Table Of ContentAir-Ice-Ocean Interaction
Miles McPhee
Air-Ice-Ocean Interaction
Turbulent Ocean Boundary Layer
Exchange Processes
ABC
MilesMcPhee
McPheeResearchCompany
Naches,WA
USA
ISBN978-0-387-78334-5 e-ISBN978-0-387-78335-2
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Preface
The outline of this monograph is based loosely on a series of lectures delivered
tostudentsenrolledintheair–sea–iceinteractioncourseattheUniversityCenterin
Svalbard.Boththelecturesandthebookareproductsofoverthreedecadesoftrying
(sometimesstruggling)todistillfrommeasurementsatnearlytwodozenice-station
projectsofvaryingsizeandcomplexity,asomewhatcogentviewofhowthebound-
ary layer that developsbetween sea ice and the underlyingocean behaves. While
frommanyotherperspectives,polaroceanographicresearchisalwayschallenging,
fromthepointofviewexpressedinthisbook,itsoverridingadvantageisthatseaice
providesaplatformformakingturbulencemeasurementsthatareextremelydifficult
elsewhere. In other words, it is a superb natural laboratoryfor studying planetary
boundarylayersthroughouttheirwholeextent.Still,itisalaboratorythatdemands
much of its users, and for useful results, almost always requires hard work, plus
ahighdegreeofcooperationandperseveranceamongmanyscientistsandsupport
personnel.Forme,thishasbeenoneofthemostrewardingaspectsofspendingmost
of a scientific careerdevotedto high-latitudestudies. Time andagain,I haveseen
theharshenvironmentbringoutthebestofpeopleintermsofinventivenessandall
aroundcompetence.Andthebestisoftenvery,verygood.Itwouldbeadisservice
tothemanywhohavehelpedwiththemeasurements,analysis,theory,andfunding,
tosingleoutindividualsforspecialthanks—ithasalwaysbeenacompletelycollab-
orativeeffort.Theoneexceptionis thatI wish to thankmy wife,Saundra,for her
patiencewith the immediatetask of my writingthis book,for heroccasionalhelp
withthefieldwork,formaintainingaclose-knitfamilyduringmyfrequentabsences
onremoteprojects,butmainlyforalwayssupportingandsharingmypassionforthe
scientificendeavor.
Naches,WashingtonUSA MilesMcPhee
2008
v
Contents
1 Introduction................................................... 1
1.1 ArcticChange ............................................. 1
1.2 TheSouthernOcean ........................................ 7
1.3 Ekman’sSeminalPaper ..................................... 8
1.4 PolarBoundary-LayerFieldStudies........................... 10
1.5 Roadmap ................................................. 12
References..................................................... 13
2 BasicPhysicalConcepts......................................... 15
2.1 ConservationEquationsinFluids ............................. 15
2.2 ReynoldsFluxes ........................................... 16
2.3 Rotation:TheCoriolisForceandGeostrophy ................... 18
2.3.1 GeostrophicShear ................................... 19
2.4 Boundary-LayerEquations................................... 19
2.5 InertialOscillations......................................... 20
2.6 EkmanPumping ........................................... 24
2.7 TheEquationofStateforSeawater............................ 28
References..................................................... 36
3 TurbulenceBasics.............................................. 39
3.1 GeneralCharacteristics...................................... 39
3.2 IOBLMeasurementTechniquesandExamples.................. 40
3.2.1 SmithRotors........................................ 40
3.2.2 TurbulenceInstrumentClusters ........................ 41
3.2.3 MomentumandScalarFluxMeasurements .............. 43
3.2.4 EstimatingConfidenceLimitsforCovarianceCalculations . 46
3.2.5 AveragingTimeandtheSpectralGap ................... 48
3.3 TurbulentKineticEnergyEquation............................ 51
3.4 ScalarVarianceConservation................................. 53
3.5 TurbulenceSpectraandtheEnergyCascade .................... 54
3.6 MixingLength,EddyViscosity,andthewSpectrum ............. 58
vii
viii Contents
3.7 ScalarSpectra ............................................. 60
References..................................................... 62
4 SimilarityfortheIce/OceanBoundaryLayer...................... 65
4.1 TheSurfaceLayer.......................................... 65
4.1.1 MixingLengthintheNeutralSurfaceLayer.............. 67
4.1.2 TheLawoftheWallandSurfaceRoughnessLength....... 67
4.1.3 Monin-ObukhovSimilarity............................ 68
4.2 TheOuterLayer ........................................... 70
4.2.1 SimilarityforTurbulentStressintheOuterLayer ......... 72
4.2.2 RossbySimilarityfortheNeutralIOBL ................. 74
4.2.3 SimilarityfortheStablyStratifiedIOBL................. 77
4.3 IOBLSimilarityandtheAtmosphericBoundaryLayer ........... 81
4.3.1 DimensionlessShear ................................. 81
4.3.2 TheRossby-SimilarityParametersforStableStratification.. 83
4.4 Ice-EdgeBands ............................................ 83
References..................................................... 85
5 TurbulenceScalesfortheIce/OceanBoundaryLayer .............. 87
5.1 NeutralOBLScales ........................................ 87
5.1.1 IceStationWeddell .................................. 87
5.1.2 IceStationPolarstern................................. 93
5.2 TheIOBLwithStabilizingBoundaryBuoyancyFlux ............ 95
5.3 TheStaticallyUnstableIOBL ................................ 98
5.4 VelocityScalesintheIOBL..................................102
5.5 SummaryofIOBLScales....................................105
References.....................................................107
6 TheIce/OceanInterface ........................................109
6.1 EnthalpyandSaltBalanceattheInterface......................110
6.2 TurbulentExchangeCoefficients..............................112
6.3 The“Three-Equation”InterfaceSolution.......................114
6.4 HeatFluxMeasurementsandtheStantonNumberforSeaIce .....116
6.5 DoubleDiffusion—Melting..................................118
6.6 DoubleDiffusionandFalseBottoms ..........................119
6.7 Freezing—IsDoubleDiffusionImportant? .....................125
References.....................................................130
7 ANumericalModelfortheIce/OceanBoundaryLayer.............133
7.1 DifferenceEquations .......................................133
7.2 BoundaryConditions .......................................135
7.2.1 FluxofVariableθSpecifiedatUpperSurface ............136
7.2.2 VariableθSpecifiedatUpperSurface...................136
7.2.3 DynamicMomentumFluxCondition ...................137
7.2.4 FluxofθSpecifiedattheBottomofModelDomain.......138
7.2.5 θSpecifiedattheBottomoftheModelDomain ..........138
Contents ix
7.3 Steady-StateMomentumEquation ............................139
7.4 DistributedSources.........................................139
7.5 SolutionTechnique .........................................140
7.6 TheLocalTurbulenceClosureModel..........................140
7.7 TheIce/OceanInterfaceSubmodel............................143
References.....................................................143
8 LTCModelingExamples........................................145
8.1 DiurnalHeatingNeartheSolstice,SHEBA.....................146
8.2 InertialOscillationsinLateSummer,SHEBA...................151
8.2.1 WindForcedModel ..................................151
8.2.2 ModelsForcedbySurfaceVelocity .....................157
8.2.3 Short-TermVelocityPrediction ........................160
8.3 MarginalStaticStability,MaudNESS..........................162
References.....................................................170
9 TheSteadyLocalTurbulenceClosureModel......................173
9.1 ModelDescription..........................................176
9.2 TheEddyViscosity/DiffusivityIteration .......................177
9.3 Applications...............................................184
9.3.1 IceStationPolarstern.................................184
9.3.2 UndericeHydraulicRoughnessforSHEBA ..............186
9.3.3 SHEBATimeSeries..................................189
References.....................................................192
ColourPlates ......................................................193
Index .............................................................213
Chapter 1
Introduction
Abstract:Earth’spolarregionsplayapivotalroleinclimate,bothasanimportant
mediatorinexchangesbetweentheatmosphereandglobalocean,andasaharbinger
ofclimatechange.Centraltothisimpactisathinlayerofseaicethatispredomi-
nantlyseasonal,andatmaximumextent(attheendofaustralwinter)coversroughly
8%oftheworldoceanarea.Seaiceaffectsclimateinseveralimportantways.Itef-
fectivelyinsulatestheoceanfromthecoldpolaratmosphere,reducingbothoutgoing
longwaveradiationandconvectiveheatexchange;itreflectsamuchhigherpropor-
tionofincomingshortwaveradiationthandoesopenwater;andbyrejectingsaltasit
freezes,iscapableofproducingthecold,salinewaterthatconstitutestheendpoint
in mixing processes that determine the density of the abyssal ocean. This chapter
discusses the rationale behind a monograph on how sea ice affects atmosphere-
oceanexchangesandhowstudiesofturbulentexchangeintheice-oceanboundary
layer have revealed much about how planetary boundary layers (where rotation is
important) work in general. It briefly describes pertinent ice-station exercises, and
laysouttheframeworkforsubsequentchapters.
1.1 ArcticChange
In early October 1997, I was part of a large party of polar scientists establishing
the Surface Heat Budget of the Arctic (SHEBA) ice station, which was slated to
driftforayearinmultiyearpackiceovertheCanadianBasininthewesternArctic
Ocean. Its purpose was to assess the various energy components responsible for
maintainingtheperennialseaiceoftheArctic.Earlier,afteralongweekwaitingin
Tuktoyaktuk,NWT,fordecentflyingweather,mostofushadboardedtheCanadian
CoastGuardicebreakerDesGrosiellier,whichwastoserveasourdriftingbasefor
thenextyear,anticipatinganarduoustripfollowingourescorticebreaker(theCCS
Louis St. Laurent) as it battered its way through thick ice toward the center of the
Beaufort Gyre. Instead, those of us who had been in that part of the Arctic before
wereastonishedathoweasyourpassagewasiniceoftenameterorlessthick.After
M.McPhee,Air-Ice-OceanInteraction,1–14. 1
(cid:1)c SpringerScience+BusinessMediaB.V.,2008
2 1 Introduction
alongsearchduringwhichwebeganto wonderifwe wouldevenfinda floewith
adecentchanceofsurvivingthroughthenextsummer,weeventuallysettledonice
about2mthick,andbegantheintenseactivityofdeployingthevariousinstrument
systems.
Sometimeduringthatfirstweekontheice,Isatforaninterviewwithreporters
fromanationalnewsnetwork,andduringthequestioningtriedtosuccinctlyvoice
thelongpracticedtalkingpointssummarizingtherationaleforthiscomplexandex-
pensiveexperiment:thatclimatemodelsweresensitivetotheinsulatingandalbedo
properties of sea ice; that polar regions were the “canary in the mine” for global
warming;that many of us suspected, even if we could not proveit unequivocally,
thatwarmingclimatewastiedtoourcollectiveappetiteforfossilcarbon,etc. The
interviewwaslong,andofcourse,Iwasanxioustogetbacktothetaskofputting
myinstrumentsinthewater,yetIalsounderstoodthenecessityofcommunicating
ourworkandwhywethoughtitimportant.1
Within a couple of days after the media interview, we were able to start the
SHEBA ocean profiler and to obtain the first samples of upper ocean temperature
andsalinity.ThateveningIlookedovertheinitialprofiles,andcomparedthemwith
data taken from a nearby location at the same time of year during the Arctic Ice
Dynamics Joint Experiment(AIDJEX) in 1975. I had trouble sleeping that night,
returningagainandagaintothe thoughtthatmychildrenor atleasttheir children
would live to see an Arctic free of perennial sea ice. What kept me awake was a
nebulousjuxtapositionof the intellectual versus emotionalsides of being a scien-
tist.JustdaysbeforeIhadtriedtoexplaintowhatmightconceivablybeatelevision
audienceofmillionsofpeoplehowourcravingforfossilfuelscould,accordingto
thebestmodelswehad,permanentlychangeatleastoneofthedistinguishingpolar
capsof our planet,and that our mission here was to try to better understandwhat
roleratheresotericprocesseslikethealbedofeedbackmightplayinthattransition.
The analytical side of me understood and accepted those physical arguments, yet
there was still somethingessentially conservativein me that rejected the idea that
my species could really modify something as fundamental as the earth’s climate
inthe shortspanofafew decades.Butherewasevidencethatthingswereindeed
changing,perhapsmuchfasterthanwehadthoughtpossible.
Whythoseinitialprofilestriggeredmyconcernrequiressomeexplanation.First,
theyindicatedthattheupperoceannearthecenteroftheBeaufortGyrewasatleast
10%fresherthanithadbeeninanypreviousmeasurementsIhadseen.Datafrom
thecentralpartoftheGyrearequitelimitedbecausecompactandthickmultiyear
sea ice had traditionally made it one of the hardest Arctic regions to sample. By
itself,thefresheningwassomewhatalarmingbutcouldhavebeenduetoavariety
offactors,includinganaccumulationoverseveralyearsoffreshwaterintothere-
gionfromenhancedcontinentalrunoffcombinedwith changesin the wind-driven
circulation.However,fromstudyingupperoceanevolutionatthefourAIDJEXdrift
1Whentheinterviewfinallyairedlaterthatfallononeofthenetworkmorningshows,itlastedfor
lessthan1min,andcomprisedmainlymycommunicatingthat,yes,Ihadaccidentallyfalleninthe
ArcticOceanbefore,andthat,yes,itwascold...Myexperiencewithothermediainterviewsand
conversationswithjournalistsduringtheSHEBAdeploymentwasingeneralmuchmorepositive.
1.1 ArcticChange 3
stationsduringthesummerof1975,weknewthatinthenormalcourseoftheannual
melt cycle, fresh water from the surface would form a relatively shallow seasonal
pycnocline(densitygradient).Justbelowthiswouldbealayerofwaterpreserving
approximatelythesametemperatureandsalinitycharacteristicsasthepreviouswin-
ter’smixedlayer. By calculatingthe changein salinityofthe water columnabove
thisremnantlayer,wecouldestimatetheamountoffreshwateraddedoverthemelt
season.ItwasclearfromthatfirstSHEBAsampleinearlyOctoberthataremnant
mixedlayerexistedfromabout30–45mdepth,andthattheseasonalmixedlayerin
October(widespreadbasalfreezinghadnotyetstarted)wassofreshthattheremust
havebeenexcessivemeltduringthesummerof1997.2Inotherwords,theevidence
indicatedthatastrongice-albedofeedbackhadkickedin,andasIlayinmybunk
aboardtheDesGrosiellierthatnightwhathadbeenupuntilthenatheoreticalexer-
cisenowseemedveryreal.
Theconceptofalbedofeedbackiseasilygrasped—basicallyiceishighlyreflec-
tiveofincomingshortwave(solar)radiationwhileopenseawaterabsorbsnearlyall
of it, so more open water melts ice which creates more open water, and so on—
yet in addition to seasonal changes in albedo of the sea ice itself (Perovich et al.
2002),therearemanysubtletiesintheproblem,includingstorageofsensibleheat
in the upperocean,the rate at which ice melts in contactwith abovefreezingwa-
ter, protection of thin ice by collection of meltwater at the ice undersurface, and
mixingofsensibleheatfrombelowtheice-oceanboundarylayer(hereafterabbre-
viatedIOBL).
Fromanearlieranalysisofocean-to-iceheatfluxduringtheAIDJEXexperiment
inthesummerof1975(MaykutandMcPhee1995),wehadgainedanappreciation
fortheimpactofrelativelysmallchangesiniceconcentrationontheicemassbal-
ance.AIDJEXcomprisedanarrayoffourdriftstations,threeofwhichmadeatrian-
glewithsidesroughly100kmlong,surroundingacentralstation.Overthecourse
ofthesummer,wefoundthatintegratedoceanheatfluxattheeasternmoststation
(Blue Fox) was about 200MJm−2 compared with about 150MJm−2 at the other
stations.Thedifference,equivalenttoroughly20cmoficemelt,nearlyallaccumu-
latedduringa ten-dayperiodbeginningaboutAugust10,nearlytwo monthsafter
the summer solstice. A mosaic of aerial photographscoveringthe entire AIDJEX
array taken fortuitously on August 18, revealed that there was considerably more
openwaterinthevicinityofBlueFoxcomparedwiththeotherstations.Apparently
this“openwindow”(weestimatedabout25%openwater)duringarelativelybrief
periodin late summerwas enoughto increaseice meltbyabouta thirdcompared
withthemorecompact(10%openwater)regionstothewest.
In the decade following the 1997–1998 SHEBA deployment, most of the sci-
entific community and indeed the mass media have become aware of profound
changesoccurringintheArctic.Withregardtoseaice,themoststrikingsymptom
2Welaterquantifiedtheseideas(McPheeetal.1998)andsuggestedthatduringthe1997summer,
fresheningequivalenttoasmuchas2.5moficemelthadoccurredintheseasonalmixedlayerin
theSHEBAvicinity.Wecitedisotopeevidence(courtesyD.Kadko)thatwaterintheintermediate
remnantlayerhadbeenincontactwiththesurfaceearlierinthesummer,andruledoutadvection
offreshrunoffastheprimarysourcebecauseofourdistancefromthecontinentalmargin.
