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Geomorphology 75 (2006) 300–317 www.elsevier.com/locate/geomorph

Climate during the in the Wasatch and southern Uinta Mountains inferred from glacier modeling

Benjamin J.C. Laabs a,*, Mitchell A. Plummer b, David M. Mickelson a

a Department of Geology and Geophysics, University of Wisconsin, Madison, WI 53706, USA b Idaho National Engineering and Environmental Laboraotry, Idaho Falls, ID 83415-2107, USA Received 5 January 2005; accepted 27 July 2005 Available online 9 November 2005

Abstract

Recent improvements in understanding glacial extents and chronologies in the Wasatch and Uinta Mountains and other mountain ranges in the western U.S. call for a more detailed approach to using glacier reconstructions to infer paleoclimates than commonly applied AAR-ELA-A¨ T methods. A coupled 2-D mass balance and ice-flow numerical modeling approach developed by [Plummer, M.A., Phillips, F.M., 2003. A 2-D numerical model of snow/ice energy balance and ice flow for paleoclimatic interpretation of glacial geomorphic features. Quaternary Science Reviews 22, 1389–1406.] allows exploration of the combined effects of temperature, precipitation, shortwave radiation and many secondary parameters on past ice extents in alpine settings. We apply this approach to the Little Cottonwood Canyon in the Wasatch Mountains and the Lake Fork and Yellowstone Canyons in the south-central Uinta Mountains. Results of modeling experiments indicate that the Little Cottonwood glacier required more precipitation during the local Last Glacial Maximum (LGM) than glaciers in the Uinta Mountains, assuming lapse rates were similar to modern. Model results suggest that if temperatures in the Wasatch Mountains and Uinta Mountains were ~6 8Cto78C colder than modern, corresponding precipitation changes were ~3 to 2 modern in Little Cottonwood Canyon and ~2 to 1 modern in Lake Fork and Yellowstone Canyons. Greater amounts of precipitation in the Little Cottonwood Canyon likely reflect moisture derived from the surface of , and the lake may have also affected the mass balance of glaciers in the Uinta Mountains. D 2005 Elsevier B.V. All rights reserved.

Keywords: Uinta mountains; Wasatch Range; Mass balance; Last glacial maximum; Glacial extent

1. Introduction is dependent on the history of its mass balance. The mass added is generally considered to be most depen- Glacial records in mountain settings provide valu- dent on winter precipitation and the mass lost on sum- able clues to the frequency and magnitude of climate mer temperature (Meierding, 1982). Thus, glacier size change during the late Quaternary Period. The areal is dependent on local climate conditions, and recon- extent and volume of glacier ice in a drainage basin structed glacier extent is often considered a proxy for paleoclimate. Glacial mapping in the southern Uinta Mountains (Laabs, 2004) and in the Wasatch Mountains * Corresponding author. Current address: Geology Department, Gustavus Adolphus College, 800 West College Ave., St. Peter, MN (Richmond, 1965; Madsen and Currey, 1979; Shakun, 56082, USA. Tel.: +1 507 933 7442; fax: +1 507 933 6285. 2003) allows past ice extents to be reconstructed. By E-mail address: [email protected] (B.J.C. Laabs). modeling energy balance and ice flow under prescribed

0169-555X/$ - see front matter D 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.geomorph.2005.07.026 B.J.C. Laabs et al. / Geomorphology 75 (2006) 300–317 301 temperatures and precipitation amounts, glacier recon- areas of 232 and 214 km2 and higher terminus eleva- structions can ultimately be used to infer climate con- tions of ~2256 and ~2264 m asl (Laabs, 2004). Glacier ditions during past glaciations. The objective of this reconstructions in these two valleys by Shakun (2003) study is to use two-dimensional, mass-balance and ice- indicate LGM equilibrium-line altitudes (ELAs) of flow modeling of past glaciers in Little Cottonwood 2470 m asl in Little Cottonwood Canyon and ~3050 Canyon (Wasatch Mountains), and Lake Fork and Yel- m asl in Lake Fork and Yellowstone Canyons. This lowstone Canyons (southern Uintas) to infer climate difference in ELA over a west–east distance of only conditions during the local LGM. ~100 km (see Fig. 1) suggests a significant paleocli- Recent improvements in understanding matic difference between the Wasatch and Uinta Moun- glacial chronologies in the western US (e.g., Phillips tains. The timing of the local Last Glacial Maximum et al., 1996; Sturchio et al., 1994; Licciardi et al., (LGM) in each of these basins is constrained by cos- 2001, 2004; Thackray et al., 2004; Gosse et al., mogenic surface-exposure and radiocarbon ages of 1995a,b; Schildgen et al., 2002; Benson et al., moraines (Laabs, 2004; Madsen and Currey, 1979) 2004a,b; among others) provide a framework for in- (Fig. 2). creasingly detailed studies of past glacial climates. Licciardi et al. (2004) summarize chronological 1.2. Description of models records in the western US, which they interpret to indicate two glacial maxima during the latest Pleisto- The modeling procedure employed in this study, cene: one during the global Last Glacial Maximum developed by Plummer and Phillips (2003), involves (LGM) at ~21 cal. ka and one at ~17 cal. ka (Lic- the use of a 2-D snow accumulation/ablation model ciardi et al., 2004 and references therein). Records in combined with a 2-D ice-flow model. It allows the the northern Rocky Mountains suggest that mountain amount of accumulation or ablation of snow at any glaciers may have been less extensive during the point in a drainage basin to be determined as a func- global LGM, reaching the maximum extents at ~17 tion of predefined temperature and precipitation para- cal. ka (Licciardi et al., 2004; Thackray et al., 2004). meters as well as topographic parameters (shading, Records in the central Rocky Mountains of southwest- aspect and avalanching, among others) that can modify ern Wyoming and Colorado indicate termination of the radiation balance and accumulation. Net accumulation local LGM by ~17 to 16 cal. ka (Benson et al., and ablation are calculated from the energy-balance of 2004a,b; Laabs, 2004). the snow surface during the melt season. The 2-D accumulation/ablation distribution becomes the prima- 1.1. Study area ry input to a second model that simulates glacier growth according to equations for ice flow. Simulated The Wasatch Mountains are a north–south trending ice extent is, therefore, a function of the climate para- range in northern Utah that borders on the central meters defined in the energy balance model and the Rocky Mountains and the eastern Great Basin (Fig. ice-flow parameters in the flow model. This approach 1A). Little Cottonwood Canyon is a steep, narrow, allows testing the effects of a range of temperature and glacial-trough valley that drains westward into Great precipitation conditions on glacial extent, which can be Salt Lake. The Uinta Mountains are an east–west trend- matched to field data and used to set limits on past ing range that is generally much higher in elevation glacial climate. than the Wasatch Mountains. Lake Fork and Yellow- Several advantages exist to using this physically stone Canyons are broad, gently sloping, glacial-trough based modeling approach to infer paleoclimate from valleys that drain southward into the Green River. glacial geomorphic features. First, it eliminates some Mountain glaciers advanced in these ranges while of the assumptions that are typically made in convert- Lake Bonneville expanded in the eastern Great Basin ing glacial geomorphic evidence into an estimate of to cover most of western Utah and parts of southern paleoclimate conditions. These include, for example, Idaho, western Nevada and northern Arizona (Fig. 1B). the significance of particular glacial features (e.g., During the Pinedale Glaciation, the glacier in Little cirque floors and lateral moraines) and the accumula- Cottonwood Canyon attained a maximum length of tion–area ratio of past glaciers. Second, the model ~19 km, covered an area of 40 km2, and terminated directly addresses many of the controls on accumula- at ~1520 m asl (Shakun, 2003). The Lake Fork and tion and ablation that are overlooked in simpler mod- Yellowstone Canyon glaciers were much larger during els, such as the dependence of irradiance on the Pinedale, with respective lengths of 38 and 41 km, topography and the dependence of annual snow/rain 302 B.J.C. Laabs et al. / Geomorphology 75 (2006) 300–317

Fig. 1. (A) Map of the western US showing the alpine glacier systems examined in this study (dark gray) and the extent of Lake Bonneville during the last glaciation. Arrows indicate directions of seasonal circulation. Modified from Munroe (2001). (B) Landsat image of northeastern Utah. White boxes indicate locations of the Little Cottonwood (LC, in the Wasatch Range) and the Lake Fork (LF) and Yellowstone (YS) Canyons (in the Uinta Range). partitioning on temperature (e.g., Seltzer, 1994). Third, 1.3. Previous inferences of LGM climate a relatively dense network of climate stations (SNO- TEL stations, coordinated by the Western Regional A paleoclimate study in the Wasatch and Uinta Climate Center, www.wrcc.dri.edu) in the study areas Mountains was pursued because of the unique location allows relatively accurate calculation of the modern and orientation of these mountain ranges, and the exist- distribution of temperature and precipitation for each ing disparity among proposed climate conditions during drainage basin (see Table 1); these data provide input the last glaciation in the central Rockies and the Great to the mass/energy balance model. Finally, the inde- Basin. During the last glaciation, glaciers in the Wasatch pendent and combined effects of increased winter Mountains were adjacent to and immediately downwind precipitation and decreased summer temperatures on (east) of Lake Bonneville, a pluvial lake that covered glacier mass balance can be tested, as can the effects 47,800 km2 in western Utah. Glaciers in the south of changes in average monthly cloudiness (which central Uinta Mountains were also downwind of Lake affects the amount of incoming solar radiation), Bonneville (Fig. 1), but more than 100 km further east. changes in the seasonal distribution of precipitation, Porter et al. (1983) summarized glacial records in the and changes in average monthly wind speed. Rocky Mountains and suggested that, under drier than B.J.C. Laabs et al. / Geomorphology 75 (2006) 300–317 303

Fig. 2. Shaded-relief of the Little Cottonwood (bottom), Lake Fork (left) and Yellowstone (right) Canyons (see Fig. 1 for locations of each canyon). Maps were produced from mosaics of 30-m U.S. Geological Survey 7.5-min digital elevation models. The grids were clipped to the boundaries of each drainage basin and resampled to cell sizes of 90 m for Little Cottonwood Canyon and 180 m for the much larger Lake Fork and Yellowstone Canyons. Field-reconstructed ice extents (black lines) for the LGM (from sources noted in the text) were digitized and used for comparing mapped ice extent with modeled ice extent. Dashed arrows indicate ice-flow direction. modern climate, LGM temperatures in the Rocky flin and Wheat, 1979; Hostetler and Benson, 1990; Mountains would have been more than 10 8C cooler Thompson et al., 1993, and references therein). Ben- than modern based mainly on ELA reconstructions. son and Thompson (1987) attribute the rise of Lakes Kaufman (2003) used amino-acid paleothermometry Lahontan and Bonneville to the presence of the south- of fossil ostracodes in Lake Bonneville deposits to ern Cordilleran and Laurentide ice sheets, which dis- show that temperatures were 7–138 C cooler than mod- placed the jet stream southward to the northern Great ern during the period ~24 to 12 cal. ka and suggested Basin, thereby increasing precipitation in this area. that decreases in effective evaporation brought about by General circulation model simulations of winter and cold summer temperatures in the eastern Great Basin summer climates during the LGM support this hypoth- may have led to the rise of Lake Bonneville. Results of esis, and indicate temperatures b10 8C cooler and regional-scale paleoclimatic and hydrologic modeling precipitation amounts greater than modern (e.g., Bar- of the Lake Bonneville basin by Hostetler et al. (1994) tlein et al., 1998). In addition, Hostetler et al. (1994) similarly suggest a significant decrease in summer tem- suggest that moisture derived from the surface of Lake perature (~7 8Cto98C cooler than modern) and a Bonneville was intercepted by surrounding mountain small increase in precipitation (~13 mm in winter and 7 ranges, including the Wasatch Mountains, and returned mm in summer) occurred in this area during the peak of to Lake Bonneville. This implies that lake-effect mois- Lake Bonneville (~17 cal. ka; Oviatt, 1997). ture affected glacier mass balance in the Wasatch Other studies suggest that climate was not only Mountains. cooler, but also wetter than modern in the eastern Recent interpretations of the glacial record in the Great Basin and central Rocky Mountains (e.g., Mif- Uinta Mountains also suggest that precipitation 304 B.J.C. Laabs et al. / Geomorphology 75 (2006) 300–317

Table 1 Sources of climate data near Little Cottonwood, Lake Fork and Yellowstone Canyons Canyon Station name Sourcea Location (dd) Elevation (m asl) Data used for model inputb Period of record Little Cottonwood Pleasant Grove RAWS N40.438 W.111.758 1585 W 1997–present Louis Meadow SNOTEL N40.838 W111.778 2043 T, P 2000–present Lookout Peak SNOTEL N40.838 W111.728 2500 T, P 1953–present Snowbird SNOTEL N40.558 W111.658 2939 T, P 1990–present Lake Fork Atlamont WRCC N40.378 W110.288 1951 T, P 1953–present YS-Altamont RAWS N40.548 W110.338 2378 T, W 1983–present Brown Duck SNOTEL N40.58 W110.588 3232 T, P 1979–present Lake Fork Basin SNOTEL N40.548 W110.58 3323 T,P 1981–present Chepeta RAWS N40.818 W110.078 3695 W 1998–present Yellowstone YS-Altamont RAWS N40.548 W110.338 2378 T, P, W 1983–present Mosby Mountain SNOTEL N40.628 W109.888 2896 T 1979–present Lakefork SNOTEL N40.608 W110.438 3079 T, P 1980–present Five Points Lake SNOTEL N40.728 W110.478 3329 T, P 1982–present Chepeta RAWS N40.818 W110.078 3695 W 1998–present Data from the YS-Alatamont and Chepeta stations were used to compute wind-speed regressions for both Lake Fork and Yellowstone Canyons. a All data were retrieved from www.wrcc.dri.edu. RAWS=Remote Automated Weather Station. SNOTEL=Snowpack Telemetry. WRCC=Wes- tern Regional Climate Center. b W = wind, T = temperature, P = precipitation. amounts were higher at the time of the local LGM. itation–elevation gradients that are varied to simulate Munroe and Mickelson (2002), Shakun (2003) and past glacial climates; these are computed from data Oviatt (1994) reconstructed equilibrium-line altitudes recorded by SNOTEL stations (Table 1). Within the (ELAs) for the LGM in the northern and southern range of elevations where SNOTEL data are available, Uinta Mountains. They documented an eastward rise a linear model best describes modern lapse rates and in ELAs across the Uinta Mountains, which is steepest precipitation gradients (Figs. 3 and 4) in each canyon. in the area within ~50 km of the eastern shore of Lake To account for the significant west–east climatic gra- Bonneville. Munroe and Mickelson (2002) attribute this dients across the study area, data from three stations pattern to significant precipitation derived from the near Little Cottonwood and Lake Fork Canyons and surface of Lake Bonneville in the Wasatch and western four stations near Yellowstone Canyon were used to Uinta Mountains, with valleys becoming progressively compute separate lapse rates and precipitation gradi- drier downwind in the eastern Uintas. They also used ents for each basin. Differences in precipitation gra- reconstructed ELAs to infer temperature and precipita- dients between the Wasatch and Uinta Mountains tion conditions and suggest that summer temperature (Figs. 3 and 4) reflect the strong orographic barrier was 5.5–8 8C cooler and precipitation in the western of the Wasatch Mountains (Zielinski and McCoy, Uintas was greatly increased (up to 10 modern) dur- 1987), where westerly precipitation is intercepted. ing the LGM by lake-effect moisture derived from the This effect is particularly noticeable during winter surface of Lake Bonneville. Disagreement among docu- months, when westerly Pacific storm tracks carry mented reconstructions of LGM climate in the eastern moisture to this area most efficiently (Fig. 4A; Mitch- Great Basin/central Rocky Mountains region calls for ell, 1976). Valleys in the Uinta Mountains become additional research in this area. We use the combination increasingly drier leeward (eastward) of the Wasatch of known glacial extents and numerical modeling to test Mountains (Fig. 5). During summer months, precipi- the likely changes in temperature and precipitation that tation gradients are steeper in the southern Uinta occurred during the LGM. Mountains than in the Wasatch Mountains and abso- lute precipitation amounts are similar (Fig. 4B). Sum- 2. Methods mer lapse rates in the three areas are similar; but the slightly steeper lapse rates in the Uinta Mountains 2.1. Local climate parameterization produce significantly cooler temperatures because maximum elevations are much higher than in the The snow accumulation/ablation model requires Wasatch Mountains (Fig. 3A). Lapse rates are also climatic input parameters, primarily modern mean slightly higher in the Yellowstone Canyon than in monthly temperature–elevation lapse rates and precip- the Lake Fork Canyon, and this trend of increasing B.J.C. Laabs et al. / Geomorphology 75 (2006) 300–317 305

Fig. 3. Monthly lapse rates in the Yellowstone (diamonds, dashed-dotted line), Lake Fork (squares, solid line) and Little Cottonwood Canyons (triangles, dotted line) for October, January, April and July. Rates are computed as least-squares linear-regressions fit to mean monthly temperatures computed from data recorded at SNOTEL and RAWS stations. Regression-line equations for each month (including those not shown here) are in Appendix A1. lapse rates with increasing downwind distance from best considered via sensitivity tests. In any case, if the Wasatch appears to be directly related to increas- winter precipitation in the study area was derived ing aridity. Relatively large amounts of summer pre- from a westerly source, it is likely that precipitation cipitation in the Uinta Mountains (Fig. 4) reflect the in the Uinta Mountains during the LGM was limited by importance of south-southwesterly circulation during efficient capture of westerly moisture by the Wasatch summer, which delivers moisture to the southern Uin- Mountains as it is today (Fig. 5). tas from the Gulf of California to produce monsoon- type storms. High pressure situated over the Great 2.2. The mass/energy balance model Basin generally prevents moist air masses from south-southwesterly source regions from reaching the The 2-D, in-the-horizontal-plane, energy balance Wasatch Mountains (Mitchell, 1976). model employed in this study is described in Plummer In using modern lapse rates to describe modern and Phillips (2003). The model calculates the annual climate and paleoclimates, we implicitly assume that rate of ice accumulation and ablation for each cell on a the controls on the vertical structure of the atmosphere digital elevation grid from the equation were essentially the same during the LGM as they are Z Z today, despite significant decreases in temperature or TN0 Tb0 increases in precipitation. This assumption is somewhat bn ¼ ðÞP E dt þ ðÞP M E dt ð1Þ Tb0 TN0 supported by studies of regional climate patterns that suggest that atmospheric circulation in northern Utah at where bn is the net annual mass balance at any location the time of the LGM was similar to modern (Benson in the x,y plane, P is snowfall, E is evaporation or and Thompson, 1987; Zielinski and McCoy, 1987). sublimation, T is temperature and M is the mass of Although differences in the frequency or seasonality snow melted. Melting is only calculated during a snow- of precipitation might alter temperature gradients, such melt season, which is defined by the period of time relationships are difficult to predict and are probably when mean monthly temperatures are above zero (in- 306 B.J.C. Laabs et al. / Geomorphology 75 (2006) 300–317

Fig. 4. Monthly precipitation–elevation gradients in the Yellowstone (diamonds, dashed-dotted line), Lake Fork (squares, solid line) and Little Cottonwood Canyons (triangles, dotted line) for October, January, April and July. Rates are computed as least-squares linear-regressions fit to mean monthly precipitation data recorded at WRCC, SNOTEL and RAWS stations. Regression line equations for each month (including those not shown here) are in Appendix A1. dicated by the second group of terms in Eq. (1)). from the shortwave and longwave radiation balances, Sublimation is the only means of loss when mean turbulent energy exchanges, and advective and conduc- monthly temperatures are below zero (the first group tive energy exchanges to a snow surface at the melting of terms in Eq. (1)). The rate of melting is calculated point:

Q ¼ R þ H L þ A þ G ð2Þ

where Q is the energy flux available for melting, R is the shortwave and longwave radiation balance, H and L are the sensible and latent heat fluxes, respectively, A is the energy advected with rain and G is the conductive heat flux from the ground. Mass balance is calculated at a monthly time step and integrated over a period of 1 year, or several years, until the net annual balance is constant. Calculation of radiation balance accounts for effects of topographic shading, angle of incidence and albedo, with the latter term dependent in a simple Fig. 5. West–east precipitation gradients across the Wasatch and Uinta manner on cloudiness and fraction of total snowfall Mountains at 2600 (diamonds, dashed-dot curve), 3000 (triangles, melted. The turbulent energy exchange equations fol- solid curve), and 3400 m asl (squares, dotted curve) during January low a bulk transfer scheme and depend primarily on (similar trends exist for all winter months; see Laabs, 2004). Points surface temperature, wind speed and relative humidity. are computed from precipitation–elevation gradients in Little Cotton- Advective and conductive energy exchanges contribute wood Canyon (LC, Wasatch), the southwestern Uintas (SWU), Lake Fork Canyon (LF), Yellowstone Canyon (YS, central Uintas), and the only a small amount to the mass/energy balance calcu- eastern Uintas. See Fig. 1 for locations of each canyon. Best-fit curves lation; energy added by advection is dependent entirely are second-order polynomials. on rainfall (which adds heat to snow/ice) and conduc- B.J.C. Laabs et al. / Geomorphology 75 (2006) 300–317 307 tion is assumed to contribute a small, constant amount mined by solving the following continuity expression of energy. for 2-D flow, Because annual mass balance is most dependent on @h @qx @qy temperature and precipitation, the regressions in Figs. 3 ¼ bn ð3Þ and 4 are the primary inputs to the mass balance model. @t @x @y

Secondary parameters include mean monthly estimates where h =ice surface elevation above datum, bn =net of relative humidity, cloudiness, and wind speed, and annual mass balance, q =ice discharge per unit width, the standard deviation of daily temperatures for each and x and y are directions of ice flow in the horizontal month. Temperature, precipitation, and wind speed data plane. The flux of ice between adjacent cells ( qx, qy) are available at a range of elevations within the vicinity is determined by the thickness and the depth-integrat- of each basin. The monthly fraction of sky cover was ed flow velocity, u, the latter computed from equa- estimated by the number of days with precipitation per tions for ice flow by sliding (us) and deformation (ud): month (i.e., sky cover=the number of days with pre- n 2 m cipitation divided by the number of days/month). Sky u ¼ us þ ud ¼ f ðÞsB þ ðÞ1 f H ðÞsA ð4Þ cover and relative humidity were determined from local 5 climate data but were more difficult to relate to eleva- where B and A are coefficients of sliding and defor- tion. These parameters were kept constant for all eleva- mation, respectively; H is ice thickness and f is a tions within each drainage basin. factor used to vary the ratio of sliding to deformation. To simulate past glaciers, the climatic input para- Following Fastook and Chapman (1989), the expo- meters of the accumulation/snowmelt model were ad- nents n and m are taken as 2 and 3, respectively. justed to reflect a range of possible glacial climates The basal shear stress, s,is (discussed below). The resultant accumulation map s ¼ qgHrh ð5Þ was used to determine the shape and extent of the steady-state glaciers that would develop. Potential where q is ice density and g is gravitational acceler- adjustments to the climatic inputs to the model are ation. Eq. (3) is solved using fully explicit five-point limited primarily by our ability to describe modern finite differences (Plummer and Phillips, 2003). and past climatic conditions, where little data exist for the latter. In this study, we limited our adjustments to 2.4. Model calibration additive variations of temperature (the temperature assigned to a cell based on its elevation minus the In parameterizing the model with modern climato- applied temperature change) and multiplicative varia- logic data, we seek to determine how the climatic tions of precipitation (the elevation-dependent precipi- conditions associated with past glacial extents differ tation times an applied factor, where 1 from modern conditions. The reliability of the calculat- precipitation=modern precipitation) (Plummer and ed differences thus depends on how well the model Phillips, 2003). Thus, the temperature–elevation lapse describes modern conditions, and how well it describes rate is translated but its gradient remains unchanged the climatic sensitivity of steady-state alpine glaciers. while the precipitation–elevation gradient increases For example, if the model overpredicts the modern when precipitation rates are increased. glacial extents, it will underestimate the changes needed to produce larger glaciers. As glaciers no longer exist in 2.3. Ice-flow modeling the Wasatch and Uintas, however, it is impossible to calibrate the model using modern glaciers in the study The snow and energy input to each cell of a digital areas. elevation model determines the accumulation and ab- Two thin, semi-perennial snowfields, however, exist lation areas for the modeled basin. In the accumulation on shaded headwalls near the summit of the central area, ice builds up and flows outward in the direction Uintas (below Mount Lovenia and the Red Castle) and of ice-surface slope (usually down hill) into the abla- the model does produce a small but positive net annual tion area until the glacier reaches a steady state. The accumulation rate in those areas. Correspondence of computed rates of accumulation and ablation deter- these local ablation minima provides at least some mine the net annual mass balance for the basin, and confidence that the model reproduces the modern ac- the transfer of mass between these two areas is based cumulation/ablation pattern reasonably accurately. on an empirical equation for ice flow via deformation Another means of evaluating model accuracy is to and sliding. The time-dependent flow of ice is deter- compare simulated monthly snowpack thickness to ob- 308 B.J.C. Laabs et al. / Geomorphology 75 (2006) 300–317 served SNOTEL snowpack thickness histories. Simu- 3. Results lated spring-season snowpack thicknesses are very sim- ilar to SNOTEL measurements of snow-water 3.1. Sensitivity and uncertainty equivalent (Table 2), but because ablation is primarily a melt-season calculation, and significant spring melt- For a steady-state glacier simulation, the mass bal- ing begins in late April to early May, agreement be- ance gradient effectively defines the extent of the gla- tween measured and modeled snowpack in May is most cier, except to the degree that the dviscosityT of the ice significant among the comparisons in Table 2 (accumu- alters the shape of the glacier. That is, if the ice deforms lation is largely an input parameter, so that comparisons or slides under little stress, it can produce a much of winter snowpack thickness are most valuable as a thinner glacier than one that responds less readily to simple check that the input functions are behaving stress. As glacier thickness affects surface mass bal- properly). Snow disappears from virtually all of the ance, differences in ice thickness can also produce SNOTEL sites by early to middle June and simulated differences in glacial extent. If the actual flow charac- melting is also complete by the end of June. The teristics of the dpaleo-iceT were known, this effect could monthly time-step currently implemented in the be used to help constrain the mass balance of the glacier model precludes tuning the timing to any better accu- because mass balance gradients, which increase with racy than that. Given that this latter comparison evi- greater accumulation rates, also affect ice thickness. In dences a reasonable match at the altitudes of the paleoclimate studies, we cannot know the flow charac- SNOTEL stations, that the model appears to match teristics of the paleoglaciers, but the shape and thick- locations of local ablation minima at the high elevations ness of the vanished glacier are tightly constrained by in the Uintas and that the temperature and precipitation trimlines, lateral moraines and other geomorphic evi- functions are based on an excellent meteorological data dence. Ice flow parameters were, thus, adjusted to set, we believe that the model reproduces modern cli- maintain, for each simulation, ice thickness consistent matic conditions well enough to provide a good basis with observations. To improve agreement between for subsequent estimates of the effects of hypothetical modeled and field-reconstructed ice thicknesses in Yel- climate shifts. lowstone Canyon, ice-flow parameters A and B (Eqs. For the ice-flow model, initial values for parameters (2) and (4)) were increased by a factor of 5 above those A and B in Eq. (4) were taken from Plummer and described in Plummer and Phillips (2003) to 5.010 7 Phillips (2003). Those parameters were subsequently and 7.510 3, respectively, still well within the range adjusted to provide a good match to LGM glacial extent of empirically determined values of these parameters in full glacial climate simulations for the study area. As (Table 3). This change reduced modeled ice thickness is discussed below, the actual flow parameters are not a by 200 m. Parameters A and B were not adjusted for critical parameter in this study because we force simu- simulations in Lake Fork and Little Cottonwood Can- lated ice thickness to match glacial geomorphic evi- yons because simulated ice thicknesses agreed with dence, and do not attempt to use ice thickness as a field-reconstructed estimates documented in Laabs guide to paleoclimatic conditions. (2004) and Richmond (1965).

Table 2 Measured and modeled snowpack at SNOTEL stations Month SNOTEL station Elevation (m asl) Drainage basin Mean measured snowpack (cm swe)a Modeled snowpack (cm swe)b April Snowbird 2939 Little Cottonwood 103.3 87.5–92.4 April Lake Fork 3079 Yellowstone 34.5 36.3–38.2 April Brown Duck 3232 Lake Fork 51.8 50.6–53.5 April Lake Fork Basin 3323 Lake Fork 55.9 59.4–61.2 April Five Points Lake 3329 Yellowstone 46.9 43.7–45.6 May Snowbird 2939 Little Cottonwood 89.7 48.0–86.0 May Lake Fork 3079 Yellowstone 19.8 15.6–28.0 May Brown Duck 3232 Lake Fork 47.5 48.5–50.9 May Lake Fork Basin 3323 Lake Fork 54.4 53.8–66.3 May Five Points Lake 3329 Yellowstone 36.8 33.9–47.0 a Data were retrieved from www.wrcc.dri.edu. b Because the locations of SNOTEL stations are not precisely known, a range of output values from within 200 m of the approximate location of each station is reported. B.J.C. Laabs et al. / Geomorphology 75 (2006) 300–317 309

Table 3 Empirically determined coefficients for ice flow Reference A (year 1 kPa 3) B (m year 1 kPa 2) Stroeven et al. (1989) 1.910 8 3.010 3 Oerlemans, 1988 2.210 8 3.210 3 Schemeitz and Oerlemans, 1997 3.010 8 7.910 3 Huybrechts et al. (1989) 8.010 8 – Plummer and Phillips (2003) 1.010 7 1.510 3 Paterson, 1994 2.110 7 – Oerlemans, 1989 3.010 6 2.810 3 This Study—Little Cottonwood and Lake Fork Canyons 1.010 7 1.510 3 This Study—Yellowstone Canyon 5.010 7 7.510 3

Ice thickness also affects glacial extent by altering curves that do not, in general, overlap. The non-linearity the surface mass balance. The climatic combinations essentially reflects that increases in precipitation are here described in Fig. 6 were based on net accumulation/ expressed as increases in precipitation gradient. The ablation maps calculated based on the modern topog- different trajectories of the curves, on the other hand, raphy. Ice advance, however, increases the elevation of reflect the different temperature lapse rates and precipi- the valley surface, which, in turn, increases precipita- tation gradients of each canyon. Although modern winter tion but decreases topographic shading. For that reason, precipitation gradients and amounts are greater in the Plummer and Phillips (2003) recommend calculating Wasatch than in the Uinta Mountains (Fig. 4), for exam- net annual accumulation and ablation on a simulated ple, modeled ice extent is greater in the Lake Fork and glacier that matches field evidence of ice thickness and Yellowstone Canyons than in Little Cottonwood Canyon extent. In this study, we took a simpler approach, and for any given decrease in temperature and/or change in calculated accumulation/ablation on the modern topog- precipitation (Fig. 7). This suggests that colder tempera- raphy. This simplification was based on observations tures in the upper parts of the Lake Fork and Yellowstone that the opposing effects of the ice-altered topography Canyons, relative to Little Cottonwood Canyon, are are of similar magnitude, so that the net effect is minor. more significant in determining mass balance than the The degree of this effect was tested in Yellowstone winter precipitation difference between the two ranges Canyon by simulating ice extent with a monthly tem- (Figs. 3B and 4A). The separate curves for each canyon perature depression of 7.2 8C and modern precipitation. emphasize one of the advantages of this modeling ap- The ice surface grid was added to the valley surface proach; (1) the ability to consider glacial response to grid, and the mass/energy balance model was run on the multiple variables at once, and (2) how local topographic new surface. Ice extent in the second simulation de- gradients may produce differing climatic sensitivity in creased by less than 2% (or an equivalent temperature relatively nearby canyons. These curves provide an in- change of less than 0.18 C). Similar results were found triguing means of reconstructing regional LGM climatic by running this test in the Lake Fork and Little Cotton- conditions, even though uncertainties in the input data wood Canyons with respective temperature depressions and potential errors in the models limit our confidence in of 8.4 8C and 9.1 8C and modern precipitation. This paleoclimatic inferences based solely on these data. indicates that ice advance did not significantly affect Considering that the LGM glaciers in each of these glacier mass balance and that neglecting that effect does canyons were contemporary, the simplest interpretation not introduce significant errors in estimating past cli- of the associated paleoclimatic conditions would be to matic conditions from model results. assume that a single combination of temperature-pre- cipitation changes explains all three glaciers. If that 4. Discussion were true, the curves should intersect at one or more points. The curves in Fig. 7 do not yield a single 4.1. Model simulations of LGM ice extents temperature–precipitation combination, however, that could produce LGM ice extent in all three canyons. For each of the three canyons studied, model simula- Only one combination, a temperature depression of 5 tions define a specific set of climatic scenarios that 8C and a precipitation increase of 2.5, produces LGM reproduced observed LGM ice extent (Figs. 6 and 7). extents in both of the Uinta canyons. This suggests Plotting the successful temperature-precipitation condi- either that climatic conditions in the three different tions for each canyon (Fig. 7) yields a set of non-linear canyons were not uniformly different from modern 310 B.J.C. Laabs et al. / Geomorphology 75 (2006) 300–317 climate in temperature and precipitation, or that the Bonneville basin, it seems likely, that it experienced uncertainties involved in this approach are too great a wetter LGM climate than the high Uintas, as it does to identify the common change. today, because of the increased potential for lake- Given that Little Cottonwood Canyon is in a dif- effect snow and rain. On the other hand, given that ferent mountain range, on the shores of the Lake all three canyons are at approximately the same lati-

Fig. 6. (A) Ice extent during the LGM simulated under four different combinations of temperature depressions (e.g., T—8.4 8C) and precipitation changes (e.g., P 0.5) relative to modern in Yellowstone Canyon. Black lines indicate estimated ice extent during the LGM based on field mapping (from Laabs, 2004). (B) Ice extent during the LGM simulated under four different combinations of temperature depressions (e.g., T—9.9 8C) and precipitation changes (e.g., P 0.5) relative to modern in Lake Fork Canyon. Black lines indicate ice extent during LGM based on field mapping (from Laabs, 2004). (C) Ice extent during the LGM reproduced under four different combinations of temperature depressions (e.g., T—10.4 8C) and precipitation changes (e.g., P 0.5) relative to modern in Little Cottonwood Canyon. Black lines indicate ice extent during the LGM based on field mapping and air-photo interpretations (from Madsen and Currey, 1979; Shakun, 2003). B.J.C. Laabs et al. / Geomorphology 75 (2006) 300–317 311

Fig. 6 (continued). tude (N408), temperature depressions in all three can- While differences in precipitation between the yons would probably have been the same. The trajec- Wasatch Mountains and the Uinta Mountains seem tories of the successful climatic scenarios in each range plausible and likely, it is considerably more problematic are consistent with this hypothesis; larger increases in to posit large precipitation differences between the two precipitation are required to reproduce LGM glaciers in canyons in the Uinta Mountains. If we assume that Little Cottonwood Canyon than in the other two can- temperature and precipitation differences from modern yons for any given drop in temperature. For example, climate would have been the same throughout the given a temperature depression of 7 8C in all three Uintas, and that temperature departures from modern canyons, the Little Cottonwood glacier would have would have been identical throughout the region, we required a 2.5 precipitation change whereas the effectively define constraints that are, in this case, Lake Fork and Yellowstone glaciers would have re- satisfied by only one climatic scenario. A temperature quired only 1.5 and 1.2 changes in precipitation, depression of ~5 8C and a precipitation change of 2.5 respectively (Fig. 7). modern yields LGM ice extent in the Lake Fork and 312 B.J.C. Laabs et al. / Geomorphology 75 (2006) 300–317

Fig. 6 (continued).

Yellowstone Canyons, while the same temperature de- We can infer slightly different temperature depres- pression in Little Cottonwood Canyon requires an ac- sions if we consider that precipitation changes might companying increase in precipitation greater than 3.5 not have been exactly uniform across the Uintas, even modern. This interpretation of the model results indi- between the nearby Lake Fork and Yellowstone can- cates that LGM climate was colder and much wetter yons. Strong east–west precipitation gradients already throughout this region and, as suggested by Munroe exist in that range (Fig. 5), and subtle differences in and Mickelson (2002), lake-effect moisture derived storm tracks could have produced non-uniform precip- from the surface of Lake Bonneville produced an itation changes. Assuming that precipitation changes even larger increase in precipitation in the Wasatch were not different by more than about 20% still widens Mountains. the range of possible temperature depressions to about

Fig. 7. Plot of temperature and precipitation combinations that yielded LGM ice extents in model experiments. B.J.C. Laabs et al. / Geomorphology 75 (2006) 300–317 313

4–6 8C. The warmer end of that range requires an even This paleoclimatic estimate is intriguing, in that it more dramatic increase in precipitation (~4.5)in appears to reflect a new way of defining the unique Little Cottonwood Canyon, while the colder end paleo precipitation–temperature combination connected reduces the necessary precipitation factor to about 3 with a particular set of glacial geomorphic features. modern. Continuing toward slightly more complicated Rather than focus on that result, however, which prob- climatic scenarios, reasons exist to consider non-uni- ably overstates our ability to accurately simulate the form temperature changes within the region. Hostetler slight difference in climatic response between the two et al. (1994) suggest that the presence of Lake Bonne- basins, we explore now the full range of LGM climatic ville may have kept local winter temperatures higher scenarios that the model suggests are possible, and and summer temperatures cooler than in surrounding attempt to better constrain our estimate of LGM tem- areas. Scenarios with warmer temperatures in the perature depression by examining paleoclimatic recon- Wasatch than in the Uintas would require even greater structions of several previous studies in light of those precipitation increases in the Wasatch than those men- results. tioned above. Previous studies have suggested colder estimates of Interpreting the model results, based on the exact LGM climate (e.g., Kaufman, 2003) than the 4 8Cto trajectories of the separate curves, assumes that the 6 8C temperature range that results from applying inverse-modeled estimates of LGM temperature–pre- reasonable climatic constraints to the model results of cipitation combinations for each canyon are the only this study. Kaufman (2003) concluded from amino acid possible scenarios. Significant uncertainties exist in paleothermometry that temperature depression in the these combinations because of a myriad of uncertainties Lake Bonneville basin during the period 24 to 12 cal. in the data input to the model and because of potential ka was between 7 8C and 13 8C. Our simulation results biases in the model calculations. These include the indicate that a temperature depression of 7 8C would lapse rates and precipitation–elevation gradients; have been accompanied by no precipitation change in which are based on data from a small number of the Yellowstone, 1.5 modern in the Lake Fork Can- weather stations; estimates of climate input data that yons, and 2 modern in Little Cottonwood Canyon. At are not available locally (e.g., relative humidity and colder temperatures, our results indicate that a depres- cloudiness) and our lack of knowledge of how numer- sion of more than ~9 8C would have been accompanied ous second-order climate variables differed during the by less-than-modern precipitation in all 3 basins, and a LGM. While we have not directly assessed uncertainty depression of more than 10.5 8C would have required in this study, sensitivity tests conducted for basins in the 0.5 modern in Little Cottonwood Canyon and less Sierra Nevada, California (Plummer, 2002), suggest than 0.1 modern in Yellowstone Canyon. Such rela- that these effects produce uncertainties in the calculated tive drops in precipitation imply that little moisture was temperature depressions and precipitation factors of available to glaciers in the central Rocky Mountains about F0.5 8C and F30%, respectively. Incorporation during the LGM. This contradicts studies with general of this uncertainty in the model results would, thus, circulation models (e.g., Bartlein et al., 1998), however, expand the curves of Fig. 7 to bands encompassing a that show a southward displacement of the polar jet wide range of temperature–precipitation combinations, stream during the LGM that would have led to in- approximately centered on the existing curves. Because creased precipitation in the northern Great Basin and the intersection of the Lake Fork and Yellowstone central Rocky Mountains (e.g., Benson and Thompson, curves forms a rather oblique angle, this would greatly 1987). If these models are correct, precipitation in the expand the range of combinations that could satisfy the Wasatch and Uinta Mountains would probably have paleoclimate constraints discussed previously, probably been greater than modern during the LGM, so based even to the extent that many combinations of temper- on our modeling results, temperature depressions of ature depression and precipitation change could have more than 9 8C are unlikely. Yet, because Kaufman’s produced all three LGM glaciers. Assuming that the amino acid data are perhaps the best available paleo- intersection of the response curves is largely a function temperature proxy for the region, we suggest that a of differing climatic gradients, not just uncertainty, the range of temperature depressions that encompasses LGM temperature depression implied by the intersect- the cold end of our estimated range and the warm end ing curves is ~4 8Cto68C, with corresponding pre- of Kaufman’s range, 6 8Cto7 8C, is most likely. cipitation increases of ~3 to 2 modern in the Uintah Corresponding precipitation increases are ~2 to 1 in Canyons and N4 to 3 modern in Little Cottonwood the Yellowstone and Lake Fork Canyons and 3 to 2 Canyon. in Little Cottonwood Canyon. 314 B.J.C. Laabs et al. / Geomorphology 75 (2006) 300–317

4.1.1. Mass balance gradients (e.g., Kuhn, 1984), and are perhaps reasonable esti- The absolute amounts of accumulation and ablation mates if, as some previous studies have concluded on glaciers and ice-surface mass-balance gradients (e.g., Hostetler et al., 1994; Munroe and Mickelson, (i.e., the change in mass balance with elevation) that 2002), Lake Bonneville was a significant moisture would have accompanied specific temperature changes source for glaciers in the Wasatch Mountains. have implications for the climatic classification of the reconstructed glaciers (Table 4). Ablation gradients on 4.1.2. Comparison with recent studies in the Uinta the modeled Lake Fork and Yellowstone glaciers were Mountains extracted by calculating the mass/energy balance on As noted above, Munroe and Mickelson (2002) the ice-elevation surface simulated for a given set of inferred an LGM temperature depression of 5.5 8C temperature/precipitation combinations that produced from glacier reconstructions in the Uinta Mountains LGM ice extent. For a temperature depression of 5.5 and suggested an important relationship between Lake 8C and precipitation 2.3 modern, ablation gradients Bonneville and glaciers in the Uinta Mountains. Our on these glaciers would have been ~6 to 8 mm/m. results support their finding that glaciers downwind These gradients for such climatic conditions are at the of Lake Bonneville received more precipitation than high end of ablation gradients on modern glaciers in modern under such a temperature depression, espe- continental mountain settings where glaciers exist cially in the case of Little Cottonwood Canyon, under cold and dry climates (e.g., Mayo, 1984), and where a depression of 5.5 8C would have been reflect the relatively steep temperature-elevation lapse accompanied by a ~3 precipitation increase. This rates during summer months that currently occur in finding is also supported by results of regional cli- the south-central Uinta Mountains (see Fig. 3). A mate modeling described in Hostetler et al. (1994), temperature depression of 5.5 8C in Little Cottonwood which suggest that moisture derived from the surface Canyon, on the other hand, would have been accom- of Lake Bonneville was likely returned to the lake panied by a ~3 precipitation increase. This implies (via surrounding drainages including Little Cotton- very high annual snowfall, exceeding 4.5 m of water wood Canyon) to maintain its hydrologic budget. In equivalent precipitation, or more than 13 m of snow at the south-central Uintas (Lake Fork and Yellowstone high elevations (~3500 m asl). Ablation rates on the Canyons), model results indicate that a temperature Little Cottonwood glacier would also have been very depression of 5.5 8C would have been accompanied high, with more than 10 m of annual melting at the by ~2 more precipitation than modern; this is terminus. These amounts of net annual accumulation slightly less than results in Munroe and Mickelson, and ablation are typical of modern coastal glaciers who estimate that winter accumulation was ~3 greater than modern in the north-central Uintas (due north of the Lake Fork and Yellowstone Canyons) during the LGM. Table 4 Reconstructed ablation gradients in the Uinta Mountains a 5. Conclusions Glacial valley Climate Ablation gradient (mm of water/m of elevation) This study used a relatively new approach to Burnt Forkb N/A 1.4 reconstructing paleoclimatic conditions from glacial Thompson Creekb N/A 2.8 geomorphic evidence by combining applications of Middle Fork N/A 2.1 numerical modeling of snow accumulation/ablation b Beaver Creek and ice flow. This method allows ready accounting Other Rocky Mountain N/A 1.0–5.0 c of the spatially varying influence of temperature, valley glaciers Yellowstone T—5.1 8C, P 2.5 8.0 precipitation, shortwave radiation, and many second- Lake Fork T—5.1 8C, P 2.5 6.0 ary parameters on glacier mass/energy balance and, Yellowstone T—8.4 8C, P 0.5 5.0 ultimately, ice extent. We find this approach signifi- Lake Fork T—8.4 8C, P 1 4.0 cantly aids in exploring the implications of the many a Temperature and precipitation combinations that yielded LGM ice potential climate scenarios that could have character- extent in Lake Fork and Yellowstone Canyons (see Figs. 6 and 7). ized past glacial climates. In this study, for example, b Valley in the northeastern Uintas; ablation gradients are from Munroe (2001). we explored glacial response to numerous changes in c From Leonard et al. (1986), Murray and Locke (1989), and temperature and precipitation, and observed that it Munroe (2001). was significantly tied to the local temperature-eleva- B.J.C. Laabs et al. / Geomorphology 75 (2006) 300–317 315 tion lapse rate and local topographic precipitation may have existed during the LGM in northern Utah gradient. and to better understand the relationship between A broad range of potential temperature and precipi- Lake Bonneville and glaciers downwind. One possi- tation conditions during the time of the LGM in northern ble approach to this would be to model the hydrologic Utah were obtained from modeling of mass/energy bal- budget of Lake Bonneville concurrently with nearby ance and ice flow in the Little Cottonwood, Lake Fork glaciers (cf. Plummer, 2002) in the western Uintas and and Yellowstone Canyons. Assuming that these temper- other Great Basin and Rocky Mountain ranges. An- ature–precipitation combinations accurately reflect gla- other way to set limits on temperature and precipita- cial sensitivity to probable climatic scenarios, a narrow tion would be to apply the approach used here to a interpretation of the intersection point of the three gla- broader area that includes low-elevation valleys that cier response curves would indicate that LGM temper- were not occupied by ice during the last glaciation; the ature depressions were ~4 8Cto68C. Given the supposition being that excessive temperature depres- uncertainties in the calculations, however, we find this sions or precipitation in model experiments would estimate premature and we consider it more compelling produce ice in such valleys. Given the spatial and to interpret these results in combination with other temporal variability of paleoclimate in the western seemingly reliable paleoclimatic data for the region. US at the time of the global and local LGM–as We, thus, estimate that temperatures during the LGM suggested here and in previous studies–continued were ~6 8Cto78C colder than modern and that pre- efforts to improve the understanding of glacial chro- cipitation was ~2 to 1 modern in the Uinta Mountains nology will provide an essential framework for these and ~3 to 2 modern in Little Cottonwood Canyon. paleoclimatic inferences. This implies that Lake Bonneville enhanced precipita- tion on downwind glaciers in the Wasatch Mountains. Acknowledgments Increased precipitation downwind of the lake may also have influenced the Uinta Mountains; however, our Funding was provided by the Geological Society of finding that LGM climate included up to ~2 modern America, the Desert Research Institute, and the Nation- precipitation is slightly greater than precipitation values al Science Foundation (EAR-0345277). Discussions estimated for LGM climate elsewhere in the western US with J. Munroe, S. Hastenrath, J. Knox, B. Singer, (e.g., Porter et al., 1983; Benson and Thompson, 1987). and A. Zhu along with reviews by F. Phillips and an Additional work is needed to improve limits on anonymous colleague were extremely helpful in pre- the temperature and precipitation combinations that paring early drafts of this paper.

Appendix A. Monthly temperature and precipitation regressions in Little Cottonwood, Lake Fork and Fork and Yellowstone Canyons

Drainage basin Month Temperature lapse rate R2 Precipitation–elevation R2 gradient (cm water/km) Little Cottonwood January y =3.4+3.7 0.969 y =13.3x 18.5 0.956 Lake Fork January y =6.8+11.8 0.934 y =5.6x 11.7 0.986 Yellowstone January y =6.8+11.8 0.934 y =5.6x 11.7 0.992 Little Cottonwood February y =3.4+4.7 0.969 y =12.017.6 0.982 Lake Fork February y =6.2+10.6 0.995 y =6.4x 10.9 0.997 Yellowstone February y =6.8+11.8 0.934 y =6.6x 14.0 0.996 Little Cottonwood March y =4.5+10.1 0.999 y =7.8x 6.6 0.988 Lake Fork March y =7.3+17.3 0.998 y =5.9x 9.8 0.999 Yellowstone March y =7.1+16.5 0.857 y =7.1x 15.3 0.982 Little Cottonwood April y =6.7+19.4 0.969 y =8.7x 9.7 0.973 Lake Fork April y =7.9+22.8 0.976 y =5.4x 8.7 0.999 Yellowstone Aprily =8.8+24.9 0.971 y =6.8x 14.4 0.994 Little Cottonwood May y =5.6+21.3 0.989 y =9.6x 13.9 0.973 Lake Fork May y =8.4+28.9 0.999 y =4.78.7 0.999 Yellowstone May y =7.9+27.7 0.932 y =5.9x 11.8 0.994 Little Cottonwood June y =5.6+25.2 0.989 y =8.2x 14.6 0.899 316 B.J.C. Laabs et al. / Geomorphology 75 (2006) 300–317

Lake Fork June y =9.5+37.5 0.999 y =2.9x 3.6 0.9.39 Yellowstone June y =9.1+36.2 0.935 y =3.5x 6.3 0.953 Little Cottonwood July y =5.6+25.4 0.760 y =2.2x 2.9 0.900 Lake Fork July y =8.4+37.9 0.999 y =3.2x 4.3 0.999 Yellowstone July y =8.3+37.4 0.861 y =4.3x 8.3 1 Little Cottonwood August y =5.6+29.2 0.989 y =3.8x 6.2 0.849 Lake Fork August y =8.4+36.9 0.999 y =3.5x 4.5 0.979 Yellowstone August y =7.9+35.3 0.928 y =5.2x 10.1 0.998 Little Cottonwood September y =5.6+24.6 0.984 y =3.0x 1.4 0.603 Lake Fork September y =8.4+31.9 0.999 y =4.1x 5.3 0.999 Yellowstone September y =7.1+28.1 0.837 y =5.8x 11.1 0.999 Liitle Cottonwood October y =3.4+13.7 0.967 y =7.7x 10.4 0.968 Lake Fork October y =7.3+23.3 0.998 y =3.9x 5.1 0.994 Yellowstone October y =6.8+21.8 0.934 y =5.8x 11.4 0.935 Little Cottonwood November y =3.4+7.0 0.968 y =8.5x 7.4 0.984 Lake Fork November y =7.3+16.3 0.998 y =5.3x 8.8 0.978 Yellowstone November y =7.1+15.5 0.857 y =6.5x 13.8 0.999 Little Cootonwood December y =3.4+3.7 0.968 y =7.4x 6.1 0.999 Lake Fork December y =7.3+12.2 0.998 y =4.3x 6.8 0.999 Yellowstone December y =6.0+9.0 0.834 y =5.1x 10.4 0.983

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