTown,SouthAfrica 1

ShenKuo (1031-1095)

Shen Kuo was a polymathic (interdisciplinary) Chinese scientist andstatesman of the Song Dynasty (960–1279), and excelled in many fieldsof study including mathematics, astronomy, meteorology, geology,zoology, botany, pharmacology, agronomy, archaeology, hydraulicengineering, poetry, and music.

FromtheIAGApointofview,averysignificantaccomplishmentwashisdiscoveryofthemagneticneedlecompassandtheconceptsoftruevs.magneticnorth,whichmayhavebeeninstrumentalinChina’sadvancementasaseafaringnation.

Vertical Wave Coupling and Space Weather in the Atmospheres of Earth and Mars

Jeffrey M. ForbesUniversity of Colorado

VerticalWaveCouplingandSpaceWeatherintheAtmospheresofEarthandMars


• Spaceweatheringeneralterms

• OverviewofwavecouplingintheatmospheresofEarthandMars

• OverviewofspaceweathereffectsatEarthdrivenbywavecoupling

• Mathematicalformulationoftidesandplanetarywaves,andrelatednomenclature

• Tidaleffectsontheuncontrolledreentryoforbitingobjects,e.g.,debris(Earth)

• PlanetarywavemodulationoftidesatEarth,productionofsecondarywavesand

complexity

• Aerobraking atMarsandrelationtotides

• EvidenceforplanetarywavemodulationoftidesatMars

• CONCLUSIONS

JeffreyM.ForbesAnnandH.J.Smead DepartmentofAerospaceEngineeringSciences

UniversityofColorado,Boulder,CO,USA

OutlineofThisTalk


NASAdefinition:Thetermspaceweathergenerallyreferstoconditionsonthesun,inthesolarwind,andwithinEarth'smagnetosphere,ionosphereandthermospherethatcaninfluencetheperformanceandreliabilityofspace-borneandground-basedtechnologicalsystemsandcanendangerhumanlifeorhealth,e.g.:

• Disturbedionosphere-magnetospherecurrentsthatinducesurgesandfailuresinpowergrids;

• Energeticparticlesthatpenetratesatellitesanddisrupttheiroperations;

• Ionosphericvariabilitythatdegradescommunications,navigationandtrackingsystems;and

• Neutraldensityvariationsthatimpactorbitalandreentrypredictions,especiallyspacedebris.

ManyoftheseeffectshavetheiroriginsintheSunandouterregionsofEarth’sspaceenvironment;however,meteorologicalinfluences arenowknowntoimpactsystemsthatareaffectedbytheionosphereandthermosphere,i.e.,near-Earthspace.

Thesemeteorologicalinfluencesarecommunicatedtotheionosphereandthermospherethroughtheverticalpropagationofwaves,whichisthesubjectofthistalk.

“SpaceWeather”

5

GravityWaves10-100min

10’s– 1000’skm

Tides24,12,8hours

1000’sto10,000km

PlanetaryWaves

2-20days1000’sto10,000km

instabilities

IR

9/3/17 ShenKuo Lecture,IAPSO-IAMAS-IAGAJointAssembly,CapeTown,SouthAfrica

Satelliteephemerisandre-entryerrors

Neutraldensity/satellitedragvariations

Altutid

e(km)

Impactlatitudevs.reentrylongitude[Leonardetal.,2012]

0

100

50

150

0-90 +90

Formationandmodulationofplasma

irregularities

GPSscintillation,S4index[Yueetal.,SpaceWeather,2016]

Height(km)

100

200

300

400

500

Equatorialregion

Low-middlelatitudelayers

TIDsWavyionosphere

à multiplepropagationpaths

OTHRtargetuncertainties,VHFgeo-location

GravityWaves

Regional-scale[e-]gradients[Pedatella etal.,2008]

GPSsignaldelay

uncertainties

Tides,PlanetaryWaves

6

Wave-DrivenSpaceWeatheratEarth

9/3/17 ShenKuo Lecture,IAPSO-IAMAS-IAGAJointAssembly,CapeTown,SouthAfrica

AtmosphericTidesNomenclature

Solarthermaltidesareexcitedbytheperiodicabsorptionofsolarradiationand/orthereleaseoflatentheatinconvectiveclouds(Earth),andthusfundamentallydependuponlocaltimeandgeographiclocation.


• Therelationbetweenlongitude,UTandlocaltimegivesthefollowingexpression:

• Waveswiths≠narecallednon-migratingtides;theycapturethelongitudedependenceofthetidalforcingorresponse.Themigratingtides(s=n)arelongitude-independent.

• Ashorthandnotationisusedtodefinethefrequency,directionofpropagation,andzonalwavenmber,e.g.,DWs,DEs,SWs,SEs,D0,S0.

! !𝐴#,% cos 𝑛Ω𝑡,- + 𝑠 − 𝑛 𝜆 − 𝜑#,%3

#45

%467

%487

Cph =dλdt

= −nΩs

• Thezonalphasespeedsare:

A=amplitude(functionoflatitudeandheight)𝜑 = phase(functionoflatitudeandheight)nΩ =frequency;n=1diurnal;n=2semidiurnal;etc.Ω =planetaryrotationfrequencyt=time,UTs=zonalwavenumber(s>0,westwardpropagation)λ =longitude

! !𝐴#,% cos 𝑛Ω𝑡 + 𝑠𝜆 − 𝜑#,%3

#45

%467

%487

DuetorotationofaplanetwithrespecttotheSun,theforcingand/orresponsecanbeexpressedmathematicallyintermsofperiodicvariationsintimeandlongitudeasfollows:


inclination

TidesViewedfromQuasi-SunSynchronousOrbit(tLT ≈const)

! !𝐴#,% cos 𝑛Ω𝑡,- + 𝑠 − 𝑛 𝜆 − 𝜑#,%3

#45

%467

%487

! !𝐴#,% cos 𝑘%𝜆 − 𝜙%3

#45

%467

%487

where𝑘%= 𝑠 − 𝑛 isthespace-basedzonalwavenumberandthephasecanbeexpressedasthelongitudeofmaximum.Differentcombinationsof𝑠 and𝑛 canyieldthesame𝑘%.

High-inclinationorbitschangeslowlyinlocaltime(tLT≈const),andthefollowingexpression

becomes

Planetarywavesinteractwiththespectrumoftidestoproducesecondarywaves

Sincesecondarywaveshavedifferentperiodsandzonalwavenumbersthantheprimarywaves,theirpresenceaddstothespatialandtemporalcomplexityofthedynamicalstate,andthereforealsotoionosphericvariabilitydrivenbythewaves.

Spectrumoftides

Wave-waveinteractionsarisemathematicallythroughnonlineartermsinthehierarchyofaperturbationapproachtothesolutionoftheprimitiveequations,andgiverisetosecondarywaveswiththe“sum”and“difference”frequenciesandzonalwavenumbersoftheinteracting(primary)waves[Teitelbaum andVial,1991]:

𝑐𝑜𝑠 𝛿Ω𝑡 + 𝑚𝜆 𝑐𝑜𝑠 𝑛Ω𝑡 + 𝑠𝜆 𝑐𝑜𝑠 𝑛Ω + 𝛿Ω 𝑡 + 𝑠 +𝑚 𝜆 +𝑐𝑜𝑠 𝑛Ω − 𝛿Ω 𝑡 + 𝑠 −𝑚 𝜆“sum” “difference”Interactingprimarywaves

tidePW


Inadditiontosourcevariability,variationsinthetidalspectrumoccurduetononlinearinteractionswith(modulationby)planetarywaves(PW).

PWcanbeexpressedas(where𝛿 < 1): 𝐴𝑐𝑜𝑠 𝛿Ω𝑡 + 𝑚𝜆 − 𝜑


Longitudinalvariabilityinnear-surfacewavesourcesgiverisetosignificantlocaltimeandlongitudevariabilityintheupperatmosphereattachedtoexponentialgrowthofthevertical-propagatingwaves.

Spatial-temporalvariabilityoftheupperatmosphereduetovertically-propagatingtides

Climatological TidalModeloftheThermosphere(CTMT)[Oberheide etal.,2011]BasedondatafromtheTIMEDsatellite

“wave-4”associatedwithDE3

Differences in impact latitude depend on longitude and local time of reentry. Empirical models do not include these longitude-local time variations [Leonard et al., 2012].

Illustration of impact trajectories for a single local time and formultiple longitudes superimposed on sample density perturbationdistribution (CTMT, January) for a single longitude [Leonard etal., 2012]


Longitude-lagitude andlocaltimevariationsinatmosphericdensityduetovertically-propagatingtidesinfluencetheimpactlocationofreenteringobjects


However,theselatitude-longitude-localtimestructuresvaryfromdaytoday,addinga“weather”(asopposedto

“climatology”)dimensiontotheproblem

DE3 is a tidal component excited in thetroposphere primarily by latent heatingassociated with deep convective clouds,and exists because of the longitudinalwave-4 dominance of land-sea difference inthe tropics.

Day-to-day variability of tidal componentslike DE3 can occur due to variations in thesource and through modulation by longer-period waves such as Rossby (planetary)waves and Kelvin waves.

Kelvin waves are equatorially-confinedeastward-propagating waves with periodsbetween about 3 and 16 days. The shorter-period “Ultra-Fast Kelvin Waves (UFKW)”have longer vertical wavelengths and fasterzonal phase speeds, are less susceptible todissipation and atmospheric filtering, andpenetrate to thermospheric heights.

Daily DE3 temperatures at 100 km estimated from ascending-descending temperature differences, and daily 3.5-day UFKWamplitudes from fits within 15-day moving windows [Gasperini,2016]. Gasperini [2016] and Gasperini et al. [2015]demonstrate that much of the DE3 variability is due tononlinear interaction with the 3.5-day UFKW (see followingslides).

TIMED/SABERTemperatures2010-2012

PW-tideinteractionsfromthesatelliteperspective

SecondarywavesduetoPWinteractionswithamigratingtide[ 𝑠 − 𝑛 =0]appearatthesamespectrallocationasalocalPWwoulditself,andthereforeprovidesnodefinitiveinformationonPW-migratingtideinteractions.Non-migratingtidesdoyieldspectralpeaksindicativeofPW-tideinteractions,butlocationsdependons,nandm,whicharegenerallynotuniquelyknown.

Amethodologyhasbeendeveloped[Moudden andForbes,2010]thatquantifies(tosomeextent)thepresenceandimpactsofPW-tideinteractions.Thismethodconsidersthesignaturesoftidesandotheroscillationsfromaquasi-sun-synchronous(𝑡𝐿𝑇 ≈const)perspective,whichtransformstheexpressionsfortidesandPWto:

cos 𝑛Ω𝑡 + 𝑠𝜆 ,cos 𝛿Ω𝑡 + 𝑚𝜆 cos 𝑛Ω𝑡,- + 𝑠 − 𝑛 𝜆 ,cos 𝛿Ω𝑡,- + 𝑚 − 𝛿 𝜆


Ifspectraareproducedfromobservationsorderedinpseudo-longitude,thenMoudden andForbes[2010]showthatspectralpeaksrelevanttothemodulationofatidebyaPWoccurat:

Definepseudo-longitudeas𝜆 + 2𝜋𝑐where𝜆 =longitudeandc=numberofcyclesaroundEarthorMars.

PW:|𝑚 − 𝛿| Tides:|𝑠 − 𝑛| Secondarywaves:𝑘% =| 𝑠 − 𝑛 ± 𝑚 − 𝛿 |

Note:Onlydataatonelocaltime(ascendingordescendingpartsoforbit)arerequired.


SecondarywavesarisingfromUFKW-DE3interactions


DE3 =4.0(1.0d,s=-3)

UFKW=1.3(3.5d,s=-1)

k1 =2.7(1.43d,s=-2)

k2 =5.3(0.77d,s=-4)


Gasperini etal.[2015]

Secondarywavesplayanimportantroleindetermininglatitudevslongitudeandtemporalstructures


Gasperini etal.[2015]

Day160



• Onceaspacecraftachievesorbit,atmosphericdragatperipapsis canbeusedtomodify(contract)theorbit.Thisfuel-savingtechniqueisreferredtoasaerobraking.

Aerobraking atMars

Aerobraking fromcaptureorbittomappingorbittakes

about130Earthdays

• Alimitingfactorisourabilitytopredictorbit-to-orbitdensityvariability. Peripasis toolowcanoverheatthespacecraft.Peripasis toohighlimitstheeffectivenessofaerobraking.

Middlemainphase(period=12hours)

Earlymainphase(period=24hours)

Earlymainphase(period=34hours)

InitialcaptureorbitWalk-inphase

(period=48hours)Latemainphase(period=6hours)

Mappingorbit(period=2hours)


Spacecraftundergoingaerobraking atMarsuseaccelerometerstomeasureatmosphericdensity,whichaidsoperatorsinmakingdecisionsaboutmaintainingsafeperiapsisaltitudesinsubsequentorbits.

Densitiesnear115kmatMarsmeasuredbyMarsGlobalSurveyor(MGS)Accelerometer

DensityvariabilityatMarsduetotidesandplanetarywaves(PW)

⦁ Longitudestructureswellapproximatedbywaves1-3.

Iikely tides⦁ wave-1:D0wave-2:DE1wave-3:DE2, SE1

⦁ModulationoftidesatPWperiodsclearlyevident.

⦁ tLT ≈1500h

⦁ Large± (50%)densityvariability

⦁ Eachdensitymeasurement(dot)representsapotentialdecision-makingpoint.


PW-tideinteractionsverified/quantifiedwithpseudolongitude spectra

MGSdensityspectraat115km[Moudden andForbes,2010]

D0 DE1 DE2,SE1

PWhavefrequenciesof1/8d,1/9d,2/9d,3/9d;periodsof8d,9d,4.5d,3d.

PWnotlikelytobepresentlocally;PW-tideinteractionsoccurinmiddleatmosphere.

Valuesofm,(s– n)and𝛿 determinethelocationsofsecondarywavespectralpeaks;mislikelytobe=-1(eastward-propagating)basedonmiddleatmosphereobservations[Banfield etal.,2014];the

IndicateslocalorremotepresenceofPW


AnothertypeofevidenceforPW-tideinteractionsatMars

MarsOdysseyMarsReconnaissanceOrbiter



CONCLUSIONS

• Vertically-propagatingtidesdrivesignificantspatial-temporalvariabilityor“weather”inEarth’sthermosphereandionospherethatinterfereswithcommunications,navigation,andtrackingsystems,aswellasorbitalandreentrypredictions.

• Planetarywaves(PW,periods~2-20days)contributetothisvariabilitythroughnonlinearinteractionswithtideswhichproducesecondarywaves.Secondarywaveshavedifferentperiodsandzonalwavenumbersthantheinteracting(primary)waves,andthusaddtothespatial-temporalcomplexity oftheionosphereandthermosphere.

• AtMarstides,PW,andPW-tideinteractionsproducethermospheredensityvariationsthatimpactaerobraking operations.

• NewaspectsofwavecouplingatEarthandMarscontinuetobediscoveredasnewobservationsandmoresophisticatedmodelsemerge.

• UnderstandingwavecouplinginMarsatmospherepointsthewayfornewempiricalmodelsandpossiblyreal-timeschemesforaerobraking prediction.

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Shen Kuo Lecture-Forbes-IAGA-2017-for pdf - CCARccar.colorado.edu/.../ShenKuoLecture-Forbes-IAGA-2017.pdf · Vertical Wave Coupling and Space Weather in the Atmospheres of Earth and