Geologic and topographic controls on fast flow in the Laurentide and Cordilleran Ice Sheets

JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 101, NO. B8, PAGES 17,827-17,839, AUGUST 10, 1996

Geologic and topographic controls on fast flow in the Laurentide and Cordilleran Ice Sheets

Shawn J. Marshall and Garry K. C. Clarke Department of Earth and Ocean Sciences, University of British Columbia, Vancouver

Art S. Dyke and David A. Fisher Terrain Sciences Division, Geological Survey of Canada, Ottawa, Ontario

Abstract. Ice streams are fast flowing arteries which play a vital role in the dynamics and mass balance of present-day ice sheets. Although not fully understood, fast flow dynamics are intimately coupled with geologic, topographic, thermal, and hydrologic conditions of the underlying bed. These are difficult observables beneath contemporary ice sheets, hindering elucidation of the processes which govern ice streaxn behavior. For past ice sheets the problem is antithetic. Geologic evidence of former ice streams exists, but spatiM and temporal histories are uncertain; however, detailed knowledge of bed geology and topography is available in many places. We take advantage of this information to compile terrain characteristics relevant to fast flow dynamics in the Laurentide and Cordilleran Ice Sheets. Using seed points where fast flowing Wisconsinan ice has been geologically inferred, discriminant analysis of a suite of North American geologic and topographic properties yields a concise measure of ice-bed coupling strength. Our analysis suggests that the interior plains and continental shelf regions of North America have low basal coupling relative to areas of variable relief or exposed bedrock in the Cordillera and on the Canadian Shield. We conclude that the interior plains and continental shelves are both topographically and geologically predisposed to large-scale basal flows (i.e., ice streaxns or surge lobes). This result holds independent of whether the mechanism of fast flow is sediment deformation or decoupled sliding over the bed.

Introduction

Glacier and ice sheet behavior is greatly influenced by the topography and geology of the underlying surface. Bed topography is important to the initiation and the dynamics of an ice mass. Topographic variability on scales of less than 10 m affects the basal flow of ice through the processes of regelation and stress- enhanced plastic flow over obstacles IN!re, 1969, 1970; Kamb, 1970]. Basal drag of Antarctic ice streams ap- pears to be concentrated at isolated pinning points on scales of 10•-104m [MacA•leal e• al., 1995]. These "sticky spots" may be geologic or topographic in nature, with enhanced ice-bed coupling resulting from o.rographic obstacles or from areas of bedrock outcrop, frozen, or well-consolidated sediment.

Fisl•er et al. [1985] and Boulton eZ al. [1985] explored the potential role of bed geology on ice sheet form. Fisl•er et al. [1985] divided the bed of the Lauren- tide Ice Sheet into yield stress regimes based on geologic province and estimated snow accumulation rates.

Copyright 1996 by the American Geophysical Union.

Paper number 96JB01180. 0148-022 7 / 96 / 96JB- 01180509.00

By introducing weak ice-bed coupling (low basal shear stress) in areas of deformable sediment, Fisher et al. produced Last Glacial Maximum (LGM) reconstructions of the Laurentide Ice Sheet which are dramat-

ically thinned. These reconstructions implicitly invoke the role of basal conditions in the fast flow of ice, as observed in surging glaciers and Antarctic ice streams [Blankenship et al., 1986; Alle•l et al., 1986, 1987; Clarke, 1987; Kamb, 1987, 1991].

Fast flow is linked to sediment deformation or de-

coupled sliding at the ice-bed contact, with the exact nature and partitioning of these mechanisms unclear. We believe that differentiation between these processes is less important than the facilitatory conditions involv- ing basal thermal regime, subglacial hydrology, and ice- bed coupling, because (1) each flow mechanism requires a temperate bed which permits free water; (2) each mechanism is encouraged by broad, continuous areas of high subglacial water pressure; and ($) each mechanism benefits from low geologic and topographic coupling with the ice (minimal basal pinning points or sticky spots).

Fast flow is not uncommon in contemporary ice masses, but basal conditions are very difficult to monitor in detail. On the contrary• the beds of former ice sheets are accessible in many places but the extent of former

17,827

17,828 MARSHALL ET AL.: TERRAIN CONTROLS ON LAURENTIDE ICE STREAMS

ice streams is uncertain. There is little doubt that

ice streams acted as critical arteries for drainage of the Laurentide Ice Sheet. Lobes of the southern mar-

gins left evidence of dramatic and repeated flow excursions (surges) with average ice velocities of order 100myr -1 [Morner and Dreimanis, 1973; Cla!/ton and Moran, 1982; Mickelson et al., 1983; Clattton et al., 1985; Fullerton and Colton, 198(}; Be!l•t, 198(}, 1987; Clark, 1994].

Debris dispersal patterns suggestive of ice streams have been identified over a range of physiographic regions [D!tke, 1984; D!tke and Prest, 1987; Hicock, 1988]. The deep-sea sediment record tells of quasi-periodic and profligate exportations of ice to the North Atlantic from the Laurentide's northeast margin [Heinrich, 1988; dreios and Tedesco, 1992; Bond et al., 1992]. These events have been linked to surging behavior or flow oscillations in ice streams issuing from the Hudson and Cabot Straits [Andrelos and Tedesco, 1992; MacA!leal, 1993a,b; Bond and œotti, 1995; Doiodesioell et al., 1995].

We assume in this paper that large-scale surging and ice-streaming behavior have similar flow mechanisms and experience similar terrain controls. This analysis therefore applies only to ice streams such as those on Antarctica's $iple Coast whose flow is basally driven. The fast flow of ice streams such as J acobshavn Is-

brm in Greenland has been attributed to thermally enhanced creep deformation rather than basal motion [Echelmetter et al., 1991;/ken et al., 1993]. Ice streams of this class are certainly plausible in the Wisconsinan ice complex in North America, but we do not consider them here. With little or no basal flow they would leave little geological signature of their history. Further, el- evated ice deformation rates such as in J acobshavn Is-

brm are only feasible under large topographic motivation and will be topographically contrained in a deep channel or fjord. Their positioning might be readily predicted from detailed topographic information. Given sufficient resolution, standard glaciological models of ice creep dynamics should readily capture this class of ice streams.

To address the question of fast basal flows, we have developed a numerical ice sheet model which has the capacity to describe subgrid ice streams and surge lobe dynamics [Marshall and Clarke, 1996]. Objective positioning of ice streams in the model is a challenge in applications with the Laurentide Ice Sheet. While the temporal evolution of fast flow dynamics is controlled by basal thermal and hydrological regimes, terrain disposition can be expected to overlay and regulate time- dependent internal dynamics. This paper concentrates on spatial variations in ice-bed coupling imposed by bed geology and topography. Present-day North American terrain is quantified on a scale of 3-10 km, and we ex- plore terrain attributes which predispose certain areas to large-scale basal flows.

Bed Characterization

Synoptic-scale finite difference models of the Lauren- tide Ice Sheet solve ice sheet dynamics at horizontal grid

cell resolutions of order 1 ø or 50-100 km [e.g., Deblonde and Peltier, 1991, 1993; Marstat, 1994; Hu!/brechts and T'Siobbel, 1995]. To analyze terrain disposition at this resolution, we divided glaciated North America into 1 ø x 1 ø longitude-latitude cells in the region (37øN - 80øN) and (165øW-45øW). Nineteen subgrid geologic and topographic parameters were compiled for each cell. We used multivariate factor analysis to isolate linearly independent attributes. Subsets of the data set were then selected to characterize areas where ice streams

were known to exist and areas where they likely did not. Discriminant analysis applied to the remaining data set yields objective numerical estimates of ice-streaming probability.

All cells are referenced on a spherical Cartesian grid, with •i and 8• indicating longitude and latitude. We denote synoptic-scale 1 ø cells with longitude-latitude indices i and j and use indices m and n for subgrid data points. Synoptic grid cells have dimensions _R• cos 8iAA x R•AS, where _R• is Earth's radius and AA = A8 = 1ø.

Geologic Characterization

We compiled surficial materials information from continent-scale surface geology maps. Canadian coverage was digitized from the synthesis of Fulton [1993]. The number of geologic units per 1 ø finite difference cell ranges from 1-8. Table 1 lists the surface units, along with estimates of typical thickness, porosity, grain size, and hydraulic conductivity. We subdivided Fulton's till blanket into six regional subclasses based on the divi- sions of Fulton [1989]. Material characterizations were specified with the assistance of L. Dyke (personal com- munication, 1994) and from Fulton [1989]. Porosities are estimated to within 10%. Hydraulic conductivities are calculated from the empirical formula k = Cd •, where k is in ms -1, C = 1.1, and d is the 10th percentfie on a "cumulative percent finer than" grain size curve, measured in mm [Freeze and Cherr!l, 1979, p. 350].

American coverage was digitized from Heath [1988], translated into geologic units which are roughly equival- ent to those on the Canadian surficial map. The U.S. information is less detailed than the Canadian counter-

part, and "equivalence" is unclear for some units. As a result, the British Columbia-Washington border occa. sionally shows up in the full compilation, but the border is elsewhere transparent. Figure 1 illustrates average sediment thickness and areal fraction of bedrock exposure in each cell. The latter includes contributions from

bedrock outcrops, alpine and volcanic complexes, and till veneer (thin and discontinuous till cover punctuated by outcrops).

Topographic Characterization

Rapid improvements in digital terrain models have opened the door for detailed topographic analysis at subgrid scales for ice sheet models. We make use of the National Geophysical Data Center's TerrainBase compilation, which includes global 5 arc min data and a number of regional models at higher resolution [Roio

MARSHALL ET AL.: TERRAIN CONTROLS ON LAURENTIDE ICE STREAMS 17,829

Table 1. Sediment Characterization

Material Unit Depth, m Porosity d, mm k, m/s x10 6 Till blanket

Shield TS 1 3. 0.1 0.004 0.18 Arctic TA 2 3. 0.1 0.004 0.18 Cordillera TC 3 3. 0.1 0.002 0.04

Interior plains TP 4 20. 0.1 0.002 0.04 Hudson lowlands TH 5 10. 0.1 0.002 0.04

Great Lakes/St. Lawrence TG 6 20. 0.1 0.002 0.04 Till veneer Tv 7 1. 0.3 0.004 0.18 Bedrock outcrops R 8 100. 0.01 1. Water (unmapped) W 9 Ice masses I 10

Glaciolacustrine, fine fL 11 5. 0.1 0.002 0.04 Glaciolacustrine, coarse cL 12 10. 0.3 0.5 2 750. Lacustrine mud mL 13 2. 0.1 0.002 0.04 Lacustrine sand sL 14 3. 0.3 0.2 440. Marine veneer Mv 15 0.5 0.3 1. 11 000. Glaciomarine, fine i'M 16 10. 0.1 0.002 0.04 Glaciomarine, coarse cM 17 2. 0.3 1. 11 000. Marine mud mM 18 2. 0.2 0.002 0.04 Marine sand sM 19 2. 0.3 0.2 440. Colluvial blocks bC 20 1. 0.3 0.004 0.18 Colluvial rubble rC 21 1. 0.1 0.002 0.04 Colluvial sand sC 22 1. 0.2 0.05 27.5 Colluvial frees fC 23 1. 0.1 0.002 0.04 Gl•ciofluvial, plain Gp 24 10. 0.3 1. 11 000. Glaciofiuvial, complex Gx 25 10. 0.3 1. 11 000. Alpine complexes Ra 26 100. 0.01 1. Alluvium A 27 10. 0.3 0.1 110. Organics O 28 2. 0.5 0.5 2 750. Eolian E 29 2. 0.3 0.2 440.

,, ,

and Hastings, 1994]. The most detailed information available for the entire North American bed is 5 arc

min coverage, which gives 144 data points within a 10 cell. Higher-resolution data are available in southern sectors of the domain and we use this where appropriate. Each point (Ai, 8j) is made up of an M x N array of subgrid elevations h,,•,,•. M = N - 12 in this study, and subgrid cells have dimensions Rr cos 8,•5), x Rr58, where 58 - 5A - 1 / 12 ø.

We collected a suite of subgrid topographic attributes which we deemed relevant to ice mechanics. Table

2 summarizes these as well as the geologic attributes available for each cell. The first class of topographic information includes directly determined subgrid stat- istics: maxima, minima, mean, range, and standard deviation. Roughness H/L measures the height of a typical "bump" above the background. Subcell elevations are ranked from low to high and H is the difference between the 75th percenttie elevation and the mean, H = h.v5 - h. L is the horizontal length scale corre- sponding to the terrain resolution, calculated from 1/4 of the subcell perimeter: L - Rs (258+cos8,_•/2 5• +

(oulr l0 km). I is a dimensionless measure of topographic distribution, calculated from

Ii,:i 1 - .-ij , am,., (1)

where Aij is cell area and am,,, is subcell area. Volume V is a measure of terrain volume within a cell above a

reference plane, h.mi." in our case. It is calculated from '-•,$

the cell range and hypsometry,

- a - - . '-*,s ' a,•,. (2)

Attributes of the second class in Table 2 examine each

subgrid point h,,,, and its eight neighbors. Define local length scales • - R• cosS,•SA and 5y - Rz:58 as shown in Figure 2. Slope amplitude IIVhm,,,11 is derived from

(3) where

The mean slope amplitude for cell (i, j) is then

1

IlVh[I,, - m

(4)

Standard deviation of this measure is

Slope •pect ffm,• defines local downslope direction,

' Mean and standard deviations of cell slope •pect fol- low accordingly. The motivation for compiling s•andard deviations of slope amplitude and aspect is to give some


•- •...•• Bedrock re

1.

0.88 0.75

0.63 ...... •:::•. :.:.. •...•...:..::..:'. • "...,.•'"•'•:.;. .. ........ :a• ............. •'" 0.5

.... :•::•:•:•:•::::::::•.:.::: •a•:•;•;•:•:•:•:• •:•:::•:•:• ................... "'.-•:::':•:: • '• '

water

_ •-..--'•'•'-•• Sediment

(m) 20.0 17.5

15.0

12.5

i

• 5.0

2.5

' 0.0

:,"•:;•...:J•i land water

Table 2. List of Topographic and Geologic Attributes

Figure 1. Results of surface geology analysis. All fields are contoured from 1 ø cell averages for the Laurentide bed. (a) Areal fraction of bedrock exposure. (b) Thick- ness of sediment cover.

description of second-order terrain variability within the cell: e.g., to differentiate hummocky terrain from monotonic continental shelf. Terrain curvature IIV2• hll is a similar measure, calculated from the second deriv- ative in the downslope direction at each subgrid point. Mean cell curvature is found from

Figure 3 depicts syntheses of selected topographic fields for the entire region. Note the close similarity between the different roughness measures plotted in Figures 3a, 3c, and 3d.

In addition to direct subgrid topographic attributes, we calculated upstream catchment area and maximum drainage path length for the full model domain [after Zevenberõen and Thorne, 1987]. These are measures of

Attribute Units Description

Topographic Attributes: First Class m minimum cell elevation m maximum cell elevation

m average cell elevation m standard deviation in cell elevation

m range in cell elevation roughness hypsometric integral

km • terrain volume

Topographic Attributes: Second Class

mean slope amplitude standard deviation in slope amplitude

degrees mean slope aspect degrees standard deviation in slope aspect m -z mean downslope curvature

Topographic Attributes: Third Class upstream area maximum upstream drainage path length

Geologic Attributes fractional bedrock exposure average sediment depth water storage capacity average hydraulic conductivity ka ms -z

the amount of terrain within the full model area which

is upflow of a given point. Following the approach of Zevenbergen and Thorne, we calculated this from a cumulative four-way sweep across the data set, to flag upstream points from all possible paths.

Upstream area maps of present-day and Last Glacial Maximum (LGM) surface topographies are shown in Figure 4. Hudson and Mississippian drainage routes are evident in the present-day case, while the LGM map ac- centuates drainage on the northern and southern flanks of the ice sheet, in Laurentide-Cordilleran confluences (both north and south), and via a saddle in Hudson Bay. LGM paleotopography is estimated from the reconstruction of Peltier [1994] for both bed and ice sur- faces. This reconstruction was based on high-resolution isostatic modeling in a viscoelastic Earth, constrained by globally distributed relative sea level histories. The initial ice surface which we approximated from Peltier [1994] has been integrated forward for 8 kyr in the ice sheet model of Marshall and Clarke [1996] to smooth an initially blocky ice distribution.

On

m ,m+l Figure 2. Notation for the subgrid digital terrain data. Elevation h,,,,• corresponds to longitude Am and latitude 8,•.

El --.- _ Range in sub-cell ,_ • Deviation in

:ography 2400 • pe aspect 48 •/•-'- •'"•'"•'•""•"••'•••••••..:...::•.,.•:• • ... 1800 •.•.., \ •. 36

:'"•::i• ....... ii...'..• "•'" 0 • .. 1500 • •::...-:?.:. 3

/ '.• •_ ": •' •:' 6

• •••• ........... •i Iwa:tder • _ i Iwa:tder C '•......• Log of terrain ,.• • LOg of deviation in

/ •""'""'--" "' -'"•"::••'•'••••••.•" • curvature "' • • ............ '••::' "•:•:• • • slope amplitude /,....•.•:f.•:•::.•!..:.•...:..•.•::•:;•....:.:,..........•.•......•.•::•.•: .... •-- ..• /,.. •..•.•.:.f.:..:•?::.:::•:.•..•;.:•..•...•.•:•.•.•.•.•:•::•.. • 0.65

•.._...,.,.!. ..... •i•i[•.•:. ?•_.. .....:•ii•...•. .. .•`•,•....... •` . ..•••••i•i•:`•:... • 0.6 //•.,.:.: .... ' •`•:??:)•;i•i.•ii:•!!i!•i•i•i?•!: •!•.``..:. .. .::i!•`i!!`•iii::•:::•:•i•:•:• • • 0.3

• .... -:'"""•'""":';';'"' '•" ":•'"•!iii'i',',ii:ii?,iii::•:• ............... '.-':'..."...-'•:•.-:...-..-:;:• iwater • '" "'"'""•'•:::•'"'••',ii•iii',ii'•i!ii:!11ii• ................ .:•"""'?":'":•:'•"• iwater

Figure $. Results of subgrid topographic analysis. All fields are contoured from 1 ø cell averages for the Laurentide bed. Each 1 ø cell cont•ns 144 subgrid points. (a) Logarithm of mean cell slope amplitudes. (b) Deviation in subgrid slope aspect. (c) Logarithm of mean cell down•lope curvatures. (d) Logarithm of deviation in subgrid slope amplitudes.

Square root of upstream area (km)

26OO

2275

1950

,.:: :.. 1625 ...

::::::::::':

"'•'?':•i 975 :•-•: 650

::.::..:::• 325 .....

.... ......

I water

Figure 4. Upstream area compilations contoured from 1 ø cell values for the Laurentide bed. Present-day bed topography. (b) Last Glacial Maximum surface topography [after Peltier, 1994].


a

.?•:...::•:::::::'-:' i!: ':'•!•'::s::::. :'::!:!: :.• .:.i,':i.:

•yx-:.:.:..'-.'.x.x. ':i•:':':':':':':':': • :'•":':':'"':'• 5::

Elevation (m)

ß ::•:•!i? • ....... .::ili•:'":!:.ii:i.. '.":':•:iii::::::ii•:•iiii::•:i!ii• :.•i- 2390

::!:•.,..•!i•i::i':i!!•::."'::•'iii!ii?:•ii:.. :":?•i•i:i•i:!::•:•i!•ii•i!? 2170

i • '•'-'?<i::i:•: •?i!i:•i:::ii!:•:•:•!? ':%:.'} •:•i:' ""•::i i::' :::::::::::::::::::::::::::::: ' :•: :: ¾ i:.•:•':::::.: :::!:::i:i:i: ::::::-'-:::'..:.'::•-:'-.::'::::- ::::: .: '.'.. '.::: :::::::::::: ... ß . ':::.:.:::!:,..:•'..<::!:"..•,.,:!.<.:!:. .'..::-:!:!:i:.::.:;[' . ' .-.:'i:•:::!.<::.,::!:::!:!:•:•:!:!:::i. ß . 1030

b Elevation (m) -:,:-:-:,:.:-:-:-:-:-.->:-:-•,•,-•-.:,:-:- ,:. ,:.>> .:...>•,,.. <,,- •.v.. '""'"'-•-"-""•i'"'" '"':'"" '"'"'""' ........ v ................. i:i:!:i:i:i`?:::.::!•`..>``.i:i``.:!:•.::i:::•i:::::•:•*:•`::i:i:i:!::::i:•:i:!:i.•::. ' .i:i:.::!i:•:•::.•.:•, ::.. ?:i•!•ii!: :.:•;..> .. ':,. :•:.:',::'.•::::!:!:::!:::i:::!:!::':i:!:!:!:i:!:!:!:i:::!:::i:!:i:::!:i

?::?:?:i•i:•:? ' ?:?:,,-,..,,, ," •-.-.<.:. :':'.."• :,:•:.•:---. ":•ai•$•' ".a,_, ::4_ •a•l•,:...•.,<..,. ß .... 41 g ii::i!11iiiiii:iliL•....i:iiii!iiiii:::,::::,:::.. •,..::•!:,' .'."-::•,?. •iiiii•i .

..... ß '--"" ............. •*"•":'•'::':": 366 ":::'-'::':'""-":•::::::::': •::':-•'•' •<'•: :,'::-:i:!>.>.::::: :::!::' ..m, .:.:::: '<-'-::,::';- ::::!'-:.x. "--; ,'.,.. ===================================== .&:• ß

'•-"ii 262 !li•I 235 209

d

353

339

325

311

:!'ii:::i:. 298 ......

:::::::::::i: :::::::::.:::

i::.i::iii.::i::11 284

.......... 270

:..:.:.::::::••: 256 :"• 243

Figure 5. Topographic contours for illustrative test points: (a) 90 arcsec data for the Canadian Rockies test point (50øN, 115øW), (b) 90 arcsec data for the Canadian Shield test point

Canadian Shield test point.

The change of upstream area over the course of the ice sheet evolution will play a large role in ice stream drainage v•gor. Regions of flow confluence are better able to sustain enhanced flow rates. This influence from

ice supply would be explicitly accommodated in an ice dynamics model; the present analysis focuses on underlying terrain properties rather than those of the ice. The underlying terrain influences ice confluence areas and also affects collection of water beneath the ice• an important control on basal flow. We therefore use bed topography rather than ice topography in the terrain characterization.

Data nlustration

Test points in the Canadian Rockies (50øN, 115øW) and north of Lake Superior (50øN, 85øW) were selected to provide an illustration of the topographic and geologic variables. Each point has 5 arc min and 90 arc sec terrain information available. Figure 5 depicts topo-

graphic contours and TaBles 3 and 4 list terrain attributes for both locations at the two resolutions.

Table 3. Test Point Topographic AttriButes

_•90 arc sec data $ arc min data Attribute Units Ontario Hockies Ontario Hockies

m 183.0 799.0 229.0 884.0 m 445.0 3078.0 366.0 2587.0 m 311.1 1870.1 309.$ 1849.8 m 1.2 12.3 2.$ 33.8 m 262.0 2279.0 137.0 1703.0 mkm -1 0.32 3.90 0.11 3.21

0.39 0.37 0.•9 0.57 kin* 1030.4 8414.2 647.2 7581.6 mkm -• 3.29 69.75 0.84 17.40 mkm -1 0.06 0.92 0.04 0.80 deg 88.3 -165.1 82.0 -150.9 deg 2.9 4.6 5.5 14.5 mkm -• 8.9 205.4 0.4 16.6 km • 64 300 23 400 km 414.8 311.4


Table 4. Test Point Geologic Attributes

Attribute Ontario Rocldcs

Surface 50% till veneer 80% rock 20% medium 15% till veneer

lacustrine 5% till blanket 15% till blanket (cordilleran)

10% Free lacustrine 5% $1aciofiuvial

Bedrock 100% igneous 100% sedimentary (folded)

• 0.5 0.95 • (m) 2.[;5 0.30 n-• (m) 0.69 0.33 ka (m/s x 10 e) 660 0.007

Multivariate Analyses

The full geologic and topographic characterization gives a collection of n• - 19 attributes at each of nc = 120 x 43 = 5160 cells. Each attribute forms a vector aj of size nc with mean pj and standard deviation •r•. The full data set is loaded into matrix which has dimensions ne x ha. We examined this data set with multivariate statistical techniques in an effort to reduce the number of terrain variables of relevance

to flow dynamics. Exploratory correspondence analysis offered a qualitative examination of cell and attribute correlation. This guided us in the selection of attributes which appear linearly independent and relevant to terrain characterization. Using a small subset of cells to typify the location of former ice streams, we applied two-group discriminant analysis to the remaining data set. The result is a quantitative likelihood measure of terrain streaminess, the capacity of each cell for hosting an ice stream.

were transformed from N (p, •r) to N (0, 1) (zero mean, unit standard deviation) distributions.

The full data set of 5160 cells includes 1662 marine

cells which underlie an arbitrarily assigned shelf break 400 m below sea level. These cells have a distinctly different nature than terrestrial cells and initial correspondence analysis separated the data into two sharply divided groups. Figure 6 illustrates this for projections onto the first two factors. The large clump on the left is the grouping of terrestrial points and the cluster on the right corresponds to marine points.

Terrestrial terrain structure is our primary interest so we stripped the data set of marine points, retaining any points which presently underlie 400 m of wa•er but con- tained ice in the LGM reconstruction of Peliie• [1994]. This gives a subset of n• - 3498 terrestrial cells. Data were renofinalized, and Figure 7 plots correspondence for the first three principal factors of the terrestrial data set. The first three eigenvalues account for 69.2% of the wriance in the data se•. There is no clear separation, rather a continuum of terrain nature. Subtle structure

is evident in Figure 7a on examination of cell identi- ties. Cordilleran points are concentrated in [he lower left tongue, for instance, while continental shelf regions span the upper left tongue and "median" interior cells form the nucleus of the clump.

Attribute correlations in Figures 7b and 7d offer more insight. A number of a•tributes are clearly correlated; they are measuring very nearly the same property and give linearly dependent votes on cell character. The various roughness measures, the central clumps in Figures 7b and 7d, are the best example of this. Upstream area and distance are also closely related. A• the other extreme, some attributes are seemingly uncorrelated with all other attributes and cells and appear meaningless.

Correspondence Analysis

Correspondence analysis is a form of principal component analysis which allows simultaneous calculation of R and Q factors [Greenacre, 1984, 1993; Cart, 1995, p. 102]. Conventional R mode factor analysis explores interrelationships between attributes and Q mode factor analysis assesses interrelationships between cells. The objective of these techniques is to simplify data set structure by reducing a large number of observations to a smaller set of linear combinations which account for most of the variance in the original data. We ad- apted and applied the program of C'arr [1995, p. 138].

Correspondence analysis implicitly assumes that variables are normally distributed. Raw topographic roughness measures are decidely non-Gaussian, as are upstream area and distance fields. Logarithms of all roughness attributes and square roots of the upstream fields [Zevenbergen and Thorne, 1987] were taken as a preconditioning step to give approximately normal distributions. A further step is required to ensure that variables have similar magnitudes, so that no particular field dominates the data set. All attribute fields a)

1.0

0.8

0.6

0.4

0.2

0.0 "'- -0.2

-0.4

-0.6

-0.8

-1.0

- Factors for full dataset -

I I I I I I I I I I

-0.8 -0.4 0.0 0.4 0.8

Factor I

Figure 6. Correspondence analysis plot. The first two principal factors for the full data set (terrestrial plus marine points), with 19 attributes. Factors for cells are plotted as crosses, and factors for attributes are plotted as triangles. The cluster on the left is the body of terrestrial and continental shelf points, and the cluster on the right corresponds to open-ocean points.


Factor 1. a .

::i . . . ' .:, .,..!... , .

-0 5 l ß :•.••'•• . .w • -1.0 -0.5 O. 0.5

Factor 2

Factor 1 ß

0.5

O.

-0.5

-1.0

b

h max

AU'• •'++7 _ I++ h+ .• +o•,

Vh

V+ + Ah

!

-0.5 O. 0.5 Factor 2

Factor 1. c . Factor 1. d . +n---d

.5 ß :' :'.' .5 + ß ,•" ß k = A up +

• . + +'J dup c• ß ß

':.• •._. Vh+ +• '0.5 [ '0.5 [ hmax •. ;,. &h

:1: v -1 0 -1 0

-0.5 O. 0.5 -0.5 O. 0.5 Factor 3 Factor 3

Figure ?. Correspondence analysis plot. The first three principal factors for terrestrial points, with 19 attributes. (a) Factor I versus factor 2 for cells. (b) Factor I versus factor 2 for attributes. (c) Factor 1 versus factor 3 for cells. (d) Factor 1 versus factor 3 for attributes. Attribute designations are from Table 2, and the clump designated Vh includes Ah, H/L, [[Vh[[, •rlvH, and IIVhll.

Hydraulic conductivity plots outside the range of most of the cluster of cells and attributes. Storage capacity and cell volume are also on the fringe, although volume is correlated with the high topography points in western North America as one would expect.

Based on the correspondence analysis and on common sense, we eliminated all attributes which we deemed redundant or irrelevant. This left us with a subset of

seven parameters: areal fraction of bedrock outcrop c•, average sediment thickness a•, upstream area A "p, terrain curvature II II, terrain hypsometry I, range in cell elevation Ah, and standard deviation of slope aspect cry. These seven attributes formed the basis of the two-group discriminant analysis.

Discriminant Analysis

We wish to quantitatively distinguish between terrain which is predisposed to ice streams and that which is not. Two-group discriminant analysis offers a tool to this end [Fisher, 1936; Dillon and Goldstein, 1984, p. 360; Cart, 1995, p. 125]. Sample cells where large- scale basal ice flows have been inferred from the geological record and sample cells where fast flowing ice was unlikely were used as seed points for the two groups.

Based on these "type" points, discriminant analysis de- rives a unique basis function bj which maximizes variance between groups and minimizes variance within a group. In this respect, discriminant analysis has a different spirit from principal component techniques; in- stead of minimizing variance to reduce the data set, the goal is to accentuate differences and segregate the data set.

We collected a diverse group of 49 cells where there is strong evidence of fast ice flow. This group includes points on the Des Moines, James, and Michi- gan Lobes of the southern margin [Clayton and Moran, 1982; Micke18on et al., 1983; Clark, 1992] and suspected ice streams on the Boothia Peninsula [D!lke, 1984], in Bale des Chaleur and the St. Lawrence Estuary [Dyke and Prest, 1987], and in the Geraldton-Hemlo area north of Lake Superior [Hicock, 1988]. While the seed point ice streams and southern margin lobes may have experienced fundamentally different dynamical histories, we believe that the terrain influence on fast flow will apply similarly to all members of this seed group.

Evidence for the various points is multifarious, and the reader is referred to the original papers for details. In most cases the evidence for fast flow is inferred from

the sedimentary record (e.g., the extent and geometry of


debris trains, sediment stratigraphy, geomorphological features, till rheoloõy (shear strenõth), lateral moraine profiles). This raises the question as to whether the record of fast flow is only preserved in a particular type of environment: one with su•cient sediments, perhaps of a particular character. This would bias our sampling and therefore the results of the discriminant analysis. We attempted to avoid this as much as possible by choosing seed points from diverse physiographic regions, including the central and western interior plains, the Arctic archipelago, the St. Lawrence and Hudson Bay lowlands, and the Canadian Shield. A number of ad- ditional seed candidates for fast flow such as Hudson

Strait and several other locations in the interior plains have been omitted to avoid excessive seeding to this terrain type.

Most of our seed points are likely to have been in- scribed in the bed during late stages of the last glaciation, whereas the signatures of many earlier fast flow events may have been obliterated. This inevitability is not a concern in the application of discriminant analysis, as our seed points are simply a sampling of terrain which is geologically and topographically predisposed to fast flow, rather than an exhaustive compilation. Hence the timing of the flow event is inconsequential, provid- ing that present-day terrain character is representative of bed conditions during the fast flow event. We discuss this assumption below.

Points where ice streams decisively did not arise over the last glacial cycle are more difficult to identify. Most of the Laurentide-Cordilleran bed bears no evidence

that can be uniquely interpreted as resulting from fast flowing ice. Points of extreme elevation in the western cordillera are good stream-free candidates, and we have arbitrarily sampled cells in the Canadian Rockies. In addition, there are extensive areas of bedrock exposure in the Canadian Shield and in the Appalachians

which are well-mapped. Striation history of these areas is complex, but there are regions with extensively preserved records of several ice flow phases within the last õlaciation that predate the deglacial flows. Because viõ- orous basal activity (either slidin• or till deformation) would be accompanied by vigorous erosion and surface regeneration, we selected a small number of these points in Labrador, Newfoundland, and the Northwest Territ- ories as representatives in the no-stream group. Table 5 lists the seed points used in each group. All seed cells were within the LGM glacial limits.

We modified the discriminant analysis program of Cart [1995, p. 146] and generated discriminant scores for all terrestrial points as shown in Figure 8. Cell scores s• are simply the projection of each cell's attributes onto the basis function, s• = Aqbj, i • (1, no). Mean score for the stream locations is 6.88, and mean score for the no-stream cells is-0.21. The compilation in Figure 8c illustrates that these mean scores do not bracket the data

set; some cells are well below the mean no-stream score, while a great number of cells appear "more streamy" than the seed points.

This is hiõhlighted in Figure 9 where we have transformed the scores to a likelihood scale with the no-

streaming mean set to 0 and the streaming mean set to 1. We interpret that cells above and below this range are simply rich in the qualities that predispose terrain for or against fast ice flow. The bulk of points below are in the Cordillera, and many of those with raw probabilities greater than 1 correspond to continental shelf, the Hudson Bay lowlands, and the interior plains.

Figure 10 plots the likelihood distribution for the whole map region. This is an interesting measure; it synthesizes the entire diverse array of geologic and topographic attributes into a single dimensionless measure of ice-bed coupling. Note that the image is dark: the likelihood distribution in Figure 10 suggests that un-

Table 5. Location of Seed Points for Discriminant Analysis Groups

Point Location Reference

Lake Michigan Lobe Des Moines Lobe

James Lobe

Baie des Chaleur, NS St. Lawrence estuary

Geraldton-Hemlo

Boothia Peninsula

Canadian Rockies

Appalachians Canadian shield

Ice Stream Points

(39-41øN, 88øW) (42øN, 93-94øW) (43øN, 93-95øW) (44-45øN, 93-96øW) (43øN, 97-98øW) (44-45øN, 97-99øW) (47øN, 64-65øW) (47-48øN, 69øW) (48-49øN, 68øW) (48øN, 85-87øW) (49øN, 84-87øW) (50øN, 83-86øW) (SIøN, 82-84øW) ($2øN, 81-82øW) (70øN, 92-94øW)

Ice $tream. Iq'ee Points

(52øN, 117øW) (•3øN, l•søW) (48øN, 57øW) ($2øN, 66-68øW) (62øN, 105-109øW)

Clark [1992] Cl•rk [1992]

Clark [1992]

D•tke and Prest [1987] Dyke and Prest [1987]

Hicocl• [•9ss]

D•ke [1984]


16 . . ' . . 2.5 ß . . 450

14

12

10

-10 0 10 20

2.

1.5

1.

0.5

-10 0 10 20

Figure 8. Raw discriminant analysis scores. points. (c) The full terrestrial data set.

40O

35O

3OO

25O

20O

15O

100

50

0

ß . , ,

-10 0 10 20

(a) Ice stream test points. (b) No-stream test

der the proper glaciological conditions a large fraction of the Laurentide bed could support ice streams. We discuss details of the synthesis map below.

Discussion

Objectivity

We emphasize that group assessments are not certain, nor are discriminant scores probabilities in a strict sense. The term likelihood is more apt. Seed cells in the stream group were very likely to have hosted ice streams or vigorous basal flows late in the last glaciation; seed cells in the no-stream group likely did not. Discriminant scores indicate which group a given cell is more akin to, hence its relative likelihood of hosting an ice stream.

450

400

350

3OO

250

200

150

IO0

, ,

-2 0 2

Figure 9. Normalized discriminant analysis scores,

with mean score of the stream group set to l(••i ! and mean score of the no-stream group set to 0 We consider the distribution to be an ice stream likelihood measure for the Laurentide-Cordilleran beds.

There is a risk of circularity in discriminant analysis; the results are determined by group selections and there is no surprise that the Des Moines and Michigan Lobes (for instance) show up in Figure 10. We are nonethe- less satisfied with the synthesis, as a number of suspected fast flow regions that were not in the seed group have come forward, including Hudson Strait, Ungava Bay, Lancaster and Viscount Melville Sounds, the Pu- get Sound Lobe, and continental shelf regions of the Atlantic seaboard, which may be the best proxy for Antarctica's Siple Coast. Furthermore, the two seed groups account for only 60 out of 3498 terrestrial cells and represent u small fraction of the synthesis map.

Interpretation

It is interesting to observe that the ice stream likelihood map (Figure 10) looks very similar to geologic maps of North America which divide the continent into deformable and rigid beds [e.g., Fisher et al., 1985; Clark, 1994]. Our likelihood map contains more detailed structure, but in general, the interior plains and continental shelf regions have high ice-stream likelihoods relative to areas of exposed bedrock in the Cordillera and on the Canadian Shield.

The fundamental difference in our methodology com- pared to that of F•shev e• al. [1985] and Clark [1994] is that we complement the geologic partitioning with topographic influences. We conclude that the interior plains and continental shelf regions favor ice streams topographically as well as geologically. Low basal- coupling strength (minimal pinning points or sticky spots) translates to fast flow potential, while high basal coupling in a region indicates topographic and/or geologic attributes that prohibit or limit fast flow. This summary map of bed disposition holds independent of whether the fast flow mechanism is sediment deforma-

tion or sliding. The approach in this paper points only to areas which

are topographically and geologically condusive to large-


Fast flow •11Fi!i!•!i!!:ii!!!!i!!i!i•.111 ß 90% likelihood ""' '• •0-90%

.............. •"• 10-50%

Figure 10. Ice stream likelihood distribution, contoured from 1 ø cell values for the Laurentide bed. This measure combines topographic and geologic properties of the bed to yield an indication of ice-bed coupling strength.

scale basal flows. We have evaluated terrain enabling without regard to glaciological controls on ice flow. Taken at face value, the likelihood map has interesting geomorphological implications. If bed conditions widely predispose the ice sheet to streaming, then (1) ice streams were much more common than either rec-

ognized or inferred from the geological record, or (2) glaciological controls such as ice divide configuration, frictional and deformational heat generation, duration of ice cover (subice permafrost dissipation), and basal water distribution regulate ice streams more effectively than terrain disposition.

We favor the latter possibility. From this perspect- ive, an area which is strongly predisposed to streaming but bears no signs of vigorous basal activity (e.g., from stratigraphic, drift dispersion, or striation records) may tell us something of glaciological conditions which pre- vented streaming. This is subject to the detail and confidence in likelihood predictions. The plausibility of unpreserved or obliterated fast flow records on much of the ice sheet bed may limit the usefulness of this application.

Terrain Variability •Vi•h Time

We have tacitly assumed that present-day terrain is an appropriate proxy for paleobed characteristics and

that these characteristics are statistically constant over the course of a glaciation. The details of topographic and geologic structure will certainly vary over a glacial cycle in response to ice sheet loading and reworking. We argue that details are not critical; bed character on a 1 ø scale will be statistically robust. Consider, for instance, the impact of "the next" glacial cycle on a representative cell in the interior plains. Till features (e.g., drumlins, moraines) would be shifted, destroyed, and created, and small-scale surface features such as lakes and cities would be digested and redistributed by the ice. Most redistribution is local, and we expect that the resultant topographic and geologic nature of the cell would change little from the present state.

Mean cell elevation and slope may be significant ex- ceptions to this, with large excursions expected from isostatic response; we do not use these fields in the discriminant analysis. Isostatic response is integrated over large spatial scales, so topographic roughness measures are unlikely to be impacted. Bed drainage patterns will change, modifying the upstream area maps. Subice hydrological models which we are developing will make use of the large-scale evolution of continental drainage patterns, and time-dependent changes to ice stream likelihood could be included. Discriminant analysis with LGM drainage patterns rather than present-day did not change the likelihood map significantly, however, so we expect that this is unnecessary.


Summary Comments

Parameters compiled in this paper such as sediment distribution, terrain hypsometry, and large-scale topographic roughness measures are needed in physically based dynamical models of the Laurentide and Cor- dilleran Ice Sheets. Models which seek to portray basal flow mechanics can make direct application of many of these bed characterization maps.

As an extension, the ice-bed coupling map indicates large areas which are able to support fast flowing ice streams or lobes. Marginally connected bed areas which have continuous distributions of low terrain coupling in- clude a region striking northeasterly from Great Bear Lake, much of the southern Laurentide margin, and drainage routes out the Amundsen Gulf, Ungava Bay, Hudson Strait, and the St. Lawrence River. These were potentially important drainage routes for ice from the Laurentide-Cordilleran complex.

As a/inal note we stress that this analysis is not exhaustive. Alternative terrain measures can certainly be included, and other influences such as the specific geologic unit and geothermal heat flux may influence ice stream distribution. Furthermore, our subgrid sampling is on a scale of 3-10 km, so we are unable to evaluate terrain attributes below this scale. This is good resolution for modeling on synoptic ice sheet scales, but it is coarse relative to detailed regional mapping efforts (e.g., the Boothia Peninsula ice streams mapped by O•ke [1984]). We believe that the techniques described here will be applicable to higher-resolution multivariate analyses in the near future, as digital elevation models and digital geologic compilations rapidly improve.

Acknowledgments. We thank Bob Fulton for provid- ing us with a preliminary copy of the surficial materials map of Canada and Larry Dyke for counsel on surface hydrologic properties. Reviews by William Harrison, John An- drews, and Niels Reeh have strengthened this paper. Chris Clark gave enthusiastic feedback on the application of multivariate methods to terrain analysis and the identification of low-probability stream locations. This paper is a contribu- tion to the Climate System History and Dynamics Program (CSHD) that is jointly sponsored by the Natural Sciences and Engineering Research Council of Canada (NSERC) and the Atmospheric Environment Service of Canada.

References

Alley, R. B., D. D. Blankenship, C. R. Bentley, and S. T. Rooney, Deformation of till beneath ice stream B, West Antarctica, Nature, $•, 57-59, 1986.

Alley, R. B., D. D. Blankenship, C. R. Bentley, and S. T. Rooney, Till beneath Ice Stream B, 3, Till deformation: Evidence and implications, J. Geophys. Res., 9•, 8921- 8929, 1987.

Andrews, J. T., and K. Tedesco, Detrital carbonate-rich sediments, northwestern Labrador Sea: Implications for ice- sheet dynamics and iceberg rafting (Heinrich) events in the North Atlantic, Geology, •0, 1087-1090, 1992.

Andrews, J. T., K. Tedesco, and A. E. Jennings, Heinrich events: Chronology and processes, east-central Lauren- tide Ice Sheet and north-west Labrador Sea, in Ice in the

Climate System, edited by W. R. Peltlet, pp. 167-186, Springer-Verlag, New York, 1993.

Beget, J. E., Modelling the influence of till theology on the flow and profile of the Lake Michigan lobe, southern Laurentide Ice Sheet, U.S.A, .L Glaciol., $•, 235-241, 1986.

Beget, J. E., Low profile of the northwest Laurentide Ice Sheet, Arct. Alp. Res., 19, 81-88, 1987.

Blankenship, D. D., C. R. Bentley, S. T. Rooney, and R. B. Alley, Seismic measurements reveal a saturated porous layer beneath an active Antarctic ice stream, Nature, $•, 54-57, 1986.

Bond, G. C., and R. Lotti, Iceberg discharges into the North Atlantic on millenial time scales during the last glaciation, Science, ,•67, 1005, 1995.

Bond, G. et al., Evidence for massive discharges of icebergs into the North Atlantic Ocean during the last glacial pe- riod, Nature, $60, 245-249, 1992.

Boulton, G. S., G. D. Smith, A. S. Jones, and J. Newsome, Glacial geology and glaciology of the last mid-latitude ice sheets, J. Geol. Soc. London, 14•, 447-474, 1985.

Cart, J. R., Numerical Analysis for the Geological Sciences, 592 pp., Prentice-Hall, Englewood Cliffs, N.J., 1995.

Clark, P. U., Surface form of the southern Laurentide Ice Sheet and its implications to ice-sheet dynamics, Geol. Soc. Am. Bull., 104, 595-605, 1992.

Clark, P. U., Unstable behaviour of the Laurentide Ice Sheet over deforming sediment and its implications for climate change, Quat. Res., 41, 19-25, 1994.

Clarke, G. K. C., Fast glacier flow: Ice streams, surging and tidewater glaciers, .L Geophys. Res., 9•, 8835-8841, 1987.

Clayton, L., and S. R. Moran, Chronology of Late Wisconsl- nan glaciation in middle North America, Quat. Sci. Rev., 1, 55-82, 1982.

Clayton, L., J. T. Teller, and J. W. Attig, Surging of the southwestern part of the Laurentide Ice Sheet, Boreas, 14, 235-241, 1985.

Deblonde, G., and W. R. Peltier, Simulations of continental ice-sheet growth over the last glacial-interglacial cycle: Experiments with a one-level seasonal energy-balance model including realistic geography, J. Geophys. Res., 96, 9189-9216, 1991.

Deblonde, G., and W. R. Peltier, Pleistocene Ice Age scen- arios based upon observational evidence, J. Clim., 6, 709- 727, 1993.

Dillon, W. R., and M. Goldstein, Multivariate Analysis, 587 pp., John Wiley, New York, 1984.

Dowdeswell, J. A., M. A. Maslin, J. T. Andrews, and I. N. McCave, Iceberg production, debris rafting, and the extent and thickness of "Heinrich layers" (H-l, H-2) in North Atlantic sediments, Geology, •$, 301-304, 1995.

Dyke, A. S., Quaternary geology of Boothia Peninsula and northern District of Keewatin, central Canadian Arctic, Mere. Geol. bury. Can., 407, 26 pp., 1984.

Dyke, A. S., and V. K. Prest, Late Wisconsinan and Holocene history of the Laurentide Ice Sheet, Gdogr. Phys. Quat., 41, 237-264, 1987.

Echelmeyer, K., R. Wade, and A. Iken, Mechanisms of ice stream motion: Jakobshavns Isbree, Greenland (abstract), Eos Trans. A GU, 7•(44), Fall Meet. Suppl., 150, 1991.

Fisher, D. A., N. Reeh, and K. Langley, Objective reconstructions of the late Wisconsinan Laurentide Ice Sheet

and the significance of deformable beds, Gdogr. Phys. Quat., $9, 229-238, 1985.

Fisher, R. A., The use of multiple measurements in tax- onomic problems, Ann. Eugenics, 7, 179-188, 1936.

Freeze, R. A., and J. A. Cherry, Groundwater, Prentice- Hall, Englewood Cliffs, N.J., 1979.

Fullerton, D. S., and R. B. Colton, Stratigraphy and correlation of the glacial deposits on the Montana plains, Quat. Sci. Rev., spec. vol. 5, 1986.


Fulton, R. J. (Ed.), The Geology of North America, vol. K1, Quaternary Geology of Canada and Greenland, Geol. Soc. of Am., Boulder, Colo., 1989.

Fulton, R. J. (Ed.), Surt•cial Materials of Canada, Map 1880A, scale 1:5,000,000, Geol. Surv. of Can., Ottawa, Ontario, 1993.

Greenacre, M.J., Theor•y and Applications of Corspond- ence Analysis, 364 pp., Academic, San Diego, Calif., 1984.

Greenacre, M.J., Correspondence Analysis in Practice, 195 pp., Academic, San Diego, Calif., 1993.

Hansel, A. K., D. M. Mickelson, A. F. Schneider, and C. E. Larsen, Late Wisconsinan and Holocene history of the Lake Michigan basin, in Quaternary Evolution of the Great Lakes, edited by P. F. Karrow and P. E. Calkin, Spec. Pap. Geol. Assoc. Can., $0, 39-53, 1985.

Heath, R. C., Hydrogeologic map of North America showing the major units that comprise the surface layer, in The Geology of North America, vol. 0-2, Hydrogeology, edited by W. Back, J. S. Rosenshein, and P. R. Seabet, Plate 2, Geol. Soc. of Am., Boulder, Colo., 1988.

Heinrich, H., Origin and consequences of cyclic ice-rafting in the northeast Arctic Ocean during the past 130,000 years, Quat. Res., 29, 141-152, 1988.

Hicock, S. R., Calcareous till facies north of Lake Super- ior, Ontario: Implications for Laurentide ice streaming, G•ogr. Phys. Quat., 4•, 120-135, 1988.

Huybrechts, P., and S. T'Siobbel, Thermomechanical modelling of northern hemisphere ice sheets with a two-level mass-balance parameterisation, Ann. Glaciol., 2I, 111- 117, 1995.

Iken, A., K. Echelmeyer, W. Harrison, and M. Funk, Mecha- nisms of fast •ow in Jakobshavns Isbr•e, West Greenland, Part 1, Measurements of temperature and water level in deep boreholes, .L Glaciol., $9, 15-25, 1993.

Kamb, B., Sliding motion of glaciers: Theory and observa- tion, Rev. Geophys., 8, 673-728, 1970.

Kamb, B., Glacier surge mechanism based on linked cavity configuration of the basal water conduit system, J. Geo- phys. Res., 92, 9083-9100, 1987.

Kamb, B., Rheological nonlinearity and •low instability in the deforming bed mechanism of ice stream motion, J. Geophys. Res., 96, 16,585-16,595, 1991.

Klassen, R. W., Quaternary geology of the southern Cana- dian Interior Plains, in ]'he Geology of North America, vol. K1, Quaternary Geology of Canada and Greenland, edited by R. J. Fulton, pp. 138-173, Geol. Soc. of Am., Boulder, Colo, 1989.

MacAyeal, D. R., Binge/purge oscillations of the Lauren- tide Ice Sheet as a cause of the North Atlantic's Heinrich

events, Paleoceanography, 8, 775-784, 1993a.

MacAyeal, D. R., A low-order model of the Heinrich event cycle, Paleoceanography, 8, 767-773, 1993b.

MacAyeal, D. R., R. A. Bindschadler, and T. A. Scambos, Basal friction of Ice Stream E, Antarctica, Y. Glaciol., 41, 247-262, 1995.

Marshall, S. J., and G. K. C. Clarke, Sensitivity analyses of coupled ice sheet/ice stream dynamics on the EISMINT experimental ice block, Ann. Glaciol., •3, in press, 1996.

Marsiat, I., Simulation of northern hemisphere continental ice sheets over the last glacial-interglacial cycle: Experi- ments with a latitude-longitude vertically-integrated ice sheet model coupled to a zonally-averaged climate model, Palaeoclirnates, 1, 59-98, 1994.

Mathews, W. H., Surface profiles of the Laurentide Ice Sheet in its marginal areas, Y. Glaciol., 13, 37-43, 1974.

Mickelson, D. M., L. Clayton, D. S. Fullerton, and H. W. Borns, The Late Wisconsinan glacial record of the Lauren- tide Ice Sheet in the United States, in Late Quaternary Environments of the [[nited States, vol. 1, edited by H. E. Wright Jr. and S.C. Porter, pp. 3-37, Univ. of Minn. Press, Minneapolis, 1983.

Morner, N.-A., and A. Dreimanis, The Erie Intersfade, in The Wisconsinan Stage, edited by R. P. Goldthwait and H. B. Willman, Mern. Geol. Soc. Am., I36, 107-134, 1973.

Nye, J. F., A calculation of the sliding of ice over a wavy surface using a NewtonJan viscous approximation, Proc. R. Soc. London A, 311, 445-467, 1969.

Nye, J. F., Glacier sliding without cavitation in a linear viscous approximation, Proc. R. Soc. London A, 315, 381- 403, 1970.

Peltlet, W. R., Ice age paleotopography, Science, •65, 195- 201, 1994.

Row, L. W., III, and D. A. Hastings, TerrainBase: World- wide Digital Terrain Data, Natl. Oceanic and Atmos. Ad- min., Natl. Geophys. Data Cent., Boulder, Colo, 1994.

Zevenbergen, L. W., and C. R. Thorne, Quantitative analysis of land surface topography, Earth Surf. Processes Landforms, 12, 47-56, 1987.

G. K. C. Clarke and S. J. Marshall, Department of Earth and Ocean Sciences, University of British Columbia, 2219 Main Mall, Vancouver, B.C., Canada, V6T 1Z4. (e-maih clarke•geop.ubc.ca; marshall•geop.ubc.ca)

A. S. Dyke and D. A. Fisher, Terrain Sciences Divi- sion, Geological Survey of Canada, 601 Booth St., Ott- awa, Ontario, Canada, KIA 0ES. (e-mail: [email protected]; f[sher•emr.ca)

(Received December 20, 1995; revised April 1, 1996; accepted April 9, 1996.)

Documents

Geologic and topographic controls on fast flow in the Laurentide and Cordilleran Ice Sheets