L. A. Rasmussen

Climate and Glacier Variability in Western North America

A simple model using once-daily upper-air values in the NCEP‐NCAR reanalysis database estimates seasonal mass balance at two glaciers in southern Alaska, one in western Canada, and one in Washington substantially better than any of several seasonally averaged, large-scale climate indices commonly used. Whereas sea level pressure and sea surface temperature in the Pacific exert a strong influence on the climate in the region, temperature and moisture flux at 850 mb have a more direct effect on mass balance processes—accumulation and ablation—because their temporal variability better matches that of those processes. The 40-yr record of 850-mb temperature shows winter warming after 1976 and summer warming after 1988 throughout the region; mass balance records reflect the summer warming at all four glaciers but winter warming only at the southern two. The only pronounced long-term change in the moisture regime is a decrease of precipitation in the south and an increase in the north. Interannual variations in the location of the moisture flux, however, apparently account for the strong negative correlation between the Alaska glaciers and the other two.

Recent thinning and migration of the Western Divide, central West Antarctica

Antarctica, is currently thinning � 0.08 m a � 1 and migrating toward the Ross Sea at 10 m a � 1 . The asymmetric pattern of thickness change across the divide is not caused by changes in the accumulation gradient, but rather by dynamical thinning that is stronger in the Amundsen Sea sector than in the Ross Sea sector. Available geological and glaciological data indicate that this pattern of thinning has persisted for at least two millennia, with increased asymmetry likely over the past few centuries. Our data however, are not sufficient to determine whether the present-day migration of the Western Divide is a response to long-term (millennial) forcing, shorter-term (centennial) forcing, or both. Citation: Conway, H., and L. A. Rasmussen (2009), Recent thinning and migration of the Western Divide, central West Antarctica, Geophys. Res. Lett., 36, L12502, doi:10.1029/ 2009GL038072.

Influence of upper-air conditions on glaciers in Scandinavia

Abstract A simple model using once-daily US National Centers for Environmental Prediction/US National Center for Atmospheric Research (NCEP/NCAR) re-analysis upper-air values estimates winter balance, summer balance and net balance at ten glaciers in Norway and two in Sweden with 0.37 ≤ r2 ≤ 0.90. The October-May Arctic Oscillation (AO), an index of sea-level pressure (SLP) in the Northern Hemisphere, correlates with winter balance and net balance with 0.09 ≤ r2 ≤ 0.82, lower than the model in all but 3 of the 24 cases. The October-May North Atlantic Oscillation (NAO), an SLP gradient in the North Atlantic, has lower correlations than the AO for all but 5 of the 24 cases. At all ten glaciers with records beginning before 1987, net balance became more positive after 1988, owing mainly to increased winter balance, with summer balance changing little. Although winter temperatures increased, they were still well below freezing, so the rain-snow division of the precipitation was only slightly affected. Increase in winter balance was due to increased precipitation caused by a change in atmospheric circulation, resulting in more frequent westerly flow concurrent with the warming. At 850 hPa, westerly flow is ≈2.5˚C warmer than easterly flow; westerly flow warmed by ≈ 0.3 °C, easterly by ≈ 0.7 °C. Both the AO and NAO, with which winter balance is positively correlated at all 12 glaciers, were more positive after 1988.

Snow densification during rain

Observations and measurements indicate rain often has a major impact on snow slope stability. Measurements to investigate the effects of wetting of low density, alpine snow were made at Snoqualmie Pass, WA, USA. Results indicate that on first wetting, the densification rate can increase by three orders of magnitude. This initial burst of densification occurs independently of the gravitational load and is probably a result of rapid structural changes and grain rearrangement that occurs when liquid water is first introduced. The rate decreases rapidly with time, although it remains about two orders of magnitude higher than that for dry snow of the same density. The rate of densification decreases as density increases. We assume snow behaves as a linear viscous fluid and that the metamorphic and gravitational components of compaction are additive. A simple model of compaction is derived empirically using the measurements. The model fits the measurements very well, although more experiments are needed to determine the dependence of the model parameters on liquid water content.

Surface mass balance, thinning and iceberg production, Columbia Glacier, Alaska, 1948-2007

A mass-balance model using upper-air meteorological data for input was calibrated with surface mass balance measured mainly during 1977-78 at 67 sites on Columbia Glacier, Alaska, between 135 and 2645 m a.s.l. Root-mean-square error, model vs measured, is 1.0 m w.e. a -1 ,w ithr 2 = 0.88. A remarkable result of the analysis was that both precipitation and the factor in the positive degree- day model used to estimate surface ablation were constant with altitude. The model was applied to reconstruct glacier-wide components of surface mass balance over 1948-2007. Surface ablation, 4k m 3 ice eq. a -1 (ice equivalent), has changed little throughout the period. From 1948 until about 1981, when drastic retreat began, the surface mass balance was positive but changes in glacier geometry were small, so the positive balance was offset by calving, ∼0.9 km 3 ice eq. a -1 . During retreat, volume loss of the glacier accounted for 92% of the iceberg production. Calving increased to ∼ ∼4.3 km 3 ice eq. a -1 from 1982 to 1995, and after that until 2007 to ∼8.0 km 3 ice eq. a -1 , which was about twice the loss by surface ablation, whereas prior to retreat it was only about a quarter as much. Calving is calculated as the difference between glacier-wide surface mass balance and geodetically determined volume change.

Bed topography and mass-balance distribution of Columbia Glacier, Alaska, U.S.A., determined from sequential aerial photography

An internally consistent data set of geometry and flow variables for the lower part of Columbia Glacier, south-central Alaska, is derived entirely from vertical aerial photography. The principle of mass conservation is imposed in the form of a centered finite-dierence approximation of the continuity equation. It is applied on a 120-node section of a square grid covering the 15 km long, high-velocity stretch ending at the grounded, heavily calving terminus of this large glacier. Photography was obtained 22 times between June 1977 and September 1981. Surface altitudes on the dates of the flights and the displacement vectors between pairs of flights were determined photogrammetrically. Natural features on the glacier surface were suciently prominent and enduring to be followed from the date of one flight to the next. Because both the altitude points and displacement vectors were irregularly posi- tioned spatially, interpolation was necessary to get values on the grid nodes. The points had already been subjected to the method of optimum interpolation to get surface altitudes on the grid nodes. The displacement vectors are subjected here to a constrained-interpolation method to get velocity vectors at the grid nodes that are consistent, through the continuity equation, with the other variables. The other variables needed to achieve closure of the variable set are bed topog- raphy and mass-balance distribution. The latter was taken to be a separate linear function of altitude for each time interval. Values for bed altitudes at 120 nodes and two coecients of each of 21 balance functions were inferred as the 162 model

Estimating Precipitation in the Central Cascades of Washington

Abstract Precipitation in the central Cascades of Washington correlates well over 1966–96 with wind and moisture in twice-daily upper-air soundings at a radiosonde station near the Pacific coast, 225 km away. A simple model estimates precipitation by using the component of the wind roughly normal to the north–south range of the Cascade Mountains, which it raises to a power and scales by the relative humidity. Values at 850 mb are taken as an index of the total moisture flux. Thresholds are imposed for the wind component and the relative humidity to reduce the likelihood of estimating precipitation from weak onshore flow on dry days. A split-sample analysis indicates that the model parameters are highly robust against sampling error. This moisture flux model estimates precipitation over 5-day periods with the coefficient of determination r2 ≈ 0.55, which increases for precipitation aggregated over 30-day periods to 0.75 and decreases to 0.30 for daily precipitation. Results over a 4-month period in the win...

Using Sequential Photography to Estimate Ice Velocity at the Terminus of Columbia Glacier, Alaska

The terminus of Columbia Glacier, Alaska, was observed with a single automatic 35 mm camera to determine velocity with a time resolution in the order of a day. The photographic coordinates of the image of a ta rget were then transformed linearly into the direction numbers of the line of sight from the camera to the target. The camera orientation was determined from the film-plane locations of known landmark points by using an adaption of vertical photogrammetry techniques. The line of sight, when intersected with some mathematically-defined glacier surface, defines the true space coordinates of a target. The time sequence of a targets position was smoothed, first in horizontal x, y space to a straight line, then in y (the principal direction of ice flow) and time with a smoothing cubic spline, and then the x-component was computed from the y-component by considering the inclination of the straight line . This allows daily velocities (about 8 m/ day) to be measured at a distance of 5 km, using a 105 mm lens. Errors in daily displacements were estimated to be I m. The terminus configuration was also measured using the same photo set. INTRODUCTION Surface velocity is one of the most important glacier variables to measure for studies of dynamics. The aim of this paper is to demonstrate methods of measuring glacier velocity by using sequential photography from a single camera location and to show results obtained in using the method at Columbia Glacier, Alaska. The method was specifically developed for Columbia Glacier to fulfill a need for short-interval velocity measurements at its terminus. It can provide ice velocities and changes in terminus positions with daily resolution . Because the calving velocity is the difference between these two quantities, it can also be obtained with the same time resolution. The calving velocity can then be used with data for other variables, e.g. fresh water run-off, tide stage, glacier thickness, in investigating the calving mechanism (Brown and others, 1982; Sikonia 1982). A large amount of surface-velocity data from the terminus of Columbia Glacier has been obtained . Beginning in 1976, vertical aerial photography has been obtained over the lower reach at time intervals of one to four months. By standard photogrammetry, the coordinates of seracs or crevasse intersections can be obtained . The same feature can usually be found on photographs from each of two successive flights and the displacement between the two positions can be used to determine the average velocity for the time interval. The accuracy of measurement of these horizontal displacements is about 4 m; considering the average velocity and interval between flights, the mean error in velocity is about two per cent. The data from July, 1976 to September, 1981 show: I) at km 66 (about 0.5 km above the 1983 terminus position), velocity reaches a seasonal maximum of about 8.2 m/ day in mid-fall and a seasonal minimum of about 2.7 m/ day in late spring; 2) the velocity increases with distance from 60 to 66 km by about 100 per cent; 3) the terminus position changes seasonally by about 300 m, with a minimum glacier length in late fall and maximum length in early summer. These data are described in detail by Meier and others (l985a). Major limitations of the aerial photogrammetry are the many-week time resolution and coarse spatial resolution close to the terminus. Furthermore, the expense of the photography and photogrammetry is high. A few features on the lower glacier have been surveyed by traditional triangulation or foresight methods, but the results have been limited to several kilometers above the terminus with several-month time resolution. To use traditional methods of surveying near the terminus for more than a few weeks would be extremely expensive. A 16 mm movie camera, overlooking the terminus, has been in operation since early 1978. When one frame per day is projected at high speed, say 6 frames per second, the ice movement is obvious . However, when the frames are taken individually, the dominating feature of the image is that of film grain and generally low resolution. When shown in rapid sequence, a mental pattern-recognition is applied to the frames, which is difficult to carry to individual scene pairs for quantitative displacement measurement, and thus no short-term velocities have been obtained from 16 mm film. The possibility of making velocity measurements was obvious, though, and a 35 mm sequence camera system was designed and installed specifically for the purpose of measuring short-term ice velocity. Velocity has also been successfully measured on other glaciers using small-format cameras (Iken and others, 1983). THE CAMERA, GENERAL GEOMETRY, LANDMARKS, AND IMAGE SETS A motor-driven, electrically-triggered 35 mm-format camera with a 30 m film reel, was installed in early 1983,overlooking the Columbia terminus (Fig. I ). The camera, a Hulcher* model 112, is mechanically robust and electronically simple as compared to modern 35 mm cameras. In practice, it was dependable, but difficult to load. Failures of the system were due either to faulty charging or faulty film loading. The camera, timer, solar array voltage regulator, 8 amp hour, lead-acid battery and weather-protecting window box were mounted on a 2 m high tower, made from heavy aluminium angle. The interior of the four legged tower was filled with rocks, for stability. The exposure time was determined with knowledge of beginning and end times, the use of a crystal-controlled timer, and the frame count. Three frames were to be taken each day (8, 12, and 16 hours) , color or black and white film was used during different periods, and the exposure was pre-set for an average sunny day . The camera was located and oriented so that several requirements could be met. The terminus must be observable; the velocity vectors should be nearly normal to the direction of view; the location should be such that the elevation angle to the ice-mass surface is large, but should *The use of brand names in this report is for identification purposes only and does not imply endorsement by the U.S. Geological Survey.

Seasonal mass-balance gradients in Norway

Previously discovered regularity in vertical profiles of net balance, b n (z), on ten glaciers in Norway also exists in profiles of both winter, bw(z), and summer, b s (z), seasonal balances. All three profiles, unlike those of many glaciers elsewhere in the world, are remarkably linear. Variations of gradients, db w /dz and db s /dz, from year to year are small and correlate poorly with glacier-total balances b w and b s . Glacier-to-glacier correlation is weak for both gradients but is strongly positive for b w and b s . There are two direct consequences of these properties of the gradients that apply to both seasonal balances b w and b s . First, because db/dz varies so little from year to year, the difference in balance, Ab, from year to year is nearly the same over the entire glacier, except near the top and bottom of its altitude range. Therefore, balance at a site near the middle of the altitude range of the glacier correlates very well with glacier-total balance. Second, this correlation, combined with the strong positive correlation of balance from glacier to glacier, is the reason balance at one altitude on one glacier correlates well with glacier-total balance at other nearby glaciers.

Using upper-air conditions to estimate South Cascade Glacier (Washington, U.S.A.) summer balance

Asimplemodelusesonce-dailymeteorologicalvaluesintheU.S.National Centers for Environmental Predictionand U.S. National Center forAtmospheric Research (NCEP^NCAR)re-analysis databaseto estimate summerbalanceof South Cascade Glacier, Washington, U.S.A., each year over1959^99.The rms error,0.30mw.e. ( r 2 ˆ0.71), is com- parable to measurement error.The model relates summer balance linearly to temperature T > 0‡ C at 2000m and to snow flux at1650m, the altitudes in recent years of the equilib- rium line and terminus.The snow flux is the product of the humidity and westerly wind component at 850hPa when temperature T <+2‡ C at 1650m. Temperatures are inter- polated linearly betweenthe 850 and 700hPa levels. Boththe positive 2000mtemperature andthe snow flux are summedfrom 26 Aprilto 4 October.Whenthe summerestimatesare combinedwiththosefromawinterbalancemodelusingthesamedatabase,thermserrorin estimating netbalance is 0.40m ( r 2 ˆ0.81).The indicated sensitivities of balance to warm- ing of 1‡ C are ^0.51m for summerand ^0.24m for winter. Onthe assumptionthatthetotal ^0.75m‡C ^1 sensitivityexists atall altitudes, awarmingof only 0.7‡ C wouldbe sufficientto overcome the1986^98 averagenetbalance +0.5matthe top of theglacier.