Joseph S. Walder

WATER FLOW THROUGH TEMPERATE GLACIERS

Understanding water movement through a glacier is fundamental to several critical issues in glaci- ology, including glacier dynamics, glacier-induced floods, and the prediction of runoff from glacierized drainage basins. To this end we have synthesized a conceptual model of water movement through a temper- ate glacier from the surface to the outlet stream. Pro- cesses that regulate the rate and distribution of water input at the glacier surface and that regulate water movement from the surface to the bed play important but commonly neglected roles in glacier hydrology. Where a glacier is covered by a layer of porous, perme- able firn (the accumulation zone), the flux of water to the glacier interior varies slowly because the firn tempo- rarily stores water and thereby smooths out variations in the supply rate. In the firn-free ablation zone, in con- trast, the flux of water into the glacier depends directly on the rate of surface melt or rainfall and therefore varies greatly in time. Water moves from the surface to the bed through an upward branching arborescent net- work consisting of both steeply inclined conduits, formed by the enlargement of intergranular veins, and gently inclined conduits, spawned by water flow along the bottoms of near-surface fractures (crevasses). Engla- cial drainage conduits deliver water to the glacier bed at a limited number of points, probably a long distance downglacier of where water enters the glacier. Englacial conduits supplied from the accumulation zone are quasi steady state features that convey the slowly varying water flux delivered via the firn. Their size adjusts so that they are usually full of water and flow is pressurized. In contrast, water flow in englacial conduits supplied from the ablation area is pressurized only near times of peak daily flow or during rainstorms; flow is otherwise in an open-channel configuration. The subglacial drainage system typically consists of several elements that are distinct both morphologically and hydrologically. An up- glacier branching, arborescent network of channels in- cised into the basal ice conveys water rapidly. Much of the water flux to the bed probably enters directly into the arborescent channel network, which covers only a small fraction of the glacier bed. More extensive spatially is a nonarborescent network, which commonly includes cav- ities (gaps between the glacier sole and bed), channels incised into the bed, and a layer of permeable sediment. The nonarborescent network conveys water slowly and is usually poorly connected to the arborescent system. The arborescent channel network largely collapses during winter but reforms in the spring as the first flush of meltwater to the bed destabilizes the cavities within the nonarborescent network. The volume of water stored by a glacier varies diurnally and seasonally. Small, temper- ate alpine glaciers seem to attain a maximum seasonal water storage of ;200 mm of water averaged over the area of the glacier bed, with daily fluctuations of as much as 20 -30 mm. The likely storage capacity of subglacial cavities is insufficient to account for estimated stored water volumes, so most water storage may actually occur englacially. Stored water may also be released abruptly and catastrophically in the form of outburst floods.

Methods for predicting peak discharge of floods caused by failure of natural and constructed earthen dams

Floods from failures of natural and constructed dams constitute a widespread hazard to people and property. Expeditious means of assessing flood hazards are necessary, particularly in the case of natural dams, which may form suddenly and unexpectedly. We revise statistical relations (derived from data for past constructed and natural dam failures) between peak discharge (Qp) and water volume released (V0) or drop in lake level (d) but assert that such relations, even when cast into a dimensionless form, are of limited utility because they fail to portray the effect of breach-formation rate. We then analyze a simple, physically based model of dam-breach formation to show that the hydrograph at the breach depends primarily on a dimensionless parameter η=kV0/gl/2d7/2, where k is the mean erosion rate of the breach and g is acceleration due to gravity. The functional relationship between Qp and η takes asymptotically distinct forms depending on whether η ≪ 1 (relatively slow breach formation or small lake volume) or η ≫ 1 (relatively fast breach formation or large lake volume). Theoretical predictions agree well with data from dam failures for which k, and thus η, can be estimated. The theory thus provides a rapid means of predicting the plausible range of values of peak discharge at the breach in an earthen dam as long as the impounded water volume and the water depth at the dam face can be estimated.

A catastrophic flood caused by drainage of a caldera lake at Aniakchak Volcano, Alaska, and implications for volcanic hazards assessment

Aniakchak caldera, located on the Alaska Peninsula of southwest Alaska, formerly contained a large lake (estimated volume 3.7 × 10 9 m 3 ) that rapidly drained as a result of failure of the caldera rim sometime after ca. 3400 yr B.P. The peak discharge of the resulting flood was estimated using three methods: (1) flow-competence equations, (2) step-backwater modeling, and (3) a dam-break model. The results of the dam-break model indicate that the peak discharge at the breach in the caldera rim was at least 7.7 × 10 4 m 3 s −1 , and the maximum possible discharge was ≈1.1 × 10 6 m 3 s −1 . Flow-competence estimates of discharge, based on the largest boulders transported by the flood, indicate that the peak discharge values, which were a few kilometers downstream of the breach, ranged from 6.4 × 10 5 to 4.8 × 10 6 m 3 s −1 . Similar but less variable results were obtained by step-backwater modeling. Finally, discharge estimates based on regression equations relating peak discharge to the volume and depth of the impounded water, although limited by constraining assumptions, provide results within the range of values determined by the other methods. The discovery and documentation of a flood, caused by the failure of the caldera rim at Aniakchak caldera, underscore the significance and associated hydrologic hazards of potential large floods at other lake-filled calderas.

Frequent outburst floods from South Tahoma Glacier, Mount Rainier, U.S.A.: relation to debris flows, meteorological origin and implications for subglacial hydrology

Destructive debris flows occur frequently at glacierized Mount Rainier volcano, Washington, U.S.A. Twenty-three such lows have occurred in the Tahoma Creek valley since 1967. Hydrologic and geomorphic evidence indicate that all or nearly all of these lows began as outburst loods from South Tahoma Glacier. Flood waters are stored subglacially. The volume of stored water discharged during a typical outburst flood would form a layer several centimeters thick over the bed of the entire glacier, although it is more likely that large linked cavities account for most of the storage. Statistical analysis shows that outburst floods usually occur during periods of atypically hot or rainy weather in summer or early autumn, and that the probability of an outburst increases with temperature (a proxy measure of ablation rate) or rainfall rate. We suggest that outburst floods are triggered by rapid water input to the glacier bed, causing water-pressure transients that destabilize the linked-cavity system. The correlation between outburst floods and meteorological factors casts doubt on an earlier hypothesis that melting around geothermal vents triggers outburst floods from South Tahoma Glacier

The dynamic response of Kennicott Glacier, Alaska, USA, to the Hidden Creek Lake outburst flood

Abstract Glacier sliding is commonly linked with elevated water pressure at the glacier bed. Ice surface motion during a 3 week period encompassing an outburst of ice-dammed Hidden Creek Lake (HCL) at Kennicott Glacier, Alaska, USA, showed enhanced sliding during the flood. Two stakes, 1.2 km from HCL, revealed increased speed in two episodes, both associated with uplift of the ice surface relative to the trajectory of bed-parallel motion. Uplift of the surface began 12 days before the flood, initially stabilizing at a value of 0.25 m. Two days after lake drainage began, further uplift (reaching 0.4 m) occurred while surface speed peaked at 1.2 md–1. Maximum surface uplift coincided with peak discharge from HCL, high water level in a down-glacier ice-marginal basin, and low solute concentrations in the Kennicott River. Each of these records is consistent with high subglacial water pressure. We interpret the ice surface motion as arising from sliding up backs of bumps on the bed, which enlarges cavities and produces bed separation. The outburst increased water pressure over a broad region, promoting sliding, inhibiting cavity closure, and blocking drainage of solute-rich water from the distributed system. Pressure drop upon termination of the outburst drained water from and depressurized the distributed system, reducing sliding speeds. Expanded cavities then collapsed with a 1 day time-scale set by the local ice thickness.

Creep closure of channels in deforming subglacial till

We examine theoretically the creep closure of subglacial tunnels cut into basal till, generalizing Nye’s classical analysis of tunnel closure in glacier ice to rheologies in which the creep rate depends on effective pressure (the difference between total pressure and pore-water pressure). The solutions depend critically on a dimensionless permeability parameter. For the appealingly simple Boulton–Hindmarsh rheology in which strain rate depends on powers of applied stress and effective pressure, solutions to the closure problem may not exist; this is related to the existence of a ‘failed’ zone next to the channel, where piping occurs, and also to a non-physical degeneracy of the assumed rheology, whereby the viscosity is indeterminate at zero effective pressure. Consideration of the failed zone allows solutions to be obtained and shows that the closure characteristics of high permeability tills and low permeability tills are very different.

Röthlisberger channel theory: its origins and consequences

The theory of channelized water flow through glaciers, most commonly associated with the names of Hans Rothlisberger and Ron Shreve and their 1972 papers in the Journal of Glaciology ,w as developed at a time when interest in glacier-bed processes was expanding, and the possible relationship between glacier sliding and water at the bed was becoming of keen interest. The R-channel theory provided for the first time a physically based conceptual model of water flow through glaciers. The theory also marks the emergence of glacier hydrology as a glaciological discipline with goals and methods distinct from those of surface-water hydrology.

Fault-dominated deformation in an ice dam during annual filling and drainage of a marginal lake

Abstract Ice-dammed Hidden Creek Lake, Alaska, USA, outbursts annually in about 2–3 days. As the lake fills, a wedge of water penetrates beneath the glacier, and the surface of this ‘ice dam’ rises; the surface then falls as the lake drains. Detailed optical surveying of the glacier near the lake allows characterization of ice-dam deformation. Surface uplift rate is close to the rate of lake-level rise within about 400 m of the lake, then decreases by 90% over about 100 m. Such a steep gradient in uplift rate cannot be explained in terms of ice-dam flexure. Moreover, survey targets spanning the zone of steep uplift gradient move relative to one another in a nearly reversible fashion as the lake fills and drains. Evidently, the zone of steep uplift gradient is a fault zone, with the faults penetrating the entire thickness of the ice dam. Fault motion is in a reverse sense as the lake fills, but in a normal sense as the lake drains. As the overall fault pattern is the same from year to year, even though ice is lost by calving, the faults must be regularly regenerated, probably by linkage of surface and bottom crevasses as ice is advected toward the lake basin.

Dimensionless erosion laws for cohesive sediment

AbstractA method of achieving a dimensionless collapse of erosion-rate data for cohesive sediments is proposed and shown to work well for data collected in flume-erosion tests on mixtures of sand and mud (silt plus clay sized particles) for a wide range of mud fraction. The data collapse corresponds to a dimensional erosion law of the form E∼(τ−τc)m, where E is erosion rate, τ is shear stress, τc is the threshold shear stress for erosion to occur, and m≈7/4. This result contrasts with the commonly assumed linear erosion law E=kd(τ−τc), where kd is a measure of how easily sediment is eroded. The data collapse prompts a re-examination of the way that results of the hole-erosion test (HET) and jet-erosion test (JET) are customarily analyzed, and also calls into question the meaningfulness not only of proposed empirical relationships between kd and τc, but also of the erodibility parameter kd itself. Fuller comparison of flume-erosion data with hole-erosion and jet-erosion data will require revised analyses o...

Crater glaciers on active volcanoes: Hydrological anomalies

Mount St. Helens is an active volcano that hosts glacier ice within its crater. Although the common picture of volcano/glacier interactions is one of rapid meltwater generation when hot material is brought into contact with snow and ice [e.g.,Major and Newhall, 1989], there have been practically no observable hydrological consequences of the ongoing episode of silicic lava dome emplacement at Mount St. Helens. The glaciological consequences have nonetheless been dramatic: The crater glacier has been cut in half since the dome growth began in September 2004, and the resulting ice bodies have in succession been squeezed between the growing lava dome and the crater wall.