5.1. Methodology: Spectral Analysis Versus Thermo-kinematic Inversion
 Although spectral analysis appears to represent a promising method for the assessment of mean relief evolution over a given period of time, our study highlights some of the difficulties that arise when dealing with natural data. These difficulties concern in particular sampling logistics (the need to obtain closely and regularly spaced data) as well as uncertainties in individual sample ages. For the Dora-Maira transect, relatively high age errors propagate into errors in the estimated gain function that exceed the “inherent” error in the analysis due to non-perfect sampling of the topography. In contrast, the lower age errors for the Pelvoux data resulted in gain estimates for which the resolution is limited by the inherent error. The spacing between samples obviously controls the inherent error, particularly at short wavelengths, resulting in better resolution as this spacing becomes smaller. On the other hand, age errors affect gain values at all wavelengths. This difference between the two transects underscores the necessity of carefully preparing the sampling strategy according to the expected ages and potential precision. Note that the absolute rather than the relative age errors will determine the resolution of the spectral analysis. As older thermochronological ages are usually associated with higher absolute age errors, attention should to be paid to sample quality to ensure optimal constraints on gain estimates. In contrast, as young ages generally are associated with lower absolute errors, the limiting factor to control is the spacing between samples.
 Comparison between results from the spectral analysis and numerical inversion methods (Figure 10) demonstrates consistent estimates of exhumation rate, although the numerical inversions obtain much better precision on these estimates. Both methods also predict rates that are consistent with previous estimates obtained independently along age-elevation profiles in the Pelvoux [van der Beek et al., 2010] and Dora-Maira [Tricart et al., 2007] massifs. The results for relief development are more difficult to compare, due to the large uncertainties on spectral gain estimates. Both methods provide consistent results for the Dora-Maira massif, suggesting moderate increase in relief over the last 18 m.y. For the Pelvoux, in contrast, the numerical inversion suggests significant relief decrease while the spectral analysis does not resolve relief development. This outcome highlights the limited resolving power of “classical” AFT and AHe data to constrain relief development even in these high-relief mountain environments. Using numerical inversions,Valla et al. [2010a]have shown recently that AFT data alone sampled along local age-elevation profiles are insufficient to provide quantitative constraints on the regional exhumation and relief history; multiple thermochronology data (AFT, AHe, track-length data) are required, but even these can provide significant constraints only in optimal circumstances, where the rate of relief change is 2–3 times higher than the background exhumation rate. Moreover, the limited quality of our AHe data set highlights potential difficulties that arise when aiming to apply multiple-thermochronometers strategies. In a follow-up study,Valla et al. [2011a] have shown that data collected along transects, such as presented here, have more potential to independently resolve exhumation rates and relief development, as possibly demonstrated by the higher resolution obtained on the R parameter in this study compared to van der Beek et al. , who used a local age-elevation profile. However,Valla et al. [2011a]also showed that using spatially distributed data collected more or less randomly along valley bottoms, combined with one or more age-elevation profiles, leads to the most accurate and precise predictions, especially when combining AFT, AHe and track-length data.
 From a general point of view, investigating the evolution of relief using thermochronology at the scale of a massif presents inherent difficulties. Both spectral analysis and thermo-kinematic inversions assume spatially uniform rock-uplift rates throughout the massif. From the overall age-elevation relationships for each transect presented in this study (Figure 4) we suspect that, at such a scale, the thermochronological ages are likely to be affected by local factors within each valley and (inferred) rock-uplift rates vary spatially. Thus, application of thermo-kinematic models or spectral analyses would require extracting both the regional and local components of exhumation to provide reliable estimates of relief evolution. This requires detailed study of local factors likely to affect the thermochronological ages and the age-elevation relationship (local tectonics, fluid circulation etc.), which may prove difficult in practice. A more general consequence is that quantification of relief evolution is more likely to be successful in stable contexts where tectonic activity is known to have been insignificant over a long period and where relief change is therefore climatically driven. The second assumption implicit in both techniques is that relief evolution is consistent over the entire massif. The comparison between the deeply carved glacial Susa valley and the other, much less glacially influenced, valleys of the Dora-Maira massif shows that a single massif can present variable relief development. When considering strategies to address relief development, one must therefore assess the scale at which the relief change has occurred. Changes in relief due to glacial valley carving are expected to occur at relatively short wavelengths (5–10 km). Spectral analysis cannot be used at such a local scale since the method explicitly compares short- and long-wavelength age-elevation relationships, based on the assumption that closure isotherms should be conformal to the long-wavelength topography. Similarly, thermo-kinematic models are limited by the closure temperature of the considered system(s): the ability to resolve relief evolution at the valley scale will strongly depend on the ratio between exhumation rate and the expected amplitude of relief change [Valla et al., 2010a].
 Given the logistical challenge of sampling a dense and evenly spaced long transect through a mountain belt (as an example, sampling the two transects presented here took about a month of full-time equivalent work for 1 person – even in these relatively accessible Alpine massifs), a more efficient strategy might be to concentrate on obtaining spatially distributed data, using multiple thermochronometers per sample and prioritizing data quality. Selecting samples based on expected data quality could, however, inherently bias the data set due to limited availability of promising lithologies. Furthermore, the assumption that both exhumation and relief evolution are spatially constant over the massif seems to be difficult to fulfill; therefore, models should be limited to quantification of local relief evolution. Such an approach has recently been applied byValla et al. [2011b, 2012], who used high-resolution4He/3He thermochronometry to derive cooling paths between ∼100°C and surface temperatures on individual samples, and compared cooling paths between samples collected at different elevations along a valley-ridge transect to infer recent relief change in the Swiss Alps.
5.2. Regional Implications
 The spectral analysis and inversion methods support a mean exhumation rate of ∼0.8 km m.y.−1since ∼8 Ma in the Pelvoux massif, whereas data from the Dora-Maira massif are consistent with slower mean exhumation rates of <0.2 km m.y.−1 since ∼18 Ma. This discrepancy between the two massifs fits within the established regional pattern of exhumation rates [Vernon et al., 2008] and is compatible with the Neogene tectonic history of the western Alps, during which the external massifs experienced transpressive to transcurrent deformation, whereas the core of the belt has undergone extension [Selverstone, 2005; Sue et al., 2007].
 Our current analysis only resolves a mean exhumation rate since the Middle Miocene for the Pelvoux massif and therefore does not allow commenting on temporal variations in exhumation rate, in particular a possible transient Late Miocene increase in exhumation rates followed by a decrease during the Pliocene, as recorded in the age-elevation profile studies byvan der Beek et al.  and suggested in other external crystalline massifs (i.e., Argentera [Bigot-Cormier et al., 2006], Mont Blanc [Glotzbach et al., 2008, 2011], Aar [Vernon et al., 2009; Valla et al., 2012]). We note, however, that both the steep AFT age-elevation gradient combined with relatively old ages (leading to a zero-age intercept at >4 km below the valley bottom) and the less steep AHe age-elevation gradient observed in the Vénéon age-elevation profile (Figure 5a) both suggest a decrease in exhumation rates since ∼6 Ma, consistent with the studies cited above.
 The AFT ages from the Dora-Maira transect are consistent with those found in the Susa and Val d'Aosta valleys to the north [Cadoppi et al., 2002; Malusà et al., 2005; Tricart et al., 2007] and confirm the contrast with younger ages found westward within the Viso ophiolites and the “Schistes Lustrés” Complex [Schwartz et al., 2007], which overlie the massif along a contact that has been interpreted as an extensional detachment. However, as previously pointed out by Tricart et al. , the diachronous age pattern is inconsistent with late-stage exhumation of the massif along this western ductile shear zone, suggesting that this structural configuration was emplaced early in the history of the massif, at temperatures well above the AFT closure temperature.
 Although our analysis was not designed to resolve potential temporal variations in exhumation rate, it appears that the data do not require such variations and are consistent with continuous slow denudation of the Dora-Maira massif throughout Neogene-Quaternary times. From the provenance analysis of sediment filling the Ligurian molasse basin to the east,Carrapa showed that incision into the basement nappes of the Dora-Maira massif likely occurred during the last 10 m.y. The late arrival of basement pebbles probably reflects erosion of overlying sedimentary nappes before ∼10 Ma. It appears that erosion through the sedimentary cover and into the crystalline core of the massif was not associated with significant changes in exhumation rate, in contrast to the suggestion that the inferred Pliocene decrease in exhumation rates in the External Crystalline Massifs is due to the erosion level reaching basement [van der Beek et al., 2010; Glotzbach et al., 2011].
 The relief history for the Pelvoux massif remains equivocal. The current data do not support a potential increase in relief associated with glacial valley carving in the massif, as strongly suggested by the geomorphology [Champagnac et al., 2007; van der Beek and Bourbon, 2008] and unambiguously recorded by low-temperature thermochronometers in the Mont-Blanc massif [Glotzbach et al., 2011] and Rhône Valley [Valla et al., 2011b], ∼200 km to the northeast. Although the numerical inversion predicts an apparently well-constrained late-stage decrease in relief that would have taken place in the last 1–1.5 Ma (Figure 9), we hesitate to place much emphasis on this outcome, as it is not confirmed by the spectral analysis. Also, as we modeled the exhumation history using a temporally and spatially constant exhumation rate, the inferred relief decrease could be an artifact; i.e., the model could try to reproduce the steep age-elevation profile by decreasing relief and thus increasing exhumation on mountain peaks with respect to valley bottoms. However, we do not exclude that this late-stage relief decrease is real and could speculate it is associated with large-scale glacial erosion around the Equilibrium Line Altitude (ELA) in a “glacial-buzzsaw” type scenario [cf.Mitchell and Montgomery, 2006; Egholm et al., 2009]. Within the Pelvoux massif, the modal elevation and local slope minima occur between at elevations between the modern ELA and that inferred for the most extensive glaciation [van der Beek and Bourbon, 2008]. These observations suggests that efficient cirque retreat and periglacial processes [Delunel et al., 2010] may have preferentially eroded the topography and limited relief development around the ELA.
 In contrast, our analyses suggest a moderate increase in relief for the Dora Maira massif during Neogene times. We cannot place tight constraints on the timing of relief increase, although the numerical inversions would suggest it occurred during Late Pliocene-Quaternary times (Figure 9) and is thus possibly associated with Quaternary glaciations. The difference in late-stage relief development between the Pelvoux and Dora-Maira massifs could thus be due to different degrees of glaciation; whereas the Dora Maira massif featured individual valley glaciers [Carraro and Giardino, 2004] that would have deepened the valleys without affecting higher-elevation regions, the Pelvoux massif was characterized by a regional ice-dome [van der Beek and Bourbon, 2008; Delunel, 2010] that would have allowed efficient glacial erosion through cirque retreat at higher elevations. Incision of the valleys might have been episodic and limited to extensive glaciations while erosion by cirque glaciers or periglacial processes would have been active even at times of less extensive glaciation.
 The phase estimates from the spectral analysis suggest that in both massifs, relief evolution took place without significant lateral shifts in valley locations, consistent with the inferred pre-Quaternary drainage pattern in the Pelvoux [Montjuvent, 1974, 1978] and with the occurrence of individual valley glaciers in the Dora-Maira massif. This style of relief development contrasts with that inferred for the Coast Mountains of British Columbia (Canada), where similar modeling of thermochronology data sets suggests that glacial erosion strongly modified the map-view valley pattern [Ehlers et al., 2006; Olen et al., 2012].
 As previously pointed out by Valla et al. [2010a], our study reveals that the relatively high closure temperatures of the AFT (and AHe) thermochronological systems only partially record the relief history of Alpine mountain belts, leading to a general under-estimation of relief changes in current thermochronological studies. This apparent problem could be overcome by future application of thermochronological systems that are sensitive to lower temperatures, such as4He/3He [Shuster et al., 2005; Valla et al., 2011b] or OSL [Herman et al., 2010b] thermochronometry.