JOllrnal oj Glaciology, r-ol. 41, .\ '0. 137, 1995

Frequent outburst floods from South Tahotna Glacier, , V.S.A.: relation to debris flows, meteorological origin and itnplications for subglacial hydrology

]OSEPH S. WALDER AND CAROLYi\' L. DRIEDGER U.S. Geological SlIrvq , Cascades r olcallo Observatory, 5400 MacArthllr Boulevard, Vancou ver, Washingtoll 98661, U.S.A.

ABSTRACT. Des tructi" e d ebris Oows occur frequently a t glacierized Mount R ainier volcano, \\'ashington, U .S.A. Twenty-three such Oows have occurred in the Tahoma Creek vall ey since 196 7. H ydrologic a nd geomorphic evidence indicate that a ll or nearl y a ll of these Oows bcgan as outburst fl oods from South . F lood waters arc stored subglacia ll y. The vo lu m e of stored water discharged during a typical outburst Oood would fo rm a layer severa l centimeters thick over the bed of the entire glacier, a lthough it is more likely that la rge linked cavities accoun t for most of the storage. Statistical analys is shows th at outburst fl oods usuall y occur during periods of atypicall y ho t or rain y weather in summer or ea rl y a utumn, and that the probability of a n outburst in creases with temperature (a proxy m easure of a bla tion rate) or rainfa ll rate. We suggest that outburst Ooods are triggered by rapid water input to the glacier bed, causing water-piT sure transients that d es ta bilize the linked­ cm'it)' s\,stem. The co rrelation between outburst fl ood. and m eteorological factors casts doubt on a n earli er hypothes is th at melting a round geothermal ,'ents triggers outburst Ooods from .

INTRODUCTION sta tistical analysis wh ich in dicate tha t debris !lows (or outburst Ooods) are predictable in the sense that they a re D estructive debris !lows freq uen Ll y move a long stream strong ly correlated with meas ured d aily rainfall a nd vall eys on glacierized :-{ount R a inier, Was hing ton, the maximum air tempera ture, data that may be consid ercd hi ghes t volcano in the co termino us United States. The proxies for the rate of water input to South Tahoma small es t. but most frequent, of these debris !lows hm'e Glacier. Finall y, wc sugges t a pla usible hydrological genera ll y been consid ered to originate as glacial o utburst mod el 0[' the glacier tha t accounts for the link between !l oods (Richardson, 1968; Crandell , 19 71; Dried ger and weather and outburst Oood . Fountain, 1989; Scott and others, 1992). Transformation f'r om water !lood to debris Oow generall y occurs in cha nnels cut into stagnant ice a nd glacia ll y d erived DESCRIPTION OF THE STUDY AREA sed im ent near glacier termini. In the last few d ecades, debris !lows have been particularly frequent a long South T ahoma Glacier retreated a nd thinned substan­ Tahoma Creek, which drains South Tahoma G lacier ti a ll y between the mid-19th ce ntury a nd about 1960 (Fig. I). Twenty-three debris Oows moved along T a homa (Sigafoos and H endricks, 1972 ), res ul ting in a stagna n t C reek during the period 1967 92, including 15 in the tongue of roc k-rich ice. The glacier advanced slightly years 1986- 92, a nd repeatedly d a maged a road and between aboLlt 1960 a nd 1975 (summa ri zed in Dried ger visitor facilities in r-.l ount R ainier ;.J a tional Pa rk. (1986)) , with advancing ice overriding o ld er, stagnant ice From 1988 to 1992, we se n 'ed as co nsulta n ts to the (Fig. 2). R apid retreat a nd thinning res umed about 1975, U.S. National Pa rk Service, stud ying debris Oows a long res ulting in yet more rock-ri ch stagna nt ice . Tahoma Creek, their rel ati on to outburst Ooods, and During th e period 1988- 92, ou tl et streams emerged associated geomorphi c change in the Tahoma Creek from the active glacier ice and Oowed over the upper d ra i nage; assessi ng hazards presen ted by debris Oows at stagna nt-ice area (Fig. 2) before merging in to a sing le Tahoma Creek; a nd examining whether th ose Om-vs might stream. Downstrcam of that point, T a homa Cree k !lows for be predictable. A discussion of geomorphic evol u tion a nd 2 km at the bottom of a go rge deeply incised in to stagna nt of hazards is presented by Wald er and Driedger ( 1994). ice, glacial till and flu vioglacial deposits. The nature a nd In the present paper, we first summarize geomorphic and history of that incision, caused by outburst Ooods from hyd rologic data supporting a n o utburst-O ood origin for South T ahoma Glacier, a re described in detail in Walder most or all d ebris Oows. "V c then present res ults of' and Driedge r (1994). BrieOy, incision was initiated by a

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.6'55'

4SOS0'

3 MILES ~-.-L~-,~,,~' • ~LOMmRS

Fig . 1. Index map of Mount Rainier showing location of South Talzoma Glacier and Tahoma Creek. Glaciers are drawn to scale, but streams, cultural features and weather stations (black dots) are shown only schematically . The Talwma Creek picnic area was destroyed by debrisjlows in 1986 and 1987. In addition to the Tahoma Creekjlows described in this paper, destructive debrisjlows triggered by outburst floods have also moved along Kautz Creek, and West Fork White River since the middle of the 20th century.

series of outburst flood s in 1967 (Fig. 2), and was increased defined channel. For purposes of later discussion, we now by fl oods over the next decade. Outburst fl oods transform summarize his observati ons. Swift visuall y estimated fl ow to debris fl ows as they pass through the incised reach. width, depth and velocity, as well as the relative fractions Debris-rich ice that formed the tongue of the active glacier of water and sediment. A hydrograph based on his as late as 1976 has itself been deeply incised since the estimates is shown in Figure 3. The fl ow lasted about renewal of outburst-flood activity in 1986.

600r---r---.----r---r--~--~r_--r_--~--,

RELATION OF OUTBURST FLOODS TO DEBRIS + Estimated discharge data FLOWS 500 -- Debris flow __ ___ . Water portion Most of the evidence for ou tburst fl oods from South '" 400 Tahoma Glacier is circumstantial, owing largely to the '1 w glacier's remoteness from the frequently visited parts of Cl ~ 300 Mount R ainier National Park. A U.S. National Park I U Service employee observed one outburst flood in 1967 (IJ Ci (cited by Crandell (1971, p. 58)) . There is also good 200 evidence that, on at least a few occasions, fl ood waters '''t, emerged near an icefall and thence fl owed over the 100 " glacier's surface, eroding ice along the way (Crandell, "'+------+-- 1971 ; Scott a nd others, 1992). Most of the evidence for 0 I I I I outburst floods, however, h as to do with their relation to 0 10 20 30 40 50 60 70 80 90 ELAPSED TIME FROM ARBITRARY DATUM (min) debris flows. Because of this circumstance, it is necessary briefl y to review pertinent d ata about debris flows at Fig. 3. Hydrograph of the dry-weather debris jlow of 26 Tahoma Creek. July 1988 along Tahoma Creek. The estimated water flux The debris flow of 26 July 1988 was serendipitously within the debris flow is also shown. The abmpt rising observed by U.S. Geological Survey hydrologist C. H . limb is typical of a debris-jlow hydrograph, although Swift (written communication, 28 July 1988) in a reach unlike that of a clear-water flood. Flo w characteristics where the fl ow was neither eroding nor depositing were visually estimated by C. H. Swift, U.S. Geological substantiall y and where it moved within a single, well- Survey, and are probably accurate to about a factor of 2.

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Fig. 2. Oblique aerial /Jhotograph ( 2 October 1984) showing South Tahoma Glacier prior to the outburst-jlood phase that began in 1986. Stagnant-ice zones are indicated. Outburst floods in 1967 initiated illcision oJ the reach oJ TallOma Creek near center . (Photograph Jrom U.S. Geological Surv'!Y archives ill Ta coma, Washing tOil.)

3 80 min. Peak water disch a rge Qp was abou t 190 m Si, excepti on, discussed below) that slum ping stream-bank and a total water volume of approximately 3 x 105 m 3 sediments in the d eepl y in cised reach ofTahoma Creek do passed befo re discharge returned to normal. Average not mobili ze directl y into d ebris fl ows, even during water disch a rge during the debris Oow was about periods of heavy rainfall. Thu we co nclude that dry­ 3 55 m s I - about 15- 20 times the base Oow. These weather d ebris flows along T a homa Creek originate as valu es a re probably accura te to within a factor of 2. outburst fl ood s. Wa ld er a nd Dried ger ( 1994) considered whether Consider n ow the wet-weath er debris Oows. One of so urces of water other tha n o utburst flood s could account these - the d ebris fl ow of 16 O ctober 1988 - evidently for debris fl ows along T a h oma Creek. Of the 23 debris in vo lved a fl owslide of satura ted morainal m a terial fl ow since 1967, 15 (including th e one seen by Swift) (Fig. 4). 16 O ctober 1988 was one of the rainiest d ays occurred during periods o f sunny, dry weather, and it is on record in the period 1986 92 (U .S. National O ceanic pl ausible that at least these 15 fl ows began as outburst and Atmospheric Administra ti on, 1986- 92) , so it is flo ods, because their es tima ted pea k water discharge was conceivabl e tha t the fl owslide was triggered simply by much greater than typical stream flow in Tahoma Creek. rai nfa ll , without an outburst Oood. H owever, between 28 Other potential water so urces are (I) stream flow impounded September (the date of an earlier aerial photograph than by a slope fai lure and then released catastrophica ll y; and Figure 4) a nd 28 O ctober 1988, there had been (2) pore water held within strea m-ba nk sediments th a t substantia l stream incision, ba nk failure, a nd stream slumped and thence moved downstream as a d ebris fl ow. avulsion upstream of the m o rainal slump, in a reach Wald er a nd Driedger ( 1994) showed that neither of these where th e stream crossed stagn a nt ice. This observation at so urces would suffi ce. Ther e is no geomorphic evid ence of least suggests that an outburst fl ood was involved in the damming along T ahoma Creek, nor could a pl ausibly 16 O ctober 1988 debris Oow. Subsequently - once sized landslide dam impound the volume of water during each of the years 1989 through 1991 a nd twice actuall y discharged in a d ebris Oow of typical size a t in 1992 d ebris fl ows moved a long Tahoma Creek T ahoma Creek. There is a lso evid ence (with one possible during rainy periods in late summer or autumn. There is

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Fig. 4. Vertical aerial photograph taken on 28 OctobeT 1988 showing part oj Tahoma Creek drainage. Upstream is toward the top. The circular feature near the center is the scar of a }lowslide that transformed into the debris }low oj 16 October 1988. The geometry of the scar is inconsistent with an origin of this feature as a rotational slump and strongly suggests that the sediment flowed in a liquified state into the gorge. Note that scars oj otha slumps along Tahoma Creek are quite different in shape. ( Photograph by State Department oj Transportation.)

3 no geomorphic evidence that these latter debris flows Glacier Island); and Qp ;::::; 26m s I for a flood with a 2% began as flowslides. annual exceedence probability (the so-called 50 year Wet-weather debris flows of 1989- 92 were comparable flood ). This order-of-magni tude discrepancy, along with to the flow observed by Swift (Fig. 3) in their effects and the lack of evidence for a flowslide origin for these debris in the extent of their deposits, so we ass ume, as an flows, leads us to conclude that the wet-weather debris 3 admittedly rough estimate, that Qp ;::::; 200 m s I for each flows of 1989- 92 probably began as outburst floods, of these flow s. For corn parison, Richardson (1968), on the although part of the water in these debris flows must basis of flood-frequency relationships suggested by comprise pore water in the entrained sediment. In the rest 3 Bodhaine and Thomas (1964), es timated Qp ~ 11 m s I of this paper, we therefore a sume that all debris flows at for the mean annual flood of meteorological origin 111 Tahoma Creek, with the possible exception of the Tahoma Creek (at a point about 5 km downstream of 16 October 1988 event, began as outburst floods.

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RELATION OF OUTBURST FLOODS TO WEATHER 1.0 +.----

All outburst flo ods from South T ahoma Glacier Slllce 1967 have occurred during either summer or early ~ 1 j .....J 0.8 dm + a utumn, as noted also by Driedger and Fountain (1989) i and Scott and others (1992). We did statisti cal analysis of i 1, .__ 1----: --r------. m e teorological data collec ted n ear South T a homa Glacier to tes t whether outburst floods have been Cl.. 0.6 ______t + Debris-flow days correla ted with a typical weather conditions, and -- Parent distribution whether meteorological data might be useful predictors - --- Debri s-flow di stribution of outburst-nood occurrence. The U.S. National Weather Service maintains two 50 100 150 sta ti ons near South T a homa Glacier: one at the Paradise DAILY RAINFALL (mm) Ranger Stati on, a bout 9 km eas t-southeast of G lacier Fig . 5. Cumulative distribution junction rifvalues oJ dai0! Isla nd, a t an elevation of about 1650 m and near rainjalL at the Paradise R anger Station, jor the months Nisqua ll y Glacier; the o ther at Longmire, 9.5 km south­ M ay-November in the years 1986-92. Solid cu rve: aLL east of Glacier Isla nd a t an elevation of about 840 m snow-Jree days. Crosses connected by dashed Line : aLL days (Fig. 1). Stati sti cal a n alysis shows that published values with debris flows . The K oLmogoro v-Smimov statistic dm (U .S . Nati onal O ceanic and Atmospheri c Administ­ is indicated. ra ti on, 1986- 92 ) of dail y rainfall a nd maximum d a ily tempera ture at these two stati ons a re well correla ted. For the period under consideration, we found from linear 1.0 regressIOn:

2 +-' Tma.x( P aradise) = - 4 .0 + 0.9Tma.x(Longmire)(r = 0.92) 0.8 I (1) r >- d t~ I- R (P aradise) = 1.4R(Longmire)(r2 = 0.84) (2) .....J 0.6 cc 1__ where ~na.x is the maximum daily Celsius tempera ture, R « 2 cc _.J is dail y precipitati on, and r2 is the coefIi cient of deter­ 0 a: 0.4 mina tion . Cl.. During the summer a nd autumn of 1989 and 1990, we tried to measure tempera ture and rainfall at an elevati on 0-2 of a bout 2050 m on G lacier Island , near South Tahom a Glacier (Figs I and 2), but data coll ecti on was fr equently 0 interrupted by equipment failures a nd we had to -10 -5 0 5 10 15 20 25 30 35 a bandon th e ex pensive effort to maintain this remo te MAXIMUM DAILY TEMPERATURE ( OC) si te. For th e 1989 d a ta, linea r regression gives the res ult: Fig. 6. Cumulative dist ribution junctioll oJ values oJ TmaA P aradise) = 7.1 + 0.63Tmax (GlaeierIsland) maximum daily temperature at Paradise Ranger Station, (r2 = 0.46). (3) jor the month s M ay- November in theyears 1986- 92. Solid curve : all days. Crosses connected b)! dashed line: aLL da)ls

\'Ve suspec t the tempera ture se nsor a t Glac ier Is la nd with deb ris flows . The KoL7IIogo rov-Smimov statistic dm might have bee n in ad equa tely protected fr om th e effects is indicated. of solar radiati on, a nd that thi s problem bears on the rela ti vely low r2 value. The rain gauge malfun ctioned , so we did not analyze precipitati on d a ta. The 1990 d a ta compiling Figure 6. ) The solid curve in each fi gure is the were too disco ntinuous for meaningfu l analys is. cumul ative distribution function (henceforth CDF); the All in all , avail a ble da ta suggest tha t temperature a nd crosses connected by dash ed lines show the distributions precipitati on on the south side of Mount R ainier a re for days on which outburst fl oods fr om So uth T ahoma spa ti all y coherent. In wha t foll ows, we wi ll ass ume tha t Glacier occurred. We now pose the ques tion: "Vhat is the weather data from Pa radise may be used as surrogates for probabili ty that the distributions of meteorological data conditions near South T ahoma Glacier. "Ve res trict our Jor days on wlz ich olltbu rst floods occurred are drawn a t random an alys is to weath er d a ta for th e period 1986- 92, because fr om th e CDFs? We use the K olmogorov Smirno\' test of fl ood da les are nol accura tely known (or ea rl ier years. goodness of fit (Cono ve r, 19 71 ) to find a n a nswer. T he The a nalys is uses d a ta for th e months May thro ugh measured tes t statisti c drn is the larges t vertical distance N ovem ber, approxima tely encompassing the typical between th e CDF a nd the stepwise sample curve a bla tion season for glaciers on M o unt R aini er. Actua l connecting values measured on days of o utburst-flood outburst-nood da tes ra nged from 29 J une to 9 November. occ urrence (Figs 5 a nd 6). For a give n number n of da ta The statisti cal distribu ti ons of rainfall and maxim um points in the sa mple popula tion, one may calculate the dail y temperature a t Paradise are shown in Figures 5 probability P that for a no ther sample of n points th e a nd 6. (Days with measurable snowfall were excluded in larges t vertical distance between th e curves would exceed

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the measured value dm . P may also be interpreted as the analogous tests using 2, 3, and 4 day moving averages of probability that the sample population (in our case, days maximum daily temperature and rainfall. (For moving with outburst flood s) is drawn at random from the parent averages, the last day of the averaging window is always population (all snow-free days from M ay through the day of the fl ood. ) We conclude that values of rainfall November). The Kolmogorov- Smirnov test is preferred and maximum daily temperature for days with outburst to the chi-square test for small sample sizes, as in the fl oods are unlikely to be drawn from the parent present case, because it does nor assume a Gaussian population, although this conclusion weakens as we distribution of the test statistic (Conover, 1971 ). consider progressively longer averaging periods. R es ults are shown in the top halves of Tables 1 and 2 We can make stronger statements once we note (Figs 5 for the cases illustrated by Figures 5 and 6, as well as for and 6) that there are two distinct sub-populations in the

Table I. Results oJ Kolmogoro v- Smirnov ( K-S) testfor rainfall dataFom Paradise Ranger Station. M eteorological data used in the analysis arefor the months May- November in the years 1986- 92. One outburstfloodfor which the exact date is uncertain was excluded Fom the analysis. The K- S statistic is difined in the text and illustrated in Figure 5

Type if rainfall data Number K- S statistic Probability that dill Notes (n) of out- (dm ) would be exceeded by bursts in another sample of n sample points

Daily, all snow-free days 14 0.408 6.36 x 10- 3 Daily, all snow-free days 13 0.364 2.36 x 10-2 Excludes 16 October 1988 fl ow Daily average, all 2 d snow-free periods 14 0.346 3.38 x 10 2 Daily average, all 3 d snow-free periods 14 0.329 4.71 x 10 2 Daily average, all 4d snow-free periods 14 0.260 3.32 x 10 I 2 sided K- S test applies Daily, snow-free days with meas urable rain 7 0.787 2.08 x 10-5 Daily, snow-free days with measurable rain 6 0.763 1.86 x 10-3 Excludes 16 October 1988 fl ow Daily average, 2 d snow-free periods with 6 0.737 3.70 x 10-4 I fl ood dropped due to snow in measurable rain averaging interval Daily average, 3 d snow-free periods with 6 0.715 6.32 x 10-+ I flood dropped due to snow in measurable rain averaging interval Daily average, 4d snow-free periods with 6 0.532 4.18 x 10 2 1 flood dropped due to snow in measurable rain averaging interval; 2 sided K- S lest applies

Table 2. Results of Kolmogorov-Smirnov ( K - S) test for maximum-temperature data from Paradise Ranger Station. M eteoTological data used in the analysis are for the months AI[ ay-November in the years 1986-92. One outburst flood for which the exact date is uncertain was excluded Fom the analysis. The K -S statistic is defined in the text and illustrated in Figure 6

Type of temperature data Number K - S statistic Probability that dill Notes

(n) of out- (dm ) would be exceeded b)1 bursts in another sample of n sample points

Daily, all days 14 0.317 4.73 x 10 2 Daily average, all 2 d periods 14 0.293 1.48 x 10 I 2 sided K- S test applies Daily average, all 3 d periods 14 0.279 9.32 x 10 2 Daily average, all 4d periods 14 0.257 2.66 x 10 I 2 sided K- S test applies

Daily, a ll dry days 7 0.702 2.80 x 10-4 Daily average, all 2 d dry periods 7 0.600 3.09 x 10-3 Daily average, all 3 d dry periods 7 0.534 1.09 x 10-2 Daily average, all 4 d dry periods 6 0.582 9.32 x 10 3 One flood dropped due to rall1 in averaging period

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data for d ays with outburst flo ods: warm, dry days o.15.------r------.------, (Tmax 20°C, R 0) and cool rain y d ays (T,l1ax 15°C, > = < + Day of debris flow R > 0). W e therefore examined the statisti cal distribution o 2-d ay average of rainfa ll excluding dry days, and that of maximum o 3-dayaverage fl. 4-day average + temperature excluding rairry days. Res ults a re presented in ~ 0.10 I]) the bottom halves of T a bles I and 2, for tests using daily Cl a: data and moving averages, as before. Values of P are in 0.. + --' some cases less than 0.00 I.

cau ti on against using Figu res 7 and 8 to predict outburst­ T"I&X ::::: 30°C, Pc ::::: 0.22 for R = 40 mm. In light of the fl ood probabiliti es , however, because thc glacier, includ­ surrogate nature of the meteorological data, the two ing, presumably, its drainagc sys tem, is ch anging with probabilities arc reasonably close. We therefore suggest time, ma king the statistical problem non-stationary. the following physical interpretation, elaborated in the If Rand T,llax measurcd at Paradise a re consid ered next section: o utburst fl oods from South Tahoma Glacier rough surrogates for rate of water input to South Tahoma are meteorologicall y driven, with the proba bility of an Glacier, the conditional probabilities shown in Figu res 7 outburst fl ood d etermined primarily by the rate of water a nd 8 are reasonably consistent with each other. To see inpu t to the glacier. this, consider that a plausible \'alu e for the abla tion rate at South T a homa Glacier on the hottest summer days (when Tmax ;:::; 30°C at Paradise) is perhaps 40 mm d I (cf. WATER STORAGE AT THE GLACIER BED AND AN HYPOTHESIS FOR THE ORIGIN OF OUT­ BURST FLOODS

+ Day of debris f low Outburst fl oods from South Tahoma Glacier involve 1.0 o 2-dayaverage 0 0 release of water stored either englaciall y or subglaciall y. >- I- o 3-d ay average ::::; For the 26 July 1988 event (Fig. 3), whieh was probably /). 4-day average 5 3 I]) typical, the total water vo lume (3 x 10 m ) , if spread

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Except early in the ablation seaso n, surficial meltwa ter or rainfall will enter the englacial drainage system rapidly and thence reach the glacier bed. Water at the base of an alpine glacier usuall y collec ts in onc or more main channels incised into the ice (Shreve, 1972; Rbthlisberger, 1972 ), but at South Tahoma Glacier the route from englacial conduit to trunk cha nnel is likely to involve passage through large linked cavities . Flow along the linked-cavity network (Fig. 9) is regulated b~ the throttling effe ct of constrictions, or orifi ces, where the ice closely approaches th e bed (Wald er, 1986; Kamb, 1987 ). Based on these concepts and on res ul ts in the previous section, we propose the following hypothesis: outburst floods from South Tahoma Glacier occur when the rate of water input to the subglacial drainage system ca uses subglacial water press ure to rise rapidly, destabilizing the orifices in the linked-cavity network, in line with Kamb's (1987 ) analysis. The' linked-cavity drainage system then degenerates into a multiple-tunnel system that rapidly drains stored water. In K a mb's (1987 ) analysis, orifice stability is con­ trolled by the dimensionless parameter :=, defin ed by o 10 METERS '------'. 1 3 SCALE APPROXIMATE E = 2 / (aA /w)3/2 (!L) 1/ 2 h7/6 (4) A A' 7r1/ 2 DM va

where a is the average hydraulic gradient, approximated as the ice-surface slope; A is the length of orifices di vided by the length of cavities; w is the tortuosity of the water­ B B' £low pa th; D is a cons tan t equal to 31 km; M is the M a nning roughness of the orifices; T] is the effec tive viscosity of the ice; v is sliding velocity; a is effecti ve press ure (ice-o ve rburden press ure minus water press ure); and h is the height of the orifice. For E greater tha n about I , orifices will enlarge unstably in res ponse to transient water-pressure increases of a n y magnitude. For Fig. 9. Schematic dra wing of the basal linked-ca vity progressively smaller values of E , the orifices are sta ble network. Areas of ice/bed contact are shaded, areas of ice/ against progressively la rger water-press ure transients. bed se/Jaration are blank. Ice separates from the bed along To e timate a value of E for th e basal-cavity sys tem of the hachured lines and re-contacts the bed along the plain South Tahoma Glacier, we adopt the parameter values lines. ( After B . Kamb (1987) .) a= 0.3, A=lO, w=4, Nf=O.lm 1/3 S, T] = O.lba ra, v = 10 m a- I and a = 5 ba r. The values for A, w, !If a nd T] follow from Kamb, a nd should be reasonable for the (averaging 20 30°) and probably £lows over large ledges South T a homa Glacier system. The value of Cl applies for eroded fr om the lavas and volcaniclastic deposits that the active ice and is based on a U.S. Geological Survey constitute most of Mount Rainier. Indeed, one such topographic map. \!I,l e have no direct measurements of ledge, several tens of meters high and form erl y beneath an sliding velocity or effecti ve press ure a t the glacier bed. icefa ll , has been exhumed as the ice has thinned during Our choice ofv is intuitive but plausible, based on th e fact the last decade. Supposing a subglacial cavity existed in that South T ahoma Glacier has been thinning and the lee of such a ledge, with a cross-sectional area along retreating for nearly 2 decades, and our judgment that 2 the i ce -£lO\~1 direction of 50 m - corresponding to a the glacier is sluggish. (For purposes of compariso n, the cavity 10 m in height and length, with a triangul a r cross­ average sliding speed of the nearby, larger Nisqually section a tOtal cavity length of6 km would be required Glacier was abou t 50 m a I in 1969, while the glacier was to stO re 3 x 105 m3 of water. Even if the stored-wa ter adva ncing (Hodge, 1974).) The value for a is approx­ volume were an order of magnitude less - corresponding ima tely equal to the estimated average ice-overburden to the case in which most debris-flow water comes from press ure (based on glacier area-and-volume es timates by the sediments themselves - a 600 m length of these Driedger and Kenna rd (1986)) and thus a rough upper enormous cavities wo uld be req uired. Yet it is hard to bound on effective pressure. ''\fith these parameter values, 7 6 imagine how the requi ite volumes of water could be we find E = 3.8h / , when h is give n in m eters. We would stored if giant cavities did not exist. If all cavities were then require h < 0.3 m for the orifices to have even decimetric in scale (such as those mapped by Walder a nd marginal stability. If m eter-scale cavities exist, as we have Hallet ( 1979 ) a nd H all et and Anderson ( 1982)) , previo usly sugges ted , even the o rifices may have hundreds of kilometers of linked cavities would be decimetric dimensions, a nd thus be unstable in th e event req uired to hold the stored volume of water. of transient increases in water press ure.

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Indirect evidence possibly bea ring on the size of (e.g. Clarke, 1982) or subglacial lakes form ed by orifices com es from a bizarre, macabre so u rce. 1 n geothermal activity (Bjornsson, 1992). South T ahoma December 1946, a U.S. Marine Corps airplane cr ashed Glacier appears to be different. W e are skepti cal of near the head of South T ahoma Glacier, with no Crandell's (1971 ) conclusion that geothermal activi ty survivors. The wreckage was quickly buried under snow causes outburst floods from South T ahoma Glacier. and was never recovered. Deposits of the 1986 and 1987 Cra ndell's argument rested on anecdotal evid ence, such d ebris flows con tained many mangled bi ts of the aircraft, as observations of supposed stea m plumes, gathered from including propell er blades and pieces of shee t metal up to a variety of observers. We beli eve it would be a a bout 0.5 m on a side (persona l communication fi'om remarkable coincidence if the statistical relationship K. M. Scott, 1993). A plausible in terpretation is that the between outburst floods and meteorological variables air plane wreckage had been advected downward to the existed independent! y of a ca usa l relationship between glacier bed, had melted out and accumulated in cavities, those variables and o u tburst fl oods, even though we and had fin all y been flu shed out as caviti es had drained understand the pertinent physics in exactl y. Furthermore, through R channels during outburst flood s. The size of there is no glacier-surface relief indicative of melting over the metal fragments would then set a lower bound on a geothermal area (cr. Bjornsson and Einarsson, 199 1). typical orifi ce dimensions. Other interpretations are Other glaciers o n M ount R ainier have released possible, of course. outburst fl oods from subglacial storage, though non e We co nclude that Kamb's model of orifice instability wi th nearly the frequency of Sou th Tahoma Glacier yields quantitatively reasona ble res ults for the case in (Driedger and Fountain, 1989 ). It may be that the bed hand. Moreover, in the context ofKamb's model, it is not geometry of South Tahoma Glacier is particularly surprising that the probability of a n outburst fl ood cond ucive to the formati on of large subglacial cavi ties. increases as the rate of water delivery to the glacier bed Bed geometry must be related to the structure a nd increases (Figs 7 a nd 8). The g reater the rate of water erodibility of the bedrock, factors which on a strato­ delivery, the larger must be the press ure transients, a nd volcano like Mount R ainier are very h eterogeneo us. YV e thus the greater the likelihood that (for give n .=) orifi ces note that the present phase of outbur:t-flood activity a t in the cavity network will grow unstabl y. South Tahoma G lacier co in cid es w ith a period of The shortest period of time between two outburst flo ods : ubsta ntia l ice retreat a nd thinning, whereas the previous from South T a homa Glacier was a bout 56 h - the interval phase of activity (1967 to the mid-1 970s) was during a between th e dry-weath er f100ds of 29 and 31 August 1967 period of ice advance, with the g lacier consid erably (Crandell, 1971 , p. 58 ). The dry-weather f100d s of 28 and thicker than at present. This suggests that the propensity 3 1 August 1987 were se parated by only about 75 h. In the for outburst f1 00ds is not related simply to ice thickness. context of the cavity model discussed a bovc, two (a t least) interpretations a re poss ible. The li nked-cavity sys tem may ra pidly reform itself after disruption leading to an outburst CONCLUSIONS fl ood; alternatively, any individual outburst fl oods may represent break-down and drainage of just part of the Sou th Tahoma G lacier, located on Mount R ainier cavity network. \Ne favor the second interpretation, volcano, has released at least 22 ou tburst f10 0ds since because th e \·olume of water released in the second of 1967, including a t least 14 in the years 1986- 92. The each pair of flood s could not pla usibly have been generated vo lu me of water released during a typical outburst fl ood by ablation in the peri od between fl oods, even if all surface­ corresponds to a ba a l water layer several ce ntimeters d eri ved meltwater had been stored subglaciall y. The thick, a physically impossible situa ti o n ; so water must be second interpretation is also in line with observations stored in large subglacia l ca\,itics. Geologic factors such as elsewhere (e.g. Fountain, 1992 ), tha t alpine glaciers may the volcano's heterogeneo us structure promote the contain se\·eral distinct internal drainage basins. existence of large basal cavities. A puzzling aspect of outburst fl oods at South Tahoma The likelih ood of a n outburst fl ood increases as either Glacier is their probabilistic nature: few occurrences of the temperature or rainrall rate increases. A reasonable hot weather or heavy rain d o in fa ct coincide with interpretation is that fl ood proba bili t y depends on the outburst f1 oods. One interpretation may be that the rate of water input to the glacier bed. We therefore glacier'S drainage system vari es signifi cantly wi th time. propose that the physicalmcchanism of fl ood release is the For example, the geometry of orifices in the cavity system breakdown of the linked-cavity network over part of the might change with time, thereby a ffecting the valu e of~. glacier bed and rapid dra in age through a multiple- tunnel Another interpretation is th at we simply have insufiicient sys tem, much as en visaged by K amb (1987 ) in his information about the rate of wa ter input to the drainage disc ussion or glacier-surge termination. sys tem through time, as well as a bout the geometry of the drainage system itself, to co nstruct a d eterministic model of outburst-flood release. ACKNOWLEDGEMENTS

The U .S . .\Iational Pa rk Sen·ice provided partial runding DISCUSSION for this study. L. IVI astin introd uced us to use of Kolmogorov- Smirnov stati sti cs. YV e benefi ted rrom re­ Many other investigators have reported cases of glaciers views of earli er versions of the paper by A. Fountain , that repeatedly spawn outburst floods, but these have N . Humphrey , R. Alley, R. LeB. Hooke and two involved drainage of either subaerial ice-dammed lakes anon ymous referees.

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REFERENCES H umphrey, N. F. 1987. Basal hyd rology of a surge-type glacier: observations and theory relating to Variegated Glacier. (Ph.D. Bjornsson, H . 1992. J okulhlaups In Iceland : prediction, characteristi cs thesis. Uni versity of W ashington. ) and simulation. Alln. Glaciol. , 16, 95 106. Humphrey. :-I., C. R aymond and W. H a n·ison. 1986. Discharges of Bjornsson, H. a nd P. Einarsson. 1991. Volcanoes beneath Vatnajokull, turbid water during mini-surges of Variegated Glacier, Al aska, Iceland: evidence [rom radio echo-sounding, earthquakes and U .S.A. ]. Glaciol .. 32( Ill ), 195 207. jokulhla ups. ]61",/1, 40, 1990, 147- 168. Kamb, B. 1987 . Glacier surge mecha nism based on linked cavity Bod hai ne, G . L. and D.lV!. Thomas. 1964. Magnitude a nd freq uenc y of confi guration or the basal wa ter conduit sys tem. ]. Geoj)/zys . Res., [l oods in the United Sta tes. Pa rt 12. Pacifi c Slope basin s in 92(B9), 9083-9100. Washington and upper Colum b ia River basin. u.s. Geol . Surv. Richardson , D. 1968. Glacier outburst nood s in th e Paci fi c Northwest. lI 'a /er-Su j)j)l)' Pap. 1687. V.S. Geol. Surv. Prrif. Pap. 600-0, D 79 D86. Clarke, G. K. C. 1982. Glacier outburst noods from " H azard Lake", R othlisberger, H. 1972. Water press ure in intra- and subglacial Yukon T erritory, and the problem of nood magnitude prediction. channels. )' Glaciol., 11 (62 ). 177 203 . ]. Glaciol., 28(98),3-2 1. SCOll, K . M. , P. T. Pringle and J. W. Valiance. 1992. Sedimentology, Conover, W.J. 197 1. Practical lIonpamme/ric statistics. New York , J ohn behavior and hazards of debris noli's a t M ount Rainier, Washington. Wil ey and Sons. U.S. Geo!. SUTV. Opell-file Rep . 90-385 . Crandell , D. R . 197 1. Postglacial la ha rs from Mount Rainier volcano, Shreve, R.1. 1972. M ovement of wa ter in glaciers. ]. Glaciol., 11 (62 ), Was hington. U.S. Geol. Surv. Pro.f. Pap. 677. 205- 214. Driedger, C. L. 1986. A visitor's guide 10 Nl oullt Rainier glaciers. Longmi re, Sigaroos, R. S. and E. L. H endricks. 1972. R ecent acti vity of glaciers of W A, Pacific Northwest National Parks and Forests Association. Mount Rainier, VV ashington. Botanical evidence of glacier acti vi ty. Driedger, C. L. a nd A. G. Fountain. 1989. Glacier outburst [l oods at U.S. Geo!. Surv. Pro.f. Pap. 387-B. Mount R a inier,Was hington State, V.S.A. Ann. Glaciol., 13, 51 55. V.S. National O ceani c and Atmospheri c Administration. 1986 92. Driedger, C. L. and P. M. Kennard. 1986. Ice vo lumes on Cascade Clima/ologiral data Wa shing/Oil. Ash evill e, NC, U.S. National volcanoes: M ount Rainier, lVl oulll H ood, Three Sisters, and Mount O ceanographic and Atmosp heri c Administration, 90-96(5- 11 ) [i n Shasta. U.S. Geol. Surv. Prof Pap. 1365. each volume]. Fountain, A. G. 1992. Subglacia l water now inferred from stream Walder,J. S. 1986. H ydraulics of sub glacial cavities. )' Glaciol., 32 ( 11 2), measurem ents at South Cascade Gl acier, vV ashington. U.S.A. 439-445. ]. Glaciol., 38(128), 51 - 64. W a ld er, J. S. and C. L. Driedger. 1994. G eomorphic change caused by Hallet, B. and R . S. Anderso n. 1982. D etailed glacial geomorphology of glacial outburst fl oods and debris fl ows at Mount R aini er, a proglacia l bedrock area at Casd eguard Glacier, Alberta, Canada. Was hi ngton, with emphasis on T ahom a Creek va lley. U.S. Geol . .(. Gle/scherkd. Gla;:,ialgeol., 16(2), 1980, 171- 184. Surv. lVa/er-Resources i nvestigations Rep. 93-4093. Hodge, S. M. 1974. Variations in the sli ding of a temperate glacier. W a ld er, J. and B. H allet. 1979. Geo metry of former subglacial water ]. Glaciol. , 13(69), 349- 369. channels and cavities. ]. Glaciol. , 23(89), 335 346.

MS received 14 May 1993 and in revised form 8 February 1994

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