IGM is a thermo-mechanical 3D glacier evolution model enhanced with physics-informed deep learning using a convolutional neural network emulator (Jouvet and Cordonnier, 2023) of the high-order “Blatter-Pattyn” ice-flow solver (Blatter, 1995). In this study, we build on the results of Leger et al. (2025) and use the exact same IGM model version (2.2.1), spatial resolution (300 m), input parameters, and forcings as used for their ensemble's (n=100) best-scoring simulation, i.e. simulation 37 (see Figs. 1, 6 in Leger et al., 2025). We also run our simulations using the same GPU (Nvidia RTX 4090). In Leger et al. (2025), a perturbed-parameter ensemble of 100 simulations was performed, covering 35–18 ka at 300 m spatial resolution across the European Alps, an order-of-magnitude improvement over previous 1–2 km models (Seguinot et al., 2018; Jouvet et al., 2023). Their model setup (and thus also ours) integrates modules for ice-enthalpy (after Aschwanden et al., 2012), surface mass balance (after Calov and Greve, 2005), isostatic adjustment (after Wickert, 2016), and avalanching for mass re-distribution down steep slopes. The climate forcing was produced by Russo et al. (2024) (also used by Jouvet et al., 2023), who conducted regional downscaling over Europe (2 km resolution) of global Earth-system model outputs using the Weather Research and Forecasting model, providing gridded fields of temperature and precipitation for both the LGM (24 ka) and the pre-industrial era (1850 AD). A glacial index scheme generates continuous climate forcing interpolating these two states using independent local proxy climate data that combines pollen and speleothem records (Fig. 2e in Leger et al., 2025; Luetscher et al., 2015; Duprat-Oualid et al., 2017). Basal sliding is parameterized following a nonlinear Weertman friction condition (e.g. Schoof and Hewitt, 2013) with a sliding coefficient also influenced by enthalpy-driven basal meltwater content and elevation-dependent basal materials' strength, following Bueler and van Pelt (2015) and the Mohr-Coulomb law (Cuffey and Paterson, 2010). For the bed topography, as in Leger et al. (2025)'s simulation 37, we use the digital elevation model from Mey et al. (2016) which includes the removal of (1) present-day glacier thicknesses and lake depths, and (2) reconstructed present-day valley-fill sediment thicknesses in main overdeepenings throughout the Alps. More detailed methods and model descriptions are presented in Leger et al. (2025).

Here, we employ this model setup to run two new simulations featuring the additional coupling of 3D Lagrangian particle tracking. The first simulation is parameterised for subglacial particle seeding whilst the second for supraglacial particle seeding (Fig. 1). We run all simulations between 40 and 18 ka, thus starting 5 kyr earlier than the original setup. While Leger et al. (2025) showed that starting the simulation before 35 ka had no noticeable impact on the modelled AIF geometry during the LGM (∼ 24.8 ka in their simulations), preliminary tests showed that it does affect the diversity of modelled particle trajectories (more details in Sect. 3).

For each model time step (every 0.01–0.04 years) and domain cell (n=6 030 036), we implement a set of conditions to determine whether to “seed” (i.e. create) a new particle or not. We exclusively focus on estimating glacial sediment trajectories and transport statistics, and do not address the volumes of glacial sediments, erosion, or deposits. Therefore, seeding of a new particle can be interpreted as the creation of a new glacial “sediment entity” within the glacier system, possibly ranging in size from grains to large boulders. Note that throughout this paper, we use the terms “glacial sediment” and “glacial transport” to describe all sediments that are transported by glacier ice, thus combining supraglacial, englacial, and subglacial debris/transport. Below, we describe the set of conditions required for both subglacial seeding and supraglacial seeding to occur in our model (Fig. 2).

The frequency and spatial distribution of subglacial seeding is here set to be a function of basal ice velocity, as frequently observed (Humphrey and Raymond, 1994; Herman et al., 2015; Cook et al., 2020; Herman et al., 2021). Here, we use the subglacial erosion law obtained by Koppes et al. (2015) from results on sediment export volumes from several outlet glaciers of the Patagonian and Antarctic Peninsula icefields. This non-linear erosion law assumes the erosion rate e˙ is proportional to the sliding velocity us raised to a power, using an erodibility constant Kg=5.2×10-11 and a sliding velocity exponent of l=2.34: 1e˙=Kgusl We follow Seguinot and Delaney (2021) and assume glacier systems studied by Koppes et al. (2015) likely yield similar dynamics to former outlet glaciers of the AIF during the LGM. Using this law, our model computes an erosion rate and cumulative erosion over time for each grid cell (Fig. 2). Computed erosion is not used to modify the bed topography dynamically but rather only as a quantitative proxy for particle seeding. Once this artificial cumulative erosion reaches a certain threshold (here set to 4 cm), seeding occurs and the erosion value is reset to 0, thus adding a new particle to the system (Fig. 2). This value (4 cm) is arbitrary and represents a parameter to control the total number of advected particles. To add stochasticity to the modelled creation and freeze-on of subglacial sediment, seeding further requires meeting a condition of time delay since last seeding occurred. This time delay is set to randomly vary between 10 and 60 years during the simulation following a uniform probability distribution (Fig. 2). Thus, even though erosion is positively correlated to basal ice velocity, some randomness is here introduced in whether seeding will occur shortly or with some delay after the cumulative erosion threshold is reached. Note that with this scheme, we do not model the glaciofluvial transport of subglacially eroded materials, as our model setup is not yet coupled to a subglacial hydrological-routing module. Instead, we exclusively focus on subglacially eroded materials which freeze on and are subsequently advected by glacier ice (Alley et al., 1998). The limitations of this assumption are further mentioned in the Discussion section.

For supraglacial seeding, our scheme was conceived to simulate mechanisms generating supraglacial debris on glaciers, i.e. gravitational mass wasting events including rockfall, rock avalanches, debris flow, avalanches, or landslides (Benn et al., 2012). We assume these events require both no (or little) ice cover and steep slopes to occur. We define all slopes steeper than 45° as susceptible to mass wasting (Fig. 2), following recommendations from Fischer et al. (2012). However, our 300 m model resolution still smooths high-elevation peaks and steep slopes resulting in fewer locations >45° steep than in reality. To avoid this bias, we use a higher-resolution digital elevation model (30 m resolution; Tadono et al., 2014) to produce a mask of pixels meeting a >45° slope condition. We consider all modelled ice that is <20 m thick and located in pixels meeting the high-resolution >45° slope mask to be an artifact of our 300 m resolution, thus representing regions that would have no (or negligible) ice cover in reality. As a result, in our setup, a given grid cell needs to both satisfy the >45° slope condition (in the high-resolution mask) and display modelled ice thickness <20 m, for supraglacial seeding to occur (Fig. 2).

As with subglacial seeding (see above), we introduce stochasticity in supraglacial debris production. Firstly, supraglacial seeding only occurs when meeting a Boolean mask condition (True/False array) randomly shuffled for all domain cells (at every time step) with a True-value likelihood of 80 %. Following this, seeding also only occurs when meeting a time delay set to randomly vary between 20 and 160 years during the simulation (Fig. 2). All random sampling follows a uniform probability distribution. These additional conditions separately add temporal and spatial randomness to supraglacial seeding, thus applying a probabilistic algorithm; common in mass-wasting event modelling (e.g. Champel et al., 2002). Therefore, while gravitational mass wasting events are highly likely where/when the model features steep slopes (>45°) and a lack of ice cover, they are not necessarily going to occur at every time step and always in the same locations (Fig. 2). Once seeded, particles are advected downslope following the steepest descent until slope angle <45°, or until reaching cells with modelled ice, in which case ice advection will take over (Fig. 2).

To track the movement of particles in 3D within the evolving glacier geometry, we use a fully GPU-optimized Lagrangian advection scheme which computes the space-time trajectory of particles created from seeding and resolves the precise 3D positions of particles at sub-grid resolution. This new scheme builds on the original IGM “particles” module (Jouvet et al., 2024) to provide additional computational gains for large-scale particle tracking. At each model timestep, IGM computes the 3D ice-flow based on a high-order stress-balance model referred to as the “Blatter-Pattyn” model (Blatter, 1995) and thus outputs a 3D velocity field. Each particle's horizontal (x,y) and vertical (z) positions are thus updated according to ice velocity components u,v,w, respectively, integrated over a model timestep, Δt, using an explicit Euler scheme. 2xn+1=xn+Δt⋅u¯,3yn+1=yn+Δt⋅v¯,4zn+1=zn+Δt⋅w¯, where u¯,v¯, w¯ represent the bilinearly interpolated horizontal and vertical velocities, respectively, at a particle's current location (xn,yn). We ensure no particles artificially leave the ice column due to numerical integration errors or transient velocity fluctuations by clipping their relative (normalized) vertical positions to between 0 (bed) and 1 (ice surface). The bilinear interpolation for a scalar field f at a sub-grid location (x,y) is computed using: 5f¯x,y=∑i,jfi,j⋅1-x-i⋅(1-y-j) where the summation runs over the four grid nodes surrounding the particle's horizontal position, and the weights (1-x-i) and (1-y-j) ensure a smooth linear interpolation based on the distances to these nodes.

We assume all particles are advected at the velocity of the ice. The limitations of this assumption are assessed in the Discussion section below. When a particle reaches the modelled ice margin and is deposited, i.e. when ice thickness at its position becomes 0 m, it is prescribed the bed elevation. If local slope is <45° this particle will remain stagnant (Fig. 2). If the modelled glacier re-advances and local ice thickness is >0 m again, the particle gets re-entrained and 3D ice advection computations restart. We thus assume that all temporarily deposited sediments freeze-on and get re-entrained by a re-advancing ice margin. Although reality is more complex whereby former deposits can be overridden and survive younger glacier advances, the process of re-entrainment is here considered to dominate (Cogez et al., 2018). This assumption is supported by the general rarity, in formerly glaciated landscapes, of preserved older moraines inboard of younger and more extensive terminal moraines (Gibbons et al., 1984).

Although particle positions are computed at every timestep (0.01–0.04 years), they are saved every 10 model years, which for our simulated timeframe (40–18 ka) generates 2200 data frames for each of the millions of advected particles (20.5 million at maximum). The data saved for each particle include its x and y coordinates, relative height in ice column, seeding year, and cumulative glacial transport time since seeding. 10 years is the highest output frequency achieved while ensuring the particle database (∼ 1.22 TB) can be post-processed at a manageable computational cost. At that output temporal frequency, the post-processing mapping of particle trajectories fully reflects the simulated ice-flow and particle advection in most cases, except where modelled ice velocities are both high (e.g. >1000 m yr⁻¹) and towards highly sinuous glacier motion (e.g. around valley bends), where mapping particle positions every 10 years can result in unrealistically straight trajectories. This will however only impact the mapped trajectory towards the bend and not reduce the accuracy of its modelled provenance nor destination.

After running the glacier-particle coupled IGM simulations, we use the output database of particle coordinates to map the time-transient trajectories of certain particles. This is conducted within the frame of two analyses. The first one, hereafter referred to as the “sink-to-source” analysis, aims at reconstructing the provenance and glacial transport pathways of specific LGM terminal ice-contact deposits. The second analysis, called “source-to-sink”, addresses the opposite question. Its objective is to estimate the possible transport pathways and deposition locations of glacial sediments eroded from a pre-determined source.

The sink-to-source analysis involves finding all particles that end up within the area of a mapped deposit at the end of the simulation (18 ka), after final glacier retreat, and trace back their glacial transport trajectories. Although this can be achieved for any user-defined polygon, we focus on ice-contact deposits located towards the terminal margins of main AIF outlet glaciers during the LGM (e.g. LGM moraines). To follow a consistent methodology across the Alps, we map a series of 49 polygons (Fig. 3a) covering the area between our most extensive time-independent modelled ice margin and the empirical LGM outline of the AIF originally produced by Ehlers et al. (2011) and improved by several studies since (Gianotti et al., 2008, 2015; Ravazzi et al., 2012; Monegato et al., 2017; Federici et al., 2017; Ivy-Ochs et al., 2018; Braakhekke et al., 2020; Kamleitner et al., 2022, 2023; Ribolini et al., 2022). Tracing polygons over that area between ensures that we isolate all particles deposited at the LGM margins even where model-data fit in ice extent is not perfect, which is still the case despite improvements relative to former AIF-wide LGM models (Seguinot et al., 2018; Jouvet et al., 2023; see Fig. 4a in Leger et al., 2025).

Importantly, our 49 sink polygons (Fig. 3a) are not a precise map of terminal LGM ice-contact deposits preserved in the Alps. However, they are useful to produce a first-order estimation of possible LGM glacial trajectories for deposits located towards major outlet glacier margins, pre-erosion. Producing an Alps-wide, digital and open-access map of all preserved terminal ice-contact deposits dating to the LGM (e.g. Clark et al., 2018; Davies et al., 2020) has yet to be achieved in the Alps and is beyond the scope of this study. To estimate the relative contributions of various provenances to the total particle number found in a sink deposit, we divide our Alps-wide domain in 241 present-day hydrological catchments; obtained from the global HydroBASINS database (Lehner and Grill, 2013), and named based on catchment-specific river names (Fig. S1 in the Supplement). Our sink-to-source analysis produces a catalogue of modelled particle trajectories, estimated provenance fractions per basin, and statistics including glacial transport time and particle age (i.e. seeding year), for all particles found in each of the 49 sink polygons shown in Fig. 3a. All results are produced separately for subglacial and supraglacial particle seeding, enabling us to compare the impacts of different sourcing mechanisms on glacial sediment transport histories and provenances.

For the source-to-sink analysis, we select sources that represent mapped outcrops of specific alpine surface lithologies, to estimate the glacial transport pathways of sediments from specific rock types between 40 and 18 ka, across the Alps. We focus on rock type as this enables us to compare modelled estimates against empirical data on ice-contact deposits (e.g. erratic boulders) of known lithologies and locations post-retreat (e.g. Braakhekke et al., 2020; Monegato et al., 2022). This requires identifying surface lithologies specific enough to be associated with mapped outcrops and uniquely recognisable through geological assessment of ice-contact deposits. The outcrops moreover need to cover a large-enough area for enough particle seeding to overlap them, given that a single grid cell is 90 000 m². To identify such lithologies, we use the open-access 1:500 000-scale geological map sheets 1 and 2 from the “Structural model of Italy” (Bigi et al., 1990a, b). These maps present a relatively high spatial resolution, are easily accessible online and georeference-able, and provide a consistent naming convention of lithologies across the entire Alps. We also use geodata derived from the Geological Map of Austria 1:50 000 sheets 197 Kötschach and 198 Weißbriach for one extra lithology (i.e. the Hochwipfel formation) (Geologische Bundesanstalt Österreich, 2021a, b). We then isolate a subset of 22 surface lithologies referred to as our “source polygons” (Fig. 3b). While these are not a comprehensive list satisfying the above criteria, they are spatially widespread and cover the main rock types described by investigations on LGM erratic boulders in the Alps. They include Mont-Blanc granite (Bussien Grosjean et al., 2018), Glarus Verrucano (Letsch et al., 2015), or Salvan-Dorénaz conglomerate (Capuzzo et al., 2003), for instance (Fig. 3b).

The source-to-sink analysis involves finding all particles seeded within our 22 source polygons during the AIF simulations, and in mapping their glacial transport pathways. Due to existing mechanisms of sediment melt-out and lodgement at the ice-bed interface (Alley et al., 1997), we consider any location along the resulting trajectories to be a possible destination for glacial sediment of the studied lithology. Thus, the source-to-sink analysis produces a catalogue of maps displaying modelled trajectories of particles seeded within each of the 22 selected surface lithologies shown in Fig. 3b. The maps are produced for both subglacial and supraglacial particle seeding allowing for a direct comparison between the two.

Consequently, the main outputs of this study are the “sink-to-source” and “source-to-sink” analyses, i.e. two catalogues of model results shared under the form of maps displaying source and sink particle trajectories, pie charts of deposit provenance fractions, histograms showing data from sink particles, and polyline shapefile data for visualization in GIS software. These data are all accessible from the Zenodo repository attached to this paper (link: 10.5281/zenodo.18374156, Leger et al., 2026).

GPUs are particularly well-suited for particle-based numerical modelling, such as Lagrangian particle tracking, due to their architecture which is optimized for massively parallel execution of small, independent computations, ideal for processing individual particles concurrently. This contrasts with traditional computing on Central Processing Units (CPU) which restricts the parallelization of such small operations on much fewer cores. Consequently, GPU-accelerated algorithms for particle-based modelling have been extensively developed in fields as varied as fluid mechanics, graphics, or geosciences (e.g. Wang et al., 2022; Aaron, 2023). In our specific application, we find that transferring all computation on the GPU makes 3D Lagrangian particle advection highly efficient, with a computational cost that remains small even when tracking tens of millions of particles within a modelled glacier (Fig. 4).

To quantify this gain, we ran a test simulation over the majority of the European Alps and, after initializing an LGM Alpine Ice Field (AIF), seeded new particles in all grid cells of the glacier accumulation area every two model years, thus quickly multiplying the total particle number. When operating on a single GPU (Nvidia RTX 4090), raising the number of particles from 0 to 50 million increases the mean cost of computing their advection linearly between 0.02 and 0.1 s per timestep (Fig. 4). Even with 50 million particles in the system, the computational cost of particle tracking remains below 26 % of the mean cost (i.e. ∼ 0.39 s per timestep) of all other IGM processes and modules in our Alps-wide simulation of the LGM at 300 m resolution. When running the same test using multiple CPUs instead, the mean costs of tracking 50 million particles reach approximately 26 and 5.5 s per timestep using 12 and 60 CPU threads, respectively (Fig. 4). These computational costs are between 274 and 55 times greater than those obtained with a single GPU, respectively. For 10 million advected particles, the costs are still 200 and 42 times greater than with the GPU, respectively. This shows that when using any traditional CPU-based glacier evolution model, coupling Lagrangian tracking of large particle numbers (>107) would substantially increase the simulation's computational cost. The alternative of accurately computing particle trajectories using post-processing only (after simulations are run), although not computationally restrictive, would be made impossible by the data volume of transient 3D velocity fields that would need to be saved at every time step (0.01–0.04 years), which in our case would quickly exceed the hundreds of Terabytes. Contrastingly, when using IGM and a GPU-based approach, 3D particle tracking of large particle numbers can be coupled to simulations with only a small additional cost relative to the ice-flow model (Fig. 4). This enables us to run IGM simulations at high (300 m) spatial resolutions with millions of particles tracked over Alps-wide and multi-millennial scales, an experiment that would be unfeasible using traditional CPU-based computing.

Our coupled glacier-particle simulations output a database of 3D particle coordinates and other statistics from the moment of seeding until the end of the glacier simulation (i.e. 18 ka). Thus, for both simulations with subglacial and supraglacial particle seeding, a map of seeding locations for each of the ∼ 20.5 million advected particles can be produced. To visualize the spatial heterogeneity of particle seeding, we transform the seeding location data into normalized seeding density maps (Fig. 5). In Fig. 5, dark purple colours (normalized density closer to 1) show regions with relatively more particle seeding events during the simulations. For subglacial seeding, these regions are associated with high basal ice velocities modelled during extended periods of the simulation, spanning 40–18 ka. These can be interpreted as likely to produce the largest volumes of glacial sediments of subglacial origin (e.g. abrasion and plucking) during the LGM. Potent subglacial sediment sourcing regions include the Rhône valley between Montreux and Sion (Switzerland), the Dora Baltea valley between Aosta and Ivrea (Italy), the Romanche valley between Le Bourg-d'Oisans and Grenoble (France), or the Rhein valley between Domat/Ems (Switzerland) and Bregenz (Austria), for instance (Fig. 5a).

For supraglacial seeding, regions of high seeding densities are those presenting steep topographies (>45°) and ice-free conditions (or thin ice cover: <20 m) during extended time-periods of the simulation. These regions also need to be near dynamic modelled glaciers for seeded particles to eventually get transported by glacier ice. These regions are interpreted as likely to have produced the largest volumes of supraglacial sediments (e.g. from rockfall, debris flow, landslides, avalanches) during the LGM. Our results suggest that high supraglacial sediment sourcing regions are widespread (Fig. 5b) but include, for instance, the Écrins Massif (France), the Lepontine Alps (Switzerland), the Dolomiti Bellunesi Massif (Italy), the Triglav Massif (Slovenia), or the Bernese Alps (Switzerland). During the LGM, these regions are most concentrated within a narrow band located towards the northern and southern peripheries of the alpine arc, where high-elevation terrain (>2500 m a.s.l.) combined with thin/no ice cover maximize the likelihood of nunatak occurrence (Fig. 5b). Contrastingly, supraglacial sediment sourcing is lower further towards the Alps' interior, where the model produces greater ice thicknesses and topographic ice covers for extended periods, thus reducing nunatak occurrence.

With the sink-to-source analysis, we produce a catalogue of modelled time-transient trajectories for terminal LGM ice-contact deposits mapped across the Alps, hereafter referred to as our “sinks” (see Sect. 2.4). Sink-to-source trajectories reveal the modelled pathways of ice-advected particles ending up within these sinks after final glacier retreat. For each sink polygon mapped (n=49; Fig. 3a), we provide a high-resolution map of particle trajectories, along with an estimation of particle provenance fractions, i.e. the proportions of sink particles originating from specific hydrological basins (see Sect. 2.4; Fig. S1). For each sink and particle in this sink, we also produce statistics on total particle glacial transport distance, cumulative glacial transport time, cumulative time in ice-free conditions during source-to-sink journey, and seeding year (i.e. timing of erosion). These data are produced for both cases of subglacial and supraglacial seeding, enabling us to quantify differences in glacial transport dynamics between the two. We consider the sink-to-source catalogue to be a main result of this study and encourage readers to download it from the Zenodo repository attached to this paper (link: 10.5281/zenodo.18374156, Leger et al., 2026). All particle trajectory data for each seeding type and sink are also available as polyline shapefiles for visualization in GIS software.

With the source-to-sink analysis, we produce a second catalogue of time-transient (40–18 ka) glacial sediment trajectories for a selection of key surface lithologies across the Alps, hereafter referred to as our “sources” (see Sect. 2.4) (link: 10.5281/zenodo.18374156, Leger et al., 2026). These trajectories reveal the pathways of particles seeded either subglacially or supraglacially within source polygons (n=22; Fig. 3b). For each source polygon and seeding type, we provide a high-resolution map of source particle trajectories. We interpret these source-to-sink trajectories as model estimates of possible locations (along the modelled trajectories) where sediments of a specific surface lithology may have been transported to and deposited by ice between 40 and 18 ka. These locations can then be compared against the coordinates of documented deposits (e.g. erratic boulders) of known lithology, which may help assess the accuracy of our modelling.

As shown above with the example of Arolla Gneiss “source-to-sink” trajectories overflowing the Jura Massif, the coupling of 3D particle tracking enables us to estimate the precise locations and time span of ice transfluences in the Alps during the LGM (Fig. 10). Ice transfluences occur when the growth of ice sheets and/or icefields cause the formation of topographically uncoupled ice domes, i.e. which accumulate away from summits and hydrological catchment divides. If the surface elevation of these domes exceeds the altitude of neighbouring cols, uncoupling from main hydrological catchments occurs causing ice-flow to cross main hydrological divides (Linton, 1949). This can result in glacial sediment transport over high-elevations ridges/cols and into different catchments (Monegato et al., 2022) (Fig. 10). Reconstructing LGM transfluences can thus help understand former ice-flow dynamics and unravel the puzzling lithologies/provenances of certain ice-contact deposits in the Alps (e.g. Reitner et al., 2010). Here, we loaded our modelled particle trajectories and thus 3D ice-flow lines into a geographic information software (ArcGIS Pro 3.4) to detect the occurrence of ice transfluences in our simulations, focusing only on the 11 largest hydrological catchments of the Alps (Rhône, Aare, Rhein, Isar, Inn, Enns, Drau, Piave, Brenta, Adige, Po) (Lehner and Grill, 2013). We present the results of this analysis in a series of maps (Figs. S8–14) highlighting the locations of modelled ice domes, flowlines, and ice transfluences across the Alps. Figure 10 shows one of these maps for the example region of the upper Inn catchment. There, the build-up of the “Engadin” ice dome centred towards Zernez (46°41^′ N, 10°05^′ E, 1465 m a.s.l.) and reaching a modelled maximum ice surface elevation of ∼ 3100 m a.s.l. leads to a complex network of topographically uncoupled flowlines causing a high concentration of ∼ 30 ice transfluences into the adjacent Rhein, Adda, Adige, and Isar catchments (Fig. 10). This causes, for instance, modelled ice from the Inn valley between St.-Moritz (46°29^′ N; 9°50^′ E) and Zernez (a 45 km stretch) flowing south-westwards over the Maloja pass (46°24^′ N; 9°41^′ E) into the Val Bregaglia, Como Lake basin, and feeding the Adda and Seveso outlet glaciers (sinks 2 and 44 in “sink-to-source” catalogue). As another example, we note that our model reproduces the well-documented Simplon pass transfluence (e.g. Florineth and Schlüchter, 1998; Kelly et al., 2004; Dielforder and Hetzel, 2014), with ice possibly transporting sediments from the Eiger-Mönch-Jungfrau mountains (e.g. Aar granites) across the Rhône valley, over the Simplon pass, and into the Ticino-Toce glacier system during the LGM (sink 48 in “sink-to-source” catalogue, Fig. S11). In our simulations, we also find that modelled ice is always warm-based towards the main ice domes and transfluences occurring during the LGM (see Fig. 6b in Leger et al., 2025). Moreover, the modelled time span of transfluence occurrence is highly case-specific and can vary from 1–3 kyr, thus only during peak LGM conditions (e.g. the Simplon pass transfluence), to up to nearly the full simulation time frame (i.e. 22 kyr) and LGM period (e.g. the Engadin ice dome, Fig. 10). Consequently, our results show that coupling 3D Lagrangian particle tracking to glacier evolution modelling can also help identify the detailed events of complex and momentary topographic uncoupling of ice-flow during major Quaternary glaciations of the Alps.

To assess the sensitivity of our particle trajectories to both the seeding scheme and model parameters, we conduct two additional AIF simulations that differ from the original setup presented above like so: (i) The first sensitivity test uses a “simple” seeding scheme, which is not process-based and instead creates particles supraglacially in a spatially- and temporally-regular manner, i.e. with seeding occurring in 20 % of grid cells exclusive to the accumulation zone, and regularly every 300 years. This simpler scheme also produces less particles (∼ 2.1 million at maximum) than the original seeding scheme. (ii) The second sensitivity test uses the same “complex” seeding as the original scheme (Fig. 2) but employs the parameter values of a different ensemble simulation (i.e. number 24) within the set of 8 Not-Ruled-Out-Yet simulations obtained by Leger et al. (2025). Whilst featuring different ensemble-varying parameter values (see Table S1 in Leger et al., 2025), simulation 24 produces Alps-wide model-data agreements in LGM ice extent and thickness that are indistinguishable from simulation 37 (used throughout this study). Input parameter differences (n=10) however generate changes in SMB, the basal sliding parameterization, ice rheology, and the magnitude of isostatic deflection. Importantly, simulation 24 uses a different bed topography than simulation 37, with no removal of valley-fill sediments.

In the first sensitivity test, which uses “simple” seeding instead, model agreement with the locations of dated erratics presented above (Sect. 3.4.2) decreases from 81 %–68 % to 74 %–58 %, with these two ranges representing whether we tolerate the small (<4 km) increase in ice extent mentioned above (Sect. 3.4.2). Whilst not substantial, this decrease in model-data agreement is noticeable and suggests that a less process-based particle seeding scheme leads to a worse model-data fit on the provenance, glacial transport, and deposition histories of ice-contact deposits during the LGM. In the second sensitivity test, as the seeding scheme is unchanged from the original (see Sect. 2.2), we can use provenance fractions (%) per hydrological basin (n=241) for each sink (see Sect. 2.4) to quantify inter-simulation differences. Here, when using parameters from Leger et al. (2025)'s ensemble simulation 24 instead of 37, we find that particle provenance fractions per hydrological basin (e.g. percentages in Figs. 6, 8) remain identical in ∼ 72 % of cases, on average (median difference: 28.5 %). When comparing particles' provenance basins irrespective of fraction percentages, we find sink particles originate from the same basins in 88.5 % of cases. Thus, running a simulation which yields a similar LGM model-data fit but uses different sensitive parameter values causes sink particles to originate from different basins in 11.5 % of cases and provenance fractions to vary by 28.5 % on average. These results show a non-negligible inter-simulation variability highlighting a noticeable sensitivity of particle trajectories and provenances to modelled ice dynamics and/or bed topography changes. However, this test also shows that the majority of particle trajectories, provenances, and glacial transport histories remain unchanged relative to the original simulation.

The computational gains of our novel GPU-based glacier modelling coupled with 3D Lagrangian particle tracking enabled us to produce an Alps-wide estimation of transient glacial sediment pathways during the last glaciation (40–18 ka). The results of this experiment are presented in the form of figure catalogues and trajectory shapefiles accessible via the Zenodo repository attached to this paper (link: 10.5281/zenodo.18374156, Leger et al., 2026). They provide the means to compare our spatially distributed modelling estimates against empirical evidence on, for instance, deposited LGM erratics and their lithologies/provenance, former ice-flow direction during the LGM, documented ice transfluences, and preserved post-retreat deposits and mapped moraines. We believe this first Alps-wide reconstruction of LGM glacial sediment transport will prove useful to glacial geologists, geomorphologists, sedimentologists, and industries studying ice-contact sediments related to the last glaciation of the European Alps. This new ability to conduct coupled glacier-particle modelling over continental and multi-millennial scales opens the door to new model-data comparisons which, in turn, can further improve the accuracy of future AIF models. Moreover, this study provides a novel, computationally efficient modelling workflow which opens the possibility to produce high-resolution estimates of the erosion, transport, and deposition dynamics of glacial sediments in numerous glaciated or formerly glaciated regions of the world.