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 nu- merically 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 in- versely proportional to valley slope. Glacier reconstructions support the empir- ical 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 Downloaded from http://pubs.geoscienceworld.org/gsa/gsabulletin/article-pdf/101/4/561/3380637/i0016-7606-101-4-561.pdf by guest on 28 September 2021 562 S. C. ACKERLY 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.