.1n/lal.r oJ GlaciologJ' 23 1996 (' Internatio na l G laciological Society NUDlerical Dlodelling of a fast-flowing outlet glacier: experiDlents with different basal conditions FR:-\;'-JK P ,\TTYi\ De/Jar/lllen / of G eograjJ/~) I . "rije ['"il'eni/eil Brum/, B-1050 Bumel, BelgiulII A BSTRACT, R ecent o iJse J'\'ati o ns in Shirase Dra in age Basin, Enderb\' L a nd, Anta rcti ca, sholl' tha t the ice sheet is thinning a t the consid(: ra ble ra te of 0,5 (,0 m ai, S urface \'clocities in the stream a rea read; m ore tha n 2000 m ai, making S hirasc G lacier one of the fas test-fl o\l'ing glaciers in East Anta rcti ca, .\ numeri cal im'esti ga ti on of the pITSe nt stress fi eld in S hirase G lacier sholl's the existence of a large tra nsition zone 200 km in leng th w here bOlh shea ring a nd stretching a rc of equal im porta nce, fo ll owed b y a slI Tam zone 0(' a pproxima tely 50 km , \I'here stretchill g is the m ajor deform a ti o n process, In o rder to imprO\ 'e insig ht into the preselll tra nsient beha\'iour of the ice-sheet sys tem , a t\\'o-dimensiona ltime-dependent fl o\l'line model has been d e\'e loped, taking into account the ice-stream m echa ni cs, Bo th bedrock adj ustment a n cl ice tempera ture a re ta ken into ac('oulll a nd the templ'I'a lU re field is full y coupled to the ice-shcet \'C locit)' fiel d, Experiments were carried o ut \\'ith dilTerent basal m o ti o n conditio ns in order to understa nd their influen ce o n the cl\'na mic beha\'io ur of th e ice sheet a nd the stream a rea in pa rticul a r. R es ults revcaled' that \I,hen basa l mo ti o n becom es the d omina nt d eforma ti o n p rocess, (partia l) disintegra ti o n of the ice sheet is counteracted by cold er basal-ice tem pera tures due to hig her ad\'Cc ti on ra tes , This giyes rise to a cycli c behayi o ur in ice-sheet res ponse a nd la rge cha nges in local imba la nce \'a lues, LIST OF SYMBOLS T' T rela ti\'C to p ress ure m elting (K v, H ori zonta l \'elocity (m a I) a Arrhenius consta nt (Pa lIa I) Basal-sliding \'C locit)' ( 111 a I ) A l ee fl ow-l a H ' pa rame ter (Pa 11 m 2" a I ) Vertical m ean \'eloeity (m a I) A, Sliding-l a w para m eter W \ ' crtical \'cloci t y (m a I ) b FI O\\'-ba nd \\' id th (m ) ,1' H o ri zonta l coordina te (m ) cl' S pecifi c heat capacity U kg 1 K I ) Z \'ertieal coordina tc (m ) 2 D DilTusio n coeffi cien t (m a I) G eom etric consta nt (;:::02 ,0 ) g G ra \'ita ti o n consta nt (9,8 Im s 2) W a ter-film d epth (111 ) G Geotherma l heat flu x (-54 ,6 m\\' 2) C ritical pa rticle size ( 111 ) h Bedrock ele\'a ti on a bo\'e present sea Ic\'(' 1 (m ) Kro neckcr d elta H Ice thickn ess (m ) H ori zonta l g radient a t d epth ( k i Therma l cond uctiyi t)' of ice (j m 1 K 1 a I ) Eflccti\'C shear-stra in ra te (a I) L Spec ifi c la tent heat of fu sion (3,35 x 10'; ] 111 1 K 1 a I) Shea r-stra in rate (a I) m Flo\\'-enha ncem ent factor G/ ki (geothe rl11 a l hea t) (Km I ) /lJ S urface m ass ba la nce (m a 1 ice equi\'a lent ) Bo unda ry n due (Q (surface) or I (bo llo m ) N ElTec ti \'e norm a l pressure (Pa ) Lithos ta ti c stress compo nent (Pa ) 11 Glen fl O\\'-l aw exponent (3) Viscosit\, of\l'a ler ( 1. 8 x 10 :l Pas) " 'l p Sliding-l a \\' coeffi cient (0 3) Ice d enSity (9 10kg m ') Pg Press ure g rad ient (P a 111 I) Sea-wa ter d ensit y ( 1028 kg 111 3) q Sliding-l a w coeffi cient (0 2) K orma l stress a t the base (P a ) Q Acti n llio n energy fo r creep U m oll ) Ice-shell' back-pressurc (Pa ) Q\\' W a ter flu x (m:ls I ) T cmpera ture-corrcctio n facto r (0 ,0 0, I Cl ) R U ni\'ersal gas consta nt (8,3 14J m ol I K I ) Basal shear stress (Pa ) R i) R es isti w' stress (Pa ) Effec ti \'(:' slress ( Pa ) S Basal-melting ra te (m a 1 ice equi\'a lent ) Dri\'ing stress Pa l t Time (a rycar j) Stress IPa ) T Ice tempera ture (K ) Stress d C'\, ia tor (Pa) 7() Absolute temperature (2 73 ,1 5 K ) V ertical dimensio n\css coordina te 237 Pattyn: Numerical modelling of a fast-flowing outlet gLacier INTRODUCTION The d ynamic behaviour of a large polar ice sheet is well understood; grounded ice flow is basically governed by shearing close to th e bed. In its most simplisti c form, the basal shear stress equals ice density times gravity times overburden depth times surface slope, whi ch Hutter (1993) defined as the glaciologist's first commandment. H owever, likc a ny physical sys tem, a n ice sheet is not onl y controlled by its internal d ynamics but a lso by its bounda ry conditions, which are less well understood. The environmental processes such as surfacc tempera ture a nd mass balance act as the upper bounda ry a nd a re in ma ny ice-shee t models regarded as the ex ternal sys tem forcing. The present environmenta l conditions th ereby se rve as a reference. The two remaining boundaries, on which we will further concentra te in this pa per, are th e basal motion as a lower and the margin d yna mics as th e outer boundary condition. The basal vclocity depends on the interna l ice dynamics, the bedrock conditions and the prese nce of water a t the ice-shee t base. Basa l velocity will thus play a role when the tempera ture of the basal ice is a t the melting point and will gain more importance cl ose to the ma rgin where it interacts with the ma rgin ice d ynamics . \Vhen the ice-sheet ma rgin termin a tes at th e sea in th e form of a flo a ting ice shelf, a tra nsition zone can be d efin ed where the ice-shee t dynami cs gradua ll y e\'olve towards ice-shelf d ynamics. E labora te studi es on this Fig. 1. Location mal) of Shirase Drainage Basin . The grounding zone have revealed th a t for small basal mo ti on dashed line represen ts the celltral.J7owline, as Inimm)' in/)lIt the width of the transition zone is of the same order of Jar the model/ing experiments. The.J7owLille starts at Dome magnitude as the ice thickness, so tha t the grounding zone F, folLo ws more or less t/ie 40° E meridian towards is reduced to a grounding line a nd the shallow-ice Llil:;,ow-Holmbukta , and ends at Sizirase GLacier in a approximation still holds, provided that there is no floating ice tongue. passive grounding of th e ice shelf. A full deri vati on of the Stokes ba la nce equa ti ons is not necessary; it suffices to calculate the longitudina l stress deviator along the grounding line and prescribe a longitudinal stress near Dome F (77 °22' S, 39°37' E ) to LLitzow-Holmbukta. gradient (Van der Veen, 1987). Grounding-lin e mO\'e­ Shirase Glacier is one of the fastes t-flowing Antarctic ment is thus only governed by ice-sheet mecha ni cs glaciers, with " elocities up to 2700 m a- I in the ice-stream (Hindma rsh, 1993). This situa ti on is the commones t region (Fujii, 1981 ). The ice flow in the central drainage outer boundary a t the edge of the East Anta rcti c ice shee t basin is furthermore characteri zed by large submergence where a steep surface slope, cha racterizing grounded ice, \'eloci ti es (Naruse, 1979). Consecutiye measurements in a bruptly changes to a sma ll surface gradient where the ice this area (N aruse, 1979; Nishio a nd others, 1989; T oh and begins floating. Shibuya, 1992) have pointed to a large thinning rate However, la rge amoun ts of An ta rctic ice are not ra nging from 0.5 to 2.0 m a I in the region where the drained along th ese ma rgins but through fas t outlet surface elevation is lower than 2800 m. K ameda and glaciers or ice streams, which a re beli eved to be more others (1990) concluded from a study of the tota l gas sensiti\'e to environmenta l changes.