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The classical equation of closure temperature ( T C ) in thermochronometry ( Dodson, 1973 ), assumed (i) no storage limitation for the accumulating radiogenic product, (ii) a negligible product concentration at the initial temperature of cooling T 0 , and (iii) a negligible product loss at the final (present-day) temperature T P . A subsequent extension ( Ganguly and Tirone, 1999 ) provided a simple correction for systems cooling from an arbitrary T 0 , at which presence of an initial concentration profile may affect final concentrations. Here, we use a combination of analytical and numerical solutions to derive a general expression for the effective closure temperature in (i) systems which cool between arbitrary initial and final temperatures, potentially still suffering from thermal product loss at T P (termed ‘leaky’), and (ii) systems which may contain a physical limit on the maximum amount of product that can be stored (termed ‘saturating’). While all conservative results can be easily reproduced, an extended use of our formulation provides meaningful effective closure temperatures even when the standard calculation schemes fail. For a first-order loss radiometric system governed by K ( T ) = s exp ( − E / R T ) , where E [J mol−1] and s [s−1] are the Arrhenius parameters and R is the gas constant, we find that the effective closure temperature T C ( T 0 , T P ) is given by: T C ( T 0 , T P ) = { 1 T P − R / E τ λ − τ K P ln [ 1 + τ λ − τ K P ( τ K P ) τ λ e − τ K P ( Γ ( τ λ , τ K P ) − Γ ( τ λ , τ K 0 ) ) ] } − 1 where K 0 and K P [s−1] are shorthand for K ( T 0 ) and K ( T P ) , respectively, λ [s−1] the production rate, τ [s] a time constant, and Γ ( a , z ) the upper incomplete gamma function. Under conventional conditions, our solution reduces to Dodsonʼs formula. Although the solution strictly applies only to systems where 1 / T increases linearly with time, it is nevertheless a useful approximation for a broad range of cooling functions in systems where closure occurs close to the systemʼs initial/final thermal boundary conditions. We clarify the use and the meaning of T C ( T 0 , T P ) by drawing a comparison between (i) a hypothetical application of apatite U–Pb dating ( T C ≈ 450 ° C ) on Venus (mean surface temperature of 450 °C, leaky behaviour), and (ii) the recently introduced thermochronometric application of optically stimulated luminescence (OSL) dating on Earth (both leaky and saturating behaviour).

Pietro Sternai : Now at: the Institut desSciences de laTerre d'Orléans - (ISTO), University of Orléans,France. Tel.: 33 631910242. E-mail addresses: pietro.sternai@univ-orleans.fr, pietro.sternai@erdw.ethz.ch; International audience; The present-day topography of the European Alps shows evidence of intense glacial reshaping. However, significant questions regarding Alpine landscape evolution during glaciations still persist. In this study, we focus on the Rhône valley (Swiss Alps), and use a numerical model to estimate patterns and magnitudes of glacial erosion. Comparing modeling results on a reconstructed pre-glacial topography and the present-day landforms, we find that the landscape response to glaciation is more complex than a simple "buzzsaw" mechanism (by which glacial erosion sets the height of mountain ranges) or increase of relief due to localized valley incision. Instead, glacial erosion propagates headward as the landforms evolve from a fluvial to a glacial state, leading to an initial increase of local relief followed by subsequent erosion at high elevations. It has also been proposed that the mid-Pleistocene climatic transition of glacial/interglacial oscillations from periods of 40 kyr (with symmetric shapes) to periods of 100 kyr (with asymmetric shapes) promoted glacial erosion within the Alps. Although this change of climate periodicity may have contributed to enhance glacial erosion, our results suggest that other factors such as an increase in rock uplift and/or progressive climate cooling are required to explain enhanced glacial carving at View the MathML source∼1Ma.

Optically stimulated luminescence (OSL)-thermochronometry has recently been proposed as a tool capable of resolving cooling histories from the top 1–2 km of the Earth's crust. This is beyond the resolution of most low-temperature thermochronometric systems, and it offers a new opportunity to investigate the interactions between climate, tectonics and surface processes over Quaternary timescales. Here we present a multi-OSL-thermochronometer which exploits the different thermal stabilities of different temperature infra-red stimulated luminescence (IRSL) signals from K- and Na-rich K-feldspar extracts, utilising the established multi-elevated-temperature (MET) measurement protocol ( Li and Li , 2011 . Luminescence dating of K-feldspar from sediments : A protocol without anomalous fading correction . Quaternary Geochronology 6 , 468–479 ). The theoretical aspects of multi-OSL-thermochronometry are discussed, prior to validation with an example from the eastern Himalayan syntaxis, one of the most rapidly exhuming settings on Earth. Our results show that multi-OSL-thermochronometry of feldspar is able to resolve rock cooling histories over timescales ≤0.2 Ma and provides much tighter constraint on late-stage cooling histories than single-system OSL-thermochronometry.

Glacial landscapes exhibit both high- and low-relief land surfaces. A comparison of fjord erosion and offshore deposition suggests that glacier erosion created both the dramatic fjords and high-elevation low-relief surfaces in western Scandanavia.

International audience; Some of Earth's greatest relief occurs where glacial processes act on mountain topography1, 2. This dramatic landscape is thought to be an imprint of Pleistocene glaciations3, 4. However, whether the net effect of glacial erosion on mountains is to increase5, 6, 7 or decrease8, 9, 10 relief remains disputed. It has been suggested that in the European Alps, the onset of widespread glaciation since the mid-Pleistocene climate transition11 led to the growth of large, long-lived and strongly erosive alpine glaciers12, 13 that profoundly influenced topography14. Here we use 4He/3He thermochronometry15 and thermal-kinematic models to show that the Rhône Valley in Switzerland deepened by about 1-1.5 km over the past one million years. Our results indicate that while the valley was incised and back-cut, high-altitude areas were preserved from erosion. We find an approximately two-fold increase in both local topographic relief and valley concavity, which occurred around the time of the mid-Pleistocene transition. Our results support the proposed link12, 13, 14 between the onset of efficient glacial erosion in the European Alps and the transition to longer, colder glacial periods at the middle of the Pleistocene epoch.

The study of the neotectonic activity in the Jura Mountains (northwestern most belt of the European Alps) represents a challenge in the application of quantitative geomorphology to extract landscape metrics and discuss potential coupling between tectonic, climatic and lithospheric mechanisms during the evolution of this mountain belt. The Jura Mountains are characterized by a karst calcareous bedrock, slightly affected by Quaternary glaciations, and by moderated uplift rates (

International audience; Optically Stimulated Luminescence (OSL) is a well-established Quaternary dating method, which has recently been adapted to application in low-temperature thermochronometry. The Infra-Red Stimulated Luminescence (IRSL) of feldspar, which so far is the most promising target signal in thermochronometry, is unfortunately prone to anomalous fading. The fading of feldspar IRSL is at times not only challenging to measure, but also laborious to incorporate within luminescence growth models. Quantification of IRSL fading is therefore a crucial step in OSL thermochronometry, raising questions regarding (i) reproducibility and reliability of laboratory measurements of fading, as well as (ii) the applicability of existing fading models to quantitatively predict the level of IRSL field saturation in nature. Here we investigate the natural luminescence signal and anomalous fading of IRSL measured at 50 °C (IRSL50) in 32 bedrock samples collected from a variety of lithologies and exhumation settings (Alaska and Norway). We report a large span of IRSL50 fading rates between samples (g2days ranging from ∼0.5 to ∼45%/decade), which further demonstrates (i) a good reproducibility between two common fading measurement protocols, and (ii) the ability of tunnelling models to predict the level of feldspar IRSL50 field saturation in nature. We observe higher IRSL50 fading in feldspar with increasing Ca content, although other factors cannot be dismissed at present. Finally, our dataset confirms that the applicability of feldspar IRSL50 in OSL thermochronometry is limited to rapidly-exhuming settings or warm subsurface environments.

[1] The late Neogene–Quaternary exhumation history of the European Alps is the subject of controversial findings and interpretations, with several thermochronological studies arguing for long-term steady state exhumation rates, while others have pointed to late Miocene–Pliocene exhumation pulses associated with tectonic and/or climatic changes. Here, we perform inverse thermal-kinematic modeling on dense thermochronological data sets combining apatite fission track (AFT) data from the literature and recently published apatite (U-Th-Sm)/He (AHe) data along the upper Rhone valley (Aar and Aiguilles Rouges massifs, Swiss Alps) in order to derive precise estimates on the denudation and relief history of this region. We then apply forward numerical modeling to interpret cooling paths quantified from apatite 4He/3He thermochronometry, in terms of denudation and relief-development scenarios. Our modeling results highlight the respective benefits of using AFT/AHe thermochronology data and 4He/3He thermochronometry for extracting quantitative denudation and relief information. Modeling results suggest a late Miocene exhumation pulse lasting until ∼8–10 Ma, consistent with recently proposed exhumation histories for other parts of the European Alps, followed by moderate (∼0.3–0.5 km Myr−1) denudation rates during the late Miocene/Pliocene. Both inverse modeling and 4He/3He data reveal that the late stage exhumation of the studied massifs can be explained by a significant increase (∼85–100%) in local topographic relief through efficient glacial valley carving. Modeling results quantitatively constrain Rhone valley carving to 1–1.5 km since ∼1 Ma. We postulate that recent relief development within this part of the Swiss Alps is climatically driven by the onset of major Alpine glaciations at the mid-Pleistocene climate transition.

International audience; We assess the importance of thermochronometric data sampling and modeling strategies for correctly estimating mountain belt exhumation. Thermochronological age-elevation profiles have been widely used to infer orogenic exhumation histories; however, recent studies have shown that this sampling strategy may not be the most pertinent for quantifying both denudation and relief history. Here, we investigate the ability of combining different thermochronology data sampling schemes with numerical modeling to better constrain denudation rates and relief changes. We produce synthetic thermochronology datasets for real Alpine topography under a specific exhumation and relief scenario using the thermal-kinematic model Pecube. We then adopt an inverse approach based on the Neighborhood Algorithm to quantitatively assess the resolution of different thermochronology datasets collected following elevation profiles, long transects and valley bottom sampling. We also test the effect of the modeling approach on denudation and relief predictions, in particular the influence of the topographic grid resolution and of potential constraints on the geothermal gradient. Our results show that sampling along a single elevation profile does not allow to quantitatively constrain both denudation and relief histories. Numerical outputs clearly evidence tradeoffs that limit the capacity of simultaneously resolving denudation rates and relief change. Quantitative predictions are only slightly different when combining elevation profiles along different valleys, but are highly improved when using long transects or valley-bottom samples combined with an elevation profile. The resolution with which relief evolution can be predicted may be increased by a factor of 2 by using spatially distributed datasets. Results of thermal parameter inversions suggest that the geothermal gradient may be better estimated using elevation profiles or long-transect sampling rather than using valley bottom samples. Simulations with different model topography resolutions show that degrading the resolution for computational efficiency may result in a loss of quantitative information on denudation rates and relief history. In summary, we highlight that both thermochronological sampling strategies and the choice of thermal parameters or model topography resolution have a significant influence on predicted denudation and relief histories. Ideally, the sampling strategy should be designed using preliminary modeling of expected denudation and relief histories, and a sensitivity study on assumed thermal parameters and model resolution should be performed when modeling the data. Although our modeling is based on a particular case study of relief evolution in the French western Alps, we believe that these inferences have general relevance for thermochronological studies within mountain belts.

International audience; Heat transfer in the crust Low-temperature thermochronology PECUBE is a three-dimensional thermal-kinematic code capable of solving the heat production-diffusionadvection equation under a temporally varying surface boundary condition. It was initially developed to assess the effects of time-varying surface topography (relief) on low-temperature thermochronological datasets. Thermochronometric ages are predicted by tracking the time-temperature histories of rockparticles ending up at the surface and by combining these with various age-prediction models. In the decade since its inception, the PECUBE code has been under continuous development as its use became wider and addressed different tectonic-geomorphic problems. This paper describes several major recent improvements in the code, including its integration with an inverse-modeling package based on the Neighborhood Algorithm, the incorporation of fault-controlled kinematics, several different ways to address topographic and drainage change through time, the ability to predict subsurface (tunnel or borehole) data, prediction of detrital thermochronology data and a method to compare these with observations, and the coupling with landscape-evolution (or surface-process) models. Each new development is described together with one or several applications, so that the reader and potential user can clearly assess and make use of the capabilities of PECUBE. We end with describing some developments that are currently underway or should take place in the foreseeable future.

International audience; Thermochronologic data collected along age-elevation profiles are commonly interpreted as recording temporally variant but spatially constant exhumation rates. However, thermochronologic age-elevation relationships are known to be perturbed by topographic effects and potential changes in relief, which are neglected in the inherently 1-D interpretation commonly applied. Such data thus potentially record both the denudation and relief history of the sampled region but extracting this information is challenging. In a companion paper, we develop a methodology for rigorously interpreting thermochronologic age-elevation profiles in terms of exhumation rates and relief development through time, and to independently quantify the resolution of these constraints. Here we test this approach using a thermochronological dataset consisting of apatite and zircon fission-track and (U-Th)/He data, collected at La Meije Peak in the Pelvoux-Ecrins massif (French Western Alps). Our data and models suggest a three-phase exhumation history in the Pelvoux-Ecrins massif, including a pulse of rapid exhumation at ˜ 6-5.5 Ma, preceded and followed by more moderate rates of denudation in the order of 0.3-0.4 km Myr‑ 1. This rapid exhumation event appears to occur coevally in other external crystalline massifs in the Alps but is not detected by qualitative inspection of the age-elevation relationships. Both our synthetic results and inversion of the La Meije data strongly suggest that apatite fission-track age-elevation relationships alone cannot resolve both denudation and relief histories independently and that multiple thermochronometers are required. Combining apatite fission-track and (U-Th)/He ages and, particularly, including fission-track-length data greatly improves the resolution of the inferred exhumation histories. Although denudation rates through time and the timing of rate changes are generally well resolved, our data have insufficient resolution to satisfactorily constrain the relief history. Synthetic results reported in the companion paper suggest that the reason for this limitation is that relief increase through valley carving has been insufficient with respect to the regional denudation rates to be unambiguously extracted from the data.

Bedrock gorges incising glacial hanging valleys potentially allow measurements of fluvial bedrock incision in mountainous relief. Using digital elevation models, topographic maps, and field reconnaissance, we identified and characterized 30 tributary hanging valleys incised by gorges near their confluence with trunk streams in the Romanche watershed, French Western Alps. Longitudinal profiles of these tributaries are all convex and have abrupt knickpoints at the upper limit of oversteepened gorge reaches. We reconstructed initial glacial profiles from glacially polished bedrock knobs surrounding the gorges in order to quantify the amount of fluvial incision and knickpoint retreat. From morphometric analyses, we find that mean channel gradients and widths, as well as knickpoint retreat rates, display a drainage area dependence modulated by bedrock lithology. However, there appears to be no relation between horizontal retreat and vertical downwearing of knickpoints. Assuming a postglacial origin of these gorges, our results imply high postglacial fluvial incision (0.5-15 mm yr−1) and knickpoint retreat (1-200 mm yr−1) rates that are, however, consistent with previous estimates. Numerical modeling was used to test the capacity of different fluvial incision models to predict the inferred evolution of the gorges. Results from simple end‐member models suggest transport‐limited behavior of the bedrock gorges. A more sophisticated model including dynamic width adjustment and sediment‐dependent incision rates predicts present‐day channel geometry only if a significant supply of sediment from the gorge sidewalls (∼10 mm yr−1) is triggered by gorge deepening, combined with pronounced inhibition of bedrock incision by sediment transport and deposition.

International audience; The potential tectonic and climatic controls on erosion rates in the European Alps and other mountain belts remain strongly debated. We have quantified denudation rates at catchment scales using in situ produced cosmogenic nuclides (10Be) in stream sediments, sampled at the outlets of twelve variously sized (27-1072 km2) catchments of the Ecrins-Pelvoux massif (French Western Alps), with average elevations ranging from 1700 to 2800 m. Spatially-averaged denudation rates, corrected for potential shielding by Little Ice Age glaciers, vary from 0.27 ± 0.05 to 1.07 ± 0.20 mm/yr on millennial timescales. Our results exhibit a correlation (ρ2 = 0.56) between denudation rate and mean catchment elevation, in the absence of significant correlation with any other morphometric parameters (relief, slope, catchment size, hypsometry, etc). Although such variations in erosion rates have been previously linked to variations in tectonic uplift rate, the relatively small size and tectonic homogeneity of our study area exclude a strongly variable tectonic control. We interpret the increase in erosion rate with elevation as the effect of frost-controlled processes, which are strongly temperature-dependent. We use a one-dimensional heat-flow model driven by high-resolution instrumental temperature records from the study area to correlate the variability in denudation rates with the integral of the absolute temperature gradient within the frost-cracking window (‑ 3 to ‑ 8 °C), a proxy of the frost-cracking intensity, for each catchment. The results imply that the efficiency of frost cracking constitutes a major control on catchment-wide denudation rates in the study area, explaining more than half the measured variability in these rates. Our study shows that present-day denudation of the Ecrins-Pelvoux massif is controlled by a climatically driven factor and suggests that frost-cracking processes impose an important control on the post-glacial topographic evolution of mid-latitude mountain belts.

International audience; We determine to what extent low-temperature thermochronology data, in particular from age-elevation profiles, provide independent and quantitative estimates on denudation rates and relief development. Thermochronological age-elevation profiles have been widely used to infer exhumation histories. However, their interpretation has remained inherently one-dimensional, neglecting potential effects of lateral offsets between samples. Furthermore, the potential effects of transient topography on crustal isotherms and consequently on thermochronological data have not yet been addressed in detail. We investigate this problem with the aim of deriving independent estimates of both denudation rates and relief history from low-temperature thermochronometers, measuring the relative uncertainties on these parameters and finally constraining the timing of potential variations in denudation rate and/or relief development. We adopt a non-linear inversion method combining the three-dimensional thermal-kinematic model Pecube, which predicts thermal histories and thermochronological ages from an input denudation and relief history, with an inversion scheme based on the Neighbourhood Algorithm. We use synthetic data predicted from imposed denudation and relief histories and quantitatively assess the resolution of thermochronological data collected along an age-elevation profile. Our results show that apatite fission-track (AFT) ages alone do not provide sufficient quantitative information to independently constrain denudation and relief histories. Multiple thermochronometers (apatite (U-Th)/He (AHe) ages and/or track-length measurements combined with AFT ages) are generally successful in constraining denudation rates and timing of rate changes, the optimum combination of thermochronometers varying with the input scenario (relief change or varying denudation rates). However, relief changes can only be quantified and precisely constrained from thermochronological age-elevation profiles if the rate of relief growth is at least 2-3 times higher than the background denudation rate. This limited resolution is due to the depth of the closure isotherm (between ˜ 70 and 110 °C) for the AFT and AHe systems, which only partly record topographic change. New thermochronometers (such as 4He/3He or OSL) that are sensitive to lower temperatures may be the key for resolving this issue.

Terra Nova, 22, 18–25, 2010 Abstract We report in-situ produced 10Be data from the Gorge du Diable (French Western Alps) to date and quantify bedrock gorge incision into a glacial hanging valley. We sampled gorge sidewalls and the active channel bed to derive both long-term and present-day incision rates. 10Be ages of sidewall profiles reveal rapid incision through the late Holocene (ca 5 ka) at rates ranging from 6.5 to 13 mm yr−1. Present-day incision rates are significantly lower and vary from 0.5 to 3 mm yr−1 within the gorge. Our data imply either delayed initiation of gorge incision after final ice retreat from internal Alpine valleys at ca 12 ka, or post-glacial surface reburial of the gorge. Our results suggest that fluvial incision rates >1 cm yr−1 into crystalline bedrock may be encountered in transient landscape features induced by glacial-interglacial transitions.