Quantifying effects of deep and near‐surface chemical erosion on cosmogenic nuclides in soils,saprolite, and sediment

Cosmogenic nuclides in rock, soil, and sediment are routinely used to measure denudation rates of catchments and hillslopes. Although it has been shown that these measurements are prone to biases due to chemical erosion in regolith, most studies of cosmogenic nuclides have ignored this potential source of error. Here we quantify the extent to which overlooking effects of chemical erosion introduces bias in interpreting denudation rates from cosmogenic nuclides. We consider two end‐member effects: one due to weathering near the surface and the other due to weathering at depth. Near the surface, chemical erosion influences nuclide concentrations in host minerals by enriching (or depleting) them relative to other more (or less) soluble minerals. This increases (or decreases) their residence times relative to the regolith as a whole. At depth, where minerals are shielded from cosmic radiation, chemical erosion causes denudation without influencing cosmogenic nuclide buildup. If this effect is ignored, denudation rates inferred from cosmogenic nuclides will be too low. We derive a general expression, termed the ‘chemical erosion factor’, or CEF, which corrects for biases introduced by both deep and near‐surface chemical erosion in regolith. The CEF differs from the ‘quartz enrichment factor’ of previous work in that it can also be applied to relatively soluble minerals, such as olivine. Using data from diverse climatic settings, we calculate CEFs ranging from 1.03 to 1.87 for cosmogenic nuclides in quartz. This implies that ignoring chemical erosion can lead to errors of close to 100% in intensely weathered regolith. CEF is strongly correlated with mean annual precipitation across our sites, reflecting climatic influence on chemical weathering. Our results indicate that quantifying CEFs is crucial in cosmogenic nuclide studies of landscapes where chemical erosion accounts for a significant fraction of the overall denudation. Copyright © 2012 John Wiley & Sons, Ltd.     

Stone-line formation processes documented by in situ-produced Be distribution, Jardim River basin, DF, Brazil

Concentrations of in situ-produced cosmogenic ¹⁰Be (T_1/2=1.5 Myr) were measured in quartz samples from a quartz vein and its connected stone line from the Jardim River basin, Distrito Federal, Brazil, in order to quantify the processes involved in the landscape evolution of that region. The exponential decrease of the ¹⁰Be concentrations along the quartz vein, as well as their systematic increase along the stone-line away from the quartz vein, suggests an autochthonous development. Two models allow to estimate the lateral displacement rate. A plugs model assuming that the sample depth, and hence the production rate, is constant, and a burial model assuming that the sample depth, and hence the production rate, varies through time, yield lateral displacement rate of 37±5 and 68±6 m Myr⁻¹, respectively.     

Cosmogenic isotope burial dating of fluvial sediments from the Lower Rhine Embayment,Germany

Cosmogenic isotope burial dating, using ¹⁰Be and ²⁶Al, was applied to Plio–Pleistocene fluvial successions from the Lower Rhine Embayment, Germany. The approach consists of three principal steps: (1) measurement of cosmogenic nuclides in depth profiles, (2) modelling of hypothetical nuclide concentrations based on a first-order conceptualisation of the geological context and the principal succession of depositions and subsequent erosional and burial phases, and (3) using parameter estimation to identify values for the a priori unknown model parameters (burial age, initial nuclide concentrations, terrace erosion rates) that result in minimal disagreement between hypothetical and measured nuclide concentrations.The Late Pliocene Kieseloolite Formation was dated to 3650 ± 1490 ka and the Early Pleistocene Waalre Formation to 900 ± 280 ka. The unconformably overlying Upper Terrace Formation revealed ages of 740 ± 210 ka and 750 ± 250 ka for the two different sites. These findings are in good agreement with independent age control derived by bio-, magneto-, and litho-stratigraphy. Furthermore, identifiability and uncertainty analysis reveal a relationship between burial depth and sensitivity of isotope concentrations to burial age and erosion rate. Our results indicate that using shallower buried samples would enable a considerably more robust estimation of the burial age and the terrace erosion rate. Uncertainties arose mainly from nuclide measurements, and not from the uncertainties derived from modelling or insufficient knowledge of nuclide production and decay properties.     

Effects of terrain smoothing on topographic shielding correction factors for cosmogenic nuclide‐derived estimates of basin‐averaged denudation rates

Estimation of spatially averaged denudation rates from cosmogenic nuclide concentrations in sediments depends on the surface production rates, the scaling methods of cosmic ray intensities, and the correction algorithms for skyline, snow and vegetation shielding used to calculate terrestrial cosmogenic nuclide production. While the calculation of surface nuclide production and application of latitude, altitude and palaeointensity scaling algorithms are subjects of active research, the importance of additional correction for shielding by topographic obstructions, snow and vegetation is the subject of ongoing debate. The derivation of an additional correction factor for skyline shielding for large areas is still problematic. One important issue that has yet to be addressed is the effect of the accuracy and resolution of terrain representation by a digital elevation model (DEM) on topographic shielding correction factors. Topographic metrics scale with the resolution of the elevation data, and terrain smoothing has a potentially large effect on the correction of terrestrial cosmogenic nuclide production rates for skyline shielding. For rough, high‐relief landscapes, the effect of terrain smoothing can easily exceed analytical errors, and should be taken into account. Here we demonstrate the effect of terrain smoothing on topographic shielding correction factors for various topographic settings, and introduce an empirical model for the estimation of topographic shielding factors based on landscape metrics. Copyright © 2008 John Wiley and Sons, Ltd.     

Local erosion rates versus active tectonics: cosmic ray exposure modelling in Provence (south-east France)

Over the past decade, in situ-produced cosmogenic nuclides have revolutionised the study of landscape evolution. In particular, numerous studies have demonstrated that, in active tectonic settings, cosmic ray exposure dating of deformed or displaced geomorphic features makes it possible to quantify long-term deformation rates. In western European countries, erosion due to climatically driven processes and human activities is probably the factor that most limits the accuracy of exposure ages and landscape modification rates. In this study, we present the results of a depth-profiling technique applied to alluvial terraces located along the Rhône and the Moyenne Durance rivers. The expected decrease with depth of the measured ¹⁰Be concentrations has been modelled using a χ² inversion method in order to constrain the exposure history of the alluvial sediments. The results suggest that: (1) over the Quaternary, the local surface erosion rates including both regional uplift and climatically driven processes acting on landforms are on the order of 30 m/Myr in southeastern France, and (2) providing a fairly good bracketing of the exposure age, the modelled abandonment age of alluvial terraces affected by the Moyenne Durance Fault allows estimating incision rates, comparing the alluvial terrace elevations with topographic river profiles, and a minimum vertical slip rate value of roughly 0.02 mm/yr for the southern segment of the Moyenne Durance Fault.     

Paired 10Be sampling of polished bedrock and erratic boulders to improve dating of glacial landforms: an example from the Western Alps

Cosmogenic nuclide dating of glacial landforms may lead to ambiguous results for ice retreat histories. The persistence of significant cosmogenic concentrations inherited from previous exposure may increase the apparent exposure ages for polished bedrocks affected by limited erosion under ice and for erratic boulders transported by glaciers and previously exposed in high-altitude rock walls. In contrast, transient burying by moraines, sediments and snow decreases the apparent exposure age. We propose a new sampling strategy, applied to four sites distributed in the Arc and Arve valleys in the Western Alps, to better constrain the factors that can bias exposure ages associated with glacial processes. We used the terrestrial cosmogenic nuclide ¹⁰Be (TCN) to estimate the exposure time from paired sampling of depth profiles in polished bedrock and on overlying erratic boulders. For a given sampling site, the exposure ages for both the polished bedrock and boulder are expected to be the same. However, in six cases out of seven, boulders had significantly higher ¹⁰Be surface concentrations than those of the associated polished surfaces. In present and past glacial processes, the ¹⁰Be distribution with depth for boulders and bedrocks implies the presence of an inheritance concentration of ¹⁰Be. Our study suggests that ¹⁰Be concentrations in erratic boulders and in polished bedrocks provide maximum and minimum exposure ages of the glacial retreat, respectively. © 2019 The Authors. Earth Surface Processes and Landforms published by John Wiley & Sons Ltd     

Postglacial to Holocene landscape evolution and process rates in steep alpine catchments

Climate change and high magnitude mass wasting events pose adverse societal effects and hazards, especially in alpine regions. Quantification of such geomorphic processes and their rates is therefore critical but is often hampered by the lack of appropriate techniques and the various spatiotemporal scales involved in these studies. Here we exploit both in situ cosmogenic beryllium-10 (¹⁰Be) and carbon-14 (¹⁴C) nuclide concentrations for deducing exposure ages and tracing of sediment through small alpine debris flow catchments in central Switzerland. The sediment cascade and modern processes we track from the source areas, through debris flow torrents to their final export out into sink regions with cosmogenic nuclides over an unprecedented five-year time series with seasonal resolution. Data from a seismic survey and a 90 m core revealed a glacially overdeepened basin, filled with glacial and paraglacial sediments. Surface exposure dating of fan boulders and radiocarbon ages constrain the valley fill from the last deglaciation until the Holocene and show that most of the fan existed in early Holocene times already. Current fan processes are controlled by episodic debris flow activity, snow (firn) and rock avalanches. Field investigations, digital elevation models (DEMs) of difference and geomorphic analysis agree with sediment fingerprinting with cosmogenic nuclides, highlighting that the bulk of material exported today at the outlet of the subcatchments derives from the lower fans. Cosmogenic nuclide concentrations steadily decrease from headwater sources to distal fan channels due to the incorporation of material with lower nuclide concentrations. Further downstream the admixture of sediment from catchments with less frequent debris flow activity can dilute the cosmogenic nuclide signals from debris flow dominated catchments but may also reach thresholds where buffering is limited. Consequently, careful assessment of boundary conditions and driving forces is required when apparent denudation rates derived from cosmogenic nuclide analysis are upscaled to larger regions. © 2018 John Wiley & Sons, Ltd.     

Basinga: A cell-by-cell GIS toolbox for computing basin average scaling factors,cosmogenic production rates and denudation rates

The calculation of denudation rates from the measured cosmogenic nuclide concentrations in river sediments requires assumptions and approximations. Several different approaches and numerical tools are available in the literature. A widely used analytical approach represents the muogenic production with one or two exponentials, assumes the attenuation length of muons to be constant and also neglects temporal variations in the Earth's magnetic field. The denudation rates are then calculated directly and analytically from the measured concentrations. A second numerical and iterative approach was more recently proposed and considers a more rigorous muogenic production law based on pre-calculated variable attenuation length of muons and accounts for temporal changes of the magnetic field. It also assumes a specific distribution of denudation rates throughout the basin and uses an iterative approach to calculate the basin average denudation rates. We tested the two approaches across several natural basins and found that both approaches provide similar denudation results. Hence, assuming exponential muogenic production and constant attenuation length of muons in the rock has little impact on the derived denudation rates. Therefore, unless a priori known distributions of denudation rates are to be tested, there does not appear to be any particular gain from using the second iterative method which is computationally less effective. Based on these findings, we developed and describe here Basinga , a new ArcGIS® and QGIS toolbox which computes the basin average scaling factors, cosmogenic production rates and denudation rates for several tens of drainage basins together. Basinga follows either the Lal/Stone or the Lifton/Sato/Dunai scaling schemes and includes several optional tools for correcting for topographic shielding, ice cover and lithology. We have also developed an original method for correcting the cosmogenic production rates for past variations in the Earth's magnetic field. © 2019 John Wiley & Sons, Ltd.     

Cosmic ray flux variations, modulated by the solar and earth’s magnetic fields, and climate changes. 1. Time interval from the present to 10–12 ka ago (the Holocene Epoch)

Direct and indirect data on variations in cosmic rays, solar activity, geomagnetic dipole moment, and climate from the present to 10–12ka ago (the Holocene Epoch), registered in different natural archives (tree rings, ice layers, etc.), have been analyzed. The concentration of cosmogenic isotopes, generated in the Earth’s atmosphere under the action of cosmic ray fluxes and coming into the Earth archives, makes it possible to obtain valuable information about variations in a number of natural processes. The cosmogenic isotopes ¹⁴C in tree rings and ¹⁰Be in ice layers, as well as cosmic rays, are modulated by solar activity and geomagnetic field variations, and time variations in these concentrations gives information about past solar and geomagnetic activities. Since the characteristics of natural reservoirs with cosmogenic ¹⁴C and ¹⁰Be vary with climate changes, the concentrations of these isotopes also inform about climate changes in the past. A performed analysis indicates that cosmic ray flux variations are apparently the most effective natural factor of climate changes on a large time scale.     

Effects of long soil surface residence times on apparent cosmogenic nuclide denudation rates and burial ages in the Cradle of Humankind,South Africa

In situ cosmogenic nuclides are an important tool for quantifying landscape evolution and dating fossil-bearing deposits in the Cradle of Humankind (CoH), South Africa. This technique mainly employs cosmogenic 10-Beryllium (¹⁰Be) in river sediments to estimate denudation rates and the ratio of 26-Aluminium (²⁶Al) to ¹⁰Be (²⁶Al/¹⁰Be), to constrain ages of sediment burial. Here, we use ¹⁰Be and ²⁶Al concentrations in bedrock and soil above the Rising Star Cave (the discovery site of Homo naledi) to constrain the denudation rate and the exposure history of soil on the surface. Apparent ¹⁰Be-derived denudation rates obtained from pebble- to cobble-sized clasts and coarse-sand in soil (on average 3.59 ± 0.27 m/Ma and 3.05 ± 0.25 m/Ma, respectively) are 2-3 times lower than the bedrock denudation rates (on average 9.46 ± 0.68 m/Ma). In addition, soil samples yield an average ²⁶Al/¹⁰Be ratio (5.12 ± 0.27) that is significantly lower than the surface production ratio of 6.75, which suggests complex exposure histories. These results are consistent with prolonged surface residence of up to 1.5 Ma in vertically mixed soils that are up to 3 m thick. We conclude that the ¹⁰Be concentrations accumulated in soils during the long near-surface residence times can potentially cause underestimation of single-nuclide (¹⁰Be) catchment-wide denudation rates in the CoH. Further, burial ages of cave sediment samples that consist of an amalgamation of sand-size quartz grains could be overestimated if a pre-burial ²⁶Al/¹⁰Be ratio calculated from the surface production is assumed. © 2019 John Wiley & Sons, Ltd.     

Quantifying soil loss with in-situ cosmogenic 10Be and 14C depth-profiles

Conventional methods for the determination of past soil erosion provide only average rates of erosion of the sediment's source areas and are unable to determine the rate of at-a-site soil loss. In this study, we report in-situ produced cosmogenic ¹⁰Be, and ¹⁴C measurements from erratic boulders and two depth-profiles from Younger Dryas moraines in Scotland, and assess the extent to which these data allow the quantification of the amount and timing of site-specific Holocene soil erosion at these sites. The study focuses on two sites located on end moraines of the Loch Lomond Readvance (LLR): Wester Cameron and Inchie Farm, both near Glasgow. The site near Wester Cameron does not show any visible signs of soil disturbance and was selected in order to test (i) whether a cosmogenic nuclide depth profile in a sediment body of Holocene age can be reconstructed, and (ii) whether in situ ¹⁰Be and ¹⁴C yield concordant results. Field evidence suggests that the site at Inchie Farm has undergone soil erosion and this site was selected to explore whether the technique can be applied to determine the broad timing of soil loss. The results of the cosmogenic ¹⁰Be and ¹⁴C analyses at Wester Cameron confirm that the cosmogenic nuclide depth-profile to be expected from a sediment body of Holocene age can be reconstructed. Moreover, the agreement between the total cosmogenic ¹⁰Be inventories in the erratics and the Wester Cameron soil/till samples indicate that there has been no erosion at the sample site since the deposition of the till/moraine. Further, the Wester Cameron depth profiles show minimal signs of homogenisation, as a result of bioturbation, and minimal cosmogenic nuclide inheritance from previous exposure periods. The results of the cosmogenic ¹⁰Be and ¹⁴C analyses at Inchie Farm show a clear departure from the zero-erosion cosmogenic nuclide depth profiles, suggesting that the soil/till at this site has undergone erosion since its stabilisation. The LLR moraine at the Inchie Farm site is characterised by the presence of a sharp break in slope, suggesting that the missing soil material was removed instantaneously by an erosion event rather than slowly by continuous erosion. The results of numerical simulations carried out to constrain the magnitude and timing of this erosion event suggest that the event was relatively recent and relatively shallow, resulting in the removal of circa 20–50 cm of soil at a maximum of ∼2000 years BP. Our analyses also show that the predicted magnitude and timing of the Inchie Farm erosion event are highly sensitive to the assumptions that are made about the background rate of continuous soil erosion at the site, the stabilisation age of the till, and the density of the sedimentary deposit. All three parameters can be independently determined a priori and so do not impede future applications to other localities. The results of the sensitivity analyses further show that the predicted erosion event magnitude and timing is very sensitive to the ¹⁴C production rate used and to assumptions about the contribution of muons to the total production rate of this nuclide. Thus, advances in this regard need to be made for the method presented in this study to be applicable with confidence to scenarios similar to the one presented here.     

Complex multiple cosmogenic nuclide concentration and histories in the arid Rio Lluta catchment,northern Chile

Terrestrial cosmogenic nuclide (TCN) concentrations measured in river sediments can be used to estimate catchment‐wide denudation rates. By investigating multiple TCN the steadiness of sediment generation, transport and depositional processes can be tested. Measurements of ¹⁰Be, ²¹Ne and ²⁶Al from the hyper‐ to semi‐arid Rio Lluta catchment, northern Chile, yield average single denudation rates ranging from 12 to 75 m Myr^–1 throughout the catchment. Paired nuclide analysis reveals complex exposure histories for most of the samples and thus the single nuclide estimates do not exclusively represent catchment‐wide denudation rates. The lower range of single nuclide denudation rates (12–17 m Myr^–1), established with the noble gas ²¹Ne, is in accordance with palaeodenudation rates derived from ²¹Ne/¹⁰Be and ²⁶Al/¹⁰Be ratio analysis. Since this denudation rate range is measured throughout the system, it is suggested that a headwater signal is transported downstream but modulated by a complex admixture of sediment that has been stored and buried at proximal hillslope or terrace deposits, which are released during high discharge events. That is best evidenced by the stable nuclide ²¹Ne, which preserves the nuclide concentration even during storage intervals. The catchment‐wide single ²¹Ne denudation rates and the palaeodenuation rates contrast with previous TCN‐derived erosion rates from bedrock exposures at hillslope interfluves by being at least one order of magnitude higher, especially in the lower river course. These results support earlier studies that identified a coupling of erosional processes in the Western Cordillera contrasting with decoupled processes in the Western Escarpment and in the Coastal Cordillera. Copyright © 2008 John Wiley & Sons, Ltd.     

Isochron‐burial dating of glaciofluvial deposits: First results from the Swiss Alps

In this study, we use isochron‐burial dating to date the Swiss Deckenschotter, the oldest Quaternary deposits of the northern Alpine Foreland. Concentrations of cosmogenic ¹⁰Be and ²⁶Al in individual clasts from a single stratigraphic horizon can be used to calculate an isochron‐burial age based on an assumed initial ratio and the measured ²⁶Al/¹⁰Be ratio. We suggest that, owing to deep and repeated glacial erosion, the initial isochron ratio of glacial landscapes at the time of burial varies between 6.75 and 8.4. Analysis of 22 clasts of different lithology, shape, and size from one 0.5 m thick gravel bed at Siglistorf (Canton Aargau) indicates low nuclide concentrations: <20 000 ¹⁰Be atoms/g and <150 000 ²⁶Al atoms/g. Using an ²⁶Al/¹⁰Be ratio of 7.6 (arithmetical mean of 6.75 and 8.4), we calculate a mean isochron‐burial age of 1.5 ± 0.2 Ma. This age points to an average bedrock incision rate between 0.13 and 0.17 mm/a. Age data from the Irchel, Stadlerberg, and Siglistorf sites show that the Higher Swiss Deckenschotter was deposited between 2.5 and 1.3 Ma. Our results indicate that isochron‐burial dating can be successfully applied to glaciofluvial sediments despite very low cosmogenic nuclide concentrations. Copyright © 2017 John Wiley & Sons, Ltd.     

Inter-comparison of cosmogenic in-situ He, Ne and Cl at low latitude along an altitude transect on the SE slope of Kilimanjaro volcano (3°S, Tanzania)

Because the intensity and energy spectrum of the cosmic ray flux are affected by atmospheric depth and geomagnetic-field strength, cosmogenic nuclide production rates increase considerably with altitude and to a lesser degree with latitude. The scaling methods used to account for spatial variability in production rates assume that all cosmogenic nuclides have the same altitude dependence. In this study we evaluate whether the production rates of cosmogenic ³⁶Cl, ³He and ²¹Ne change differently with altitude, which is plausible due to the different threshold energies of their production reactions. If so, nuclide-specific scaling factors would be required.Concentrations of the three cosmogenic nuclides were determined in mafic phenocrysts over an altitude transect between 1000 and 4300 m at Kilimanjaro volcano (3°S). Altitude dependence of relative production rates was assessed in two ways: by determination of concentration ratios and by calculation of apparent exposure age ratios for all nuclide pairs. The latter accounts for characteristics of ³⁶Cl that the stable nuclides ³He and ²¹Ne do not possess (radioactive decay, high sensitivity to mineral composition and significant contributions from production reactions other than spallation). All ratios overlap within error over the entire transect, and altitudinal variation in relative production rates is not therefore evident. This suggests that nuclide-specific scaling factors are not required for the studied nuclides at this low-latitude location. However, because previous studies have documented anomalous altitude-dependent variations in ³He production at mid-latitude sites, the effect of latitude on cross-calibrations should be further evaluated.We determined cosmogenic ²¹Ne/³He concentration ratios of 0.1864 ± 0.0085 in pyroxenes and 0.377 ± 0.018 in olivines, agreeing with those reported in previous studies.Despite the absence of independently determined ages for the studied lava surfaces, the consistency in the dataset should enable progress to be made in the determination of the production rates of all three nuclides as soon as the production rate of one of the nuclides has been accurately defined.To our knowledge this is the first time that ³⁶Cl has been measured in pyroxene. The Cl extraction method was validated by measuring ³⁶Cl in co-existing plagioclase phenocrysts in one of the samples.     

Reporting of cosmogenic nuclide data for exposure age and erosion rate determinations

We propose guidelines for the reporting of in situ cosmogenic nuclide data for exposure age and erosion rate determinations. This is motivated by the need to maintain the utility of such data in the future, and to delineate best scientific practice. These guidelines will allow published exposure ages and erosion rates to be recalculated with confidence by others in the future, if, as is likely, procedures to calculate cosmogenic nuclide production rates are modified in the meantime.     

Cosmic-ray-induced fission of heavy nuclides: Possible influence on apparent U-fission track ages of extraterrestrial samples

The rates of cosmic-ray-induced fission of U, Th, Bi, Pb, and Au in mineral samples as a function of burial depth in the lunar surface layer are calculated using the available experimental particle flux and cross section data. Theoretical correction factors are given for apparent fission track ages of extraterrestrial samples of different burial depths which were exposed to cosmic rays for various time fractions of their solidification age. Samples having typical lunar heavy element contents can yield apparent fission track ages which are too high by a factor of up to 13 due to cosmic-ray-induced fission. The interference may be neglected, if the ratio of exposure age to solidification age remains 5 × 10⁻³. The calculations show, that the induced fission of Bi, Pb, and Au which are known to have high meteoritic abundances may dominate spontaneous ²³⁸U-fission in long-time exposed meteorites of low U and Th contents.     

Cosmogenic21Ne and22Ne depth profiles in chondrites

The production rate profiles of²¹Ne and²²Ne as a function of depth in meteoroids due to spallation by solar flare cosmic rays (SCR) and galactic cosmic rays (GCR) are calculated and their dependence on size and composition of meteoroids has been evaluated. The GCR production rate at a given depth increases with size for radii<25cm and then decreases whereas the²²Ne²¹Ne ratio (NeR) generally decreases with size and depth. The calculated GCR production rates and NeR are consistent with the measurements in several Chondrites. A plot of track production rate vs. NeR shows that some chondrites have NeR values smaller than those expected for their sizes. Thes obeervation suggestsat least a two-stage irradiation for such meteorites; the meteoroid exposure as a small body in the interplanetary space must have been preceded by exposure under deep shielding, possibly in its parent body.     

General models for episodic surface denudation and its measurement by cosmogenic nuclides

In order to use cosmogenic nuclides to infer erosion rates and exposure ages, it is necessary to apply a quantitative model for the accumulation of these nuclides in an eroding surface. The most straightforward model assumes that the surface continuously erodes at a constant rate. In many cases, however, the erosion is episodic: denudation is the result of the spalling off of slabs of rock in a series of discrete events. In a previous paper, we discussed two models for such episodic erosion; in one model slabs of rock spalled off periodically, while in the other slabs spalled off at stochastic time intervals. In both models we took the slabs to have a given, fixed width. In this paper we expand the previously treated models to allow for a statistical distribution of widths; this makes the models more realistic, and broadens our discussion of the fluctuations in the nuclide concentration that may be observed. We present general results for both models, results which allow for any distribution of widths. We then explore the stochastic model in more detail, applying a particular choice of width distribution. This allows us to address an interesting limiting case: when the widths are very small, the average nuclide concentration is accurately given by the standard continuous erosion model; yet, perhaps surprisingly, the fluctuations about this average can be quite significant.     

Combining surface exposure dating and burial dating from paired cosmogenic depth profiles. Example of El Límite alluvial fan in Huércal-Overa basin (SE Iberia)

Cosmogenic nuclide depth-profiles are used to calculate the age of landforms, the rates at which erosion has affected them since their formation and, in case of deposits, the paleo-erosion rate in the source area. However, two difficulties are typically encountered: 1) old deposits or strongly affected by cosmogenic nuclide inheritance often appear to be saturated, and 2) a full propagation of uncertainties often yields poorly constrained ages. Here we show how to combine surface-exposure-dating and burial-dating techniques in the same profile to get more accurate age results and to constrain the extent of pre-depositional burial periods. A ¹⁰Be–²⁶Al depth-profile measured in an alluvial fan of SE Iberia is presented as a natural example.     

P–PINI: A cosmogenic nuclide burial dating method for landscapes undergoing non-steady erosion

Existing methods of cosmogenic nuclide burial dating perform well provided that sediment sources undergo steady rates of erosion and the samples experience continuous exposure to cosmic rays. These premises exert important limitations on the applicability of the methods. And yet, high mountain sediment sources are rife with transient processes, such as non-steady erosion by glacial quarrying and/or landsliding, or temporary cosmic-ray shielding beneath glaciers and/or sediment. As well as breaching the premises of existing burial dating methods, such processes yield samples with low nuclide abundances and variable ²⁶Al/¹⁰Be ratios that may foil both isochron and simple burial-age solutions. P–PINI (Particle-Pathway Inversion of Nuclide Inventories) is a new dating tool designed for dating the burial of sediments sourced from landscapes characterized by abrupt, non-steady erosion, discontinuous exposure, and catchments with elevation-dependent ²⁶Al/¹⁰Be production ratios. P–PINI merges a Monte Carlo simulator with established cosmogenic nuclide production equations to simulate millions of samples (¹⁰Be–²⁶Al inventories). The simulated samples are compared statistically with ¹⁰Be–²⁶Al measured in field samples to define the most probable burial age. Here, we target three published ¹⁰Be–²⁶Al datasets to demonstrate the versatility of the P–PINI model for dating fluvial and glacial sediments. (1) The first case serves as a robust validation of P–PINI. For the Pulu fluvial gravels (China), we obtain a burial age of 1.27 ± 0.10 Ma (1σ), which accords with the isochron burial age and two independent chronometers reported in Zhao et al. (2016) Quaternary Geochronology 34, 75–80. The second and third cases, however, reveal marked divergence between P–PINI and isochron-derived ages. (2) For the fluvial Nenana Gravel (USA), we obtain a minimum-limiting burial age of 4.5 ± 0.7 Ma (1σ), which is compatible with unroofing of the Alaska Range starting ∼ 6 Ma, while calling into question the Early Pleistocene isochron burial age presented in Sortor et al. (2021) Geology 49, 1473–1477. (3) For the Bünten Till (Switzerland), we obtain a limiting burial age of <204 ka (95th percentile range), which conforms with the classical notion of the most extensive glaciation in the northern Alpine Foreland assigned to the Riss glaciation (sensu marine isotope stage 6) contrary to the isochron burial age presented in Dieleman et al. (2022) Geosciences, 12, 39. Discrepancies between P–PINI and the isochron ages are rooted in the challenges posed by the diverse pre-burial ²⁶Al/¹⁰Be ratios produced under conditions characteristic of high mountain landscapes; i.e., non-steady erosion, discontinuous cosmic-ray exposure, and elevation-dependent ²⁶Al/¹⁰Be production ratios in the source region, which are incompatible with the isochron method, but easily accommodated by the stochastic design of P–PINI.