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Uplift-based limits to the thickness of ice in the Lake Agassiz basin of North Dakota during the Late Wisconsinan
Geomorphology 32 Ž2000. 161–169
Uplift-based limits to the thickness of ice in the Lake Agassiz basin of North Dakota during the Late Wisconsinan Eric C. Brevik a,) , John R. Reid b,1 b
a Soil Morphology and Genesis, Agronomy Department, Iowa State UniÕersity, Ames, IA 50011, USA Department of Geology and Geological Engineering, UniÕersity of North Dakota, Grand Forks, ND 58202, USA
Received 6 November 1998; received in revised form 17 July 1999; accepted 17 August 1999
Abstract Upper and lower limits to ice thickness in the southern Lake Agassiz basin Žnortheast North Dakota. during the Late Wisconsinan have been calculated. The oldest well-preserved tilted strandline of glacial Lake Agassiz, the Herman, was used to determine how much the basin was depressed by the ice sheet and, from that, how much ice was necessary to cause the given depression. Based upon the difference in elevation between the southernmost part of the strandline near Dumont, MN, and where it crosses the US–Canadian border, the absolute minimum rebound Žand thus, earlier depression. in the southern Lake Agassiz basin is 54.5 m. The rebound that occurred over the 300 years between deglaciation and the Herman level of Lake Agassiz was added, yielding a total initial depression of 70 m. The added effects of about 46 m of accumulated lake sediments has caused an unrecovered crustal depression of approximately 23 m. Total minimum depression, therefore, was about 93 m. Assuming that up to 73% of rebound was ‘‘restrained’’, the initial depression may have been as much as 340 m. These values Ž93 to 340 m. were used to calculate minimum and maximum ice thicknesses in the basin of 250 to 920 m, respectively. These thicknesses correspond to basal shear stress values of 0.32 to 4.4 kPa, respectively. q 2000 Elsevier Science B.V. All rights reserved. Keywords: Laurentide ice sheet; ice thickness; Lake Agassiz
1. Introduction Ice near the margins of the Laurentide Ice Sheet during the Late Wisconsinan was initially thought to be considerably thicker than is now believed. For
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Corresponding author. Fax: q1-515-294-3517. E-mail addresses: [email protected] ŽE.C. Brevik., [email protected] ŽJ.R. Reid.. 1 Fax: q1-701-777-4449.
example, Sugden Ž1977. depicted ice thickness in eastern North Dakota at about 2250 m. But other studies by Mathews Ž1974., Beget Ž1986., Clark Ž1992., Clark et al. Ž1994. and Peltier Ž1994. interpreted ice thicknesses of only about 700 m or less along the southern margins of that ice sheet. The marginal ice was concluded to have been thin because of the soft, deformable sediments and poorly consolidated rocks over which the Laurentide Ice Sheet flowed ŽBoulton and Jones, 1979; Clark, 1992, 1994; Hicock and Dreimanis, 1992..
0169-555Xr00r$ - see front matter q 2000 Elsevier Science B.V. All rights reserved. PII: S 0 1 6 9 - 5 5 5 X Ž 9 9 . 0 0 0 9 3 - 8
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E.C. BreÕik, J.R. Reid r Geomorphology 32 (2000) 161–169
The problem with the thin ice interpretation is that it cannot be tested by comparison with any modern ice sheets on the scale of the Laurentide Ice Sheet. Several lines of evidence, however, have been offered to support the thin ice over a deforming-bed model. This includes rapid melting along ice margins at the end of the Wisconsinan ŽBryson et al., 1969;
Andrews, 1973; Dyke and Prest, 1987., rapid fluctuations along ice margins that were over deformable sediments ŽJohnson and Hansel, 1990; Clark, 1994., the lobate form of parts of the ice sheet that rested on deformable sediments ŽClark, 1994., reported deformation features and fabrics preserved in some tills ŽHicock and Dreimanis, 1992., study of longitudinal
Fig. 1. The maximum extent of Glacial Lake Agassiz, and its location in North America. The extent of Lake Agassiz is modified from Teller Ž1994..
E.C. BreÕik, J.R. Reid r Geomorphology 32 (2000) 161–169
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Lake Agassiz, provide additional indirect evidence for the theory of thin ice.
2. Lake Agassiz strandlines Glacial Lake Agassiz began to form against the retreating margin of the Laurentide Ice Sheet approximately 11,700 C 14 years B.P. ŽFig. 3. ŽFenton et al., 1983; Teller, 1990; Thorleifson, 1996.. By approximately 11,200 C 14 years B.P. the edge of the ice had retreated to the present-day border between the United States and Canada ŽFig. 3. ŽFenton et al., 1983.. As the lake level fluctuated in response to changes in ice margin position, downcutting at the outlets, and rebound, numerous strandlines were
Fig. 2. The study area and its position within the Lake Agassiz basin. The southern Lake Agassiz basin is the area within the Herman strandline in the exploded view. The extent of Lake Agassiz is modified from Teller Ž1994.. The position of the Herman strandline is from Johnston Ž1946..
shear ridges ŽBluemle et al., 1993., and computer models of sub-glacial sediment transport ŽAlley, 1991.. A large lake basin exists today along what was once the southern margin of the Laurentide Ice Sheet. This basin once contained glacial Lake Agassiz ŽFigs. 1 and 2.. Tilted strandlines of glacial lakes, such as
Fig. 3. The ice edge in the southern Lake Agassiz basin about 11,700 and 11,200 C 14 years B.P., as marked, and the southwestern edge of the Canadian Shield in the study area. Lake Agassiz was beginning to form approximately within the Herman strandline south of each respective ice edge. Older strandlines above the Herman strandline that mark the earlier positions of Lake Agassiz are poorly formed and difficult to trace ŽBluemle, 1991.. Position of the ice edges is from Fenton et al. Ž1983.; position of the Herman strandline is from Johnston Ž1946.; position of the shield edge is from Espenshade Ž1990..
E.C. BreÕik, J.R. Reid r Geomorphology 32 (2000) 161–169
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formed along the shores. Many of these strandlines are still well preserved, including the Herman strandline, dated at about 10,900 C 14 years B.P. ŽFenton et al., 1983; Thorleifson, 1996.. These strandlines are tilted; they rise to the north as a result of differential isostatic rebound, with older strandlines showing greater tilt ŽJohnston, 1946.. Hence, the minimum ice thickness required to cause the original depression, indicated by the amount of tilt of the oldest strandlines, can be calculated. For this reason the oldest distinct strandline of Lake Agassiz, the Herman strandline, was used for this study. The North Dakota Geological Survey ŽNDGS. has mapped the Herman strandline throughout eastern North Dakota. Appropriate NDGS County studies were used to locate the Herman strandline in a number of places. The Herman strandline was then located on the appropriate United States Geological Survey ŽUSGS. 7.5 min topographic maps with a 1.52-m Ž5 ft. contour interval. Elevations at selected points along the strandline were then determined from the USGS maps ŽFig. 2, Table 1.. Because the original strandline was probably discontinuous and irregular, and because subsequent modification has probably occurred through differential erosion and disruption by humans, for example, elevations were taken at intersections of a 5 mm by 30 mm overlay grid divided into 5 mm segments Ž120 m ground distance. to reduce bias. The grid was centered over the strandline at each location where elevation was measured. Eighty-four data points were compiled at six locations on the strandline ŽBrevik, 1994.. The
Table 1 Location of the points where the elevation of the Herman strandline was measured Site a Location
USGS 7.5 min quadrangleb
1 2 3 4 5 6
Vang, ND Edinburg, ND Inkster, ND Ayr NW, ND Embden, ND La Mars, ND–SD
Sec. 32, T164N, R57W Sec. 26, T158N, R56W Sec. 16, T154N, R55W Sec. 7, T143N, R53W Sec. 3, T138N, R54W Sec. 32 and 33, T129N, R48W a
See Fig. 2 for relative location of sites. The name of the USGS 7.5 min quadrangle on which the given site is located. b
Herman strandline is lowest at its southernmost extremity near Dumont, MN, at 325.3 m above sealevel ŽJohnston, 1946.. Its highest point in North Dakota, at the International Border near Walhalla, is 379.8 m above sealevel. This gives a minimum differential rebound Žand therefore original depression. of 54.5 m for the southern Lake Agassiz basin.
3. Age correction The ice margin was at the International Border about 11,200 years B.P. while the Herman strandline is dated at about 10,900 years B.P. Some post-glacial rebound must have occurred during this 300-year interval. Therefore, the differential rebound Žand thus, depression. indicated by the Herman strandline does not represent absolute post-deglaciation rebound in the Lake Agassiz basin. The amount of rebound that occurred before the formation of the Herman can be calculated, however. The amount of isostatic rebound that has occurred as a function of time is given by: F Ž k ,t . s F0 Ž k . eyt a Ž k .r Tr ,
Ž 1.
where F Ž k,t . is the amount of depression as a function of k Žthe wavenumber. at time t; F0 Ž k . is the initial amount of depression resulting from a harmonic ice load; e is the base for the natural logarithm Žwhich has the value 2.71828.; t is the amount of elapsed time since rebound began; a is the ‘‘lithospheric filter’’; and Tr is the asthenosphere relaxation time ŽFjeldskaar, 1997.. For the Lake Agassiz basin a s 205 km ŽWalcott, 1970a.. Total elapsed time at the International Border is 11,200 C 14 years ŽFenton et al., 1983.. The asthenosphere relaxation time is given by: Tr s Ž 4p Õ . r Ž ra gl . ,
Ž 2.
where p is 3.14, Õ is asthenosphere viscosity, ra is asthenosphere density, g is gravitational acceleration, and l is the ‘‘wavelength’’ of the ice sheet ŽTurcotte and Schubert, 1982.. Asthenosphere density is 3300 kgrm3 ŽBraile, 1989; Fjeldskaar, 1997.. Asthenosphere viscosity beneath the Lake Agassiz basin has been calculated to be 10 22 Pa s ŽWalcott,
E.C. BreÕik, J.R. Reid r Geomorphology 32 (2000) 161–169
1970a.. This value of asthenosphere viscosity is consistent with most recently published values, which tend to fall between 10 20 and 10 22 Pa s ŽPeltier, 1981, 1996; Hager, 1990; Mitrovica and Peltier, 1991; Nakada and Lambeck, 1991; Jaupart et al., 1998.. In addition, Nakada and Lambeck Ž1991. have concluded that the highest values of asthenosphere viscosity occur beneath the Canadian Shield. The portion of the Lake Agassiz basin covered in this study is on the southwest margin of the Canadian Shield ŽFig. 3.. Therefore, we assumed that asthenosphere viscosity beneath the Lake Agassiz basin is 10 22 Pa s for the purposes of this study. Using Eqs. 1 and 2, it can be determined that an initial depression of 70 m at 11,200 years B.P. would have resulted in a continued depression of approximately 54.5 m at 10,900 years B.P., after 300 years of rebound.
4. Effect of water and sediments In addition to crustal depression caused by the ice, the subsequent inundation of the basin by water and sediments add to the complexity of calculating the thickness of the ice based on strandline rebound. The depression caused by lake sediments can be determined with a mass-balance relationship as follows ŽBrevik, 1994.: z s d s Ž Ž rayrs . rra .
Ž 3.
where d s is the sediment thickness in m; ra is asthenosphere density Ž3300 kgrm3, Braile, 1989; Fjeldskaar, 1997.; rs is the density of the sediment Žkgrm3 .; and z is the thickness of sediment above the original surface, in m. The amount of crustal depression Žm. caused by the sediments is designated ys , and can be found by subtracting z from d s after solving for z. Average density of the sediments in the Lake Agassiz basin is 1643 kgrm3. This is the moist average of 24 bulk density values for Lake Agassiz sediments tested in the Fargo and Grand Forks areas ŽJohnson, written communication, 6r1997.. The original bulk density values given were for dry bulk density, but percent moisture by weight was also
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given for each sample. Because the weight of the sediments causing depression in the field includes the weight of water, the weight of the moisture was added back into each bulk density value to obtain the moist sediment bulk density used in this study. The depth of sampling for these bulk density measurements ranged from 3 to 23 m. Lake Agassiz sediments eventually accumulated to an average thickness of about 46 m in the Grand Forks, ND, area ŽNordstog and Reid, 1984., which would have resulted in an equilibrium depression of about 23 m. The sediments have a maximum thickness of about 90 m in the center of the basin, along the Red River, and pinch out a few kilometers west of the Herman strandline. An average value for sediment thickness is used in this study because sediment thickness varies considerably in this part of the Lake Agassiz basin. Because the sediments are still present, they are still causing about 23 m of depression ŽFig. 4.. The water in Lake Agassiz reached an average depth of as much as 100 m in the southern Lake Agassiz basin ŽNordstog and Reid, 1984. and would have caused a depression of about 30 m. The depression can be calculated using Eq. 3 and substituting d w Ždepth of water. for d s , r w Ždensity of water, assumed as 1000 kgrm3 . for rs , and w Ždepth of water above the original surface. for z. This is only slightly more than the depression caused by the lake sediments. In addition, the water was present before the sediments and, in general, the water level dropped as the sediments accumulated, until the lake drained completely from the southern Lake Agassiz basin. The water would have slowed the rate of rebound following deglaciation, but it would not have prevented rebound. Because the lake no longer exists Ži.e., the water is no longer present., it is assumed that the water mass does not significantly affect the ice thickness calculation and can be ignored. The sediments are considered more important because they are still present and have prevented complete rebound. Absolute minimum depression, therefore, is represented by the minimum depression indicated by the Herman Ž70 m. plus the rebound that never took place Ž23 m., an amount equal to about 93 m. To estimate maximum depression, we assumed that 73% of rebound was ‘‘restrained’’ Ži.e., rebound that occurred while the ice sheet was thinning; An-
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Fig. 4. Steps in the depression and rebound of the Lake Agassiz basin. ŽA. Pre-glacial position of the land surface. ŽB. Ice advance caused depression of the crust. ŽC. The crust rebounded beneath Lake Agassiz as the ice mass thinned and the ice edge retreated to the north. At the same time, sediments accumulated. ŽD. The Lake Agassiz basin as it is today. The pre-glacial land surface is still depressed about 23 m below its original position because of the Lake Agassiz sediments present in the basin. But, the present land surface is about 23 m higher than the pre-glacial land surface was originally Žin step A. because of the accumulation of lake sediments that are less dense than the crust.
drews, 1970.. Although this percentage value was for arctic Canada, it does establish an effective upper limit to ice thickness. Because the ice melted from the Lake Agassiz basin more rapidly than from arctic Canada ŽBryson et al., 1969; Andrews, 1973; Dyke and Prest, 1987. less ‘‘restrained’’ rebound should have occurred in the Lake Agassiz basin. Any error introduced by assuming 73% ‘‘restrained’’ rebound, therefore, will lead to an overcalculation of ice thickness, thus forming an effective upper limit for ice thickness in the Lake Agassiz basin. With 73% ‘‘restrained’’ rebound, maximum depression in the
Lake Agassiz basin would have been approximately 340 m. 5. Ice thickness The same mass-balance principle that was used to calculate crustal depression from sediments can also be used to calculate ice thickness. When the amount of crustal depression is known, ice thickness can be found by solving for x: x y x Ž Ž ra y r i . rra . s y i Ž Ž rayr i . rra .
Ž 4.
E.C. BreÕik, J.R. Reid r Geomorphology 32 (2000) 161–169
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Fig. 5. Depression of the crust by ice, where y is the amount of depression, x is the amount of ice above the depression, and x q y is total ice thickness Žall in m..
where r i is the density of ice, x is the thickness of the ice above the original surface, and y i the depression below the original surface ŽBrevik, 1994; Fig. 5.. Total thickness of the ice is the sum of x plus y i . This assumes the ice was present long enough for the crust to reach static equilibrium. The 93 m of minimum rebound in the Lake Agassiz basin reflects a minimum ice thickness of about 250 m at the present International Border, assuming an ice density of 900 kgrm3 and an asthenosphere density of 3300 kgrm3. The maximum calculated depression of 340 m would reflect an ice thickness of approximately 920 m.
6. Discussion The limits on ice thickness, calculated using the Herman strandline, are valid only if post-glacial rebound in the Lake Agassiz Basin is complete. Using Eqs. 1 and 2, post-glacial rebound of a 93-m depression would take approximately 6700 years, and approximately 8400 years for a 340-m depression. We can, therefore, conclude that post-glacial rebound in the United States portion of the Lake Agassiz basin is complete. This conclusion is supported by free-air gravity anomalies on the Canadian Shield as mapped by Walcott Ž1970b.. The study reported here does not give an ice sheet profile. Rather, it gives limits to ice thickness at a single point, in this case, the point where the Herman strandline intersects the present day border between
the United States and Canada. Maximum and minimum profiles of the ice sheet could be constructed by determining the amount of rebound that has occurred at a number of points along a predicted flow line. That task, however, is beyond the scope of this paper. The mass-balance model ŽEq. 4., used to calculate ice thickness in this study, is admittedly a simple model. The primary factor controlling ice thickness in the marginal lobes of the Laurentide Ice Sheet was the shear stress of the basal sediments ŽMathews, 1974; Clayton et al., 1985; Beget, 1986; Clark, 1992, 1994.. Therefore, we calculated the basal shear stresses that are indicated by the limits of the thickness of the ice in this study and compared them to basal shear stresses calculated for this area by other workers as a check on our model. The limits to ice thickness in this study indicate basal shear stresses of 0.32–4.4 kPa for the Des Moines Lobe, using Eq. 3 from Beget Ž1986.. This compares favorably to the ranges calculated for the Des Moines lobe by Clark Ž1992. Ž0.7–4.3 kPa., Clayton et al. Ž1985. Ž0.5–5.0 kPa., and Mathews Ž1974. Ž0.7–2.2 kPa., respectively. The lower limit of basal shear stress in this study Ž0.32 kPa. is lower than the other values that have been reported, but that was expected. In reality, some rebound in the Lake Agassiz basin would have been ‘‘restrained’’, and that ‘‘restrained’’ rebound is not accounted for in the measurement of absolute minimum rebound. The lower limit to the thickness of ice in this study, however, is based on absolute minimum rebound in the Lake Agassiz basin. We
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can say with confidence the ice was no thinner than the thickness value calculated using absolute minimum rebound because that value does not account for ‘‘restrained’’ rebound. The 73% ‘‘restrained’’ rebound assumed for the Lake Agassiz basin should be an over-estimate, as discussed previously in this paper. Therefore, we believe this study provides reasonable upper and lower limits to ice thickness in the Lake Agassiz basin. These limits can provide a check for other ice thickness studies conducted in this area, as any ice thickness value should fall within these limits.
nold, Geophysicist, University of North Dakota, provided assistance with the asthenosphere viscosity portion of this research. Carolyn Eyles, McMaster University, Richard LeFever, University of North Dakota, and an anonymous reviewer provided helpful comments and critical reviews of the ideas in this paper. This research was conducted while the senior author was a student in the Department of Geology and Geological Engineering at the University of North Dakota.
References 7. Conclusion A lower limit to the thickness of ice in the Lake Agassiz Basin is relatively easy to determine; at a minimum, the ice had to have been thick enough to account for the 93 m of depression indicated by the Herman strandline and the Lake Agassiz sediments remaining in the basin. Maximum thickness of the ice, however, is another matter. That the ice was present in the Lake Agassiz basin long enough to reach equilibrium, and the maximum amount of ‘‘restrained’’ rebound was equal to or less than 73%, must be assumed. With these assumptions, maximum crustal depression was approximately 340 m. Corresponding minimum and maximum thicknesses of the ice were therefore 250 and 920 m, respectively. In reality, the thickness of the ice was most likely somewhere between these limits. For example, the thickness of the ice at the International Border was calculated at about 430 m using Mathews’ Ž1974. method ŽBrevik, 1994.. Regardless of the actual thickness of the ice, study of the Lake Agassiz strandlines establishes limits to the thickness of the ice in the Lake Agassiz basin and supports other recent studies that indicate relatively thin ice Žless than 1000 m thick. along the margins of the Laurentide Ice Sheet.
Acknowledgements Keith Johnson of Midwest Testing Laboratory in Fargo, ND, supplied data on density and water content of the Lake Agassiz sediments. William Gos-
Alley, R.B., 1991. Deforming-bed origin for Southern Laurentide Till Sheets? Journal of Glaciology 37 Ž125., 67–76. Andrews, J.T., 1970. A Geomorphological Study of Post-Glacial Uplift with Particular Reference to Arctic Canada, Institute of British Geographers, London. Andrews, J.T., 1973. The Wisconsin Laurentide Ice Sheet: dispersal centers, problems of rates of retreat, and climatic implications. Arctic and Alpine Research 5 Ž3., 185–199. Beget, J., 1986. Modeling the Influence of till rheology on the flow and profile of the Lake Michigan Lobe, Southern Laurentide Ice Sheet, USA. Journal of Glaciology 32 Ž111., 235–241. Bluemle, J.P., 1991. The Face of North Dakota, Revised Edition, North Dakota Geological Survey, Bismarck, ND. Bluemle, J.P., Lord, M., Hunke, N., 1993. Exceptionally long, narrow drumlins formed in subglacial cavities, North Dakota. Boreas 22, 15–24. Boulton, G.S., Jones, A.S., 1979. Stability of temperate ice caps and ice sheets resting on beds of deformable sediment. Journal of Glaciology 24 Ž90., 29–43. Braile, L.W., 1989. Crustal structure of the continental interior. In: Pakiser, L.C., Mooney, W.D. ŽEds.., Geophysical Framework of the Continental United States. Geological Society of America, Boulder, CO, pp. 285–315. Brevik, E.C., 1994. Isostatic rebound in the Lake Agassiz Basin since the Late Wisconsinan. MA Thesis, University of North Dakota, Grand Forks, ND. Bryson, R.A., Wendland, W.M., Ives, J.D., Andrews, J.T., 1969. Radiocarbon isochrones on the disintegration of the Laurentide Ice Sheet. Arctic and Alpine Research 1 Ž1., 1–14. Clark, J.A., Hendriks, M., Timmermans, T.J., Struck, C., Hilverda, K.J., 1994. Glacial isostatic deformation of the Great Lakes Region. Geological Society of America Bulletin 106, 19–31. Clark, P.U., 1992. Surface form of the Southern Laurentide Ice Sheet and its implications to ice-sheet dynamics. Geological Society of America Bulletin 104, 595–605. Clark, P.U., 1994. Unstable behavior of the Laurentide Ice Sheet over deforming sediment and its implications for climate change. Quaternary Research 41, 19–25.
E.C. BreÕik, J.R. Reid r Geomorphology 32 (2000) 161–169 Clayton, L., Teller, J.T., Attig, J.W., 1985. Surging of the southwestern part of the Laurentide Ice Sheet. Boreas 14, 235–241. Dyke, A.S., Prest, V.K., 1987. Late Wisconsinan and Holocene retreat of the Laurentide Ice Sheet. Geographie Physique et Quaternaire 41 Ž2., 237–263. Espenshade, E.B. ŽEd.., Goode’s World Atlas. 18th edn. Rand McNally, New York. Fjeldskaar, W., 1997. Flexural rigidity of Fennoscandia inferred from the postglacial uplift. Tectonics 16 Ž4., 596–608. Fenton, M.M., Moran, S.R., Teller, J.T., Clayton, L., 1983. Quaternary stratigraphy and history in the southern part of the Lake Agassiz Basin. In: Teller, J.T., Clayton, L. ŽEds.., Glacial Lake Agassiz. Geological Association of Canada, Waterloo, Ontario, pp. 49–74. Hager, B.H., 1990. The viscosity profile of the mantle: a comparison of models on postglacial and convection time scales. EOS, Transactions of the American Geophysical Union 71 Ž43., 1567. Hicock, S.R., Dreimanis, A., 1992. Deformation till in the Great Lakes Region: implications for rapid flow along the southcentral margin of the Laurentide Ice Sheet. Canadian Journal of Earth Science 29, 1565–1579. Jaupart, C., Mareschal, J.C., Guillou-Frottier, L., Davaille, A., 1998. Heat flow and thickness of the lithosphere in the Canadian Shield. Journal of Geophysical Research 103 ŽB7., 15269–15286. Johnson, W.H., Hansel, A.K., 1990. Multiple Wisconsinan glacigenic sequences at Wedron, Illinois. Journal of Sedimentary Petrology 60 Ž1., 26–41. Johnston, W.A., 1946. Glacial Lake Agassiz, with Special Reference to the Mode of Deformation of the Beaches. Geological Survey of Canada, Ottawa. Mathews, W.H., 1974. Surface profiles of the Laurentide Ice Sheet in its marginal areas. Journal of Glaciology 13 Ž7., 37–43. Mitrovica, J.X., Peltier, W.R., 1991. Radial resolution in the inference of mantle viscosity from observations of glacial isostatic adjustment. In: Sabadini, R., Lambeck, K., Boschi, E.
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ŽEds.., Glacial Isostasy, Sea-Level and Mantle Rheology. Kluwer Academic Publishers, Dordrecht, pp. 63–78. Nakada, M., Lambeck, K., 1991. Late Pleistocene and Holocene sea-level change; evidence for lateral mantle viscosity structure? In: Sabadini, R., Lambeck, K., Boschi, E. ŽEds.., Glacial Isostasy, Sea-Level and Mantle Rheology. Kluwer Academic Publishers, Dordrecht, pp. 79–94. Nordstog, J., Reid, J.R., 1984. Unpublished map. Myra Museum, Grand Forks, ND, 1 sheet. Peltier, W.R., 1981. Ice Age geodynamics. Annual Review of Earth and Planetary Sciences 9, 199–225. Peltier, W.R., 1994. Ice Age paleotopography. Science 265, 195– 201. Peltier, W.R., 1996. Mantle viscosity and Ice-Age Ice Sheet topography. Science 273, 1359–1364. Sugden, D.E., 1977. Reconstruction of the morphology, dynamics, and thermal characteristics of the Laurentide Ice Sheet at its maximum. Arctic and Alpine Research 9 Ž1., 21–47. Teller, J.T., 1990. Volume and routing of Late-Glacial runoff from the Southern Laurentide Ice Sheet. Quaternary Research 34, 12–23. Teller, J.T., 1994. Lake Agassiz; Manitoba, Ontario, Saskatchewan, North Dakota and Minnesota ŽCanada and USA.. In: Gierlowski-Kordesch, E., Kelts, K. ŽEds.., Global Geological Record of Lake Basins. Cambridge University Press, Cambridge, pp. 363–370. Thorleifson, L.H., 1996. Review of Lake Agassiz history. In: Teller, J.T., Thorleifson, L.H., Matile, G., Brisbin, W.C. ŽEds.., Sedimentology, Geomorphology, and History of the Central Lake Agassiz Basin. Geological Association of Canada, Winnipeg, Manitoba, pp. 55–84. Turcotte, D.L., Schubert, G., 1982. Geodynamics. Wiley, New York. Walcott, R.I., 1970a. Flexural rigidity, thickness, and viscosity of the lithosphere. Journal of Geophysical Research 75 Ž20., 3941–3954. Walcott, R.I., 1970b. Isostatic response to loading of the crust in Canada. Canadian Journal of Earth Science 7, 716–727.
Uplift-based limits to the thickness of ice in the Lake Agassiz basin of North Dakota during the Late Wisconsinan Eric C. Brevik a,) , John R. Reid b,1 b
a Soil Morphology and Genesis, Agronomy Department, Iowa State UniÕersity, Ames, IA 50011, USA Department of Geology and Geological Engineering, UniÕersity of North Dakota, Grand Forks, ND 58202, USA
Received 6 November 1998; received in revised form 17 July 1999; accepted 17 August 1999
Abstract Upper and lower limits to ice thickness in the southern Lake Agassiz basin Žnortheast North Dakota. during the Late Wisconsinan have been calculated. The oldest well-preserved tilted strandline of glacial Lake Agassiz, the Herman, was used to determine how much the basin was depressed by the ice sheet and, from that, how much ice was necessary to cause the given depression. Based upon the difference in elevation between the southernmost part of the strandline near Dumont, MN, and where it crosses the US–Canadian border, the absolute minimum rebound Žand thus, earlier depression. in the southern Lake Agassiz basin is 54.5 m. The rebound that occurred over the 300 years between deglaciation and the Herman level of Lake Agassiz was added, yielding a total initial depression of 70 m. The added effects of about 46 m of accumulated lake sediments has caused an unrecovered crustal depression of approximately 23 m. Total minimum depression, therefore, was about 93 m. Assuming that up to 73% of rebound was ‘‘restrained’’, the initial depression may have been as much as 340 m. These values Ž93 to 340 m. were used to calculate minimum and maximum ice thicknesses in the basin of 250 to 920 m, respectively. These thicknesses correspond to basal shear stress values of 0.32 to 4.4 kPa, respectively. q 2000 Elsevier Science B.V. All rights reserved. Keywords: Laurentide ice sheet; ice thickness; Lake Agassiz
1. Introduction Ice near the margins of the Laurentide Ice Sheet during the Late Wisconsinan was initially thought to be considerably thicker than is now believed. For
)
Corresponding author. Fax: q1-515-294-3517. E-mail addresses: [email protected] ŽE.C. Brevik., [email protected] ŽJ.R. Reid.. 1 Fax: q1-701-777-4449.
example, Sugden Ž1977. depicted ice thickness in eastern North Dakota at about 2250 m. But other studies by Mathews Ž1974., Beget Ž1986., Clark Ž1992., Clark et al. Ž1994. and Peltier Ž1994. interpreted ice thicknesses of only about 700 m or less along the southern margins of that ice sheet. The marginal ice was concluded to have been thin because of the soft, deformable sediments and poorly consolidated rocks over which the Laurentide Ice Sheet flowed ŽBoulton and Jones, 1979; Clark, 1992, 1994; Hicock and Dreimanis, 1992..
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The problem with the thin ice interpretation is that it cannot be tested by comparison with any modern ice sheets on the scale of the Laurentide Ice Sheet. Several lines of evidence, however, have been offered to support the thin ice over a deforming-bed model. This includes rapid melting along ice margins at the end of the Wisconsinan ŽBryson et al., 1969;
Andrews, 1973; Dyke and Prest, 1987., rapid fluctuations along ice margins that were over deformable sediments ŽJohnson and Hansel, 1990; Clark, 1994., the lobate form of parts of the ice sheet that rested on deformable sediments ŽClark, 1994., reported deformation features and fabrics preserved in some tills ŽHicock and Dreimanis, 1992., study of longitudinal
Fig. 1. The maximum extent of Glacial Lake Agassiz, and its location in North America. The extent of Lake Agassiz is modified from Teller Ž1994..
E.C. BreÕik, J.R. Reid r Geomorphology 32 (2000) 161–169
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Lake Agassiz, provide additional indirect evidence for the theory of thin ice.
2. Lake Agassiz strandlines Glacial Lake Agassiz began to form against the retreating margin of the Laurentide Ice Sheet approximately 11,700 C 14 years B.P. ŽFig. 3. ŽFenton et al., 1983; Teller, 1990; Thorleifson, 1996.. By approximately 11,200 C 14 years B.P. the edge of the ice had retreated to the present-day border between the United States and Canada ŽFig. 3. ŽFenton et al., 1983.. As the lake level fluctuated in response to changes in ice margin position, downcutting at the outlets, and rebound, numerous strandlines were
Fig. 2. The study area and its position within the Lake Agassiz basin. The southern Lake Agassiz basin is the area within the Herman strandline in the exploded view. The extent of Lake Agassiz is modified from Teller Ž1994.. The position of the Herman strandline is from Johnston Ž1946..
shear ridges ŽBluemle et al., 1993., and computer models of sub-glacial sediment transport ŽAlley, 1991.. A large lake basin exists today along what was once the southern margin of the Laurentide Ice Sheet. This basin once contained glacial Lake Agassiz ŽFigs. 1 and 2.. Tilted strandlines of glacial lakes, such as
Fig. 3. The ice edge in the southern Lake Agassiz basin about 11,700 and 11,200 C 14 years B.P., as marked, and the southwestern edge of the Canadian Shield in the study area. Lake Agassiz was beginning to form approximately within the Herman strandline south of each respective ice edge. Older strandlines above the Herman strandline that mark the earlier positions of Lake Agassiz are poorly formed and difficult to trace ŽBluemle, 1991.. Position of the ice edges is from Fenton et al. Ž1983.; position of the Herman strandline is from Johnston Ž1946.; position of the shield edge is from Espenshade Ž1990..
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formed along the shores. Many of these strandlines are still well preserved, including the Herman strandline, dated at about 10,900 C 14 years B.P. ŽFenton et al., 1983; Thorleifson, 1996.. These strandlines are tilted; they rise to the north as a result of differential isostatic rebound, with older strandlines showing greater tilt ŽJohnston, 1946.. Hence, the minimum ice thickness required to cause the original depression, indicated by the amount of tilt of the oldest strandlines, can be calculated. For this reason the oldest distinct strandline of Lake Agassiz, the Herman strandline, was used for this study. The North Dakota Geological Survey ŽNDGS. has mapped the Herman strandline throughout eastern North Dakota. Appropriate NDGS County studies were used to locate the Herman strandline in a number of places. The Herman strandline was then located on the appropriate United States Geological Survey ŽUSGS. 7.5 min topographic maps with a 1.52-m Ž5 ft. contour interval. Elevations at selected points along the strandline were then determined from the USGS maps ŽFig. 2, Table 1.. Because the original strandline was probably discontinuous and irregular, and because subsequent modification has probably occurred through differential erosion and disruption by humans, for example, elevations were taken at intersections of a 5 mm by 30 mm overlay grid divided into 5 mm segments Ž120 m ground distance. to reduce bias. The grid was centered over the strandline at each location where elevation was measured. Eighty-four data points were compiled at six locations on the strandline ŽBrevik, 1994.. The
Table 1 Location of the points where the elevation of the Herman strandline was measured Site a Location
USGS 7.5 min quadrangleb
1 2 3 4 5 6
Vang, ND Edinburg, ND Inkster, ND Ayr NW, ND Embden, ND La Mars, ND–SD
Sec. 32, T164N, R57W Sec. 26, T158N, R56W Sec. 16, T154N, R55W Sec. 7, T143N, R53W Sec. 3, T138N, R54W Sec. 32 and 33, T129N, R48W a
See Fig. 2 for relative location of sites. The name of the USGS 7.5 min quadrangle on which the given site is located. b
Herman strandline is lowest at its southernmost extremity near Dumont, MN, at 325.3 m above sealevel ŽJohnston, 1946.. Its highest point in North Dakota, at the International Border near Walhalla, is 379.8 m above sealevel. This gives a minimum differential rebound Žand therefore original depression. of 54.5 m for the southern Lake Agassiz basin.
3. Age correction The ice margin was at the International Border about 11,200 years B.P. while the Herman strandline is dated at about 10,900 years B.P. Some post-glacial rebound must have occurred during this 300-year interval. Therefore, the differential rebound Žand thus, depression. indicated by the Herman strandline does not represent absolute post-deglaciation rebound in the Lake Agassiz basin. The amount of rebound that occurred before the formation of the Herman can be calculated, however. The amount of isostatic rebound that has occurred as a function of time is given by: F Ž k ,t . s F0 Ž k . eyt a Ž k .r Tr ,
Ž 1.
where F Ž k,t . is the amount of depression as a function of k Žthe wavenumber. at time t; F0 Ž k . is the initial amount of depression resulting from a harmonic ice load; e is the base for the natural logarithm Žwhich has the value 2.71828.; t is the amount of elapsed time since rebound began; a is the ‘‘lithospheric filter’’; and Tr is the asthenosphere relaxation time ŽFjeldskaar, 1997.. For the Lake Agassiz basin a s 205 km ŽWalcott, 1970a.. Total elapsed time at the International Border is 11,200 C 14 years ŽFenton et al., 1983.. The asthenosphere relaxation time is given by: Tr s Ž 4p Õ . r Ž ra gl . ,
Ž 2.
where p is 3.14, Õ is asthenosphere viscosity, ra is asthenosphere density, g is gravitational acceleration, and l is the ‘‘wavelength’’ of the ice sheet ŽTurcotte and Schubert, 1982.. Asthenosphere density is 3300 kgrm3 ŽBraile, 1989; Fjeldskaar, 1997.. Asthenosphere viscosity beneath the Lake Agassiz basin has been calculated to be 10 22 Pa s ŽWalcott,
E.C. BreÕik, J.R. Reid r Geomorphology 32 (2000) 161–169
1970a.. This value of asthenosphere viscosity is consistent with most recently published values, which tend to fall between 10 20 and 10 22 Pa s ŽPeltier, 1981, 1996; Hager, 1990; Mitrovica and Peltier, 1991; Nakada and Lambeck, 1991; Jaupart et al., 1998.. In addition, Nakada and Lambeck Ž1991. have concluded that the highest values of asthenosphere viscosity occur beneath the Canadian Shield. The portion of the Lake Agassiz basin covered in this study is on the southwest margin of the Canadian Shield ŽFig. 3.. Therefore, we assumed that asthenosphere viscosity beneath the Lake Agassiz basin is 10 22 Pa s for the purposes of this study. Using Eqs. 1 and 2, it can be determined that an initial depression of 70 m at 11,200 years B.P. would have resulted in a continued depression of approximately 54.5 m at 10,900 years B.P., after 300 years of rebound.
4. Effect of water and sediments In addition to crustal depression caused by the ice, the subsequent inundation of the basin by water and sediments add to the complexity of calculating the thickness of the ice based on strandline rebound. The depression caused by lake sediments can be determined with a mass-balance relationship as follows ŽBrevik, 1994.: z s d s Ž Ž rayrs . rra .
Ž 3.
where d s is the sediment thickness in m; ra is asthenosphere density Ž3300 kgrm3, Braile, 1989; Fjeldskaar, 1997.; rs is the density of the sediment Žkgrm3 .; and z is the thickness of sediment above the original surface, in m. The amount of crustal depression Žm. caused by the sediments is designated ys , and can be found by subtracting z from d s after solving for z. Average density of the sediments in the Lake Agassiz basin is 1643 kgrm3. This is the moist average of 24 bulk density values for Lake Agassiz sediments tested in the Fargo and Grand Forks areas ŽJohnson, written communication, 6r1997.. The original bulk density values given were for dry bulk density, but percent moisture by weight was also
165
given for each sample. Because the weight of the sediments causing depression in the field includes the weight of water, the weight of the moisture was added back into each bulk density value to obtain the moist sediment bulk density used in this study. The depth of sampling for these bulk density measurements ranged from 3 to 23 m. Lake Agassiz sediments eventually accumulated to an average thickness of about 46 m in the Grand Forks, ND, area ŽNordstog and Reid, 1984., which would have resulted in an equilibrium depression of about 23 m. The sediments have a maximum thickness of about 90 m in the center of the basin, along the Red River, and pinch out a few kilometers west of the Herman strandline. An average value for sediment thickness is used in this study because sediment thickness varies considerably in this part of the Lake Agassiz basin. Because the sediments are still present, they are still causing about 23 m of depression ŽFig. 4.. The water in Lake Agassiz reached an average depth of as much as 100 m in the southern Lake Agassiz basin ŽNordstog and Reid, 1984. and would have caused a depression of about 30 m. The depression can be calculated using Eq. 3 and substituting d w Ždepth of water. for d s , r w Ždensity of water, assumed as 1000 kgrm3 . for rs , and w Ždepth of water above the original surface. for z. This is only slightly more than the depression caused by the lake sediments. In addition, the water was present before the sediments and, in general, the water level dropped as the sediments accumulated, until the lake drained completely from the southern Lake Agassiz basin. The water would have slowed the rate of rebound following deglaciation, but it would not have prevented rebound. Because the lake no longer exists Ži.e., the water is no longer present., it is assumed that the water mass does not significantly affect the ice thickness calculation and can be ignored. The sediments are considered more important because they are still present and have prevented complete rebound. Absolute minimum depression, therefore, is represented by the minimum depression indicated by the Herman Ž70 m. plus the rebound that never took place Ž23 m., an amount equal to about 93 m. To estimate maximum depression, we assumed that 73% of rebound was ‘‘restrained’’ Ži.e., rebound that occurred while the ice sheet was thinning; An-
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Fig. 4. Steps in the depression and rebound of the Lake Agassiz basin. ŽA. Pre-glacial position of the land surface. ŽB. Ice advance caused depression of the crust. ŽC. The crust rebounded beneath Lake Agassiz as the ice mass thinned and the ice edge retreated to the north. At the same time, sediments accumulated. ŽD. The Lake Agassiz basin as it is today. The pre-glacial land surface is still depressed about 23 m below its original position because of the Lake Agassiz sediments present in the basin. But, the present land surface is about 23 m higher than the pre-glacial land surface was originally Žin step A. because of the accumulation of lake sediments that are less dense than the crust.
drews, 1970.. Although this percentage value was for arctic Canada, it does establish an effective upper limit to ice thickness. Because the ice melted from the Lake Agassiz basin more rapidly than from arctic Canada ŽBryson et al., 1969; Andrews, 1973; Dyke and Prest, 1987. less ‘‘restrained’’ rebound should have occurred in the Lake Agassiz basin. Any error introduced by assuming 73% ‘‘restrained’’ rebound, therefore, will lead to an overcalculation of ice thickness, thus forming an effective upper limit for ice thickness in the Lake Agassiz basin. With 73% ‘‘restrained’’ rebound, maximum depression in the
Lake Agassiz basin would have been approximately 340 m. 5. Ice thickness The same mass-balance principle that was used to calculate crustal depression from sediments can also be used to calculate ice thickness. When the amount of crustal depression is known, ice thickness can be found by solving for x: x y x Ž Ž ra y r i . rra . s y i Ž Ž rayr i . rra .
Ž 4.
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Fig. 5. Depression of the crust by ice, where y is the amount of depression, x is the amount of ice above the depression, and x q y is total ice thickness Žall in m..
where r i is the density of ice, x is the thickness of the ice above the original surface, and y i the depression below the original surface ŽBrevik, 1994; Fig. 5.. Total thickness of the ice is the sum of x plus y i . This assumes the ice was present long enough for the crust to reach static equilibrium. The 93 m of minimum rebound in the Lake Agassiz basin reflects a minimum ice thickness of about 250 m at the present International Border, assuming an ice density of 900 kgrm3 and an asthenosphere density of 3300 kgrm3. The maximum calculated depression of 340 m would reflect an ice thickness of approximately 920 m.
6. Discussion The limits on ice thickness, calculated using the Herman strandline, are valid only if post-glacial rebound in the Lake Agassiz Basin is complete. Using Eqs. 1 and 2, post-glacial rebound of a 93-m depression would take approximately 6700 years, and approximately 8400 years for a 340-m depression. We can, therefore, conclude that post-glacial rebound in the United States portion of the Lake Agassiz basin is complete. This conclusion is supported by free-air gravity anomalies on the Canadian Shield as mapped by Walcott Ž1970b.. The study reported here does not give an ice sheet profile. Rather, it gives limits to ice thickness at a single point, in this case, the point where the Herman strandline intersects the present day border between
the United States and Canada. Maximum and minimum profiles of the ice sheet could be constructed by determining the amount of rebound that has occurred at a number of points along a predicted flow line. That task, however, is beyond the scope of this paper. The mass-balance model ŽEq. 4., used to calculate ice thickness in this study, is admittedly a simple model. The primary factor controlling ice thickness in the marginal lobes of the Laurentide Ice Sheet was the shear stress of the basal sediments ŽMathews, 1974; Clayton et al., 1985; Beget, 1986; Clark, 1992, 1994.. Therefore, we calculated the basal shear stresses that are indicated by the limits of the thickness of the ice in this study and compared them to basal shear stresses calculated for this area by other workers as a check on our model. The limits to ice thickness in this study indicate basal shear stresses of 0.32–4.4 kPa for the Des Moines Lobe, using Eq. 3 from Beget Ž1986.. This compares favorably to the ranges calculated for the Des Moines lobe by Clark Ž1992. Ž0.7–4.3 kPa., Clayton et al. Ž1985. Ž0.5–5.0 kPa., and Mathews Ž1974. Ž0.7–2.2 kPa., respectively. The lower limit of basal shear stress in this study Ž0.32 kPa. is lower than the other values that have been reported, but that was expected. In reality, some rebound in the Lake Agassiz basin would have been ‘‘restrained’’, and that ‘‘restrained’’ rebound is not accounted for in the measurement of absolute minimum rebound. The lower limit to the thickness of ice in this study, however, is based on absolute minimum rebound in the Lake Agassiz basin. We
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can say with confidence the ice was no thinner than the thickness value calculated using absolute minimum rebound because that value does not account for ‘‘restrained’’ rebound. The 73% ‘‘restrained’’ rebound assumed for the Lake Agassiz basin should be an over-estimate, as discussed previously in this paper. Therefore, we believe this study provides reasonable upper and lower limits to ice thickness in the Lake Agassiz basin. These limits can provide a check for other ice thickness studies conducted in this area, as any ice thickness value should fall within these limits.
nold, Geophysicist, University of North Dakota, provided assistance with the asthenosphere viscosity portion of this research. Carolyn Eyles, McMaster University, Richard LeFever, University of North Dakota, and an anonymous reviewer provided helpful comments and critical reviews of the ideas in this paper. This research was conducted while the senior author was a student in the Department of Geology and Geological Engineering at the University of North Dakota.
References 7. Conclusion A lower limit to the thickness of ice in the Lake Agassiz Basin is relatively easy to determine; at a minimum, the ice had to have been thick enough to account for the 93 m of depression indicated by the Herman strandline and the Lake Agassiz sediments remaining in the basin. Maximum thickness of the ice, however, is another matter. That the ice was present in the Lake Agassiz basin long enough to reach equilibrium, and the maximum amount of ‘‘restrained’’ rebound was equal to or less than 73%, must be assumed. With these assumptions, maximum crustal depression was approximately 340 m. Corresponding minimum and maximum thicknesses of the ice were therefore 250 and 920 m, respectively. In reality, the thickness of the ice was most likely somewhere between these limits. For example, the thickness of the ice at the International Border was calculated at about 430 m using Mathews’ Ž1974. method ŽBrevik, 1994.. Regardless of the actual thickness of the ice, study of the Lake Agassiz strandlines establishes limits to the thickness of the ice in the Lake Agassiz basin and supports other recent studies that indicate relatively thin ice Žless than 1000 m thick. along the margins of the Laurentide Ice Sheet.
Acknowledgements Keith Johnson of Midwest Testing Laboratory in Fargo, ND, supplied data on density and water content of the Lake Agassiz sediments. William Gos-
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