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Glacial Geology and Geomorphology, 1999 |
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Glacier surfaces and equilibrium line altitudes (ELA) are reconstructed from Younger Dryas moraines (Egesen Stadial) in the Ferwall group (western Austria). Traditional manual reconstruction and a raster-based Geographical Information System (GIS) are used. The interactive GIS-based reconstruction uses the theoretical profile of a glacier tongue for the glacier tongue and a constant shear stress model for the cirque areas. A Digital Terrain Model with 20 m grid mesh width provides the geometrical basis to the GIS. Moraines and other ice marginal features are used as input data. The results of the manual and computer based reconstruction agree surprisingly well. Therefore, the calculated shear stress values and ELAs should be reliable. Shear stresses range between 1.23 bars for the Egesen maximum (early Younger Dryas) and 0.39 bars for the Egesen III advance (late Younger Dryas). Equilibrium line depressions relative to the mid-19th century maximum range between -290 m and -120 m respectively. In total, the GIS-supported models based on simple glaciological theory seem to be reliable tools for the reconstruction of former glacier surfaces.
Glacier reconstruction, Alps, GIS, Equilibrium line, moraines,Younger Dryas
Equilibrium lines of Lateglacial glaciers are important sources for palaeoclimatic information, because the equilibrium line altitude (ELA) of a glacier is entirely determined by climatic factors (cf. Kuhn 1979, 1989; Ohmura et al. 1992). If some other independent palaeotemperature information is available on a comparable timescale and temporal resolution, then they can be used to infer Late Glacial precipitation patterns in High Mountains (Kerschner 1985; Kaser and Kerschner 1994). These, in turn, can be used as benchmarks to test the reliability of Atmospheric General Circulation Models (AGCM). In the case of the Younger Dryas climatic fluctuation, this has been done recently by Renssen (1997). As the ELA is very sensitive to changes in the climatic environment, it must be determined with a rather high degree of accuracy (±20 m). This level of accuracy can usually only be reached with the ablation area ratio (AAR) method (Gross et al. 1978; Kerschner 1990), using an AAR of 0.67. A careful and accurate reconstruction of the glacier surface with contour line intervals of 100 m is necessary to apply the AAR method successfully. Until now, this has usually been done manually, using the relevant moraines and bedrock morphology as guidelines. If a sufficient number of lateral moraines are available, the manual reconstruction of a glacier tongue poses no real problems, and therefore the method has been widely used in the Alps during the past two decades (cf. Maisch 1987, 1995; Kerschner 1985). However, if lateral moraines are few or completely missing, the manual reconstruction of the former glacier surface is difficult and, sometimes, even impossible. The aim of our paper is to show a possible way for a semi-automatic reconstruction of glacier tongues in valleys with 'simple' bedrock morphology with a Geographic Information System (GIS) using ARC/INFO software. Morphometric parameters of the glacier bed (valley slope, cross profiles of the valley, position of end moraines), which are easy to determine, are used as input data. A Digital Terrain Model (DTM) with a grid mesh width of 20 m is used for the calculations.
This semi-automatic model leads to a reconstruction of former glaciers which is largely independent of the experience of the scientist. The few input parameters coupled with the model algorithms govern the reconstruction routine and lead to reproducible results. The three-dimensional glacier model delivers some interesting glaciological quantities as cross-section, ice thickness or shear stress at any required cross profile along the glacier tongue.
Our research area is the Ferwall group. It is situated at the western margin of the Tyrolean central Alps (Fig. 1). In the north, it is bordered by the Stanzertal, Arlberg pass and Klostertal, in the south by the Paznauntal and in the west by the Montafon valley. In the east, the highest peaks are around 3000 m, whereas the highest peaks in the west are considerably lower (2600 - 2650 m). Valleys in the north and west are usually several kilometres long and of simple geometry. In the south, short and steep valleys lead down from the large cirque areas to the Paznauntal. At the border between the central and the western part of the Ferwall group, wide and open mountain passes ('Winterjöcher') are a characteristic geomorphological feature. Due to its topo-graphic characteristics, the Ferwall group is a very convenient area for our goals, as diffi-culties due to the geometry of the valleys are minimal (straight long profiles without abrupt changes in slope; Fig. 2). As the mountains are mainly com-posed of metamorphic rock (various gneisses, amphibolites), the general morphology is readily comparable to that of the type localities of the Alpine Late Glacial in the Stubai Mountains (Mayr and Heuberger 1968). Therefore, the morphostratigraphic correlation of the Late Glacial moraines with the type localities is easy. Glacial deposits in the Ferwall have been mapped several times in the past (Ampferer 1929; Bobek 1933; Reithofer 1931, 1933, 1934; Senaclens-Grancy 1956; Kerschner 1977; Fraedrich 1979; Eberhard 1987). However, according to our present-day knowledge, even the most recent investigations are not complete and the stratigraphic positioning of the moraines and related deposits is in many cases not correct.
The Schönferwall and Ochsental valley is situated at the border between the western and central part of the Ferwall group. A series of prominent lateral and end moraines can be found (Fig. 3). Generally, they are well preserved and, in some places, there are many large boulders. According to their position in the field and their 'fresh' appearance (well preserved, steep slopes, many large boulders), they can be classified as moraines of the Egesen Stadial in the sense of Heuberger (1966, 1968), which is the equivalent to the Younger Dryas climatic fluctuation (e.g. Patzelt 1972; Kerschner 1978a; Müller et al. 1981; Ivy-Ochs et al. 1995, 1996, Ivy-Ochs1996). The maximum advance reached the confluence of Schönferwall and Fasul valleys. During that phase a dendritic glacier system existed, covering most of the southwestern part of the Ferwall group. A correlation with the well-dated Egesen moraines at Julier pass in neighbouring Switzerland (Ivy-Ochs et al. 1995, 11996, Ivy-Ochs1996) is easily possible. From this point of view, the moraines at Konstanzer Hütte were deposited during the earlier part of the Younger Dryas (ca 12.000 cal. BP). There are many more moraines at Silbertaler Winterjoch (Winterjoch i.e. winter col), which indicate that many phases of advance and retreat followed after the maximum, thus demonstrating the 'flickering switch' of Late Glacial climatic change (Taylor et al. 1993). During a distinct second phase of the Egesen Stadial the glacier terminated at the southern end of Silbertaler Winterjoch. We assume that it could be the equivalent of the Bocktentälli phase (Maisch 1981). During a third phase prominent lateral moraines were deposited just below Gaschurner Winterjoch (Fig. 3 and 4). The respective end moraine can be found near the Schönferwall Hütte. Finally, end moraines and lateral moraines in the upper part of Ochsental valley can be correlated with the Kromer/Kartell advance (Fraedrich 1979; Gross et al. 1978), which could be of early Preboreal age. Dating of the moraines with cosmogenic radionuclides is in progress.
During the colder phases of the Holocene, small glaciers existed
in some cirques and at the very end of Ochsental. Lichenometric
checking shows that most of the moraines were deposited during
the 1850 (Little Ice Age) advance. Today, only three small patches
of ice exist in the upper part of Ochsental.
An accurate map of the glacier surface with a scale of at least 1:25000 and with contour lines at 100 m intervals is needed to determine the ELA of a glacier with the AAR method. Traditionally, this has been done by hand with the help of the moraines and some implicit assumptions about ice thickness in the accumulation areas, where moraines are missing. However, this approach is rather subjective and the results depend to a large extent on personal experience. For a more objective approach, the theoretical long profile of a glacier tongue by Nye (1952, Fig. 5) can be used to calculate the ice thickness in a valley, if the glacier length and some parameters governing the shear stress along the valley walls are known (Kerschner 1978b). Considering the static equilibrium of a glacier tongue with the surface slope a resting on an inclined valley floor with slope b and the boundary condition a > b, the relation between glacier length x and glacier thickness h is (Nye 1952):
x = (h'0 / b
2) ln (h'0
/ (h'0 - b h))
- h / b (1)
where
h'0 = t' / (r g) (2)
with r as the density of ice (900 kg/m3) and g the acceleration due to gravity (9.81 m/s2). In equation (2), t ' is the basal shear stress of the glacier in the valley. It is calculated as
t '= t / c (3)
where the shear stress is
t = r g h sin a (4) (4)
In equation (3), c is a constant which can be calculated from the hydraulic radius R of the cross section of a glacier as
c = R / h (5)
on the assumption that the geometry of the valley remains constant or changes only very slowly. This is the case in Schönferwall and Ochsental valley. In the future, the assumption of a constant hydraulic radius will be replaced by the shape factor for a parabolic cross section (Nye 1965, cf. Paterson 1994).
All necessary parameters for equation (1) can be calculated from the topographical data contained in the Digital Terrain Model (DTM). Therefore, this approach is well suited for a GIS based reconstruction of former glacier tongues. Details are provided in the appendix. The glacier length at a given point can be determined from end moraines, glacier thickness and surface slope from lateral moraines. Although Nye's (1952) theoretical long profile does not account for longitudinal stresses due to changes in the bed topography, the results are in good agreement with the manual reconstruction from the moraines only.
The manual reconstruction of the upper parts of a glacier is usually more complicated and prone to errors, because moraines are missing and assumptions about the ice thickness have to be made. The outlines of the glacier in the cirque areas are usually fixed by the bedrock topography. This can easily be done by hand. For the determination of the ice thickness in the accumulation area, a constant basal shear stress is used. In that case, equation (4) contains two unknowns, h and a . However, recent investigations on the ice thickness and bedrock topography of various glaciers in the Ötztal (Massimo 1997) have shown that there is a reasonably good relationship between surface slope a and bedrock slope b. Regression analysis of the data from Gepatschferner shows that the difference between a and b can be expressed as a linear relation of b, which has the form
a - b = ds = 4.34 - 0.82 b (6)
with a correlation coefficient of -0.83 (all angles in degrees). This is statistically sufficient to reconstruct the glacier in the cirque area, because the largest deviations occur where b is steep and h is, therefore, small. Additionally, the topography of Gepatschferner is complicated with several confluences and subglacial basins. Therefore, equation (6) can be rather safely applied to glaciers with simple topography, as is the case in Schönferwall and Ochsental. Then, under the assumption of a constant shear stress, the ice thickness for any single grid point can be calculated from (4) and (6) as
h = t / [r g sin (b + d s)] (7)
All parameters needed for the reconstruction of the glacier tongue can be taken either from the DTM or from topographical maps. Surface slope a and bed slope b, the position of the relevant valley cross profiles and the altitude of the ice surface at the starting point for the reconstruction are chosen interactively. For Lateglacial glaciers, moraines and other ice marginal features provide the necessary information. The surface geometry for the calculation of the hydraulic radius R and the ice thickness h at the starting point are calculated from the DTM.
In most cases, reconstruction is done in the downvalley direction (Fig. 5 and 6). Equation (1) is the basis for all calculations. Starting from a given cross profile with known values for h, a and b, the glacier length x is calculated from (1). This step also determines the glacier terminus, which remains fixed. Then the cross profile is moved downvalley for n steps with
n = x / M (8)
where M is the grid mesh width. For each step, the ice thickness hn, the hydraulic radius Rn, the surface slope an and the altitude of the glacier surface Hn is calculated, where the distance xn from the starting point is
x'i = M * i, i=1,..,n (9)
the change in ice thickness is
D hi = hi-1 - hi (10)
and the altitude of the glacier surface follows as
Hi =Hi-1 - D hi - tan b * x'i (11)
In most cases, the cross section to start with is located below the position of the equilibrium line. Therefore, the glacier surface altitude is also calculated upvalley as
Hi =Hi-1 - D hi + tan b * x'i (12)
In that case, Dhi is negative and the altitude of the ice surface increases. When Hi reaches an altitude where the equilibrium line is supposed to be the iteration terminates. From there on, the ice surface is calculated with a simple constant shear stress model.
The calculated shear stress of the glacier tongue is used to calculate
the ice surface in the cirque areas of the glaciers. In a first
step, the probable surface slope is calculated with the help of
equation (6) from the bed slope b as:
a = b + d s (13)
Then the ice thickness h and finally the altitude of the glacier surface H can be calculated from the shear stress equation (equation 4). Any influence of the valley walls is disregarded, as glacier width is usually very large compared with the ice thickness. However, using a DTM with a grid mesh width of 20 m results in a very irregular pattern of the contour lines. Therefore, the calculated surface slope is smoothed twice using a 7 x 7 pixel surrounding (140 m x 140 m) for each pixel and using the mean value of all according pixels. This is roughly equivalent to three to five times the ice thickness in cirque areas.
The model has been developed to reconstruct the Younger Dryas Glaciers of the Ferwall valleys. The numerical reconstruction of the Egesen I and III glaciers are good in accordance with the manually reconstructed ('conventional') glacier topographies (Fig. 7 and 8). The ELA of the Egesen I glacier is exactly the same (2320 m) for the manual and the GIS-based reconstruction. For the Egesen II substadial, a numerical reconstruction was impossible, because the necessary input data could not be determined due to a lack of lateral moraines. The manually reconstructed ELA of the Egesen II glacier is 2420 m. A first conventional attempt to calculate the ELA of the Egesen III glacier resulted in a value of 2480 m, which was 35 m higher than the value derived from the GIS-based model. A closer inspection showed that the manually drawn contour lines of the glacier surface at the tongue / cirque transition caused an unrealistic ice thickness in this specific part of the glacier. A further conventional reconstruction resulted in an ELA of 2450 m, which is only 5 m higher than the GIS-modelled value of 2445 m.
ELAs and D ELAs relative to the LIA
(1850 AD; cf. Fig. 3) maximum for
the reconstructed glaciers are in the order of 2320 m/-290 m for
the Egesen Maximum, 2420 m / -190 m for the halt at Silbertaler
Winterjoch (Egesen II) and 2450 m / -160 m for the Egesen III
advance, which is documented by distinct moraines (Fig.
4). The depression values are rather similar to those in other
more oceanic areas of the Eastern Alps and typical for the Younger
Dryas (cf. Kerschner 1985, 1993).
The ELA depression for the Kartell stadial in the upper part of
Ochsental is -90 m, which is the same as at the type locality
(Fraedrich 1979). Actual shear stresses
are 0.69 bars for the maximum and only 0.2 bars for the Egesen
III glacier. Disregarding the influence of the valley walls, the
respective figures (equation 3) are 1.23 and 0.39 bars. While
the larger values are similar to those of modern glaciers of similar
size, the shear stresses for the Egesen III glacier are surprisingly
small. However, as the glacier tongue is well documented by numerous
moraines, they must be regarded as realistic. They can tentatively
be interpreted as characteristic for a glacier in a cold and fairly
dry environment, as it was typical for the latter half of the
Younger Dryas.
Although the present results are promising, there are still a few critical points remaining to discuss. Above all, the calculated shear stress of a glacier and, therefore, the theoretical long profile of a glacier tongue by Nye (1952) is extremely sensitive to changes in surface slope. If surface slope data are taken from moraines in the field, this can lead to difficulties, because the present-day position of Lateglacial moraines is often the result of hillslope processes. Careful geomorphologic mapping is therefore an absolute necessity.
If the correct figures for the surface slope and/or the bed slope
cannot be determined with the necessary accuracy, it is still
possible to use the theoretical long profile in many cases to
calculate minimum and maximum glacier lengths from field data
under the assumption of realistic shear stresses. If only the
terminal position of a glacier is known from end moraines, it
is possible to calculate the thickness of the glacier tongue with
a reasonable degree of accuracy (±20 m). This can be particularly
useful for ELA estimates, because the ELA does not vary considerably
unless changes in glacier length or ice thickness are very large.
At least, realistic ELAs can be bracketed with a known inaccuracy.
Two glaciological problems are still unsolved. The first problem
relates to the very front of the glacier tongue. The theoretical
model (Nye 1952) delivers too high
amounts for the ice thickness at the end of the tongue. In the
GIS-based model, this problem is solved by a simple logarithmic
decay of the ice thickness downvalley from an interactively chosen
cross-section near the end. The second remaining problem relates
to the usually convex shape of the glacier tongue. To approximate
the shape of the glacier tongue, an increase of the ice thickness
from the margin to the centre in the order of a few percent is
integrated in the model, based on empirical values. Although both
solutions are not satisfying from a glaciological point of view,
the results are accurate enough to pursue the main goal of the
GIS-based model, which is to find reliable ELAs of Lateglacial
glaciers. Due to the very limited effect on the glacier topography
and on the ELA, the mechanisms of extending and compressive flow
are not incorporated in the GIS-based model.
Finally, as the basal shear stress is the only stress variable
in the model, its application is limited to valleys with simple
topography and more or less constant cross section. Complex glaciers,
or glaciers which are situated in valleys with abrupt changes
in geometry, can still only be reconstructed manually. The same
is true for the accumulation areas, which must be delimited by
hand. However, if the criteria are met, the interactive GIS -
based approach seems to be a reliable tool for the reconstruction
of glacier surfaces. The calibration of the GIS-based model with
glaciers where both the surface and the bed topography are known,
has already been done but is not published yet. The preliminary
results show a good agreement of the calculated quantities with
the quantities derived from maps.
The theoretical method to calculate long profiles of glaciers
with a raster based GIS is the basis of a computer aided model
which offers new perspectives for the reconstruction of former
ELAs. In the accumulation area (i.e. cirque area) the constant
shear stress model based on equations (6) and (13) is helpful
in any case. Most manual input has to been done where the glacier
tongue passes into the cirque area. Apart from the glacier tongue
/ cirque area transition, the GIS-based processing is independent
of the experience of the scientist. Thus, the principal advantage
of the GIS-based model over the conventional reconstruction of
glacier topographies is a higher degree of objectivity and reproducibility
of the results.
In general, the model is restricted to glaciers with a geometrically
simple bed topography and a geometrically simple catchment area.
Only in very special cases it is possible to reconstruct dendritic
glacier systems, which is very time-consuming. In general the
time necessary for the GIS-based processing is not very different
from that for the conventional reconstruction. However, it offers
a reliable tool to check the manually drawn surface contour lines
of former glaciers.
The application of the model to Egesen Stadial (Younger Dryas)
glaciers of the Schönferwall valley (Ferwall group, Western
Central Alps, Austria) show a good agreement between GIS-based
and manually reconstructed ELAs, long profiles and glacier extents.
The differences are surprisingly small. This supports the assumption
that the GIS-based reconstruction gives indeed realistic results
and can be applied to other glaciers as well.
In contrast to dynamic flow models, which are based on specific
balance profiles, the GIS-based model works without any information
about the mass balance gradients of former glaciers, which usually
are not available. As all geometric values of the glacier are
stored in a data base, all quantities (i.e. cross section area,
ice thickness, glacier width, shape factor, bed and surface slope)
are readily available to form the basis for palaeoclimatic interpretations
as described by Kerschner et al.
(in press).
We would like to acknowledge the fruitful discussion on glaciological topics with our colleagues Marius Massimo, Norbert Span (both at the Institut für Meteorologie, Universität Innsbruck) and Georg Kaser (Institut für Geographie, Universität Innsbruck). The comments of two anonymous reviewers were most helpful during the final stages of the manuscript. The project was supported by the Austrian "Fond zur Förderung der wissenschaftlichen Forschung" under grant No. P12600-GEO. This support gratefully acknowledged.
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Fig. 1: Location of the study area.
(Click on image to enlarge.)
Fig. 2: Simple bed topography of the upper part of the Schönferwall valley.
Fig. 3: Moraines and glacier extents in the Schönferwall and Ochsental valley.
Fig. 4: The prominent lateral moraines of the Egesen III advance below Gaschurner Winterjoch.
Fig. 5: Theoretical long profile of a glacier tongue (Nye 1952); see text for details.
Fig. 6: Cross profile at the start of the GIS-based processing; see text for details.
Fig. 7: Comparison between the manual and GIS-supported reconstruction of the Egesen III glacier surface. (click on image to magnify)
Fig. 8: Long profile of the reconstructed Egesen I glacier with the moraine evidence from geomorphological mapping. (Click on image to enlarge)
The computer aided model is mainly based on the raster based
module GRID of the GIS software ARC/INFO Version 7.1. The GRID
module of ARC/INFO offers the advantage of built-in matrix calculations
with the possibility to handle each cell, each line and each column
seperately.The reconstruction model uses the advanced macro language
(AML) of ARC/INFO with a summarized script length of about 2250
lines enriched with short Fortran 77 scripts. The statistical
analysis was done with the S-PLUS program package, which is a
powerful tool for processing large data sets.
To compute the DTM from contour lines, the SPANS software was
used as well. Regardless of the inadequacy of the according routines
the slope and aspect grids (grid is the ARC/INFO synonym for raster
files) were also calculated with ARC/INFO. In the GIS-based model
it is assumed that the central flow lines follow the rivers. All
main program steps are shown in the following flowcharts.
