Antarctic ice shelf caverns

33 Pages·2014·6.33 MB·English

TheCryosphereDiscuss.,8,919–951,2014 O D
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doi:10.5194/tcd-8-919-2014 Discussionscc s
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Thisdiscussionpaperis/hasbeenunderreviewforthejournalTheCryosphere(TC). p
e Antarctic ice shelf
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A data-constrained model for D D.Olbersetal.
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compatibility check of remotely sensed s
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basal melting with the hydrography in P
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front of Antarctic ice shelves r
Conclusions References
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D. Olbers1, H. H. Hellmer1, and F. F. J. H. Buck2 D Tables Figures
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1AlfredWegenerInstituteHelmholtzCentreforPolarandMarineResearch,Bussestr.24, us J I
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27570Bremerhaven,Germany io
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2Leibniz-InstituteforBalticSeaResearch,18119Rostock-Warnemünde,Germany P J I
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Received:19December2013–Accepted:1January2014–Published:5February2014 e Back Close
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Correspondenceto:D.Olbers([email protected]) | FullScreen/Esc
PublishedbyCopernicusPublicationsonbehalfoftheEuropeanGeosciencesUnion. D
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Abstract D
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The ice shelf caverns around Antarctica are sources of cold and fresh water which s
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contributes to the formation of Antarctic bottom water and thus to the ventilation of the io 8,919–951,2014
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deep basins of the World Ocean. While a realistic simulation of the cavern circulation P
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5 requires high resolution, because of the complicated bottom topography and ice shelf pe Antarctic ice shelf
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morphology, the physics of melting and freezing at the ice shelf base is relatively sim- caverns
ple.Wehavedevelopedananalyticallysolvableboxmodelofthecavernthermohaline |
state, using the formulation of melting and freezing as in Olbers and Hellmer (2010). D D.Olbersetal.
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There is high resolution along the cavern’s path of the overturning circulation whereas c
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10 the cross-path resolution is fairly coarse. The circulation in the cavern is prescribed sio
and used as a tuning parameter to constrain the solution by attempting to match ob- n TitlePage
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served ranges for outflow temperature and salinity at the ice shelf front as well as of a
p Abstract Introduction
themeanbasalmeltrate.Themethod,testedforsixAntarcticiceshelves,canbeused e
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for a quick estimate of melt/freeze rates and the overturning rate in particular caverns, Conclusions References
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giventhetemperatureandsalinityoftheinflowandtheabovementionedconstrainsfor
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outflowandmelting.Inturn,themodelcanalsobeusedfortestingthecompatibilityof is
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remotely sensed basal mass loss with observed cavern inflow characteristics. u
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1 Introduction P
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Thephysicalprocessesinsideiceshelfcavernsarestillmostlyunobservable.Assatel-
lite and airborne observations became available, better estimates of the mass budget | FullScreen/Esc
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of the ice lid were possible (Rignot, 1998; Corr et al., 2001; Shepherd et al., 2004; D
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Rignot et al., 2013). Autonomous vehicles have been developed for entering a cav- c Printer-friendlyVersion
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ern and measure bathymetric, hydrographic, chemical and turbulence parameters, but s
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the range of such vehicles is very limited and only few expeditions took place so far ion InteractiveDiscussion
(Nicholls et al., 2006; Jenkins et al., 2010). Numerical models of various complexity P
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havebeendeveloped(HellmerandOlbers,1989;Jenkins,1991;HollandandJenkins, e
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1999; Gerdes et al., 1999; Beckmann et al., 1999; Losch, 2008; Timmermann et al., D
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2012) that are driven by the observed hydrographic characteristics (temperature and c TCD
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salinity)attheiceshelffrontorontheboundaryoftheadjacentoceanpart.Suchmod- s
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els help putting the scattered information together, but it is by no means evident that n
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5 the collected knowledge should be consistent with the model output, i.e., that a model a
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driven by observations at the ice front yields the melt rate which is inferred from mass e Antarctic ice shelf
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budget calculations. If the model possesses a sufficient scope in terms of the dynam- caverns
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ics,thermodynamicsandresolution,itisatthesametimestilltooelaboratetoscanthe
D D.Olbersetal.
space of tuning parameters adequately.
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10 The approach introduced in the present study uses a highly simplified model, al- u
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lowing for an analytical solution and having hence the potential to scan the complete s
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parameter space and possibly finding a parameter set for which the solution agrees n TitlePage
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with the observations (within a reasonable range of uncertainties) available for a par- a
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ticularcavern.Themodelaimstodescribetheoverturninginacross-cavernintegrated r
sense, the balances of heat and salt are solved analytically for a steady state, assum- Conclusions References
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ing a given overturning rate and pattern; there are thus no dynamics considered. The
D Tables Figures
model simply transfers the thermohaline inflow conditions and the coupling to the heat is
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and freshwater exchanges at the ice shelf/ocean interface into the outflow conditions. u
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The melting/freezing physics at this interface are those usually implemented in high- io
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resolution ice shelf cavern circulation models, the “three-equations model” of Hellmer J I
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and Olbers (1989); Olbers and Hellmer (2010). Analyzing the solution as function of p
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theoverturningrate,arangeoffeasiblevaluesisextractedwhichmeettheconstraints r
claimed by the observations. The constraints are simply formulated as intervals of al- | FullScreen/Esc
lowed values (the mean plus/minus an uncertainty), in our case for the temperature
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and salinity of the cavern outflow and the overall basal melt rate. The feasibility range is
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fortheoverturningrateisthentransferredbythemodelsolutiontofeasibilityrangesfor s
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prognosticmodelvariables.Thiswaywecomeupwithabestestimateoftheoverturn- io InteractiveDiscussion
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ing and basal melt rate for the specific cavern. Depending on the a priori knowledge – P
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thedataconstraints–thefeasibilityrangemaybyquitewide,narroworevenempty.In p
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thatcaseallsolutionsfailtopassthroughtheconstrainedregioninthedataspaceand D
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thedata,comingfromdiversesourcessuchashydrographyandremotesensing,must c TCD
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be judged as incompatible. s
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InSect.2thegoverningequationsarederivedandsolved.InSect.3themodelsetup n
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5 is described and the method of data constraints is explained simulating the Amery Ice a
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Shelf (AMY) cavern, followed by the application of the model to five more caverns, e Antarctic ice shelf
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namelyPineIslandIceShelf(PIIS),Ross(ROS),Fimbulisen(FIM),Ronne(RON),and caverns
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LarsenC(LAR)iceshelves(Sect.4).Thepaperendswithconcludingremarksandan
D D.Olbersetal.
Appendix configuring the procedure for setting up the box model geometry.
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10 2 Governing equations and solution ion TitlePage
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The model represents in a crude manner the circulation in oceanic caverns beneath p Abstract Introduction
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ice shelves and aims at to provide an efficient calculation of melting and/or freezing r
Conclusions References
ratesfrominflowconditions.Thegoverningequationsareformulatedsimilartotheap- |
proach of Olbers and Hellmer (2010), but simplified with respect to the dynamics of D Tables Figures
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15 theoverturningrateandpattern(whicharenowspecifiedparameters)andextendedto cu
a multitude of boxes under the ice draft (see Fig. 1). In contrast to Olbers and Hellmer s J I
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(2010),theattempttomodelthewatercharacteristicsinfrontoftheicecavernisaban- ion
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doned. The model is thus restricted to the immediate cavern domain and includes an P
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arbitrarilylargenumberofboxesbeneaththeicedraftandasinglebottombox(labeled e Back Close
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with index d) between the bottom and the layer of sub-ice boxes. The equations for
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temperature and salinity are formulated as balance between (horizontal and vertical) | FullScreen/Esc
advection, (vertical) diffusion and heat and freshwater exchange with the ice shelf by D
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melting/freezing. c Printer-friendlyVersion
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Weregardaparticularsub-iceboxwithvolumeV andcontactareaAtotheice.The D
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heat and salt balances are written as: c TCD
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V dT =(u−w)T +wT −uT −Aκ(T −T )+A(γ +m)(T −T) ion 8,919–951,2014
dt 0 d d T f P
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dS p
V =(u−w)S +wS −uS−Aκ(S−S )+A(γ +m)(S −S) (1) e Antarctic ice shelf
dt 0 d d S f r
5 caverns
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Heremisthelocalmeltrate(negativeforfreezing),andγ aretheturbulentexchange
T,S
coefficientsforthelayernexttotheiceshelfbase.Furthermore,uisthehorizontalad- Dis D.Olbersetal.
3 −1 c
vectivevolumeflux[m s ],positiveoutoftheboxandtowardstheiceshelffront,and u
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κ =K /h derives from vertical diffusion with a diffusivity K and a vertical scale h. The s
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temperature T and salinity S are prescribed as inflow values from the preceding box n TitlePage
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in the system while Td and Sd are the values in the bottom box. The model considers ap Abstract Introduction
upwellingintothesub-iceboxbyincorporatingafluxw [m3s−1],directedfromthedeep er
Conclusions References
box into the respective sub-ice box. Conservation of mass has been considered, i.e., |
u−w enters from the upstream sub-ice box, w from the deep box, and u leaves to the
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downstream sub-ice box. Note that Eqs. (1) are valid only for u>0 and w >0. is
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The effect of the mixing terms is only marginal: deviations from the zero-mixing ap- us J I
proach only occur for low transport values q∼Aκ, which are typically 103m3s−1. In sio
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view of other model deficiencies and the uncertainty in the prescribed values at the P J I
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ice front we thus abandon the diffusive term in the present study. Without diffusion T p
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and S are fixed and equal to the respective inflow values at the ice shelf front. The r
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linearized freezing temperature: | FullScreen/Esc
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T =aS +b−cp (2) is
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determines the freezing point of seawater for the box with pressure p, represen- sio InteractiveDiscussion
tative for the ice draft, and the constants a=−0.057◦Cpss−1, b=0.0832◦C, and n
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25 c=7.64×10−4◦Cdbar−1. The placement of the pressure point to calculate the freez- ap
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ing temperature Eq. (2) is a critical issue if the resolution is low. It is obvious that the r
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deeper the location in the respective box the higher the resulting local melt rate. In D
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all applications of this study we have chosen the deepest point of the ice draft in the c TCD
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respective box for providing the pressure p (for the resolution with 50 boxes, used in ss
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this study, the location of p is irrelevant). The salinity S is calculated from the “three- n
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5 equations model” (Hellmer and Olbers, 1989; Olbers and Hellmer, 2010), resulting in a
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a quadratic equation for S, the salinity of the melting/freezing layer at the ice shelf e Antarctic ice shelf
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base: caverns
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(T −T)S −δ(S −S)=0 (3) D D.Olbersetal.
f f f is
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withδ =λγS/γT,λ=L/cp=84K(hereListhelatentheatoffusionandcp thespecific uss
10 heat of seawater). The pressure p is set as being representative for each box (see ion TitlePage
below). The solution is given by: P
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s e
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S =F(T,S)= (T −b+cp+d)+ (T −b+cp+d)2− S (4) Conclusions References
f 2a 4a2 a |
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with d =λγ /γ . The local melt rate is determined as: is
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m=γT(T −Tf)/(νλ) (5) sio
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15 where ν=ρice/ρwater=0.89. In the following applications the values for γT=3× Pap
10−5ms−1 and γ =1.2×10−6ms−1 are fixed. e Back Close
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The m term in Eqs. (1) accounts for the change of volume when melting or freezing
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occurs (Jenkins et al., 2001). It appears a bit anachronistic if this term is retained
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whileothermassfluxesrelatedtotheicedynamicsareabsent,whichareimportantfor is
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the volume budget. We will abandon the m term in the present study not only for this u
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reasonbutalsobecausegenerallyγT(cid:29)γS(cid:29)mapplies.Withrespecttotheensemble sio InteractiveDiscussion
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of caverns investigated here, this assumption is questionable only for PIIS where melt
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rates of the order of 40myr−1 (Jacobs et al., 2011) are expected and m thus has ap
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a similar size as γ . r
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WenowsearchforananalyticalsolutionforthesteadystateofthesystemEqs.(1)– D
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(5)foranyofthesub-iceboxes,neglectingthemcorrectionandconsideringtheequa- c TCD
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tions with κ =0. With the abbreviations u =γ A, u =γ A, we obtain the two equa- ss
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tions: n
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5 (u+uT) T =(u−w) T0+wTd+uT(a F(T,S)+b−cp) per Antarctic ice shelf
(u+u ) S =(u−w) S +wS +u F(T,S) (6) caverns
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fortemperatureT andsalinityS inthebox.Mathematically,wefindaquadraticequation D D.Olbersetal.
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foreitherT orS,whichisreadilysolved.However,onlyonesolutionconformswiththe c
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10 positive root in Sf, as given by Eq. (4). sio
Knowing the solution for the outflow as function of the inflow for a single sub-ice n TitlePage
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box we may iterate it for an ensemble of subsequent boxes. The inflow values of tem- a
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perature and salinity are then the outflow values of the upstream box. Counting the e
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sub-iceboxesbyj =1,···,n,startingatthegroundingline,theoutwardfluxu ofboxj Conclusions References
j |
is given by u =Pj w . The upwelling w pattern, which will be prescribed and used
15 j i=1 i i D Tables Figures
as a tuning parameter, might change from box to box. The total overturning strength is
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is q=u =Pn w . The complete model is thus a stack of modules with the above u
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described thermodynamics, with the inflow values of temperature and salinity into the io
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bottom box at the grounding line and outflow Tn,Sn at the front. The latter are then P J I
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determined as function of the upwelling pattern w , the inflow characteristics, and the p
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other fixed parameters. r
An important issue of modeling ocean-ice shelf interaction is the resolution of the | FullScreen/Esc
cavern geometry. A two-box configuration along the ice shelf base, as used in Olbers D
andHellmer(2010),iscertainlytoocoarsetoresolvethemeltingclosetothegrounding is
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line. The resolution of the present model can be increased at no expense as only s
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additional modules of the above described dynamics have to be placed in the stack. io InteractiveDiscussion
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Figure 2 compares the results for different resolutions of the AMY cavern by means of P
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the mean basal melt rate: D
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m¯ =Xn m A /Xn A (7) cuss TCD
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i=1 i=1 n
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shown as function of the total overturning rate q for a specific upwelling pattern (the a
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“fast decrease” scenario, see Sect. 3). The conversion at about 50 sub-ice boxes be- r
caverns
comes obvious. We emphasize that the distribution of melting and its rate in boxes
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close to the grounding line strongly depend on the number of boxes resolving the sub-
D D.Olbersetal.
ice cavern. This difference is mainly due to the above mentioned pressure effect. In is
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all applications of the present study we keep the number of sub-ice boxes fixed to 50, us
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corresponding to the blue line in Fig. 2. io
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3 Model setup and evaluation – Amery Ice Shelf e
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Conclusions References
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We first evaluate the impact of three scenarios of upwelling into the sub-ice boxes un-
derneathAMYonmeltrateandsub-icetemperatureandsalinity,representingdifferent D Tables Figures
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views on the interaction of the inflowing water with the ice shelf base. The upwelling w cu
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is either distributed uniformly along the ice shelf’s center line or concentrated near the s
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groundinglinewitheithersloworfastdecreasetowardsthecaverninterior(Fig.3–left n
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column).Suchdistributiondirectlycontrolsthesub-iceoverturningcirculationreaching a
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itsmaximumattheiceshelffronteitherlinearlyorexponentially(Fig.3–rightcolumn). e Back Close
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TheaveragedmeltrateatthebaseofAMYasafunctionofthemaximumoverturning
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(red lines in Fig. 3 – right column) changes with the prescribed upwelling distribution.
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is strongest when most of the upwelling occurs near the grounding line (Fig. 4). The u
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latter demonstrates the importance of pressure, i.e. depth of the ice shelf base, on the io InteractiveDiscussion
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in-situfreezingpointandthusontheamountofpotentialheatformelting.Theaverage
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melt rate is largest when most of the heat is delivered to – and used at – a deep ice ap
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shelf base. r
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The corresponding T/S diagrams (Fig. 5) show two significant differences for the D
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properties of the sub-ice boxes, namely (1) a warmer temperature minimum for up- c TCD
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welling concentrated near the grounding line and small overturning rates together with s
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(2) a smaller spread of the T/S lines. The latter becomes smaller as the bulk of up- n
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welling moves towards the grounding zone. All lines start at the inflow values (upper a
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right corner) following the “Gade line” (Gade, 1979), which represents the dilution re- e Antarctic ice shelf
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lation for ice melting/forming in sea water, towards the salinity minimum and related caverns
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in-situ freezing temperature. The latter increases as the water reaches the freezing
D D.Olbersetal.
pointatlowerpressure,i.e.shallowericeshelfbase.Beyondthispointfreezingoccurs, is
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adding salt and heat to the sub-ice boxes. Deviations from the straight line are due to u
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the upwelling, which extends to the ice shelf front in the “uniform” case and prevents sio
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the formation of ice in the sub-ice boxes (Fig. 6 – upper left panel). With no upwelling
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along most of the ice shelf base and strong overturning the T/S characteristics follow ap Abstract Introduction
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the “Gade-line” (Fig. 5 – right panel). r
The impact of different upwelling distributions on the melt/freeze pattern and related Conclusions References
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temperature and salinity in the sub-AMY boxes as well as at the ocean/AMY interface
D Tables Figures
is shown in Fig. 6. As mentioned above, uniform upwelling along the ice shelf base is
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cutsofficeformationforlowoverturningrates,preventingtheT/S characteristicsfrom us J I
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following the “Gade line”. In contrast, intense upwelling in the grounding zone slightly io
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20 reducesthefastdecreaseofmeltingbutcausesanearlierandamorepronouncedshift P J I
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into the freezing zone. Especially for low overturning rates part of the basal mass loss p
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is compensated by the basal accretion of ice. Temperatures and salinities in the sub- r
iceboxesalmostfollowthesamepatternwithafastreductionoverthegroundingzone | FullScreen/Esc
followed by a moderate increase towards the ice shelf front. The reduction becomes D
25 lessastheoverturningrateincreases,extendingallthewaytotheiceshelffrontforthe isc Printer-friendlyVersion
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“fast decrease” upwelling scenario (Fig. 6 – lower row). Non-uniform upwelling causes s
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a crossing of the T/S lines near the ice shelffront, indicating either intense freshening io InteractiveDiscussion
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of the sub-ice boxes due to longer lasting melting for high overturning or intense salt P
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rejection due to longer lasting freezing for low overturning. pe
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In summary, the pattern of upwelling into the sub-ice boxes has a significant impact D
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on the basal mass flux and thus on the ice thickness distribution with consequences c TCD
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for the ice shelf dynamics, e.g. Determann (1991). s
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4 Data-constrained application p
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5 Inthefollowing,weusethe50-boxversionforfiveothercavernslocatedaroundAntarc- |
tica: Pine Island Ice Shelf (PIIS), Ross (ROS), Fimbulisen (FIM), Ronne (RON), and
D D.Olbersetal.
LarsenC(LAR)iceshelves.AsforAMY,theinflowtemperatureandsalinity,T andS , is
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arechosenfromhydrographicobservationsattherespectivecavernfront.Tocompare s
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themodeloutputwithobservationsweconcentrateonthemeasuredhydrographicout- io
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flowcharacteristics,T andS ,andthemeanbasalmeltratem¯.Themostlikelyvalues P
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ofT ,S andm¯,includingreasonableuncertainties(asminimaandmaxima),arelisted p Abstract Introduction
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inTable1,obtainedfromobservationsasreferenced.Thoughtheminima-maximacon-
Conclusions References
straintsarecertainlyabitarbitrary(Table2),theentiretyofconstraintsshouldrepresent |
the feasibility space reasonably well. D Tables Figures
15 The model is evaluated for a certain range of transport values q in a specified up- iscu
welling scenario and fixed values for the other parameters (Table 1). From a math- s J I
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ematical point of view, we are looking at the trajectory Tn(q),Sn(q), and m¯(q) in the ion J I
three-dimensional space with coordinates T ,S and m¯. A rough measure of consis- P
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tency of the model and the data with their uncertainties is found when the trajectory e Back Close
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enterstheconstraingboxdefinedbyT ±∆T ,S ±∆S ,m¯ ±∆m¯ derivedfromthecon-
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straintsofminimumandmaximumvalues.Thevaluesq ofentranceofthetrajectory | FullScreen/Esc
min
into and q of exit of the trajectory out of the constraining box defines the feasibility D
max is
range q <q<q where the model has solutions consistent with all constraints. If c Printer-friendlyVersion
min max u
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non-empty,thefeasibilityrangeisplottedasblacklinesegmentinthefollowingfigures. s
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We continue with AMY to illustrate the data constraint method, though AMY turns n
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out to be an extreme case. Within the given thresholds only the “fast decrease” sce- a
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nario (blue line) is able to meet all constraints (Fig. 7) for the interval q =0.08Sv< e
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