The Roda Catchment is located a few kilometers southeast of Jena in Thuringia, Germany (Fig. 1). The Roda River is a tributary to the Saale. The bedrock within the Roda Catchment mainly consists of siliciclastic sedimentary rocks (Buntsandstein; Hartmann and Moosdorf, 2012). The overall relief does not exceed 260 m: the uppermost parts are mostly flat (Fig. 2d), while incision of the Roda River and its tributaries (e.g., Fig. 2e) at least partly leads to steep slopes. The climate is temperate oceanic with a mean annual temperature of ∼ 8 °C and with mean annual precipitation of ∼ 660 mm (Fick and Hijmans, 2017). The main land use types are forest and farmland (Figs. 1 and 2). KMZ files in the Supplement are provided to visualize the catchments and sampling sites in Google Earth.

A total of 22 ¹⁰Be samples were collected: 17 river sand samples and 5 soil samples (Figs. 1 and 2). River sand samples were taken from active streams. There are no extensive terraces and floodplains in the Roda Catchment, indicating low sediment storage within the catchment. Soil samples were collected from flat agricultural fields near the catchment divides. All soils are very sandy and rich in quartz.

Samples were first sieved to 250–710 µm, and quartz was enriched and purified using HCl (32 %), magnetic separation, and a mixture of 1 : 1 (by volume) of H₂SiF₆ (35 %) and HCl (32 %) (Brown et al., 1991; Merchel et al., 2019). We then partially dissolved the samples three times (∼ 10 % each step) using HF (48 %) to remove meteoric ¹⁰Be (Brown et al., 1991). About 0.36 mg ⁹Be was added to every ∼ 50 g quartz sample and processing blank. More information about our self-made ⁹Be carrier is provided in Appendix A. The samples were dissolved in 48 % HF at room temperature using high-density polyethylene bottles placed on a shaker table. They were then fumed three times with HNO₃ (> 65 %) and then three times with HCl (32 %). Thereafter, beryllium was separated by anion and cation exchange chromatography and pH-selective precipitation (Merchel and Herpers, 1999), oxidized to BeO, mixed with Nb (1 : 2 by weight), and finally pressed in copper accelerator mass spectrometry (AMS) targets using Cu pins. The AMS analyses were performed at the Vienna Environmental Research Accelerator (VERA) facility with a dedicated ¹⁰Be detector described by Steier et al. (2019). The ¹⁰Be / ⁹Be ratios were normalized to the in-house standard SMD-Be-12 with ¹⁰Be / ⁹Be = (1.704 ± 0.03) × 10¹² (Akhmadaliev et al., 2013), which is traceable to the NIST 4325 standard material (Nishiizumi et al., 2007).

For an eroding surface, the cosmogenic nuclide concentrations in mineral grains decrease with increasing denudation rates, and for commonly used cosmogenic radioactive nuclides, ¹⁰Be and ²⁶Al, this relationship can be described by the following equation (e.g., Lal, 1991): 1Niz=∑x=sp,fm,smPi,x(0)λi+εΛx⋅e-zΛx, where Ni is the nuclide concentration of cosmogenic nuclide i (atoms g⁻¹), and z and ε are the mass depth (g cm⁻²) and mass denudation rate (g cm⁻² yr⁻¹), respectively. x stands for three nuclide production pathways: high-energy neutron spallation (sp), slow muon (sm) capture, and fast muon (fm) interactions. Pi,x(0) is the production rate of nuclide i by production pathway x at the surface (z=0) (atoms g⁻¹ yr⁻¹), λi is the decay constant of nuclide i (yr⁻¹), and Λ is the attenuation length of the production pathway x (g cm⁻²) (Lal, 1991; Gosse and Phillips, 2001). This model assumes that (a) the production rates of cosmogenic nuclides decrease exponentially with depth in soil or rock, (b) the initial cosmogenic nuclide concentrations are negligible, (c) the denudation is in steady state, and (d) the surface has been continuously exposed to cosmic rays for a long period of time, i.e., t≫1/(λ+ε/Λ) (e.g., Lal, 1991; Granger and Riebe, 2014; Balco, 2017; Knudsen et al., 2019).

The cosmogenic nuclide method was initially used to estimate rock surface denudation rates and soon extended to derive catchment-wide denudation rates based on the following assumptions: (a) river sediment is well mixed and representative of the entire catchment, (b) each area of the catchment contributes quartz to the river channel in proportion to its long-term denudation rate, (c) sediment storage within the catchment is negligible, (d) denudation rates are independent of sediment grain size, and (e) denudation is rapid enough that cosmogenic nuclide loss is primarily driven by denudation rather than radioactive decay (Brown et al., 1995; Bierman and Steig, 1996; Granger et al., 1996; von Blanckenburg, 2005; Granger and Riebe, 2014). Several calculators have been developed accordingly, such as CosmoCalc (Vermeesch, 2007), CRONUS-Earth (Balco et al., 2008), CAIRN (Mudd et al., 2016), BASINGA (Charreau et al., 2019), and RIVERSAND (Stübner et al., 2023).

We use the Catchment-Averaged denudatIon Rates from cosmogenic Nuclides (CAIRN), a freely available pixel-based calculator (Mudd et al., 2016), to calculate catchment-wide denudation rates. CAIRN calculates ¹⁰Be production rates for each pixel in a catchment and then uses a temporary denudation rate to obtain pixel-based ¹⁰Be concentrations and their average. CAIRN determines the catchment-wide denudation rates by adjusting this temporary denudation until the averaged ¹⁰Be concentrations match the measurements. CAIRN uses the commonly used Lal/St scaling model (Lal, 1991; Stone, 2000). The inputs to the CAIRN calculator include sample location, ¹⁰Be concentrations, and a digital elevation model (DEM) of the study area. We used a 25 m DEM for the Roda Catchment, downloaded from the geoportal Thuringia (https://geoportal.thueringen.de/gdi-th/download-offene-geodaten/download-hoehendaten, last access: 6 February 2026). The default density of 2.65 g cm⁻³ was used to allow for consistent comparison with most published denudation data. Topographic shielding corrections for catchments were automatically performed by the CAIRN calculator. Corrections for lithology and snow shielding are not applied, as lithology (dominated by siliciclastic sedimentary rocks) and quartz content (> 50 %) are relatively homogeneous in the Roda Catchment, and snow cover is limited in both duration and thickness.

We also use CAIRN to calculate local denudation rates for the 5 soil samples, with the same parameters to ensure consistency. In addition, due to plowing in recent decades, the top ∼ 30 cm of soil is well mixed and has a density of approximately 1.3 g cm⁻³. The plowing depth is equivalent to 14.7 cm of rock with a density of 2.65 g cm⁻³. The sample thickness was therefore set to 14.7 cm. Topographic shielding is negligible for these high, flat sites.

To investigate denudation across different spatial and temporal scales, we combined our results with previously published short- and long-term denudation rates for comparison. The Octopus database compiles global ¹⁰Be-derived long-term denudation rates (Codilean et al., 2018, 2022; Codilean and Munack, 2025). As these rates were recalculated using CAIRN, direct comparison and integration with our data are justified. Chen et al. (2022) compiled global short-term erosion rates estimated from suspended sediment fluxes measured at gauging stations. Their Fig. 1 shows the gauging stations used worldwide. Chen et al. (2022) assumed a uniform density of 1.6 g cm⁻³ to convert sediment yields to catchment-averaged erosion rates. For consistency with the ¹⁰Be-derived long-term denudation rates, we used a density of 2.65 g cm⁻³ instead. In addition, as Chen et al. (2022) did not provide catchment polygons, we assigned catchment polygons from the HydroBASINS database (https://www.hydrosheds.org, last access: 6 February 2026) to each gauging station based on station locations and catchment area records in the dataset, using visual inspection in ArcGIS Pro^® with satellite imagery as a basemap. Automated catchment delineation tools in ArcGIS Pro^® were tested but yielded implausible catchment extents for some gauging stations; therefore, a visual assignment approach was adopted. The assigned catchments in Europe are shown in Fig. 5.

Before comparing our results with published denudation rates, we briefly discuss several potentially confounding factors.

First, chemical weathering occurs throughout soil, regolith, and bedrock and contributes to denudation rates. However, ¹⁰Be concentrations are mainly sensitive to near-surface mass removal (Dixon et al., 2009; Ott et al., 2022). This leads to a systematic underestimation of denudation rates. The Roda Catchment is dominated by weathering-resistant siliciclastic sedimentary rocks. Therefore, the chemical weathering effect is likely limited.

Second, catchment-wide denudation rates can be biased by sediment storage and remobilization. Ideally, river sediments at catchment outlets originate from the entire catchment, and the required time for sediment transportation is negligible compared to the time for denudation on hillslopes (e.g., von Blanckenburg, 2005; Granger and Riebe, 2014; Dosseto and Schaller, 2016). In the Roda Catchment, no vast terraces or floodplains exist. The catchment is small, and sediment transport distance is short (Fig. 1). Therefore, sediment storage and remobilization are minimal.

Third, farming may locally elevate denudation rates above long-term averages and bias catchment-wide denudation rates toward human-influenced subareas (Granger et al., 1996). This effect is likely small in the Roda Catchment because slope, the primary control on erosion, is similar between farmland (6°) and non-farmland areas (8°), and other factors, such as lithology, precipitation, and vegetation cover, are consistent across the catchment.

Fourth, other human activities, such as construction work, can disturb ¹⁰Be signals. The anomalously low denudation rate derived from sample Roda4 (Fig. 3c) may be related to extensive urban development along the upstream river reach. As illustrated in Fig. 2f, the river channel is largely modified by humanmade stone revetment constructed from abundant allochthonous lithic materials. KMZ files in the Supplement allow further inspection of anthropogenic disturbances within this catchment using Google Earth.

The catchment-wide denudation rates in the Roda Catchment fall within the range of existing European data (Fig. 4a). Denudation rates from the Roda Catchment, Europe, and around the globe show similar slope dependence (Fig. 4a). Global data, including European records, are sourced from the Octopus database. European data represent denudation rates in relatively high latitude (Fig. 4b). The cumulative distribution function (CDF) plot indicates that denudation rates in Europe are much higher than global rates, with a CDF 0.5 value > 40 mm kyr⁻¹ and thus more than twice the global value (Fig. 4c).

The European data range from 30 to 65 mm kyr⁻¹, representing the 25th and 75th percentiles, respectively. These rates integrate averaging timescales of approximately 9 to 20 ka (von Blanckenburg, 2005), extending back into the last glacial period. During this time period, Europe experienced widespread glaciation and extensive periglacial processes, including cryoturbation and solifluction (Isarin and Renssen, 1999; Eissmann, 2002). Syntheses of European periglacial geomorphology indicate that frost-related processes extended far beyond glacier margins, affecting large ice-free lowland areas of northern and central Europe (e.g., Oliva et al., 2022). Palaeopermafrost reconstructions further demonstrate that periglacial conditions were widespread across large parts of western and central Europe during the Last Glacial Maximum (e.g., Vandenberghe and Pissart, 1993). Consistent with geomorphological and palaeopermafrost evidence, the widespread cover-bed sequences on slopes between 37 and 56° N indicate that periglacial processes once affected large parts of the European continent during the Quaternary (Kleber, 1997). The periglacial processes may have altered landscape erodibility and potentially increased denudation rates across Europe (Schaller et al., 2001; Delunel et al., 2010; Roda-Boluda et al., 2023). Therefore, the generally higher denudation rates from Europe are probably due to past glacial and periglacial dynamics.

We compare ¹⁰Be-derived long-term denudation rates with gauged short-term erosion rates in Europe (Fig. 5) to investigate denudation on different timescales. Results show that long-term denudation rates are positively correlated with slope (Fig. 6a). The short-term erosion rates display greater variability than the long-term denudation rates (Fig. 6a). This likely documents human activities, such as deforestation, farming, mining, and quarrying (Ferrier et al., 2005). Those activities are more stochastic compared to natural denudation drivers, such as topographic gradient and precipitation. As a result, human activity may lead to great variability in short-term erosion rates and a weaker correlation between slope and erosion rates (Fig. 6a). The variability decreases for slopes > 20°, probably because human activities are relatively weak in steep regions.

The CDF plot indicates that ¹⁰Be-derived long-term denudation rates are generally higher than the short-term erosion rates in Europe (Fig. 6b). This observation is consistent with Chen et al. (2022). Many factors can lead to this pattern. The first reason is the difference between gauged erosion rates and ¹⁰Be-derived denudation rates. Denudation rates derived from cosmogenic nuclides represent the total mass loss by physical removal of particles and chemical removal of solutes (von Blanckenburg, 2005; Granger and Riebe, 2014). The gauged measurements used account for only suspended sediment flux and miss the dissolved mass loss. Studies have shown that chemical weathering can even dominate denudation rates in limestone or carbonate settings (e.g., Ott et al., 2023; Schaller et al., 2025).

However, chemical weathering may not be the only or main reason for this pattern (Fig. 6b). ¹⁰Be-derived long-term denudation rates average over timescales of thousands of years, while gauged measurements cover only decades and usually cannot capture rare extreme heavy floods (Kirchner et al., 2001; Schaller et al., 2001; Meyer et al., 2010a; Granger and Riebe, 2014).

Moreover, land-cover changes in Europe over the last several thousand years need to be considered. Reconstructions of land-cover change show that Europe experienced extensive forest clearance during the Roman and Medieval periods, reflecting agricultural expansion and the exploitation of forests for fuel wood and construction materials (Kaplan et al., 2009). This deforestation has been widely linked to enhanced hillslope erosion and increased sediment fluxes recorded in fluvial and lacustrine archives across Europe (Dotterweich, 2008, 2012). A synthesis of global erosion-rate data further indicates that human activities can accelerate natural erosion rates by a factor of ∼ 2–3 under moderate land use and by up to an order of magnitude under intensive land use (Saunders and Young, 1983). Together with the geomorphic legacy of periglacial processes during the last glacial period, widespread anthropogenic disturbances may have also contributed to long-term denudation rates exceeding short-term erosion rates (Fig. 6b).

In the Roda Catchment, we constrained both catchment-wide and local denudation rates on catchment divides. The mean catchment-wide denudation rate is ∼ 62 mm kyr⁻¹ (if we treat sample Roda4 as an outlier), which is much higher than the mean local denudation rate of ∼ 34 mm kyr⁻¹. The averaging timescales are about 10 and 18 kyr, respectively, so we can assess changes in topographic relief since then. At face value, the average surface lowering rate in the catchment area exceeds that at the catchment divides by 28 mm kyr⁻¹.

However, a relatively thick soil layer has been observed at the catchment divides. Assuming that all eroded material was soil with a density of 1.3 g cm⁻³, this would result in a mean denudation rate of 69 mm kyr⁻¹, rather than 34 mm kyr⁻¹. Consequently, the results indicate that denudation may have contributed to relief changes in the Roda Catchment, ranging from ∼ 0 to 28 mm kyr⁻¹. This relief change is broadly consistent with the observations in the Harz Mountain (5–10 mm kyr⁻¹) (Hetzel et al., 2024) and the Black Forest (24 mm kyr⁻¹) in Germany (Meyer et al., 2010b).