Be depth profiles in glacial sediments on the Swiss Plateau : deposition age , denudation and ( pseudo-) inheritance

During the Pleistocene, glaciers advanced repeatedly from the Alps onto the Swiss Plateau. Numeric age control for the last glaciation is good and thus the area is well suited to test a method which has so far not been applied to till in Switzerland. In this study, we apply in situ produced cosmogenic 10Be depth profile dating to several till deposits. Three sites lie inside the assumed Last Glacial Maximum (LGM) extent of the Rhône and Aare glaciers (Bern, Deisswil, Steinhof) and two lie outside (Niederbuchsiten, St. Urban). All sites are strongly affected by denudation, and all sites have reached steady state, i.e., the 10Be production is in equilibrium with radioactive decay and denudational losses. Deposition ages can therefore not be well constrained. Assuming constant denudation rates of 5 cm kyr−1, total denudation on the order of 100 cm for sites within the extent of the LGM and up to tens of meters for older moraines are calculated. Denudation events, for example related to periglacial conditions during the LGM, mitigate the need to invoke such massive denudation and could help to explain high 10Be concentrations at great depths, which we here dub “pseudo-inheritance”. This term should be used to distinguish conceptionally from “true inheritance”, i.e., high concentrations derived from the catchment. Kurzfassung: Die Alpengletscher stiessen während des Pleistozäns wiederholt in das Schweizer Mittelland vor. Da die Vergletscherungsgeschichte des Mittellandes relativ gut untersucht ist, ist die Region gut geeignet um eine Methode zu testen, welche bisher noch nicht an Grundmoränen in der Schweiz angewandt wurde. Für die vorliegende Studie erstellten wir 10Be Tiefenprofile für verschiedene Moränenstandorte im Schweizer Mittelland. Drei der Standorte liegen innerhalb der vermuteten LGM (Letztes Glaziales Maximum) Ausdehnung des Rhone und Aare Gletschers (Bern, Deisswil, Steinhof), zwei ausserhalb (Niederbuchsiten, St. Urban). Sämtliche Profile sind stark durch Denudation beeinflusst und alle Standorte, ausser Bern, sind im Gleichgewicht, das heisst die 10Be Produktion entspricht Published by Copernicus Publications on behalf of the Deutsche Quartärvereinigung (DEUQUA) e.V. 58 L. Wüthrich et al.: 10Be depth profiles in glacial sediments on the Swiss Plateau dem radioaktiven Zerfall und Verlust durch Denudation. Exakte Depositionsalter können deshalb nicht bestimmt werden. Konstante Denudationsraten können auf ca. 5 cm kyr−1 geschätzt werden. Dies ergibt eine totale Denudation von ungefähr 100 cm für die LGM Profile und mehrere Meter bis Dekameter für die älteren Profile. Denudationsereignisse, hingegen, zum Beispiel in Zusammenhang mit periglazialen Bedingungen während des LGMs, erklären niedrige Oberflächenkonzentrationen auf alten Standorten und hohe 10Be Konzentrationen in der Tiefe. In diesem Zusammenhang schlagen wir den Begriff “Pseudo Inheritance” vor, um konzeptionell von “Wahrer Inheritance” zu unterscheiden, welche der Präexposition im Einzugsgebiet geschuldet ist.

Since the 1960s Middle and Late Quaternary deposits of the Rhône and Aare glaciers (Fig. 1) have been investigated in several studies, focusing on glacial sediments and stratigraphy (Zimmermann, 1963), paleosols (Mailänder and Veit, 2001) and chronology (Ivy-Ochs et al., 2004;Preusser et al., 2007;Preusser, 2009).Although the extent of the Last Glacial Maximum (LGM) is controversial (Bitterli et al., 2011;Bläsi et al., 2015), the references cited above show that the chronology of the last glaciation in Switzerland is in general well established (Preusser et al., 2011).This makes the LGM deposits of the LGM Rhône and Aare glaciers suitable sites to test a method that has so far not been applied on till.In this study, we present one of the first applications of in situ produced 10 Be depth profile dating on moraines.In situ produced 10 Be is produced at the Earth surface by cosmic radiation, and production decreases exponentially with depth (Gosse and Phillips, 2001).Until now, depth profile dating has mainly been applied to terraces and alluvial fans (Hidy et al., 2010;Rixhon et al., 2011;Haghipour et al., 2014;Akçar et al., 2014;Delmas et al., 2015;Ruszkiczay-Rüdiger et al., 2016;Claude et al., 2017;Schaller et al., 2009).In order to determine the deposition age of a moraine, one would generally sample large, stable erratic boulders for 10 Be surface exposure dating (Heyman et al., 2016).However, boulders on the Swiss Plateau are often either completely destroyed or at least affected by human influence (Akçar et al., 2011).Under such circumstances, depth profile dating might be a promising alternative.Apart from dating, 10 Be depth profiles also allow to quantify denudation and inheritance (Braucher et al., 2009;Siame et al., 2004).Our study specifically aims to i. evaluate the potential of 10 Be depth profile dating of moraines, ii. investigate denudation rates and total denudation, and iii. quantify inheritance.

Sampling sites and sampling
The research area is situated in the western part of the Swiss Plateau, which lies south of the Jura Mountains, which are built of marine sediments deposited in a shallow shelf ocean of Triassic to Jurassic age (Pfiffner, 2009).The Swiss Plateau is mainly built of clastic sediments deriving from erosion of the Alps during the Cenozoic, called the molasse (Pfiffner, 2009).For the present study we sampled till, which overlays the molasse deposits.The sampling sites are located on lateral moraines (Bern), on the valley floor (Deisswil) or on the top of molasse hills (Steinhof, Niederbuchsiten, St. Urban).
Five sites have been selected for depth profile dating .The youngest site considered in the present study is Bern, deposited by the Aare glacier during its retreat (Wüthrich et al., 2017a), followed by Deisswil and Steinhof.Both lie inside the LGM extent of the Rhône Glacier according to Bini et al. (2009).Additionally, we sampled two more depth profiles from till deposits, which are attributed to older glaciations.They are at least 130 kyr old (Preusser et al., 2011;Bitterli et al., 2011) and are situated near Niederbuchsiten and St. Urban.Because of the human influence on the landscape, the selection of these sites was quite challenging.As the profiles in quarry pits are already exposed, they are basically perfect for the application of depth profiles.Unfortunately, an unknown amount of material is often pushed away.In the selected quarry pits, anthropogenic removal during work in the pit was estimated based on both conversations with workers and evidence in the field.Steinhof is the only site in the present work without a quarry pit.The depth profile in this location is rather important because boulders, only several hundred meters away from the sampling site, were dated by Ivy-Ochs et al. (2004).That is why we excavated a trench using a shovel and pickaxe.

Bern
The profile is located in a small quarry pit right on the top of a lateral moraine, which was deposited by the Aare Glacier along the eastern slopes of Gurten mountain.According to Wüthrich et al. (2017a), the glacier retreated 18 ka from this position.The uppermost 30 cm of the sampled profile is decalcified and consists of loamy sand and some coarser clasts.
Below is an unweathered, compact till, composed of clasts of diverse lithologies from the catchment of the Aare Glacier.

Deisswil
Inside the extent of the LGM Rhône glacier, a gravel pit near Deisswil exposes several meters of fluvial and fluvioglacial sediments at the base and a 200 cm thick till above.The decalcification depth varies between 140 and 200 cm.Three discrete samples were collected at depths of 50, 80 and 200 cm (DW1 to 3), the lowest one being just below the local decalcification depth of 180 cm.

Steinhof
South of Steinhof, a 2 m deep trench was excavated close to the top of a molasse hill covered by till.According to Ivy-Ochs et al. (2004), who applied surface exposure dating on boulders at Steinhof, the Rhône Glacier reached the site during the global LGM and disappeared ∼ 24 ka.Seven discrete samples down to 190 cm were collected for the 10 Be depth profile (SH1 to SH7; Table 1).The sediment changes at 150 cm depth from a sandy loam with almost no pebbles, possibly a water lain till (Dreimanis, 1979), to a diamict (Flint et al., 1960a, b) with unknown thickness but at least 400 cm.The decalcification depth was reached in a drill core at 360 cm depth.The hiatus expressed in the sediments is also confirmed in the XRF data and the grain size analysis (L.Wüthrich, unpublished data).

Niederbuchsiten
The sediment located on top of a molasse hill belongs to the penultimate glaciation (Bitterli et al., 2011) and is thus at least 130 kyr old.The 10 m thick till of the Rhône glacier overlies gravel with a thickness of several decameters.We collected five samples (NB1 to NB5) for depth profile dating from 30, 70, 100, 150 and 220 cm depth (Table 1).The uppermost 20 cm of the profile consists of silty sand.This cover bed may have been deposited during the Younger Dryas (Mailänder and Veit, 2001;Semmel and Terhorst, 2010).The decalcification depth is at 300 cm.

St. Urban
An active quarry near St. Urban exposes freshwater molasse (Gerber and Wanner, 1984) covered by 600 cm of completely decalcified till.The deposit lies outside the extent of the LGM boundaries (Bini et al., 2009) and is thus at least 130 kyr old.We collected four samples down to a depth of 380 cm (U1 to U4; Table 1).The uppermost sample from this site comes from the ∼ 60 cm thick silty top part of the profile.
The sediment was probably deposited by the ancient Rhône Glacier.

Sample preparation and AMS analyses
The depth profile samples were dispersed in Calgon and sieved to 63 to 1000 µm.We followed standard lab procedures to obtain clean quartz and then extract the beryllium (Kohl and Nishiizumi, 1992).The 10 Be / 9 Be analyses were conducted with the TANDY accelerator mass spectrometer (AMS) at the Laboratory of Ion Beam Physics, ETH Zurich.
The measured ratios were normalized to the ETH Zurich inhouse 10 Be / 9 Be standard S2007N with a nominal ratio of 28.10 ± 0.76 × 10 −12 (Christl et al., 2013).Two blanks were processed together with the samples.They had 10 Be / 9 Be ratios of 0.006 × 10 −12 , i.e., mostly more than 10 times smaller than the samples.The blank ratios were subtracted from the samples before calculating exposure and depth profile ages.

Depth profile calculations
Rock samples from the upper meters of Earth surface, bombarded by secondary particles originated from the cosmic rays, accumulate cosmogenic nuclide; as a result the concentration of these nuclides increase with altitude and latitude at a rate that depends on the local denudation rate. 10Be is one of these in situ produced cosmogenic nuclides with a half-life of 1.387 Ma (Chmeleff et al., 2010;Korschinek et al., 2010).Its concentration reaches equilibrium as soon as the radioactive decay of 10 Be is equal to its production. 10Be is produced by neutrogenic spallation and by muogenic interaction, mainly with oxygen (Gosse and Phillips, 2001;Heisinger et al., 2002a, b).In the last years, the application of 10 Be depth profiles has become an important method to date unconsolidated sediments (Hidy et al., 2010;Rixhon et al., 2011;Haghipour et al., 2014;Akçar et al., 2014;Delmas et al., 2015;Ruszkiczay-Rüdiger et al., 2016;Claude et al., 2017;Schaller et al., 2009).The advantage of this method is that it allows not only to calculate the age of the deposit but also denudation rate and the inherited share of 10 Be, accumulated in the catchment.As unconsolidated sediments are eroded much faster that boulders, equilibrium between production and decay is reached much faster.Because at the surface the production rate of 10 Be is dominated by neutrons and high, the equilibrium is reached quite quickly.Spallogenic production is exceeded by muogenic production at greater depths (Braucher et al., 2003) and it takes longer to reach steady state in deeper parts of the profile.To determine whether a depth profile has reached equilibrium, the time in Eq. ( 1) is set to infinity and the concentration at each depth is modeled as function of denudation rate: where C is concentration (atoms g −1 ), z is depth (cm), t is time (years), ε is denudation rate (cm a −1 ), C inh is the inherited concentration (atoms g −1 ), P (0) i is the site-specific production rate of 10 Be via production pathway i, ρ z is the cumulative bulk density (g cm −3 ) and i is the attenuation length of pathway i (g cm −2 ).The attenuation length is the depth in a sediment with the density ρ z at which the production rate is 1/e, compared to the surface production rate.When modeled steady-state denudation rates increase with depth, equilibrium has not been reached yet.Decreasing denudation rates indicate inheritance and/or complex deposition histories (Delmas et al., 2015;Ruszkiczay-Rüdiger et al., 2016).Constant denudation rates with depth indicate that the 10 Be production rate has reached the equilibrium and one can only calculate the minimum deposition age T eff (Lal, 1991), which is the time needed to reach equilibrium with the modeled denudation rate.
is the attenuation length of neutrons (160 g cm −2 ).We also used the MATLAB code version 1.2, published by Hidy et al. (2010), to calculate deposition ages, i.e., the time when the glacier has left the area, denudation rates and inheritance for our sites.The code uses a Monte Carlo approach to find solutions for Eq. ( 1).Apart from the measured 10 Be concentrations at specific depths, critical input parameters are the allowed age range (time, t), ranges for denudation rate (cm a −1 ) and inheritance (atoms g −1 ), as well as a denudation threshold.We used a reference production rate for neutrogenic spallation of 3.93 atoms g −1 a −1 (Heyman, 2014) and the scaling model by Lal (1991) and Stone (2000) to calculate the production rate for each site.Because the standard files for calculating muogenic production rate after Heisinger et al. (2002a, b) yield too-high values (Braucher et al., 2003(Braucher et al., , 2011(Braucher et al., , 2013;;Phillips et al., 2016), we used the .mfiles provided Ruszkiczay-Rüdiger et al. ( 2016).Calculations were done until 100 000 solutions were found.No corrections were applied for snow and vegetation cover and/or shielding.For density, the allowed range was between 2.1 and 2.3 g cm −3 , i.e., realistic values for till (Schlüchter, 1989a).

Bern
10 Be concentrations of the three samples from the Bern decrease with depth and range from 8.1 × 10 4 atoms g −1 at 10 cm depth to 1.0 × 10 4 atoms g −1 at 165 cm depth (Fig. 4, Table 1).Because of the poor fit, no reliable results could be obtained with the Hidy et al. (2010) calculator and also T eff could not be calculated.

Deisswil
In the Deisswil profile, 10 Be concentrations decrease with depth and range from 6.2 × 10 4 atoms g −1 at 50 cm depth to 2.7 × 10 4 atoms g −1 at 200 cm depth (Fig. 4, Table 1).The steady-state denudation rate between the first and second sample does not increase with depth.Between DW2 and DW3 it does.The results from the Monte Carlo simulation did not yield any useful results and are thus not used in the paper.Minimum age T eff for the uppermost two samples is 14 kyr, and calculated steady-state denudation rate is 5.2 cm kyr −1 (Table 2).

Steinhof
Concentrations decrease exponentially with depth and range from 7.7 × 10 4 atoms g −1 at 10 cm depth to 2.1 × 10 4 atoms g −1 at 120 cm depth (Fig. 4).The two lowermost samples (150 and 190 cm) have higher concentrations than expected from the exponential trend.Based on that and our sedimentological observations, we suspect that two phases of till deposition may have occurred and that the sediments below 150 cm may have experienced exposure predating the deposition of the uppermost 150 cm of the profile.The two lowermost samples were excluded from further calculations.The profile has reached steady state, with a T eff of 11 kyr and a denudation rate of 6.6 cm kyr −1 (Table 2).The most probable Bayesian age, denudation rate and inheritance of the Monte Carlo simulation are 16.3 kyr, 6.2 cm kyr −1 and 0, respectively (Table 2).

St. Urban
Concentrations decrease with depth and range from 12.3 × 10 4 atoms g −1 at 66 cm depth to 6.5 × 10 4 atoms g −1 at 380 cm depth (Fig. 4, Table 1).The uppermost sample from a depth of 27.5 cm has been excluded from the calculations due to its relatively low concentration of 8.8 × 10 4 atoms g −1 , which indicates that the uppermost 60 cm of the profile were deposited as loess cover long after deposition of the underlying till.The profile has reached equilibrium.In fact, steady-state denudations rates decrease with depth, indicating inheritance or a complex deposition history.We have not calculated T eff because of the loess cover.The Monte Carlo calculations yield 32.6 kyr, 2.8 cm kyr −1 and 7.3 × 10 4 atoms g −1 for age, denudation rate and inheritance, respectively (Table 2).

Ages in chronological context
The 10 Be concentrations in all profiles are much lower than what may be expected from the assumed deposition ages of the tills (∼ 20 kyr and more).The uppermost samples for all profiles but St. Urban, for example, are within 10 to 50 cm from the surface but have less than 5 × 10 5 atoms g −1 .For comparison, 10 Be concentrations from boulder surfaces in that area with an age of ∼ 20 kyr are 2 times higher (Ivy-Ochs et al., 2004).This indicates that denudation of the landform surface has led to substantial loss of surface sediments.Ignoring denudation in the depth profile calculations would E&G Quaternary Sci.J., 66, 57-68, 2017 www.eg-quaternary-sci-j.net/66/57/2017/ lead to an obvious, massive underestimation of the deposition ages.The low values for T eff indicate that equilibrium was reached quite fast due to high denudation rates and/or denudation events.The minimum deposition ages T eff of 14, 11 and 16 kyr for Deisswil, Steinhof and Niederbuchsiten, respectively, do not provide useful age constraints and only point to high denudation.They do not even exceed the age of the Late Glacial readvances of the Gschnitz Stade in the Alps ∼ 16 ka (Ivy-Ochs et al., 2006a;Reitner, 2007;Federici et al., 2012).It is important to emphasize that the ages in this study obtained from the Monte Carlo calculations should not be overinterpreted either: The age ranges are extremely large and, more importantly, all profiles have reached equilibrium.In that sense, no meaningful age can be inferred for any site.The fact that the concentrations in the profiles have reached equilibrium is graphically also illustrated in the denudation rateage plots (Fig. 5), where the ages go towards infinity and are only restricted by our input parameters given for the Monte Carlo approach.Solutions are found for age ranges spanning several hundreds of thousands of years, and even the 100 best fits (blue dots in Fig. 5) scatter widely and cannot provide useful constraints for the deposition ages of the moraines.However, when equilibrium is reached, denudation rates can be estimated reasonably well, and total denudation since deposition can be inferred if independent age control is available.For this purpose, we here briefly summarize the currently available data and the state of knowledge.All exposure ages have been (re)calculated using the CRONUS web calculator (Marrero et al., 2016) with the time-dependent scaling model by Lifton et al. (2014) and a reference production rate of 3.93 (±0.1) atoms g −1 a −1 (Heyman, 2014).
For the Bern site, unpublished 10 Be surface exposure ages on three boulders show that the Aare glacier started to retreat 18 ka from this position (Wüthrich et al., 2017a).The Deisswil site must be older than the Bern site based on stratigraphical considerations, but it is younger than Steinhof.The two oldest boulders in Steinhof (out of four) yield exposure ages of 24.4 and 23 kyr (Ivy-Ochs et al., 2004).The deposition age of the boulders in Steinhof has been questioned by Bitterli et al. (2011) and Bläsi et al. (2015) due to the high decalcification depth.At this point, we find that decalcification is also strongly affected by other factors than time -mainly the initial content of carbonates in the sediment, which decreases from west to east (Gasser and Nabholz, 1969) -and that the exposure ages are a good estimate for the deposition age of the moraine at Steinhof.Schlüchter (1988) suggested the absence of glaciers in the Swiss Alpine Foreland during MIS 6, based on sedimentological and palynological evidence from the sections Thalgut and Meikirch, ∼ 15 km south and ∼ 10 km north of Bern, respectively.
This conflicts with the classical notion that the penultimate glaciation (i.e., Riss, Beringen, MIS 6) in the Alps was more extensive than the ultimate glaciation (Würm, Birrfeld)  2010).Red dots mark all possible solutions and blue dots the 100 best χ 2 fits.(Doppler et al., 2011;van Husen and Reitner, 2011;Preusser et al., 2011) and implies that the Niederbuchsiten till may have been deposited already during one of the early mid-Pleistocene glaciations.Attempts have been made recently to solve this controversy by applying 10 Be surface exposure dating on erratic boulders in the Jura Mountains by Graf et al. (2007Graf et al. ( , 2015)), yet with limited success, as the oldest dated boulders date into MIS 6 but are interpreted to have been deposited much earlier.Various novel dating techniques based on luminescence and cosmogenic nuclides have been applied to sediments in Meikirch (Preusser et al., 2005) and its vicinity (Dehnert et al., 2010), and these studies do suggest that the penultimate glaciation was more extensive than the LGM.In any case, the till at Niederbuchsiten does very likely not document the oldest extensive glaciation, because it overlies fluvioglacial sediments that were deposited after an even earlier glacial advance and the respective denudational event.The till in St. Urban is completely weathered down to its base (∼ 4 m) and lies directly on molasse sediments.We can tentatively infer that it is at least MIS 6 in age and likely corresponds to the Möhlin glaciation.

Denudation rate and total denudation
The results from the Bern site do not allow to calculate age and denudation rate because of the very poor fit between the samples and the trend line (Fig. 4).We speculate that decalcification is responsible for this: decalcification means a loss of material and thus a decrease in thickness and a lowering of the surface.The samples in 10 Be depth profile "move" closer together.The other profiles may have been influenced by this process as well but to a lower degree, because the initial calcite content is highest in the sediments of the Aare Glacier and decreases from west to east in the deposits of the Rhône Glacier (Gasser and Nabholz, 1969).Decalcification cannot yet be corrected for and will be ignored in the following discussion.
The steady-state denudation rates of 5.2 and 6.6 cm kyr −1 for Deisswil and Steinhof are comparable to the most probable Bayesian denudation rates of 6.2 cm kyr −1 for Steinhof.Assuming constant denudation rates of ∼ 6 cm kyr −1 and exposure ages of ∼ 24 kyr for these three sites yields total denudation on the order of 120 cm.Denudation was probably www.eg-quaternary-sci-j.net/66/57/2017/ E&G Quaternary Sci.J., 66, 57-68, 2017 not constant over time, and another back-of-the-envelope calculation could assume most recent denudation due to anthropogenic activity.As the 10 Be production decreases to half of its surface value at ∼ 50 cm depth, total denudation would thus be at least on that order of magnitude.
For the Niederbuchsiten site denudation rates between 3.7 and 6.3 cm kyr −1 can be modeled (Table 2), yet all best fits are close to the most probable Bayesian denudation rate of 4.9 cm kyr −1 and the steady-state denudation of 4.5 cm kyr −1 (Fig. 5).Assuming constant denudation on that order of magnitude yields a total denudation of > 6 m in the case that the till was deposited during the Beringen Glaciation (MIS 6).In the case that the till at Niederbuchsiten was deposited during MIS 8, 300 ka or earlier, a total denudation of > 13 m can be calculated.Again, however, constant denudation is unlikely, particularly in view of the old age spanning at least one glacial-interglacial cycle, and we evaluate an alternative more complex scenario: as the 10 Be production decreases to 10 % of its surface value at ∼ 380 g cm −2 (∼ 170 cm with a density of 2.2 g cm −2 ) depth, deposition during MIS 6 and the most recent anthropogenic truncation of the profile on that order of magnitude is one scenario.Also, periglacial solifluction during the LGM may have removed much of the 10 Be that accumulated close to the surface since MIS 6.In that case denudation must additionally have been active since the LGM because, like in the case of Steinhof, Deisswil and Bern, the surface 10 Be concentration at Niederbuchsiten is only about half of the concentration than one would expect from a stable surface exposed since the LGM.
The denudation rates obtained from the Monte Carlo simulations for St. Urban are between 1.5 and 5.7 cm kyr −1 and the most probable Bayesian denudation rate is 2.8 cm kyr −1 (Table 2, Fig. 5c).With such denudation rates, one would calculate ∼ 4 m total denudation if the till was deposited during the penultimate glaciation and ∼ 25 m if the till was deposited 800 ka.Again, several meters of denudation due to intensive periglacial dynamics during the LGM (and possibly earlier) could have played an important role in lowering the 10 Be concentrations.For St. Urban, this is most probably the case, because the depth profile can be fitted best with an attenuation length of 835 g cm −2 (Fig. 4).Such a high value strongly exceeds the attenuation length of 160 g cm −2 related to neutrogenic production (dominant only near the surface) and points to a significant muogenic contribution (1500 g cm −2 for slow muons and 4320 g cm −2 for fast muons; Braucher et al., 2009Braucher et al., , 2013)).The attenuation lengths are expressed in the slope (a) of the trend line in Fig. 4. Interestingly, Niederbuchsiten also shows this indication for massive denudation (fitted attenuation lengths of 370 g cm −2 ), although not to such a degree, whereas Bern and Steinhof do not, consistent with their presumably last glacial age.
We conclude that denudation rates can be reasonably constrained with the help of 10 Be depth profiles, and total denudation can be estimated provided that the deposition age Figure 6.Illustration of "pseudo-inheritance".The plot shows a theoretical profile which was exposed for 700 kyr.Then 3 m were truncated immediately.Afterwards, the profile was again exposed to the cosmic radiation for 20 kyr.We modeled the age (31 kyr) and inheritance (19 × 10 4 atoms g −1 ) using excel.
of the parent material is known.This works particularly well for sites not older than the LGM, where constant denudation rates are ∼ 5 cm kyr −1 and total denudation is on the order of 0.5 to 1 m.For older sites, constant denudation rates can be constrained by the Monte Carlo simulations to 3-5 cm kyr −1 .However, the assumption of constant denudation is very likely wrong and would result in several meters of total denudation for MIS 6 sites and even several tens of meters for older sites.Total denudation of even more than 100 m is necessary to explain the 10 Be depth profiles in Deckenschotter (Häuselmann et al., 2007;Akçar et al., 2014;Claude et al., 2017).We suggest that denudational events related to periglacial dynamics might play an important role for the denudation history.This would substantially mitigate the need to invoke massive total denudation.It might therefore be a promising endeavor for future studies to modify the Monte Carlo simulations in a way that denudational events can be evaluated.

Inheritance and "pseudo-inheritance"
The most probable Bayesian inheritance is zero for Steinhof (Table 2) and also low for Bern and Deisswil (Fig. 4), whereas Niederbuchsiten and St. Urban have a much higher inheritance of 2.2 × 10 4 and 7.3 × 10 4 atoms g −1 (Table 2).This might be a systematic pattern, with less inheritance for the younger sites and more inheritance for the older ones.The pattern might document that the earlier glacial advances eroded a landscape that had accumulated substantial amounts of cosmogenic nuclides near the surface before the onset of the massive glaciations.During the course of the Pleistocene glaciations, the glaciers eroded deeper and deeper and therefore transported and deposited sediments with less inheritance.In the following, however, we elucidate that the high inheritance in Niederbuchsiten and St. Urban may not neces-sarily reflect "true" inheritance from the catchment but can alternatively be explained with denudation events during the long exposure history of the sites since deposition.
When a site is exposed to cosmic radiation over hundreds of thousands of years, notable amounts of 10 Be are produced not only at the surface but also at greater depth, mostly due to muogenic production (Heisinger et al., 2002a, b;Braucher et al., 2003Braucher et al., , 2011Braucher et al., , 2013)).Massive denudation, related for example to periglacial conditions, could truncate the site but still leave considerable amounts of these muogenic 10 Be atoms that decrease in concentration with depth with a much smaller slope than 10 Be atoms that are produced close to the surface by neutrons.New exposure after the denudational event leads to accumulation of new 10 Be, and the concentration in the upper few meters will soon again have the steep slope related to the neutron flux.When age, constant denudation and inheritance are calculated from such a depth profile, the high 10 Be concentration at depth is therefore wrongly interpreted as inheritance.We dub the high concentration at depth "pseudo-inheritance" when it is the result of long exposure of the site and massive denudation rather than "true" inheritance from the catchment.
To illustrate the concept of pseudo-inheritance, we create a 800 cm deep depth profile that has experienced a 700 kyr long exposition without denudation.Then we truncate 300 cm in a single event.After that, we allow an exposure of 20 kyr without denudation.In the following, we modeled the concentrations using Excel with unconstrained inheritance and age and zero denudation (Fig. 6).The results yield a best fit age of 31 kyr and an inheritance of 19 × 10 4 atoms g −1 .The young apparent age and high apparent inheritance reflect the denudational loss of the neutron component and the dominance of the muogenic component, respectively.The apparent inheritance is not derived from the catchment and should not be confused with "true" inheritance.

Conclusions
-Our results show that 10 Be depth profiles on the Swiss Plateau reach steady state within a few thousand years and do not provide new robust age control for the timing of Pleistocene glaciation.
-Concentrations of the Niederbuchsiten and St. Urban profiles decrease with a suspiciously low slope, possibly indicating significant muogenic contributions, pre- LGM deposition ages and massive denudation since deposition.
-The 10 Be depth profiles can be used to reasonably constrain modeled constant denudation rates to ∼ 5 cm kyr −1 .Given independent age constraints for the MIS 2 sites, total denudation amounted to ∼ 100 cm since deposition.Alternatively, most recent anthropogenic denudation would be on the order of 50 cm to explain the low 10 Be concentrations at all three sites.
-For Niederbuchsiten and St. Urban, the 10 Be depth profiles also yield denudation rates of ∼ 5 cm kyr −1 , but the assumption of constant denudation would imply several or even tens of meters of total denudation.Denudation events related to periglacial activity, for example during the LGM, would substantially mitigate the need to invoke massive total denudation.Only a few meters of periglacial denudation during glaciations would be sufficient to explain the low observed 10 Be concentrations.Massive denudation and/or denudation events result in relatively high concentrations at depth stemming from muogenic production, and as this may wrongly be interpreted as inheritance, we dub this phenomenon "pseudo-inheritance". Modifications in the depth profile calculations should be made so that denudation events can be included in the Monte Carlo simulations.
We finally conclude that 10 Be depth profiles are an innovative tool to quantitatively investigate Earth surface processes.Deposition ages can be inferred for fluvial terraces and moraines, yet ages should always be discussed in context with denudation, which itself is generally poorly constrained.We see great potential for studying denudation histories at specific sites and for whole catchments, where the age of the parent material is known independently.In the future, dating of soft sediments in such a dynamic environment as the Swiss Plateau with high denudation rates can be improved with the combination of samples from shallow depths, with many more samples (than in this study) from greater depths (> 700 g cm −2 ), which allows us to calculate denudation in steady state from the upper part and better constrained ages from the lower part.Also the combination of several cosmogenic nuclides might help to (i) constrain the timing of denudational events in the past (Fülöp et al., 2015) and (ii) obtain burial ages (Balco and Rovey, 2008).

Figure 1 .
Figure 1.(a) Location of the research area in Europe.(b) LGM map of the research area modified after Bini et al. (2009).The black dots mark the sample locations (reproduced with permission of Swisstopo, BA15134).The equidistance of the contour lines is 200 m.

Figure 2 .
Figure 2. Digital elevation models for all sites (source: Federal Office of Topography).

Figure 3 .
Figure 3. Photographs of the sampled profiles.U4 is not shown but is taken from the same sediment unit at 380 cm depth.

Figure 4 .
Figure 4. Measured depth profiles with error bars.The trend lines y = a•ln(x)+b, which calculate how the particles are attenuated are for the uppermost 200 cm (440 g cm −2), where neutrogenic spallation is the dominant production pathway.The calculated attenuation lengths are 160 g cm −2 for Bern, 400 g cm −2 for Deisswil, 173 g cm −2 for Steinhof, 370 g cm −2 for Niederbuchsiten and 835 g cm −2 for St. Urban.Values exceeding 160 g cm −2 indicate denudational events and/or high denudation rates.

Figure 5 .
Figure 5. Denudation rate and age plots, acquired using the depth profile calculator by Hidy et al. (2010).Red dots mark all possible solutions and blue dots the 100 best χ 2 fits.

Table 1 .
Locations and 10Be concentrations of all samples.The steady-state denudation rate for each depth is used to find out whether the 10 Be concentration in the profile is in equilibrium.

Table 2 .
Minimum ages (T eff ) and steady-state denudation rates for the profiles, calculated using Excel and the results of the Monte Carlo approach.