# Quaternary denudation rates in the eastern Tianshan

Julien Charreau, Pierre-Henri Blard, Dimitri Saint-Carlier, Jérôme Lavé, Etienne Large, Catherine Zimmermann, Stéphane Dominguez, Shengli Wang

► To cite this version:

Julien Charreau, Pierre-Henri Blard, Dimitri Saint-Carlier, Jérôme Lavé, Etienne Large, et al. Quaternary denudation rates in the eastern Tianshan. Geomorphology, 2025, 479, pp.109734. 10.1016/j geomorph.2025.109734. hal-05406978

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# Quaternary denudation rates in the eastern Tianshan

Julien Charreau<sup>a,*</sup>, Pierre-Henri Blard<sup>a</sup>, Dimitri Saint-Carlier<sup>a</sup>, Jérôme Lavé<sup>a</sup>, Etienne Large<sup>a</sup>,
Catherine Zimmermann<sup>a</sup>, Stéphane Dominguez<sup>b</sup>, Shengli Wang<sup>c</sup>

## ARTICLE INFO

### Keywords:

- Denudation rates

- Tianshan

- <sup>10</sup>Be cosmogenic nuclides

- Quaternary

## ABSTRACT

Predicting how denudation will change in the future, and hence impact the Earth's surface, requires an understanding of the links between past climate variability and denudation responses, especially during the Quaternary. In this study, we reconstructed Quaternary paleo-denudation rates in the eastern Tianshan range (central Asia) and compared the results to climate changes documented by geochemical variations recorded in nearby speleothems. Based on a reanalysis and inversion of 18 published cosmogenic in situ <sup>10</sup>Be depth profiles collected across abandoned Quaternary alluvial surfaces, combined with analyses of five new profiles in the northern Tianshan piedmont, we constrained the inherited <sup>10</sup>Be paleo-concentrations and when the surfaces were abandoned. To extend the dataset beyond the Mid-Pleistocene Transition, when important changes in denudation are hypothesized to have occurred, we also collected nine ancient river sand samples along the Jingou He section in the northern Tianshan, previously dated by magnetostatigraphy to ~1.5 to ~1 Ma. To calculate paleo-denudation rates based on the measured paleo-concentrations, we used both uncorrected cosmogenic paleo-production rates (assuming no ice in the drainage basin) and rates corrected for maximum ice cover extent. Paleo-denudation rates were then normalized to modern values derived from in situ <sup>10</sup>Be cosmogenic concentrations previously measured in modern river sand. We observed steady Early Pleistocene denudation rates similar to those at present day in the Jingou He basin. However, since 700 ka during the Middle Pleistocene, paleo-denudation rates were more variable, but uncorrelated with climate oscillations. Those variations may have been due to climatic cooling and a stronger glacial influence that had a nonlinear effect on denudation, yielding spatial variations between drainage basins. However, we see no sustained acceleration in denudation despite the increased amplitude of glacial cycles during the Late Pleistocene.

## 1. Introduction

The Earth's surface is strongly affected by denudation, the combined effect of physical erosion and chemical weathering. Denudation impacts soil formation and agriculture (Egli et al., 2014), affects relief stability (Viles, 2013), and, at geological timescales, partly controls the atmospheric CO₂ content via the weathering of silicates (e.g. Dessert et al., 2003) and the production of sediments that ultimately bury organic matter in the oceans (e.g. Galy et al., 2008). Denudation is strongly modulated by spatial variations in climate (Schlunegger et al., 2023). In the context of global warming, it is therefore particularly important to predict how denudation will change and impact the Earth's surface. This

requires an understanding of the links between past climate variability and denudation rates, especially during the Quaternary, when the Earth experienced rapid climate oscillations at amplitudes similar to those expected due to anthropogenic impacts (see Intergovernmental Panel on Climate Change reports). Such an understanding requires quantitative estimates of Quaternary denudation rates, which can be constrained using sedimentary budgets in closed basins where the spatial distribution of sediment bodies can be determined in detail (Hinderer, 2012). However, such rare conditions most often occur in continental areas where the dating of associated clastic deposits may be challenging especially to get precise ages (Hinderer, 2012). Despite the development of new dating techniques for clastic deposits, only a limited number of

<footnote><sup>a</sup> CRPG, CNRS, Université de Lorraine, UMR 7358, 54501 Vandœuvre-lès-Nancy, France</footnote>

<footnote><sup>b</sup> Laboratoire Géosciences Montpellier, CNRS, Université de Montpellier; UMR 5243, 34095 Montpellier Cedex, France</footnote>

<footnote><sup>c</sup> School of Earth Sciences and Engineering, Nanjing University, 163 Xianlin Ave, Qixia District, Nanjing, Jiangsu Province 210046, China</footnote>

<footnote>* Corresponding author.</footnote>

<footnote>E-mail addresses: julien.charreau@univ-lorraine.fr (J. Charreau), pierre-henri.blard@univ-lorraine.fr (P.-H. Blard), jerome.lave@univ-lorraine.fr (J. Lavé), etiennelarge@univ-lorraine.fr (E. Large), catherine.zimmermann@univ-lorraine.fr (C. Zimmermann), dominguez@gm.univ-montp2.fr (S. Dominguez), wangsl@nju.edu.cn (S. Wang).</footnote>
studies have reconstructed denudation rates from Quaternary sedimentary budgets and compared them to climatic variations, and the scopes of those studies have remained spatiotemporally limited (e.g. Zolitschka, 1998).

Alternatively, basin-averaged denudation rates in open-drainage catchments can be derived from analyses of in-situ cosmogenic $^{10}$Be concentrations in fluvial sediments (e.g. Brown et al., 1995). Similarly, basin-scale paleo-denudation rates can be reconstructed from the analysis of in situ $^{10}$Be concentrations in ancient sediments (Bekaddour et al., 2014; Charreau et al., 2011; Madella et al., 2018; Mandal et al., 2021; Puchol et al., 2017; Schaller et al., 2002). In particular, fluvial sediments initially buried for instance in foreland basins and now exposed along the frontal tectonic structures of a given orogen can be analyzed to reconstruct paleo-denudation rates of the range (Charreau et al., 2011, 2020; Fisher et al., 2023; Mandal et al., 2021; Puchol et al., 2017). Past denudation rates can be also calculated from inherited $^{10}$Be concentrations recorded in simple alluvial terraces not necessarily located in foreland basin. For instance, Schaller et al. (2002, 2016) reconstructed denudation rates in the Meuse and other European basin since ~2 Ma based on cosmogenic depth profile inversion measured in alluvial terraces, which can constrain both the terrace abandonment age and the inherited $^{10}$Be concentration at the time of deposition (Braucher et al., 2009; Hidy et al., 2010; Repka et al., 1997). Other sedimentary archives have also been analyzed for cosmogenic nuclides, including lake deposits, cave sediments, and marine turbidites (Lenard et al., 2020; Mariotti et al., 2021). In all those cases, the cosmogenic technique can provide paleo-denudation rates at timescales of $10^2-10^5$ a, which are suitable for studying the potential impact of climate oscillations during the Quaternary (e.g. Fisher et al., 2023; Mariotti et al., 2021).

Although several studies have used this approach to reconstruct Quaternary paleo-denudation rates in various geological contexts (Bekaddour et al., 2014; Fisher et al., 2023; Fuller et al., 2009; Grischott et al., 2017; Hidy et al., 2014; Mariotti et al., 2021; Marshall et al., 2017; Schaller et al., 2002), few of those records are sufficiently continuous and temporally precise to study the impacts of climate oscillations (Fisher et al., 2023; Mariotti et al., 2021; Marshall et al., 2017). For example, in Oregon, Marshall et al. (2017) observed that climate variations since 50 ka modulated denudation rates over glacial-interglacial timescales mainly via the effects of periglacial frost cracking. In the southern Central Andes, Fisher et al. (2023) observed long-term synchronicity between denudation rate variations and Milankovitch-driven,

400-ka eccentricity cycles, implying a significant climatic impact on denudation. However, they did not invoke the role of frost-cracking, instead attributing the observed synchronicity to fluctuations in precipitation inducing synchronous, nonlinear responses in denudation rates. Based on an analysis of $^{10}$Be in turbidites shed from the south-eastern Alps, Mariotti et al. (2021) reconstructed a 70-ka record of paleo-denudation rates in the region; there, denudation rates were 2-7 times higher during the Last Glacial Maximum (LGM) than those today or during previous more moderately glacial episodes. Their results also suggest a nonlinear response of denudation to climate changes. Therefore, although several studies have demonstrated that Quaternary climate changes can modulate denudation rates in various regions, several mechanisms have been proposed, and the observed modulations can be nonlinear and depend on threshold effects. The link between climate oscillations and denudation during the Quaternary therefore remains obscure, and more quantitative data are needed in various geological and climatic contexts.

In this study, we reconstructed Quaternary paleo-denudation rates in the Tianshan range of Central Asia. Several aspects of this mountain belt motivate this work. First, it is a major orographic barrier that likely played an important role during the onset of Quaternary glaciations by transferring low-salinity fresh water to the Arctic Ocean (Prud'homme et al., 2021). Second, regional climate variations are well documented geochemically and isotopically by speleothems (Cheng et al., 2016; Wang et al., 2008) (Fig. 1). Third, the abundant Quaternary deposits in the piedmonts have been well dated, either by geomorphic analyses of recent alluvial terraces (Cording et al., 2014; Grin et al., 2018; Huang et al., 2014, 2019; Pang et al., 2022) or by magnetostratigraphy of older fluvial sediments that have been folded and tilted in the frontal structures and are now exposed along incised rivers (e.g. Charreau et al., 2009b).

In the Tianshan, several studies have already used the cosmogenic technique to reconstruct paleo-denudation rates (Charreau et al., 2011, 2023; Grin et al., 2018; Puchol et al., 2017). Nonetheless, for the Quaternary, only Charreau et al. (2023), by inverting $^{10}$Be cosmogenic depth profiles, provided enough data to discuss the temporal variability of denudation rates, suggesting that values have remained steady since at least ~160 ka. Although several other studies have constrained terrace abandonment ages in the region using $^{10}$Be cosmogenic depth profile analyses (Cording et al., 2014; Grin et al., 2018; Huang et al., 2019, 2014; Pang et al., 2022), they restricted their analyses to the terrace ages

<figure><img src="image_3.png" /><figcaption>**Fig. 1.** Topographic map of the Tianshan range (SRTM DEM) with the locations of cosmogenic depth profiles analyzed for paleo-denudation rate reconstruction. Associated drainage basins are colored based on the modern denudation rates measured from in situ cosmogenic $^{10}$Be concentrations in river sands.</figcaption></figure>
and direct geomorphological implications without exploiting the inherited ¹⁰Be concentrations derived from the depth profile inversion.

In this study, we reprocessed these pre-existing data and analyzed five new cosmogenic nuclide depth profiles from the northern Tianshan (Fig. 1). For homogeneity, we used a unique inversion technique that can account for several parameters’ uncertainties and includes a formulation to consider the potential late deposition of loess, as is often encountered in the region. The inherited concentrations derived from this inversion were then used to reconstruct paleo-denudation rates during the Quaternary. Important perturbations to denudation are expected at the Mid-Pleistocene transition (MPT, ~1.2–0.7 Ma) because the amplitude of climate cyclicity increased (e.g. Molnar, 2004). However, in the Tianshan, no terrace has yet been dated to before this transition (e.g. Charreau et al., 2018; Gong et al., 2014; Poisson and Avouac, 2004). Given the geomorphic context of the northern Tianshan piedmont (Avouac et al., 1993; Poisson and Avouac, 2004), the five new terraces analyzed for cosmogenic nuclide depth profiles herein are also unlikely to be older than 0.7 Ma. Therefore, to extend the dataset beyond the MPT, we also collected nine ancient river sand samples along the Jingou He section in the northern Tianshan (Fig. 2 and Table 1 for samples coordinates). This section was entrenched by the Jingou He river across the Huerguosi anticline and offers a continuous exposure of Quaternary deposits that have been well dated by magnetostratigraphy (Charreau et al., 2009a). Collected samples range from ~1.5 to ~1 Ma. To compare these datasets, paleo-denudation rates were normalized to modern ¹⁰Be-derived denudation rates across the same drainage basin. This yields a 1.5–0 Ma record of paleo-denudation rates that we compared to climate variations to discuss the potential links between the two.

## 2. Materials and methods

### 2.1. Abandonment ages of alluvial terraces and their inherited cosmogenic ¹⁰Be concentrations

The abandonment ages of alluvial surfaces can be constrained by measuring and inverting the concentrations of in-situ cosmogenic ¹⁰Be in quartz along vertical depth profiles (e.g. Braucher et al., 2009; Hidy et al., 2010; Repka et al., 1997). This technique also provides the inherited cosmogenic ¹⁰Be concentration at the time of deposition, i.e. before river abandonment, and can accordingly be used to reconstruct paleo-denudation rates (Fig. 3). It has been applied to date several terraces around the Tianshan (Fig. 1). However, to remove spatial variation and reveal only temporal changes in the paleodenudation rates, we restricted our analyses to sites where ¹⁰Be concentrations were also measured in modern rivers, allowing us to normalize paleo-denudation rates to the modern values and compare between different locations. We reprocessed 15 previously published cosmogenic depth profiles (Table 2) using the same procedure for homogeneity. To derive exposure ages from the depth profiles, we used the inversion approach described in Saint-Carlier et al. (2016) and Charreau et al. (2017). The inversion model as the other methods used in the literature (Table 2) explores, using a Monte Carlo inversion procedure that tests thousands of parameters, the combinations of three unknown variables: the exposure age, the average cosmogenic inheritance and the average erosion rate at the surface of the sampled terraces. The best fitting solution were found by minimizing the difference between the model and the data (e.g. Braucher et al., 2009; Saint-Carlier et al., 2016). The final uncertainties were evaluated following the approach of Braucher et al. (2009), i.e. by investigating the combinations of parameters for which $\chi^2$ (the difference between the observed and expected values weighted by their

<figure><img src="image_4.png" /><figcaption>**Fig. 2.** a. Topographic map of the northern Tianshan, with the locations of ¹⁰Be cosmogenic depth profiles analyzed in the literature (blue circles) and new depth profiles analyzed in this study (red circles). Yellow circles show the two terraces dated by OSL where ¹⁰Be concentrations were also measured for paleo-denudation rates (Puchol et al., 2017). Blue text indicates the names of main rivers draining the northern piedmont b. Google Earth image of the Jingou He river, with locations of the nine samples collected for paleo-denudation rate reconstruction (blue circles) along the magnetostratigraphic section (yellow line) of Charreau et al. (2009a, 2009b).</figcaption></figure>
<caption>**Table 1**</caption>

In-situ $^{10}$Be cosmogenic results of samples collected in the Jingou He section. $^{10}$Be$_{dep}$ gives the concentration at the time of deposition (i.e. corrected for radioactive decay). $\varepsilon$ and R are the denudation rates and ratio between the paleo and the modern values, respectively. Suffix g indicates denudation and ratio corrected for ice cover.

<table><thead><tr><th>Age<br>Ma</th><th>Total counts<br><sup>10</sup>Be</th><th><sup>10</sup>Be/<sup>9</sup>Be<br>(10<sup>-14</sup>)</th><th>Mass of<br>quartz<br>(g)</th><th>Added <sup>9</sup>Be<br>(×10<sup>19</sup>at)</th><th><sup>10</sup>Be<br>(×10<sup>4</sup> at/<br>g)</th><th><sup>10</sup>Be<sub>dep</sub><br>(×10<sup>4</sup> at/<br>g)</th><th>ε<br>mm/a</th><th>ε<sub>g</sub><br>mm/a</th><th>R<sub>c</sub></th><th>R<sub>ε</sub></th><th>R<sub>eg</sub></th></tr></thead><tbody><tr><td>1.509</td><td>145</td><td>12.6 ± 1.1</td><td>20.4</td><td>3.202</td><td>5.2 ± 0.5</td><td>11.1 ± 1</td><td>0.27 ±<br>0.03</td><td>0.07 ± 0.01</td><td>1.53 ±<br>0.14</td><td>0.93 ± 0.15</td><td>0.24 ±<br>0.04</td></tr><tr><td>1.466</td><td>145</td><td>17 ± 1.3</td><td>19.9</td><td>3.200</td><td>5.4 ± 0.4</td><td>11.2 ± 0.9</td><td>0.27 ±<br>0.03</td><td>0.07 ± 0.01</td><td>1.53 ±<br>0.12</td><td>0.93 ± 0.14</td><td>0.24 ±<br>0.04</td></tr><tr><td>1.425</td><td>145</td><td>30.8 ± 1.4</td><td>7.7</td><td>3.214</td><td>5.5 ± 0.3</td><td>11.1 ± 0.5</td><td>0.27 ±<br>0.02</td><td>0.07 ± 0.01</td><td>1.53 ±<br>0.07</td><td>0.93 ± 0.13</td><td>0.24 ±<br>0.03</td></tr><tr><td>1.406</td><td>145</td><td>23.4 ± 1.6</td><td>16.9</td><td>3.174</td><td>5.4 ± 0.4</td><td>10.9 ± 0.8</td><td>0.27 ±<br>0.03</td><td>0.07 ± 0.01</td><td>1.5 ± 0.11</td><td>0.95 ± 0.14</td><td>0.24 ±<br>0.04</td></tr><tr><td>1.393</td><td>145</td><td>21.6 ± 1.3</td><td>20.2</td><td>3.056</td><td>5.9 ± 0.4</td><td>11.8 ± 0.8</td><td>0.25 ±<br>0.02</td><td>0.06 ± 0.01</td><td>1.62 ±<br>0.11</td><td>0.88 ± 0.13</td><td>0.22 ±<br>0.03</td></tr><tr><td>1.256</td><td>145</td><td>47.2 ± 1.6</td><td>9.1</td><td>3.213</td><td>7.1 ± 0.3</td><td>13.3 ± 0.5</td><td>0.23 ±<br>0.02</td><td>0.06 ±<br>0.004</td><td>1.82 ±<br>0.06</td><td>0.78 ± 0.11</td><td>0.2 ± 0.03</td></tr><tr><td>1.069</td><td>145</td><td>29.4 ± 1.5</td><td>20.6</td><td>3.184</td><td>6.1 ± 0.3</td><td>10.3 ± 0.6</td><td>0.29 ±<br>0.02</td><td>0.07 ± 0.01</td><td>1.42 ±<br>0.08</td><td>1.005 ±<br>0.14</td><td>0.25 ±<br>0.04</td></tr><tr><td>1.069</td><td>145</td><td>40.7 ± 1.5</td><td>18.6</td><td>3.166</td><td>7.3 ± 0.3</td><td>12.4 ± 0.5</td><td>0.24 ±<br>0.02</td><td>0.06 ±<br>0.004</td><td>1.71 ±<br>0.06</td><td>0.83 ± 0.11</td><td>0.21 ±<br>0.03</td></tr><tr><td>1.066</td><td>145</td><td>12.9 ± 1.3</td><td>7.2</td><td>3.207</td><td>8.1 ± 0.9</td><td>13.8 ± 1.5</td><td>0.22 ±<br>0.03</td><td>0.06 ± 0.01</td><td>1.89 ±<br>0.21</td><td>0.75 ± 0.13</td><td>0.19 ±<br>0.03</td></tr><tr><td>17</td><td></td><td>0.08 ±<br>0.02</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>10</td><td></td><td>0.08 ±<br>0.03</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr></tbody></table>

uncertainties) is $<\chi^2_{min} + 1$. The results of the inversion also depend on the local $^{10}$Be production rates for neutrons, fast muons, and slow muons which were calculated based on the updated average sea level and high latitude (SLHL) $^{10}$Be global production rate in CREp (Martin et al., 2017) and then scaled for local latitude and altitude according to Stone (2000), and local atmospheric pressures were extracted from the ERA40 dataset (Uppala et al., 2005).

The choice of this inversion model is also motivated by the fact that it accounts for uncertainties in soil density, cosmogenic radionuclide concentration, and inheritance, including sample variability in inheritance (see appendix of Saint-Carlier et al., 2016).

The need for homogenization also stems from the necessity to provide a coherent account of the loess cover deposited atop several of the dated terraces after they were abandoned by the river (see Table 2 for loess thicknesses). Previously, these deposits were either disregarded or assumed present since terrace abandonment (Cording et al., 2014). In contrast, our inversion model includes a revised formulation of Lal (1991) and a more realistic scenario of the potential deposition of loess and/or soil after terrace formation (see Charreau et al., 2017 for details). Based on optically stimulated luminescence (OSL) dating of loess sections in the region (e.g. Long et al., 2014; Song et al., 2012), we can first assume that the few tens of centimeters of loess covering some of the studied terraces (Fig. 2) accumulated at a constant rate after terrace abandonment. However, we also calculated endmember ages by assuming 1) instantaneous deposition of the entire loess layer at once immediately after terrace abandonment (maximum age), and 2) very recent deposition of the entire loess layer, meaning that it did not affect the cosmogenic depth profile in the underlying deposits (minimum age, ignoring attenuation in the loess). The sensitivity of the results (terrace abandonment ages and inherited concentrations) to the choice of loess deposition scenario is discussed in the Results part.

In our cosmogenic dataset, we also included literature data from two terraces previously dated using OSL (terraces KTN-T0 and JGH-T0 in Puchol et al., 2017; Table 2). In addition to the other 15 depth profiles, this brings the total number of previously dated terraces reprocessed for paleo-denudation rates to 17 (Table 2).

Moreover, we extended this dataset by dating five alluvial terraces in the northern Tianshan piedmont (Figs. 1 and 3, Table 3). ANJ1W and

ANJ2W depth profiles are located in the western part of the Northern Tianshan piedmont in a wind gap created by the rise of the Anjihai-Halaande anticline (Fig. A in online supplementary information). The two profiles were collected across two strath-terraces deposited and abandoned by the former Anjihai river that now crosses the fold Eastward. The JGH-T2 profile is located 30 km south-east of the previous ones and was collected across the main strath-terrace abandoned by the Jingou He river. The profile was sampled ~20 km south of the Huer-guo's anticline and its associated thrust fault (Fig. B in online supplementary information). TS12-TXH and TS12-HTB profiles were collected in strath-terraces abandoned by the Taxi and Hutubi rivers, respectively. Both alluvial surfaces were uplifted by the rise of the Tugulu anticline and movements on the associated thrust faults (Fig. A).

For each depth profile, four to five samples of sand and gravel were collected from the surface to a maximum depth of 3–7 m (Table 3). Sand and fine pebbles (ø < 1.5 cm) were taken for the depth profiles. In two profiles (ANJW-T2 and JGH-T2), samples were also taken at the surface. When possible, the top 1–2 cm of blocks were collected for the surface sample. We also sampled cobbles (6 cm < ø < 15 cm) and coarse pebbles (1.5 cm < ø < 6 cm) at the surface. To avoid bias due to recent exposure, sampling sites were chosen in man-made pits when available, or on terrace edges along actively incising valleys after digging back into the exposure to at least 50 cm depth. Moreover, all outcrops were systematically refreshed by digging a few tens of centimeters before collecting samples.

## 2.2. The Jingou He section

The fold and thrust belts of the northern Tianshan piedmont deform Permian to Quaternary sediments that are mainly of continental origin (e.g. Hendrix et al., 1992). Most of the sedimentary pile that is faulted and folded in the piedmont was initially deposited in the foreland basin of the Tianshan during the Tertiary, while the orogen was reactivated by the India-Asia collision. The Jingou He section is in the western part of the northern Tianshan piedmont (Fig. 2). Here, the Jingou He river has deeply entrenched the Huerguosi anticline during the Holocene, exposing five stratigraphic formations that have been dated by magnet stratigraphy to between ~24 Ma and ~ 1 Ma (Charreau et al., 2009a).
<figure><img src="image_5.png" /></figure>

**Fig. 3.** $^{10}$Be cosmogenic concentration depth profiles for each of the newly analyzed terraces in the northern Tianshan (see Fig. 2 and Table 3 for locations). Green circles show the mean values of samples collected at the surface when available. Yellow layers correspond to loess, considered to have a bulk density of 1.6 ± 0.2 g/cm$^3$ and converted to a theoretical thickness corresponding to the densities of the respective terraces. The calculated depth uncertainties for each sample include not only the uncertainty in the depth below the surface and sample thickness, but also the uncertainty in soil density estimated to be 0.2 g/cm$^3$ (see eq. A.2 in the Appendix of Saint-Carlier et al., 2016). The sampling points for the cosmogenic depth profiles are shown in the photographs. GPS coordinates for each profile are reported in Table 3. The figures given online provide more detailed information regarding the geomorphic setting of each sampling sites. Panels a to f correspond to the measured profiles, with the profile identifier indicated in the upper left side of the diagrams. Panel g shows a schematic profile with the theoretical evolution of the concentration (in red) shown as a function of time and the inherited concentration $C_0$, which corresponds to the asymptote at depth of the exponential curve that fits the data.
<caption>**Table 2**</caption>

Results of depth profile inversions, with terrace abandonment ages, inherited ¹⁰Be concentrations, and corresponding basin-averaged paleo-denudation rates. Uncertainties are given at 1σ. Means are weighted averages. S<sub>r</sub> is the sedimentation rates when loess deposition is considered, tab is the time of abandonment, C<sub>inh</sub> and C<sub>mod</sub> are the inherited and modern concentrations in ¹⁰Be, respectively. ε and R are the denudation rates and ratio between the paleo and the modern values, respectively. Suffix g indicates denudation and ratio corrected for ice cover while suffix mod is for the modern denudation rates. Suffixes ε and C for R indicates denudation and concentration ratio, respectively.

<table><thead><tr><th>Profile name</th><th>Latitude</th><th>Longitude</th><th>Elevation</th><th>Loess thickness</th><th>S<sub>r</sub></th><th>t<sub>ab</sub></th><th>C<sub>inh</sub></th><th>ε</th><th>ε<sub>g</sub></th><th>C<sub>mod</sub></th><th>ε<sub>mod</sub></th><th>R<sub>c</sub></th><th>R<sub>ε</sub></th><th>R<sub>eg</sub></th><th>References</th></tr><tr><th></th><th>*</th><th>*</th><th>m</th><th>cm</th><th>m/Ma</th><th>ka</th><th>(10<sup>4</sup> at/g)</th><th>mm/a</th><th>mm/a</th><th>(10<sup>4</sup> at/g)</th><th>mm/a</th><th></th><th></th><th></th><th></th></tr></thead><tbody><tr><td>Dushanzl East</td><td>44.2754</td><td>84.9490</td><td>847</td><td>0</td><td></td><td>82.8±20.8/13.7</td><td>5.1±1.9/3.5</td><td>0.5±0.34</td><td>0.3±0.2</td><td>4.1±0.6</td><td>0.52±0.08</td><td>1.2±0.7</td><td>1±0.7</td><td>0.5±0.3</td><td>Pang et al. (2022)</td></tr><tr><td>Terrace T4</td><td>44.3412</td><td>79.9069</td><td>1132</td><td>33</td><td>-0.9±0.2</td><td>270.7±83.8/54.7<br>409.3±40.7/109.3<br>259.5±30.5/49.5</td><td>22±16.4/21<br>22.7±1.3/2.7<br>21.8±1.2/0.8</td><td>0.1±0.1<br>0.1±0.01<br>0.1±0.01</td><td>0.02±0.02<br>0.02±0.003<br>0.02±0.002</td><td>7.5±0.4</td><td>0.3±0.02<br>0.3±0.02<br>0.3±0.02</td><td>3±2.5<br>3±0.3<br>2.9±0.2</td><td>0.3±0.3<br>0.3±0.1<br>0.3±0</td><td>0.1±0.1<br>0.1±0<br>0.1±0</td><td>Cording et al. (2014)</td></tr><tr><td>F4_HJF</td><td>42.3784</td><td>86.2194</td><td>1355</td><td>0</td><td></td><td>307.5±70.7/57.4</td><td>48.4±17.2/19.2</td><td>0.05±0.02</td><td>0.03±0.01</td><td>22±1.2</td><td>0.11±0.01</td><td>2.2±0.8</td><td>0.5±0.2</td><td>0.3±0.1</td><td></td></tr><tr><td>F3_HJF</td><td>42.3872</td><td>86.2276</td><td>1298</td><td>0</td><td></td><td>541.3±152.5/108.9</td><td>55±19.3/20</td><td>0.04±0.02</td><td>0.03±0.01</td><td></td><td>0.11±0.01</td><td>2.5±0.9</td><td>0.4±0.2</td><td>0.2±0.1</td><td>Huang et al. (2014)</td></tr><tr><td>F2_HJF</td><td>42.3967</td><td>86.2358</td><td>1263</td><td>0</td><td></td><td>448.1±159.2/106.7</td><td>31.4±22.6/31.4</td><td>0.08±0.08</td><td>0.05±0.05</td><td></td><td>0.11±0.01</td><td>1.4±1.2</td><td>0.7±0.7</td><td>0.4±0.4</td><td></td></tr><tr><td>KTN-T3</td><td>44.3009</td><td>84.7763</td><td>828</td><td>0</td><td></td><td>13.4±1.6/1.6*</td><td>6.4±0.7/0.7</td><td>0.4±0.05</td><td>0.2±0.03</td><td>4.2±1.1</td><td>0.51±0.14</td><td>1.5±0.5</td><td>0.8±0.2</td><td>0.4±0.1</td><td>Charreau et al. (2018)</td></tr><tr><td>KTN-T0</td><td>44.2901</td><td>84.7599</td><td>1040</td><td>0</td><td></td><td>116±15/15*</td><td>4.1±0.3/0.3</td><td>0.62±0.06</td><td>0.31±0.03</td><td>4.2±1.1</td><td>0.51±0.14</td><td>1±0.3</td><td>1.2±0.4</td><td>0.6±0.2</td><td>Puchol et al. (2017)</td></tr><tr><td>JGH-T0</td><td>44.1739</td><td>85.4583</td><td>984</td><td>0</td><td></td><td>66±5/5*</td><td>10±0.3/0.3</td><td>0.25±0.02</td><td>0.09±0.01</td><td>7.3±0.7</td><td>0.26±0.03</td><td>1.4±0.1</td><td>1±0.1</td><td>0.3±0</td><td></td></tr><tr><td>ANJ-T1B</td><td>44.1052</td><td>85.0973</td><td>1370</td><td>15</td><td>-41.2±8.9</td><td>4.6±1.3/1.5<br>5.2±1.7/1.7<br>4.5±1.5/1.4</td><td>9.9±0.8/0.7<br>9.9±1/0.8<br>10±0.7/0.9</td><td>0.3±0.03<br>0.3±0.03<br>0.3±0.03</td><td>0.08±0.01<br>0.09±0.01<br>0.08±0.01</td><td>5.2±0.6</td><td>0.41±0.05<br>0.41±0.05<br>0.41±0.05</td><td>1.9±0.3<br>1.9±0.3<br>1.9±0.3</td><td>0.7±0.1<br>0.7±0.1<br>0.7±0.1</td><td>0.2±0<br>0.2±0<br>0.2±0</td><td>Malatesta et al. (2018)</td></tr><tr><td>Ya-T1</td><td>41.8818</td><td>83.3289</td><td>1295</td><td>0</td><td></td><td>68.2±2.6/9.8</td><td>8.9±1.4/1.5</td><td>0.14±0.03</td><td>0.14±0.03</td><td>7.4±0.5</td><td>0.16±0.01</td><td>1.2±0.2</td><td>0.8±0.2</td><td>0.8±0.2</td><td>Charreau et al. (2019)</td></tr><tr><td>YAK1</td><td>41.8001</td><td>83.3193</td><td>1183</td><td>0</td><td></td><td>123.6±7.9/3.6</td><td>6.3±0.8/0.9</td><td>0.19±0.03</td><td>0.19±0.03</td><td>7.4±0.5</td><td>0.16±0.01</td><td>0.8±0.1</td><td>1.2±0.2</td><td>1.2±0.2</td><td></td></tr><tr><td>YAK2</td><td>41.8845</td><td>83.6235</td><td>1163</td><td>0</td><td></td><td>43.7±8.7/7.4</td><td>7.9±0.8/0.6</td><td>0.22±0.03</td><td>0.22±0.03</td><td>7.4±0.5</td><td>0.24±0.02</td><td>1.1±0.1</td><td>0.9±0.1</td><td>0.9±0.1</td><td></td></tr><tr><td>KU1</td><td>41.7609</td><td>83.1057</td><td>1125</td><td>0</td><td></td><td>128.1±20.1/8.1</td><td>4.8±3.2/3</td><td>0.41±0.27</td><td>0.26±0.18</td><td>10.3±2.1</td><td>0.18±0.04</td><td>0.5±0.3</td><td>2.2±1.5</td><td>1.4±1</td><td>Saint-Carlier et al. (2016)</td></tr><tr><td>KU2</td><td>41.7625</td><td>83.1145</td><td>1111</td><td>0</td><td></td><td>61.6±3.9/5.3</td><td>9.2±1.5/1.4</td><td>0.21±0.04</td><td>0.14±0.02</td><td>10.3±2.1</td><td>0.18±0.04</td><td>0.9±0.2</td><td>1.2±0.3</td><td>0.72±0.2</td><td></td></tr><tr><td>BBK4-T2</td><td>43.0467</td><td>84.1445</td><td>2491</td><td>15</td><td>-1.9±0.2</td><td>59.9±5/6.2<br>65.9±8/6.5<br>56.8±4.3/5.8</td><td>17.7±4.2/4.8<br>17.8±4.2/4.8<br>18.1±3.9/4.5</td><td>0.14±0.04<br>0.14±0.04<br>0.14±0.04</td><td>0.14±0.04<br>0.14±0.04<br>0.14±0.04</td><td>28±1.5</td><td>0.09±0.01<br>0.09±0.01<br>0.09±0.01</td><td>0.6±0.2<br>0.6±0.2<br>0.6±0.2</td><td>1.6±0.5<br>1.6±0.5<br>1.5±0.4</td><td></td></tr><tr><td>BBK3-T2</td><td>43.0690</td><td>84.0747</td><td>2616</td><td>25</td><td>-2±0.2</td><td>20.3±1.5/1.4<br>23.4±1.9/1.7<br>18.2±1.3/1.2</td><td>17.6±1.3/1.4<br>17.7±1.3/1.3<br>17.6±1.3/1.3</td><td>0.15±0.01<br>0.15±0.01<br>0.15±0.01</td><td>0.15±0.01<br>0.14±0.01<br>0.15±0.01</td><td>28±1.5</td><td>0.09±0.01<br>0.09±0.01<br>0.09±0.01</td><td>0.6±0.1<br>0.6±0.1<br>0.6±0.1</td><td>1.6±0.2<br>1.6±0.2<br>1.6±0.2</td><td>Charreau et al. (2017)</td></tr><tr><td>BBK3-T3</td><td>43.0712</td><td>84.0713</td><td>2644</td><td>25</td><td>-2.2±0.2</td><td>87.4±8.5/9<br>106.2±10.6/16.2<br>77±9.4/5.8</td><td>6±12.4/6<br>6±12.4/6<br>7.4±9.6/7.3</td><td>0.43±0.88<br>0.43±0.89<br>0.35±0.45</td><td>0.43±0.88<br>0.43±0.89<br>0.35±0.45</td><td>28±1.5</td><td>0.09±0.01<br>0.09±0.01<br>0.09±0.01</td><td>0.2±0.3<br>0.2±0.3<br>0.3±0.3</td><td>4.7±9.6<br>4.7±9.8<br>3.8±5</td><td></td></tr><tr><td>ANJW-T1</td><td>44.2509</td><td>85.1872</td><td>923</td><td>60</td><td>-10.9±1.7</td><td>42±7.7/6.7<br>58.4±13/9.4<br>31.2±4.1/3.3</td><td>9.6±1/9.2/2<br>9.6±2/2.3<br>9.7±1.6/1.6</td><td>0.29±0.07<br>0.29±0.07<br>0.28±0.05</td><td>0.1±0.02<br>0.1±0.02<br>0.1±0.02</td><td>5.2±0.6</td><td>0.39±0.05<br>0.39±0.05<br>0.39±0.05</td><td>1.8±0.5<br>1.9±0.5<br>1.9±0.4</td><td>0.2±0.1<br>0.2±0.1<br>0.2±0.1</td><td></td></tr><tr><td>ANJW-T2</td><td>44.2757</td><td>85.1628</td><td>850</td><td>35</td><td>-64.9±23.4</td><td>4.1±1.1/1.1<br>5.9±1.5/1.4<br>4.2±1/1</td><td>6.9±0.4/0.4<br>6.7±0.3/0.4<br>6.7±0.3/0.4</td><td>0.34±0.05<br>0.34±0.05<br>0.33±0.06</td><td>0.09±0.01<br>0.09±0.01<br>0.08±0.02</td><td>5.2±0.6</td><td>0.39±0.05<br>0.39±0.05<br>0.39±0.05</td><td>1.3±0.2<br>1.3±0.2<br>1.3±0.2</td><td>0.9±0.2<br>0.9±0.2<br>0.8±0.2</td><td>This study</td></tr><tr><td>JGH-T2</td><td>44.0998</td><td>85.4426</td><td>1011</td><td>10</td><td>-3.9±8.4</td><td>12.8±6.9/6.6<br>14.2±4.7/4.5<br>12.9±4.1/4</td><td>9.1±1.6/1.6<br>8.8±1.3/1.3<br>8.9±1.3/1.3</td><td>0.5±0.06<br>0.49±0.07<br>0.49±0.06</td><td>0.26±0.03<br>0.25±0.03<br>0.25±0.03</td><td>7.3±0.7</td><td>0.29±0.03<br>0.29±0.03<br>0.29±0.03</td><td>1.3±0.2<br>1.2±0.2<br>1.2±0.2</td><td>3.1±0.3<br>1.7±0.3<br>1.7±0.3</td><td>0.9±0.1<br>0.9±0.2<br>0.9±0.1</td></tr><tr><td>THX</td><td>44.0835</td><td>86.3435</td><td>867</td><td>10</td><td>-14.9±1.5</td><td>8.1±1.3/1.4<br>8.6±1.4/1.4<br>7.7±1.1/1.2</td><td>4.5±0.4/0.5<br>4.6±0.3/0.6<br>4.6±0.3/0.4</td><td>0.4±0.03<br>0.41±0.03<br>0.41±0.03</td><td>0.24±0.04<br>0.24±0.04<br>0.24±0.04</td><td>12.6±0.5</td><td>0.15±0.01<br>0.15±0.01<br>0.15±0.01</td><td>0.4±0<br>0.4±0<br>0.4±0</td><td>0.8±0.1<br>0.8±0.1<br>0.8±0.1</td><td>0.3±0<br>0.3±0<br>0.3±0</td></tr><tr><td>HTB</td><td>44.0536</td><td>86.7705</td><td>804</td><td>30</td><td>-15±1.7</td><td>15.3±1.7/1.6<br>17.9±2.2/2<br>13.1±1.4/1.2</td><td>4.7±0.7/0.7<br>4.7±0.6/0.7<br>4.8±0.5/0.7</td><td>0.47±0.07<br>0.47±0.07<br>0.46±0.07</td><td>0.14±0.01<br>0.14±0.01<br>0.14±0.01</td><td>3.9±0.2</td><td>0.53±0.04<br>0.53±0.04<br>0.53±0.04</td><td>0.4±0<br>0.4±0<br>0.4±0</td><td>3.1±0.5<br>3.1±0.5<br>3.1±0.5</td><td>1.6±0.3<br>1.6±0.3<br>1.6±0.3</td></tr></tbody></table>

The top of the sedimentary pile corresponds to the Yiyu formation, which is mainly composed of massive to horizontally and cross-bedded sandstones to conglomerates that were deposited by a fan-shaped braided fluvial system (Charreau et al., 2009a). This formation is interpreted as a diachronous gravel wedge prograding at the front of the Tianshan while deformation encroached toward the foreland basin (Charreau et al., 2009b). In the Jingou He section, the Yiyu formation is ~2 km thick and was dated by magnetostratigraphy to between ~7.5 Ma and ~1 Ma (Charreau et al., 2009a). To better document Quaternary denudation rates in the Tianshan before the MPT, we focused our analyses to the top ~150 m of this formation, from which we collected nine sand samples for in situ cosmogenic ¹⁰Be analyses; based on magnetostratigraphy, these samples date to between ~1.5 Ma to ~1 Ma (Charreau et al., 2009a; Table 1). At each sampling site, 1–2 kg of sand were taken at the base of 20–30 m cliffs to avoid contamination by recent exposure to cosmic rays.

## 2.3. Paleo-denudation rates from ¹⁰Be cosmogenic concentrations

Paleo-denudation rates $\bar{\epsilon}$ (cm/a) can be derived from ¹⁰Be cosmogenic concentrations determined in ancient sediments ($N_{total}$, at/g) by solving the following equation (Charreau et al., 2020; Puchol et al., 2017):

$$N_{\text{total}} = e^{-\lambda t} \sum_j \left[ \frac{\bar{P}_j}{\bar{\epsilon} \rho_r / \Lambda_j} + \frac{P_j^{\text{sed}}}{\frac{\Lambda_j \rho_s}{\Lambda_j} - \lambda} \left( 1 - e^{-\left(\frac{\Lambda_j \rho_s}{\Lambda_j} - \lambda\right)t} \right) \right] + N_{\text{fp}} + N_{\text{recent}}$$

where $\lambda$ is the radioactive decay constant, $\rho_r$ and $\rho_s$ are the densities of denuded rocks in the source area and sediments, respectively, $\Lambda_j$ is the typical attenuation length of production mechanism j (g/cm²; including neutron spallation, slow muon captures and fast muon processes), $\bar{P}_j$ and $P_j^{\text{sed}}$ are the overall basin-averaged and at the location of sediment deposition cosmogenic production rates (at/g/a), respectively, A is the sediment accumulation rate (cm/a), and t (a) is the time since sediment
<table><caption>**Table 3**

In-situ $^{10}$Be cosmogenic results of samples collected for depth profile analysis of 5 new terraces from the Northern Tianshan.</caption><thead><tr><th>Sample</th><th>Depth (cm)</th><th>Blank series</th><th>Total counts <sup>10</sup>Be</th><th><sup>10</sup>Be/<sup>9</sup>Be<br>(10<sup>-15</sup>)</th><th>Mass of quartz<br>(g)</th><th>Added <sup>9</sup>Be<br>(×10<sup>19</sup>at)</th><th><sup>10</sup>Be<br>(×10<sup>4</sup> at/g)</th></tr></thead><tbody><tr><td colspan="8"><strong>ANJW-T1 (44.25088°N, 85.187222°E, Z = 923 m)</strong></td></tr><tr><td>TS12_ANJW_T1_P0</td><td>-65 ± 5</td><td>20</td><td>418</td><td>38.69 ± 1.95</td><td>2.9</td><td>2.72</td><td>34.3 ± 1.9</td></tr><tr><td>TS12_ANJW_T1_P1</td><td>-105 ± 5</td><td>20</td><td>212</td><td>16.01 ± 1.12</td><td>1.7</td><td>2.74</td><td>22.9 ± 2</td></tr><tr><td>TS12_ANJW_T1_P2</td><td>-140 ± 5</td><td>20</td><td>212</td><td>16.01 ± 1.12</td><td>1.9</td><td>2.74</td><td>21.2 ± 1.8</td></tr><tr><td>TS12_ANJW_T1_P3</td><td>-260 ± 10</td><td>20</td><td>171</td><td>12.05 ± 1.04</td><td>2.5</td><td>2.71</td><td>11.4 ± 1.3</td></tr><tr><td colspan="8"><strong>ANJW-T2 (44.27424°N, 85.16134°E, Z = 850 m)</strong></td></tr><tr><td>TS12_ANJW_T2_P0b</td><td>0</td><td>17</td><td>256</td><td>24.36 ± 1.55</td><td>7.2</td><td>2.72</td><td>8.6 ± 0.6</td></tr><tr><td>TS12_ANJW_T2_P0d</td><td>0</td><td>17</td><td>153</td><td>16.27 ± 1.35</td><td>5.1</td><td>2.73</td><td>7.9 ± 0.8</td></tr><tr><td>TS12_ANJW_T2_P0e</td><td>0</td><td>15</td><td>416</td><td>51.16 ± 2.59</td><td>10.2</td><td>2.74</td><td>13.3 ± 0.7</td></tr><tr><td>TS12_ANJW_T2_P0f</td><td>0</td><td>22</td><td>649</td><td>60.92 ± 2.5</td><td>15.8</td><td>2.73</td><td>10.2 ± 0.4</td></tr><tr><td>TS12_ANJW_T2_P1</td><td>-45 ± 5</td><td>15</td><td>83</td><td>9.49 ± 1.06</td><td>2.4</td><td>2.76</td><td>9 ± 1.4</td></tr><tr><td>TS12_ANJW_T2_P2</td><td>-60 ± 5</td><td>15</td><td>285</td><td>25.55 ± 1.55</td><td>7.0</td><td>2.70</td><td>9.2 ± 0.6</td></tr><tr><td>TS12_ANJW_T2_P3</td><td>-100 ± 5</td><td>15</td><td>119</td><td>10.6 ± 0.98</td><td>2.8</td><td>2.72</td><td>8.8 ± 1.1</td></tr><tr><td>TS12_ANJW_T2_P4</td><td>-155 ± 5</td><td>15</td><td>139</td><td>17.58 ± 1.75</td><td>5.4</td><td>2.69</td><td>8 ± 0.9</td></tr><tr><td>TS12_ANJW_T2_P5</td><td>-270 ± 5</td><td>15</td><td>143</td><td>13.79 ± 1.17</td><td>4.6</td><td>2.71</td><td>7.1 ± 0.8</td></tr><tr><td>TS12_ANJW_T2_P6</td><td>-470 ± 10</td><td>15</td><td>224</td><td>29.66 ± 2.03</td><td>11.9</td><td>2.70</td><td>6.4 ± 0.5</td></tr><tr><td colspan="8"><strong>THX (44.08350°N, 86.343468°E, Z = 857 m)</strong></td></tr><tr><td>TS12_THX_T_P1</td><td>-32.5 ± 7.5</td><td>19</td><td>236</td><td>16.53 ± 1.09</td><td>4.0</td><td>2.73</td><td>10.1 ± 0.8</td></tr><tr><td>TS12_THX_T_P2</td><td>-55 ± 5</td><td>19</td><td>265</td><td>20.68 ± 1.29</td><td>7.2</td><td>2.72</td><td>7.2 ± 0.5</td></tr><tr><td>TS12_THX_T_P3</td><td>-105 ± 5</td><td>19</td><td>134</td><td>12.8 ± 1.12</td><td>5.0</td><td>2.72</td><td>6.1 ± 0.7</td></tr><tr><td>TS12_THX_T_P4</td><td>-147.5 ± 2.5</td><td>19</td><td>168</td><td>11.65 ± 0.91</td><td>5.1</td><td>2.72</td><td>5.4 ± 0.6</td></tr><tr><td>TS12_THX_T_P5</td><td>-580 ± 20</td><td>19</td><td>75</td><td>5.82 ± 0.68</td><td>2.2</td><td>2.73</td><td>5.3 ± 1.1</td></tr><tr><td colspan="8"><strong>HTB (44.05363°N, 86.77047°E, Z = 804 m)</strong></td></tr><tr><td>TS12_HTB_T_P1</td><td>-32.5 ± 2.5</td><td>20</td><td>246</td><td>18.22 ± 1.26</td><td>3.4</td><td>2.74</td><td>13.4 ± 1.1</td></tr><tr><td>TS12_HTB_T_P2</td><td>-57.5 ± 2.5</td><td>20</td><td>851</td><td>53.11 ± 1.93</td><td>10.2</td><td>2.74</td><td>13.9 ± 0.5</td></tr><tr><td>TS12_HTB_T_P3</td><td>-72.5 ± 2.5</td><td>21</td><td>237</td><td>17.71 ± 1.17</td><td>4.5</td><td>2.74</td><td>9.8 ± 0.8</td></tr><tr><td>TS12_HTB_T_P4</td><td>-137.5 ± 2.5</td><td>21</td><td>191</td><td>12.83 ± 1.03</td><td>4.8</td><td>2.73</td><td>6.4 ± 0.7</td></tr><tr><td>TS12_HTB_T_P5</td><td>-680 ± 10</td><td>21</td><td>89</td><td>6.98 ± 0.77</td><td>2.9</td><td>2.73</td><td>5.1 ± 0.9</td></tr><tr><td colspan="8"><strong>JGH-T2 (44.0998°N, 85.4426°E, Z = 1110 m)</strong></td></tr><tr><td>TS10_JGH_T2_P0a</td><td>0</td><td>CEREGE</td><td>145</td><td>52.64 ± 4.42</td><td>6.9</td><td>13,475.90</td><td>15.3 ± 1.3</td></tr><tr><td>TS10_JGH_T2_P0b</td><td>0</td><td>CEREGE</td><td>306</td><td>127.23 ± 7.45</td><td>3.2</td><td>13,427.72</td><td>81 ± 4.8</td></tr><tr><td>TS10_JGH_T2_P0c</td><td>0</td><td>CEREGE</td><td>40</td><td>9.19 ± 1.46</td><td>2.6</td><td>13,474.56</td><td>5.9 ± 1.2</td></tr><tr><td>TS10_JGH_T2_P0d</td><td>0</td><td>CEREGE</td><td>562</td><td>107.43 ± 4.73</td><td>21.9</td><td>13,438.43</td><td>9.9 ± 0.4</td></tr><tr><td>TS10_JGH_T2_P0e1</td><td>0</td><td>CEREGE</td><td>209</td><td>149.66 ± 10.52</td><td>5.7</td><td>13,400.96</td><td>53.5 ± 3.8</td></tr><tr><td>TS10_JGH_T2_P0e2</td><td>0</td><td>CEREGE</td><td>217</td><td>33 ± 2.28</td><td>10.6</td><td>13,071.75</td><td>5.9 ± 0.4</td></tr><tr><td>TS10_JGH_T2_P0e2</td><td>0</td><td>CEREGE</td><td>369</td><td>49.61 ± 3.17</td><td>6.4</td><td>13,443.78</td><td>15.5 ± 1</td></tr><tr><td>TS10_JGH_T2_P0e4</td><td>0</td><td>CEREGE</td><td>1218</td><td>517.6 ± 16.18</td><td>12.3</td><td>13,429.06</td><td>86.2 ± 2.7</td></tr><tr><td>TS10_JGH_T2_P0e5</td><td>0</td><td>CEREGE</td><td>446</td><td>69.36 ± 3.4</td><td>9.1</td><td>13,411.66</td><td>15.3 ± 0.8</td></tr><tr><td>TS10_JGH_T2_P0e6</td><td>0</td><td>CEREGE</td><td>888</td><td>168.18 ± 6.06</td><td>12.9</td><td>13,427.72</td><td>26.6 ± 1</td></tr><tr><td>TS10_JGH_T2_P0f</td><td>0</td><td>CEREGE</td><td>135</td><td>57.04 ± 4.96</td><td>5.5</td><td>13,458.50</td><td>20.9 ± 1.9</td></tr><tr><td>TS10_JGH_T2_P4</td><td>-400 ± 10</td><td>Mean 5-7</td><td>266</td><td>62.81 ± 3.93</td><td>9.2</td><td>1.36</td><td>11.3 ± 0.5</td></tr><tr><td>TS10_JGH_T2_P3</td><td>-135 ± 10</td><td>CEREGE</td><td>47</td><td>24.21 ± 3.55</td><td>3.7</td><td>13,470.54</td><td>12.4 ± 2</td></tr><tr><td>TS10_JGH_T2_P2</td><td>-87 ± 5</td><td>CEREGE</td><td>64</td><td>31.8 ± 3.99</td><td>5.1</td><td>13,441.10</td><td>12.1 ± 1.6</td></tr><tr><td>TS10_JGH_T2_P1</td><td>-45 ± 5</td><td>CEREGE</td><td>73</td><td>42.33 ± 4.98</td><td>5.1</td><td>13,427.72</td><td>16.5 ± 2</td></tr><tr><td colspan="8"><strong>Blank values</strong></td></tr><tr><td>CEREGE</td><td></td><td></td><td></td><td>3 ± 1.5</td><td></td><td></td><td></td></tr><tr><td>Blank 5</td><td></td><td>14</td><td></td><td>1.8 ± 0.5</td><td></td><td></td><td></td></tr><tr><td>Blank 6</td><td></td><td>15</td><td></td><td>2.5 ± 0.7</td><td></td><td></td><td></td></tr><tr><td>Blank 7</td><td></td><td>15</td><td></td><td>1.7 ± 0.4</td><td></td><td></td><td></td></tr><tr><td>Blank 14</td><td></td><td>15</td><td></td><td>1.7 ± 0.4</td><td></td><td></td><td></td></tr><tr><td>Blank 15</td><td></td><td>10</td><td></td><td>1.0 ± 0.3</td><td></td><td></td><td></td></tr><tr><td>Blank 17</td><td></td><td>19</td><td></td><td>1.6 ± 0.4</td><td></td><td></td><td></td></tr><tr><td>Blank 19</td><td></td><td>14</td><td></td><td>1.4 ± 0.4</td><td></td><td></td><td></td></tr><tr><td>Blank 20</td><td></td><td>20</td><td></td><td>1.8 ± 0.4</td><td></td><td></td><td></td></tr><tr><td>Blank 21</td><td></td><td>15</td><td></td><td>1.5 ± 0.4</td><td></td><td></td><td></td></tr></tbody></table>

deposition.

$N_{\text{recent}}$ represents any cosmogenic nuclide concentration accumulated during recent exposure. For terraces, this is estimated from the inverted depth profiles so that the inherited cosmogenic $^{10}$Be concentration at the time of deposition corresponds to $N_{\text{total}}$ (e.g. Norton et al., 2008). The Jingou He river incision, which exposed the sampled

sections, occurred over the Holocene at a rate sufficiently fast to ensure that the cosmogenic nuclide concentration due to recent exposure in the sampled sediments accounts for <0.5 % of the total measured signal (Puchol et al., 2017). Therefore, in both cases (terraces and the Jingou He section), $N_{\text{recent}}$ is negligible or already accounted for.

$N_{\text{fp}}$ is the cosmogenic concentration accumulated by the sediments
during their transport and final deposition in the foreland. In the Tian-
shan, sediment transport modeling suggests that the modification of the
cosmogenic concentration during transport in the river flood plain
through the folded and thrusted piedmont is negligible when compared
to other sources of uncertainties (Puchol et al., 2017).

The sediment accumulation rate A was introduced into the formula
to account for cosmogenic accumulation during progressive sediment
burial (Charreau et al., 2011; Puchol et al., 2017). This formulation
assumes that sediments are nearly continuously and progressively
buried at a rate equal to the long-term mean deposition rate. However,
the Xiyu formation sediments sampled in the Jingou He section
(Charreau et al., 2009a, 2009b), as well as those analyzed in the fluvial
terraces, were deposited by a coarse fan-shaped braided fluvial system
dominated by powerful braided streams (Charreau et al., 2009a). We
can therefore expect rapid channel migration or avulsion, high sediment
accumulation rates (>0.3–0.5 mm/a; e.g. Charreau et al., 2005, 2006,
2009a, 2009b), and, therefore, rapid sediment burial. Accordingly,
cosmogenic nuclide production during this stage is assumed negligible
similarly to Thompson Jobe et al. (2018).

By these arguments, the previous equation can be simplified to:

$$
N_{\text{total}} = e^{-\lambda t} \sum_{j} \left[ \frac{\bar{P}_j}{\frac{\bar{\rho}_t}{A_j}} \right]
$$

2.4. <sup>10</sup>Be cosmogenic production rates and glacial modeling

We assumed that the basin-averaged production rates at the time of
deposition were similar to modern values. We estimated modern basin-
averaged production rates using the cell-by-cell GIS tool Basinga, which
approximates muogenic production rates at depth using exponential
laws (Charreau et al., 2019) (Supplementary Table A). Latitude- and
elevation-scaling was performed using the Stone (2000) model, a 90-m-
resolution SRTM digital elevation model (DEM), the ERA-40 atmosphere
atlas (Uppala et al., 2005), and the average SLHL <sup>10</sup>Be production rate
computed from the global production rate dataset in CREp (Martin et al.,
2017, and references therein).

Rigorously, assuming steady cosmogenic production rates implies
that the extents of the drainage basins were constant. Basin-averaged
cosmogenic production rates are therefore mainly a function of the
elevation and hypsometry of the basins. Oxygen isotopic analyses of
pedogenic carbonates in Northern Tianshan suggest the elevation of the
drainage basins was steady over the last ~10 Ma (Charreau et al., 2012).
Over the time period considered in this study (1.5–0 Ma), even if some
drainage basin reorganization occurred, the associated changes in
elevation and hypsometry, and, hence, in cosmogenic production rates,
were likely negligible.

Changes in glacial coverage are more problematic. Because glaciers
can shield against cosmic rays, past variations in glacial extent may
impact the paleo-production rates of cosmogenic nuclides. To account
for these variations, we considered two endmember scenarios. In the
first, we assumed that no glaciers were present and computed the basin-
averaged ¹⁰Be production rates accordingly. This scenario yields
maximum production rate estimates (Supplementary Table A) and, for
the same measured concentration, hence, maximum denudation rates.
Conversely, in the second scenario, we calculated basin-averaged pro-
duction rates considering the maximum possible glacial extent during
the Last Glacial Maximum (LGM). This approach yields minimum pro-
duction rate estimates and, again for the same measured concentration,
minimum denudation rates. We relied on a modeling approach to
reconstruct glacial cover in the watersheds using a 2D glacier-flow
model run in Matlab (Blard et al., 2007; Harper and Humphrey,
2003). This model describes the ice extent at equilibrium with the
climate, ice motion is determined using the shallow-ice approximation,
and the surface mass-balance is computed from a positive degree-day
approach including a positive degree-day mass-balance informed with

a paleoclimate fitting the paleo-equilibrium-line altitude (ELA) re-
constructions during the LGM (Blard et al., 2007; Li et al., 2014). Model
inputs are (i) the landscape topography, for which we used a 1400-m-
resolution DEM, and (ii) the local meteorological conditions at
Urumqi. Cooling of 9 °C under constant precipitation was necessary to
reproduce the LGM paleo-ELA reconstructions at ca. 3500 m elevation in
the eastern Tianshan (e.g. Li et al., 2014). For instance, the modern ELA
in the Urumqi valley lies at 4000–4100 m a.s.l. (Xu et al., 2010 and
references therein) and was estimated at ~3500–3600 m during the
LGM based on moraine mapping and dating (Li et al., 2014). In the
western Tianshan, in the Dzungarian Alatau, where Cording et al. (2014)
dated one alluvial terrace, the LGM paleo-ELA was modeled at a lower
elevation of 3200 m, consistent with the lower modern ELA there. One of
the model outputs is glacier thickness (Fig. C in online supplementary
information), which we converted into shielding factors to estimate
subglacial cosmogenic ¹⁰Be production rates. Uncertainties associated to
glacier reconstruction were neglected because they are one order lower
than the differences between the production rates calculated with the
two scenarios. Paleo-denudation rates were normalized to modern rates,
which were estimated based on the modern basin-average production
rates corrected for the modern glacial extent mapped according to the
Global Land Ice Measurements from Space (GLIMS) database (Raup
et al., 2007).

2.5. Sample treatment for cosmogenic $^{10}$Be measurement

Samples collected for our new depth profile analyses (ANJT1,
ANJT2, THX, HTB, and JGH) and along the Jingou He section (HD9–19)
were treated using the same procedure. All samples were processed to
yield pure quartz and extract in situ ¹⁰Be at the Centre de Recherches
Pétrographiques et Géochimiques (CRPG). Samples were first sieved to
isolate the 200–800 µm fraction. The quartz fraction was then enriched
through successive magnetic separations and leaching with a mixture of
4/5 H₂SiF₆ + 1/5 HCl. The isolated quartz fraction then underwent three
partial dissolutions in concentrated HF, removing 30 % of the quartz, to
eliminate atmospheric ¹⁰Be (Brown et al., 1991). The purified quartz
fraction was then spiked with 100 µL of a carrier solution with a ⁹Be
concentration of 3025 ppm (Puchol et al., 2017) before being
completely dissolved in HF. Following subsequent purification in chro-
matographic columns by anion exchange, cation exchange, alkaline
precipitations, and oxidation, the purified beryllium oxides were
analyzed at the French national accelerator mass spectrometer facility
ASTER (CEREGE Laboratory, Aix en Provence, France). ¹⁰Be/⁹Be ratios
measured at ASTER were normalized using the NIST SRM 4325 refer-
ence material (¹⁰Be/⁹Be = (2.79 ± 0.03) × 10⁻¹¹). This standardization
is equivalent to 07KNSTD within rounding errors (Nishiizumi et al.,
2007).

3. Results

3.1. In-situ cosmogenic $^{10}$Be concentrations in the northern Tianshan

The complete raw cosmogenic ¹⁰Be data measured along the Jingou
He section and the new depth profiles are reported in Tables 1 and 3,
respectively. Total analytical ¹⁰Be/⁹Be blank ratios at the CRPG for the
depth profiles ranged between (1.03 ± 0.33) × 10⁻¹⁵ and (2.49 ± 0.73)
× 10⁻¹⁵ with an average of (1.55 ± 0.27) × 10⁻¹⁵, representing on
average ~ 8 % (0.5–24 %) of the measured ¹⁰Be (Table 3). In-situ
cosmogenic ¹⁰Be concentrations (blank corrected) measured along the
depth profiles ranged between (5.1 ± 0.9) × 10⁴ at/g and (34.3 ± 1.9)
× 10⁴ at/g. All depth profiles showed a clear exponential decrease in
¹⁰Be concentration with increasing depth, suggesting a simple deposi-
tion/abandonment history (Fig. 3). The surface samples were more
variable, with values ranging between (5.9 ± 1.2) × 10⁴ at/g and (86.2
± 2.7) × 10⁴ at/g (Table 3). This scattering may suggest a non-
continuous surface exposure, either because of a late disruption by
anthropogenic or biological activity, or because of erosional removal of the finest grains on the terrace. In the samples of Jingou He section, blank ratios at the CRPG averaged (0.8 ± 0.3) × 10⁻¹⁵, representing <2 % of the measured ¹⁰Be (Table 1). The blank corrected ¹⁰Be concentrations ranged between (5.2 ± 0.5) × 10⁴ at/g and (8.1 ± 0.9) × 10⁴ at/g. In average, the measured concentrations decreased with time, consistent with the depositional ages determined by magnetostatigraphy (Charreau et al., 2009a).

## 3.2. Terraces ages and ¹⁰Be paleo-concentrations

All literature ¹⁰Be depth profiles reprocessed herein show a distinct exponential decrease in concentration with increasing depth (see references in Table 2). The inversions of all profiles are thus robust and reliable and can be used to determine both abandonment ages of the terraces and the inherited in situ ¹⁰Be concentrations required to reconstruct paleo-denudation rates. All abandonment ages are reported in Table 2, including the different loess deposition scenarios considered when loess was present over the alluvial surfaces. The oldest terrace (F3_HJF) was abandoned at ~540 ka (Table 2); it is in the Yanqi basin in the western part of the range (Fig. 1) (Huang et al., 2014). The youngest terraces (ANJ1-T1B and ANJW-T1) were dated to 5–4 ka (Table 2) in the Anjihai River region in the northern piedmont of the Tianshan (Fig. 2). Eighteen terraces were abandoned during the period 150–0 ka, providing a dense record of paleo-denudation rates during this period with, on average, a value every 0.5–16 ka. Only four of the analyzed terraces were abandoned between ~700 ka and ~150 ka; because they have larger uncertainties (Table 2), they provide a less robust record during this period.

For terraces covered by loess, the three different scenarios that we considered for the deposition of the wind deposits yielded terrace age

variations averaging 35 % (minimum 5 %, maximum 87 %) (Table 2).

Inherited ¹⁰Be concentrations for each terrace and profile inversion are also reported in Table 2. Inherited concentrations varied between (4.5 ± 0.5) × 10⁴ at/g and (55.0 ± 20.0) × 10⁴ at/g and, fortunately, were not greatly impacted by the choice of the loess deposition scenario: the variation between the scenarios averaged <3 % except for profile BBK3-T3, in which the recent deposition of loess would imply an inherited ¹⁰Be concentration ~ 22 % higher than the other scenario. Paleo-concentrations measured in the Jingou He section and corrected for radioactive decay were homogenous, ranging between (10.3 ± 0.6) × 10⁴ at/g and (13.8 ± 1.5) × 10⁴ at/g.

Fig. 4a shows the time evolution of the ¹⁰Be concentrations measured in ancient sediments normalized by the ¹⁰Be concentrations of their corresponding modern sediments. For simplicity, we consider here only the scenario with loess accumulated at a constant rate atop the abandoned alluvial surfaces after abandonment. The ratios calculated based on the terraces inherited concentration ranged between 0.2 ± 0.3 and 3.0 ± 2.5 with a weighted mean of 0.9 ± 0.1 (MSWD = 4 calculated using online IsoplotR tools; Vermeesch, 2018). In the Jingou He section, the concentration ratios varied between 1.4 ± 0.1 and 1.9 ± 0.2 with a weighted mean of 1.6 ± 0.06 (MSWD = 3.1).

## 3.3. Paleo-denudation rates

The maximum and minimum paleo-denudation rates estimated by considering the above-mentioned glacial cover scenarios are reported in Table 2, alongside the ratios comparing paleo and recent denudation rates in the same basin. Assuming loess accumulated at a constant rate atop the abandoned alluvial surfaces after abandonment, the paleo-denudation rates ranged from 0.05 ± 0.02 mm/a to 0.4 ± 0.9 mm/a without any glacial cover and from 0.03 ± 0.01 mm/a to 0.43 ± 0.9

<figure><img src="image_6.png" /><figcaption>**Fig. 4.** Paleo/modern ¹⁰Be concentration and denudation rate ratios as functions of terrace abandonment ages, assuming that loess was deposited continuously after terrace abandonment. Ratios are compared to climate oscillations, either documented by the geochemical analyses of regional speleothems for the period 700–0 ka (red curve) (Cheng et al., 2016; Wang et al., 2008) or by the oxygen record in deep-sea foraminifera during the Early Pleistocene (black curve) (Zachos et al., 2001). The red line and gray boxes show the mean average of the data and associated uncertainties, respectively.</figcaption></figure>
mm/a when corrected for maximum glacier extent, respectively. Similarly, the denudation ratio between the modern rates derived from cosmogenic $^{10}$Be in modern river sands and paleo-denudation rates uncorrected for ice cover varied between 0.3 ± 0.3 and 4.7 ± 9.6, with a weighted mean average value of 0.9 ± 0.1 (MSWD = 1.1) (Table 2, Fig. 4b). Considering the maximum glacial extent, the ratios varied between 0.1 ± 0.1 and 4.7 ± 9.6, with a weighted mean average of 0.3 ± 0.04 (MSWD = 8) (Table 2, Fig. 4c). The paleo-denudation rates calculated in the Jingou He section varied between 0.22 ± 0.03 mm/a and 0.29 ± 0.02 mm/a (uncorrected for ice cover) and between 0.06 ± 0.01 mm/a and 0.07 ± 0.01 mm/a (corrected for ice cover) between (Table 1); the weighted mean averages of these paleo-denudation rates are 0.060 ± 0.004 mm/a (MSWD = 1.2) and 0.25 ± 0.01 mm/a (MSWD = 1.2), respectively. The respective ratios between paleo- and modern denudation rates varied from 0.9 ± 0.1 to 1.0 ± 0.1 and from 0.20 ± 0.03 to 0.25 ± 0.04 (Table 1), with weighted mean averages of 0.9 ± 0.08 (MSWD = 0.42) and 0.2 ± 0.02 (MSWD = 0.4), respectively.

# 4. Discussion

## 4.1. Timings of terrace formation and abandonment

Terrace formation results from alternating phases of river incision and sediment accumulation. Whether river incises or accumulates sediments is controlled by the ratio between the sediments supply and the river transport capacity. Many factors drive the balance between these two competing processes, but in the Tianshan, climate and tectonics are the main factors (Charreau et al., 2018; Malatesta and Avouac, 2018; Poisson and Avouac, 2004). One may therefore wonder if the different terraces studied in the Tianshan, despite their wide variety of abandonment ages, could have resulted from a particular combination of these factors. Indeed, most analyzed and dated terraces in the Tianshan are strath terraces formed and abandoned mainly during periods of river incision. For instance, Schlunegger et al. (2023) propose terrace are abandoned once sediments reservoir upstream is void after a period of downstream aggradation when the landscape steepness and precipitation rates reached a threshold enabling the release of sediment stored on the hillslopes. Similarly, Malatesta et al. (2018) proposed that sediment aggradation in the Tianshan piedmonts has been driven by greater water discharge at stadial-interstadial transitions, effectively washing out glacial sediment accumulated in the high range. During this period, the sediment fluxes could have been higher than the sediment transport capacity of the river yielding to deposition and aggradation in the piedmont. Then, after the glacial deposits were flushed out, their model suggested that sediment flux decreased below river transport capacity yielding to fluvial incision, and thus terrace abandonment. If the Tianshan terraces formed exclusively in this manner, they would always capture the same geomorphic conditions within the watershed, and would always include a significant portion of glacial sediments lacking cosmogenic $^{10}$Be information on denudation processes and rates. This may result in a sampling bias in our denudation record. Indeed, this scenario is supported by the fact that most $^{10}$Be concentrations calculated in terrace sediments are lower than those measured in modern rivers, consistent with the fact that glacial sediments are depleted in $^{10}$Be (Mariotti et al., 2021) (Fig. 4). However, the overall volume of alluvial Quaternary terraces and alluvial fans stored in the piedmont (Guerit, 2014) is inconsistent with the one produced only by glaciers. A simple mass-balance model shows that the relative volume of glacial sediment required to bias the cosmogenic signal in modern rivers is high (>20 %) and higher than the volume of glacial deposits known and available in the range (Charreau et al., 2023). Moreover, in both Schlunneger's or Malatesta's scenari, Tianshan terraces should have been formed during similar climatic conditions and their abandonment ages should be grouped at particular periods of time. Fig. 5 compares the probability distribution function of all terrace ages considered in this study against the regional speleothem oxygen isotopic record (Cheng

<figure><img src="image_7.png" /><figcaption>**Fig. 5.** Probability density function (PDF) of terrace ages compared to climate oscillations inferred from geochemical analyses of speleothems (red curve) (Cheng et al., 2016; Wang et al., 2008). Black curves are individual PDFs for each terrace; the blue curve represents the sum of all terrace PDFs. The blue, red, and green curves for regional geochemical analyses represent isotopic records from different speleothems (see references). The inset shows an enlarged view of the PDF for the last 200 ka, as well as a comparison of terrace ages vs. mean $\delta^{18}$O values and their associated uncertainties.</figcaption></figure>

et al., 2016; Wang et al., 2008). For homogeneity, we restricted our analyses to terraces dated using cosmogenic $^{10}$Be depth profiles and, to avoid a methodological bias, we disregarded the other numerous terraces dated using other techniques such as luminescence. In Fig. 5, it is apparent that more terraces were abandoned since the end of the LGM, as suggested by Malatesta et al. (2018). However, many other terraces were also abandoned at the middle of glacial stades, and not necessarily during transitional phases. We see no particular link between abandonment ages and climate; there is no obvious correlation with mean $\delta^{18}$O values (Fig. 5; for consistency this graph excludes terraces with age uncertainties exceeding the 100 ka glacial cycle). This suggests that sediments deposited below terrace surfaces captured various climatic conditions and landscape erosional processes without a sampling bias. How the denudation rates recorded by terrace sediments (i.e. the inherited $^{10}$Be cosmogenic concentrations) is forced by climate on the upstream watershed is investigated below.

## 4.2. Impact of climate on paleodenudation rates

Early Quaternary $^{10}$Be paleo-concentrations measured in the Jingou He section are remarkably steady and homogenous despite $\delta^{18}$O variations during the same period in regional speleothems records. This suggests that climate changes poorly impacted denudation during the early Quaternary. Paleo-concentrations in the Jingou He section are, on average, 60 % higher than those in modern river sediments averaged over three different sites where $^{10}$Be concentrations are similar within uncertainties (see Fig. 5 in Charreau et al., 2023). This suggests that the $^{10}$Be signal in river sediments was not impacted by sediment recycling throughout the piedmont. The higher $^{10}$Be concentrations observed in ancient sediments (older than 1.5–0.7 Ma) compared to modern ones more likely resulted from changes to the glacial coverage over the drainage basin. Today, 20 % of the Jingou He basin is covered by ice; however, during the warmer Early Pleistocene, glacial extents were likely more limited on average. For instance, in ancient sediments, assuming no ice cover in a basin restricted to the high range without any contribution from the piedmont, the calculated basin-averaged paleo-denudation rates are very similar to those measured today, with a denudation rate ratio near 1 (Table 1, Fig. 4). These results suggest that denudation rates were steady across the Jingou He basin during the early, and maybe the entire, Quaternary. However, this conclusion
should be taken with caution given the high uncertainties on glacial
cover and its evolution through time, especially during the Early Pleis-
tocene. Moreover, ¹⁰Be concentrations measured across two terraces of
the same river dated to ~13 ka and 66 ka (Table 2) show a 20 % and 40
% variation with respect to modern concentrations, respectively. Simi-
larly, paleo-concentrations calculated in other terraces show larger

variations when compared to modern values (concentration ratio Rc
from 0.6 to 3) (Table 2). The paleo-concentrations we determined for the
terraces deposits are based on a model inversion that includes several
assumptions and parameters that may vary (inherited concentration,
age of abandonment, surface erosion, loess deposition...), and hence
may yield a less accurate approach for determining paleo-

<figure><img src="image_8.png" /></figure>

**Fig. 6.** Mean and instantaneous δ¹⁸O values measured in speleothems compared to paleo/modern ratios of ¹⁰Be concentrations and endmember denudation rates (calculated for the maximum glacial extent during the LGM ice or in the absence of glaciers in the drainage basin). Mean δ¹⁸O values were calculated over the period of time in which the terraces could have been abandoned, according to uncertainties (see Discussion). The “instantaneous” δ¹⁸O values represent the mean isotopic values at the mean abandonment time averaged over a period that preceded the abandonment and corresponds to the characteristic timescale of the denudation rate determined for the same terrace. For instance, if a terrace was abandoned at 100 ± 30 ka and the denudation rate is 0.1 mm/a, the characteristic time is 6000 a (60 cm/0.01 cm/a) and the instantaneous δ¹⁸O value is the mean isotopic value calculated from 106 to 100 ka. For simplicity and visibility, terrace BBK3_T3 was removed from these plots because its ratio uncertainties are significantly larger than those of other terraces, and would otherwise obscure the diagrams.
concentrations, and greater variability in the results. In contrast, in the Jingou He section, ¹⁰Be concentrations were directly measured in sediments and only corrected for their depositional ages. However, inherited ¹⁰Be cosmogenic concentrations are not very sensitive to the parameters used to model the cosmogenic depth profiles. For instance, the way loess is deposited on terraces has little influence on the inherited concentration determined at depth. Similarly, the erosion rate of the alluvial surface has little to no impact on the inversion results.

We may therefore assume that our results for the 700–0 ka period are not methodically biased and reflect true variations of the ¹⁰Be paleo-concentrations. A first important outcome of this new dataset is that denudation has not permanently or persistently accelerated since the MPT. Molnar (2004) hypothesized that denudation rates during the Quaternary should have increased with increasing amplitude of climatic forcing, particularly across the MPT, when the amplitudes of climatic cycles rapidly increased. Nonetheless, in the Tianshan, even if the variability of denudation rates increased, we do not observe any lasting acceleration since the MPT. Within uncertainties, over the period 700–0 ka, paleo-concentrations were similar to modern concentrations (weighted mean ratio of ~0.9), reinforcing the idea that paleo-denudation rates have not accelerated since the MPT. However, the origin of these variations remains to be identified. To investigate how climate and precipitation (Cheng et al., 2016) may have controlled denudation rates during 700–0 ka, we compared the mean and instantaneous δ¹⁸O values measured in speleothems with the concentration ratios between modern and past, as well as the denudation ratios estimated for the absence of glaciers and for the maximum possible glacial extent during the LGM (Fig. 6). The mean δ¹⁸O values are calculated during which the terraces could have been abandoned according to the age uncertainties and assuming a Gaussian distribution; for instance, for a terrace abandoned at 100 ± 30 ka, the mean would be calculated from 70 to 130 ka with a Gaussian distribution centered at 100 ka as for the terrace age. The instantaneous δ¹⁸O value represents the isotopic value at the mean time of abandonment, but calculated over a period corresponding to the characteristic time of denudation; in this case, for a terrace abandoned at 100 ± 30 ka with a basin average denudation rate of 0.1 mm/a, the characteristic time is 6000 a (60 cm/0.01 cm/a; see Von Blanckenburg, 2005 for a more detailed explanation of this calculation) and the instantaneous δ¹⁸O value is the mean isotopic value calculated from 106 to 100 ka. Using this approach, we do not observe any particular correlation, neither between ¹⁰Be concentration ratios and δ¹⁸O, nor between denudation ratios and δ¹⁸O, regardless of how the δ¹⁸O value is calculated (instantaneous or mean). The δ¹⁸O variations in speleothems in central Asia mainly record the hydroclimate variability of the region and are closely coupled with the Asian monsoon (Cheng et al., 2016). Therefore, the lack of correlation observed herein suggests that climate oscillations, and more specifically precipitation changes, have not strongly impacted denudation rates in the central Tianshan during 700–0 ka.

The timescales of the uncertainties on abandonment ages are, on average, much larger than the characteristic timescale of δ¹⁸O variations recorded in caves. Moreover, abandonment ages are also sensitive to the way loess is deposited on terraces and this add a degree of uncertainty and could bias the correlation with δ¹⁸O. The absence of correlation with the mean δ¹⁸O value calculated over the entire age range is therefore not surprising. Moreover, the “instantaneous” δ¹⁸O values assume that terraces were abandoned at the mean ages, whereas, given the uncertainties, a wide range of other possible abandonment ages, and hence instantaneous δ¹⁸O values, should also be considered. Therefore, for each terrace, we randomly drew 200,000 possible ages within the age bounds determined by the cosmogenic depth profile inversion; for each possible age, we calculated the average δ¹⁸O value over the characteristic timescale determined from the denudation rates. For instance, for the terrace abandoned at 100 ± 30 ka, a first draw gives an age of 105 ka and the mean δ¹⁸O value is calculated from 111 to 105 ka. For a second terrace dated at 30 ± 10 ka with denudation rates of 0.2 mm/a, a first

draw gives an age of 25 ka and the mean δ¹⁸O value is calculated from 28 to 25 ka (characteristic time of 3000 a = 60 cm/0.02 cm/a). Then, we linearly correlated those two averaged δ¹⁸O values to the denudation ratios of those terraces. A second draw gives ages of 85 ka and 33 ka, with δ¹⁸O values calculated from 91 to 85 ka and from 36 to 33 ka, respectively. A second correlation coefficient is then calculated for the second draw. We repeated this operation for all terraces together and 200,000 times. Our tests suggest that the optimal number of draws is at least 100,000; above this value, the correlation coefficients did not significantly improve (Fig. 7). Therefore, we ran 200,000 draws to ensure that the best correlation was found while the R² value remained low (~0.3; Fig. 7). This means that, even if we consider the best combination of terrace abandonment ages, the denudation variations poorly correlate to δ¹⁸O variations and hence to variations in climate and precipitation (Fig. 7). In glaciated basins, the cosmogenic ¹⁰Be signal exported by rivers is likely controlled by the interplay between glacier velocity and basin topography (Mariotti et al., 2021). The cosmogenic response to glacial cycles and glacial advance/retreat may therefore be nonlinear and depend on threshold effects. The variations of paleo-denudation rates we observe between 700 and 0 ka may thus belie spatial disparities between drainage basins that may have responded differently to climatic changes in terms of glacial advances/retreats, glacial velocity, etc. Therefore, overall, the paleo-concentrations obtained herein appear to vary randomly. The contrasted response of denudation between the Early Pleistocene (1.6–1 Ma) and since the Middle Pleistocene (700–0 ka) may be due to a change in climate cyclicity after the MPT and/or a general cooling of the climate with a growing influence of glaciers, which, from one basin to the other, reacted differently to climatic changes during the late Quaternary (Mariotti et al., 2021). During the warmer Early Pleistocene, glaciers were smaller, limiting their influence on denudation. However, despite these possible variations and spatial disparities, our results contrast with previous studies in other regions where climatic variations are thought to have modulated denudation rates (Fisher et al., 2023; Mariotti et al., 2021; Marshall et al., 2017). Indeed, because the Tianshan is a very arid and intracontinental region, such previously reported variations may exist, but at lower amplitudes than in other regions closer to oceans.

## 5. Conclusions

Analyses of in situ cosmogenic depth profiles across abandoned alluvial terraces are powerful tools for reconstructing past denudation rates during the Quaternary. When the geological and climatic settings are favorable for the good preservation of original morphological surfaces, many paleo-denudation rates and associated ages can be reconstructed. Our study provides a new dataset of paleo-denudation rates across the central Tianshan during the Quaternary. These data improve our understanding of the potential links between climate and denudation rates in this region: our results suggest a steady denudation during the early Quaternary, but possible variations since at least since 700 ka. However, these variations seem uncorrelated with δ¹⁸O variations and may therefore reflect a nonlinear impact of climate on denudation rates, with strong spatial variations among landscape responses to climate modifications. This discrepancy may indicate a change in climate cyclicity or the growing impact of glaciers as the climate cooled during the Quaternary. However, this conclusion must be taken with caution because the paleo-denudation rates during those two periods were reconstructed using different approaches that may induce a bias in the record. To avoid this bias, late Quaternary paleo-denudation rates should be reconstructed based on high-resolution sampling of sedimentary archives in the same section of a given river, as we have done in the Jingou He section for the early Quaternary.

### CRediT authorship contribution statement

Julien Charreau: Writing – original draft, Supervision,
<figure><img src="image_9.png" /><figcaption>Fig. 7. a. Concentration ratios plotted against the optimal instantaneous δ¹⁸O values measured in speleothems. Ages of terraces were adjusted using a Monte Carlo approach in order to provide the best possible correlation between the instantaneous δ¹⁸O values and the concentration ratio. b. Correlation coefficients R² obtained between the instantaneous δ¹⁸O value and paleo/modern ¹⁰Be concentration ratio for a given number of tested ages.</figcaption></figure>

**Methodology, Investigation, Funding acquisition, Conceptualization.**
**Pierre-Henri Blard:** Writing – review & editing, Methodology, Data curation.
**Dimitri Saint-Carlier:** Writing – review & editing, Methodology, Data curation. **Jérôme Lavé:** Writing – review & editing, Methodology, Data curation. **Etienne Large:** Writing – review & editing, Data curation.
**Catherine Zimmermann:** Data curation. **Stéphane Domínguez:** Writing – review & editing, Data curation.
**Shengli Wang:** Data curation.

## Declaration of competing interest

We do not declare any conflict of interest and certify that all funding and associated organizations have been declared in the acknowledgements.

## Acknowledgments

This study was financed by the French INSU Syster program. We thank one anonymous reviewer and Fritz Schlunegger for their careful reviews which greatly improved our manuscript. This is CRPG contribution n°2862.

## Appendix A. Supplementary data

Supplementary data to this article can be found online at https://doi.org/10.1016/j geomorph.2025.109734.

## Data availability

All data are available in the manuscript as tables.

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