Pierre G Valla
email: pierre.valla@unil.ch

Sally E Lowick

Frédéric Herman

Jean-Daniel Champagnac

Philippe Steer

Benny Guralnik

Exploring IRSL 50 fading variability in bedrock feldspars and implications for OSL thermochronometry

Keywords: luminescence, feldspar IRSL, anomalous fading, OSL thermochronometry

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 (IRSL 50 ) in 32 bedrock samples collected from a variety of lithologies and exhumation settings (Alaska and Norway). We report a large span of IRSL 50 fading rates between samples (g 2days 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 IRSL 50 field saturation in nature. We observe higher IRSL 50 fading in feldspar with increasing Ca content, although other factors cannot be dismissed at present. Finally, our dataset confirms that the applicability of feldspar IRSL 50 in OSL thermochronometry is limited to rapidly-exhuming settings or warm subsurface environments.

Introduction

OSL thermochronometry

Understanding the processes operating at the Earth's surface requires quantitative methods to measure erosion and sedimentation rates. In that context, low-temperature thermochronometric methods (see [START_REF] Reiners | Using thermochronology to understand orogenic erosion[END_REF] for a review) have been increasingly used over the past decades to quantify bedrock cooling histories within the top ~2-8 km of the upper crust, and subsequently to interpret them into exhumation histories (e.g. [START_REF] Braun | Quantitative thermochronology: numerical methods for the interpretation of thermochronological data[END_REF]2012). However, linking long-term exhumation rates (10 5 -10 8 year timescales) to short-term erosion measurements (10 0 -10 3 year timescales) remains challenging, because different spatial scales and processes are involved. An ongoing debate [START_REF] Herman | Plio-Pleistocene increase in erosion rates in mountain belts in response to climate change[END_REF][START_REF] Willenbring | The null hypothesis: globally steady rates of erosion, weathering fluxes and shelf sediment accumulation during Late Cenozoic mountain uplift and glaciation[END_REF], regarding the impact of Quaternary climate and glacial/interglacial oscillations on global-scale erosion rates, highlights the current shortage of quantitative estimates of bedrock erosion and relief evolution over Quaternary to sub-Quaternary timescales (e.g. [START_REF] Herman | Worldwide acceleration of mountain erosion under a cooling climate[END_REF][START_REF] Champagnac | Late-Cenozoic relief evolution under evolving climate: A review[END_REF]. Recent methodological developments of low-temperature thermochronometers, such as 4 He/ 3 He (Shuster and Farley, 2005) and Optically Stimulated Luminescence (OSL) (Guralnik et al., 2015a;[START_REF] King | Multi-OSLthermochronometry of feldspar[END_REF], offer an unprecedented resolution to constrain rock cooling histories within the upper ~1-3 km of the Earth's crust, and thus to potentially reconstruct erosion histories and/or topographic relief changes over sub-Quaternary timescales (e.g. Shuster et al., 2005;[START_REF] Rhodes | Optically stimulated luminescence dating of sediments over the past 200,000 years[END_REF]Valla et al., 2011a;[START_REF] King | Multi-OSLthermochronometry of feldspar[END_REF].

OSL dating (e.g. [START_REF] Aitken | An Introduction to Optical Dating: The Dating of Quaternary Sediments by the Use of Photon-Stimulated Luminescence[END_REF] has recently been adapted for low-temperature thermochronometry by considering the competing effects of filling and emptying of naturallyoccurring electron traps (linked to the OSL signal) in crystal lattices due to environmental radiation and temperature, respectively [START_REF] Herman | Uniform erosion rates and re-lief amplitude during glacial cycles in the Southern Alps of New Zealand, as revealed from OSL-thermochronology[END_REF][START_REF] Li | Determining the cooling age using luminescence-thermochronology[END_REF][START_REF] Guralnik | Effective closure temperature in leaky and/or saturating thermochronometers[END_REF][START_REF] King | Multi-OSLthermochronometry of feldspar[END_REF]. While other "trapped charge dating" methods (e.g. [START_REF] Grün | Trapped charge dating (ESR, TL, OSL)[END_REF] have been proposed and tested, including thermoluminescence (TL; e.g. [START_REF] Prokein | Analysis of thermoluminescent glow peaks in quartz derived from the KTB-drill hole[END_REF][START_REF] Tang | Low temperature thermochronology using thermoluminescence signals from quartz[END_REF] and electron-spin resonance (ESR; [START_REF] Koshchug | Accumulation of structural radiation defects in quartz in cooling systems: Basis for dating[END_REF][START_REF] Grün | A new method for the estimation of cooling and rates using paramagnetic centers in quartz: a case study on the Eldzhurtinskiy Granite, Caucasus[END_REF], the advantage of OSL techniques in thermochronometry lies in their rapid methodological development and expanding use in Quaternary science (see reviews by [START_REF] Wintle | Luminescence dating: where it has been and where it is going[END_REF][START_REF] Rhodes | Optically stimulated luminescence dating of sediments over the past 200,000 years[END_REF]. One major intrinsic limitation in trapped charge dating, common to OSL, ESR and TL alike, is signal saturation (i.e. when all available electron traps become M A N U S C R I P T A C C E P T E D ACCEPTED MANUSCRIPT filled). If the target luminescence signal for dating is close to its saturation limit, only minimum ages may be provided. Consequently, when luminescence is used to decipher rock cooling rates, near-saturation signals can only characterise maximum (upper-bound) rates of cooling and exhumation (e.g. [START_REF] Guralnik | Effective closure temperature in leaky and/or saturating thermochronometers[END_REF]. Fortunately, the first OSL-thermochronometry applications [START_REF] Herman | Uniform erosion rates and re-lief amplitude during glacial cycles in the Southern Alps of New Zealand, as revealed from OSL-thermochronology[END_REF][START_REF] Wu | A feasibility study on the application of luminescence dating for quartz from different rock types as a thermochronometer[END_REF][START_REF] De Sarkar | Rapid denudation of Higher Himalaya during late Pliestocence, evidence from OSL thermochronology[END_REF][START_REF] Wu | Luminescence characteristics of quartz from Hsuchshan Range (Central Taiwan) and the implications as a thermochronometer[END_REF] addressed settings of extremely rapid exhumation (where signal saturation should not be a problem), and quantified bedrock cooling histories below ~100 °C and over sub-Quaternary timescales. Despite the fact that a standard mineral/signal pair was chosen (quartz "fast OSL component"; [START_REF] Wintle | A review of quartz optically stimulated luminescence characteristics and their relevance in single-aliquot regeneration dating protocols[END_REF], the low sensitivity [START_REF] Herman | Uniform erosion rates and re-lief amplitude during glacial cycles in the Southern Alps of New Zealand, as revealed from OSL-thermochronology[END_REF]Jeong and Choi, 2012), anomalous characteristics [START_REF] Li | Comparison of De estimates using the fast component and the medium component of quartz OSL[END_REF][START_REF] Preusser | Quartz as a natural luminescence dosimeter[END_REF], and the ubiquitous lack of the "fast component" in bedrock quartz of different petrology/mineralogy (Guralnik et al., 2015b), appeared to narrow the use of bedrock quartz for OSLthermochronometry, and stimulated the continued search for alternative mineral/signal combinations (Guralnik et al., 2015b).

Infra-Red Stimulated Luminescence (IRSL) from feldspar is advantageous over quartz in several ways (e.g. [START_REF] Huntley | Ubiquity of anomalous fading in K-feldspars and the measurement and correction for it in optical dating[END_REF], with (i) a higher luminescence sensitivity in both sediment and bedrock samples (e.g. [START_REF] King | Towards successful OSL sampling strategies in glacial environments: deciphering the residual OSL signals of quartz and K-feldspar from modern glacial sediments[END_REF], (ii) in general, a higher charge storage capacity (i.e. later saturation) offering a wider dating range (e.g. Buylaert et al., 2012), and (iii) a negligible signal contamination from quartz OSL, if present (e.g. [START_REF] Sohbati | Na-rich feldspar as a luminescence dosimeter in infrared stimulated luminescence (IRSL) dating[END_REF]. Recently, OSL thermochronometry using bedrock Na-feldspar was investigated in a deep continental drillhole (Guralnik et al., 2015a), where IRSL signals measured at 50 °C (hereafter IRSL 50 ) were successfully characterised in the laboratory and translated into environmental palaeotemperatures in the ~40-70 °C range over a ~50 ka timescale (Guralnik et al., 2015a). Moreover, the recently-introduced protocol of multiple elevated temperature post-IR (MET-pIRIR) measurement of feldspar (Li and Li, 2011a,b) conceptually offers access to multiple thermochronometric subsystems within a single mineral, as the different subsignals display higher thermal stabilities with increasing stimulation temperatures (Li and Li, 2011b;[START_REF] King | Multi-OSLthermochronometry of feldspar[END_REF].

Anomalous fading in feldspar IRSL

Although feldspar IRSL appears in many ways preferable to quartz OSL for thermochronometry, one of the drawbacks of feldspar IRSL is its anomalous fading (e.g. [START_REF] Spooner | The anomalous fading of infra-red stimulated luminescence from feldspars[END_REF][START_REF] Huntley | Ubiquity of anomalous fading in K-feldspars and the measurement and correction for it in optical dating[END_REF], an athermal loss of trapped electrons via quantum

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mechanical tunnelling to their nearest recombination centres [START_REF] Visocekas | Tunneling in afterglow, its coexistence and interweaving with thermally stimulated luminescence[END_REF][START_REF] Huntley | An explanation of the power-law decay of luminescence[END_REF].

Since anomalous fading is ubiquitous in feldspar IRSL 50 [START_REF] Huntley | Ubiquity of anomalous fading in K-feldspars and the measurement and correction for it in optical dating[END_REF][START_REF] Huntley | Some observations on tunnelling of trapped electrons in feldspars and their implications for optical dating[END_REF], recent efforts have mainly focused on extracting a more stable feldspar signal using pIRIR protocols (e.g. [START_REF] Thomsen | Laboratory fading rates of various luminescence signals from feldspar-rich sediment extracts[END_REF][START_REF] Rhodes | Optically stimulated luminescence dating of sediments over the past 200,000 years[END_REF]Li and Li, 2011a;Buylaert et al., 2012). Although the latter protocols exhibit a reduced, perhaps even negligible, anomalous fading, it is generally at the expense of a higher thermal stability of the target electron trap (Li and Li, 2011a,b;Guralnik et al., 2015c;[START_REF] King | Multi-OSLthermochronometry of feldspar[END_REF]. This in turn leads to higher residual doses in sediment dating (e.g. [START_REF] Wintle | Luminescence dating: where it has been and where it is going[END_REF], and higher closure temperatures in thermochronometry (e.g. Guralnik et al., 2015c), which may once again limit the benefit of non-fading IRSL signals in low-temperature thermochronometry (e.g. [START_REF] Qin | Estimating rock cooling rates by using multiple luminescence thermochronometers[END_REF].

Moreover, the MET-pIRIR protocol often exhibits progressively lower IRSL sensitivity with increasing stimulation temperature (Li and Li, 2011b;[START_REF] King | Multi-OSLthermochronometry of feldspar[END_REF], which can hinder signal extraction for some bedrock samples with low luminescence sensitivity. Despite the presence of anomalous fading in feldspar IRSL 50 , and in light of recent success in avoiding it via pulsed stimulation at low temperature [START_REF] Tsukamoto | Time-resolved luminescence from feldspars: New insight into fading[END_REF]Jain et al., 2015a), IRSL 50 remains highly relevant for OSL thermochronometric investigations.

Over the years, several protocols have been proposed to quantify the anomalous fading of feldspar over laboratory timescales [START_REF] Huntley | Ubiquity of anomalous fading in K-feldspars and the measurement and correction for it in optical dating[END_REF][START_REF] Auclair | Measurement of anomalous fading for feldspar IRSL using SAR[END_REF] and to correct for fading in the linear dose response range (e.g. [START_REF] Lamothe | A solution to anomalous fading and age shortfalls in optical dating of feldspar minerals[END_REF][START_REF] Huntley | Ubiquity of anomalous fading in K-feldspars and the measurement and correction for it in optical dating[END_REF][START_REF] Lamothe | Towards a prediction of long-term anomalous fading of feldspar IRSL[END_REF]. More recently, [START_REF] Huntley | An explanation of the power-law decay of luminescence[END_REF] formulated a physical description of electron tunnelling that further enabled the application of fading corrections within the entire dose response range [START_REF] Kars | A new approach towards anomalous fading correction for feldspar IRSL dating -tests on samples in field saturation[END_REF][START_REF] Li | Investigations of the dose-dependent anomalous fading rate of feldspar from sediments[END_REF]. In particular, these models allow the prediction of luminescence intensities in "field saturation" [START_REF] Huntley | Some observations on tunnelling of trapped electrons in feldspars and their implications for optical dating[END_REF], in which the natural intensity of feldspar IRSL 50 becomes insensitive to time, and is governed only by the counterbalancing effects of environmental radiation and anomalous fading [START_REF] Kars | A new approach towards anomalous fading correction for feldspar IRSL dating -tests on samples in field saturation[END_REF].

In the present study, we investigate anomalous fading of the IRSL 50 signal in bedrock feldspar, and highlight its key implications for OSL thermochronometry. As described earlier, OSL thermochronometry exploits the thermal dependence of trapped electrons in minerals during their exhumation towards the Earth's surface. Given zero fading, a non-saturated natural IRSL 50 signal in bedrock feldspar should, in theory, reflect the sample's cooling history.

Anomalous fading of the signal would, however, lower the measured IRSL 50 level in a given

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bedrock sample, preventing full saturation of the signal and influencing the determination of a cooling rate (if not accounted for). While the incorporation of the effects of IRSL 50 fading in OSL-thermochronometric interpretation has been demonstrated as important (Guralnik et al., 2015a;[START_REF] King | Multi-OSLthermochronometry of feldspar[END_REF], there is a lack of consensus at present, as to whether laboratory measurements of IRSL fading are reproducible and/or reliable (see [START_REF] Li | Review and assessment of the potential of post-IR IRSL dating methods to circumvent the problem of anomalous fading in feldspar luminescence[END_REF] for a review), and thus whether the use of fading models (and their associated age correction schemes) is appropriate. Moreover, the recent notion that all luminescence processes in feldspars are intrinsically related to fading [START_REF] Jain | Stimulated luminescence emission arising from localized recombination within randomly distributed defects[END_REF]2015b) raises a renewed interest in the fading model of [START_REF] Huntley | An explanation of the power-law decay of luminescence[END_REF] and its later derivatives. More specifically, it raises the need for validation studies, where a laboratory measurement of fading rate can be related to its natural fading rate in nature. To date, only a handful of studies [START_REF] Huntley | Some observations on tunnelling of trapped electrons in feldspars and their implications for optical dating[END_REF][START_REF] Kars | A new approach towards anomalous fading correction for feldspar IRSL dating -tests on samples in field saturation[END_REF]Guralnik et al., 2015a) have quantitatively evaluated the effects of natural versus laboratory fading rates. It is therefore necessary to assess (i) whether anomalous fading of the feldspar IRSL 50 signal can be accurately measured, and (ii) for a given fading rate, whether the field saturation of the IRSL 50 signal can be quantitatively predicted. To this aim, we extracted a wide range of K-and Ca-/Na-feldspars from 32 bedrock samples in different lithologies and exhumation environments, and measured their natural feldspar IRSL 50 intensities alongside the anomalous fading of the laboratory-regenerated signals. A large geochemical dataset, including whole-rock major and trace elements as well as selected feldspar mineralogy, enables us to discuss potential causes for the wide range of IRSL 50 anomalous fading observed. Finally, we use this dataset to test the theoretical ability of tunnelling models [START_REF] Huntley | An explanation of the power-law decay of luminescence[END_REF][START_REF] Kars | A new approach towards anomalous fading correction for feldspar IRSL dating -tests on samples in field saturation[END_REF]Guralnik et al., 2015a,c) to predict IRSL 50 field saturation levels, and to discuss the implications for OSL thermochronometry.

Samples and methods

Sampling strategy and sample preparation

Bedrock samples from old crystalline or metamorphic basements have been collected in different exhumation settings in Norway and Alaska to explore the applicability of feldspar IRSL 50 thermochronometry over a wide range of long-term (i.e. 10 5 -10 8 years) exhumation rates. All sample locations and lithological descriptions are given in Table 1. Eight samples are distributed along the Sognefjord and its vicinity (SOG samples; western Norway) where exhumation rates are ~0.01-0.05 km Ma -1 (e.g. [START_REF] Hendriks | A fission track data compilation for Fennoscandia[END_REF][START_REF] Nielsen | The evolution of western Scandinavian topography: a review of Neogene uplift versus the ICE (isostasy-climate-erosion) hypothesis[END_REF]. The SOG samples were collected at varying elevations, from sea-level towards ~1000-m a.s.l. lowrelief surfaces (e.g. [START_REF] Steer | Bimodal Plio-Quaternary glacial erosion of fjords and low-relief surfaces in Scandinavia[END_REF]. Fifteen samples have been collected in the Granite indicates long-term exhumation rates of 0.1-0.5 km Ma -1 (e.g. [START_REF] Spotila | Long-term glacial erosion of active mountain belts: Example of the Chugach-St. Elias Range[END_REF][START_REF] Berger | Architecture, kinematics, and exhumation of a convergent orogenic wedge: A thermochronological investigation of tectonic-climatic interactions within the central St. Elias Orogen, Alaska[END_REF]. In the Granite Range, our sampling strategy was to collect bedrock samples across elevation profiles [START_REF] Wagner | Fission track tectonics: the tectonic interpretation of fission track apatite ages[END_REF]Valla et al., 2011b). Finally, nine samples have been collected in the Yakutat terrain (YAK samples; southern Alaska), all locations at sea-level along the Disenchantment Bay -Russel Fjord. This area is tectonically active with reported long-term exhumation rates of ~1-3 km Ma -1 (e.g. [START_REF] Mcaleer | Exhumation along the Fairweather Fault, Southeast Alaska, based on Low-Temperature thermochronometry[END_REF][START_REF] Enkelmann | Low-temperature thermochronology of the Yakutat Plate corner, St. Elias Range (Alaska): bridging short-term and long-term deformation[END_REF]. Our sampling strategy thus covers two orders of magnitude of long-term bedrock exhumation rates, from 0.01 km Ma -1 (SOG) up to 1-3 km Ma -1 (YAK). Moreover, we targeted different lithologies (sandstone, gneiss and granite/diorite samples), probing a large diversity in bedrock geochemistry and consequently also in feldspar mineralogy. Finally, we restricted our study to cold environments (mean annual surface temperatures <10 °C, Table 1) to exclude potential luminescence signal loss at surface temperature conditions in tropical to sub-tropical regions [START_REF] Wu | Luminescence characteristics of quartz from Hsuchshan Range (Central Taiwan) and the implications as a thermochronometer[END_REF].

Bedrock samples were prepared under subdued orange light to ensure the extraction of feldspar minerals from the interior of the sample, where the luminescence signal is unaffected by surface bleaching. Initial sample dimensions were at least 10 cm (length/width/thickness) to allow the removal of the light-exposed sample surface (at least 2-3 cm) using a water-cooled diamond saw. The light-safe internal part was then gently hand crushed to 180-212 µm grain size using a mortar and pestle to avoid mineral grinding and potential luminescence resetting via triboluminescence (e.g. [START_REF] Bateman | Investigating the effects of glacial shearing of sediment on luminescence[END_REF]. All 180-212 µm grains were treated with 32% hydrochloric acid to remove potential surface carbonates and with 30% hydrogen peroxide to remove any organic component. After chemical treatment, mineral fractions were rinsed thoroughly with water to remove dust particles. Feldspar and quartz fractions were isolated by density separation using LST Fastfloat (sodium heteropolytungstate). Densities of 2.58 g cm -3 and 2.70 g cm -3 were used in order to isolate potassium-rich feldspars (K-feldspars, <2.58 g cm -3 ) from quartz and other feldspars (2.58-2.70 g cm -3 ), and from remaining heavy minerals (>2.70 g cm -3 ). For SOG samples (except SOG-22) we selected K-feldspars for analysis.

For GRA, YAK and SOG-22 samples, density separation at 2.58 g cm -3 yielded no light fraction, suggesting the dominance of calcium/sodium-plagioclases (Ca-/Na-feldspars), which were thus taken for further analysis. Further mineral purification was deemed unnecessary, as the contribution from quartz to IRSL 50 is negligible [START_REF] Sohbati | Na-rich feldspar as a luminescence dosimeter in infrared stimulated luminescence (IRSL) dating[END_REF] therein). Feldspar extracts were not etched before luminescence measurements [START_REF] Duller | Luminescence chronology of raised marine terraces, south-west North Island[END_REF], and feldspar grains were directly mounted on stainless steel discs to produce large aliquots (4 to 6 mm diameter, ~500-1500 grains per disc).

Luminescence equipment and protocols

All IRSL 50 measurements were made on automated Risø TL/OSL DA-20 readers (Institute of Geological Sciences, University of Bern), each possessing a 90 Sr/ 90 Y beta source (~0.1-0.2 Gy s -1 ) and a heater plate (20-700 °C), with systematic instrumental uncertainties of ~1.5% for single-aliquot measurements [START_REF] Bøtter-Jensen | Review of optically stimulated lumi-nescence (OSL) instrumental developments for retrospective dosimetry[END_REF]. Luminescence stimulation was performed with infrared (870 ±40 nm) light-emitting diodes at 90% power (delivering ∼130 mW cm -2 at the aliquot position); the emitted luminescence signal was detected through a 410nm interference and a 2-mm Schott BG-39 filters by an EMI 9235QA photomultiplier tube. All luminescence protocols described below (adapted from Guralnik, 2015a) are fully detailed in Table 2.

Feldspar natural IRSL 50 signals, and their subsequent laboratory dose-response curves, were measured using the Single-Aliquot Regenerative-dose (SAR) protocol [START_REF] Wallinga | The single-aliquot regenerative-dose (SAR) protocol applied to coarse-grain feldspar[END_REF].

For each sample, at least three individual aliquots were measured using a preheat at 250 °C for 60 s (to empty unstable electron traps), followed by IRSL 50 for 200 s (Table 2). We used laboratory beta irradiation doses from 0 up to ~2800 Gy to fully characterize the dose response curve, a test dose of 44 Gy to monitor sensitivity changes throughout the protocol, and a hightemperature optical wash (IRSL at 290 °C) between measurement cycles [START_REF] Buylaert | Testing the potential of an elevated temperature IRSL signal from K-feldspar[END_REF]. Given the recent interest in and the research into "test dose plateaus" (Yi et al., in press), we believe that a test dose of 44 Gy is readily applicable to obtain equivalent doses in the ~4.4-440 Gy range (cf. Yi et al., in press), and likely even beyond. While small variations in the laboratory saturation level as a function of test dose have also been documented (Yi et al., in press), these effects are demonstrably minor and were hence considered beyond the scope of the present study.

All analysed aliquots fulfilled the standard performance criteria for recuperation (<5%), recycling ratio (<10%) and maximum test dose error (<10%). To test the efficacy of the SAR protocol parameters, a dose recovery experiment was conducted for each sample (Supplementary Table S5). To this end, two to three fresh aliquots per sample were optically bleached using IRSL 50 for 300 s, and were subsequently given a 200-Gy laboratory dose which

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was then treated as an unknown and recovered using the same SAR protocol as the natural doses.

To explore the fading variability of IRSL 50 signals in individual bedrock samples, we conducted fading experiments on two sensitised aliquots from the dose response experiments.

We used two different approaches to measure feldspar IRSL 50 fading (Table 2), namely a SARbased long-shine method (modified from [START_REF] Huntley | Ubiquity of anomalous fading in K-feldspars and the measurement and correction for it in optical dating[END_REF], and a non-SAR shortshine method (modified from [START_REF] Auclair | Measurement of anomalous fading for feldspar IRSL using SAR[END_REF], with the objective to test the agreement between the two protocols. In the long-shine protocol, after a given dose of 200 Gy, the luminescence signal was measured following variable delays, each lasting between 0.3 and 48 hours (Table 2). In the short-shine protocol, a dose of 72 Gy was given only once, and followed by a series of consecutive short-shine (0.1 s) measurements, separated from each other by pauses lasting between 0.1 and 55 hours. To account for signal loss due to the short optical excitation, the delayed short-shine measurements were normalized to an otherwise identical series of prompt (undelayed) measurements, done once before and once after the delayed experiment (Table 2).

Geochemistry and environmental dose rate determination

We obtained the whole-rock geochemistry (major and trace elements) of all 32 samples using inductively-coupled plasma mass spectrometry (Supplementary Tables S2-S3) to measure the dominant radionuclide content used for the environmental dose rate estimate (U, Th and K, Table 1). For a subset of 12 samples (GRA and YAK), we used the X-ray fluorescence (XRF) attachment to the Risø TL/OSL reader [START_REF] Kook | A Risø XRF attachment for major element analysis of aliquots of quartz and feldspar separates[END_REF]Guralnik et al., 2015a) to determine feldspar mineralogical composition (Supplementary Table S4) and infer the internal potassium content (K int , Tables 1 andS4). XRF data confirms that, in GRA and YAK samples, the aliquot mineralogy is dominated by Ca-/Na-feldspars (with up to 50% wt. quartz content), translating to an internal potassium content K int between 0.2 and 4% (Supplementary Table S4). Based on these measurements, we assumed for the other GRA and YAK samples (incl. SOG-22) an averaged K int of 1.9 ±1.4% (Table 1), in agreement with previous estimates reported in the literature for Ca-/Na-feldspars [START_REF] Barré | Luminescence dating of archaeosediments: A comparison of Kfeldspar and plagioclase IRSL ages[END_REF][START_REF] Sohbati | Na-rich feldspar as a luminescence dosimeter in infrared stimulated luminescence (IRSL) dating[END_REF]Guralnik et al., 2015a). For SOG samples (except SOG-22), we used K int of 12.5 ±1% for K-feldspars following standard literature values [START_REF] Huntley | The K content of the K-feldspars being measured in optical dating or in thermoluminescence dating[END_REF][START_REF] Barré | Luminescence dating of archaeosediments: A comparison of Kfeldspar and plagioclase IRSL ages[END_REF].

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For each sample, the whole-rock radionuclide content (U, Th and K) and feldspar K int have been converted into environmental dose rates using the conversion factors of Guérin et al. (2012), beta and gamma attenuation factors of Guérin et al. (2012) and Guérin and Mercier (2012), and alpha attenuation factors of [START_REF] Bell | Alpha dose attenuation in quartz grains for thermoluminescence dating[END_REF] and [START_REF] Brennan | Attenuation of alpha particle track dose for spherical grains[END_REF]. For alpha attenuation, an a-value of 0.15 ±0.05 was used after [START_REF] Balescu | Comparison of TL and IRSL age estimates of feldspar coarse grains from waterlain sediments[END_REF]. The average water content in our bedrock samples was estimated at 2 ±2% (e.g. [START_REF] Aitken | Moisture correction for annual gamma dose[END_REF].

Cosmic dose rate was treated as negligible, being comparable in magnitude to uncertainty on the total environmental dose rate [START_REF] King | Multi-OSLthermochronometry of feldspar[END_REF]. Based on thin-section observations, and because the original grain size has been affected by rock crushing and sieving during feldspar extraction, we used a 180-2500 µm grain size range for SOG and GRA samples and a 180-1000 µm grain size range for YAK samples.

To address the two entangled uncertainties regarding (i) the grain size of the target feldspar, and (ii) the feldspar phase which is actually contributing to the IRSL 50 signal (e.g. [START_REF] Sohbati | Na-rich feldspar as a luminescence dosimeter in infrared stimulated luminescence (IRSL) dating[END_REF], we considered several (2 or 4, Supplementary Table S1) dose rate scenarios following the approach of Guralnik et al. (2015a). Specifically, for all feldspars, we calculated dose rates for two end-member grain sizes (180 and 2500 µm for GRA and SOG, and 180 and 1000 µm for YAK), assuming a homogeneous distribution of internal potassium (K int , Table 1) and IRSL 50 signal contribution from the entire feldspar crystal. For Na-/Ca feldspars (GRA, YAK and SOG-22), we calculated two additional scenarios, in which all the IRSL 50 signal originates only from K-feldspar inclusions (1 and 100 µm, K int ~12.5%) within the Na-/Cafeldspar host crystal (e.g. [START_REF] Sohbati | Na-rich feldspar as a luminescence dosimeter in infrared stimulated luminescence (IRSL) dating[END_REF]. We then averaged these end-member scenarios to obtain representative environmental dose rates, which ranged across more than an order of magnitude between samples, from 0.3 to 9 Gy ka -1 (Table 1). This range, and the associated conservative errors, reflect the variability between K-rich and K-poor feldspar phases, and the averaging across the diverse dose-rate scenarios as listed above (Supplementary Table S1).

Results

Dose response and fading measurements

Dose response and fading measurements are illustrated for four representative GRA, SOG and YAK samples (Figure 1), and are fully documented for all samples in the Supplementary Information (Supplementary Table S6). Analysed aliquots (4-to 6-mm diameter) usually yielded bright signals with typical IRSL 50 decay curves. Laboratory dose-response curves (left panels in Figure 1) have been fitted using the General-Order Kinetics (GOK) growth function 10) in Guralnik et al., 2015c). The characteristic dose (D 0 ), the electron-trapping order (α), as well as the equivalent dose (D e ), are reported in Tables 3 andS5. For each aliquot, we also derived the natural IRSL 50 signal L n /T n (Figure 1) and calculated the natural trap filling level (n/N) nat by multiplying the apparent IRSL 50 intensity relative to its laboratory maximum (open stars in Figure 1) by the predicted number of occupiable traps in the laboratory (Eq. ( 3) in Guralnik et al., 2015a). The majority of best-fit D 0 and α values are well-constrained with typical relative uncertainties of <10% and <4%, respectively (Table 3). Natural trap filling levels (n/N) nat exhibit varying uncertainties (1-70%; clearly anticorrelated with (n/N) nat itself), and cover almost three orders of magnitude (i.e. 0.003-0.85; Table 3), thus offering a robust dataset for evaluating the net effects of environmental radiation, anomalous fading and possibly long-term cooling on the natural IRSL 50 intensity of bedrock feldspar.

M A N U S C R I P T A C C E P T E D ACCEPTED MANUSCRIPT 10 (Eq. (
Fading results obtained using both the long-shine (central panels in Figure 1) and shortshine (right panels in Figure 1) methods are also summarised in Table 3. Two aliquots were measured individually and averaged to calculate sample-specific g-values and standard deviations (g 2days in %/decade; [START_REF] Huntley | Ubiquity of anomalous fading in K-feldspars and the measurement and correction for it in optical dating[END_REF]. Fitting the same datasets using Eq. ( 5) in [START_REF] Kars | A new approach towards anomalous fading correction for feldspar IRSL dating -tests on samples in field saturation[END_REF], we obtained an alternative measure of fading -the nearestneighbouring hole-centre density ρ' as defined in [START_REF] Huntley | An explanation of the power-law decay of luminescence[END_REF] -which we later used in the kinetic model to predict the IRSL 50 field saturation levels (Guralnik et al., 2015a). Inter-aliquot variability is small, confirming the good reproducibility of the fading measurement protocols, with more robust estimates for the long-shine method as explained below (Table 3). Although the short-shine protocol is less time-consuming (approximately half the time), the integrated IRSL 50 signal at each short-shine measurement is considerably lower, and therefore associated with larger uncertainties propagated into the resulting g-value (Table 3 and Figure 1). For feldspars with intermediate to low luminescence sensitivity (roughly one third of our dataset), the short-shine protocol yielded signals with a very low signal-to-background ratio that could not be used to derive meaningful g-values (Table 3). Figure 2 shows that, on average, fading rate estimates are in excellent agreement between the long-and the short-shine protocols. Thus, to further reduce experimental noise, in the subsequent modelling we used averaged g-values (wherever possible) from both protocols. Sample-specific IRSL 50 g 2days values reveal a wide range from ~0.5 to ~45 %/decade (Table 3). K-feldspars from SOG samples exhibit g 2days values between 3 and 11 %/decade, which is typical for K-feldspars from both bedrock and sediment origin [START_REF] Huntley | Ubiquity of anomalous fading in K-feldspars and the measurement and correction for it in optical dating[END_REF][START_REF] Huntley | Some observations on tunnelling of trapped electrons in feldspars and their implications for optical dating[END_REF]. Na-/Ca-feldspars show

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ACCEPTED MANUSCRIPT a higher variability in measured g 2days values between samples (Figures 2 and3), especially for GRA samples (from 0.5 to >45 %/decade).

Predictions of feldspar IRSL 50 field saturation

To evaluate whether fading variability in our dataset is the main controlling factor for the natural IRSL 50 intensities, we first examined the relationship of the laboratory-derived g 2days values with the measured (n/N) nat values (Figure 3). Our results show a clear inverse correlation between g 2days and (n/N) nat values, in agreement with previous observations [START_REF] Huntley | Some observations on tunnelling of trapped electrons in feldspars and their implications for optical dating[END_REF] but over a considerably wider range of fading rates. Even prior to modelling, such an inverse correlation suggests that the measured (n/N) nat in most of our samples is mainly controlled by anomalous fading. Only some YAK samples appear to deviate from the overall trend, with their (n/N) nat values markedly below field saturation (Figure 3). However, the relation in Figure 3 is only qualitative, because this empirical relationship might be influenced not only by sample-specific kinetic parameters, but also by thermal loss (which cannot be accounted for in this figure). In the following section, we test our current dataset against a recently proposed physical model predicting feldspar IRSL 50 field saturation under anomalous fading (Guralnik et al., 2015a, incorporating the tunnelling term of Huntley, 2006, and extending the dose response of [START_REF] Kars | A new approach towards anomalous fading correction for feldspar IRSL dating -tests on samples in field saturation[END_REF] to non-first order).

Athermal IRSL signal loss in feldspars is caused by the quantum mechanical tunnelling of electrons from their traps towards electron holes [START_REF] Huntley | Ubiquity of anomalous fading in K-feldspars and the measurement and correction for it in optical dating[END_REF]). Here we use the physical model of [START_REF] Huntley | An explanation of the power-law decay of luminescence[END_REF] which is based on the assumptions that (i) the tunnelling of electrons is governed by the distance to their nearest recombination centre, and (ii) recombination centres within a feldspar crystal are randomly distributed with a given density. This model [START_REF] Huntley | An explanation of the power-law decay of luminescence[END_REF]) can be used to estimate sample-specific field saturation values (e.g. [START_REF] Kars | A new approach towards anomalous fading correction for feldspar IRSL dating -tests on samples in field saturation[END_REF]Guralnik et al., 2015a;[START_REF] King | Multi-OSLthermochronometry of feldspar[END_REF]. Following Guralnik et al. (2015a), we use a Monte-Carlo approach to numerically predict, on a sample to sample basis, the IRSL 50 trap filling saturation values in nature (n/N) ss (termed "field saturation"). In the simulation (1000 runs per sample), random instances of the kinetic parameters (D 0 and α, Table 3), natural dose rates (Table 1), and ߩ ᇱ (Table 3, averaged wherever possible between the long-and shortshine experiments) are drawn from their normal distributions (as given by their best-fit values).

The modelling results, reported as median (n/N) ss and associated 68% confidence interval, are given in Table 3 and visualised against measured natural trap filling (n/N) nat values in Figure 4.

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Figure 4 highlights the quantitative agreement between predicted (n/N) ss and measured (n/N) nat values, confirming that most of our samples are either in full field saturation, or hardly discernible from it (<15%; Guralnik et al., 2015b). In other words, the natural feldspar IRSL 50 signal in the majority of our samples (n = 25) is controlled by electron tunnelling and does not include a detectable thermal signature of the rock exhumation history. However, more than half (66%) of YAK samples, representing the fastest-exhuming setting, exhibit (n/N) nat values that are considerably (more than 15%) below their predicted (n/N) ss values, suggesting field disequilibrium and thus high likelihood of a thermal signature that can be translated into a cooling history. The thermal signature of two additional samples remains in doubt, requiring further investigation that will either link them to exceptional thermal histories, or dismiss them as outliers (one in each locality).

Dose recovery results

Calculated dose recovery ratios (Supplementary Table S5) were typically within 10% of unity for all but four (GRA-13/-14/-17 and SOG-21) samples. Although imperfect, the 15-20% underestimation in the dose recovery of SOG-21 is within familiar values, even when working with a SOL2 solar simulator (e.g. Buylaert et al., 2012;[START_REF] King | Multi-OSLthermochronometry of feldspar[END_REF], and may relate to an irreversible trapping efficiency change [START_REF] Kars | Are feldspar SAR protocols appropriate for post-IR IRSL dating?[END_REF]. On the other hand, it is hard to blame the considerable dose recovery overestimates in GRA-13/-14/-17 (30 to 65%) on the test dose/given dose ratio (here 18%), which is in the 15-80% trust zone and certainly close to the recently recommended ~30% value (Yi et al., in press). To test whether the observed overestimation is due to a large residual dose, we measured the latter in GRA-13 and GRA-BR after an IRSL 50 bleach for 300 s. Low residuals of ~5-8 Gy correspond to less than 2% of the equivalent doses, and to 2-3% of the recovered dose, and therefore cannot explain the observed overestimations. To test whether the problem lies in a thermal transfer (e.g. [START_REF] Huntley | Optical dating using inclusions within quartz grains[END_REF], we extended the dose recovery experiments further by conducting the IRSL bleach at higher temperatures (100 and 200 °C). Bleaching at higher temperatures did not significantly improve dose recovery in GRA-13/-14/-17, and had no effect on a well-behaving sample (GRA-BR). Overall, unacceptable dose recovery affects only a minor subset (13%) of our dataset and might not necessarily imply that the obtained (n/N) nat values are not reliable (Buylaert et al., 2012). However, such dose recovery over-and underestimations do raise the question of what thermal/optical bleach is most appropriate for resetting the natural IRSL 50 intensity in feldspars that were never previously exposed to light.

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Discussion

IRSL 50 and anomalous fading in bedrock feldspars

Our results confirm that feldspar IRSL 50 signals from bedrock extracts show consistent and reproducible luminescence characteristics using the SAR protocol. This is a clear advantage compared to OSL of bedrock quartz which, apart from a very few cases (e.g. [START_REF] Wu | Luminescence characteristics of quartz from Hsuchshan Range (Central Taiwan) and the implications as a thermochronometer[END_REF], is generally deemed dim and unsuitable (Jeong and Choi, 2012;Guralnik et al., 2015b).

Moreover, the vast majority of our bedrock feldspars (87%, n = 28, Supplementary Table S5) also fulfilled the dose recovery test, which is a fundamental acceptance criterion for luminescence dating. Dose responses were successfully fitted with a General-Order Kinetics model, with a median order of 2.4±0.8, in agreement with Na-feldspars from the KTB borehole (Guralnik et al., 2015a), therefore capturing the non-linearity of the dose response curve in just a single parameter.

Fading measurements exhibit a large variability in bedrock feldspars from ~0.5 to ~45 %/decade, beyond the previously published value range [START_REF] Huntley | Ubiquity of anomalous fading in K-feldspars and the measurement and correction for it in optical dating[END_REF][START_REF] Huntley | Some observations on tunnelling of trapped electrons in feldspars and their implications for optical dating[END_REF]. Moreover, we compared two established fading protocols in sediment dating [START_REF] Huntley | Ubiquity of anomalous fading in K-feldspars and the measurement and correction for it in optical dating[END_REF][START_REF] Auclair | Measurement of anomalous fading for feldspar IRSL using SAR[END_REF] and demonstrated that both are applicable for bedrock feldspars, yielding comparable results between the two methods (Figure 2). Given the considerable experimental differences between the protocols (SAR-based and non-SAR), the agreement of the obtained results is striking. The dependence of the fading rate on the given laboratory dose [START_REF] Huntley | Some observations on tunnelling of trapped electrons in feldspars and their implications for optical dating[END_REF][START_REF] Li | Investigations of the dose-dependent anomalous fading rate of feldspar from sediments[END_REF][START_REF] Kars | IRSL dating of K-feldspars: Modelling natural dose response curves to deal with anomalous fading and trap competition[END_REF] is not evident from our dataset, although the administered laboratory doses (200 and 72 Gy for the long-shine and short-shine protocols, respectively) may be too close to detect any systematic deviation.

In our suite of bedrock feldspars, (n/N) nat values are mostly inversely correlated with laboratory-measured fading rates (Figure 3), qualitatively suggesting field saturation in the majority of samples. Quantitatively, we have demonstrated that field saturation can be successfully predicted across almost three orders of magnitude of IRSL 50 electron trap occupancy (Figure 4), using a recent extension (Guralnik et al., 2015c) of familiar electron tunnelling models [START_REF] Huntley | An explanation of the power-law decay of luminescence[END_REF][START_REF] Kars | A new approach towards anomalous fading correction for feldspar IRSL dating -tests on samples in field saturation[END_REF]. Despite successful prediction of field saturation in both sedimentary feldspars [START_REF] Kars | A new approach towards anomalous fading correction for feldspar IRSL dating -tests on samples in field saturation[END_REF][START_REF] Kars | IRSL dating of K-feldspars: Modelling natural dose response curves to deal with anomalous fading and trap competition[END_REF] and bedrock feldspars (Guralnik et al., 2015a;[START_REF] King | Multi-OSLthermochronometry of feldspar[END_REF], the underlying model(s) and the ability to accurately measure the g-value in the laboratory remains a debateable subject (Li et al., 2014). Here, we exploited the large variability in measured fading rates to provide a quantitative validation of our predictive model over a large range of dose rates, trap occupancies, and fading rates (Figure 4).

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We also used the wide range of observed IRSL 50 fading rates to discuss potential geochemical control, starting with the whole-rock geochemistry (Supplementary Tables S2-3) as a first-order proxy. However, we found no convincing relationship between the whole-rock trace element content (Supplementary Table S3) and feldspar IRSL 50 fading rate. Figure 5A illustrates the lithological variability within our dataset as shown by representative major oxides (SiO 2 and Fe 2 O 3 ), suggesting that, at first order, the fading rate would increase with decreasing SiO 2 content or increasing Fe 2 O 3 (or CaO) content. Felsic lithologies (i.e. >63% wt.

SiO 2 content) all show relatively low feldspar fading rates (less than 10 %/decade) regardless of the feldspar type. However, for intermediate (i.e. 52-63% wt. SiO 2 content) and mafic (i.e. <52% wt. SiO 2 content) lithologies, a large spread in fading rates is observed (Figure 5A). For a representative subset of GRA and YAK feldspar separates, we also performed XRF mineralogical determination (Supplementary Table S4). Figure 5B shows that the feldspar fading rate increases with Ca content, in agreement with previous observations [START_REF] Huntley | Some observations on tunnelling of trapped electrons in feldspars and their implications for optical dating[END_REF][START_REF] Huntley | Tunnelling in plagioclase feldspars[END_REF]. In summary, neither the whole-rock geochemistry, nor the trace elements, seem to be a good proxy for feldspar anomalous fading (although we did not apply multivariate analysis); however, our results show that the feldspar internal chemistry (i.e. Ca content, Figure 5B) may be a first-order proxy for the IRSL 50 fading rate. Further investigations are required to better understand the potential causes of fading rate variability in bedrock feldspars; these include both internal factors (e.g. the origin of the IRSL 50 signal in Ca-/Na-feldspars; e.g. [START_REF] Sohbati | Na-rich feldspar as a luminescence dosimeter in infrared stimulated luminescence (IRSL) dating[END_REF] as well as external drivers, such as the metamorphic grade or terrain age [START_REF] Huntley | Ubiquity of anomalous fading in K-feldspars and the measurement and correction for it in optical dating[END_REF], or weathering processes [START_REF] Parish | The application of sedimentological analysis and luminescence dating to waterlain deposits from archaeological sites[END_REF][START_REF] Huntley | Comment on "Isochron dating of sediments using luminescence of Kfeldspar grains[END_REF].

Implications for OSL thermochronometry

Our extensive bedrock dataset offers an opportunity to discuss the applicability of feldspar IRSL 50 in OSL thermochronometry. First, the variability of the fading rates measured for both K-and Ca-/Na-feldspars is significantly broader than those reported in previous OSL thermochronometric studies (Guralnik et al., 2015a[START_REF] King | Multi-OSLthermochronometry of feldspar[END_REF]. This reinforces the notion that anomalous fading in feldspar should be measured for each sample, as it can strongly affect the natural IRSL 50 signal (Figure 3). Moreover, one further complexity in OSL

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thermochronometry is that a sample's thermal history can be inverted only from the natural trap filling (n/N) nat , and not from the equivalent dose alone (D e ) as in OSL sediment dating. This prevents the application of classical fading correction schemes (e.g. [START_REF] Huntley | Ubiquity of anomalous fading in K-feldspars and the measurement and correction for it in optical dating[END_REF] and requires the quantitative prediction of the field saturation level of the luminescence signal (e.g. [START_REF] Kars | A new approach towards anomalous fading correction for feldspar IRSL dating -tests on samples in field saturation[END_REF][START_REF] Li | Investigations of the dose-dependent anomalous fading rate of feldspar from sediments[END_REF] in order to screen for a potential "thermal signature" in a given sample. For most of our samples, and within a wide range of fading rates, the quantitative agreement of observed field saturation levels of the IRSL 50 signal with numerical results from the standard tunnelling model [START_REF] Huntley | An explanation of the power-law decay of luminescence[END_REF], coupled with a General-Order Kinetics dose response (Guralnik et al., 2015c), confirms the need to include fading measurements in preliminary screening of samples before any thermochronometric applications using feldspar IRSL 50 . This first-step investigation of the feldspar athermal stability would ultimately be combined with the experimental characterisation of each sample's thermal stability (Guralnik et al., 2015a;[START_REF] King | Multi-OSLthermochronometry of feldspar[END_REF], which can vary greatly between K-and Na-/Ca-feldspars (e.g. [START_REF] Tso | Determination of life time of infrared stimulated signals from potassium and sodium feldspars[END_REF][START_REF] Li | Parameters of OSL traps determined with various linear heating rates[END_REF] and thus significantly influence thermochronometric interpretation.

Our sampling strategy, covering a wide range of exhumation rates (from 0.01 to 3 km Ma -1 ), provides further information regarding the range of applicability of feldspar IRSL 50 to OSL thermochronometry in diverse natural settings. All GRA and SOG samples appear in field saturation (Figure 4), with just one outlier per locality (GRA-BR and SOG-17). SOG-17 was a translucent bedrock sample, which may immediately be suspected of suffering optical resetting (in nature and/or during sample preparation), that may have biased the observed luminescence signal to below the predicted field saturation level. GRA-BR is a spatial outlier within the GRA dataset, situated at low-elevation within a very wide and deeply-carved valley. Pending additional experimental confirmation (beyond the scope of this study), its deviation from field saturation could potentially reflect recent accelerated exhumation by efficient glacial processes.

Finally, more than half of the YAK samples exhibit a thermal signature in their measured natural IRSL 50 signal (Table 3 andFigure 4). Samples YAK-17/-18/-50 (all with a "thermal signature") are located along a deeply-carved fjord with very high long-term exhumation rates (2-3 km Ma -1 ; [START_REF] Enkelmann | Low-temperature thermochronology of the Yakutat Plate corner, St. Elias Range (Alaska): bridging short-term and long-term deformation[END_REF]. Interestingly, the field-saturated YAK-09/-13/-15/-19 also belong to this area but are located ~20 km eastwards along another smaller fjord [START_REF] Enkelmann | Low-temperature thermochronology of the Yakutat Plate corner, St. Elias Range (Alaska): bridging short-term and long-term deformation[END_REF]. These spatial differences in IRSL 50 intensities would suggest spatial variations in the late-Quaternary exhumation history of this area that were not detected by higher-temperature thermochronometers [START_REF] Mcaleer | Exhumation along the Fairweather Fault, Southeast Alaska, based on Low-Temperature thermochronometry[END_REF][START_REF] Enkelmann | Low-temperature thermochronology of the Yakutat Plate corner, St. Elias Range (Alaska): bridging short-term and long-term deformation[END_REF] but

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may be evidenced in our dataset. Finally, YAK-03/-07 exhibit exceptionally low natural trap filling levels (Figure 4), which may have been caused by hydrothermal reheating from crustal fluid circulations in a highly-fractured area (Fairweather Fault;[START_REF] Mcaleer | Exhumation along the Fairweather Fault, Southeast Alaska, based on Low-Temperature thermochronometry[END_REF], rather than by extremely rapid bedrock cooling. Further work beyond the scope of the present study will focus on constraining thermal kinetic parameters for these samples to derive their thermal histories.

In summary, our dataset confirms that feldspar IRSL 50 would be applicable only in very rapidly-exhuming settings (>1 km Ma -1 ; e.g. [START_REF] King | Multi-OSLthermochronometry of feldspar[END_REF] or in high-temperature environments such as boreholes or tunnels (>35 °C; Guralnik et al., 2015a). Feldspar anomalous fading, even if correctly accounted for, ultimately reduces the trapped charge capacity in a given crystal because of athermal instability, and thus initiates a faster arrival at field saturation. This might preclude the applicability of feldspar IRSL 50 in OSL thermochronometry. MET-pIRIR protocols (Li and Li, 2011a,b) offer the advantage of multithermochronometric systems in a single mineral [START_REF] Qin | Estimating rock cooling rates by using multiple luminescence thermochronometers[END_REF], with promising outcomes in providing robust constraints on bedrock cooling rates over sub-Quaternary timescales [START_REF] King | Multi-OSLthermochronometry of feldspar[END_REF]. Other feldspar protocols such as thermally-transferred IRSL [START_REF] Reimann | Testing the potential of a transferred IRSL (T-IRSL) feldspar signal for luminescence dating[END_REF] or pulsed IRSL 50 (although the thermal stability of pulsed IRSL 50 remains to be experimentally constrained; [START_REF] Tsukamoto | Time-resolved luminescence from feldspars: New insight into fading[END_REF][START_REF] Roskosch | Luminescence dating of icemarginal deposits in northern Germany: evidence for repeated glaciations during the Middle Pleistocene (MIS 12 to MIS 6)[END_REF]Jain et al., 2015b) may also be interesting to explore for thermochronometric application, providing that these protocols show good luminescence characteristics as well as low thermal stability for bedrock feldspar extracts.

Alternatively, quartz protocols based on thermally-transferred OSL [START_REF] Duller | A review of the thermally transferred optically stimulated luminescence signal from quartz for dating sediments[END_REF], Violet Stimulated Luminescence (VSL, [START_REF] Ankjaergaard | Towards dating quaternary sediments using the quartz violet stimulated luminescence (VSL) signal[END_REF]2015) or (red-)thermoluminescence (TL or red TL, [START_REF] Schmidt | Thermochronometry using red TL of quartz? e Numerical simulation and observations from in-situ drill-hole samples[END_REF][START_REF] Tang | Low temperature thermochronology using thermoluminescence signals from quartz[END_REF] could allow for later saturation and thus a wider dating range in thermochronometry.

Conclusions

We report feldspar IRSL 50 luminescence characteristics, natural signal and anomalous fading for 32 bedrock samples collected from a large variety of lithologies and exhumation settings. Our results show that feldspar IRSL 50 signals from bedrock extracts are bright and reproducible using established protocols in OSL dating. We measured a large variability in IRSL 50 fading rates between samples. Our results show that it is essential to measure anomalous fading and account for it on a sample-to-sample basis for OSL thermochronometry, as it may otherwise obscure any thermochronometric information. Furthermore, we exploited

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the wide range of observed fading rates to demonstrate the ability of electron tunnelling models in quantitatively predicting the feldspar IRSL 50 level in field saturation for rather diverse environmental conditions. While the potential causes for feldspar IRSL 50 fading still require further investigation, our observations point towards a significant influence of Ca content in feldspar on its anomalous fading rate. Finally, our results suggest that the applicability of feldspar IRSL 50 in OSL thermochronometry would be limited to rapidly-exhuming settings (i.e. >1 km Ma -1 ) or warm subsurface environments (i.e. >35 °C). 2 and3 for experimental details and results, respectively. The dose-response curves (left panels) have been obtained following the single aliquot regenerative-dose (SAR) protocol for 3 individual aliquots. The natural luminescence signal (white stars) and each regenerative dose (black circles) are normalised to a given test dose, and used to build the dose-response curve (fitted by the GOK approach, black line and grey envelope; α: electron-trapping order, D 0 : characteristic dose) and to calculate the sample natural luminescence level (L n /T n ) and natural trap filling (n/N) nat (Guralnik et al., 2015a).

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Fading experiments, following the long-shine (central panels) and short-shine (right panels) protocols, were used to derive the sample fading rate (sample-specific g 2days are given by the slope of the black lines normalized to 2 days; [START_REF] Huntley | Ubiquity of anomalous fading in K-feldspars and the measurement and correction for it in optical dating[END_REF]. 3). The symbols represent individual GRA (black circles), YAK (grey squares)

and SOG (open triangles) samples. The dashed line defines the 1:1 relationship. The inset shows a zoom-in to the low-fading rate region (dashed box in main panel). Figure 3. Natural trap filling (n/N) nat and g 2days values (long-shine method, Table 3) for GRA (black circles), YAK (grey squares) and SOG (open triangles) samples. Samples in field saturation define a well-characterised inverse relationship between laboratory-measured fading rates (g 2days ) and the natural trap filling (n/N) nat values over a wide range of fading rates (from ~0.5 to ~45 %/decade). analysed samples plot along the 1:1 relationship (dashed line), validating the approach of Guralnik et al. (2015a) to numerically predict sample field saturation (after [START_REF] Huntley | An explanation of the power-law decay of luminescence[END_REF][START_REF] Kars | A new approach towards anomalous fading correction for feldspar IRSL dating -tests on samples in field saturation[END_REF]. Some samples have (n/N) nat below 0.85(n/N) ss (dotted line), bearing potential thermochronometric information. See text for details and discussion. S2). (B) Feldspar mineralogical compositions for a subset of samples (Ab: albite; An: anorthite; Or: orthoclase; Supplementary Table S4). GRA: circles; YAK: squares; SOG: triangles. Symbols are coloured according to the respective sample's g 2days value (see legend). See text for discussion. Notes. 1 Derived from Worldclim database [START_REF] Hijmans | Very high resolution interpolated climate surfaces for global land areas[END_REF]. 2 Measured on a Perkin Elmer Sciex ELAN 6100/9000 ICP-MS, with an estimated analytical precision of 2.3 (U), 3.4% (Th) and 1.2% (K). See Supplementary Tables S2-S3 for all elements and further details. 3 Measured or estimated as follows: a measured using the Risø XRF attachment [START_REF] Kook | A Risø XRF attachment for major element analysis of aliquots of quartz and feldspar separates[END_REF]); b assumed value for Na/Ca-feldspars (average of the Risø XRF data above) c assumed value for K-feldspars [START_REF] Huntley | The K content of the K-feldspars being measured in optical dating or in thermoluminescence dating[END_REF][START_REF] Barré | Luminescence dating of archaeosediments: A comparison of Kfeldspar and plagioclase IRSL ages[END_REF] 4 For calculation of feldspar dose rates, we used conversion factors of Guérin et al. (2012), water content of 2(±2)%, and negligible cosmic radiation. The reported dose rates cover two (or four) end-member scenarios after Guralnik et al. 2015a (see Table S1). For K-feldspars, two end-member grain sizes were considered (180 and 1000 or 2500 µm); for Na/Cafeldspars, two additional scenarios, in which the entire luminescence signal originates from K-feldspar inclusions (1 or 100 µm) were further included (Table S1). [START_REF] Wallinga | The single-aliquot regenerative-dose (SAR) protocol applied to coarse-grain feldspar[END_REF] were Dx = [0, 22,44,87,175,349,698,1396,2792,0,87] Gy, and the test dose was Dtest = 44 Gy. The first and the penultimate zero-doses (no irradiation) extract the natural dose and signal recuperation, respectively. b The irradiation and test doses of the long-shine fading experiment [START_REF] Huntley | Ubiquity of anomalous fading in K-feldspars and the measurement and correction for it in optical dating[END_REF] were Dfading = 240 Gy and Dtest = 44 Gy, respectively, and the holding times were tx ≈ [1200, 1200, 1200, 136660, 1200, 7970, 1200, 143450, 1200, 1200 1200] s. c The short-shine fading experiment [START_REF] Auclair | Measurement of anomalous fading for feldspar IRSL using SAR[END_REF] consisted of a single irradiation dose Dfading = 72 Gy which was given, followed by delay times of tx ≈ 10 2.34+0.37x s, where x = [1, 2, ... Notes. Dose response curves (with recycling ratio within 10% of unity) have been fitted using the General-Order Kinetics GOK function (Guralnik et al., 2015a,c), to obtain the characteristic dose D 0 and the kinetic order α (note: a limiting value of α = 4 was adopted for a few datasets which did not exhibit sufficient flattening off of the luminescence signal at high doses). Fading decay curves were fitted (a) following [START_REF] Huntley | Ubiquity of anomalous fading in K-feldspars and the measurement and correction for it in optical dating[END_REF] to obtain the gvalue (normalized to 2 days); (b) following [START_REF] Huntley | An explanation of the power-law decay of luminescence[END_REF] to obtain the density of recombination centres ρ' (reported as log 10 ρ'), assuming an escape frequency factor of 3×10 15 s -1 [START_REF] Huntley | An explanation of the power-law decay of luminescence[END_REF]. Results of the short-shine method were accepted only when there existed two replicates with acceptable signal to noise ratio (luminescence signal ten times higher than background). Natural trap filling (n/N nat ; reported as mean and std. dev.) and predicted field saturation (n/N ss ; reported as median and 68% conf. int.) were derived following Guralnik et al. (2015a), the latter using a Monte-Carlo approach (1000 iterations, each with randomized input of the kinetic parameters and the dose rate; note that wherever possible, an average ρ' between the long-and short-shine experiments was used). Laboratory dose rates vary between 0.099 and 0.207 Gy s -1 for the different instruments used.

  samples; southern Alaska) where low-temperature thermochronometric data

Figure captions Figure 1 .

 captions1 Figure captions Figure 1. IRSL 50 dose-response curves (left panels) and fading experiments (central and right panels) for representative samples GRA-08 (A-B-C), GRA-12 (D-E-F), SOG-06 (G-H-I) and YAK-09 (J-K-L). See Tables2 and 3for experimental details and results, respectively. The

Figure 2 .

 2 Figure 2. Comparison of fading rate measurements (g 2days ) using the short-shine and long-shine methods (Table3). The symbols represent individual GRA (black circles), YAK (grey squares)

Figure 4 .

 4 Figure 4. Predicted field saturation (n/N) ss vs. measured natural trap filling (n/N) nat for GRA (circles), YAK (squares) and SOG (triangles) samples (A: lineal plot; B: logarithmic plot). Symbols are coloured according to the individual sample g 2days values (see legend). Most of

Figure 5 .

 5 Figure 5. Feldspar geochemistry and laboratory-measured fading rate. (A) Whole-rock representative oxides showing the lithological variability between analysed samples (Supplementary TableS2). (B) Feldspar mineralogical compositions for a subset of samples

  , 8]. The test dose was Dtest = 72 Gy. Lx and Tx in both SAR protocols (left and central column) were derived by integrating the first 15 s of the stimulation curve (signal) after subtraction of the last 100 s (background). Lx and Tx of the short-shine experiment (right column) were derived by integrating the entire stimulation period of 0.1 s, after subtraction of a 20 ms background (immediately following the IRSL stimulation). Note: All preheats were done with a linear heating rate of 5 °C s -1 .

Table 1 .

 1 Overview of sample locations, lithology and climate, alongside measured radionuclides and calculated natural dose rate.

	Sample	Latitude/	Elevation	Lithology	Mean Annual	Whole-rock geochemistry 2	Feldspar	Natural dose rate
		Longitude (°N)/(°W)	(m)		Temperature 1 (°C)	U (ppm)	Th (ppm)	K (wt. %)	minimum K int 3 (%)	4 (Gy ka -1 ) D rate
	Granite Range ( southern Alaska)
	GRA-03	60.853/ 141.451	1419	Diorite	-5.8	0.4	1.1	0.79	0.7 a	1.12 (±0.24)
	GRA-04	60.832/141.467	1761	Diorite	-4.5	0.2	0.6	0.82	1.7 a	1.22 (±0.23)
	GRA-05	60.835/141.469	1995	Diorite	-6.3	0.4	1.1	0.86	1.4 a	1.31 (±0.14)
	GRA-06	60.841/141.501	2388	Diorite	-6.8	0.3	0.5	0.76	1.0 a	1.06 (±0.14)
	GRA-08	60.905/141.970	2188	Diorite	-7.3	0.3	0.8	0.97	1.4 a	1.34 (±0.13)
	GRA-09	60.901/141.954	1691	Diorite	-5.7	0.1	0.1	0.50	0.8 a	0.70 (±0.15)
	GRA-10	60.900/141.934	1412	Diorite	-4.2	0.3	1.1	2.02	3.9 a	2.72 (±0.53)
	GRA-11	60.908/141.919	970	Diorite	-3	0.6	1.1	0.81	1.4 a	1.33 (±0.16)
	GRA-12	60.991/142.763	1554	Schist	-2.5	0.3	0.5	1.03	1.9 b	1.46 (±0.22)
	GRA-13	61.003/142.741	1253	Granitoïde	-1.5	1.2	9.4	0.72	1.9 b	2.37 (±0.61)
	GRA-14	60.991/142.782	1979	Granitoïde	-4.2	0.9	1.3	1.09	1.9 b	1.79 (±0.20)
	GRA-17	60.943/142.475	1818	Granitoïde	-6.1	0.3	0.5	0.61	1.9 b	1.11 (±0.35)
	GRA-18	60.957/142.378	1395	Schist	-4.1	0.1	0.3	0.61	1.9 b	1.02 (±0.39)
	GRA-19	61.008/142.362	720	Granitoïde	-1.4	1.6	3.6	0.73	1.9 b	1.95 (±0.39)
	GRA-BR	61.109/142.420	392	Monzogranite	-0.2	1.6	3.9	2.17	4.2 a	3.62 (±0.49)
	Sognefjord (western Norway)
	SOG-02	61.096/-5.681	33	Granitic gneiss	7.4	1.8	10.4	4.18	12.5 c	8.45 (±3.44)
	SOG-06	61.155/-6.461	883	Granitic gneiss	2.4	2.2	8.3	5.13	12.5 c	9.01 (±3.01)
	SOG-10	61.146/-6.542	47	Granitic gneiss	6.5	1.1	10.3	4.76	12.5 c	8.68 (±3.24)
	SOG-17	61.233/-7.593	961	Granodiorite	1.1	0.2	0.2	4.13	12.5 c	7.51 (±3.94)
	SOG-21	61.239/-7.664	10	Anorthosite	3.5	0.7	10.5	5.15	12.5 c	8.87 (±3.10)
	SOG-22	61.263/-7.867	1274	Gabbro	-0.9	0.1	0.8	0.52	1.9 b	1.00 (±0.40)
	SOG-25	61.272/-7.765	48	Anorthosite	4.8	0.6	5.5	5.30	12.5 c	8.65 (±3.19)
	SOG-38	61.151/-6.728	21	Granitic gneiss	7.0	0.4	3.7	5.13	12.5 c	8.40 (±3.34)

Table 2 .

 2 Laboratory protocols for luminescence measurements of feldspar IRSL 50 .

	Dose response	Anomalous fading
	SAR protocol a	SAR protocol, (Long-shine method b )	Short-shine method c
		1. IRSL at 290 °C (200 s)	1. IRSL at 290 °C (200 s)
	1. Give dose Dx	2. Give dose Dfading	2. Give dose Dfading
	2. Preheat (250 °C for 60 s)	3. Preheat (250 °C for 60 s)	3. Preheat (250 °C for 60 s)
		4. Hold at room T °C for tx s	4. Hold at room T °C for tx s
	3. IRSL at 50 °C (200 s) → Lx	5. IRSL at 50 °C (200 s) → Lx	5. IRSL at 50 °C (0.1 s) → Lx
			6. Return to step 4
			7. IRSL at 290 °C (200 s)
	4. Give test dose Dtest	6. Give test dose Dtest	8. Give test dose Dtest
	5. Preheat (250 °C for 60 s)	7. Preheat (250 °C for 60 s)	9. Preheat (250 °C for 60 s)
	6. IRSL at 50 °C (200 s) → Tx	8. IRSL at 50 °C (200 s) → Tx	10. IRSL at 50 °C (0.1 s) → Tx
	7. IRSL at 290 °C (200 s)
	8. Return to step 1	9. Return to step 1	11. Return to step 10
	Protocols adapted from Guralnik et al. (2015a).

a

The irradiation doses of the SAR dose response protocol

Table 3 .

 3 Best-fit parameters and model results for feldspar IRSL 50 .

	Fitted kinetic parameters

Acknowledgments

We thank S. Tsukamoto and S.-H. Li for constructive and helpful reviews, A.S. Murray and M. Jain (Nordic Laboratory for Luminescence dating / DTU Risø) for hosting an early pilot study in 2010, M. Kook for XRF measurements, and G. King and D. Sanderson for fruitful discussions and feedback. P.G.V. acknowledges funding from the SNSF (grant Ambizione PZ00P2_148191) and the ETH-Zürich COFUND. S.E.L. receives funding from the National Cooperative for the Disposal of Radioactive Waste (Nagra). F.H. and B.G. were funded through SNSF grants PP00P2-38956 and 200021-127127. B.G. acknowledges support from the NWO VENI grant 863.15.026. P.S. acknowledges the financial and scientific support from R.S. Huismans, the Statoil Earth System Modelling project and the University of Bergen.

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Appendix A. Supplementary material Supplementary material, including details about the dose rate scenarios (Table S1), full geochemical reports (Tables S2-S4), supplementary experimental results (Table S5) and all sample raw data (Table S6) related to this article can be found on-line at ...