Quantifying glacial erosion on a limestone bed and the relevance for landscape development in the Alps

Abstract

Glacial erosion is the basic process that has shaped the landscapes of the Alps. Despite intense research over centuries, and the use of various techniques, determination of glacial erosion rates remains challenging. This is not only because the location where the process occurs is almost inaccessible, but also because it is dependent on many different factors including, ice thickness and velocity, glacier thermal regime, and lithology. Reported glacial erosion rates range over several orders of magnitude (0.01– (>) 10 mm/a). Most studies focus on crystalline bedrock, whereas few researchers have investigated glacial erosion on limestone. Here we analyse glacially polished bedrock surfaces at the recently deglaciated forefield of the Tsanfleuron glacier, Swiss Alps. The nearly horizontally bedded limestone hosts a well‐developed karst system. Meltwater from the glacier drains into the subsurface within a few meters of the ice margin. By combining geomorphological mapping, measurement of cosmogenic 36Cl concentrations of glacially eroded bedrock surfaces, and a numerical model (MECED), we quantify at each sample location the amount of rock removed during glacier occupation. The glacial erosion rates calculated from these values range from zero to 0.08 mm/a. These are orders of magnitude lower than values measured at comparable sites on crystalline bedrock. The high 36Cl concentrations we measured show that the Tsanfleuron glacier was unable to effectively erode the gently dipping, strongly karstified limestone. We suggest that this effect may play a key role in formation and preservation over many glacial cycles of high‐elevation, low‐relief limestone plateaus in the Alps.

Full text

Quantifying glacial erosion on a limestone bed and
the relevance for landscape development in the
Alps
Olivia Steinemann,
1
*Susan Ivy-Ochs,
1
Sandra Grazioli,
2
Marc Luetscher,
3
Urs H. Fischer,
4
Christof Vockenhuber
1
and
Hans-Arno Synal
1
1
Laboratory of Ion Beam Physics, ETH Zürich, Otto-Stern-Weg 5, 8093 Zürich, Switzerland
2
ETH Zürich, Institute of Geology, Sonneggstrasse 5, 8092 Zürich, Switzerland
3
Swiss Institute for Speleology and Karst Studies (SISKA), Rue de la Serre 68, 2301 La Chaux-de-Fonds, Switzerland
4
Nationale Genossenschaft für die Lagerung radioaktiver Abfälle (NAGRA), Hardstrasse 73, 5430 Wettingen, Switzerland
Received 10 May 2019; Revised 20 December 2019; Accepted 29 December 2019
*Correspondence to: Olivia Steinemann, Laboratory of Ion Beam Physics, ETH Zürich, Otto-Stern-Weg 5, 8093 Zürich, Switzerland. E-mail: okronig@phys.ethz.ch
ABSTRACT: Glacial erosion is the basic process that has shaped the landscapes of the Alps. Despite intense research over centu-
ries, and the use of various techniques, determination of glacial erosion rates remains challenging. This is not only because the lo-
cation where the process occurs is almost inaccessible, but also because it is dependent on many different factors, including ice
thickness and velocity, glacier thermal regime and lithology. Reported glacial erosion rates range over several orders of magnitude
(0.01 to >10 mm a
1
). Most studies focus on crystalline bedrock, whereas few researchers have investigated glacial erosion on lime-
stone. Here we analyse glacially polished bedrock surfaces at the recently deglaciated forefield of the Tsanfleuron glacier, Swiss Alps.
The nearly horizontally bedded limestone hosts a well-developed karst system. Meltwater from the glacier drains into the subsurface
within a few metres of the ice margin. By combining geomorphological mapping, measurement of cosmogenic
36
Cl concentrations
of glacially eroded bedrock surfaces and a numerical model (MECED), we quantify at each sample location the amount of rock re-
moved during glacier occupation. The glacial erosion rates calculated from these values range from 0 to 0.08 mm a
1
. These are or-
ders of magnitude lower than values measured at comparable sites on crystalline bedrock. The high
36
Cl concentrations we
measured show that the Tsanfleuron glacier was unable to effectively erode the gently dipping, strongly karstified limestone. We sug-
gest that this effect may play a key role in formation and preservation over many glacial cycles of high-elevation, low-relief limestone
plateaus in the Alps. © 2020 John Wiley & Sons Ltd.
KEYWORDS: cosmogenic
36
Cl; glaciokarst; Swiss Alps; limestone plateau; Tsanfleuron
Introduction
Over a century ago, researchers realized that glaciers are the
dominant agents in shaping some of the most impressive Qua-
ternary landscapes like fjords, deep alpine valleys and foreland
overdeepenings (Agassiz, 1838; Wright, 1887; Penck and
Brückner, 1901; Voskule, 1904; Penck, 1905). Ever since then
there has been intense debate on how fast glaciers erode. Yet,
quantitative investigations on the rates and spatial patterns of
glacial erosion are rare, especially on limestone. This is be-
cause of the complex nature of the erosion processes: abrasion,
plucking/quarrying, scour by meltwater and chemical denuda-
tion (Boulton, 1982; Drewry, 1986; Hallet et al., 1996; Iverson,
2002; Cook and Swift, 2012), and the difficulty of accessing the
ice–bedrock interface to do on-site observations and measure-
ments. De Quervain (1919) and Lütschg-Loetscher (1944) mea-
sured glacial erosion rates between 0.1 and 2.7 mm a
1
,ona
polished limestone ridge at the Oberer Grindelwaldgletscher
during its readvance around 1920, comparing the depth of
boreholes before and after the readvance. Boulton (1982)
cemented plates of marble and basalt underneath an Icelandic
and an Alpine glacier and measured values from 0.9 mm a
1
for the basalt up to 37.5 mm a
1
on the marble plate. Measur-
ing the volume of suspended sediment load of meltwater
streams and integrating it over the catchment area allows cal-
culation of glacial erosion rates that vary between 1 and
2mm a
1
in Alaska, 0.4 and 1.7 mm a
1
in the Swiss Alps
and 0.1 and 0.5 mm a
1
in Scandinavia, all for temperate gla-
ciers (Hallet et al., 1996 and references cited therein; Riihimaki
et al., 2005). Numerical models have also been implemented
to further our understanding of erosion patterns and long-term
erosion rates (Harbor et al., 1988; Egholm et al., 2012; Sternai
et al., 2013; Ugelvig et al., 2016).
In the past decades, scientists have begun to make use of cos-
mogenic nuclide concentrations measured in bedrock surfaces
to determine glacial erosion rates (Briner and Swanson, 1998;
Fabel and Harbor, 1999). Cosmogenic nuclide concentrations
increase predictably with depth in rock during exposure to
EARTH SURFACE PROCESSES AND LANDFORMS
Earth Surf. Process. Landforms (2020)
© 2020 John Wiley & Sons Ltd.
Published online in Wiley Online Library
(wileyonlinelibrary.com) DOI: 10.1002/esp.4812

cosmic rays. If the glacial fluctuation history is known, nuclide
concentrations can be used to derive the rate of glacial erosion
(Briner and Swanson, 1998; Fabel et al., 2004; Goehring et al.,
2011; Young et al., 2016; Wirsig et al., 2017). The advantage
of the cosmogenic nuclide approach is that it allows quantifica-
tion of glacial erosion directly on the eroded bedrock. Glacial
erosion mainly occurs under temperate glaciers and is negligible
or largely inefficient under cold-based ice (Fabel et al., 2002;
Linge et al., 2006; Blomdin and Harbor, 2017). Measured ero-
sion depths or erosion rates using cosmogenic nuclides range
between 0.09 mm a
1
, measured in gabbro (Briner and
Swanson, 1998), to over 5 mm a
1
measured at a recently ice-
free gneiss outcrop inside the Little Ice Age (LIA) extent (Wirsig
et al., 2017). A comprehensive summary of measured glacial
erosion rates determined with cosmogenic nuclides can be
found in the supplementary material of Delmas et al. (2009).
In theory, limestone is more erodible than gneiss (Kühni and
Pfiffner, 2001; Hinderer et al., 2013), thus it should be much
easier to abrade beneath a sliding glacier. However, glacial ero-
sion has never been quantitatively measured on limestone
beds, all reported values were determined in silicate bedrock.
The differences in erodibility and the processes of erosion of
the two classes of bedrock must have led to markedly different
Alpine landscapes. In general, deep, steep-walled valleys dom-
inate regions underlain by granites and gneisses of the Aar and
Gotthard Massifs, while in limestone terrains of the Helvetic
nappes, high-elevation, low-relief surfaces are characteristic.
The presence of these high plateaus seems counterintuitive in
light of the apparent higher erodibility of limestone. Critically,
these plateaus are found in strongly karstified regions and gener-
ally bear abundant evidence of the past presence of a glacier
(Maire, 1977; Plan et al., 2009; Dertnig et al., 2017). Thus, al-
though all of the factors are apparent, a process-based under-
standing of the formation of the plateaus has remained elusive.
Indeed, basic quantitative information on the shaping processes
is lacking. Therefore, the goal of this project is to use a quantita-
tive approach to understand how glaciers erode limestone,
which may provide insight into how some of the classical Alpine
landscapes formed. Our study site is the limestone forefield of
the Tsanfleuron glacier. We use a multidisciplinary approach
combining geomorphological evidence from field surveys, ob-
servation and analysis based on acquired high-resolution drone
data,
36
Cl cosmogenic nuclide analysis and numerical model-
ling. Gained results give the first directly measured glacial ero-
sion rates on limestone and help to enhance the understanding
of glacier–karst interactions and landscape development.
Study Site
The investigated study site, called ‘Le Lapis de Tsanfleuron’
(Lapis: grooves and ridges formed on a limestone surface by
dissolution), is located at the border between the cantons of Va-
lais, Vaud and Bern, in the western Swiss Alps (Figure 1, insets).
It is, with a surface area of around 10 km
2
, one of the largest
karst fields in Switzerland. Presently the higher parts are still
Figure 1. Geological map of the Lapis de Tsanfleuron, modified after Badoux et al. (1959, 1990) and Gremaud et al. (2009). Black dots indicate sample
locations, the white dot is the weather station SLFDIA. The background map is a hillshade map (reproduced with authorization of swisstopo (JA100120)).
Black rectangles show the extent of Figures 3 and 4. Coordinates in black are the metric swiss grid (CH1903/LV03) and in grey the World Geodetic Sys-
tem (WGS84). BE: Bern, VD: Vaud, VS: Valais, Wi: Wildhorn nappe, Di: Diablerets nappe. [Colour figure can be viewed at wileyonlinelibrary.com]
O. STEINEMANN ET AL.
© 2020 John Wiley & Sons Ltd. Earth Surf. Process. Landforms, (2020)

covered by the Tsanfleuron glacier. Geologically, the karst pla-
teau belongs to the sedimentary Helvetic Wildhorn (Wi) and
Diablerets (Di) nappes. This is mainly composed of a massive,
thick-bedded (10 m), bioclastic limestone (Schrattenkalk) with
a gentle (<30°) northeastward dip (Figure 1) (Badoux et al.,
1959, 1990; Menkveld-Gfeller, 1994). Faults have a general
NE orientation; a few are aligned NW.
The Tsanfleuron glacier is a rather small plateau glacier
(3 km
2
, 2015) except for a 700 m-long narrow tongue in the
northern part of the glacier. To the north the glacier is confined
by a ridgeline that extends from the Oldehore (3123 m a.s.l.) to
the Sanetschhore (2924 m a.s.l.). To the south, there is an abrupt
1400 m-high cliff. The glacier surface has an average inclina-
tion of about 5° ENE, steepening to around 15° towards the
snout. Based on radiomagnetotelluric (RMT) and borehole
data, Gremaud and Goldscheider (2010) measured ice thick-
ness in 2007/2008. It averaged around 30 m and ranged up to
75–100 m in local depressions upglacier. Even though sporadic
small ice advances (<20 m) were recorded during the 130 years
of monitoring, the glacier has retreated almost 2 km in total
(www.glamos.ch).
The glacier and its well-developed karstic forefield have
been the focus of numerous studies, on basal ice motion (Hub-
bard et al., 2000; Hubbard, 2002), bedrock–ice interaction
(Sharp et al., 1989) and control of quarrying (Hooyer et al.,
2012). In their detailed study on the interaction between geo-
logical structures and the subsurface drainage of the karst aqui-
fer system, Gremaud et al. (2009) and Gremaud and
Goldscheider (2010) measured fast water flow (60–900 m h
1
)
between the injection point and the spring, confirming the ex-
istence of a well-developed karst system.
Two sediment cores were taken from the Emines pond (Fig-
ure 1), which is located about 500 m outside the LIA extent,
to unravel the tree line and timberline variations and climate
history of the Sanetsch Pass. The authors combined detailed
palynology with radiocarbon dating of macrofossils (Berthel
et al., 2012). Their dating indicates that the lake formed around
12 kyr cal BP and since that time has never been covered by a
glacier.
Methods
Fieldwork
Field survey of landforms and sediment was conducted be-
tween 2015 and 2018 supported by a tablet. We mapped fea-
tures directly onto georeferenced maps using the Garafa GIS
Pro application (Garafa, LLC, Version 3.21.1). A drone (E-Bee
from senseFly) was used to capture high-resolution aerial
photos (8 cm), from which a digital surface model was made
with the associated software (eMotion3 from senseFly). Com-
bining field investigations, the high-resolution drone data and
information of previous studies (Gremaud et al., 2009), a de-
tailed geomorphological map was created.
Sample preparation,
36
Cl measurement and
production rates
During field surveys, 19 bedrock samples were taken for
36
Cl
analysis. The first set of samples (Tsan1–Tsan14) were chosen
equally distributed over the entire width of the forefield, as well
as inside and outside the prominent LIA moraine. From the sec-
ond sample set, three are located right in front of the glacier
(Tsan15–Tsan17) and the other two are from a bedrock step
(Tsan18 and Tsan19), where one was sampled on top of the
step (Tsan18) and the other inside a small cavern at the bottom
of the step (Tsan19). Only striated or polished bedrock surfaces
at topographic highs were sampled (except Tsan19), to mini-
mize the shielding effect of temporary sediment cover during
exposure.
Sample preparation for
36
Cl analysis was done at the Labora-
tory of Ion Beam Physics (ETH Zürich) and follows the proce-
dure described in Stone et al. (1996) and Ivy-Ochs et al.
(2004). The
36
Cl was measured on the 6-MV TANDEM system
at the Laboratory of Ion Beam Physics (ETH Zürich), relative
to the internal K382/4 N
36
Cl/Cl standard and corrected for a
procedural laboratory blank (for details, see Table I) (Synal et al.,
1997; Christl et al., 2013; Vockenhuber et al., 2019). Major and
trace elements were measured in aliquots of leached sample
material with ICP-MS at Act Labs S.A. (Ontario, Canada)
(Table II).
Apparent exposure ages (without corrections for karst
weathering and snow shielding) were calculated using an in-
house MATLAB code (Wirsig et al., 2017). The code is based
on constants and equations given in Alfimov and Ivy-Ochs
(2009 and references cited therein). The code includes produc-
tion though all pathways, calculated for each sample based on
the measured elemental concentrations (Table II). We used the
spallation production rate of 48.8 ± 3.4
36
Cl atoms g
Ca
1
a
1
(Stone et al., 1996). Treatment of muon production is described
in detail in Alfimov and Ivy-Ochs (2009) and Stone et al.
(1998). The contribution of neutron capture on
35
Cl was calcu-
lated based on a value of 760 ± 150 neutrons g
air
1
a
1
(Alfimov
and Ivy-Ochs, 2009). These values are in excellent agreement
with the recently published production rates of Marrero et al.
(2016). As shown in Figure 2, at Tsanfleuron spallation of cal-
cium dominates
36
Cl production and as given by the very low
natural
35
Cl concentrations (<12 ppm), the contribution by
neutron capture is minor. Similarly, enhanced production of
36
Cl due to a hydrogen-rich layer (snow cover) can be
neglected (Dunai et al., 2014). Nevertheless, the code does in-
clude this calculation (see Wirsig et al., 2017).
MECED modelling
To calculate the evolution of
36
Cl concentrations with time,
theoretical final nuclide concentrations and glacial erosion
rates for each sample, we use the MECED model (Multi-nu-
clide-Exposure-Coverage and Erosion Depth profile) (Wirsig
et al., 2017). Minor adaptations were made in the MATLAB
code to be suitable for the specific requirements of this study.
The following input parameters are needed: duration of expo-
sure periods (production), duration of glacial coverage periods
(no production), snow height and duration (reduced produc-
tion) and karst weathering rate (removal of rock therefore re-
moval of
36
Cl). Each of these was evaluated from literature
data and snow height records.
In a first step, and considering all the carefully defined in-
puts, the model performs a forward calculation of increase in
cosmogenic nuclide concentration with depth in the bedrock
for defined time steps. A time interval of 100 years and depth
steps of 0.01 cm were chosen (cf. Wirsig et al., 2017). For each
time step, the model checks the defined settings (is there a gla-
cier or not, how much snow for how many months of the year
and how much karst erosion) and calculates according to that a
new concentration–depth profile before it continues with the
next time increment. Modelled
36
Cl concentrations with depth
for a given time step are added to the concentrations obtained
from the previous step. This continues stepwise through 100-
year steps going through the glacier coverage scenarios
QUANTIFYING GLACIAL EROSION ON A LIMESTONE BED
© 2020 John Wiley & Sons Ltd. Earth Surf. Process. Landforms, (2020)

Table I. List of samples, basic parameters, measured cosmogenic nuclide concentrations and calculated apparent exposure ages, erosion depths and rates
Sample Location
East Nord Latitude Longitude Elevation Thickness Topographic
shielding
36
Cl concentration
a,b
Apparent exposure age
c
Erosion depth Erosion rate
d
CH1903/LV03 WGS 84 (m a.s.l.) (cm) (10
6
at g
rock
1
) (ka) (cm) (mm a
1)
Tsan1 inside LIA 585250 129398 46.316 7.247 2556 1.5 0.9986 1.26 ± 0.04 8.4 ± 0.4 2.9 –7.5 0.01 –0.03
Tsan2 inside LIA 585431 129212 46.314 7.250 2550 1.0 0.9986 1.54 ± 0.04 10.3 ± 0.5 0.0 –0.0 0
Tsan3* inside LIA 585419 129045 46.313 7.249 2554 1.0 0.9995 1.49 ± 0.03 10.0 ± 0.4 0.0 –0.0 0
Tsan4 outside LIA 585552 128678 46.309 7.251 2525 1.5 0.9995 1.62 ± 0.05 11.0 ± 0.5 0.0 –0.0 0
Tsan5* outside LIA 585580 128916 46.312 7.251 2507 1.0 0.9992 1.26 ± 0.03 8.8 ± 0.4 7.7 –10.8 0.05 –0.08
Tsan6* outside LIA 585833 129224 46.314 7.255 2508 1.5 0.9996 1.53 ± 0.03 10.6 ± 0.4 0.0 –0.0 0
Tsan7* inside LIA 585608 130257 46.323 7.252 2488 1.5 0.9925 1.07 ± 0.03 7.4 ± 0.3 14.1 –17.4 0.06 –0.07
Tsan8 inside LIA 585637 130095 46.322 7.252 2511 1.5 0.9955 1.26 ± 0.04 8.8 ± 0.4 1.5 –6.0 0.01 –0.02
Tsan9* inside LIA 585545 129941 46.321 7.251 2502 2.0 0.9972 1.27 ± 0.04 8.9 ± 0.4 0.2 –4.2 0.00 –0.02
Tsan10 inside LIA 585462 129724 46.319 7.250 2522 2.0 0.9987 1.05 ± 0.05 7.2 ± 0.4 13.8 –20.3 0.06 –0.08
Tsan11* inside LIA 585765 129553 46.317 7.254 2502 1.5 0.9987 1.38 ± 0.10 9.7 ± 0.7 0.0 –2.0 <0.01
Tsan12 inside LIA 586150 129561 46.318 7.259 2467 1.5 0.9987 1.60 ± 0.07 11.4 ± 0.6 0.0 –0.0 0
Tsan13* outside LIA 587155 130758 46.328 7.272 2333 1.5 0.9925 1.26 ± 0.03 10.1 ± 0.4 0.0 –2.8 0.00 –0.02
Tsan14 outside LIA 587376 130722 46.328 7.275 2317 2.0 0.9925 1.18 ± 0.04 9.8 ± 0.5 2.5 –7.8 0.02 –0.06
Tsan15 close glacier 584676 130088 46.322 7.240 2601 2.0 0.9981 0.77 ± 0.02 5.0 ± 0.2 7.1 –10.8 0.01 –0.01
Tsan16 close glacier 584266 129965 46.321 7.234 2663 2.0 0.9924 0.91 ± 0.03 5.7 ± 0.2 0.0 –2.4 <0.01
Tsan17 close glacier 584141 129798 46.319 7.233 2681 3.0 0.9989 0.87 ± 0.02 5.4 ± 0.2 2.5 –6.4 0.00 –0.01
Tsan18 close glacier 584477 129467 46.316 7.237 2612 3.0 0.9986 0.84 ± 0.02 5.6 ± 0.2 0.7 –4.3 0.00 –0.01
Tsan19 inside cavern 584477 129467 46.316 7.237 2606 0.02 ± 0.00 0.2 ± 0.03
a
Measured against standard K382/4 N (17.36(±0.35) × 10
12
) (Christl et al., 2013; Vockenhuber et al., 2019).
b
Corrected for processed blank of (3.1 ± 2.7) × 10
15 36
Cl/
35
Cl or (2.5 ± 0.4) × 10
15 36
Cl/
35
Cl if sample is marked with an asterisk (*).
c
Production rates as in Alfimov and Ivy-Ochs (2009) and references therein (SpCa 48.8 ± 3.4 at g
Ca
1
a
1
).
d
Erosion rate of <0.01 means that the max. Value was smaller than 0.01mm a
1
, 0 if it was not possible to calculate an erosion rate.
O. STEINEMANN ET AL.
© 2020 John Wiley & Sons Ltd. Earth Surf. Process. Landforms, (2020)

described in detail below. The calculation includes the radio-
active decay of
36
Cl.
To obtain the depth of erosion (i.e. the thickness of missing
rock), the model plots a sample specific modelled
36
Cl
concentration–depth profile based on the input parameters
and chosen glacial history scenario. The concentration at the
surface (0 cm) corresponds to the final modelled
36
Cl concen-
tration. At this point the model has not been including glacial
erosion, as that is what we are trying to find out. If the AMS-
measured
36
Cl concentration is plotted on the same graph,
the intersection point with the curve shows at what depth the
measured concentration would be found (see also below). In
other words, we compare the modelled surface
36
Cl concentra-
tion with the
36
Cl concentration measured in the actual rock
surface. The difference of the two concentrations viewed on
the
36
Cl vs. depth plot shows the total thickness of rock that
was removed by the glacier. To calculate an average erosion
rate, the obtained erosion depth is divided by the total time of
glacier coverage, which was already defined by the glacier
exposure/coverage input.
Results and Interpretation
Geomorphology
Karst landforms
The Lapis de Tsanfleuron is famous for its variety of karst land-
forms. The area outside the LIA extent (Figure 3) was longer ex-
posed to environmental influences and therefore the most
pronounced karren field is found in the lowest elevation,
mostly vegetated part of the study area. There, it was observed
that karren in depressions are up to 1.0 m deep, whereas on
bedrock highs they are almost absent. On vegetation-free
slopes of bedrock highs, a crosshatch pattern exists of faint pre-
served horizontal glacial striations that are cross cut by karren
which follow the gradient of the hillslope. This suggests that
the karst weathering rate is rather low as it was not able to
completely erase glacial striations formed more than 11
000 years ago (Berthel et al., 2012).
Numerous vertical shafts and swallow holes, often aligned
along faults or factures, are present within the entire study area
(Figure 4). Their depth ranges between a few decimetres and
several tens of metres (Favre, 2006). Active swallow holes
where abundant supra- and subglacial meltwater enters the
karst system directly were observed near the glacier front (Fig-
ure 4c). However, not all the water seems to drain into the sub-
terranean karst system. Some of the water is stored in numerous
little lakes and ponds. The largest and deepest lakes seem to be
associated with collapsed karst features (subsidence doline or
collapse doline). Those collapsed features are 5–20 m deep
and have diameters up to 20 m.
Glacial depositional landforms
The most prominent depositional landform is the broad LIA mo-
raine ridge, which divides the Lapis de Tsanfleuron into inside
and outside LIA domains. The intact parts of the moraine form
not a single and straight continuous ridge, but rather a winding
and hummocky chain. At some locations, several parallel
ridges can be observed. The frontal LIA moraine ridge is gener-
ally between 2 and 6 m high, but can go up to 8 m in height.
The sediment is poorly sorted and composed of very angular
components ranging from sand to decimetre-sized clasts; large
boulders are rare. The boundary between the LIA moraine and
Table II. Elemental composition of leached samples. Values below detection limit are marked <. Cl values are from AMS measurements.
Sample Al
2
O
3
CaO Fe
2
O
3
K
2
O MgO MnO Na
2
OP
2
O
5
SiO
2
TiO
2
Sm Gd U Th Cl
(%) (%) (%) (%) (%) (%) (%) (%) (%) (%) (ppm) (ppm) (ppm) (ppm) (ppm)
Tsan1 0.29 56.14 0.08 0.06 0.15 0.006 0.10 0.03 0.75 0.004 0.1 0.2 0.6 0.1 2.88 ± 0.02
Tsan2 0.29 56.14 0.08 0.06 0.15 0.006 0.10 0.03 0.75 0.004 0.1 0.2 0.6 0.1 3.30 ± 0.01
Tsan3 0.15 55.35 0.11 0.03 0.19 0.008 0.03 <0.01 0.64 0.007 0.3 0.4 0.4 0.2 3.94 ± 0.02
Tsan4 0.09 56.15 0.07 0.02 0.12 0.005 0.02 0.03 0.22 0.003 0.2 0.2 0.5 0.1 2.77 ± 0.02
Tsan5 0.23 54.82 0.28 0.04 0.13 0.013 0.05 0.01 0.76 0.011 0.6 0.6 0.3 0.6 4.76 ± 0.03
Tsan6 0.14 55.58 0.06 0.03 0.12 0.005 0.05 <0.01 0.35 0.002 <0.1 <0.1 0.4 <0.1 3.23 ± 0.02
Tsan7 0.19 55.56 0.10 0.03 0.15 0.010 0.04 0.01 0.81 0.007 0.4 0.4 0.3 0.4 8.56 ± 0.03
Tsan8 0.16 55.37 0.12 0.03 0.14 0.007 0.05 0.02 0.40 0.003 0.2 0.2 0.3 0.1 4.21 ± 0.01
Tsan9 0.11 55.45 0.09 0.02 0.20 0.019 0.02 0.02 1.30 0.005 0.2 0.1 2.4 <0.1 3.55 ± 0.02
Tsan10 0.22 55.51 0.07 0.04 0.14 0.006 0.09 0.02 0.65 0.002 <0.1 <0.1 0.4 <0.1 4.40 ± 0.02
Tsan11 0.10 55.35 0.07 0.02 0.14 0.008 0.03 <0.01 0.37 0.004 0.1 0.2 0.5 0.1 3.20 ± 0.13
Tsan12 0.10 55.12 0.08 0.02 0.16 0.007 0.02 0.02 0.58 0.005 0.2 0.2 0.5 0.1 4.24 ± 0.01
Tsan13 0.39 53.22 0.13 0.10 0.88 0.005 0.02 0.04 1.30 0.022 0.5 0.5 1.9 0.5 7.99 ± 0.05
Tsan14 0.66 52.26 0.31 0.08 0.78 0.010 0.04 0.04 2.25 0.027 0.4 0.4 1.5 0.5 10.83 ± 0.05
Tsan15 0.39 55.92 0.16 0.05 0.17 0.009 0.03 0.01 0.83 0.020 0.4 0.2 0.9 0.3 4.70 ± 0.22
Tsan16 0.16 55.81 0.10 0.02 0.29 0.011 0.04 <0.01 0.64 0.006 0.05 0.05 0.9 0.05 4.74 ± 0.21
Tsan17 0.32 55.64 0.09 0.05 0.22 0.011 0.04 <0.01 0.61 0.014 0.2 0.3 0.4 0.3 4.54 ± 0.23
Tsan18 1.13 53.83 0.42 0.20 0.34 0.011 0.05 0.08 2.21 0.049 0.6 0.3 1.6 0.8 4.77 ± 0.22
Tsan19 1.57 51.79 1.58 0.21 0.36 0.012 0.04 0.13 4.50 0.070 1.3 1.3 1.2 1.5 4.78 ± 0.18
Figure 2. Different
36
Cl production mechanisms and the total produc-
tion rate with increasing depth in limestone. Calculated using the ele-
mental and location data of Tsan10. [Colour figure can be viewed at
wileyonlinelibrary.com]
QUANTIFYING GLACIAL EROSION ON A LIMESTONE BED
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the bare bedrock surface outside the LIA extent is sharp. In con-
trast, inside the LIA moraine ridge, (sub-)glacial sediment thins
out over tens to hundreds of metres upglacier. Within this till,
some streamlined (almost drumlin-like; cf. Johnson et al.,
2010) landforms were observed. They are aligned parallel to
the former flow direction of the glacier, up to 50m long and
10 m wide, and composed of mainly angular components sim-
ilar to the sediment in the moraine. Most of the study area is
bare bedrock; there is nothing like a subglacial till on the lime-
stone plateau outside the area of the LIA moraine (Figure 4).
Figure 3. Geomorphological map showing the large-scale features and apparent
36
Cl exposure ages (ka). Samples are colour-coded according to
their position and the glacier exposure/coverage history into: outside LIA (dark green), inside LIA (medium green) and close to the glacier (bright
green). The background map is a multidirectional hillshade map generated with the acquired drone data. To complement areas which were not cov-
ered by the drone flights, the slightly brighter multidirectional hillshade map based on the SwissAlti3D digital elevation model was used (reproduced
with authorization of swisstopo (JA100120)). Only fractures and faults >50 m in length are shown. The legend includes also the mapped small-scale
features shown on the detail map (black square) in Figure 4. [Colour figure can be viewed at wileyonlinelibrary.com]
O. STEINEMANN ET AL.
© 2020 John Wiley & Sons Ltd. Earth Surf. Process. Landforms, (2020)

Striking are the up to 40 m wide and several kilometre long
sediment stripes present all across the forefield (Figures 3
and 4d). They consist of very angular blocks and clasts
(centimetre to metre size), but are completely lacking in
fines. The sediment is for the most part bright Schrattenkalk,
like the underlying bedrock. A few stripes are composed of
a much darker lithology (marls), indicating an upglacier
source. The sediment stripes clearly follow the flow direction
of the glacier, whether straight or radial (Figure 3). Stripes
often go right over bedrock highs, ruling out the involvement
of water in transport or deposition. From field observations
(Figure 4d) and aerial images, we saw that the sediment
stripes originate from layers inside the ice and not from be-
low the glacier. It seems that blocks of bedrock were plucked
from subglacial outcrops, then incorporated into the ice pos-
sibly through englacial thrusting (Benn and Evans, 2014). As
the glacier melts, the sediment is released and deposited
passively.
Figure 4. Close-up of the geomorphological map showing small-scale features (for legend and location, see Figure 3). Photographs of features
discussed in text. (a) Area with straight channels and bedrock steps in the back. (b) Nye channel with a second-generation channel cut into it. (c) Large
swallow hole/vertical shaft in the foreground (about 2 m across) where the meltwater from the glacier is draining into the karst system. (d) Sediment
stripe emerging from within the glacier and continuing over a bedrock high (near the person in red). [Colour figure can be viewed at
wileyonlinelibrary.com]
QUANTIFYING GLACIAL EROSION ON A LIMESTONE BED
© 2020 John Wiley & Sons Ltd. Earth Surf. Process. Landforms, (2020)

Erosional landforms
At first sight, the Lapis de Tsanfleuron appears to be a strongly
glacially modified landscape. The entire forefield is highly
polished and striations can be seen both inside and outside the
LIA moraine. On closer examination, large 1–8 m-high bedrock
steps called Schichttreppen karst or stepped-pavement karst
(Bögli, 1980) are seen to dominate the area (Figures 4a and 5).
Some steps are more than several hundred metres wide and of-
ten have a crescent shape. They have surprisingly flat surfaces,
which roughly correspond to the bedding planes of the
Schrattenkalk. Rarely, roche moutonnées are carved into the
bedrock step surfaces, some as high as 3 m. At the bottom of
the rock steps, we observed straight channels (10 cm wide and
10–30 cm deep) emerging along the bedding planes (Figure 4a).
The channels are straight, regular and arranged in a parallel pat-
tern, suggesting that they developed along pre-existing bedrock
structures like joints and fractures. They sometimes end at verti-
cal karst shafts, which suggests that those channels are part of the
karst system and not of glacial origin, although formation or fur-
ther use while the area was covered by the glacier seems likely.
Coexisting with the rather straight channels are more sinuous
channels, interpreted as Nye channels (Figure 4b), which
formed by (pressurized) subglacial meltwater (Nye, 1973). On
the almost horizontal bedding planes, they have distinctly tor-
tuous flow paths with confluence of smaller channels to larger
ones. These are 30–50 cm deep and up to 30 m long before
they end in vertical shafts, swallow holes or just fade out at
the surface. Some of the channels are filled with gravel or have
a smaller sinuous channel incised deeper into them (Figure 4b).
It is therefore likely that those channels were reused by (melt-)
water (cf. Walder and Hallet, 1979).
Small glacial features like spoon-shaped dissolution scallops
(3–5 cm) on the lee side of bedrock obstacles (Richardson and
Carling, 2005) and subglacial calcite precipitates close to the
ice margin were frequently observed (Sharp et al., 1990).
36
Cl results
Apparent exposure ages
In a first step, we discuss apparent
36
Cl exposure ages (not
corrected for karst weathering or snow shielding) (Table I,
Figure 3). We divided the samples into three groups according
to distance from the glacier front: (a) outside LIA; (b) inside LIA;
and (c) close to the glacier. Samples in the first set (Tsan4,
Tsan5, Tsan6, Tsan12, Tsan13, Tsan14) have apparent exposure
ages between 8.8 ± 0.4 and 11.4 ± 0.6 ka. The second group of
samples, those located close to the LIA moraine but inside it
(Tsan1, Tsan2, Tsan3, Tsan7, Tsan8, Tsan9, Tsan10, Tsan11),
have ages that range from 7.2 ± 0.4 to 10.3 ± 0.5 ka. For the
third group, those located right at the front of the glacier
(Tsan15, Tsan16, Tsan17, Tsan18), apparent exposure ages are
between 5.0 ± 0.2 and 5.7 ± 0.2 ka.
Remarkable about the results of the first two groups is that they
have practically the same
36
Cl concentrations and apparent ex-
posure ages, although they must have experienced very different
exposure histories. The samples outside the LIA moraine proba-
bly became ice-free as the Egesen stadial Tsanfleuron glacier
retreated around 11.5 ka (Berthel et al., 2012). In contrast, the
samples inside the LIA moraine were undoubtedly covered by
the LIA glacier advances (Dufour, 1844). If the glacier had
eroded all
36
Cl nuclides accumulated during previous ice-free
periods, their exposure ages should be around 150 years, the
time when the LIA glacier started retreating. This indicates the
presence of
36
Cl inherited from previous ice-free periods. Some
of the sample sites of the third group, those right in front of the
glacier, only became ice-free in the summer when they were
sampled (2018) or at most around the early 1990s, according
to older topographic maps (source: Federal Office of Topogra-
phy swisstopo). This means that their true exposure age or nu-
clide concentration should be almost zero; measured apparent
exposure ages for those samples are 5.0–5.7 ka.
Considerations regarding
36
Cl production with depth
To understand
36
Cl production with depth in the limestone, we
took two additional samples, one from the top of a 6 m-high bed-
rock step (Tsan18) and one from inside the small cavern at the
base of the step (Tsan19) (Figure 5). In case of long-term
36
Cl pro-
duction at depth (>0 m) by muons, the measured concentration
of the two samples would be similar. However, the measured
concentration inside the little cave (Tsan19) is almost 40 times
less than at the surface of the rock step (Tsan18: 0.838 × 10
6
at
g
rock
1
, Tsan19: 0.023 × 10
6
at g
rock
1
). We approximated the
Figure 5. Comparison of model-calculated profiles and measured
36
Cl concentrations for samples above (Tsan18) and below (Tsan19) a 6 m-high
bedrock step. The magenta curve shows the vertical concentration–depth profile with a shielding factor measured for sample Tsan18 (0.99). The blue
curve represents the horizontal concentration–depth profile from the front of the bedrock step, using a shielding correction factor of 0.5. c
V
is the cal-
culated nuclide concentration produced from the top (6m depth, magenta curve) and c
H
the nuclides contributed from the front (2.5 m depth, blue
curve). Inset shows close-up between 0 and 0.5 × 10
5
atoms g
rock
1
and from 160 to 600 cm depth. The AMS-measured
36
Cl concentrations of Tsan19
and Tsan18 are plotted with associated uncertainties (grey bar) for comparison. The red vertical line is the estimated total (c
V
+c
H
) nuclide concen-
tration for sample Tsan19. The photo shows the location of the two samples Tsan18 and Tsan19; view is to the west. [Colour figure can be viewed at
wileyonlinelibrary.com]
O. STEINEMANN ET AL.
© 2020 John Wiley & Sons Ltd. Earth Surf. Process. Landforms, (2020)

theoretical amount of
36
Cl nuclides in sample Tsan19 by sum-
ming the amount of
36
Cl produced vertically (top down from
the surface, magenta line in Figure 5) and horizontally (from
the front, blue line). The two concentration–depth profiles were
calculated with the local glacial coverage history (III) including
snow shielding and karst weathering (see following sections for
further details of glacial coverage histories). The
36
Cl concentra-
tion produced from the surface vertically at 6 m depth is 8 × 10
3
at g
rock
1
, the contribution horizontally at 2.5 m depth is 21 × 10
3
at g
rock
1
. The sum of these two (29 × 10
336
Cl at g
rock
1
) is well com-
parable to the AMS-measured value of Tsan19 (23.0 ± 4.0 × 10
3
36
Cl at g
rock
1
). This first test suggests that our measured concentra-
tions across the Tsanfleuron forefield are not an artefact of deep
muon production.
Implementation of the MECED model
Definition of input parameters
Crucial in implementation of the MECED model is the defini-
tion of the main input parameters. These include glacier
exposure/coverage history, snow height and duration, and karst
erosion. Accordingly, parameters were adopted only after close
scrutiny of the literature. At the study site, production of
36
Cl
during ice-free phases is 120–140 at g
rock
1
a
1
(depending on
the elevation), whereas during the time of glacier coverage
there is no production at all. To envision the magnitude of the
effect due to karst weathering and snow shielding (values will
be discussed in more detail later), we note that a karst
weathering rate of 5 mm ka
1
reduces the concentration of
36
Cl that will be measured at the rock surface by ~5%; cover-
age of the rock by 50, 100 and 200 cm of snow during 6months
of the year reduces the production of
36
Cl by 7, 13 and 21%,
respectively.
For each sample, a higher final model-calculated
36
Cl con-
centration compared to the measured concentration allows gla-
cial erosion, because glacial erosion would decrease the
concentration in the limestone. The difference of the two de-
fines the depth of rock removed beneath the glacier and thus
the glacial erosion rate. If the difference between model and
measured
36
Cl concentration is small, then the glacial erosion
rate allowed is low. Similarly, if the model-calculated
36
Cl con-
centration is less than the measured one, then glacial erosion is
zero or the impact of one of the parameters (snow or karst) that
we have adopted is too great. For this reason, the chosen pa-
rameters are generally on the conservative side.
The exposure/glacier cover history has the most influence on
the results, and is dependent on the sample position with re-
spect to the location of the ice margin at a given time. For each
of the sample groups, a different exposure/coverage history is
required: (I) samples outside the LIA moraine; (II) samples in-
side the LIA moraine; and (III) samples close to the present ice
margin. The three exposure/glacier coverage histories are
depicted in Figure 6, with blue bars showing periods of ice cov-
erage (I, II, III). The bars are divided into two scenarios; (A) starts
during the Oldest Dryas and includes the Bølling-Allerød inter-
stadial (14.6–12.9 ka) and (B) starts after the Younger Dryas
cold phase (11.5 ka). As a first step, we plot the resulting growth
of
36
Cl with time curves for each of the three groups, without
considering reduction of
36
Cl concentrations due to snow
cover or karst weathering. The horizontal lines show AMS-
measured
36
Cl concentration of a representative sample from
each group (colour coded for the sample location group).
How the three exposure/coverage histories were reconstructed
is explained in the following sections.
Constraints for the first boundary condition for the
exposure/coverage history was given by the analysis of the
apparent exposure ages of the samples outside the LIA (group I,
dark green). To obtain apparent exposure ages of ~10 ka, the
glacier history has to include at least a total of 10 ka of exposure
(ice-free phases). It is unlikely that a Holocene glacier covered
these samples (Dufour, 1844). Therefore, the simplest exposure
history would be continuous exposure since the retreat of the
Egesen stadial glacier around 11.5 ka (I-B in Figure 6). Compar-
ison of the final model-calculated nuclide concentration of
Tsan6 to its measured concentration shows that the former is
only slightly higher (Figure 6). However, if snow shielding
and karst weathering are taken into account (both reduce the fi-
nal
36
Cl concentration), the model-calculated value would be-
come smaller than the measured concentration. This indicates
that the assumed exposure time is too short and strongly sug-
gests that the Bølling-Allerød interstadial must be included as
a period of exposure and production of
36
Cl in the rock surfaces
(I-A). Based on this first evaluation, the glacier exposure/
coverage history for the samples outside the LIA extent (dark
green) was defined to include the Bølling-Allerød interstadial
(I-A) which began at 14.6 ka, followed by glacier coverage dur-
ing the Younger Dryas cold period (12.9–11.5 ka) and constant
exposure afterwards until today.
The exposure/coverage history for the samples located just
inside the LIA extent (group II, medium green) is more complex
because they may have been covered repeatedly by the glacier
during the Holocene (II-A/B). Synthesis of Holocene glacier
Figure 6. At the top, the three implemented glacier exposure/cover-
age histories for the different sample locations are shown. Colour-cod-
ing as follows: (I) dark green for samples outside LIA extent; (II) medium
green for samples inside LIA extent; and (III) bright green for samples
close to the present ice margin. Blue bars show phases of glacier cover-
age, white bars are phases of exposure. A and B are two different
starting points for the calculation: scenario A starts during the Oldest
Dryas (OD) cold phase and includes exposure during the Bølling-
Allerød (B/A) interstadial (14.6–12.9 ka), whereas scenario B starts after
the Younger Dryas (YD) cold phase (12.9–11.5 ka). The plot below
shows the evolution of the
36
Cl concentration in the sample groups I
(dark green) and II (medium green), calculated for both scenarios A
and B. For group III (bright green), exposure starts at 10.5 ka. Flat parts
of the curves are phases of glacier coverage, thus no production of cos-
mogenic nuclides. No correction for snow coverage and karst
weathering is applied at this point. For each glacier exposure/coverage
history group (I, II, III), a representative sample with an intermediate
36
Cl concentration is plotted as a horizontal line, including its measure-
ment uncertainty (grey shadow). If the final calculated concentration is
higher than the measured concentration, then the possibility of glacial
erosion exists (see text). [Colour figure can be viewed at
wileyonlinelibrary.com]
QUANTIFYING GLACIAL EROSION ON A LIMESTONE BED
© 2020 John Wiley & Sons Ltd. Earth Surf. Process. Landforms, (2020)

fluctuation studies (Nicolussi et al., 2005; Holzhauser, 2007;
Luetscher et al., 2011; Schimmelpfennig et al., 2012; Le Roy
et al., 2015; Badino et al., 2018) led to the following scenario.
Exposure during the Bølling-Allerød followed by glacier cover-
age during the Younger Dryas (similar to the samples outside
the LIA extent), no glacier during the mid-Holocene warm
phase and several late Holocene glacier fluctuations covering
the samples between 2.6–2.5, 1.7–1.6, 1.5–1.3, 0.9–0.5 and
0.4–0.1 ka (II-A). The late Holocene glacier fluctuations add
up to a total of 1100years of glacier coverage.
The samples close to the present ice margin (group III, bright
green), due to their high elevation (around 2500 m a.s.l.), must
have been covered longer by the Tsanfleuron glacier than the
other groups. Although there are numerous studies on when
and how far glaciers advanced, constraining how far back gla-
ciers retreated during the Holocene warm phases is more diffi-
cult (Nicolussi et al., 2005; Joerin et al., 2008). For the
Tsanfleuron glacier it is thought, based on studies of other re-
cords (Nicolussi et al., 2009; Berthel et al., 2012; Le Roy
et al., 2015), that the glacier was smaller than today during
the middle Holocene up until around 3.3 ka, when cold inter-
vals became more frequent (Wanner et al., 2011; Solomina
et al., 2015). These sites were likely covered by the glacier until
the end of the Younger Dryas. Again, in light of their high
Figure 7. Plots showing the model-calculated growth of
36
Cl with time vs. AMS-measured
36
Cl concentrations for representative samples (Tsan6,
Tsan11, Tsan17) of the different glacier exposure/coverage histories: (a) outside the LIA extent (group I); (b) inside the LIA extent (group II); and (c) close
to the present glacier extent (group III). Blue bars indicate phases of glacier coverage (no
36
Cl production). Grey curves show the theoretical concen-
tration evolution without considering snow shielding and karst weathering (cf. Figure 6); green bands include varying snow heights (50–200 cm snow)
during phases of no ice (including karst weathering). See inset in (a) or text for further details. The bold black line uses an intermediate snow height
estimate, which is the one we have used to calculate erosion depths. Horizontal lines show AMS-measured
36
Cl concentrations of the corresponding
sample with its uncertainty indicated as grey bars. Additional information shown in the plots. (a) For the sample outside the LIA moraine to show the
effect of karst weathering alone, the concentration evolution was calculated considering a karst weathering of 5mmka
1
during ice-free phases (no
snow), green dashed line. (b) To show the magnitude of the effect of strong glacial erosion on the
36
Cl concentration, the two red lines were calculated
with a hypothetical glacial erosion rate of 1 mm a
1
(dotted) and 0.1 mm a
1
(dashed). Pictures to the right show a sample location corresponding to
the group shown to the left. [Colour figure can be viewed at wileyonlinelibrary.com]
O. STEINEMANN ET AL.
© 2020 John Wiley & Sons Ltd. Earth Surf. Process. Landforms, (2020)

elevation and location at the present ice margin, we hypothe-
size that they became ice-free somewhat later (10.5 ka) com-
pared to the more distal samples (cf. Schimmelpfennig et al.,
2012, 2014). Group III were exposed throughout the Holocene
climate optimum until 3.3 ka and then were continuously gla-
cier covered until 2018, or at most 10–20 years ago (Topo-
graphic maps of the 1990s (LK25, Les Diablerets and Saint-
Léonard, 1992, swisstopo)).
Karst weathering should be included during ice-free phases,
as dissolution progressively removes the top surface of the lime-
stone with the cosmogenic nuclides that were in the dissolved
rock. We have intentionally chosen a rather low karst erosion
value of 5 mm ka
1
to allow maximal glacial erosion (Plan,
2005; Häuselmann, 2008; Krklec et al., 2017). A higher karst
erosion rate would result in lower model-calculated
36
Cl con-
centrations, hence there would be fewer excess
36
Cl nuclides
left for glacial erosion. Häuselmann (2008) measured a karst
weathering value of 14 ± 7 mm ka
1
on the same lithology as
present in the study area (Schrattenkalk). The location in that
study is located less than 100 km away from the Lapis de
Tsanfleuron and precipitation (1700 mm a
1
) and elevation
(1800 m a.s.l.) are comparable. Therefore, a karst weathering
rate value of 5 mm ka
1
is a low, but still realistic, assumption.
The influence of karst weathering on the
36
Cl concentration is
shown in Figure 7a (dashed line).
To estimate snow height and duration for the past, we started
with current measured data (2012–2018) from the study area
(source: MeteoSchweiz). These snow height measurements in-
dicate a mean snow cover of approximately 200 cm for
6 months of the year. During the middle Holocene, when cli-
mate was warmer in the Alps, snow height was probably less
(Hormes et al., 2001; Nicolussi et al., 2005; Joerin et al.,
2008). Due to the high uncertainties associated with defining
a snow height for the past, we show the
36
Cl concentration evo-
lution as a broad green swath (Figures 7a–c). The lower bound-
ary was calculated using a snow cover of 200 cm for 6 months
a
1
during all ice-free periods. The upper boundary was calcu-
lated with a snow cover of 200 cm for 6 months a
1
during the
Bølling-Allerød interstadial and the late Holocene, but only
50 cm for 6 months a
1
during the mid-Holocene (200–50–
200). The bold black line within the green band represents an
intermediate snow scenario, with the following snow thick-
nesses: 200 cm for 6 months a
1
during both the Bølling-
Allerød interstadial and the late Holocene, and 100 cm during
the mid-Holocene (200–100–200). This snow scenario (bold
black line in the green bands) is the one used for further calcu-
lation of the erosion depth. Calculated growth of
36
Cl concen-
trations with time for the three glacier exposure/coverage
histories (I, II, III) and the measured nuclide concentration from
a sample of intermediate concentration (Tsan6, Tsan11,
Tsan17) are shown in Figures 7a–c. These calculations were
made for every single sample.
For example, as shown in Figure 7b, for Tsan11 (group II) the
glacier exposure/coverage history begins with exposure during
the Bølling-Allerød and
36
Cl increases (bold black line),
followed by ice coverage during the Younger Dryas; the con-
centration does not increase (line remains flat), but decreases
slightly due to radioactive decay (not visible in the figure). In
the early and middle Holocene, as the site is no longer covered
by the glacier,
36
Cl increases. In the late Holocene, the sam-
ples were more frequently covered by glacier advances, which
causes the step-like accumulation of
36
Cl in the growth curve.
For Tsan11, the final modelled nuclide concentration overlaps
with the measured concentration (within its uncertainty),
which would allow very little glacial erosion. The inclusion
of hypothetical glacial erosion is visualized with the two red
lines, where the dotted line includes a glacier erosion rate of
1mm a
1
, a common value proposed in the literature (Hallet
et al., 1996; Koppes and Montgomery, 2009) and the dashed
line a value of 0.1 mm a
1
. These are not measured, they are
simply shown to give an idea of the magnitude of change in
36
Cl concentration with such glacial erosion rates. The re-
moval of cosmogenic nuclides during glacier coverage,
implementing a glacial erosion rate of 1 mm a
1
, is immense.
It almost completely removes the entire
36
Cl signal (dotted
red line Figure 7b).
Determination of erosion depths and rates
Based on the intersection of the calculated depth profile and
the AMS-measured nuclide concentration, the amount of rock
removed by the glacier is determined (example of Tsan7 shown
in Figure 8). Including measurement uncertainties, we obtain a
minimum and maximum glacial erosion depth for each sample
(Table I). Sample specific averaged glacial erosion rates are de-
termined by dividing the erosion depth by the total time of gla-
cier coverage, which is different for each of the three scenarios
(group I outside LIA, group II inside LIA, group III close to the
glacier). Accordingly, erosion depths should not be compared
between different sample groups, while erosion rates can be
compared directly (Figure 9). For several samples (Tsan2, 3, 4,
6, 12) the calculated concentration was lower than the mea-
sured
36
Cl concentration, hence it was not possible to calculate
erosion depth or glacial erosion rate.
For samples outside the LIA (group I, dark green), calculated
maximal erosion depths and erosion rates vary between 2.8 cm
and 0.02 mm a
1
(Tsan13) and 10.8cm and 0.08mm a
1
(Tsan5), respectively. Maximal erosion depths and rates of the
samples inside the LIA moraine (group II, medium green) range
between 2 cm and <0.01 mm a
1
(Tsan11) and 20.3 cm and
0.08 mm a
1
(Tsan10). The latter is the highest determined ero-
sion rate of this study. For the samples of the third group, lo-
cated right in front of the glacier (group III, bright green), the
maximal erosion depth ranges between 2.4 cm (Tsan16) and
10.8 cm (Tsan15) with maximal erosion rates of <0.01–
0.01 mm a
1
. Glacial erosion rates inside and outside the LIA
extent are never higher than 0.08 mm a
1
, and there is no ap-
Figure 8. Determination of the sample-specific erosion depth using
the elemental and location data of Tsan7. Intersection of the calculated
36
Cl concentration–depth profile (green curve) with the AMS-measured
36
Cl concentration (blue line, grey bar with errors) indicates the thick-
ness of rock that had to be removed by the glacier to reach the mea-
sured concentration. Green area shows the influence of varying snow
heights (see text for details). Minimum and maximum depth of eroded
bedrock can be read directly on the y-axis (cm). Dividing the erosion
depth by the total glacier coverage time (scenario II) yields average ero-
sion rates (mm a
1
), displayed in parentheses. [Colour figure can be
viewed at wileyonlinelibrary.com]
QUANTIFYING GLACIAL EROSION ON A LIMESTONE BED
© 2020 John Wiley & Sons Ltd. Earth Surf. Process. Landforms, (2020)

parent trend of increasing glacial erosion rates towards the gla-
cier. Interestingly, depth of erosion and associated erosion rates
seem to be higher on the northern part of the limestone plateau.
Reflecting on input parameters and sensitivity of the MECED
model
Despite the fact that the input parameters were chosen to allow
maximal glacial erosion, their values are open for discussion.
Nevertheless, they must remain within the limits of plausibility.
For erosion rates to be higher, the final nuclide concentration
calculated with the model would have to be higher. This can
be achieved by reducing the karst erosion rate, reducing the
amount of snow and/or reducing the time that the glacier
covers the sites.
The karst denudation rate we used, 5 mm ka
1
, is already a
very low value compared to reported values. In any case, the
effect of karst weathering on calculated concentrations is only
about 5% (Figure 7a). Less snow would allow production of
more
36
Cl. Changes in snow coverage are already plotted
within reasonable limits (green band), considering modern
data. Further reduction, or assuming no snow coverage at all
during the early and mid-Holocene, seems rather unrealistic
and during the late Holocene, there would have been rather
more than less snow during the winter months (Vincent et al.,
2005; APCC, 2014).
To reach higher erosion rates, the total time of exposure
would have to be longer. Options would be to prolong the his-
tories further back in time, or shorten the intervals of ice cover-
age. Nevertheless, mapping evidence suggests that during both
the Last Glacial Maximum and the Lateglacial (before 14.6 ka),
the Tsanfleuron glacier reached much further down the valleys
(Badoux et al., 1959, 1990; Hantke, 1983; Burri, 1990; Bini
et al., 2009). Therefore, it seems implausible that there are
inherited nuclides from before the Oldest Dryas cold phase.
The late Holocene glacier fluctuations (II) could be simplified
and reduced to glacier coverage only during the LIA (glacier
coverage from 0.6–0.5 and 0.4–0.1 ka; Holzhauser et al.,
2005; Le Roy et al., 2015), which would prolong the total
ice-free time. Notably, final calculated concentrations with this
simple, glacier-hostile scenario results in only 7% higher
36
Cl
concentrations compared to the glacier fluctuation history used
in II (Figure 6). Calculated maximal erosion rates would in-
crease from 0.01 to 0.04 mm a
1
(Tsan11) or for the sample
Tsan10 with the highest value from 0.08 to 0.15 mm a
1
. Alter-
native glacier exposure/coverage histories for the samples close
to the present glacier front (III) are more challenging due to the
lack of information about how far back glaciers retreated. One
study that gives evidence is based on speleothem records in a
cave at the Grindelwald glacier (Luetscher et al., 2011). This re-
cord suggests a warm and largely ice-free phase until 5.8 ka,
followed by only short and sporadic glacier advances until
complete coverage from ca. 2.2 ka onward. Summing up, this
would give a total of ice-free time between 5.2 and 6.0 ka. This
would be even less exposure time than in scenario III (7.2 ka of
exposure), and hence would result in less or no erosion due to
the high measured
36
Cl concentrations.
Formation of Lapis de Tsanfleuron
Our calculated glacial erosion rates, <0.01–0.08 mm a
1
, are
remarkably low (Figure 9) and up to two orders of magnitude
lower than values (0.1–1mma
1
) obtained for small alpine gla-
ciers on crystalline bedrock (Riihimaki et al., 2005; Delmas
et al., 2009; Wirsig et al., 2017). Depending on location, during
the Younger Dryas and the late Holocene glacier advances, the
Tsanfleuron glacier must have removed only some centimetres
(<17 cm) from the underlying limestone (Table I). Notably, the
Figure 9. 3D view of the Tsanfleuron area, created using the multidirectional hillshade map based on the SwissAlti3D digital elevation model
(reproduced with authorization of swisstopo (JA100120)) and the digital elevation model derived from the drone data (2016). Blue lines show glacier
extents for the years 1850, 1933 and 1992. Samples are colour-coded according to their position and glacier exposure/coverage history: samples out-
side LIA are dark green (I), samples inside LIA medium green (II), samples close to the glacier bright green (III). Green bars indicate sample-specific
minimum and maximum calculated glacial erosion depth (cm) and red bars sample-specific calculated erosion rates (mm a
1
), see legend for details.
For samples Tsan2, 3, 4, 6 and 12, no erosion rate could be determined. Distance between the LIA moraine (1850) and the present glacier front (2016)
is approximately 2 km. [Colour figure can be viewed at wileyonlinelibrary.com]
O. STEINEMANN ET AL.
© 2020 John Wiley & Sons Ltd. Earth Surf. Process. Landforms, (2020)

erosion rates exhibit a striking spatial pattern. All five of the
samples that have
36
Cl concentrations too high to calculate
an erosion rate (Tsan2, 3, 4, 6, 12) lie along the southern side
of the limestone plateau (Figure 9).
At first glance, our results of very limited glacial erosion are
surprising because the bedrock of the Lapis de Tsanfleuron ap-
pears to be profoundly glacially eroded, as evidenced by abun-
dant glacial polish, striations and roche moutonnées.
Nevertheless, taking a closer look, there is geomorphological
evidence that supports our hypothesis of very little glacial ero-
sion. To convey our concept of how the Tsanfleuron glacier has
made its own plateau, we compare features on the southern
and northern sides of the plateau.
On the southern and central parts of the plateau, the area
known as the Lapis de Tsanfleuron, apart from the LIA moraine
ridge itself there is very little sediment and nothing like a sub-
glacial till. Most of the forefield is bare bedrock except for the
sediment stripes. There are no streams as meltwater enters the
karst system immediately. This contrasts sharply with the land-
forms along the northern edge of the glacier, where the bedrock
is completely covered by subglacial till, and a meltwater stream
flows through the valley.
We think this difference relates to the stratigraphic sequence
and the fact that the glacier cannot effectively erode the massive
limestones due to loss of subglacial water into the karst system.
Along the southern side of the plateau the glacier has eroded
away the overlying (not karstified) sandy limestones and marls
of the Sanetsch Formation (Tsanfleuron Member) (Figure 1). As
soon as the glacier reached the massive and highly karstified
Schrattenkalk Formation, erosion switched from vertical to lat-
eral removal of rock. Overlying units were planed off. Over time
(and many glaciations) the limestone plateau emerged, also
leading to a positive feedback. The lack of slope on the flat pla-
teau promoted slow ice flow (see also below).
The northern side of the glacier is completely different and
actually somewhat similar to a cirque glacier that is deepening
its bed. Here the glacier has carved a linear valley, which is
now filled by a small glacier tongue, abundant sediment was
produced and several frontal moraines formed during late Ho-
locene advances. In this area, the glacier is still eroding the
stratigraphically higher Sanetsch Formation and has not yet
reached the Schrattenkalk limestones (Figures 1 and 3). Rem-
nants of the now eroded overlying units (marls and sandstones)
are exposed in the steep peaks to the north of the limestone pla-
teau (Figure 1). That this area is more strongly incised by the
glacier compared to the limestone plateau to the south is likely
related to both the change in lithology and the presence of a
thrust fault (Badoux et al., 1959, 1990).
Many of our conceptual points relate to the fact that the
Tsanfleuron glacier is moving slowly, which has been mea-
sured in several studies. Grust (2004) found a mean surface ve-
locity of 15 m a
1
and Hubbard (2002) determined a basal
velocity of 3.5 m a
1
at the ice–bed interface. For comparison,
measured glacier surface velocities of temperate Alpine gla-
ciers are between 10 and 160 m a
1
(Zekollari et al., 2019). In-
terestingly, Grust (2004) measured the highest horizontal flow
velocities in the northern part, where the small tongue extends
from the glacier (Figures 3 and 9). The basal sliding velocity of a
glacier is strongly dependent on the amount of subglacial wa-
ter; abundant subglacial water enables high velocities, and
low basal sliding velocities are a sign of little or no subglacial
water (Bindschadler, 1983). Observations at Tsanfleuron
showed that the abundant meltwater actually disappears into
the subsurface within only a few metres of the glacier front. This
Figure 10. Slope map of areas higher than 2000 ma.s.l. overlain on a multidirectional hillshade map (DHM25 data reproduced with authorization
of swisstopo (JA100120)). White square shows extent of the geological map and location of Tsanfleuron study area (Figure 1). Red/green scale is used
for slopes in the Helvetic nappes (mainly limestone), other lithologies are coloured red/blue. Glacier extents are based on the geological map (GK500,
2008). Black coordinates are metric swiss grid (CH1903/LV03), grey the World Geodetic System (WGS84). [Colour figure can be viewed at
wileyonlinelibrary.com]
QUANTIFYING GLACIAL EROSION ON A LIMESTONE BED
© 2020 John Wiley & Sons Ltd. Earth Surf. Process. Landforms, (2020)

has a decisive negative impact on the glacial erosional capacity
as the sliding velocity is directly linked to the efficacy of glacial
erosion (Hallet, 1979; Herman et al., 2011; Koppes et al., 2015;
Ugelvig et al., 2018). To consider again the geomorphological
evidence, the near total lack of subglacial sediment is already
a strong indicator of very low erosion rates (cf. Smart, 1983,
1984). Finally, the lack of water could explain the enormous
difference between our rates and that observed on the marble
plate, where Boulton (1982) measured a glacial erosion rate
of 37 mm a
1
. The marble plate was mounted below a temper-
ate glacier (Glacier d’Argentière) that is located on a crystalline
bed with a ‘normal’water-rich subglacial environment (surface
glacier flow velocity ~55 m a
1
; Benoit et al., 2015).
Implications for Landscape Development in
the Alps
We identify several factors that are essential forthe development
of the Lapis de Tsanfleuron. The limestone is massive, thick-
bedded, nearly horizontally oriented; rock damage due to
faulting is minor and, critically, there is a well-developed karst
system that removes water from the glacier bed. Therefore, to ex-
plore whether Tsanfleuron is a unique case, we checked if high-
elevation, plateau-like (low-slope) surfaces are more common in
areas underlain by limestone. We created a slope–elevation
map of the region (Figure 10) to see if generally there could be
a correlation between lithology, slope and elevation. Areas
higher than 2000 m a.s.l. are depicted on slope maps on a multi-
directional hillshade map (based on DHM25 data, reproduced
with the authorization of swisstopo (JA100120)). The red/green
colour scheme shows slope values for the sedimentary Helvetic
nappes (mainly limestones), while the red/blue scheme shows
slope values in areas of all the other lithologies (granite, gneiss,
schist, metabasalts). In this figure we see that areas underlain
by limestone have numerous low-slope surfaces above
2000 m a.s.l. (the vast green areas in Figure 10). In contrast, in
areas of granites and gneisses, steep slopes (red/yellow) domi-
nate and only the narrow crests reach high elevations. Blue (flat)
areas are those that were or are still filled by valley glaciers. Al-
though not specifically aimed at understanding high-elevation
limestone plateaus, Kühni and Pfiffner (2001) noted that the re-
lief in valleys in Helvetic limestone nappes (medium erodibility)
is almost as high as the relief in valleys in lithologies classified as
very low to low erodibility (granites and gneisses).
The Lapis de Tsanfleuron is not an exceptional site, in the
Alps there are many more examples of such high-elevation,
limestone plateau areas; Bündnerbergjoch in front of the
Vorab glacier (2520m a.s.l.) in Switzerland, the forefield of
the Hallstätter glacier (2100 m a.s.l.) and glacier forefields in
the Dachstein Massif and Steinernes Meer in Austria, and in
the Julian Alps in (Slovenia, Italy), to name just a few (Plan
et al., 2009; Veress et al., 2019). Many famous and well-
studied Alpine cave systems are found at high-elevation
locations (e.g. Hölloch-Silberen, 2450 m a.s.l.; Siebenhengste,
2000 m a.s.l.; Schönber Höhlensystem, 1720 m a.s.l.;
Eisriesenwelt, 1660 m a.s.l.; Mammuthöle, 1200 m a.s.l.)
(Maire, 1977; Wildberger, 1997; Spötl and Mangini, 2010;
Audra and Palmer, 2015). A comprehensive overview of the
most famous glaciokarst terrains, not only in the Alps but also
worldwide, is given by Telbisz and Tóth (2019).
Most research on high-elevation limestone areas has focused
on the geomorphology of karst landforms, the formation and
evolution of cave systems, and on speleothems. Often the exis-
tence of high-elevation limestone plateaus has been explained
by tectonic uplift of palaeosurfaces or planation surfaces (e.g.
Frisch et al., 2001; Dertnig et al., 2017). Less attention has
been given, however, to clarify why those areas were not
eroded –or at least not more strongly affected –by the numer-
ous Pleistocene glaciations, which elsewhere (often in close vi-
cinity) carved deep glacial valleys. Some authors consider little
modification by glaciers, but mainly in context with the evolu-
tion and genesis of the caves (Audra et al., 2002, 2007). Others
completely disregard probable landscape modification during
glaciations. Frisch et al. (2001) realized that the Dachstein pla-
teau was probably preserved because erosion (not specified)
during uplift was mainly by subsurface karstification and miss-
ing surface runoff, whereas the overlying Augenstein Forma-
tion (conglomerates and sandstones) was almost completely
eroded. Blessing (1976) realized in his studies about karst in
the Bernese Alps that glaciers have difficulty eroding lime-
stone, probably because of the surface morphology. He hy-
pothesizes that limestone, due to its fine-grained sedimentary
structure, easily forms smooth surfaces and calcite precipitates
often fill fractures and irregularities, and this makes it difficult
for the glacier to find a weak zone or defects in the rock to
attack it.
The process that we highlight here, the inability of a glacier
to erode limestone due to the lack of water at the base, could
also play an important role in the formation of cross-valley
riegels. A good example is the riegel which is cut by the fa-
mous Aareschlucht (Switzerland), about 90 km northeast of
Tsanfleuron. Although the area was once a glacier confluence
where glacial erosion should be extremely high (MacGregor
et al., 2000), there is a prominent 150 m-high riegel across
the valley. The location of the riegel is right where the bed-
rock lithology changes from crystalline (Aar Massif) to lime-
stone. Notably, at the riegel, strata of the massive, thick-
bedded Quinten and Öhrli Formation limestones are horizon-
tal (Arbenz and Müller, 1934). During many glaciations, sev-
eral deep gorges were cut into the limestone riegel by
pressurized subglacial meltwater (Hantke and Scheidegger,
1993; Montgomery and Korup, 2011). A process likely
favoured by joint clefts in the bedrock (Hantke and
Scheidegger, 1993). As soon as there was effective meltwater
drainage through the gorge, the glacier was unable to erode
the underlying bedrock any further. Montgomery and Korup
(2011) showed –with analysis of topographic data –that
gorges in the Swiss Alps could not have formed fluvially after
the last glaciation. The required incision rates are just too
high. The gorges were made subglacially, with meltwater un-
der pressure, and must have formed over many glaciations. As
is true at a number of bedrock gorges, at Aareschlucht the
presence of ‘abandoned’gorges verifies the fact that the bed-
rock riegel has survived numerous glaciations. Other famous
Alpine gorges are located at similar geological (limestone)
boundaries (e.g. Lammschlucht –Dürst Stucki et al., 2011
and Viamalaschlucht –Wyss et al., 2015).
In their summary of publications on the degree of modifica-
tion of high Alpine karstified limestones by glaciers, Veress
et al. (2019) pointed out a striking dichotomy: whereas some
authors interpreted the impact of glaciers on karst as pro-
found, others found it to be insignificant (Smart, 2004;
Djurović, 2009; Kunaver, 2009). Until our study, the effect
has never been directly quantified. Based on
36
Cl concentra-
tions measured in bedrock all across the Tsanfleuron forefield,
we find the effect of glacial erosion to be insignificant. Gla-
ciers on a strongly karstified limestone bed have a difficult
time eroding their beds because efficient drainage of subgla-
cial meltwater leads to reduced sliding. We suggest that this
process plays a fundamental role in the formation and preser-
vation of the enigmatic high-elevation limestone plateaus
of the Alps.
O. STEINEMANN ET AL.
© 2020 John Wiley & Sons Ltd. Earth Surf. Process. Landforms, (2020)

Conclusions
To assess glacial erosion rates on a limestone bed we applied a
multi-method approach combining detailed field study, cosmo-
genic
36
Cl concentrations and numerical modelling. Previous
observations at glacially polished karst environments were ei-
ther interpreted as profound or insignificant glacial erosion,
but rates were never directly quantitatively measured on lime-
stone. We determined
36
Cl in 19 samples from inside and out-
side the prominent LIA moraine in the forefield of the
Tsanfleuron glacier, a small (3 km
2
) plateau glacier in the Swiss
Alps. Measured
36
Cl concentrations yield apparent exposure
ages that are much higher than their actual post-LIA exposure.
To determine glacial erosion depth, we implemented a model
(MECED) that calculates
36
Cl concentrations during user-
defined periods of exposure. Snow shielding and karst
weathering are included in the model.
Evaluation of the obtained data shows extraordinarily low
glacial erosion rates, which vary between 0 and 0.08 mm a
1
.
This goes against the intuition that limestone, as a rather soft
rock, should be easy to erode. The obtained glacial erosion
rates are strikingly lower than measured erosion rates of tem-
perate glaciers on crystalline lithologies (0.1 to >10 mm a
1
).
The deciding factors are probably the combination of the
nearly horizontal bedding of the massive limestone and the
well-developed karst system. Basal sliding and thus erosion of
a rigid-bed glacier is strongly linked to the availability of sub-
glacial meltwater. Our observations suggest that the immediate
drainage of subglacial meltwater down into the karst system
limits glacier sliding, which hinders glacial erosion. The results
of our study and the derived conceptual model of inhibited gla-
cial erosion on limestone provides new insight for understand-
ing the development of Alpine landscapes, especially the
formation of flat limestone plateaus at high elevations.
Acknowledgements—We would like to thank Jochem Braakhekke,
Ewelina Bros, Marcus Christl, Reinhard Kronig and Ueli Steinemann
for their assistance during fieldwork, as well as for inspiring discussions
and useful comments on the manuscript. Insightful discussions with
John Gosse helped us to focus this work. For support in the laboratory
and excellent AMS measurements, we thank all members of the Labo-
ratory of Ion Beam Physics (ETH Zürich). We are grateful for Sean F.
Gallen’s and Katherine Schide’s support with drone equipment and
data acquisition. We appreciate the comments from two anonymous re-
viewers and the associate editor that led to marked improvement in the
manuscript. Funding for this project was provided by “Schweizerischer
Nationalfonds zur Förderung der Wissenschaftlichen Forschung”(SNF)
Project 175794 and 156187. MeteoSchweiz, the Swiss Federal Office
of Meteorology and Climatology, provided local weather data (snow
heights and precipitation).
Data Availability Statement
All data generated or analysed during this study are included in
the published paper.
Conflict of Interest
The author and co-authors have no conflict of interest to
declare.
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