Reconstructions of Mountain Glacier Profiles, Northeastern United States

Reconstructions of mountain glacier profiles, northeastern United States

SPAFFORD C. ACKERLY Department of Geological Sciences, Cornell University, Ithaca, New York 14853

ABSTRACT

Ice surface profiles are reconstructed for 37 proposed mountain glacier localities in the northeastern United States, including sites in Figure 1. Highland areas of the the Catskill and Adirondack Mountains, New northeastern United States, proposed York; the Green Mountains, Vermont; the as locations of former mountain glacia- White Mountains, New Hampshire; and the tion (after Bradley, 1981, p. 320). Longfellow Mountains and Mount Katahdin, Maine. The reconstructions, determined numerically from the shear-stress equation r = pgh sin a, show estimated ice thickness as a function of valley position and slope. In general, ice thickness increases from zero at the position of the glacier terminus (terminal position is a required input to the model) to some equilibrium "slab" thickness in the upper valley, where the slab thickness is inversely proportional to valley slope. Glacier reconstructions support the empirical evidence for former local glaciation in the debate centers mainly on the timing of local gla- slopes are steep, the ice is thin, and where slopes Catskill and White Mountains and in some ciation. Did it occur prior to (Goldthwait, 1913; are gentle, the ice is thick. We may ask, there- localities in the Adirondack Mountains. In R. P. Goldthwait, 1970; Davis and Waitt, 1986) fore: Approximately what ice thicknesses are re- several proposed glacier locations in the Adi- or subsequent to (Antevs, 1932; Johnson, 1933; quired in a given locality to support active ice rondack and Green Mountains (in very shal- Thompson, 1961) the last advance of Lauren- flow? Are proposed locations for valley glaciers low basins and in very gently sloping valleys), tide ice? In other areas, however, mainly in the in the northeastern United States suitable, topo- however, estimated ice thicknesses exceed the Green Mountains of Vermont and in the Adi- graphically, for the development of confined, depth of their respective valleys or the eleva- rondack Mountains of New York, the evidence local valley glaciers? Theoretical reconstructions tion of up-valley cols, suggesting a re- for local glaciation is more equivocal, and there offer a quantitative approach to the study of evaluation of these localities as sites of local is disagreement about whether certain features local glaciation in the northeast United States, confined ice flow. Confirmed localities of (notably cirques and moraines) are products of supplementing the long history of empirical in- local glaciation are mostly in valleys with local ice (Wagner, 1970; Craft, 1979) or conti- vestigations of this problem. mean gradients greater than about 5° where nental ice (Stewart, 1971). The evidence for The regional scope of the paper is intended to reconstructed ice thicknesses are less than local glaciation in the Catskill Mountains, as provide a comparative basis for the analysis. about 200 m. recognized by Rich (1906, 1935) and Johnson Well-studied and confirmed examples of local (1917, 1933), has received less attention (but, glaciation in the Presidential Range of New INTRODUCTION see Cadwell, 1986). Hampshire establish a relationship between This paper addresses this long-standing prob- theoretically and empirically derived ice-surface In the nearly 150 yr since Louis Agassiz in- lem on the former distribution and extent of reconstructions. The theoretical reconstructions troduced the glacier theory to North America, a local glaciation by reconstructing, from theoreti- offer reasonable first-order approximations of great deal of evidence has been cited both sup- cal principles, the surface profiles of proposed the former valley glaciers in this range. The porting and refuting the concept of local moun- local glaciers, in order to test the assertions that analysis is then extended to a more regional tain glaciation in the highlands of the northeast- various localities could harbor active local ice. level, considering proposed sites of local glacia- ern United States. In some areas, notably the The analysis is based on the observation that for tions in the Green Mountains of Vermont, in the White Mountains of New Hampshire and on small and confined valley glacier systems, ice Catskill and Adirondack Mountains of New Mount Katahdin in Maine (Fig. 1), the evidence thickness is inversely related to valley slope (for York, and in the Longfellow Mountains and on for local glaciers is widely acknowledged, and example, Porter and others, 1983). Where Mount Katahdin in Maine.

Geological Society of America Bulletin, v. 101, p. 561-572, 10 figs., 4 tables, April 1989.

561

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ICE-SURFACE PROFILES valley with a 5° gradient, ice thickness reaches T = P g h sin a 90% of the slab thickness (f = 0.9) at a distance Methods for reconstructing the surface pro- of about 2.5 km from the glacier terminus (for files of valley glaciers (see, for example, ho = 13.3 m). In general, valleys with mean Mathews, 1967; Pierce, 1979; Schilling and gradients greater than about 5° contain "slab- Hollin, 1981) are based on the shear-stress type" glaciers (for example, Porter and others, equation 1983) and the thickness in these glaciers is pri- marily a function of valley slope. The slab rb = pgh sin a, (1) thickness is easily estimated from equation 3 by substituting the value of the valley slope /3 for a, where rt, is the shear stress at the base of the ice, W = pgh thus bypassing the tedious numerical calcula- p is the ice density, g is gravity, h is the ice tions that are otherwise necessary for recon- thickness, and a is the surface gradient of the ice Figure 2. An idealized slab of ice of con- structing ice thickness. (Fig. 2). The shear stress is acting in a direction stant thickness h and surface slope a on a bed Necessary inputs to the equations for calculat- parallel to ice flow, and the shear force is due to with constant gradient. Stresses at the base of ing ice surface profiles are the values of the criti-

the weight of overlying ice (pgh in eq. 1). When the ice are due to the weight of the slab. The cal basal shear stress Tb and the shape factor F. the basal shear stress exceeds some critical value, shear stress r acts in a direction parallel to the Calculations of basal shear stresses in mountain because of either excess ice thickness or surface bed and has magnitude r = pgh sin a. glacier systems (Nye, 1952a; Kanasewich, 1963; slope, the ice will begin to flow, by either inter- Mathews, 1967; Pierce, 1979; Schilling and Hol- nal deformation or basal slip. Reconstructions lin, 1981) show that in general, "effective" shear based on equation 1 assume infinite flow rates parallel to the valley floor (ice surface slope a stresses at the base of the ice are on the order of above the critical shear stress and zero flow equals the valley slope /?). In the more general 50 to 150 kPa (0.5 to 1.5 bars). Pierce (1979), in below the critical shear stress (the behavior of a case, the ice surface slope a is expressed as a = studies of Rocky Mountain glacier systems, perfect plastic), a reasonable first-order approx- dH/ds, giving, from equation 3, the differential found that basal shear stress varied from about imation for glacial ice, flowing either by defor- equation 0.84 bars for decelerating flow conditions (pro- mation (for example, Glen, 1952) or by sliding moted by downflow divergence of flow lines, (for example, Weertman, 1957, 1964). More downflow increase in ice thickness, and abla- h dH = h0 ds, (4) complex models, using more realistic flow laws tion) to 1.21 bars for accelerating flow (pro- and mass-balance equations (for example, where dH is the change in the ice surface eleva- moted by downflow convergence of flow lines, Hughes, 1981), appear unnecessary for valley tion over distance ds (ds measured parallel to the by downflow ice thinning, and in zones of ice glacier reconstructions (for example, Schilling bed). For glaciers on a flat bed, equation 4 inte- accumulation). The shape factor F typically var- and Hollin, 1981). grates to ies from about 0.75 to 0.95 (for example, Equation 1 applies strictly to a parallel-sided Pierce, 1979).

slab of ice and must be modified for the analysis h = (2 h0s)*. (5) of valley glacier systems. Valley walls increase METHODS OF GLACIER the contact area of the ice (per unit volume of For glaciers on an irregular bed topography, RECONSTRUCTION ice) and distribute the mass over a larger basal equation 4 must be solved numerically (see area, thereby reducing the value of the mean Methods). Ice surface profiles represent numerical solu- basal shear stress. This effect is generally mod- In valley glaciers, the ice thickness in- tions to the differential form of the shear-stress eled by introducing a shape factor F into equa- creases upstream from the glacier snout and ap- equation (eq. 4). This analysis uses a computer tion 1, so that proaches some "slab" thickness in the upper reaches of the valley (see inset, Fig. 3). Figure 3 Tb = pghF sin a, (2) shows the position on a glacier (distance from Figure 3. A glacier rest- snout) where the ice thickness approaches 90% ing on a bed of constant where F < 1. The shape factor depends both on and 98% of the slab thickness. For example, in a slope ¡5 reaches some the shape of the valley cross section (for exam- proportion f of the "slab" ple, circular or parabolic) and on the ratio of thickness at a distance Sf glacier width to depth. Most authors use a shape from the glacier terminus. factor developed by Nye (1965) and assume a For example, for a glacier parabolic valley cross section (for example, on a 5° bed, the ice will be Graf, 1970; Pierce, 1979). 90% of the slab thickness Equations 1 and 2 define an inverse relation- a> at a distance of about 2 o ship between the ice thickness h and the ice c km from the glacier ter- to surface slope a, which is (for small a) CA minus. Curves are based •a 2.5 - on the equation (see App. 2 h = ho/a, (3) 1) sf = (h0//J ) {ln[l/(l - f)] - 1} and on the values T where h0 is a constant (= rb/pgF). Equation 3 = 100 kPa, p = 900 5 10 3 2 provides a simple and direct estimate of ice kg/m , g = 9.8 m/s , F = thickness for cases in which the ice surface is bed slope (degrees) 0.85.

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TABLE 1. PROPOSED LOCATIONS OF FORMER LOCAL GLACIATION IN THE NORTHEASTERN UNITED STATES, WITH SUMMARY STATISTICS ON RECONSTRUCTED LONGITUDINAL GLACIER PROFILES AND ON VALLEY TOPOGRAPHY

Terminus Schrund Horizontal Mean Mean "Slab" Maximum elevation elevation reach slope thickness thickness thickness F (m) (m) (m) (degrees) (m) (m)t (m)

WHITE MOUNTAINS Great Gulf 610 1,320 5,600 7.2 121 140 150 0.7 King Ravine 670 1,170 2,520 11.1 90 no 119 0.65 Tuckerman Ravine 670 1,400 3,420 12.0 68 70 102 0.8 Huntington Ravine 670 1,270 4,165 11.9 85 90 100 0.6 Castle Ravine 670 985 3,230 7.9 98 110 113 0.7 Madison Gulf 945 1,255 1,250 13.9 60 70 84 0.75 Bumpus Basin 792 970 1,270 8.0 83 100 108 0.75 Jobildunc Ravine 975 1,120 1,590 5.2 96 144 0.85 Benton Brook 885 1,030 655 12.6 60 72 0.7

MAINE Katahdin, S Basin-1 745 925 2,180 4.7 108 164 0.85 Katahdin, S Basin-2 850 935 1,380 3.5 105 149 0.85 Katahdin, N Basin 950 1,165 1,170 10.5 66 75 91 0.85 Northwest Basin 670* 875 1,670 7.0 89 100 111 0.8 Crocker Mtn., E cirque 730 860 1,280 5.7 75 80 105 1.0 Crocker Mtn., N cirque 550 700 1,860 4.6 102 120 123 0.9

GREEN MOUNTAINS Miller Brook 305 405 2,960 1.9 182 251 0.7 Ritterbush Valley 290 325 1,380 1.5 110 164 0.9 West Branch 305 515 5,080 2.3 165 228 1.0 Belvidere Pond-1 305 350 5,930 0.43 233 345 1.0 Belvidere Pond 2 345 355 975 0.65 98 135 1.0 Grayling Brook, WY 2,195 2,345 10,730 0.81 310 444 0.85

ADIRONDACK MOUNTAINS White Brook 600 850 1,550 9.2 80 90 93 0.75 Whiteface Mtn., E cirque 550* 780 1,145 11.4 62 70 75 0.8 Roaring Brook-1 330 745 3,930 6.0 124 188 0.8 Roaring Brook 2 510 750 1,670 8.2 81 90 95 0.8 Mt. Redfield, S cirque 1,025 1,150 770 9.2 57 65 68 1.0 Boreas Mtn. 700* 920 1,260 9.9 63 70 74 0.9 Lost Pond 862 885 485 2.6 65 90 1.0 Moss Pd 1,290 1,305 190 4.8 39 59 1.0 Blue Ridge 365 700 14,430 1.3 284 422 1.0 Styles Brook-1 240* 545 6,710 2.6 176 260 1.0 Styles Brook-2 450* 550 3,580 1.6 167 213 1.0

CATSKILL MOUTAINS Johnson Hollow-1 395 550 3,330 2.6 158 195 218 0.8 Johnson Hollow-2 545 685 975 8.0 79 90 101 0.8 Little West Kill 410 645 5,340 2.5 189 235 250 0.9 Bearpen Mtn., E cirque 610 760 870 56 60 66 1.0 Hunter Mtn., N cirque 615 775 1,370 93 105 115 0.8 West Kill-1 475 680 9,125 1.3 264 320 354 0.9 West Kill-2 560 820 2,070 106 120 131 0.9 Bearpen-Vly col 535 620 585 63 75 81 0.8 Batavia Kill 675 830 1,680 5.2 101 120 128 0.85 Balsam Mtn., NW cirque 490 660 1,070 80 90 95 0.7 Cook Brook 600 795 2,180 118 135 154 0.75 Irish Mtn., NW cirque 535 660 975 7.1 70 85 88 0.9

Note: see Figures 5, 7-10. •My estimate of the glacier terminus elevation; otherwise, these data are from cited references (see text). ^Not given for glaciers departing from the "slab-type" profile (see text).

algorithm essentially the same as the program The reconstructions are based on a basal the shear stress and the shape factor are held VALLEY in Schilling and Hollin (1981), and shear stress of 100 kPa (1 bar), an ice density of constant along the length of the valley, although the reader is referred to this source and to Ap- 900 kg/m3, gravity equal to 9.8 m/s2, and a in actual glaciers, the values of these parameters pendix 2 for details. The analysis considers the constant shape factor over the length of the val- must vary in response to variations in valley proposed valley glacier locations listed in Table ley. The shape factor is calculated from a "repre- morphometry (for example, width, shape), ice 1. Topographic profiles of the valleys were ob- sentative" valley cross section, chosen at a point tained by digitizing the contour spacing on U.S. roughly midway along the valley where valley Geological Survey topographic maps. Longitud- TABLE 2. VALUES OF THE SHAPE FACTOR F walls are approximately parallel, and using an FOR DIFFERENT VALUES OF W, inal topographic profiles reflect the valley bot- initial estimate of ice thickness to determine the THE RATIO OF GLACIER HALF-WIDTH TO GLACIER DEPTH tom gradient projected onto straight line seg- ratio of glacier half-width to depth. The valley ments which roughly parallel the valley trend. A cross sections used to find F are illustrated in the W F

FORTRAN program calculates the ice surface figures. A parabolic valley cross section is as- 0.445 profiles, starting at some specified terminus posi- sumed for the value of F, and a value of F = 1 is 0.646 0.746 tion, using the arrays of topographic data to de- used for very shallow valleys (see Table 2). 0.806 1.000 termine local ice thickness. The glacier terminus Inherent limitations of the reconstruction position is usually taken at a location described method are in the choice of the effective shear Noie: after Nye, 1952b. An approximation of F is given by F = 0.45 W0-44 for or proposed in the literature (see below and 1 < W < 3.7 and by F = 0.67 W014 for 3.7 < W < 16 (based on some values stress (r = 1 bar), the shape factor F, and the of F given in Pierce, 1979, p. F70, Table 3). Table 1). position of the glacier terminus. In the analysis,

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flow patterns (for example, at the confluence of 44° ' 21' tributary valleys), and other variables. A fixed- N parameter model will not capture all of the details of an ice surface profile in a given valley. The fixed-parameter model, however, does have the advantage that the model is simple, and the effects of the parameters are, in most cases, easy to gauge. For example, the glaciers in most valleys have a slab-type profile, where ice thickness is governed by the simple shear-stress equation (eq. 3). An error in the value of either r or F will have a corresponding linear effect on the value of the ice thickness h. For example, if the value of r is 0.8 instead of 1, then the reconstructed ice thickness should be approximately 80% of what is observed in the figures. Moving values for the various parameters might add more realism to the model, but also more uncertainty as to what the reconstructed profiles actually represent. Furthermore, the empirical constraints on the theoretical reconstructions are weak in many cases and may not warrant more complex reconstruction models. The value of r = 1 bar is chosen for the reconstructions because it is a value observed in other glacier systems (see above) and because this value gives reasonable reconstructions of former glaciers in the Presi- dential Range, New Hampshire (see below and Fig. 4). Table 1 shows, in summary form, some results of the analysis for the different proposed valley glacier locations: the shape factor F, mean slope of the valley from the glacier terminus to the schrund elevation (defined below), mean and maximum ice thicknesses, and the estimated "slab" thickness. The slab thickness is the ap- proximate thickness (+5 to 10 m) in the middle reaches of a reconstructed glacier, where the ice surface is approximately parallel to the ground surface. Slab thicknesses are not determined for reconstructed glaciers departing from the slab- type profile (in the sense used in Porter and others, 1983). The schrund elevation is taken as 44* the "line separating a cliff or steeper slope above 71° 21 W 71° 15' 15 from a gentler, usually scalable slope below" (Gilbert, 1904, p. 582; also see Goldthwait, Figure 4. Distribution and extent of former mountain glaciers in the Presidential Range, 1970) and is determined by visual examination White Mountains, New Hampshire, as estimated by Goldthwait (1970). Straight line segments of longitudinal valley profiles and by inspection indicate positions of reconstructed glacier cross sections in Figure 5. of computer output giving valley slope at successive elevations in the valley. Schrund elevations determined in this analysis are mostly similar to indicated). Valley cross sections are shown as if glaciation (for example, Goldthwait, 1913, those obtained by other workers (to within 25 looking up the valley. 1916, versus Antevs, 1932; R. P. Goldthwait, m, Table 3). Exceptions (Castle Ravine, Madi- 1970, versus Thompson, 1961; Bradley, 1981, son Gulf, Roaring Brook, and White Brook lo- RESULTS AND ANALYSIS 1982, versus Fowler, 1984, and Gerath and calities) may be due to the recent availability of Fowler, 1982). The general consensus is that 7.5-minute topographic maps in these areas. Re- White Mountains local glaciation, if it did occur in post-Laurentide constructed ice-surface profiles are shown in time, was probably minor, and most of the Figures 5 and 7-10. In the figures, the vertical The former existence of valley glaciers in the cirque erosion occurred prior to the last advance scale is preserved throughout, and the horizontal Presidential Range, White Mountains, is widely of continental ice (for example, Waitt and scale is varied to accommodate valleys of differ- acknowledged, although there is some contro- Davis, 1988). Thus, most direct indicators of the ent lengths (vertical exaggeration of each profile versy concerning the timing of the local former extent of mountain glaciers in the Presi-

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TABLE 3. COMPARISON OF SCHRUND ELEVATIONS Hanson, 1986; Thompson, 1961, provides a (IN METERS) DETERMINED IN THIS ANALYSIS WITH (1) Goldthwait's estimates are biased by percep- RESULTS OF OTHER WORKERS tions that glacier thickness is related to the good review). absolute size of the basin, rather than to the The reconstructed South Basin glacier profile This study Other work magnitudes of the valley slope and the shape in Figure 7 is for a terminus position at the Basin

Great Gulf 1,320 1,341" factor as assumed in the numerical reconstruc- Ponds moraine, elevation 745 m (former termini King Ravine 1,170 1,164* tions, or (2) the numerical reconstructions are could have been higher or lower than this posi- Tuckerman Ravine 1,400 1,378* Huntington Ravine 1,270 1,286* omitting a factor that is related, directly or tion), giving mean and maximum thicknesses of Castle Ravine 985 1,067* Madison Gulf 1,255 1,213* indirectly, to basin size. 105 and 164 m, respectively, with an estimated Bumpus Basin 970 963* Despite the differences between Goldthwait's ice surface elevation at about 1,100 to 1,110m Katahdin, S Basin 935 945Í Katahdin, N Basin 1,165 l,065t reconstructions and the results of the numerical (Table 1 also gives statistics for a glacier with Katahdin, NW Basin 880 899Î terminal position at the Bear Den moraine, ele- Crocker Mtn., N cirque 700 725§ analysis, the data from the two sources are in Crocker Mtn., E cirque 860 847§ reasonable agreement, considering the assump- vation 850 m, Tarr, 1900). The reconstructed Miller Brook 405 366« Belvidere Pond 350 323** tions and simplifications of the theoretical analy- South Basin glacier departs from the slab-like Ritterbush Valley 325 323** Roaring Brook 750 908tt sis and the potential for subjective bias in the form of the Presidential Range glaciers, being White Brook 850 914tt empirical approach. Qualitatively and quantita- relatively thicker up valley than down valley. tively, the Presidential Range glaciers have all The calculated ice thickness is continually in- Note: there is close agreement in elevations in most cases, with some exceptions {notably in Castle Ravine, Madison Gulf, Roaring Brook, and White Brook). the characteristics of the "slab-type" glaciers in creasing from the terminus to the schrund eleva- Differences may be due to use of recently available 7.5-minute quadrangle maps in the White Mountains and in the Adirondack Mountains in this study. the Rocky Mountains (Porter and others, 1983). tion, and the ice surface is nowhere parallel to •Goldthwait (1970). They are relatively thin (60 to 150 m), they the valley bottom. These characteristics are re- tDavis (1976), cited in Boms and Calkin (1977). Wns and Calkin (1977). occur in valleys with relatively steep slopes (7° lated to the relatively low gradient of the South "Wagner (1970), cited in Borns and Calkin (1977). t^Craft (1979). to 14°), and they are restricted to the uppermost Basin cirque floor (about 3.5°). 10 km of the valley systems. Ice thicknesses in Thompson (1961) gave an estimate of the the reconstructed glaciers are controlled primar- former elevation of ice in the South Basin cirque ily by the slope of the valley floor and the value from the downward termination of avalanche dential Range cirques (for example, moraines) of the shape factor. The position of the glacier chutes on the cirque headwall. From 1:62,500- are missing, and there are no precise measures of terminus appears to have little effect on ice scale topographic map data, this position ap- depth and length of the former glaciers. Gold- thickness, except very near to the terminus pears to be at approximately 1,125 to 1,160 m, thwait (1970), however, on the basis of many position. which is higher than the numerically predicted years of study in the area, gives some estimates Two other localities of proposed mountain ice-surface elevation (with ice terminus at the of former thicknesses and down-valley extents of glaciers in the White Mountains are in Jobil- Basin Ponds moraine). The numerical recon- these glaciers. Goldthwait estimated the former dunc Ravine and in Benton Brook, both on struction would agree with Thompson's estimate position of glacier termini as from 1,000 to Mount Moosilauke (Haselton, 1975; Gold- only if the model parameters were varied (r and 5,000 ft (300 to 1,500 m) beyond the lowest thwait, 1970). Predicted ice thicknesses in F) or if the ice terminus position used in the abraded features in each glacial trough; these Jobildunc Ravine are large (mean 96 m, maxi- model was located downhill from the Basin glacier terminus positions are used in the present mum 144 m), nearly filling the cirque in its Ponds moraine. The possibility of a more distal analysis (Table 1). upper reaches (Fig. 7). The ravine itself is larger terminus for the South Basin glacier is supported Longitudinal ice-surface profiles were con- than those in the Presidential Range (compare by the fact that the South Basin cirque is one of structed for seven glacier locations: Tuckerman cross sections). The significance of these results the largest in the northeast and by correlations of Ravine, Huntington Ravine, Great Gulf, Madi- is not clear. The reconstructed Benton Brook cirque size and glacier size (Dort, 1962). These son Gulf, Bumpus Basin, King Ravine, and Cas- glacier has the characteristic slab form of a typi- considerations suggest that the South Basin was tle Ravine. Ice thicknesses in the reconstructed cal mountain glacier, and an ice thickness (mean the origin of a fairly large glacier system flowing glaciers are compared with the empirical recon- 60 m, maximum 72 m) comparable to that of eastward from the mountain. structions of Goldthwait (Fig. 4). Goldthwait's the reconstructed Madison Gulf glacier. A reconstructed glacier profile for localized thickness estimates are indicated on the valley ice in the North Basin shows ice thicknesses and cross sections of Figure 5 by a dashed line, and Mount Katahdin surface slopes similar to those observed in Presi- these thicknesses are compared with numerically dential Range glaciers, although it is possible derived thickness values in Table 4. In general, Approximately five to seven well-defined that the North Basin glacier was at one time the numerical results are within about 20% to cirques occur on the flanks of Mount Katahdin, much larger and confluent with ice in the South 30% of Goldthwait's estimates, although there Maine, providing good evidence for the former Basin. The reconstructed glaciers on Crocker are two notable exceptions (King Ravine and existence of local glaciers (Davis, 1976; Thomp- Mountain conform to the slab-type glacier pro- Bumpus Basin). son, 1961). Possible moraines in the North and file but show relatively thick ice (reflecting low Although the data base is not large, it appears South Basins may be evidence for post-Lauren- valley gradients) compared to reconstructed that the numerical reconstructions underesti- tide glaciers (Thompson, 1961; Caldwell, 1966; Presidential Range glaciers. mate ice thicknesses in the larger basins and but see Davis, 1976; Waitt and Davis, 1988), overestimate thicknesses in the smaller basins, although the main period of cirque formation Green Mountains relative to Goldthwait's reconstructions. This was either prior to or during the last advance of pattern is indicated in Figure 6, showing the continental ice. The Basin Ponds moraine, once The most compelling evidence for former difference between Goldthwait's and the numer- thought to be an end moraine of local ice (for local glaciers in the Green Mountains, Vermont, ically determined thickness values plotted example, Tarr, 1900) or a medial moraine (An- is the occurrence of end moraines in the Miller against glacier area (measured from Goldthwait's tevs, 1932), was probably a lateral moraine to Brook and Ritterbush Valleys (Wagner, 1970). map, Fig. 4). These data suggest that either continental ice in the lowlands (Caldwell and Other possible moraines are at Belvidere Pond

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Figure 5. Reconstructed longitudinal ice-surface profiles for proposed former glaciers in the White Mountains, New Hampshire (excluding Mount Moosilauke glaciers; see Fig. 7). The reconstructions are based on the shear-stress equation r = pgh sin a. Valley cross sections are shown as if looking up the valley. Dashed lines indicate ice thicknesses estimated by Goldthwait (see Fig. 4). Table 1 gives a summary of reconstructed glacier characteristics.

and in its drainage to the west and at a locality The reconstructed glacier profiles for all of the due to the very low valley gradients in these on the West Branch of the Waterbury River Vermont localities (Fig. 8) are rather unusual by valleys, generally less than 2.5° (compare with (Wagner, 1970). There may be evidence for comparison with typical mountain glacier pro- gradients in Presidential Range valleys of 7° to local glaciation in other Vermont valleys (north- files. Ice thicknesses are unusually large (225 to 14°). Importantly, the maximum ice thicknesses ern Vermont, Wagner, 1971, and Connally, 350 m) for glaciers of this length (1 to 6 km), in the reconstructed Vermont glaciers typically 1972; southern Vermont, Hubbard, 1917, and and the profiles are characteristic of the terminal exceed the depths of their respective valleys. The Goldthwait, 1970), but these localities are not regions of "intermediate-type" or "outlet-type" profiles in all of the reconstructed glaciers pro- well documented in the literature and are not glaciers (see Porter and others, 1983). These ject over their respective cols when traced up considered herein. characteristics of the reconstructed profiles are valley to the crest of the Green Mountains.

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TABLE 4. A COMPARISON OF ICE THICKNESSES IN PRESIDENTIAL RANGE BASINS, AT THE LOCATIONS small (gradients in the Blue Ridge and Styles OF VALLEY CROSS SECTIONS INDICATED IN FIGURES 4 AND 5 Brook valleys are 1.3° and 2.5°, respectively).

Numerical Goldthwait's Thickness Mean Area Also, the predicted maximum ice thicknesses at thickness (m) thickness (m) difference difference (km2) Lost Pond and Moss Pond (90 and 59 m, respectively) are greater than the depths of these small Great Gulf, upper 110 150 40 35 87 Great Gulf, lower 150 180 30 basins. King Ravine 120 160 40 40 21 Tuckerman R., upper 70 80 10 13 46 The diversity of results obtained for recon- Tuckerman R., lower 80 90 10 Huntington Ravine 100 120 20 structed Adirondack mountain glaciers suggests Castle Ravine 80 70 -10 -10 -14 a re-evaluation of concepts of local glaciation in Madison Gulf 110 80 -30 -30 6.3 Bumpus Basin 100 40 -60 -60 4.6 this area. Some of the proposed localities show topography and reconstructed ice-surface pro- Note-, numerical thickness is by analysis (this paper). Goldthwait's thickness is as estimated from Goldthwait ( 1970). Area of the former glacier is from Figure 4. Mean difference is plotted against glacier area in Figure 6. files characteristic of local glaciers, particularly in the higher and steeper valleys, such as at White Brook and on Whiteface and Redfield Mountains. Very small, shallow basins, such as It is possible that the moraines in Vermont A possible analogue for continental ice flow- at Lost Pond and Moss Pond, and very large, valleys are deposits of continental, rather than ing across passes in the Green Mountains, al- valley bottom systems, such as at Blue Ridge, local, ice (for example, Stewart, 1971; Waitt though on a slightly larger scale, occurs in the however, are probably not favorable sites, topo- and Davis, 1988). In particular, the Miller Grayling Brook valley, western Yellowstone graphically, for local glaciers because these val- Brook, Ritterbush, and West Branch valleys Park, Wyoming (Fig. 8). Moraines in the lower leys are not sufficiently deep, and lack sufficient occur down valley from relatively low-elevation Grayling Brook valley formed at the margin of gradient, to sustain active local ice flow. At the cols in the crest of the range and may represent Pinedale ice when the valley ice was about 450 Blue Ridge locality, moraines might have been sites where late-stage Laurentide ice was flowing m thick (Pierce, 1979). Stagnation of the Gray- deposited by tongues of continental ice, flowing southeastward across and through gaps in the ling Brook lobe apparently occurred when ice south through passes at the head of Keene Val- Green Mountain crest (Stewart and MacClin- on the up-valley threshold had thinned to about ley and terminating at Blue Ridge. These obser- tock, 1969). Nebraska Notch and Smugglers 200 m (Pierce, 1979). By analogy, the moraines vations, if correct, indicate that active continen- Notch, up valley from the Miller Brook and in Vermont valleys may have been deposited tal ice remained in the Adirondack valleys West Branch moraine localities, respectively, are when predicted ice thicknesses on up-valley during déglaciation of the high peaks region. In- the lowest points in the range between the thresholds were about 50 to 150 m. dividual peaks may have been nunataks in this Winooski River to the south and the Lamoille late-stage flow, but the massif as a whole may not have been ice-free in the sense of Fairchild River to the north. The col above the Ritterbush Adirondack Mountains valley is the lowest pass through the Green (1913) or Coates and Kirkland (1974). Mountains from the Lamoille River north to the Numerous cirques in the Adirondack Moun- Canadian border. All of the proposed valley tains provide evidence for the former existence Catskill Mountains glacier locations in Vermont are at very low of local glaciers (Kemp, 1898; Ailing, 1918, elevations (schrund elevations: 290 to 345 m) 1920). In some of the cirques, moraines, till Cirques and end moraines provide evidence compared to glacier locations in other areas fabrics, and striation directions are cited as evi- for post-Laurentide local glaciation in the Cats- (schrund elevations mostly above 500 m). dence that local glaciation postdates the retreat kill Mountains, New York (for example, Rich, of continental ice (Johnson, 1917; Ailing, 1918; 1906, 1935; Johnson, 1917; Cadwell, 1986). Craft, 1970, 1979). Proposed localities of late The most compelling evidence for local glaciers Pleistocene local ice include the White Brook is arcuate end moraines in the north-facing val- 60 • King Ravine Great Gulf basin on Esther Mountain, the Roaring Brook leys of Johnson Brook (Fly Brook of Rich, E 40 • H • basin on Giant Mountain, an east-facing cirque 1935; Schoendorf cirque in Cadwell, 1986) and m o 20 - c Tuckerman/ on Whiteface Mountain, a south-facing cirque Little West Kill, although Rich (1935) identified o • o- Huntington R. on Mount Redfield, a northwest-facing cirque numerous other localities. •P ® Castle Ravine XI -?o • on Boreas Mountain, small basins at Lost Pond Figure 10 shows reconstructed glacier profiles in HI Madison Gulf (Weston Mountain) and Moss Pond (Mount for ten localities which offer particularly strong ¡c8 -40 • X Redfield), the Styles Brook basin, and the mo- evidence (according to Rich, 1935) for local o -KU • Bumpus Basin •C raine complex at Blue Ridge (Craft, 1979). glaciation (terminal moraine positions also after -80 Many reconstructed Adirondack glaciers Rich, 1935). Two ice surface profiles are shown 20 40 60 80 100 glacier area (sq. km) (Fig. 9) show profiles characteristic of local for the Johnson Hollow and West Kill valleys, mountain glaciers, with predicted thicknesses of representing successive ice margin positions of Figure 6. The thickness difference, be- 60 to 95 m and mean valley slopes of 8° to 12° Rich (1935), although recent studies in Johnson tween the estimates of Goldthwait (1970) and (White Brook, Roaring Brook, Whiteface Hollow confirm only the uppermost moraines as results of the numerical analysis, plotted Mountain, Boreas Mountain, Mount Redfield). deposits of local ice origin. "Slab-type" glacier against area of the former glacier (data in A number of reconstructed glaciers, however, profiles with thicknesses on the order of 60 to Table 4). A positive correlation (Spearman show rather atypical mountain glacier profiles. 140 m occur in valleys with gradients from 4.5° rank correlation coefficient = 0.77; significant At the Blue Ridge and Styles Brook localities, to 9.8°; they are neither as long nor as steep as at p = 0.06) suggests that either Goldthwait's the ice surfaces project over their up-valley cols the Presidential Range glaciers, and their slab- thickness estimates are biased by the size of (Elk Pass and Madden Brook Pass, respec- like form is more poorly developed. Reconstruc- the basin or the numerical reconstructions are tively), and ice thicknesses exceed the depths of tions of "intermediate-type" glacier profiles in not accounting for some factor related to these basins. The situation is similar to that ob- the Johnson Hollow, West Kill, and Little West glacier size. served in Vermont, where valley gradients are Kill valleys show ice thicknesses between 195

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MT. MOOSILAUKE

1500 -, 1500

C -S 1000 .S 1000 >(0 1>3 a> Jobildunc Ravine 0) Benton Brook

500 500 2000 4000 2000 4000

WEST-CENTRAL MAINE

MT. KATAHDIN

1500 1500 -,

C 0 c 1000 ê 1000 _g1> >(0

Figure 7. Reconstructed longitudinal ice- surface profiles for proposed former glaciers on Mount Moosilauke, New Hampshire, and on Crocker Mountain and Mount Katahdin, Maine. See text and Table 1 for additional information.

and 320 m that occur in valleys with mean gra- records show that déglaciation occurred slowly where the contribution of each depends upon dients of 1.3° to 2.6°. These reconstructed glaci- in the south and was followed by about 2,000 yr the nature of the problem or the question at ers approximately fill their valleys, although of tundra-type vegetation as compared to dura- hand. At one end of the spectrum, well- their profiles terminate up slope on valley walls tions of only about 600 yr in the northern constrained empirical data on a glacier system rather than projecting over ridge crests and cols Hudson-Champlain valleys (Connally and Sir- may be used as a guide to developing and refin- as observed in the reconstructed Vermont kin, 1973; also see Davis and Jacobson, 1985). ing theoretical ice-surface models. Empirical ob- glaciers. servations offer constraints on the parameters of An important factor favoring the occurrence DISCUSSION a flow model, thereby providing information on of local glaciers in the Catskill Mountains is the the physics and rheology of glacier flow. At the evidence for a prolonged duration of peri-glacial Methods for reconstructing glacier systems other end of the spectrum, where observational climates in southern New England and New involve a combination of empirical and theoret- data on a glacier system are weak or equivocal, York during Laurentide déglaciation. Pollen ical approaches (for example, Pierce, 1979), one may apply the theoretical principles of gla-

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1000 1000

I 500 I 500 m >(0 > JJ> ® œ West Branch, Waterbury R. Ritterbush Valley X 1 -i—i 4000 8000 m 1000 2000

cier rheology to develop a better understanding Figure 8. Reconstruct- of a glacier's morphology. This approach, used ed longitudinal ice-surface in this study of glacier systems in the northeast- profiles for proposed 3000 ern United States, helps to clarify and resolve former glaciers in the questions about a region's glacial history. Green Mountains, Ver- Numerical reconstructions of valley glaciers mont. See text and Table 2500 are generally based on a simple application of >(T I 1 for additional informa- the shear-stress equation, which relates ice

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1500 -,

1500

••£ 1000 È Moss Pond x 1 5 ® a> 1000 Weston Mountain 1000 m

500 1000 2000 m

Figure 9. Reconstructed longitudinal ice-surface profiles for proposed former glaciers in the Adirondack Mountains, New York. See text and Table 1 for additional information.

1962). The small vertical extent of the recon- northeastern United States, using the shear-stress surface profiles in Green Mountain localities, and structed Catskill glaciers suggests that accumula- equation to determine ice thickness and surface at localities in the Adirondack Mountains, where tion and ablation were perhaps controlled by slope. Comparisons of reconstructed glaciers in estimated ice thicknesses exceed the depth of seasonal, rather than altitude-dependent, temper- the Presidential Range of New Hampshire with their respective valleys. The reconstructed pro- ature fluctuations. the empirical reconstructions of Goldthwait files in these locations suggest a continental, (1970) indicate that reasonable reconstructions rather than local, source of ice for moraines and CONCLUSIONS may be obtained using a basal shear-stress value associated deposits. The profiles constructed for of T = 100 kPa (1 bar) and a shape factor of F = Mount Katahdin are for small glaciers that per- Longitudinal ice-surface profiles were con- 0.6 to 0.85. Probably the most interesting results haps occupied, but did not form, these cirques, structed for former proposed local glaciers in the of the analysis are for the reconstructed ice- and the reconstructed Catskill Mountain glaciers

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1000-, 1000 c o (5 > 500 •B 500 Irish Mtn, WNW cirque >(0 ® o 1000 2000 3000 m (!) Balsam Mtn, NW cirque

1000 2000 Too o m

Figure 10. Reconstructed longitudinal ice-surface profiles for proposed former glaciers in the Catskill Mountains, New York. See text and Table 1 for additional information.

are relatively short and confined as compared to system. Glacier reconstructions could become ACKNOWLEDGMENTS reconstructed glaciers in other areas. The re- more sophisticated, incorporating lateral com- gional scope of the present analysis provides a ponents of flow, more-complex flow laws, mass- I wish to thank A. Bloom, R. Mellors, and comparative basis for studying phenomena of balance equations, and corrections for diverging, P. Flemings, of Cornell University, and T. Lowell local glaciation in the northeast United States, converging, accelerating, and decelerating flow of the University of Cincinnati, for helpful but it largely ignores local details of a glacier conditions. comments on the manuscript.

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Fowler, B. K., 1984, Evidence for Late Wisconsinan cirque glacier in King APPENDIX 1. ANALYTICAL SOLUTION APPENDIX 2. NUMERICAL METHODS Ravine, northern Presidential Range, New Hampshire, U.S.A.— FOR THE ICE-Sl/RFACE PROFILE FOR RECONSTRUCTING ICE- Alternative interpretations: Arctic and Alpine Research, v. 16, OF A GLACIER ON A BED SURFACE PROFILES p. 431-437. Gerath, R. F., and Fowler, B. F., 1982, Discussion of "Late Wisconsinan OF CONSTANT SLOPE mountain glaciation in the northern Presidential Range, New Hamp- A numerical method for reconstructing the surface shire": Arctic and Alpine Research, v. 14, p. 369-370. profiles of valley glaciers is given in the program Gilbert, G. K., 1904, Systematic asymmetry of crest lines in the High Sierra: The differential equation for an ice surface profile VALLEY of Schilling and Hollin (1981). This analysis Journal of Geology, v. 12, p. 579-588. (after Nye, 1952c) is Glen, J. W., 1952, Experiments on the deformation of ice: Journal of Glaciol- uses essentially the same algorithm, but with the fol- ogy, v. 2, p. 111-114. lowing minor differences. Schilling and Hollin approx- Goldthwait, J. W., 1913, Glacial cirques near Mt. Washington: American imate sin a (of eq. 1) by Ah/Ax, where Ah is the Journal of Science, 4th Series, v. 35, p. 1-19. h dH = h0 ds, (Al) 1916, Glaciation in the White Mountains of New Hampshire: Geologi- change in ice surface elevation over the horizontal cal Society of America Bulletin, v. 27, p. 263-294. distance Ax, measured parallel to the Earth's surface, Goldthwait, R. P., 1970, Mountain glaciers of the Presidential Range in New where dH is the change in elevation of the ice surface Hampshire: Arctic and Alpine Research, v. 2, p. 85-102. whereas I use the approximation Ah/As, where As is Graf, W. L., 1970, The geomorphology of the glacial valley cross section: in a distance ds (see text, eq. 4). Part of the change in measured along the ice surface. Schilling and Hollin Arctic and Alpine Research, v. 2, p. 85-102. elevation is due to change in ice thickness dh, and part compute ice thickness in a vertical direction. My algo- 1976, Cirques as glacier locations: Arctic and Alpine Research, v. 8, is due to change in elevation of the bed, given approx- p. 79-80. rithm determines ice thickness as the distance between Haselton, G. M., 1975, Glacial geology in the Mount Moosilauke area, New imately by p ds, where p is the bed slope, so that the point on the ice surface and the nearest point on Hampshire: Appalachia, v. 40, p. 44-57. the bed surface (the bed surface is defined by an array Hubbard, G. D., 1917, Possible local glaciation in southern Vermont [abs.]: Association of American Geographers Annals, v. 7, p. 77. dH = dh + P ds, (A2) of points consisting of 10 interpolated values between Hughes, T. J., 1981, Numerical reconstruction of paleo-ice sheets, in Denton, each contour line). My algorithm specifies a small, G. H., and Hughes, T. J., eds., The last great ice sheets: New York, Wiley, Chapter 5, p. 221-261. initial ice thickness at the position of the glacier termi- Johnson, D. W., 1917, Date oflocal glaciation in the White, Adirondack, and giving, by substitution into equation Al, w nus, equal to the value of (2h0) (= 4.76 m for F = 1), Catskill Mountains: Geological Society of America Bulletin, v. 28, which is equivalent to the thickness of a glacier on a p. 543-552. 1933, Date of local glaciation in the White Mountains: American Jour- h (dh + p ds) = ho ds, (A3) flat bed at a distance of 1 m from the glacier terminus. nal of Science, v. 25, p. 49-67. The program uses a step length As of 10 to 50 m, Kanasewich, E. R., 1963, Gravity measurements on the Athabasca Glacier, depending on the length of the glacier. Alberta, Canada: Journal of Glaciology, v. 4, p. 617-631. or, by rearranging, Kemp, J. F., 1898, Geology of the Lake Placid region: New York State Mu- seum Bulletin, no. 21, p. 49-67. Mathews, W. H., 1967, Profiles of Late Pleistocene glaciers in New Zealand: New Zealand Journal of Geology and Geophysics, v. 10, p. 146-163. ds = (h dh)/(ho - p h). (A4) Nye, J. F., 1952a, The mechanics of glacier flow: Journal of Glaciology, v. 2, REFERENCES CITED p. 82-93. 1952b, A comparison between the theoretical and measured long pro- Ailing, H. L., 1918, Pleistocene geology of the Lake Placid quadrangle: New file of the Unteraar glacier: Journal of Glaciology, v. 2, p. 103-107. Integration of equation 4A gives York State Museum Bulletin, no. 211-212, p. 71-95. 1952c, A method of calculating the thicknesses of the ice-sheets: Nature, 1920, Glacial geology of the Mount Marcy quadrangle, Essex County, v. 169, p. 529-530. New York: New York State Museum Bulletin, no. 229-230, p. 62-84. 2 1965, The flow of a glacier in a channel of rectangular, elliptic or s = -(h/y3) - (h //3 ) ln(ho - p h) + C, (A5) Antevs, E., 1932, Alpine zone of Mt. Washington range: Auburn, Maine, 0 parabolic cross-section: Journal of Glaciology, v. 5, p. 661-690. Merrill and Webber, ] 18 p. Paterson, W.S.B., 1981, The physics of glaciers: Oxford, Pergamon, 380 p. Bradley, D. C., 1981, Late Wisconsinan mountain glaciation in the northern Pierce, K. W., 1979, History and dynamics of glaciation in the northern Yel- Presidential Range, New Hampshire: Arctic and Alpine Research, v. 13, where the integration constant C is found by setting h lowstone National Park area: U.S, Geological Survey Professional p. 319-327. Paper 729-F, 90 p. = 0 at s = 0, so that 1982, Reply to discussion of "Late Wisconsinan mountain glaciation in Porter, S. C., Pierce, K. L., and Hamilton, T. D., 1983, Late Wisconsin moun- the northern Presidential Range, New Hampshire": Arctic and Alpine tain glaciation in the western United States, in Porter, S. C., ed., Late Research, v. 14, p. 370-371. Quaternary environments of the United States, Volume 1, The late 2 Cadwell, D. H., 1986, Late Wisconsinan stratigraphy of the Catskill Moun- C = (h0//3 ) ln(ho), (A6) Pleistocene: Minneapolis, Minnesota, University of Minnesota Press, tains: New York State Museum Bulletin, no. 455, p. 73-88. p. 71-111. Caldwell, D. W., 1966, Pleistocene geology of Mt. Katahdin, in Caldwell, Rich, J. L., 1906, Local glaciation in the Catskill Mountains: Journal of Geol- D. W., ed., New England Intercollegiate Geological Conference, guide- or ogy, v. 14, p. 113-121. book (1966): p. 51-61. 1935, Glacial geology of the Catskiils: New York State Museum Bul- Caldwell, D. W., and Hanson, L. S., 1986, The nunatak stage of Mt. Katahdin, letin, no. 209, 180 p. northern Maine, persisted through the Late Wisconsin: Geological So- 2 Schilling, D. H., and Hollin, J. T., 1981, Numerical reconstructions of valley s = (V0 ) WOK) " fi h)] ciety of America Abstracts with Programs, v. 18, p. 8. glaciers and small ice caps, in Denton, G. H., and Hughes, T. J., eds.. Coates, D. R., and Kirkland, J. T., 1974, Applications of glacial models for The last great ice sheets: New York, Wiley, Chapter 4, p. 207-220. large scale terrain derangements, in Mahaney, D. C., ed., Quaternary Stewart, D. P., 1971, Pleistocene mountain glaciation, northern Vermont: Dis- - h/ft (A7) environments: Proceedings of a symposium: Geographical Monographs, cussion: Geological Society of America Bulletin, v. 82, p. 1759-1760. no. 5, p. 99-136. Stewart, D. P., and MacClintock, P., 1969, The surficial geology and Pleisto- Connally, G. G., 1972, Proglacial lakes in the Lamoille Valley, Vermont, in cene history of Vermont: Vermont Geological Survey Bulletin, no. 31, which is the expression given by Mathews (1967) and Doolan, B. L., and Stanley, R. S., eds., New England Intercollegiate 251 p. Geological Conference, guidebook (1972): Burlington, Vermont, Schilling and Hollin (1981). By setting the value of h Tarr, R. S., 1900, Glaciation of Mount Katahdin, Maine: Geological Society of p. 343-358. America Bulletin, v. 11, p. 433-448. at some proportion of the slab thickness (from eq. 3 in Connally, G. G., and Sirkin, L. A., 1973, Wisconsinan history of the Hudson- Thompson, W. F., 1961, The shape of New England mountains, Part III: text), Champlain lobe: Geological Society of America Memoir 136, p. 47-69. Appalachia, v. 27, p. 458-478. Craft, J. L., 1970, Late Pleistocene local glaciation and glacial climate in the Trenhaile, A. S., 1976, Cirque morphometry in the Canadian Cordillera: Asso- high peaks region, Adirondack Park, N.Y. [abs.]: American Quaternary ciation of American Geographers Annals, v. 66, p. 451-462. Association, First Meeting, Bozeman, Montana, p. 23. h = f ho/a, (A8) Wagner, W. P., 1970, Pleistocene mountain glaciation, northern Vermont: 1979, Evidence oflocal glaciation, Adirondack Mountains, New York: Geological Society of America Bulletin, v. 81, p. 2465-2470. Eastern Friends of the Pleistocene, Annual Reunion, 42nd, Proceedings, 1971, Pleistocene mountain glaciation, northern Vermont: Reply: Geo- 75 p. logical Society of America Bulletin, v. 82, p. 1761-1762. where a - sin a, and assuming that the ice sur- Davis, P. T., 1976, Quaternary glacial history of Mt. Katahdin, Maine [M.S. Waitt, R. B., and Davis, P. T., 1988, No evidence for post-icesheet cirque thesis]: Orono, Maine, University of Maine, 115 p. face is approximately parallel to the ground sur- glaciation in New England: American Journal of Science, v. 288, Davis, P. T., and Waitt, R. B., 1986, Cirques in the Presidential Range revisited: face for values of f close to 1 (a ~ fi), we derive p. 495-533. No evidence for post-Laurentide mountain giaciation: Geological So- Weertman, J., 1957, On the sliding of glaciers: Journal of Glaciology, v. 3, ciety of America Abstracts with Programs, v. 18, p. 11. p. 33-38. Davis, R. B., and Jacobson, G. L., Jr., 1985, Late glacial and early Holocene 2 1964, The theory of glacier sliding: Journal of Glaciology, v. 5, sf = (ho/>3 ) {ln[l/(l - f)] - f}, (A9) landscapes in northern New England and adjacent areas of Canada: p.287-303. Quaternary Research, v. 23, p. 341-368. Dort, W., Jr., 1962, Stage of cirque development a major determinant of which is the equation in the caption of Figure 3. When distance of glacial advance [abs.]: Geological Society of America Special Paper 68, p. 165-166. MANUSCRIPT RECEIVED BY THE SOCIETY JUNE 29,1987 f < 1 (near terminus), a > /3, and sf is smaller than the Fairchild, H. L., 1913, Pleistocene geology of New York State: Geological REVISED MANUSCRIPT RECEIVED APRIL 11,1988 value predicted by equation A9. Society of America Bulletin, v. 24, p. 133-162. MANUSCRIPT ACCEPTED APRIL 22,1988

Primed in U.S.A.

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