In the present contribution, three main types of periglacial moving landforms are considered, namely rock glaciers, push moraines and high-altitude deep-seated rockslides. In reality, other types of landforms resulting from ground movements can usually be observed in periglacial mountain environments, as is for instance the case of solifluction lobes or debris-covered ice bodies, and may potentially participate to transfer sediments towards the torrential network system. Occurring only at shallow depth (maximally ca. 1 m, e.g., Matsuoka, 2001), solifluction is however expected to have a limited impact in terms of transported volumes. Movements related to debris-covered massive-ice bodies are generally characterized by a dominating vertical component due to ice melt, especially during summer periods (e.g., Bosson and Lambiel, 2016). Even though their content in rock debris can be important, their dynamic renders them weakly efficient in transporting sediments downward (Shroder et al., 2000; Benn et al., 2003). Conversely, rock glaciers, deep-seated rockslides and push moraines represent often important volumes of transported sediment and may contribute to feed torrents with rock debris. Rock glaciers consist of tongue-shaped or lobate landforms composed by a mix of variously sized rock particles, which, under a few meters of nonpermanently frozen rock debris (i.e., the active layer, Williams and Smith, 1989), are cemented by interstitial ice (Barsch, 1992). The deformation of the interstitial ice explains the downslope movement of a rock glacier (i.e., the rock glacier creep; e.g., Haeberli et al., 2006) and concentrates mostly in one main shear horizon (e.g., Arenson et al., 2002; Buchli et al., 2012), in some cases in several of them (e.g., Kummert et al., 2018). Push moraines also consist of frozen sediments moving through permafrost creep (Haeberli, 1985; Delaloye, 2004). They are thus often comparable to rock glaciers in terms of size, surface morphology and internal structure. Push moraines are always found in the periphery of glacier forefields and their movement results mainly from the disturbance caused by a former glacier advance. For that reason, their motion is generally oriented towards the center of the area formerly occupied by the glacier (back-creeping). Finally, deep-seated landsliding masses can often be observed on high mountain hillslopes located in permafrost environments. They generally correspond to large rockslides affecting important volumes and surfaces. Their movement is likely to be related to deep slide planes (up to >100 m) and reach typical velocities of a few centimeters to several tens of centimeters per year. Their internal content is vastly unknown but is probably composed of fractured bedrock with a surface usually composed by an open-work structure of big dislocated boulders, which are being transported downward by the slow motion of the whole landform. Recent studies focusing on their dynamic seem to indicate that their kinematical behaviors share similarities with the ones of rock glaciers, indicating that a part of their total movement may be related to permafrost creep (e.g., Delaloye et al., unpublished data). In addition, studies conducted on low-altitude landslides (e.g., Korup, 2005; Schwab et al., 2008) showed that such types of deep-seated moving landforms may represent significant sediment sources for torrential as well as lowland river basins. For these reasons, it is expected that high-altitude deep-seated rockslides may participate in transferring sediments downwards towards torrents.

The study region is located in the southwest of Switzerland and is entirely comprised in the Valais canton. It encompasses nine lateral valleys (see the names in Fig. 1) generally oriented on a south–north axis, with rivers flowing towards the north into the Rhône River (Fig. 1). The western half of the Entremont valley was excluded from the study region because it is not covered by the slope movement inventory used as input data. The overall study region is about 2000 km2, 54 % located above 2500 m a.s.l., which can be considered the local approximation for the lower limit of discontinuous permafrost (Delaloye and Morand, 1997; Lambiel and Reynard, 2003). Higher altitudes are commonly found in the southern halves of the valleys and are generally characterized by the presence of glaciated areas (typically above 3000 m a.s.l.) and steep rock walls leading upwards to ridges constituting the drainage divides among the valleys. The highest point of the study region is reached at 4634 m a.s.l. at the summit of the Pointe Dufour (Monte Rosa) in the southeastern limit of the Mattertal valley. The flanks of each valley correspond to relatively steep slopes divided into numerous torrential systems linking high-altitude glacial and periglacial areas with the respective bottom of the valleys (Fig. 1). The study area constitutes the common focus of research projects conducted at the Unit of Geography of the University of Fribourg for several years and therefore a large number of data exist, especially concerning the detection and the monitoring of slope instabilities such as rock glaciers, rockslides and push moraines. For instance, ongoing projects using dGNSS (differential Global Navigation Satellite System) or TLS (terrestrial laser scanning) surveys at specific site locations were helpful for the validation of the developed method (Delaloye et al., 2010, 2013; Kummert and Delaloye, 2015, 2018; PERMOS, 2016).

The developed methodology is based on the exploitation of various available datasets: (i) a slope movement inventory, (ii) a DEM and (iii) series of aerial images covering the entire study region.

The first step relies on checking whether a moving landform is connected to a torrential channel in each catchment and interfluve located in the study region. The sedimentary connection between moving landforms and torrents was assessed by evaluating the level of both structural and functional connectivity (Lexartza-Artza and Wainwright, 2009; Messenzehl et al., 2014) from the identification of visual clues on recent aerial images (2010–2012).

Once identified, the approximate sediment transfer that characterizes moving landforms connected to the torrential network can be assessed using a simple approach, based on previous work for instance by Delaloye et al. (unpublished data). This estimation method is based on the hypothesis that the sediment transfer occurs through a constrained transit section, namely the front of the moving landform. If we assume that the position of the front does not change in time, as observed for several cases in the study region (Delaloye et al., unpublished data; Kummert et al., 2018), the annual sediment transfer rate between a moving landform and the torrential network corresponds to the volume of sediment that passes through this transit section each year and can be assessed roughly by multiplying the surface of the transit section by the annual displacement rate of the landform.

Out of 642 delimited catchments (n=323) and interfluves (n=319), the detailed connectivity assessment applied in the study region allowed the identification of 42 catchments and interfluves classified as A or B (6.5 % of the total) and in which at least one moving landform is connected to the torrential network system (Fig. 7). In terms of spatial distribution, 52 % of the inventoried catchments are located in only two of the investigated valleys (Mattertal and Saastal), while 31 % are located in the Mattertal only. The vast majority of these catchments and interfluves develop on west-oriented slopes, probably in relation to the overall orientation of the local geological ensembles, which generally dip to the southeast, favoring the establishment of both gentle southeast-oriented and steep northwest-oriented slopes, the latter favoring direct sediment connectivity. Amongst the 42 catchments, 52 moving landforms have been identified as connected to the torrents (∼8 % of all slope movements detected with InSAR). The large majority are rock glaciers (69 %), followed by deep-seated rockslides (25 %) and push moraines (6 %). The overall number of connected landforms has been reduced by 28 % from the original connectivity assessment by applying the more in-depth analysis of movement flux direction (72 moving landforms before and 52 after). The moving landforms that have been reclassified as unconnected during the second in-depth connectivity assessment were essentially ruled out due to their inadequate flux direction or due to clear topographic buffering (e.g., flat terrain). They consisted for instance of push moraines located close to channels in the outer edges of Little Ice Age (LIA) glacier forefields but back-creeping towards the center of the forefield (Fig. 8). In addition, the spatial extent of some DInSAR polygons was too large, giving the misleading impression that the moving landforms were directly adjacent to the torrential channel while the real moving parts were located at a sufficient distance to be disconnected for instance by the presence of flat areas between them and the channel (Fig. 8). Finally, several deep-seated rockslides were classified as not connected as no clear sediment transit section could be identified and defined. In such a case, the movement usually affected entire hillslopes but no traces of loose sediment transfer could be specifically observed between the rockslides and the torrents.

The estimated sediment transfer rates calculated for each connected landform are mapped in Fig. 7 and can be found in more detail in the Supplement. A relatively wide spectrum of values was obtained, ranging roughly from 6500 m3 yr-1 to almost zero. The majority (71 %) of moving landforms was characterized by moderate transfer rates, typically lower than 500 m3 yr-1, and only nine exceeded 1000 m3 yr-1, with a median sediment transfer rate of 238 m3 yr-1. In terms of landform type, mostly rock glaciers were associated with high sediment transfer rates, with only two rockslides and no push moraines yielding more than 500 m3 yr-1. In general, rock glaciers were characterized by higher flow rates but smaller transit sections than deep-seated rockslides, while push moraines commonly displayed very small transit sections. The spatial distribution shows a strong concentration of moving landforms characterized by high sediment transfer rates in the west-oriented side of the Mattertal. Aside from that specific case, no definite spatial patterns can be observed.

The applied methodology relies strongly on the visual analysis of aerial images and is dependent on the interpretation of the observer. The visual indicators for the connectivity assessment are clearly defined in order to lower the subjectivity but in some cases, the choice between two scores of connectivity can be difficult. To overcome this problem, the determination of the connectivity between moving landforms and torrential channels was performed by two users separately for about half of the study region, i.e., in the valleys of Entremont, Bagnes, Nendaz, Hérémence and Hérens. As the same results have been obtained by both users, we can argue that subjectivity has a limited impact, as long as the users have a certain level of skills and experience with such types of geomorphological analysis. Another option to overcome the subjectivity is the application of automatic approaches to infer connectivity. As mentioned, recent studies proposed semiquantitative methods based mostly on the geomorphometric analysis of DEMs (Cavalli et al., 2013) and numerical modeling of transfer processes (Heckmann and Schwanghart, 2013) to map potential connectivity. These approaches are interesting because they spatially constrain areas where the connection with the main fluvial network is most probable. However, important limitations characterizing these methods can be pointed out and render them unsuitable for our research objectives. For instance, several authors have replicated the methodology developed by Cavalli et al. (2013) and highlighted the indispensability of coupling such automatic approaches with geomorphological analysis based on aerial images and in situ field surveys, as relatively frequent discrepancies between computed connectivity index values and field observations were detected (e.g., Messenzehl et al., 2014; Micheletti and Lane, 2016; Tiranti et al., 2018). In addition, these different approaches for automatically inferring connectivity are generally developed at the catchment scale and aim at representing the spatial variability in sediment connectivity. They are therefore not suited to investigate the very local scale, at which the connection between two morphological units typically is. They may also be time consuming to apply at the regional scale, i.e., for a lot of different catchments at once, because they necessitate relatively important computational power. We therefore argue that, despite the interest of such automatic approaches, the methodology developed here is best adapted to the aims of the study. This methodology relies on the analysis of aerial images, which is in any case needed to complement automatic approaches and has the advantage of being easy to apply at the regional scale.

Estimations of sediment transfer rates were obtained using a simple geometrical approach whose application implies some difficulties and uncertainties. For instance, the transit section is not always easy to identify and delimitate. In some cases, especially for rockslides, there is no clear front between the moving landform and the torrential channel. For these landforms, the delimitation of a transit section is based on very uncertain morphological clues observed in the images (e.g., in Fig. 9). In addition, rockslides are treated here as if their behavior in terms of sediment transfer is comparable to that of rock glaciers. However, conversely to rock glaciers (Kummert et al., 2018; Kummert and Delaloye, 2018), the potential sedimentary connection between high-altitude rockslides and torrents has never been properly observed and measured. Existing studies focusing on landslides located at lower altitudes (not in periglacial environments) seem to indicate that the connectivity between landslides and fluvial systems is highly variable spatially. For instance, Korup (2005) defines five types of coupling interface (i.e., transit section): area, linear, point, indirect and null. In comparison to rock glaciers, rockslides usually affect entire hillslopes and are characterized by a less concentrated sediment flux, featuring spatially variable flow directions. However, compared to lowlands, high-altitude rockslides share attributes with rock glaciers, as for example a high fraction of coarse debris, at least at the surface, and a kinematical behavior that is influenced by permafrost conditions (Delaloye et al., unpublished data). In terms of sediment yield characteristics, high-altitude rockslides are assumed to behave partly as lowland landslides and partly as permafrost creep landforms. However, deep-seated rockslides have been poorly studied and further investigations would be needed in order to better understand their dynamics and their potential sedimentary connection with torrents.

The determination of the surface velocity rates is also subject to uncertainties. First, no accuracy assessment has been carried out concerning the orthoimages and some deformations and lateral deviations may occur and alter the obtained velocity values. In addition, the manual tracking of boulders on the orthoimages only allows the 2-D velocity to be assessed. These values of 2-D velocity are understandably lower than 3-D values but were used anyway for the estimations of sediment transfer rates, arguing that it would certainly avoid overestimations. As future developments, values of 3-D velocity could be obtained combining 2-D values with the general slope angle that can be extracted for instance from the DEM. More advanced feature tracking procedures based on an image correlation algorithm and coupled with pairs of DEMs can also provide 3-D surface velocities but are more time-consuming. For the large majority of cases, both velocities derived from aerial images and from DInSAR yielded very similar results (Supplement). The differences that remain between the two velocity estimation methods are mainly due to small-scale local variations in surface velocity that could be observed in the images but not in the interferograms. The DInSAR-derived velocity class often represents the displacement rate of the whole landform while the value of surface velocity issued from the analysis of orthophotos is determined at the front, where the velocity might be slightly different than for the rest of the landform (e.g., Fig. 5). In addition, classes of velocity derived for DInSAR data may represent slight overestimations as interferograms only cover summer periods and do not account for seasonal changes in velocity rates. For these reasons, velocity values issued for the aerial image analysis were used for the transfer rate estimations, while DInSAR velocity classes were only used as a control. Big differences between values yielded by the two methods were here taken as an indicator of error and led to a reanalysis of the aerial images in order to recalculate velocity values.

In Barboux et al. (2014), the authors mention the possibility of obtaining more detailed classes of deformation rates from the new sets of data used for the update of the inventory (mainly TerraSAR-X, 10 m resolution, half wavelength = 1.55 cm). Such an approach was not applied here but more precise evaluation of velocity rate could theoretically be gained from the available DInSAR interferograms and enhance the confidence over the velocity estimations.

Values of both surface velocities and transit sections contain uncertainties and for these reasons the resulting estimations of sediment transfer rates should be taken as order of magnitudes more than as absolute values. The sediment transfer rates of three rock glaciers present in this inventory, namely Dirru, Gugla and Tsarmine, were calculated from repeated lidar surveys in the frame of previous studies (see Kummert and Delaloye, 2018). Lidar-derived values of annual sediment transfer rates and a comparison with values obtained from the simplified approach used in the present paper are displayed in Fig. 10. The orders of magnitude yielded by these two different studies are similar and indicate that, even if the simplified approach cannot represent temporal variations, it can be used as a good first estimation. Given the aim of the developed methodological framework, such a simplified approach represents a good compromise to quickly obtain reliable orders of magnitude of sediment transfer rates for a relatively large number of landforms. Values of surface velocity used to produce these estimations are however valid for a period spanning from 2007 to 2012 and thus represent a state of activity that may not be representative of current dynamics. Some sites may have encountered a strong destabilization since 2012, or on the contrary, may have slowed down or even deactivated. The inventory thus remains indicative and further investigations would be needed to assess the current sediment transfer activity characterizing identified sites.

One of the objectives of the study was to develop an easily reproducible methodology. The same type of problematic most likely occurs in other alpine regions as well as in other mountain ranges and such connectivity assessments could be of interest in other areas. Therefore, the method relies on relatively simple input data: a high-resolution DEM, high-resolution aerial images and an inventory of periglacial moving landforms. The availability of these three datasets is mandatory for the application of the methodology, but not especially in the same format and quality. For instance, the connectivity assessment can be accomplished with lower-resolution DEM and aerial images. In most cases, the second in-depth connectivity check can be performed via detailed geomorphological mapping and should not necessarily rely on the availability of time series of orthoimages. Finally, the key issue is probably the availability of an initial inventory that can be used to localize the periglacial moving landforms in the study region. The inventory does not have to be inferred from SAR interferometry and can be based for instance on field surveys or interpretation of aerial images and DEMs (e.g., Delaloye et Morand, 1997; Lambiel and Reynard, 2003; Kellerer-Pirklbauer et al., 2012; Sattler et al., 2016; Marcer et al., 2017). Though, in the absence of such an inventory, a preparatory step should be undertaken at least to localize the moving landforms in the chosen perimeter of the study. The second step of the methodology, i.e., the estimation of sediment transfer rates between moving landforms and torrents, could be more difficult to apply in data scarce areas as both high-resolution DEM and surface velocity data are needed.