Calving Rates In Fresh Water

Calving remains one of the least understood glaciological processes. Calving glaciers are sensitive to trough geometry, and because of the instability of calving termini they can fluctuate independently of climate (Reference Meier and Post.Meier and Post, 1987; Reference WarrenWarren, 1991, Reference Warren1992). Calving rates correlate strongly with both water depth and ice thickness at the terminus (Reference Brown, Meier and Post.Brown and others, 1982), but the physical nature of these relationships remains unclear (Reference HughesHughes, 1992; Reference Meier and ReehMeier, 1994), Temperate tide-water glaciers have been extensively studied, whereas fresh-water calving glaciers have received little attention despite the significance of fresh-water calving for glacio-climatic relationships today and in geological time (Reference KirkbrideKirkbride, 1993; Reference WarrenWarren, 1994). Interest in fresh-water calving was stimulated by hydro-power schemes in glacierized catchments (Reference Laumann. and Wold.Laumann and Wold, 1992). Such studies revealed that, in any given water depth (h _w), calving rates (v _c) are about an order of magnitude less than those in tide water (Reference Funk. and Röthlisberger.Funk and Röthlisberger, 1989). The v _c/h _w relationship for fresh water proposed by these authors was:

(1)

This was based on just six sites. At four of these, h _w was ≤20 m, limiting the reliability of the relationship for predicting v _c in deeper water.

The need for an improved database of fresh-water calving rates prompted this work in Patagonia. The major eastern outlet glaciers of Hielo Patagónico Sur (southern Patagonia ice field) all calve into large, deep lakes (Reference Warren and Sugden.Warren and Sugden, 1993). In this study of the historic behaviour of Glaciar Upsala, we document the onset of rapid retreat following the initiation of rapid calving in a new proglacial lake. We also present a revised v _c/h _w relationship for fresh water, combining new data from Patagonia with published information. At seven of the 14 sites h _w exceeds 50 m.

Glaciar Upsala

Glaciar Upsala (49°50′S, 73°17′W) has a surface area of 870 km² and a length of about 60 km, making it one of the largest Southern Hemisphere glaciers outside Antarctica, and South America’s longest (Reference Aniya. and Skvarca.Aniya and Skvarca, 1992). 20th-century thinning has caused the terminus to divide into three distributaries (Fig. 1). The largest arm, Upsala west, terminates in Lago Argentino at a calving front 4 km wide and 60–80 m high. Ice velocities 4 km behind the calving front are 700 m a⁻¹, and the equilibrium-line altitude (ELA) is estimated to be 1150 m, giving an accumulation-area ratio of 0.63 (Reference Aniya. and Skvarca.Aniya and Skvarca, 1992). Surface gradients in the terminal 20 km do not exceed 2.5°, but crevassing is intense, especially west of the medial moraines. Proglacial water depths are unknown. However, the great size and the tabular form of the icebergs suggest that water depths are considerable: icebergs with estimated volumes greater than 10⁶m³ are common, some of them detaching without rolling over. Upsala central and east calve into Lago Guillermo, a lake formed by recent glacier retreat (Fig. 2). Upsala central descends steeply to the lake, cut by regular crescentic crevasses, whereas Upsala east has a lower gradient and is less crevassed, with large areas of smooth ice within 2 km of the terminus. Calving activity is infrequent and small-scale relative to that at Upsala west. Meteorologically, the glacier terminus lies in the transition zone between mountain and pampas climates. The western margin of the glacier is wetter, cloudier and less windy than the east side, and the vegetation reflects this contrast (Reference MercerMercer, 1965).

Fig. 1.

Primary retreat stages of Glaciar Upsala since about 1600. Details of sources are given in the text. EC, Estancia Cristina.

Fig. 2.

Bathymelry of Lago Guillermo and ice-front positions of Upsala east during retreat through the lake. Contour interval is 50 m in the lake and 100 m elsewhere. Contours on the glacier and in areas deglaciated since 1981 have been estimated. V, ice-velocity survey points; X, velocity markers (1992); B, bathymetry survey point; A, ablation stakes; and M, meteorological station (1993).

Methodology

The fluctuation history is derived from published sources (Reference AgostiniAgostini, 1945; Reference MercerMercer, 1965; Reference Malagnino., Strelin., Naruse and Aniya.Malagnino and Strelin, 1992) and remotely sensed data: aerial photographs from 1945, 1967, 1968, 1975 and 1981, and a LANDSAT image of 14 January 1986. The ice-front position of Upsala east in March 1992 and 1993 was fixed using a theodolite/EDM and a satellite-positioning system. An approximate ice-margin position in 1914 was provided by J. Masters whose family founded Estancia Cristina (Fig. 1) in that year.

Work at Upsala east was carried out in the late austral summers of 1992 and 1993. In March 1992 two markers were positioned close to the geometric centre line, and displacements measured during a 13 d period using a “total-station” Geodimeter theodolite/EDM and standard survey methods (Fig. 2). A network of five ablation stakes was monitored daily for 14 d in February and March 1993, and standard meteorological data were recorded concurrently (Fig. 2). To map the bathymetry of Lago Guillermo, 291 individual echo soundings were taken along 23 transects. In the eastern sector of the lake, locational accuracy was achieved using a theodolite/EDM; in the western sector, transects were chosen between prominent lake-shore features, rowing on still days to minimize drift. Ice-cliff heights were surveyed from the lake shore. Qualitative observations of the evolving nature of the calving front, and of the characteristics and frequency of calving, were recorded throughout both field seasons. Visual estimates of iceberg volumes incorporated water-depth measurements near grounded bergs.

Results

Glaciar Upsala has been retreating throughout historical time (Fig. 1). The neoglacial maximum and subsequent retreat positions are marked by pronounced vegetation trim-lines and moraines. The maximum was dated dendrochronologically by Mercer (1965) to the period 1600–1760 AD; rapid retreat (≈l20 m a⁻¹) commenced in the early 19th century. BY the beginning of the 20th century the glacier had reached a narrowing point, and it retreated more slowly (≈50 m a⁻¹) until the late 1960s. Between 1970 and 1978, a central part of Upsala west advanced about 400 m (Reference Aniya. and Skvarca.Aniya and Skvarca, 1992). The eastern margin retained its position from 1931 until 1981, but then retreated at 800 m a⁻¹ until 1990. Between March 1992 and 1993 the eastern half of Upsala west retreated about 1000 m. Retreat rates of Upsala east are given in Table 1. When observed in 1928 by Reference AgostiniAgostini (1945), the bedrock ridge now separating Upsala west and east was still under ice. By 1967 it had been exposed by thinning, and Lago Guillermo was beginning to form. Rapid retreat occurred throughout the 1980s.

Table 1.

Upsala east: 20th-century retreat statistici

Results of the ice-velocity measurements are given in Table 2. The annual velocities are simple extrapolations, not incorporating seasonal variability. No seasonal velocity data exist for any Patagonian glacier, so the error is unknown. Mean ablation rates ranged from 3.6 to 11.2 cm w.e.a⁻¹ with a mean of 6.8 cm w.e.a⁻¹. Melt-rate variations correlate significantly (at the 0.05 level) with variations in minimum daily temperature (r _s = 0.64) and wind speed (r _s = 0.60) but not with maximum temperature (r _s = −0.18), mean daily temperature (r _s = 0.15) or sun hours (r _s = −0.4). On and around the glacier, wind speeds are frequently extreme, gusting to 40 m s⁻¹ at times.

Table 2.

Upsala east: surface ice-velocity data, March 1992

The bathymetry of Lago Guillermo is shown in Figure 2. About 100 m in front of Upsala east the mean depth (n = 32) is 65 m, and there is no consistent shallowing or deepening trend towards the glacier. The average ice-cliff height is 34 m (range: 29–41 m). Combining ice-cliff heights with the near-ice bathymetry, the maximum ice thickness at the calving front is estimated to be 150 m and the mean thickness (n = 15) to be 101 m. Given a glacier width of 1600 m and a width-averaged ice velocity of about 60 m a⁻¹, the annual mass flux at the terminus of Upsala east is approximately 9.7 × 10⁶ m³ a⁻¹ or 0.01 km³a⁻¹. Following Reference Powell and Molnia.Powell and Molnia (1989), mean annual calving speed (v _c) can be derived using the equation

(2)

where v _c is related to frontal change (v _r[1992-93] = −25 m a⁻¹, ice velocity (v _i = 60 m a⁻¹) and ice melting (v _m) at the calving face. However, subaqueous melt rates at calving fronts are poorly known, and theoretical calculations yield values of uncertain validity (Reference Warren, Glasser., Harrison, Winchester, Kerr and Rivera.Warren and others, in press) so v _c was determined simply using

(3)

This yields a calving speed of 85 m a⁻¹. Given that v _m could be about 20–30 m a⁻¹, the true value of v _c could be 55–65 m a⁻¹.

At Upsala east the calving cliff is essentially vertical along its western half, but sections of the eastern half overhang at angles of ≤30°. Calving activity consists of high-magnitude/low-frequency events, producing prismatic icebergs which contrast with the large tabular bergs typical at Upsala west. Visual estimates of berg volumes suggest that most are in the range 1000–50000 m³ with an upper limit of 500 000 m³. Large bergs survive in Lago Guillermo for more than 2 weeks before breaking up and melting. Calving fluxes from Upsala east are probably about two orders of magnitude lower than those from Upsala west.

Discussion

Fresh-Water Calving Rates

Table 3 presents calving data for 14 temperate, grounded glaciers that calve in fresh water. Ideally, v _c should be calculated using Equation (2). Given the poor knowledge of v _m at calving fronts, however, Equation (3) was used. All three terms are in m a⁻¹ and averaged over the width of the glacier. The data in Table 3 are of variable quality. For the glaciers for which only centre-line ice velocities (v _max) are known, v _i was calculated by multiplying v _max by 0.73. This empirical constant is derived from the temperate-tide-water glacier data set of Brown and others (1982) in which the relationship between v _max and v _i for 12 glaciers is remarkably consistent (0.73 ± 0.05). Values of v _i calculated in this way are underlined in Table 3. For the Patagonian glaciers (10–13), ice velocities were measured 1–5 km behind the calving front. The calving speeds given for glaciers 2 and 8 differ from those in the original sources because Laumann and Wold (1992) used v _max to calculate v _c while Reference Goldthwait, McKellar and Cronk.Goldthwait and others (1963) used a minimum ice velocity. At Glaciar Grey, h _w was measured by plumb-line soundings (personal communication from A. Mansilla, 1992), and at Glaciar Pio XI h _w has been estimated from maps drawn before and after the lake formed. Estimating v _r and v _c at Tasman Glacier, New Zealand, is problematic because the terminus was evolving from a melting to a calving condition through a phase with complex terminus geometry (Reference KirkbrideKirkbride, 1989, Reference Kirkbride1993). Nevertheless, it is clear that v _c remained very low while h _w increased to a maximum of 130 m. “Normal’ calving commenced in 1991, producing small numbers of icebergs with volumes of several million cubic metres (Reference Hochstein, Claridge, Henrys, Pyne, Nobes and Leary.Hochstein and others, in press).

Table 3.

Fresh-water calving data for 14 grounded, temperate glaciers, temperate glaciers, h _max, maximum watei depth at the calving front; h _w width-averaged water depth; v _max, centre-line surface ice velocity; v _i, width-averaged surface ice vetocity; v _r, mean glacier relreat rule: and v_c, calving rate. Melt rates at the calving face have not been incorporated. For further explanation and discussion, see text

Figure 3 presents v _c/h _w relationships for fresh water based on the numerical values in Table 3. The empirical data are expressed in the form

(4)

(5)

in which c is a calving coefficient. For h _w the best estimate of c is 2.5 ± 0.5, and for h _max, the best estimate of c is 1.8 ± 0.5. This contrasts with a value of c for temperate tide-water glaciers of 27.1 ± 2 (Reference Brown, Meier and Post.Brown and others, 1982).

Fig. 3.

The relationship between calving speed and water depth for 14 fresh-water glaciers, showing relationships for width-averaged water depth (h_w) (data points shown as dots) and maximum water depth (h _max) (crosses). Data and sources are given in Table 3. Relationships proposed by Funk and Röthlisberger (1989), and by Brown and others (1982) for tide water, are also shown

The revised v _c/h _w relationship for fresh water confirms the robust but unexplained dependence of calving rate on water depth. This dependency is apparently linear. However, the data also allow the possibility that v _c increases non-linearly with h _w. The suggestion of a non-linear increase is more pronounced for the v _c/h _max distribution (Fig. 3).

Conclusion

Fluctuations of Glaciar Upsala show that the influence of climate change on the position of a calving front is less significant in the short term than that of the transition from melting to calving, and than subsequent changes in calving rate. The relative importance of melting as against true mechanical calving, and the effect of the former on the latter, are important unknowns. Data relating to fresh-water calving are still limited, while the physics of calving in fresh water and ride water, the differences between the two, remain largely unknown. However, the strong dependence of calving rates on water depth in both tide water and fresh water is now beyond doubt.