Calving rates

Calving data are presented in Table 1. Calving rates (u_c in m a⁻¹) were obtained from the equation:

where u_i is ice velocity, dL/dt is rate of change in glacier length, and um is melt rate at the calving face, all in ma⁻¹ and width-averaged. Because uc is low, melting accounts for significant proportions of total retreat (17–56%), but um is the least well-constrained term in Equation (1). Though limited by site constraints, our ablation data yield a mean cliff-melt rate of 50 mmd⁻¹ over 11days. During more rigorous measurements on Tasman Glacier from 1985 to 1987 (Reference KirkbrideKirkbride,1995) an ablation rate of 47 mmd⁻¹ was measured over 28 days in the same season and at a similar altitude. The similarity of these values suggests that both the magnitude and seasonal variability of ablation rates at the study glaciers (which terminate at altitudes of 727–1095m with calving cliffs orientated southwest to southeast) are comparable. This permits the annual contribution of melt to glacier retreat to be estimated from our short-term measurements, yielding a value of 18.0ma⁻¹ (cf. the measured annual value of 17.7 ma⁻¹ at Tasman Glacier (Reference KirkbrideKirkbride, 1995)). This single value of u_m has then been applied at all sites to provide estimates of rates of mechanical ice loss. Since most published calving rates disregard the melt term, we used u_c + u_m for the New Zealand glaciers when testing the dependence of u_c on water depth (h_w).

Regression of h_w against u_c was carried out for (1) the global dataset compiled by Reference Warren, Greene and GlasserWarren and others (1995), and (2) these data with the addition of eight further glaciers: the six New Zealandglaciers; Svartisheibreen, Norway (Reference Kennett, Laumann and KjøllmoenKennett and others, 1997); and Glaciar Ameghino, Argentina (Reference WarrenWarren, 1999)− a total of 21 glaciers. Coefficients of variation (r²) are 0.75 and 0.83, respectively, significant at the 0.01level.Correlations using maximum water depth instead of h_w are slightly weaker. The global relationship is now described by:

This applies for grounded lake-calving termini; data from sites where calving is driven by buoyant forces at floating or near-floating termini (e.g. Glaciar Nef, Chile (Reference Warren, Benn, Winchester and HarrisonWarren and others, 2001); Glaciar Upsala, Argentina (Reference Skvarca, de Angelis, Naruse, Warren and AniyaSkvarca and others, 2002)) have been excluded. Calving at all the New Zealand glaciers occurs through the four-stage mechanism of thermal undercutting described in detail by Reference Kirkbride and WarrenKirkbride and Warren (1997).This mechanism is driven by thermo-erosion at the water-line followed by the progressive development of an overhang through flake calving (or spalling) from the subaerial cliff face. Such flakes often have high width/thickness ratios, as high as 25:1 (Fig. 1). Sub-horizontal melt notches at the water-line typically extend ≤4 m into the base of the cliff, but Reference Purdie and FitzharrisPurdie and Fitzharris (1999) report undercuts up to 10m deep at Tasman Glacier. Retreat of the subaerial cliff produces a subaqueous ice foot from which all the largest icebergs are calved.

Fig. 1. Godley Glacier terminus, 2 April 1994: thin flake prior to calving. The flake measured about 18 m high by 14 m wide by 1m thick. The calving cliff at this point rises 26 m above lake level.

Fluctuation histories

Fluctuation histories and areal retreat rates are shown in Figures 2 and 3. Given the highly irregular patterns of retreat during lake initiation, areal rates of change are more meaningful than linear rates. During the early stages of lake formation, when low-gradient termini are gradually inundated, retreat rates increase only slightly, but the onset of calving at terminal cliffs dramatically increases retreat rates (e.g. the 19-fold acceleration at Hooker Glacier, 1982–86 (Fig. 3)). At Grey–Maud and Classen Glaciers, this acceleration occurred pre-1958 and is documented by Reference KirkbrideKirkbride (1993); at Godley and Grey–Maud Glaciers, recession increased by factors of 10 and 4, respectively. These transitions coincided with the period of greatest 20th-century warming, when retreat rates would have increased without lake formation (Reference ChinnChinn,1996), but much of the acceleration can nevertheless be attributed to the onset of calving. Despite this shift into a more negative net mass-balance regime, a climate signal can still be discerned in the fluctuations of the calving termini. This does not apply during the three-stage dynamic adjustment from non-calving to calving (cf. Reference KirkbrideKirkbride, 1993) (e.g. Godley Glacier, 1965–74). However, once a calving cliff (as opposed to a drowned terminus) has been established, a measure of synchrony in terminus behaviour is apparent. For example, apparently synchronous reductions in retreat rate occur in the early 1970s at Grey–Maud and Classen Glaciers, and retreat rates increased at all glaciers after 1974. Most strikingly, readvances and/or reductions in retreat rate took place at all sites in the mid-1990s.

Fig. 2. Fluctuation histories for six of the study glaciers. Bathymetry is simplified from Reference Warren and KirkbrideWarren and Kirkbride (1998); bathymetric data do not exist for Classen Lake. In 1965, Hooker Glacier filled the current lake basin, and lake initiation began in the The fluctuation history of Tasman Glacier, also studied during this research, is discussed by Reference Kirkbride and WarrenKirkbride and Warren (1999).

Fig. 3. Areal retreat rates of the study glaciers, 1958–97. Grey– Maud and Godley–Ruth were confluent prior to 1990 1996, respectively. For Hooker Glacier, a 1982 lake area of 70 000 m2has been taken from Reference Hochstein, Watson, Malengrenau, Nobes and OwensHochstein and others (1998).

Calving in freshwater

A linear correlation between u_c and h_w exists in a diversity of geographical settings, but the constant of proportionality varies widely. In particular, existing data consistently show that calving occurs much more slowly in lakes than in comparable tidewater settings. This applies for grounded termini in shallow and deep water (Reference Warren, Greene and GlasserWarren and others, 1995) and for calving fronts which reach flotation (Reference Warren, Benn, Winchester and HarrisonWarren and others, 2001; Reference Skvarca, de Angelis, Naruse, Warren and AniyaSkvarca and others, 2002). Reference Van der VeenVan der Veen (2002) has challenged the water-depth model, arguing that the u_c/h_w correlation does not signify causality. Reference Hanson and HookeHanson and Hooke (2000), however, advance some possible physical explanations for the observed u_c/h_w relation. Their modelling of grounded tidewater fronts suggests that the development of flow-induced oversteepening of calving faces, possibly exacerbated by submarine melting, may partly explain the correlation. Causative or not, the New Zealand data confirm that u_c correlates linearly with h_w in fresh water, and that, for any given water depth, grounded temperate glaciers calve more than an order of magnitude slower in fresh water than in tidewater. These data also suggest that, at least for temperate glaciers, calving rates and mechanisms are driven by the effects of limnological processes on glaciological processes.

At cold-based glaciers, Reference IkenIken (1977) and Reference HughesHughes (1992, Reference Hughes2002) have suggested that the rate-controlling process is forward-bending along englacial shear bands created by unrelieved tensile stresses. At grounded, temperate lake-calving glaciers we have proposed that water-line melting is the rate-controlling process (Reference Kirkbride and WarrenKirkbride and Warren, 1997). Reference Purdie and FitzharrisPurdie and Fitzharris (1999) also document a causal relationship between thermo-erosional water-line notches and subaerial calving. Overhangs are common along subaerial sections of fresh-water termini, but these are created by thermal undercutting and progressive spalling above thermo-erosional notches, not primarily by forward bending. At compressional termini, full-height slab calving is defined by surface crevasses which open in response to the combination of water-line melting and increasing overhang of the subaerial cliff. Slab calving occurs too frequently to allow overhangs to be created by the bending creep mechanism proposed by Reference HughesHughes (1992, Reference Hughes2002). This and other arguments have led some (e.g. Reference Hanson and HookeHanson and Hooke, 2000) to suggest that Hughes’ elastic-beam theory approach is inappropriate. Similarly, we found that glacier dynamics more than a few metres upstream from the cliffs did not affect, nor were affected by, the calving process (Reference Kirkbride and WarrenKirkbride and Warren, 1997). Our observations do not rule out the possibility that oversteepenings are partly created by the distribution of longitudinal stresses and velocities, as proposed by Reference Hanson and HookeHanson and Hooke (2000), but they show that overhangs can form primarily in response to water-line melting.

The geometry of the submerged parts of calving termini has long been debated (cf. discussion inReference Warren and KirkbrideWarren and Kirkbride, 1998). The existence of projecting platforms or “ice feet”, inferred from the distal emergence of subaqueous icebergs, has been rejected by some in favour of vertical or even undercut and submerged ice cliffs, a geometry also inferred for Tasman and Hooker Glaciers by Reference Hochstein, Claridge, Henrys, Pyne, Nobes and LearyHochstein and others (1995, Reference Hochstein, Watson, Malengrenau, Nobes and Owens1998). However, ). our observations and those of Reference Purdie and FitzharrisPurdie and Fitzharris (1999) show that ice feet are present along the majority of these termini, commonly consisting of a small (1–4 m) subhorizontal shelf just below the water-line and a ramp of ice dipping lakewards at 20–45°. Ramps may intersect the cliff close to the water-line or at depth. Ice feet have also been reported at Alaskan tidewater glaciers (Reference MotykaMotyka, 1997; Reference Hunter and PowellHunter and Powell, 1998) and may be significant through their control on effective hw (cf. Table 1 caption), circulation patterns and hence heat advection to calving fronts.

The glaciological results reported here represent an end-member of the spectrum of calving behaviour, the other extreme being catastrophically retreating tidewater glaciers such as Columbia Glacier, Alaska, U.S.A., at which calving rates are two orders of magnitude greater (Reference Pfeffer, Cohn, Meier and KrimmelPfeffer and others, 2000). The styles of calving observed in New Zealand have not been reported at temperate tidewater sites, presumably because the frequency of calving exceeds the rate of melt-water notch development and because calving in such settings is defined by crevasses formed up-glacier of the termini by extending flow. At glacier termini where velocities are low and crevassing is limited because of compressive flow, freshwater calving is driven by water-line melting. This may also be the case at polar tidewater glaciers (A. Vieli and others, unpublished information). Aquatic factors appear to dominate at compressional margins, and glaciological factors at extensional margins.

Climatic response of calving glaciers

The terminus fluctuations of all types of calving glaciers may at times be subject to non-climatic (notably topographic) controls (Reference WarrenWarren,1992; Reference MeierMeier, 1997). However, our data support the hypothesis that, in terms of climatic sensitivity, lake-calving glaciers occupy an intermediate position between tidewater glaciers (least sensitive) and non-calving glaciers (most sensitive). Glaciers in the Southern Alps thinned and retreated through much of the 20th century (Reference ChinnChinn, 1996). All the large valley glaciers retreated from terminal moraines and outwash heads, initiating lake formation (Reference KirkbrideKirkbride, 1993; Reference WarrenKirkbride and Warren, 1999), and the subsequent onset of calving greatly increased retreat rates, from a mean of 12 ma⁻¹ prior to lake formation to a mean of 50 ma⁻¹ thereafter (Reference ChinnChinn, 1996; Reference Purdie and FitzharrisPurdie and Fitzharris, 1999). Because of exceptionally heavy precipitation, New Zealand glaciers are at the high end of the glacier sensitivity range, responsive to small climate variations (Reference Fitzharris, Chinn and LamontFitzharris and others, 1997). Although the onset of calving increases the rate of frontal recession, reducing this sensitivity, terminus changes do not become entirely isolated from climatically induced changes in mass balance. Periods of regionally positive mass balance, recorded by advances of non-calving glaciers, can be discerned as near-synchronous periods of readvances and/or reduced retreat rates of calving glaciers. Thus, for example, the readvances and reduced retreat rates observed in the mid-1990s (Fig. 3) probably represent a delayed response to the strongly positive mass-balance years of the 1980s and early 1990s which caused thickening and advance of most non-calving glaciers and lowering snowlines on calving glaciers (Reference ChinnChinn, 1996). A shift towards more positive mass balance increases ice velocities at the terminus and reduces the excess of calving losses over ice supply, thereby reducing retreat rates or (if sufficient) triggering readvances.

As would be expected for calving glaciers, the picture is neither straightforward nor uniform, partly because the glaciers underwent dynamic adjustment from non-calving to calving at different times, and partly because of the variable strength of topographic controls which are of great importance for calving-glacier fluctuations (Reference WarrenWarren, 1991; Reference Vieli, Funk and BlatterVieli and others, 2001). Nevertheless, some of the observed retreat-rate changes occur at locations of invariant topographic geometry and so cannot be attributed to topographically driven changes in massbalance. These complexities make it all the more striking that any measure of synchrony is apparent. It suggests that the onset of calving does not decouple these glaciers from climate, as it typically does in tidewater settings. Rather, it translates them into a new glacio-climatic regime of enhanced ablation which persists throughout the period of retreat through the lake basin. In this regime, annual net balances are consistently more negative than prior to the non-calving/ calving transition, but changing climatic stimuli can still be discerned in patterns of frontal change. The reason for this may for be that water-line melting is the rate-controlling mechanism. Since u_m at the water-line is likely to vary within restricted range, u_c too may vary little during retreat through the lake basin, permitting climatically driven increases in ice supply to be expressed as fluctuating retreat rates.

However, if uc is controlled by water-line melting, why does the uc/hw correlation persist? It is not clear whether the correlation indicates causation, or whether deeper water enhances some other process. For example, more vigorous lake circulation may enhance heat advection to the waterline, or faster subaqueous calving and/or melting may affect ice-cliff stability. Both possibilities suggest that ice-proximal water temperatures and circulation patterns may significantly affect calving rates and terminus dynamics, as suggested by Reference Hanson and HookeHanson and Hooke (2000) and Reference Motyka, Hunter, Echelmeyer and ConnorMotyka and others (2003). Empirical data with which to test this suggestion are limited, but Figure 4 shows that uc correlates positively with tw. (All water temperatures were measured in the summer or early autumn within a few tens of metres of glacier termini and at a depth of 10 m.) The correlation is stronger with a non-linear than a linear fit (r2 = 0.85 and 0.67, respectively, both significant at the 0.01 level), and the strength of correlation is similar to that between u_c and h_w in fresh water. Reference Brown, Meier and PostBrown and others (1982) believe that there is no direct evidence that t_w needs to be considered explicitly as a separate variable at Alaskan tidewater glaciers, and propose a simple one-coefficient, one-independent-variable calving relation. In fresh water, the strength of the positive correlations between u_c, on the one hand, and both h_w and t_w, on the other, suggests that the correlation between u_c and h_w is largely explained by ice-proximal lacustrine processes.

Fig. 4. Calving rates plotted against water temperatures New Zealand glaciers in this study, and for the following glaciers: Glaciar Moreno, Argentina (Rott and others, Reference WarrenWarren, 1999); Glaciar Ameghino, Argentina (Reference WarrenWarren, 1999); Glaciar Leones, Chile (E. Haresign and C. R. Warren, unpublished); and Svartisheibreen, Norway (Kennett others, 19 97). Ice-proximal water temperatures were measured in summer or early autumn at a depth of 10 m.

The data in Figure 4 provide empirical support for Reference Funk and RothlisbergerFunk and Rothlisberger’s (1989) suggestion that u_c is strongly dependent on water density through its impact on meltwater upwelling and subaqueous melt rates. They also support Reference Hanson and HookeHanson and Hooke’s (2000) conclusion that h_w is probably only one of several variables affecting u_c, other likely candidates being water temperature and longitudinal strain rate. Reference Van der VeenVan derVeen (2002) also appeals to water-density differences to explain the tidewater/fresh-water contrast in u_c, but suggests that they affect calving through their influence on effective basal pressures and hence sliding speeds near the terminus. The processes observed at slow, uncrevassed, lake-terminating glaciers such as those in New Zealand are likely to be overwhelmed by the much faster calving mechanisms which dominate at fast-flowing, heavily crevassed tidewater glaciers.