Reconstruction of former glacier ELAs

In addition to the maximum elevation of lateral moraines (MELM) (Fig. 2 and Fig. 3 ), the traditional ways to find former ELAs include the median elevation of glaciers (MEG), the toe-to-headwall ratio (THAR), accumulation area ratio (AAR), and the balance ratio method (see Nesje and Dahl, 2000, and references therein). In cases when only sparse remnants of marginal moraines are available, Dahl et al. (2002) introduced a new technique termed the Little Ice Age ratio to estimate the ELA of glacier advances predating the Little Ice Age maximum. In addition to defining the modern ELA of existing glaciers, these techniques are important for calibrating reconstructed ELAs based on proglacial sites.

Local watersheds
If combined with a proglacial lacustrine or terrestrial site, rerouting of glacial meltwater streams across local watersheds may give accurate estimates of former ELAs, if the extent of the corresponding glacier terminus is known from marginal moraines, historical records, air photographs, etc. (e.g. Dahl and Nesje, 1994; Dahl et al., 2002). Whenever the glacier is in an advanced position beyond the local watershed, glaciermeltwater- induced sediments may be deposited at the proglacial site, while only organic sediments accumulate when the glacier is behind the local watershed. This setting makes it possible to date whenever the glacier and the corresponding ELA are at, or close to, this on/off threshold. Local watersheds consisting of 'permanent' bedrock thresholds are preferred to ensure that this on/off signal has existed throughout the Holocene. Such watersheds (especially inside the Little Ice Age glacier maximum) appear to be near, while rerouting of proglacial meltwater streams caused by 'temporary' marginal moraines are more common. Due to the sharp on-off signal related to local watersheds, reconstructed glacier termini are normally very accurate. If the reconstructed glacier front can be linked to a known ELA by AAR, MELM, etc., reconstructed ELA variations related to local watersheds can be used to calibrate ELAs based on downstream proglacial sites (Fig. 2).

Chain of proglacial lakes
Based on data from nine Norwegian glaciers (Roland and Haakensen, 1985) there is a significant correlation (r ¼ 0:86) between glacier size/area and calculated sediment transport in proglacial meltwater streams. A similar relationship between the downstream transport distance of glacier-induced sediments in suspension and GS is suggested (Fig. 4), and consequently a chain of proglacial lakes can be used to record temporary variations in former glacier activity/ELAs. Small glaciers tend only to be recorded at the most sensitive sites, while larger glaciers in addition are recorded at sites further downstream. Depending on the size and response time, a lowering of the ELA results in a larger glacier when it has obtained climatic steady state. As a larger glacier/lower ELA leads to an increased meltwater discharge, a longer downstream distance of sediments in suspension is expected. Observations suggest that even a small increase in GS may correspond to an enlarged transport of sediments in suspension for several kilometres downstream (e.g. Dahl and Nesje, 1994). If this GS/ sediments in suspension distance ratio (GS/SSDratio) is known, records of glacier-induced sediments from a chain of proglacial lakes may give sensitive estimates of former variations in glacier magnitude. The Finse Valley in central southern Norway is a simple catchment with a chain of proglacial lakes completely dominated by meltwater from the northern sector of the ice cap Hardangerjøkulen. Based on modern analogue studies during the ablation season (e.g. Fig. 5), well-dated stratigraphies from both proglacial lakes and basins related to local watersheds (Dahl and Nesje, 1994), and possibilities to establish fixed points for these sites which relate former glacier magnitudes to known ELAs (Dahl and Nesje, 1996), an approximate GS/SSDrati o of 1:4 for this catchment is suggested and used as a tentative example in Fig. 4. Any GS/SSDratio is suggested to be catchment specific, however, and the ratio depends on a complex interaction between factors like nonglacial tributaries, relief of the river profile, water discharge, residence time of water in the proglacial lakes, etc. GS given in square kilometres (km2) is converted to an ELA estimate using the AAR method. To adjust for catchment dependent factors, the amplitude of the glacier/ELA signal in the proglacial lakes can be calibrated by the use of independent ELA observations of known age based on lateral moraines, local watersheds, etc. If the ELA and the corresponding GS/SSD ratio can be established for at least three fixed points spanning from small to large glaciers, a chain of proglacial lakes can be used to calculate continuous variations in former ELAs as schematically illustrated in Fig. 4. For small glaciers only the most sensitive proglacial lake closest to the glacier can record. Fluctuations in GS/ELA, while for large glaciers only the most distant proglacial lake is sensitive for variations in GS/ELA (see Fig. 6). If the investigated chain of proglacial lakes has a GS/ SSDratio which allows all variations in GS within a given time span to be recorded, error bars for the estimated ELAs of less than 750m are suggested. Reconstructed ELAs must normally be adjusted for glacio-isostatic land uplift (e.g. Dahl and Nesje, 1996).

One-site approaches
Downstream of many glaciers, suitable proglacial sites are often lacking or scarce. Hence, in many cases a setting with only one proglacial lake is all that is available to investigate how such glaciers and the corresponding ELAs have fluctuated backwards in time. If a glacier exists in the catchment at present, various proxies can record whenever former glaciers existed by using 'the modern analogue principle'. With a multi-site approach these proxies can be calibrated against independent sites with different sensitivity to record variations in glacier magnitude/ELA. For one-site approaches, variations in glacier activity/ELAs depend on the interpretation and sensitivity of the available methods (Fig. 6). However, some of these methods may be sensitive to record variations in small glaciers, while others can be used to record fluctuations in larger glaciers.

Discussion
Effective rates of glacial erosion varies from 0.01mmyr_1 for polar glaciers and thin temperate plateau glaciers on crystalline bedrock, to 0.1mmyr_1 for temperate valley glaciers on resistant crystalline bedrock in Norway, to 1.0mmyr_1 for small temperate glaciers on various bedrock types in the Swiss Alps, and to 10-100mmyr_1 for large and temperate valley glaciers in the tectonically active mountain ranges of southeast Alaska (Hallet et al., 1996, and references therein). Hence, the link between variations in GS and the corresponding ELA based on proglacial lakes must be established for each glacier. The bedrock beneath a glacier can be regarded as 'constant', whereas both temperature regime and thickness may vary with the size of the glacier. The temperature regime of a glacier also depends on air temperature and winter precipitation, and shifts from polar or polythermal to temperate may have taken place at the Younger Dryas/Holocene transition or from temperate to polythermal after the Holocene climatic optimum. Variations in the turnover time of ice in temperate glaciers may also have some influence on rates of effective glacial erosion. The annual sediment transport along glacier meltwater streams normally exceeds by several orders of magnitude nonglacial streams with similar water discharge in Norway (e.g. Roland and Haakensen, 1985). This transport occurs as rolling, sliding and saltation along the channel bed, or in suspension. Some grains descending during saltation may be temporarily buoyed by upward movement in turbulent flow, and this condition can be described as incipient suspension. The weight of fine particles in true suspension is entirely supported by the upward pulses of flow generated by eddies (e.g. Summerfield, 1996). It is particles deposited from true suspension which make the ideal basis for using proglacial sites to reconstruct variations in glacier extent/ELA. Depending on the site and the competence of the meltwater stream, however, particles from incipient suspension are commonly found as coarser grains (coarse silt to sand) in sediments deposited at proglacial sites. For most proglacial sites, however, the glacier signal is found in fine- to medium silt (e.g. Leemann and Niessen, 1994; Matthews et al., 2000; Nesje et al., 2001). Hence, proglacial sites dominated by sedimentation from true suspension are preferred (Fig. 2). In a study on the relationship between glacial activity and sediment production in the varved Hector Lake, Alberta in Canada, Leonard (1997) found that longterm variations (century to millenial duration) in sedimentation rate reflected changes in glacier extent on the same timescale. However, decadal-scale variability more complexly related to upstream ice extent is superimposed on the longterm changes. High sedimentation rates were associated with glacier maximum positions, or with transitional periods preceding or post-dating periods of maximum ice extent. The glacier-covered area in the catchment of Hector Lake has varied from 60% during the Little Ice Age to 40% at present, a coverage of glaciers four to six times higher than for the majority of similar investigations in southern Norway. The first lake in a chain of proglacial lakes acts as a sediment trap for coarser sediments. If the first lake is covered by the glacier, this is reflected as a shift from a low-energy mode to a high-energy mode in the lacustrine sedimentation of the second proglacial lake (e.g. Nesje et al., 2001). As temporary ice-dammed lakes commonly occur along glacier margins both during advance and retreat, this may explain some of the difficulties in interpreting whether high sediment production is directly linked to glacier maximum positions or not. In a multidisciplinary study, Snowball and Sandgren (1996, 1997) recored proglacial lakes in the Kársa valley in northern Sweden first investigated by Karlén (1976, 1981, 1997). Based on different methodological approaches, Snowball and Sandgren (1996) found that following the last deglaciation, glaciers had existed in the catchment only for the last 3000 14C yr BP, a result which strongly contrasted the interpretation of Karlén (1976, 1981) who had suggested several glacier advances throughout the entire Holocene. Based on this investigation, Snowball and Sandgren (1996) strongly argued against single-core (site) studies. They also argued that only features that are consistently reproducible and can be dated in spatially distributed cores should be interpreted in terms of glacier activity, environmental conditions and climate change. However, the problems of getting reproducible results can normally be solved by using proglacial lakes with a .at bottom. Brauer et al. (2001) compared four sediment profiles from lakes Holzmaar and Meerfelder Maar in the Eifel region, Germany. Based on varve-dating and pollen profiles from the two lakes, former discrepancies between the two lakes were explained after detailed correlation. They concluded that even in small lakes like Holzmaar discrepancies of several hundred years may occur, and that a multi-core study on two lakes from the same region is necessary to detect errors in single-core studies on nonvarved sediments. Multi-core/site approaches are therefore preferred (e.g. Snowball and Sandgren, 1996; Brauer et al., 2001). However, suitable proglacial sites are difficult to find in many regions, and in many cases none or very few sites are available. To minimize within lake variance and maximize between lake variance, basins distal from the inlet and/or the deepest part of the lake appear to give the best reproducable results when more than one core/site are taken into account. For one-site studies, only features that are consistently reproducible based on several independent proxies in two or more cores should be interpreted in terms of glacier variations and climate change. The principal coupling between various techniques/proxies and former glacier activity/ELAs is demonstrated in Fig. 6. Hence, for one-site approaches it is especially important that these principles are followed. Church and Ryder (1972) defined the term 'paraglacial' as referring to ''nonglacial processes that are directly conditioned by glaciation''. The term has been widely used to describe the reworking of glacigenic sediments by colluvial processes and running water after the withdrawal of glacier ice, including the landforms and sediment accumulations produced by such processes (e.g. Ballantyne, 1995). Attributed to nonglacial activity, thin (p2 cm) minerogenic layers and less-regular layers composed of coarse, angular sand and gravel particles, are found in both glacial and nonglacial lakes with steep slopes in the catchment (Matthews and Karlén, 1992). The thin layers are suggested to result from precipitation- induced events, including debris flows (Østrem and Olsen, 1987; Jonasson, 1991), while the less-regular layers are interpreted as ice-rafted colluvial debris (e.g. Luckman, 1975). Colluvial activity often occurs within a limited area and as short (hours to days) events. However, similar minerogenic layers in nonglacial control lakes (Matthews and Karlén, 1992) and multi-core/site approaches reflecting the same glacier may reveal the origin of a nonglacial layer. Due to the longevity of many glacier-induced events (several hundred years) compared to colluvial events, radiocarbon dates above and below the actual layer may in some cases disclose the depositional agent. By using 'ward sorting' on grain-size distributions to establish cumulative platforms, 'true' glacial meltwater sediments may be separated from deposits originating from colluvial activity (Blott and Pye, 2001).