Abstract

Cirques form and evolve as glaciers attack the bed and subaerial processes dismantle the surrounding walls. Collectively, these processes—which can make a cirque longer, or deeper, or both—profoundly influence near-divide regions of glaciated mountains and yet are rarely studied in a systematic way. Toward this end, we developed a theoretical framework for the sediment budget of a cirque that includes sediment sources, transport pathways, and storage elements. We quantified each component of the sediment budget using field measurements and remote-sensing data of a glaciated alpine cirque in British Columbia, Canada. The cirque has a plan-view area of 1.64 km2 and relief of ∼780 m. Our budget values, which correspond to a period of substantial glacier retreat, are based on measurements reflecting time intervals ranging from 1 yr to 80 yr. We report errors as a range (enclosed in parentheses), analogous to 95% confidence bounds.

On average, 1640 (250–7950) metric tons of rock are released by the headwall each year; nearly 90% of this debris leaves the wall as small rockfalls or in snow avalanches. Our field observations indicated that snow avalanches originating as cornice failures are currently the most important transport process on the headwall. We estimated the mass of debris transported annually by the glacier to the foreland using (1) the volume and age of the foreland ground moraine and (2) the product of rock mass per unit volume of ice and glacier velocity. Over the past several decades, the glacier delivered 6440 (1180–14930) tons/yr to the foreland via forward ice motion and margin retreat (mostly in subglacial till or sediment-rich basal layers). Less than 3% of the glacierborne sediment flux traveled as supraglacial debris (170 [50–320] tons/yr). At present, sediment evacuation from the cirque occurs in a single meltwater stream. We monitored water discharge and suspended sediment concentration in this stream between 29 June and 28 August 2007. By season’s end, 650 (80–1860) tons of sediment had passed our gauging station (equivalent to an erosion rate of 0.2 [0.03–0.70] mm/yr, when averaged over the glacier bed). Approximately one third of the total annual streamborne sediment transport occurred over a 2 d period during the first major melt event of the year.

Using our budget relations and flux magnitudes, we estimate the glacier is removing between 1240 and 2470 tons of rock from its bed per year, a rate equivalent to 0.5–0.9 mm/yr of erosion glacierwide. The headwall, by comparison, is being worn away horizontally at ∼1.2 (0.2–5.9) mm/yr. Thus, our results suggest that the headwall is retreating at rates roughly equivalent to vertical incision by the glacier. Our sediment budget results demonstrate that the wide variety of sediment sources and transport processes active in cirques necessitates a holistic view of cirque formation, one that most morphometric, range-scale, and glacial erosion analyses ignore.

INTRODUCTION

Cirques are emblematic features of mountain ranges that have felt the icy chisel of glacial erosion (e.g., Hobbs, 1910). Their unmistakable morphology—steep fluted bedrock walls and overdeepened rock basins containing resplendent tarns—has motivated alpine geomorphologists for more than a century to investigate the mechanisms driving their formation (e.g., Tyndall, 1862; Gastaldi, 1873; Helland, 1877; Hooke, 1991; MacGregor et al., 2009; Sanders et al., 2012). From the Alps to the Sierra Nevada, from Scandinavia to Snowdon, the question of cirque evolution remains the same: What processes are responsible for the development of cirques and at what rates do they act?

The formation of cirques, more than any other alpine process, ultimately controls the topographic structure of glaciated mountain crests. Early alpine enthusiasts, recognizing the significance of the imprint of cirques, speculated as to how they formed and about the effect cirque evolution had on slope, relief, and peak heights in near-divide regions of glaciated mountain ranges (Matthes, 1900; Richter, 1900; de Martonne, 1901; Gilbert, 1904; Johnson, 1904; Lawson, 1904; Daly, 1905; Penck, 1905; Davis, 1906). In particular, these authors postulated that (1) glaciers in cirques erode headward (horizontally) by undermining the headwall, (2) on alpine ridges, glacial erosion outpaces nonglacial processes, and (3) headward erosion may eventually truncate entire mountain massifs (for a more thorough historical overview, see Evans, 2006). Indeed, recent studies of cirque form have begun to validate many of these original hypotheses (Brocklehurst and Whipple, 2002; Oskin and Burbank, 2005; Mitchell and Montgomery, 2006; Naylor and Gabet, 2007; Foster et al., 2008; Anders et al., 2010), and despite their diminutive size, cirque glaciers—that is, glaciers residing in cirques—may have a large role in the alpine system (Gilbert, 1904). With each glacial cycle, cirque glaciers have been the first glaciers to form and are the last glaciers to melt. Even in many low-elevation or low-latitude mountain ranges, where large-scale glaciation is absent, cirque glaciers often exist in favorable topographic positions. It is this ability to survive as isolated glaciers on the peripheries of glacial environments that has led to the use of cirque floor elevations as paleoclimate indicators (e.g., Porter, 1964).

Modern efforts to understand cirque evolution have drifted away from their mechanistic roots. Despite rigorous attempts to demonstrate that cirque erosion is one method by which glaciers place limits on the height of mountain ranges (the so-called “glacial buzz saw”; see Brozovic et al., 1997; Mitchell and Montgomery, 2006), these studies are primarily correlative and do not attempt to develop a process-based understanding of cirque evolution (e.g., Mitchell and Montgomery, 2006; Anders et al., 2010). Numerical models of glacier erosion (e.g., MacGregor et al., 2009), moreover, may shed light on feedbacks or unforeseen behavior in cirques, but they remain poorly parameterized and overly simplistic. Cirques exist at the interface between glacial and periglacial processes, where rock-wall, glacial, fluvial, and groundwater processes are all acting simultaneously. A given rock, for example, may release from the headwall, fall into the bergschrund, participate in subglacial abrasion, be flushed from the glacier by subglacial streams, and roll out of the cirque as bed load in a proglacial channel. Treating cirque glacier erosion as a strict function of ice flux, while a logical first step, is not adequate (e.g., Egholm et al., 2009; MacGregor et al., 2009).

Despite a renewed interest in cirques (e.g., Oskin and Burbank, 2005; Mitchell and Montgomery, 2006; Anders et al., 2010), and the clear need for data to parameterize models, very little on-site field investigation of cirques has been performed recently (cf. Humlum, 2000). In this work, we aim to qualitatively and quantitatively advance our process understanding of cirques by constructing a sediment budget for a “classic” cirque. A drainage basin sediment budget seeks to quantify the rate of production, transport, and discharge of sediment (Dietrich et al., 1982). The sediment budget approach is valuable for several reasons. First, it allows contributions from glacial and nonglacial processes to be compared (Harbor and Warburton, 1993). In cirques where rock-wall processes outpace erosion at the glacier’s bed, for example, we can expect headward retreat but very little relief generation (e.g., Brocklehurst and Whipple, 2002). Second, sediment budgets allow storage terms to be quantified rather than assumed (Dietrich et al., 1982). Calculation of subglacial erosion rates from sediment transport rates in proglacial streams, for example, requires the change in storage to be negligible—a dubious assumption. Finally, the results of a sediment budget can also help to clarify the dominant processes and guide future monitoring efforts (Dietrich et al., 1982). In this work, we are guided by two principal motivating questions: (1) At what rates do geomorphic processes active in cirques produce sediment? and (2) What do these rates imply about cirque evolution? Previous studies have used several techniques to calculate cirque erosion rates (Table 1), including moraine, lake, rock glacier, or other sediment volume (Reheis, 1975; Anderson, 1978; Grout, 1979; Larsen and Mangerud, 1981; Hicks et al., 1990), landform change (Andrews and LeMasurier, 1973), stream sediment flux (Bogen, 1996), and space for time substitution (Brook et al., 2006). At the conclusion of this manuscript, we compare our results to these previous studies.

THEORETICAL FRAMEWORK OF A CIRQUE SEDIMENT BUDGET

The development of a sediment budget for a cirque, as in other types of watersheds, requires the identification of all processes, transport pathways, and storage elements operating within the basin of interest (e.g., Dietrich and Dunne, 1978; Dietrich et al., 1982). Cirques, in general, experience the same geomorphic processes as much larger glacial basins. In some respects, cirque sediment budgets are simpler than those for other comparably sized, lower-elevation basins because of the negligible influence of flora or fauna on high-elevation landscapes. On the other hand, it is difficult to directly quantify erosion rates in the part of a basin covered by glacial ice. Before describing the sediment budget that is specific to our field site, we will develop a more general set of relations that can then be modified as necessary given specific transport paths and storage elements in alpine cirques.

For a sediment budget to be meaningful, one must define both the geographical extent and time period over which the budget is to be performed (Dietrich et al., 1982). Although it is relatively straightforward to delineate the geographic boundary (especially in the case of an individual landform such as a cirque), it is often not as easy to define the relevant time period because geomorphic processes act over a wide range of time scales. Small rockfalls, for example, occur nearly every hour over the course of the summer, whereas large rockfalls are generally rare, occurring perhaps once a century. Ideally, a sediment budget would include long-term monitoring efforts (years to decades), but this is often prohibited by logistical constraints. In this work, for example, we present the sediment flux measured in a proglacial stream over the course of a single summer season, as well as the sediment flux resulting from large-volume rockfalls, which occurred several centuries ago. In order to compare sediment fluxes related to processes with distinct recurrence intervals such as these, we assume that each sediment flux is constant over time scales equal to the largest recurrence interval considered.

The sediment budget flux boundary should be designed to encompass the area of interest while minimizing unnecessary complexities. Herein, we diverge from the classic description of a cirque and include the recently deglaciated foreland (the proglacial zone) beyond the riegel (the bedrock ridge that traverses the open end of the cirque; see Evans and Cox, 1974) as part of a “cirque” basin (Figs. 1 and 2). The perimeter of a cirque is usually defined by a line running along the crest of the headwall and lateral arêtes, and across the riegel. Our definition, however, permits us to measure the output from the whole budget region and thus calculate the present-day basin-averaged vertical erosion rate (forumla): 

graphic
where Qc is the sediment efflux, Ac is the area of the cirque basin, and the subscript c refers to the entire cirque. Equation 1 does not distinguish between subaerial rock-wall (as per tradition, we will refer to the subaerial rock wall simply as the “headwall”), glacial, or proglacial sources of sediment. Thus, we also split a cirque basin into three separate spatial domains—the headwall, the glacier and its bed, and the glacier foreland (Figs. 2B and 3). Inclusion of the glacier foreland in a cirque sediment budget is a useful approach because all sediment leaving a cirque glacier must pass through this zone. Thus, the foreland can play a critical role in sediment routing to lower-elevation streams (e.g., Hammer and Smith, 1983) or as a storage element. With this in mind, a simple description of the sediment dynamics in a cirque is as follows. Sediment originates from the headwall and glacier bed and is transported by ice and/or water to the glacier margin. In some cirques, if the glacier does not reach beyond the lateral arêtes (sidewalls), mass wasting may deliver sediment directly to the proglacial zone. Some proportion of the sediment that leaves the glacier is then quickly evacuated from the cirque by proglacial streams; the rest is deposited in foreland lakes or as ground moraine. In some cirques, the dissolved load may be significant. Direct erosion of bedrock by proglacial streams is also possible. Lastly, the glacier foreland may receive sediment from streams or glaciers that originate outside the cirque. For the entire cirque, then, this description is given by 
graphic
where P terms represent production of sediment within the cirque, I represents inflows of sediment that originate outside the cirque boundary, Q represents transport out of the cirque (which includes the foreland), S represents storage, and all terms are expressed as mass per time (we will use metric tons per year). Here and elsewhere, Δ refers to a change in a variable. Subscripts h, g, f, and c refer to the headwall, glacier, glacier foreland, and entire cirque, respectively. Sediment can be stored on the headwall (Sh), in or beneath the glacier (Sg), or in the foreland (Sf). Here, we treat the transformation of bedrock to sediment (Ph, Pg, or Pf) as an “input” to the cirque. We can also create analogous, independent relations for each of the three spatial domains: 
graphic
 
graphic
 
graphic
where production and inflow terms (P and I) represent inputs of sediment to each domain, and the transport term (Q) represents transfer of sediment out of each domain (Fig. 3). The input terms Ih and Ig are negligible in most cirques because most cirques exist at topographic divides. Some cirques, however, are carved into plateaus. In these cirques, eolian, overland flow, or creep processes can deliver sediment to the headwall or glacier from outside the cirque boundary.

Large uncertainties in some terms of our sediment budget are unavoidable, given the short duration of our monitoring and the inaccessibility of the glacier bed. There is no feasible way, for example, to accurately measure the average thickness of till beneath the ice. To assess the uncertainty of our results, we therefore defined conservative plausible limits on such unmeasured variables, guided by field observations and geomorphological constraints. The resulting bounds are analogous to 95% confidence limits in the sense that the probability of actual values lying outside our reported ranges is very small but nonzero.

Helmet Mountain Cirque and West Washmawapta Glacier

Helmet Mountain, a horn-type peak in the Canadian Rocky Mountains, contains an “armchair” cirque on its eastern flank that is occupied by West Washmawapta Glacier (Figs. 1 and 2; Table 2). Helmet Mountain (3124 m above the sea) is composed of west-dipping, Cambrian to Ordovician, brown to buff slates and shales of the McKay Formation (Cook, 1975; Price et al., 1978). The majority of the proglacial zone and ∼7% of West Washmawapta Glacier are underlain by the Ottertail Formation, a massive blue-to-gray limestone with dolomite interbeds (Cook, 1975; Price et al., 1978; Fig. 4).

West Washmawapta Glacier is a temperate cirque glacier, sitting in an overdeepened bowl greater than 60 m deep (Sanders et al., 2010). The glacier has an average and maximum thickness of ∼70 m and ∼185 m, respectively. Horizontal ice motion, in general, is convergent in the accumulation zone and divergent in the ablation zone (Sanders et al., 2010). As recently as 1949, West Washmawapta Glacier and its eastern counterpart, Washmawapta Icefield, were still a single glacier—the entire glacier foreland (the proglacial zone) has been exposed by retreat in the past 60 yr (Figs. 2 and 4). Vegetation in the cirque is sparse as a consequence of recent deglaciation and high elevation.

Individual Budget Relations

Headwall

At Helmet Mountain, the top of the cirque wall is the highest local topographic feature, and therefore the sediment flux from outside the cirque is negligible (Ih = 0). Because the headwall is generally very steep, we may assume that the storage elements on the headwall are small relative to Ph (the headwall has an average slope of ∼60°) and quickly reach capacity (ΔSh = 0). Thus the conservation of mass equation for the headwall (Eq. 3) becomes 

graphic
which simply states that as weathered material is freed from bedrock, it is quickly transported down the wall and onto the glacier or into the bergschrund (cf. Krautblatter and Dikau, 2007).

Glacier

We define the glacier domain as including all of West Washmawapta Glacier, including any subglacial till between the glacier sole and underlying bedrock. Headwall mass wasting (Ph = Qh = Ig) and subglacial erosion (Pg) provide sediment to the glacier. Combining Equations 4 and 6, it follows that 

graphic
where Qg represents all sediment that leaves the glacial domain and enters the glacier foreland (Fig. 3). Any imbalance in the left-hand terms of Equation 7 leads to an increase or decrease in (1) the total mass of rock contained in the glacier or (2) the subglacial till volume (thickening, thinning, or spatial coverage).

Proglacial Zone

For the purpose of this sediment budget, we designated the area bounded by the 1949 and 2007 glacier margins as “the foreland.” During this time interval, the front margin of West Washmawapta Glacier retreated, and thus the foreland domain expanded. The proglacial zone receives sediment from West Washmawapta Glacier (Qg) and from a single meltwater stream that originates from Washmawapta Icefield (Qwi) and enters our study region from the east (Figs. 3 and 4): 

graphic

We assume fluvial erosion of bedrock by meltwater streams likely occurs but is of relatively minor importance compared to Qg when weighted for channel area (the glacier bed area is roughly 1000 times larger than the proglacial stream bed). As such, we take Pf = 0, and using Equation 8, the budget relation for the glacier foreland becomes 

graphic
with terms as before. The present-day sediment flux out of the foreland (Qf) occurs in a single proglacial stream that exits the basin 20 m north of the point labeled SG2 in Figure 4. At Helmet Mountain cirque, then, Qc = Qf, because West Washmawapta Glacier terminates upstream of the flux boundary. We separate the storage term, ΔSf, into two spatial components, ground moraine and deposits in proglacial lakes: 
graphic
where ΔSgm represents material deposited as ground moraine, and ΔSlk represents material deposited in proglacial lakes. At our study site, ΔSf is a positive quantity because contributions from the glacier (englacial and subglacial sediment deposited at the retreating glacier front) exceed subsequent removal by overland flow or scour of lake beds. The effect of such removal processes is only to winnow fines. Combining Equations 7–10, we get 
graphic
which is the governing budget equation for Helmet Mountain cirque. In the following, we describe our research strategy and the associated results for each domain (headwall, glacier, and foreland), with the end goal of quantifying each term in Equation 11.

HEADWALL

Overview of Headwall

At the head of a cirque, by definition, there is a headwall. Cirque headwalls are steep bedrock slopes, hundreds (but sometimes thousands) of meters high (e.g., Helland, 1877); in many cases, the headwall height constitutes more than 50% of local ridge-to-valley relief (Evans, 2006; Mitchell and Montgomery, 2006; Sanders, 2011, p. 11). Alpine peaks are frequently nothing more than the residue left as three or more cirque headwalls converge (e.g., Davis, 1911, his Fig. 3). The headwall, furthermore, is not a passive entity gnawed at by the adjacent glacier; in climates at the threshold of glaciation, the headwall enhances the glacier mass balance by shading the accumulation zone, inducing lee-side deposition of windblown snow, and producing snow avalanches that come to rest on the glacier surface (Matthes, 1900; Gibson and Dyson, 1939; Rapp, 1960).

Although the connection between glacier undermining of the headwall and resultant retreat was recognized long ago (e.g., Johnson, 1904; Gilbert, 1904), less attention has been directed toward the processes by which cirque headwall retreat actually occurs (Battle and Lewis, 1951; Rapp, 1960; Hallet et al., 1991; Matsuoka and Sakai, 1999; Sanders et al., 2012). It is widely assumed that the headwall simply maintains a strength equilibrium slope (e.g., Mitchell and Montgomery, 2006). As the wide variety of micro- and macro-headwall morphologies demonstrates (Fig. 5), numerous geomorphic agents act to carve, dissect, shape, or otherwise disassemble cirque headwalls. Specifically, subaerial weathering and erosion of cirque headwalls has been attributed to rockfalls (Rapp, 1960), debris flows (Ono and Watanabe, 1986), refreezing of surface or groundwater (e.g., Johnson, 1904; Chamberlin and Chamberlin, 1911; Lewis, 1938), and nivation (Matthes, 1900; Strom, 1945). The relative efficacy of each individual process will depend on the morphology of the cirque, bedrock properties, and climate (Graf, 1976; Olyphant, 1977; Evans, 1997). Subaerial weathering processes become especially important during interglacial periods when many cirques are glacier-free (Olyphant, 1981; Olyphant, 1983).

At Helmet Mountain cirque, we observed three principal mass-wasting processes that transfer sediment from the surrounding walls to the glacier. On the steep southern and western walls, we witnessed both snow avalanches (usually triggered by cornice failures) and rockfalls, similar to those described by previous authors working in the Canadian Rockies (Gardner, 1970; Luckman, 1978a; Gardner, 1980). The northern wall, which has a gentler slope (Fig. 6), is mantled by sediment (Figs. 1A and 4); there, talus creep and small rockfalls appear to dominate sediment transport (as also demonstrated elsewhere in the Canadian Rockies; Luckman, 1978b). We suspect that heavy rainfall (a common occurrence in the Canadian Rockies each summer) spawns debris flows from small pockets of colluvium on many cirque headwalls, but we did not observe any within Helmet Mountain cirque.

We did not quantify the sediment flux from the northern wall to the glacier surface. Safety concerns precluded direct measurements of talus creep or installation of rockfall nets. We did observe rocks tumbling onto the glacier surface from a few points where the talus slope is adjacent to the ice. Three observations, however, indicate that the northern wall is not contributing a significant quantity of sediment to the glacier at this time. First, the northern margin of the glacier is not covered with sediment (Fig. 1A). Second, subglacial till exposed during recent retreat still exhibits subglacial flow features, suggesting it is not modified by mass-wasting events originating upslope. Third, a low-relief spur ridge and low-angle terrace both obstruct sediment produced east of point d on Figure 4 from reaching the glacier—in this region of the northern wall, all sediment produced from bedrock is transferred directly to headwall storage (as opposed to the rest of the headwall, where storage is minimal). Unless the glacier expands laterally to the north and entrains the debris on the northern wall, the accommodation space east of point d will eventually fill up, allowing sediment to spill onto the glacier surface.

Headwall Measurements and Results

The production of sediment from the headwall occurs over many spatial and temporal scales. Small rockfalls are especially common and can be heard on an hourly basis over much of the summer (see Gardner [1980] for a more thorough discussion of rockfall frequency in the Canadian Rockies). Snow avalanches and cornice failures (herein we will refer to both simply as avalanches) occur nearly every day in late spring and early summer when the headwall is still mantled by snow. Evidence for low-frequency, large-volume rockfalls at Helmet Mountain is also present (Fig. 1; Fig. 4, R1–R3). We calculated the rate at which sediment is produced by the headwall using the three techniques described next.

Snow Apron

Sediment that is transported by avalanches or as rockfall tumbles onto the snow apron at the head of the glacier and comes to rest. Unless the preceding winter’s snowfall is completely melted by summer’s end, the rocks at the surface represent one year of headwall production (ablation stakes left in the snow confirmed that the new snow did not all melt). To measure the sediment flux of these high-frequency, low-magnitude events, we mechanically weighed all of the rock in ten regions of the snow apron using a bucket and scale (Fig. 4, squares 1–10). The sampling areas ranged from 9 to 400 m2 (boxes on Fig. 4 are to scale). We subsampled some regions where large rocks were abundant. We calculated the volume (Vrock) of large rocks (that is, rocks of greater volume than would fit in a 5 gallon [∼18.9 liters] bucket) as 

graphic
where lrock, wrock, and hrock represent the length of each rock along the three principal axes, and γrock is a constant. We estimated maximum and minimum volumes by varying γrock from 0.4 to 0.7 (Luckman, 1988). Individual measurement locations were chosen to represent the full range of surface sediment mass densities present across the snow apron with the specific goal of relating sediment mass per area to pixel brightness on a high-resolution aerial photograph taken 2 d before our sampling. We normalized pixel brightness using the median value of clean snow in the vicinity of each sample area.

Using a least-squares linear regression relationship between pixel brightness and surface mass density (Fig. 7; root mean square error [RMSE] = 1 kg/m3), we estimated the total mass of rock deposited on the glacier from the headwall between our visit to the glacier in May 2007, when the snow apron had very little rock on it, and the date of the aerial photograph (15 August 2007) to be between 2.3 × 105 kg and 2 × 106 kg. When comparing snow brightness to surface mass, we excluded two sampling sites where large rocks made up a significant proportion of the total mass (44% at region 5; 69% at region 9; Fig. 7). These sites are “brighter” than their masses predict because thick rocks do not “darken” the aerial photo as much as their mass implies. These calculated masses represent the combined contributions of avalanches and rockfalls that occurred in summer 2007. Although avalanches create easily identified lobate deposits, we cannot distinguish between debris that traveled within an avalanche from that of subsequent rockfalls.

When calculating the range of values for this component of the headwall flux, we incorporated two other important sources of error: the amount of material still buried beneath the snow surface at the time of our sampling, and the amount of material that descends into the bergschrund. With respect to the former, we emphasize that during our visit in May 2007, the snow surface was relatively clean (Fig. 1B). Most of the cornices remained plastered to the ridge tops, and much of the rock wall was covered with snow. On the other hand, the ability of the bergschrund to capture rockfalls remains unknown: the quantity of rock that enters the bergschrund relative to the total produced by the wall above has never been measured. We descended into the bergschrund several times over the course of the summer, and based on a visual assessment of the amount of rock we found there, we estimate that <20% of the sediment produced by the wall is swallowed by the bergschrund. The percentage that enters the bergschrund is relatively low because (1) early in the melt season, the bergschrund is still bridged by snow, causing snow avalanches to slide past the moat, and (2) late in the summer, rockfalls (which dominate debris transport after the headwall snow melts) released by the face bounce well beyond the outer lip of the bergschrund.

Large-Volume Rockfalls

We define large-volume rockfalls as greater than ∼400 m3 because rockfalls of this size and larger seem to create morphologically distinctive deposits that are relatively thin, spread out, and composed of a wide distribution of grain sizes. Although relatively infrequent, these rockfalls may account for a significant fraction of the total sediment produced by the headwall when averaged over the appropriate time scale. At present, a single large rockfall deposit is clearly visible on the glacier’s surface (Figs. 1A and 4, R1). To expand our temporal record of large rockfall events, we scrutinized six historical aerial photographs (1949, 1966, 1973, 1978, 1993, and 2002) in search of evidence for older rockfalls. The 1993 and 2002 aerial photographs revealed two additional large rockfall deposits that had emerged from within the glacier as it retreated (R2 and R3, respectively, in Fig. 4). Further glacier retreat caused these rockfall deposits to be incorporated into the foreland till, making them no longer distinguishable. Although we have no way of knowing if much larger and rarer events occur in Helmet Mountain cirque, we note that there is no obvious failure surface preserved on the headwall.

Approximating the total large rockfall sediment flux requires the average mass of rock produced per fall and the frequency of events: 

graphic
where Qrf is the large rockfall flux, Mrf is the mass of a single event, frf is the event frequency, nrf is the number of events, and Tobs is the duration of observation. Overbars indicate the average value. The mass of an individual large rockfall is 
graphic
where Arf is the area of the rockfall deposit, hrf is the rockfall thickness, ρrock is the rock density (2800 kg/m3), and ϕrf is the porosity of the deposit. Based on visual inspection and the shape of individual rocks, we estimated the deposit porosity to be between 0.1 and 0.3. These values bracket a porosity measured recently in a rockfall deposit in Yosemite National Park, California (Zimmer et al., 2012). We mapped Arf for each rockfall using orthorectified aerial photographs. We used three sources of information to place bounds on the average thickness for the two rockfalls mapped using only the aerial photographs. First, we assumed each rockfall deposit had roughly the same clast size, thickness, and bulk density as the rockfall deposit that still remains on the glacier (R1). Second, we measured the size of 51 rocks on the ice surface within the ablation zone in order to get a representative sample of rock sizes produced by the headwall. Third, we surveyed the thickness of the proglacial ground moraine across a section of R2 (this provides a maximum estimate of R2 thickness because we do not know what percentage of the sediment was produced subglacially). All three methods suggest that the large rockfall deposits were between 0.1 and 0.4 m thick.

The rockfall frequency is more difficult to constrain. There were no large-volume rockfalls during our 3 yr of field work, nor can we directly measure the number of rockfalls entombed within the glacier. Instead, we used two approaches to estimate the range of plausible recurrence intervals for large rockfalls within the cirque.

Although we were unable to assess the amount of rockfall debris hidden within the present-day glacier directly, we were able to estimate the mass of large rockfalls per unit volume of ice (equivalent to the large rockfall concentration) using our estimate of the mass of rock in the three rockfalls we mapped (R1–R3) and an estimate of the volume of ice that melted between 1966 and 2007. The total volume of ice that melted between 1966 and 2007 is 

graphic
where V1966 is the whole-glacier volume in 1966, V2007 is the whole-glacier volume in 2007, t is time, and qice is ice flux at the equilibrium line. The first term represents the change in glacier volume; the second term represents the total ice flux between 1966 and 2007. To calculate an approximate change in volume, we traced the margin of the ablation zone on the 1966 aerial photograph and then re-created the ice surface using linear interpolation (because the ablation zones of land-terminating glaciers are normally convex, linear interpolation underestimates the volume loss). Based on the intersection of the 1966 northern margin with the bedrock topography, we estimate that the 1966 glacier surface was ∼20 m higher than the present-day glacier surface. Between 1966 and 2007, then, we assume the ice flux steadily declined as the glacier thinned, but the magnitude of thinning through time (and thus ice flux, qice[t]) is unknown. Instead, we used the present-day ice flux, determined from our glacierwide surface velocity and ice thickness surveys, as representative of the time period 1966 through 2007 (Sanders et al., 2010). These two methods (linear interpolation and present-day ice flux) provide a lower bound on the total volume of ice that melted over this period, and thus an upper bound on the number of rockfalls buried in the ice.

Using Equation 15, we estimate that at least ∼1.4 × 107 m3 of ice melted between 1966 and 2007. For a time-invariant large-rockfall frequency, the ratio of the current ice volume (∼6.6 × 107 m3; Sanders et al., 2010) to our value for Vmelted implies that up to 14 rockfalls are currently buried inside West Washmawapta Glacier. For a constant ice flux per year of 4.4 × 105 m3/yr, the average age of ice in West Washmawapta Glacier is ∼150 yr. Therefore, we estimate there have been up to 14 rockfalls in the past 150 yr (a recurrence interval of ∼10 yr). This method places a lower bound on the large-rockfall recurrence interval.

In our second approach, used to assess the upper limit of the recurrence interval, we assumed that the three known rockfalls are the only rockfalls present within the cirque. We then estimated each rockfall’s age by measuring the distance along their respective flow lines (using our interpolated 1966 ice surface) from the rockfall back to the headwall. Each distance was then divided by the average deformational velocity (again along each flow line) using the present-day velocity field (it would be more precise to use the integral of the inverse velocity to calculate the traveltime, but given the uncertainties associated with the velocity history, our adopted approach seems adequate). Using this approach, the maximum age of the three rockfalls is ∼250 yr, making the recurrence interval ∼80 yr.

Light Detection and Ranging (LiDAR) Survey

On 24 August 2008, a 313 ± 6 m3 block detached from the west wall of Helmet Mountain cirque and crashed onto the glacier surface. The rock that released during this event remained largely intact after it struck the glacier surface. We were able to determine a precise value for the volume of rock that broke free using repeat terrestrial-LiDAR–derived topographic data of the headwall collected after and, serendipitously, the day before the rockfall. The rockfall volume was determined by collecting ∼2200 points of the immediate rockfall area during each scan using a Riegl Z210 laser scanner at ∼320 m range. Surface models were generated using spherical triangulated irregular network (TIN) surfaces, and a volume was calculated using I-Site Studio 3.4 software. We classify this rockfall in a separate category distinct from daily rockfalls and the “large” rockfall events described previously because it is of intermediate volume and because most of the debris released remained intact. This single rockfall event is equivalent to ∼1.2 mm of headwall retreat if spread evenly over the entire west and south walls (Fig. 2). We cannot constrain the frequency of events of this magnitude, but we can place loose bounds on the recurrence interval by (1) recognizing that one occurred during 3 yr of field work (lower bound) and (2) noting there is one other comparably sized rock on the glacier surface (for an average age of the ice equal to 150 yr, the recurrence interval is 75 yr [upper bound]).

GLACIER

Overview of Glacier

By scouring their beds and undermining their headwalls, glaciers in cirques are the architects of their own accumulation basins. At present, West Washmawapta Glacier continues to modify its cirque by (1) directly eroding the cirque floor and lower headwall and (2) transporting subaerial weathering products away from the headwall.

Our field observations suggest quarrying and abrasion are both actively occurring at the glacier bed. Quarrying faces, many with sets of cracks running perpendicular to the abrasion marks, are found in the northern sector of the proglacial zone. Some patches of bedrock exposed within the last 5 yr exhibit sparkling, glass-like glacial polish. We also made detailed observations in a subglacial tunnel near the front margin. The tunnel was similar to that visited by Anderson et al. (1982) at Grinnell Glacier, Montana. In some places, small blocks lying on the bed could be matched up with voids in the bedrock; in others, rocks embedded in the glacier sole exhibited abrasion marks.

As described previously, rocks released by subaerial weathering frequently plummet from the headwall and either land on the glacier surface or disappear into the bergschrund (as described by Lliboutry, 1994). Unless rock particles come to rest beyond the equilibrium line, they will be buried by the following winter’s snow (in our experience, rock particles rarely bypass the equilibrium line at West Washmawapta Glacier, except for those falling from the easternmost 200 m of the south wall). This fraction of the headwall sediment flux is then transported englacially until, one by one, each rock reemerges down glacier in the ablation zone (as described by Small, 1987). Detritus that enters the bergschrund, on the other hand, may be transported englacially or subglacially (Small, 1987; Lliboutry, 1994). Regardless of source, sediment suspended in the glacier is eventually carried to the proglacial zone and deposited as the ice ablates.

These two sources of sediment (subglacial and subaerial) lead to a distinct depth-rock concentration relationship in the glacier ice (e.g., Hunter et al., 1996). Rocks that enter the bergschrund mix with products of subglacial erosion to create a thin layer near the bed with a high concentration of sediment. In the rest of the glacier—that is, the bulk of the volume—the sediment concentration is relatively low as a consequence of the wide spatial distribution of particles deposited by headwall processes. In this section, we first quantify the englacial sediment flux, and then we demonstrate the pathway by which the greatest amount of sediment in this cirque glacier reaches the margin, and the percentage of the glacier sediment flux that is transported by subglacial streams.

Glacier Measurements and Results

The total glacier sediment flux, Qg, can be partitioned between supraglacial (Qsd), englacial (Qen), glaciofluvial (Qgf), and subglacial till (Qti) transport pathways, such that 

graphic

We begin by describing the methods we used to quantify Qen and return to Qgf and Qti in our discussion of the glacier foreland. The supraglacial and englacial flux, passing through a flux gate of width W and thickness H, aligned perpendicular to ice flow, are given by 

graphic
and 
graphic
where msd is the mass of rock per unit area at the glacier surface, us is surface velocity, Cen is the englacial rock concentration, and u is local velocity. The variables msd and us are a function of horizontal distance y from the edge of the flux gate, whereas Cen and u are a function of y and height z above the bed (a graphical representation of Eq. 17 and Eq. 18 is shown in Fig. 8A). Because Qg is the flux across the boundary between glacier and foreland, rather than the flux past a fixed location, the velocity, u, must be calculated with respect to the front margin of the glacier: u = ub(y) + ud(y,z) – ur(y), where subscripts b, d, and r refer to basal sliding, internal deformation, and margin retreat, respectively. Given the ongoing retreat occurring at West Washmawapta Glacier today, ur is negative, and thus u is greater than the forward velocity of the ice.

We designed our field strategy to constrain Cen(y,z) at West Washmawapta Glacier by sampling the rock concentration within vertical sections at several sites distributed across the width of the glacier. We encountered four distinct ice facies: (1) regelation ice (coarse-grained ice rich in fines overlying the bedrock), (2) basal dispersed (ice near the bed with a relatively large concentration of debris), (3) englacial diffuse (the bulk of the glacier ice where rock particles are less common), and (4) supraglacial debris (rock at the ice surface; all terms modified after Hunter et al., 1996). We consider the regelation layer, distinguished by its large crystals and profuse fine sediment, to be separate from the basal dispersed facies of Hunter et al. (1996). Once Cen(y,z) was known, we calculated Qen by combining it with ub(y) and ud(y,z), which were both taken from the ice dynamics model of Sanders et al. (2010), and ur(y), which we determined by comparing recent and historical aerial photographs. We approximated the double integral in Equation 18 by splitting the englacial flux gate into seven subsections, each of which is centered on the surface velocity vectors shown in Figure 4. Cen(y,z) is assumed constant within each subsection.

Regelation Layer

Regelation ice is accessible along the glacier margin at the base of the ice face (Fig. 8B). To sample the regelation ice, we first cleaned fine sediment and detritus deposits from the sample surface. Then, using a chainsaw, we cut out fist-sized blocks of ice and placed them in a plastic bucket (Fig. 8B). Each sample aliquot was allowed to melt on-site before being vacuum filtered using a hand pump. In the laboratory, we heated each filter in an oven to 500 °C to remove organic debris. The minimum and maximum concentration values include small errors (scale accuracy and minor spilling) associated with measuring sediment mass and water volume (Table 3).

Basal Dispersed

In the subglacial tunnel, where the regelation layer was completely absent, we found an unobstructed view of the basal dispersed ice facies (Fig. 8C). Rocks with varying angularity can be discerned in the photo. The sampling strategy and filter analysis were the same as for the regelation layer, except we weighed rock particles >2 mm in diameter separately. Based on visual inspection of the glacier sole from within the tunnel, we estimate the basal dispersed layer is from 1 to 3 m thick.

Englacial Diffuse

We used 10 boreholes (Dow et al., 2011) and two englacial flux profiles (EFP1 and EFP2 in Fig. 4) to estimate the rock concentration inside the glacier. We classified all rocks within 0.1 m of the borehole walls by size (particles less than a few millimeters in diameter were not common enough to be volumetrically significant) using a fiber-optic camera. In this case, we calculated the rock concentration as the total mass of rock within a hollow cylinder 0.2 m wider than the borehole (borehole diameter was ∼0.12 m). One borehole had an especially high amount of sediment in the lowest ∼3 m, indicating it probably overlapped with the basal dispersed layer.

Due to operational constraints, we did not drill any boreholes in the southern half of the glacier. As an alternative approach, we sampled along two transects of the ice face (Fig. 4; EFP 1 and EFP 2). This approach is roughly equivalent to a vertical transect because (1) the front face is steep, and (2) annual bands dipping up the glacier are clearly visible in the ice (Fig. 1A); this approach is analogous to sampling up section through a geological formation. Samples were collected with a chainsaw (Fig. 8D) and analyzed as described already.

Supraglacial Debris (Qsd)

West Washmawapta Glacier, like most alpine temperature glaciers, has debris (mostly of subaerial origin) scattered across the snow and ice surface. Overall, the supraglacial debris flux (Eq. 17) is a function of the mass of debris on the surface, the area of the glacier, and the average surface velocity (e.g., Mills, 1979). To quantify msd, we mechanically weighed the mass or measured the volume (see methods described previously for the snow apron) of all sediment within four regions ranging in size from 2500 m2 to 2830 m2 (Fig. 4, SD1–SD4). A single rock (located in SD4) weighed between 3000 and 6000 kg and accounted for ∼25% of all sediment measured at the glacier surface.

Table 3 presents minimum and maximum estimates for rock concentration in each of the ice facies. The basal dispersed facies has the highest average concentration. Except for a few outliers, the englacial facies rock concentrations are relatively low (borehole median = 0.7 kg/m3; englacial flux profile median = 0.02 kg/m3). Supraglacial debris content increased from south to north (SD1→SD4) commensurate with the increase in subaerial relief of the headwall source region for each sampling area (Fig. 6).

FORELAND

Overview of Foreland

At West Washmawapta Glacier, the glacier foreland consists of a discontinuous layer of ground moraine incised by anastomosing meltwater streams that, on average, flow parallel to the glacier margin (Figs. 1, 2, and 4). The proglacial stream bankfull channel width is typically from ∼1 to 3 m, and channel depth varies from 0.1 to 0.5 m. Water discharge is on the order of 1 m3/s. Small lakes are also common (Figs. 1A and 4). We observed numerous point sources of fine sediment along the glacier margin, and we cannot eliminate the possibility that sediment-laden seepage emanates from beneath the glacier as well. Pebbles and cobbles reach the glacier foreland by glaciofluvial sediment transport, by rolling down the ice face, and by melt-out at the margin. Most of the glacier foreland is underlain by carbonate rocks, but the morainal debris is mostly siliciclastic (Table 4). A single stream originating from Washmawapta Icefield to the east also contributes water and sediment to the proglacial zone (Figs. 2 and 4). The proglacial streams (both from West Washmawapta Glacier and Washmawapta Icefield) are dry for much of the year, although we cannot say with certainty when they cease to flow, or when they reappear. During our one cold-season visit (8–18 May 2007), the streams and proglacial lakes were dry. At the end of August 2007, the stream discharge emanating from West Washmawapta Glacier was severely diminished (Fig. 9).

In many respects, the glacier foreland behaves like an Alpine sieve: It receives a wide distribution of sediment sizes (ranging from clay to meter-wide boulders) from the glacier, yet, under all but the most extraordinary circumstances, the proglacial streams are not competent enough to transport the coarse fraction of sediment. Over time, the glacier foreland should coarsen as proglacial streams and overland flow remove the fines. This appears to be taking place; within the northern half of the proglacial zone, we observed an unmistakable decrease in the quantity of fine sediment as one moves away from the glacier margin. The absence of meltwater streams in the southernmost proglacial zone reduces this effect.

We used the volume of sediment stored in the proglacial zone to constrain the flux of sediment transported in the near-bed region of the glacier (where our field measurements were the most spatially limited) and, as a result, gained a more complete assessment of the total glacier sediment flux, Qg. To do this, it was necessary to revisit Equation 9, the budget relation for the foreland, and Equation 16, which separated Qg into four basic transport pathways. We assume the component of Qti arising from till deformation (forward motion of the till) is dwarfed by till exposure during rapid retreat of the front margin. Recall that the proglacial storage term (Sf), furthermore, can be subdivided into two elements (Eq. 10): ground moraine (Sgm) and proglacial lakes (Slk). It follows that Equation 9 can be rewritten 

graphic
with Qf = Qc. Although we treat the lakes as a separate entity, the stream beds are considered part of the ground moraine.

Two primary unknowns guided our efforts to investigate the proglacial zone: the amount of sediment deposited as ground moraine and in proglacial lakes during recent retreat, and the amount of sediment transported out of the basin by proglacial streams.

Glacier Foreland Measurements and Results

Ground moraine. As with the large rockfalls, we tried to determine the volume of till in the proglacial zone by constructing a map of moraine coverage and thickness. Mapping the area covered by till (Agm) in ArcGIS™ is straightforward. Using a high-resolution aerial photograph (pixel spacing = 0.5 m) to distinguish between exposed bedrock (pixels with a blue-gray cast) and sediment coverage (brown cast), we subtracted areas devoid of till. The total area covered by till is 2.0 ± 0.2 × 105 m2. Visually, the till deposits appear to have a similar porosity to the large rockfall deposits, ranging from ∼0.3 in the north to ∼0.1 in the south.

The till thickness (hgm), however, proved much more difficult to measure. In areas of sparse till cover, we could estimate values for hgm by measuring thickness directly where gaps in the sediment revealed bedrock (Fig. 4, GMP1 and GMP2; Table 4). The southern half of the glacier foreland has regions that are completely mantled by till, and in these areas this approach was not feasible. We performed four ground-penetrating radar surveys, but these produced inconclusive results and will not be discussed. For the northern half of the proglacial zone (48% of total foreland area), we conservatively estimate, based on our ground moraine thickness profile data, that the average till thickness is between 0.05 m and 0.6 m (note that 0.05 m is well below the average thickness measured along GMP1 and GMP2 (0.17 m; Table 4). For the southern half, we are forced, instead, to make an educated guess as to the thickness of the unsurveyed ground moraine. We believe, from the following observations, that the southern ground moraine average thickness is between ∼0.2 m and 2 m. Two meters may at first seem too small, but we are confident this is adequate for two reasons. First, bedrock exposures, while less abundant in the southern half than the northern half, are still common (especially along the glacier margin). The amplitude of well-exposed proglacial bedrock topography in the northern half is only ∼1–2 m over a distance of several meters, and thus till pockets should not be much thicker than this. Second, because we are using an average thickness to calculate till volume, the many thinly mantled areas offset many of the regions of abnormally thick pockets of till that may exceed 2 m. The total sediment stored as ground moraine, using the assumptions just described, is 3.2 × 105 (5.5 × 104–6.4 × 105) tons.

The lakes in the glacier foreland provide a second storage site for sediment (Slk). To constrain the quantity of sediment trapped in the proglacial lakes, we performed a cursory survey of sediment thickness in the two lakes immediately downstream from stream gauge 1 (SG1; Fig. 4). It is not immediately obvious whether the lake sediment originated from the headwall or cirque floor, but three small sediment cores analyzed at the University of Minnesota Limnological Research Center consisted primarily of fine sediment (clay and silt) with a bulk density of 2000 kg/m3. We therefore tentatively attribute the lake sediment to subglacial abrasion processes. Based on the aerial photographs, it appears these two lakes formed and then began to trap sediment in 1994. We also assume that lakes downstream of the two we surveyed contain deposits with similar thicknesses to those we did measure. Our surveys indicate that a total of 4160 (2470–25,000) tons of sediment is stored in the lakes.

Proglacial streams. At present, a single stream carries all sediment leaving Helmet Mountain cirque. This stream has four sources of sediment: scour of its own channel fill or banks, sheetwash from the glacier foreland, West Washmawapta Glacier, and Washmawapta Icefield. Whereas the first three sources are an integral part of our Helmet Mountain sediment budget, the fourth is not. As such, we installed two gauging stations (Fig. 4), one to measure the total flux from the basin (SG2) and the other to remove the contribution from Washmawapta Icefield (SG1). Water discharge of West Washmawapta Glacier is equal to the discharge at SG2 minus the discharge at SG1.

The total sediment mass conveyed past SG2 (MSG2) over the course of the field season is 

graphic
where t1 and t2 are the start and end dates of the monitoring record. Qss, Qbl, and Qdl represent suspended, bed, and dissolved load (all with units of mass per time), respectively. Qss, furthermore, is a function of water discharge (qSG2) and suspended sediment concentration (Css), such that 
graphic

In this formulation, we assume the surface value of Css is a good estimate of the average in the water column because the stream is very turbulent in the reaches adjacent to each stream gauge. To quantify Qss, we performed a combination of stream gauge monitoring and suspended sediment sampling between 29 June 2007 and 28 August 2007. During this time period, we did not measure bed-load transport (Qbl) directly and will instead use results from a previous study at Hilda Glacier (located 125 km north of our site) to assess the errors associated with missing this component of the sediment flux (Hammer and Smith, 1983). Hilda Glacier is in an east-facing, 1.7-km-wide cirque composed of dolomite, quartzite, shale, and limestone (Hammer and Smith, 1983). At the time of measurements (1977), Hilda Glacier was 2.5 km long and terminated at 2170 m elevation (West Washmawapta Glacier is ∼1 km long and terminates at ∼2350 m). Hammer and Smith (1983) reported that dissolved load contributions to the sediment flux were insignificant (1.5%–3% of total), despite the presence of dolomite and limestone bedrock. Water conductivities of the meltwater stream at Hilda Glacier (40–70 mS/cm) were also similar to those measured at SG2 (50–60 mS/cm). We assume, therefore, that Qdi can be neglected.

At SG1, we monitored stage, conductivity, and turbidity every 15 min using a Druck PDCR 1230 pressure transducer, Campbell Scientific CS547A conductivity meter, and Campbell Scientific OBS 3+ turbidity sensor, respectively. The stream gauge SG2 was identical to SG1 except that treacherous channel conditions precluded the use of a pressure transducer to measure stage. Instead, we installed a Campbell Scientific SR50 Sonic Ranging Sensor above the stream using a polyvinyl chloride (PVC) mount attached to the bedrock channel bank with steel cables. We dangled each turbidity sensor from a PVC-pipe apparatus reminiscent of a fishing pole. We intended to use the relationship between turbidity and suspended sediment concentration to increase the temporal resolution of sediment flux passed each gauge; unfortunately, at both locations, all our turbidity data were rendered useless by algae growth on the sensor.

In order to use stage as a proxy for discharge, we developed independent discharge rating curves for each stream gauge. We measured discharge simultaneously at SG1 and SG2 using the salt dilution technique (described by Kite, 1994) roughly every hour from 8:00 a.m. to 8:00 p.m. on 31 July 2007, 4:00 p.m. to 10:00 p.m. on 1 August 2007, and 9:00 a.m. to 8:00 p.m. on 8 August 2007. We calculated 98% confidence bounds on our season-long discharge records using a Monte Carlo bootstrap (e.g., Efron and Gong, 1983).

A malfunction at SG2 erased the gauge data acquired between 30 June 2007 and 12 July 2007. As a result, we can only estimate bounds on the early season SG2 discharge using the relationship between discharge at SG1 and SG2 from the second half of the summer (r2 = 0.94). A strong correlation is expected because (1) discharge at SG2 includes discharge at SG1 and (2) the physical processes and climate variables controlling melt on both glaciers (and foreland snow) are very similar. For reasons that are not yet clear, stage data from between 12 July and 25 July were distorted by instrument problems. To avoid this issue, we chose instead to use the relationship between conductivity and discharge from the second half of the melt season to determine discharge at SG1, SG2, and from the glacier during this time interval.

During each salt-dilution discharge experiment, we also collected suspended sediment samples from the stream surface using 250 or 500 mL bottles. These hourly samples were complemented at SG2 by samples collected with an ISCO 6712 portable sampler (24 bottle capacity) that we installed in late June 2007. The ISCO sampler ran in our absence from 23 June 2007 to 15 July 2007 (samples taken between 23 June and 29 June preceded our discharge record and were not included in our calculation). At the time of installation, we positioned the intake tube ∼100 mm beneath the water surface. We filtered and measured each suspended sediment sample using the same procedure as described previously for englacial ice samples.

Our measurements demonstrate that daily discharge is primarily a function of air temperature (e.g., Hammer and Smith, 1983), although the seasonal peak in daily discharge (and instantaneous discharge, not shown) at SG2 occurred on July 19 amidst a heavy downpour (Figs. 9A–9B). We suspect storms of comparable magnitude (compare 8–11 August 2007) did not cause an equivalent discharge response later in the season because the snow cover was much reduced and the daily mean temperatures tended to be lower.

Suspended sediment concentration and Qss both exhibit a major early season peak—a peak so severe that approximately one third of the seasonal total occurred in just 2 d (Fig. 9C, 4 and 5 July 2007). This pattern of early season peak sediment flux has been seen at other glaciers as well (Ostrem et al., 1967). As a consequence of the low sampling frequency early in the record, our sampling may have missed a much larger peak (the peak value, 0.68 kg/m3, was collected at midnight, a time at which concentration typically approached the daily minimum in the rest of the record; see Fig. 10). During the second half of the season, suspended sediment concentration fluctuated daily between 0 and 0.1 kg/m3 unless interrupted by storms (Fig. 9C); peak concentrations occurred in the early afternoon (∼2:00 p.m.; Fig. 10). A limited set of suspended sediment concentration measurements (41 total) made in the proglacial stream during summer 2006 had similar values (mean of 0.06 kg/m3 and standard deviation of 0.06 kg/m3) to those made in 2007 (mean of 0.04 kg/m3 and standard deviation of 0.05 kg/m3; Fig. 9C). Our measurements of suspended sediment concentration at SG1 revealed that an insignificant amount of sediment enters our budget region from the east side of the basin (Qwi ∼ 0). Thus, it appears that the lake shown with an asterisk in Figure 2 is a very efficient sediment trap.

Given the temporal resolution of, and frequent gaps in, our discharge and suspended sediment concentration records, we elected to use daily discharge and the median suspended sediment concentration value for each period of measurement (rather than our higher frequency measurements) to calculate suspended sediment flux. Our reasoning is thus: First, daily discharge values reduce the weight of erroneous stage measurements. Second, during the first half of the field season, we only sampled suspended sediment concentration once a day. Third, we do not have direct measurements of discharge at SG2 before 12 July 2007.

ESTIMATION OF WEST WASHMAWAPTA GLACIER SEDIMENT FLUX AND THE EROSION RATE OF HELMET MOUNTAIN CIRQUE

Glacier Sediment Flux and Erosion Rate

We now return to Equation 19 to place bounds on the glacier sediment flux (Qg). We have already shown that the contribution from Washmawapta Icefield is minimal (Qwi ≈ 0) because the sediment produced by the icefield is deposited in a lake outside Helmet Mountain cirque. With this in mind, 

graphic
with terms as before. Using the values shown in Table 5, Qg is 6440 (1180–14,930) tons/yr. Given that our estimate for the quantity of sediment transported englacially and supraglacially (Qen and Qsd) is 590 (160–1500) tons/yr combined, it is clear that the vast majority of sediment transfer occurs in the near-bed region of the glacier. It is also worth reemphasizing that Qg is a measure of sediment leaving the glacier, not the cirque, and because the glacier domain has shrunk in recent decades, the Qti component of Qg (Eq. 16) can be positive without any sediment actually moving anywhere. If all fine-grained sediment in subglacial streams is either trapped by lakes or transported out of the cirque, the glaciofluvial sediment flux is given by 
graphic

The glaciofluvial flux, then, using values from Table 5 is 970 (230–3860) tons/yr. We can also use direct measurements of suspended sediment concentration taken from a glacier outlet stream (denoted by an “x” in Fig. 4) to calculate a second, independent estimate of Qgf. Based on 31 individual samples taken over a wide range of discharges, the average suspended sediment concentration of water emanating from the glacier is 0.06 kg/m3. The total discharge from West Washmawapta Glacier (the difference between the cumulative discharge measured at each stream gauge) was between 6 × 104 and 2 × 105 m3, implying roughly 60–200 tons of sediment came from West Washmawapta Glacier. This value is lower than the estimate we calculated previously (970 tons/yr), perhaps because it neglects any early season peaks (Fig. 9C), but given the size of our errors and the simplicity of the approach, the similarity is encouraging.

In our calculation of the glaciofluvial stream flux (Qgf), we neglected any contribution to the stream load from sheetwash occurring in the glacier foreland, an approximation that is not strictly correct. We suspect that fine sediment is winnowed from the ground moraine during rainstorms and as the winter snow cover melts each summer. The “proglacial sheetwash flux,” (Qsw), therefore, should be subtracted from Qc before calculating Qgf with Equation 23. We attempted to quantify Qsw by sampling suspended sediment concentration simultaneously at both stream gauges and at one primary West Washmawapta Glacier outlet stream on a sunny day (31 July 2007) and rainy day (8 August 2007) (see Fig. 4; the outlet stream is labeled with an “x”). On a third day (16 August 2007), we only measured suspended sediment concentration at the glacier outlet stream; these data were compared to samples taken concurrently by the autosampler. If we assume that the contribution from sheetwash is negligible on the two sunny days (by midsummer, very little snow is left in the foreland), then on the rainy day, any reduction in the relative proportion of Qgf to Qc (for that day) must be caused by contributions from sheetwash. Because we only measured one (albeit large) outlet stream, we must also assume that the sediment flux measured there is representative of the glacierwide total. On the sunny days, between 83% and 96% of the sediment came from the outlet stream, whereas on the rainy day, the proportion dropped to 36%, implying ∼0.75 tons of sediment was transported to the streams by sheetwash on a single rainy day. If we extrapolate this value to a yearly total by multiplying by the number of rainy days (∼15 d; Fig. 9A) and assuming melting snow contributes a similar amount of runoff, the proglacial sheetwash flux is roughly 20 (10–50) tons/yr. Although nonzero, the present-day magnitude of Qsw is nevertheless rather small (Table 6).

Estimating the production rate of sediment beneath a glacier is difficult because the glacier bed is hard to access. Some fraction of any recently eroded sediment is flushed from the glacier by glaciofluvial streams, and some fraction is added to storage. Typically, the problem is made tractable by assuming that the fraction added to storage is negligible (e.g., Warburton and Beecroft, 1993; Riihimaki et al., 2005). For a “hard-bedded” glacier (meaning subglacial till is absent or exceedingly thin) with a stable margin, this assumption implies that a balance exists between the quantity of sediment that the glacier erodes from bedrock and the amount of sediment subglacial streams evacuate over a meaningful time interval (which is usually taken to be a year) and that sediment melting out of the ice face can be ignored. Under this set of assumptions, Pg = Qgf, which we solved for previously herein. At Helmet Mountain cirque, we cannot make this assumption: West Washmawapta Glacier is retreating and is partly underlain by till. Instead, we will use the volume of sediment in the glacier foreland, as well as the rate of retreat, to place limits on Pg.

We begin by assuming that the foreland moraine forms as supraglacial sediment, englacial sediment, and subglacial till are deposited during glacial retreat; this sediment is then later winnowed by sheetwash: 

graphic

Substituting the right -hand side of Equation 23 into Equation 11, and rearranging, we get 

graphic

As explained already, the change in glacier storage (ΔSg) is fundamentally unknown because the glacier bed is inaccessible. Nevertheless, at West Washmawapta Glacier, a fraction of ΔSg arises from either thinning or thickening of till and/or from a general increase in the concentration of debris in the glacial ice (collectively referred to as ΔSgr). A second fraction arises from retreat of the glacier margin (ΔSgo), such that 

graphic

Whether or not till at the glacier bed is thinning or thickening is hard to say. On the one hand, if we return to Figure 9C and note the large decline in suspended sediment concentration with time, despite quasi-steady daily discharges from West Washmawapta Glacier (Fig. 9B), it appears the subglacial sediment reservoir accessible to subglacial streams is exhausted by late summer (e.g., Ostrem, 1975; Collins, 1979, 1989). If suspended sediment concentration were a function of transport capacity, rather than supply, late-summer sediment transport should be similar to early summer. We do not mean to imply all sediment at the glacier bed is removed, but rather the fraction of sediment contacted by subglacial streams within a single summer season is removed. On the other hand, our borehole video camera captured footage of sediment that looked like till deposits at the glacier bed (we were not able to estimate thickness or spatial coverage), and thus it is clear that not all sediment produced by the glacier is being removed.

The change in storage due to glacier retreat is given by 

graphic
with γu approximated by 
graphic
where, as before, ur is the retreat velocity, and U is the total forward velocity. Between 1949 and 2007, γu was ∼0.3. Substituting Equations 26 and 27 into Equation 25 leads to 
graphic

If ΔSgo were zero (meaning that storage changes only because of retreat), then Equation 29 and the values listed in Table 5 imply a subglacial sediment production rate of Pg = –320 (–7490–4620) tons/yr. By definition, Pg cannot be less than zero. Thus, three hypotheses are consistent with our budget data: (1) till thickness and debris concentration are increasing, at a total mass accumulation rate as high as 7660 tons/yr, but bed erosion is negligible; (2) the glacier erodes its bed at a negligible to moderate rate (0–4620 tons/yr), and the thickness of basal till and concentration of englacial debris remain approximately constant; or (3) bed erosion and mass accumulation both occur, at unknown rates, but the former exceeds the latter by as much as 4620 tons/yr.

The first hypothesis can be rejected because several lines of evidence demonstrate that the limiting case of negligible bed erosion (Pg = 0) is almost certainly wrong. First, the subglacial and proglacial streams contain a significant amount of suspended sediment (Table 5). Second, Sanders et al. (2010) demonstrated that West Washmawapta Glacier is sliding above the riegel and along the northern and eastern margins. Third, exposed bedrock in the glacier foreland appears striated, polished, or quarried.

An additional constraint, independent of Equation 29, comes from our estimate of total sediment deposited in the glacier foreland since 1949. In this period, the foreland has received sediment at an average rate of 3830 (–7000–10,820) tons/yr in excess of the headwall sediment flux. In one end-member interpretation, which requires no change to Equation 29, all of this excess sediment was till covering the glacier bed (with a minimum average thickness of ∼0.5 m) that simply transferred from the glacier to the foreland moraine as the ice edge retreated (the term Qti in Eq. 16). We regard this interpretation as improbable because cavities and tunnels near the glacier margin reveal only a patchy cover of loose material on bedrock surfaces. A second end-member interpretation is that our estimate of Qen (Table 5) is far too low, probably because of difficulty assessing the rock concentration of basal ice layers and past rates of sliding motion. If we assume that the foreland moraine originated entirely as sediment emerging from the ice, rather than from subglacial till, we can increase our estimate of Qen by an amount equal to the excess sediment flux, for a new total of 4420 (–6840–12,320) tons/yr. Denoting this “missing flux” Qen*, Equation 29 becomes 

graphic

Taking values from Table 5, this relation yields Pg = 2470 (–11,990–12,220) tons/yr, assuming ΔSgo = 0.

The most likely scenario is intermediate between these two end members, in which the glacier bed consists of patches of bare rock amid patches of sediment. The northern foreland displays such a mix. Using this region’s average sediment thickness (∼0.17 m; Table 4) gives a Pg of 1240 tons/yr. Because some of the sediment in this case must have derived from the ice, the average thickness was probably less than 0.17 m and hence Pg exceeded 1240 tons/yr. Our best guess range is thus Pg = 1240–2470 tons/yr, while values as low as 0 or as high as 12,220 tons/yr cannot be excluded by our budget (Table 6).

Converting Pg values to mean erosion rates by normalizing them to the glacier area indicates that subglacial erosion occurs at ∼0.5–0.9 mm/yr (with outer limits of 0.0–4.6 mm/yr). Thus, despite its modest dimensions (∼1 km2), West Washmawapta Glacier is eroding its bed at a rate comparable to much larger temperate valley glaciers (e.g., Hallet et al., 1996; Koppes and Montgomery, 2009).

The erosion rates reported here do not include any contribution from bed-load transport that may have passed SG2. At Helmet Mountain cirque, sediment processes in the proglacial stream are more complex than previously studied elsewhere (Ostrem et al., 1967; Ostrem, 1975; Hammer and Smith, 1983; Riihimaki et al., 2005) because of the vast quantities of sediment involved and because the foreland is undergoing a rapid, transient response to recent retreat of the glacier. Even when proglacial streams are relatively stable, sediment transport rates are notoriously difficult to measure (Ostrem, 1975; Hammer and Smith, 1983), but at Helmet Mountain, numerous bifurcations, a sequence of small lakes, and perilous conditions at the basin outlet made some measurements nearly impossible. Small deltas, and other coarse deposits observed in the lakes, indicate that a large portion of bed load debouched by the glacier is immediately trapped, but we cannot eliminate the possibility that scour occurs early and late in the melt season as lake levels wane. Furthermore, previous studies of sediment transport in proglacial streams have measured a wide range of bed-load transport rates, both as absolute quantities and as a fraction of the total flux (Ostrem, 1975; Beecroft, 1983; Hammer and Smith, 1983; Gurnell et al., 1988; Warburton, 1990; Pearce et al., 2003; Loso et al., 2004; Riihimaki et al., 2005). At Hilda Glacier (described previously herein), Hammer and Smith (1983) determined that bed load accounted for 57% of the total stream flux. At their site, however, there were no obvious sediment traps between the outlet stream and the gauging station. Nevertheless, if we apply this bed-load fraction at Helmet Mountain cirque, it suggests that we failed to measure ∼860 (110–2470) tons/yr of sediment (Table 5), equivalent to an average rate of 0.3 mm/yr of bedrock lowering beneath the glacier (Table 7). This is a considerable overestimation of the bed-load contribution because lakes are present for most of the melt season.

Headwall Sediment Flux and Erosion Rate

Given the highly fractured rock typical of the Canadian Rockies, it is not surprising that Helmet Mountain is rife with rockfall. On an annual basis, the subaerial headwall produced 1640 (250–7950) tons of sediment, equivalent to 1.2 (0.2–5.9) mm/yr of headward retreat of the south and west walls. The majority of this sediment came from small rockfalls and cornice failures (1430 [230–7380] tons/yr). The south wall (northern aspect) produced 350 (60–1730) tons/yr, and the west wall (eastern aspect) produced 1080 (170–5650) tons/yr. The sediment yield, however, for each section of the wall was nearly equivalent: ∼5.7 tons/km2/yr for the south wall and ∼5.6 tons/km2/yr for the west wall. Large rockfalls, while non-negligible, only amount to ∼3% of the total headwall sediment yield. As mentioned already, we were not able to distinguish between rocks that free fell off the headwall from those transported in snow avalanches. Snow avalanches, more often than not, originated as cornice failures from the cirque rim. We place qualitative estimates for the fraction transported by snow avalanches, based on numerous visits to fresh avalanche deposits as compared to the snow apron at season end, at 15%–50%. We believe that, based on our observations of the snow from cornice failures shifting from white to brown as it descended the wall, these events may be the most important geomorphic process removing rock mass from the subaerial headwall. Indeed, one of a few cornices still left in late August clung to the cliff above one of the most sediment-bare sections of snow apron. We attempted to trigger a cornice failure late in the summer by sawing through it with high-grade steel wire, but the effort failed.

Synthesis of Sediment Budget and Implications for Cirque Evolution

Our measurements demonstrate that even in the current, relatively warm climate, Helmet Mountain cirque continues to enlarge. As described herein, the glacier has been eroding its bed at an average rate of ∼0.5–0.9 mm/yr over roughly the past century (Table 7); likewise, the headwall has retreated horizontally at ∼1.2 mm/yr (on average) over this time span. Thus, our best estimates for the average rate of vertical and headward incision imply they are roughly equivalent (on the order of 1 mm/yr). However, given the size of our uncertainties, it is also possible that the headwall retreat rate significantly outpaced lowering. In detail, the subglacial erosion rate is most likely far from spatially uniform. Sanders et al. (2010) inferred that basal sliding reaches a minimum in the center of the cirque basin. As erosion rate is generally thought to be a function of sliding rate (Hallet, 1979, 1996), the results of Sanders et al. (2010) imply that the area of active erosion is much smaller than the full glacier footprint. In this respect, headward erosion may only outpace the average vertical incision rate and actually be slower than the maximum rates occurring in the cirque. Our measurements, furthermore, do not allow us to estimate the rate of headwall backwearing occurring below the glacier surface. If undermining of the headwall is suppressed during warm climate intervals, the headwall slope may, on average, be diminishing unless a separate process is driving bedrock fracturing at the base of the wall (e.g., Hooke, 1991).

It is also evident that the sediment production and routing are much more complicated than frequently assumed for cirques (e.g., Fenn, 1987; Heimsath and McGlynn, 2008). There does not seem to be a relationship between production of sediment by the headwall and the flux of rock at the glacier surface (Table 5). The near-bed ice may be similarly devoid of rock (Table 5, regelation and basal dispersed facies), implying that most headwall-sourced rocks must impact the bed and undergo rapid comminution (Lliboutry, 1994). At our site, the net flux from the cirque (Qc, Eq. 1) implies a spatially averaged subglacial erosion rate of 0.2 (0.03–0.7) mm/yr, which is a good approximation for our best guess range (0.5–0.9 mm/yr, Table 7) derived using the full sediment budget (Eq. 30), but only if the classic assumption that changes in storage at the glacier bed are minimal is correct. Thus, in summer 2007, calculating the glacierwide erosion rate using only the sediment transported in streams would lead us to underestimate the actual erosion rate by roughly a factor of 2. Although we are hesitant to place too much emphasis on these values because of the large errors associated with our techniques, they do nevertheless highlight the important role played by storage in sediment budget studies.

The large volume of sediment stored in the glacier foreland also reveals the inability of meltwater streams to transport sediment in near-divide regions of alpine landscapes relative to their icy counterparts. Our modified value of the englacial flux dwarfs the quantity of sediment leaving the foreland (Qc); ∼5140 tons of rock are being deposited each year in excess of the total suspended load (if we include our bed-load flux estimate, the volume deposited is reduced to 4280 tons per year). Furthermore, approximately one third of the fine-sediment (clay and silt) is trapped by the lakes (Table 5). It appears that, until a readvance of West Washmawapta Glacier, most of the sediment produced by the headwall and at the glacier bed is stuck at high elevation.

The sediment budget values listed in Tables 5 and 6, while appropriate for the time period 1949–2007, will not apply if West Washmawapta Glacier expands beyond the foreland-bounding cliff or retreats behind the crest of the riegel (Fig. 4). At present, the ongoing, monotonic decrease in size since at least 1949 suggests the latter is much more likely than the former. Based on the average retreat rate between 1949 and 2007, we predict this margin will reach the riegel crest in 30–80 yr. Once behind the riegels crest, a lake will begin to form. When this occurs, all sediment, save that which remains suspended in the lake water, will be trapped. It is difficult to predict what effect this transition will have on streamborne sediment, because the daily and seasonal stream hydrograph may change concomitantly with the caliber of sediment introduced upstream. In qualitative terms, we offer the following conjectures: (1) Storage of rock mass within the cirque will increase dramatically, (2) the coarse fraction of sediment in the stream will shrink, and potentially vanish, (3) sheetwash will become the primary erosional mechanism over most of the present-day proglacial zone (the outlet stream from the notional lake will form on the north side of the riegel and bypass most of the foreland sediment), (4) glacial erosion will cease, and (5) rock-wall processes will become the principal means by which the cirque continues to evolve.

A comprehensive sediment budget of a cirque, such as that presented here, has never before been performed. Erosion rates within cirques are also rarely calculated. Our best-guess erosion rates fall near the middle of the range presented in Table 1, and are roughly equivalent to several cirques located at lower latitudes in the American Rocky Mountains (Sangre de Cristo and Front Range, Colorado). West Washmawapta Glacier also appears to conform to relationships developed for larger glacial systems. The proglacial stream suspended sediment flux at West Washmawapta Glacier is in accord with a compilation prepared by Gurnell et al. (1996) that compares suspended sediment flux to catchment area. Moreover, the cirque-wide sediment yield, given the current percent glacier cover (58%, Table 2), falls just slightly below the best-fit relationship presented in Guymon (1974). Insofar as our results are typical of cirques and cirque glaciers elsewhere, it would appear that smaller glaciers are fundamentally the same as their larger brethren.

The size of our errors, and the infrequency with which cirque erosion rates are measured, does leave many questions unanswered. Our sediment fluxes, for example, suggest the cirque is expanding proportionally, a scenario at odds with that proposed for many cirques elsewhere based on analyses of range-scale topography (Beaty, 1962; Oskin and Burbank, 2005; Naylor and Gabet, 2007). In Fiordland, New Zealand, Shuster et al. (2011) showed that the near-divide regions (including cirques) were the last part of the landscape to develop. Given the rates calculated here and the size of Helmet Mountain cirque, it too could have formed completely in the last million years. Are our measured rates typical, or is the present day unrepresentative of the long-term evolution? Questions such as these highlight our limited collective understanding of cirque evolution over time scales ranging from thousands to millions of years, and point toward new directions in cirque studies (Shuster et al., 2011).

CONCLUSION

We constructed a sediment budget for an alpine cirque containing a small glacier. Over the past half-century, headward retreat and vertical incision have been roughly equivalent. We estimate that subaerial headward retreat occurred at ∼1.2 (0.2–5.9) mm/yr. Vertical incision by the glacier amounted to ∼0.5–0.9 (0.0–4.6) mm/yr, if the proglacial stream sediment flux measured over one melt season is representative of multidecadal time scales. Although our best-guess erosion rates do not support the headward retreat idealization of the cirque buzz saw hypothesis (Daly, 1905), our errors are such that headwall back wearing may be significantly outpacing vertical incision. Headwall back wearing primarily occurs by small-scale rockfalls and sweeping by snow avalanches. Of the total glacier sediment flux, the overwhelming majority is transported near the bed by glaciofluvial streams or in the basal ice layers. Small proglacial lakes trap about one third of the fine-sediment flux from West Washmawapta Glacier. In 2007, the only proglacial stream exiting Helmet Mountain cirque transported between 80 and 1860 tons of sediment, a third of which left the cirque in a period of 2 d early in the melt season. Our study highlights the need for further field-based investigations of cirques, and particularly of subglacial erosion processes.

LIST OF VARIABLES

Ac plan-view area of the cirque

Agm proglacial ground moraine plan-view area

Arf individual large rockfall plan-view area

Cen englacial rock concentration

Css suspended sediment concentration in proglacial stream

forumla spatially-averaged cirque-wide erosion rate

hgm ground moraine thickness

hrf large rockfall thickness

hrock short-axis length of individual rock

H flux gate depth

Ic sediment flux into the cirque

If sediment flux into the foreland domain

Ig sediment flux into the glacier domain

Ih sediment flux into the headwall domain

lrock long-axis length of individual rock

msd supraglacial debris mass per unit area

MSG2 total sediment mass measured at stream gauge 2

Mrf individual large rockfall mass

frf large rockfall event frequency

nrf number of large rockfall events

Ph headwall domain sediment production rate

Pg glacier domain sediment production rate

Pf foreland domain sediment production rate

qice ice discharge

qSG2 proglacial stream discharge at stream gauge 2

Qc sediment flux out of the cirque

Qbl bed-load flux in proglacial stream

Qdl dissolved load flux in proglacial stream

Qen englacial sediment flux

Qen* component of englacial sediment flux potentially missed during sampling

Qf sediment flux out of foreland domain

Qg sediment flux out of glacier domain

Qgf glaciofluvial sediment flux

Qh sediment flux out of headwall domain

Qrf large rockfall sediment flux

Qsd supraglacial debris sediment flux

Qss suspended sediment flux in proglacial stream

Qsw sheetwash sediment flux

Qti subglacial till sediment flux

Qwi Washmawapta Icefield meltwater stream sediment flux

Sc mass of sediment stored in the cirque

Sf mass of sediment stored in the foreland domain

Sg mass of sediment stored in the glacier domain

Sgo change in Sg independent of glacier retreat

Sgr change inSg caused by glacier retreat

Sgm mass of sediment stored in the ground moraine

Sh mass of sediment stored in the headwall domain

Slk mass of sediment stored in the proglacial lakes

Tobs time of observation

u total glacier velocity relative to the front margin

ub basal sliding velocity

ud deformational velocity

ur glacier margin retreat rate

us glacier surface velocity

U total forward glacier velocity

Vmelted ice volume melted

Vrock individual rock volume

V1966 1966 West Washmawapta Glacier volume

V2007 2007 West Washmawapta Glacier volume

wrock intermediate-axis length of individual rock

W flux gate width

y horizontal distance orthogonal to flow across flux gate

z vertical distance above glacier bed

φrf large rockfall deposit porosity

γrock individual rock volume parameter

γu ratio of margin retreat velocity to forward ice velocity

ρrock bedrock density

We are indebted to Tom Tobin, Jeffrey Kavanaugh, Christine Dow, Justin Beckers, Jeffrey Moore, Luke Sanders, Andrew Bliss, Yosuke Adachi, Vernon Legakis, Chris Miller, Leigh Johnson, Dom Galic, Sabrina Belknap, Ian Nicholson, Elena Evans, Jenny Cooper, and Mary Dain for field assistance, CH2M Hill (formerly Veco) Polar Services for logistical support, and William Dietrich for his comments on an earlier draft of the manuscript. We thank Simon Brocklehurst, Brad Johnson, and Emmanuel Gabet for their thorough and thoughtful reviews. Don McTighe, Craig Ward, Paul Quanstrom, and Ryan Harris of Alpine Helicopters (Golden, British Columbia) are commended for their professionalism and generosity. Brett Degner generously helped draft several of the figures. Claire Le Gall translated de Martonne (1901) from the French. This research was partially funded by National Science Foundation Geomorphology and Land Use Dynamics grants awarded to Cuffey and MacGregor.

Science Editor: Christian Koeberl
Associate Editor: Anne Jefferson