In the empirical study of jökulhlaups, the peak discharge, Qmax, and water volume drained by the ice-dammed lake during the floods, Vt, appear to follow a power-law relation , where K are b are constants determined from field data. First identified by Clague and Mathews (1973), this relation is a useful reference for predicting flood magnitude, but its physical origin remains unclear. Here, we develop the theory that connects it to contemporary models for simulating the flood hydrograph. We explain how the function Qmax = f(Vt) arises from Nye’s (1976) theory of time-dependent water flow in a subglacial channel coupled to a lake, and we describe how discharge–volume data record the (monotonically increasing) form of this function so long as the lake is not emptied in the floods. The Grímsvötn jökulhlaups present an example where, because of partial draining of the lake, agreement between the model-derived f and data is excellent. It is documented that other lake systems drain completely, but we explain how the exponent b ≈ 2/3 observed for them collectively is due primarily to a scaling effect related to their size, modified by other factors such as the flood initiation process.

Ice-flow velocities were measured at Koryto glacier on Kamchatka Peninsula, Russia, during a 37 day period in the middle of the 2000 melt season. Six survey points from the upper to the lower reaches of the glacier exhibited daily fluctuations in surface horizontal speed with major peaks that appeared at all points.We argue that basal motion is the major cause of flow on Koryto glacier. Downward vertical velocities measured over most of the glacier during the survey period are likely due to shrinking of englacial and subglacial cavities. This result may imply that a large amount of water is deposited in the early summer. Since 1960, Koryto glacier has retreated by 450 m and this retreat has accelerated following a decrease in winter precipitation after the mid 1970s.The glacier has thinned by 10–50 m during the last 40 years.

During the austral summer field season of the Russian Antarctic Expedition in 1999/2000, wide-angle reflections experiments were performed in the vicinity of the Russian station Vostok. A 60 MHz ice radar system with 12-bit digital recording was used. The measurements were taken along two perpendicular lines directed south–north and east–west with a distance of 200 m between marks. We used a one-layer model (without snow–firn zone influence) for the calculations. We calculate that the average velocity of radio-wave propagation in the ice sheet is168.4 ± 0.5 m μs−1.The same velocity was derived from hyperbolic diffractions from internal discontinuities. The results allow more accurate depth interpretation of radio-echo soundings.

A series of experiments was undertaken to determine the origin of filaments found in grain boundaries and impurity spots found in grain interiors of polar ice during observation in the scanning electron microscope. It is shown that although the filaments are artifacts, they demonstrate the presence of impurities segregated to the grain boundary planes. It is also demonstrated that the impurities observed in the grain interior reside there and were not transported from the grain boundaries during specimen preparation or observation.

A series of laboratory experiments in a 6 m long chute using glass particles of mean diameter 100 μm were performed to investigate the interaction of a supercritical, granular flow with obstacles. It was found that the collision of the flow with a row of mounds led to the formation of a jet, whereby a large fraction of the flow was launched from the top of the mounds and subsequently landed back on the chute. The retarding effect of the mounds was investigated quantitatively by direct measurements of the velocity of the flow, its runout length and the geometry of the jet. The effects of several aspects of the layout of the mounds on their retarding effects were examined. It was observed that a row of steep mounds with an elongated shape in the transverse direction to the flow and with a height several times the flow depth led to dissipation of a large proportion of the kinetic energy of the flow.

Non-steady-state vertical velocities of up to 5 m a−1 exceed the vertical surface-parallel flow (SPF) components over much of the ablation area of Storstrømmen, a large outlet glacier from the East Greenland ice sheet. Neglecting a contribution to the vertical velocity of this magnitude results in substantial errors (up to 20%) also on the south–north component of horizontal velocities derived by satellite synthetic aperture radar interferometry (InSAR) measurements. In many glacier environments, the steady-state vertical velocity component required to balance the annual ablation rate is 5–10 m a−1 or more. This indicates that the SPF assumption may be problematic also for glaciers in steady state. Here we derive the three-dimensional surface velocity distribution of Storstrømmen by using the principle of mass conservation (MC) to combine InSAR measurements from ascending and descending satellite tracks with airborne ice-sounding radar measurement of ice thickness. The results are compared to InSAR velocities previously derived by using the SPF assumption, and to velocities obtained by in situ global positioning system (GPS) measurements. The velocities derived by using the MC principle are in better agreement with the GPS velocities than the previously calculated velocities derived with the SPF assumption.

We present a method for analyzing the errors involved in measuring three-dimensional glacier velocities with interferometric radar. We address the surface-parallel flow assumption and an augmented approach with a flux-divergence (FD) term. The errors in an interferometric ERS-1/-2 satellite radar dataset with ascending- and descending-orbit data covering Storstrømmen glacier, northeast Greenland, are assessed. The FD error assessment is carried out on airborne 60 MHz ice-sounding radar data from the same area. A simple model of an interferometric radar system is developed and analyzed. The error sources considered include phase noise, atmospheric distortions, baseline calibration errors, a dry snow layer, and the stationary-flow assumption used in differential interferometry. The additional error sources in the analysis of FD errors are noise, bias and unknown variations of the ice thickness, and approximations of the ice-flow model. The example glacier is now building up following a surge. The analysis shows that in the case study presented the errors are small enough to justify the use of both the estimated surface-parallel flow term of the vertical velocity and the estimated FD term of the vertical velocity.

Repeat airborne laser altimeter measurements are used to derive surface elevation changes on parts of Whillans Ice Stream and Ice Stream C, West Antarctica. Elevation changes are converted to estimates of ice equivalent thickness change using local accumulation rates, surface snow densities and vertical bedrock motions. The surveyed portions of two major tributaries of Whillans Ice Stream are found to be thinning almost uniformly at an average rate of ∼1 m a−1. Ice Stream C has a complicated elevation-change pattern, but is generally thickening. These results are used to estimate the contribution of each surveyed region to the current rate of global sea-level rise.

Jakobshavn Isbræ is the most active glacier in Greenland, with an annual discharge of about 30 km3 of ice, and it is one of the few recently surveyed glaciers to thicken between 1993 and 1998, despite locally warm summers. Repeated airborne laser-altimeter surveys along a 120 km profile in the glacier basin show slow, sporadic thickening between 1991 and 1997, suggesting a small positive mass balance, but since 1997 there has been sustained thinning of several m a−1 within 20 km of the ice front, with lower rates of thinning further inland. Here, we use weather-station data from the coast and the ice sheet to estimate the effects on surface elevation of interannual variability in snowfall and surface melt rates, and thus to infer the temporal and spatial patterns of dynamic thinning. These show the glacier to have been close to balance before 1997 followed by a sudden transition to rapid thinning, initially confined to the lower reaches of the glacier (below about 500 m elevation), but progressively spreading inland until, between 1999 and 2001, thinning predominated over the entire surveyed region, up to 2000 m elevation. If this continues, the glacier calving front and probably its grounding line will retreat substantially in the very near future.

Mega-scale glacial lineations (MSGLs) are longitudinally aligned corrugations (ridge–groove structures 6–100 km long) in sediment produced subglacially. They are indicators of fast flow and a common signature of ice-stream beds. We develop a qualitative theory that accounts for their formation, and use numerical modelling, and observations of ice-stream beds to provide supporting evidence. Ice in contact with a rough (scale of 10–103 m) bedrock surface will mimic the form of the bed. Because of flow acceleration and convergence in ice-stream onset zones, the ice-base roughness elements experience transverse strain, transforming them from irregular bumps into longitudinally aligned keels of ice protruding downwards. Where such keels slide across a soft sedimentary bed, they plough through the sediments, carving elongate grooves, and deforming material up into intervening ridges. This explains MSGLs and has important implications for ice-stream mechanics. Groove ploughing provides the means to acquire new lubricating sediment and to transport large volumes of it downstream. Keels may provide basal drag in the force budget of ice streams, thereby playing a role in flow regulation and stability. We speculate that groove ploughing permits significant ice-stream widening, thus facilitating high-magnitude ice discharge.

We apply a time-dependent distributed glaciohydraulic model to Vatnajökull ice cap, Iceland, aiming to determine the large-scale subglacial drainage structure, the importance of basally derived meltwater, the influence of a permeable glacier bed and Vatnajökull’s discharge contribution to major rivers in Iceland. The model comprises two coupled layers that represent the subglacial horizon perched on a subsurface aquifer in the western sector and bedrock in the eastern sector. To initialize and drive the simulations, we use digital elevation models of the ice surface and bed, the 1999/2000 measured mass balance and an estimate of subglacial geothermal heat fluxes. The modelled subglacial flow field differs substantially from that derived by hydraulic-potential calculations, and the corresponding distribution of basal effective pressure shows a strong correlation between low effective pressure and surge-prone areas in northeastern and southern sectors of Vatnajökull. Simulations suggest that geothermally derived basal melt may account for up to ∼5% of the annual glacial discharge, and buried aquifers may evacuate up to ∼30% of subglacialwater.Time-dependent tests yield estimates of the glacial discharge component in various outlet rivers and suggest a possible seasonal migration of subglacial hydraulic divides. This study of present-day Vatnajökull hydrology forms the starting point for investigations of its future evolution.

Discharge measurements, climate observations and hydrochemical samples gathered monthly (1998/99) in the Yanamarey and Uruashraju glacier-fed catchments of the Cordillera Blanca, Peru, permit an analysis of the glacier meltwater contribution to stream-flow. These glacier catchments feed the Río Santa, which discharges into the Pacific Ocean. Based on a water-balance computation, glacier melt contributes an estimated 35% of the average discharge from the catchments. For comparison, a volumetric end-member mixing model of oxygen isotopes shows glacier melt contributes 30–45% to the total annual discharge. Based on stream geochemistry, discharge from the Yanamarey glacier catchment provides 30% of the annual volume discharged from the Querococha watershed, which is <10% glacierized. By analogy, the larger Río Santa watershed, also <10% glacierized, receives at least 12% of its annual discharge from melting glacier ice. Tributary watersheds to the Río Santa with larger fractions of glacier cover have less variable runoff and enhanced discharge, demonstrating that the glaciers effectively buffer stream discharge seasonally. With continued glacier melting, stream-flow will likely become more variable, and there will be less dry-season runoff.

There is no discernible river discharge from Austre Okstindbreen, Norway, in winter; any water formed by basal melting is likely to be stored in isolated cavities or sediments at the bed. In summer, a baseflow component of discharge, relatively depleted of 18O, is diluted by water more enriched in 18O. Glacier ice meltwater with a high δ18O value passes rapidly through channelized systems, and emerges in the glacier river within a few hours. Headward extension of the systems in late summer may tap water stored within the glacier since the previous summer’s close-down. Stored water also is released during early melt-season events, when the low-capacity drainage systems cannot accommodate inputs. The high δ18O value indicates that the probable source of the released water is glacier ice or low-altitude snowfall. Stratigraphic variations of δ18O values, resulting from changing weather conditions, characterize the accumulating winter snowpack. During the melt season, the mean δ18O value of the residual pack rises. The water leaving it, depleted of 18O, passes slowly through the glacier, smoothing out variations of supply. δ18O values of rain vary between and within events, and their effect on glacier-river δ18O values is unpredictable.

Using a slightly modified form of the Spring–Hutter equations, glacial outburst floods are simulated from three classic sites, “Hazard Lake”, Yukon, Canada, Summit Lake, British Columbia, Canada, and Grímsvötn, Iceland, in order to calibrate the hydraulic roughness associated with subglacial conduits. Previous work has suggested that the Manning roughness of the conduits is remarkably high, but the new calibration yields substantially lower values that are representative of those for natural streams and rivers. The discrepancy can be traced to a poor assumption about the effectiveness of heat transfer at the conduit walls. The simulations reveal behaviour that cannot be inferred from simplified theories: (1) During flood onset, water pressure over much of the conduit can exceed the confining pressure of surrounding ice. (2) Local values of fluid potential gradient can differ substantially from the value averaged over the length of the conduit, contradicting an assumption of simple theories. (3) As the flood progresses, the location of flow constrictions that effectively control the flood magnitude can jump rapidly over large distances. (4) Predicted water temperature at the conduit outlet exceeds that suggested by measurements of exit water temperature.

We assess the accuracy and precision of the U.S. National Science Foundation’s Support Office for Aerogeophysical Research (SOAR) laser profiling system for mapping topography and detecting surface elevation changes of West Antarctic ice streams. The procedures used to process, calibrate and validate the laser, navigation and global positioning system (GPS) data are presented. The primary objective is to produce surface elevations with the best possible resolution. Repeat surveys of a grid of lines over Whillans Ice Stream and Ice Streams C and E were conducted in the 1997/98 and 1999/2000 seasons. The procedure has been calibrated using special test flights conducted over areas that have been surveyed with precise geodetic GPS equipment mounted on snow-mobiles. After calibration, agreement between the two surfaces is ±10 cm rms. The accuracy and precision of the procedure have been evaluated at points where laser flight-lines cross over one another. The accuracy of the system is found to range from 0.09 to 0.22 m.