A supply-limited torrent that does not feel the heat of climate change

Debris flows are fast-moving, sediment-laden flows that pose significant hazards on alpine fans and are commonly triggered by intense precipitation and slope instability. Many studies in transport-limited (supply-unlimited) catchments report increased debris-flow frequency and magnitude under recent climate warming, linked to more frequent rainstorms, glacier retreat, rock-glacier acceleration, and permafrost degradation that enhance sediment supply. However, long-term, systematic records are scarce, often biased toward recent, damaging events, and results are not unequivocal, with some studies showing no clear trend or reduced activity. This study addresses these gaps by reconstructing a multi-centennial debris-flow chronology for the Multetta fan (Eastern Swiss Alps), a supply-limited system, to test whether historical and ongoing climate warming has altered debris-flow frequency or magnitude. The key research questions are whether debris-flow activity at a supply-limited site shows trends attributable to climate variability and warming, and how sediment supply and recharge cycles govern event occurrence.

Prior work has emphasized climatic controls on debris-flow triggering via precipitation extremes and cryospheric changes, with numerous case studies indicating increased activity in recent decades in supply-unlimited settings. Conversely, other analyses and reconstructions report no significant trends or even decreases, highlighting complex, indirect links among climate, sediment availability, and geomorphic connectivity. Historical datasets often suffer from non-uniform observation rates, limited timespans, and reporting biases, complicating detection and attribution. Conceptually, transport-limited basins with abundant sediment tend to exhibit irregular, near-exponential repose-time distributions, whereas supply-limited (weathering-limited) systems show more regular or clustered occurrence consistent with Weibull or log-logistic distributions, underscoring the role of sediment recharge intervals. These frameworks inform expectations for Multetta, a bedrock-dominated headwater catchment with limited sediment sources primarily from frost-weathering rockfall.

Study area and geomorphic context: The Multetta fan (Tschierv, Grisons; 46.63°N, 10.31°E) comprises a main (1.03 km²) and secondary (0.21 km²) fan, underlain by Triassic Engadin Dolomites (dolomite upper, sandstone lower). Debris flow supply originates from the steep Vallun da Piz Daint headwater (0.59 km²; mean slope 43.5°; Melton index 1.24; proximal fan slope 22%), subdivided into nine subunits largely consisting of bedrock with limited sediment production via freeze–thaw weathering. Geomorphic mapping: Active sediment sources were delineated via aerial photo interpretation (2022, 10 cm orthoimages) and LiDAR DEM hillshade (2023, 1 m) from swisstopo. Unvegetated, steep, connected surfaces were mapped, distinguishing bedrock vs colluvium to quantify relative source areas. Dendrogeomorphic sampling: On the main fan, 478 Pinus mugo ssp. rotundata trees were sampled along four transects (T1–T4; ~1780–1900 m a.s.l.). Trees exhibiting growth disturbances (GDs: scars/injuries, decapitation, tilting) consistent with debris-flow impacts were cored (two increment cores, 5.5 mm Pressler borer) oriented with presumed flow direction; wedges/cross-sections were collected at scars or from dead trees/stumps. Trees with GDs unrelated to debris flows were excluded. GPS positions were recorded with ~1 m accuracy. Laboratory analyses: Samples were prepared and ring widths measured from scanned images; cross-dating used CDendro/CooRecorder (v9.8.1) and quality assessed with COFECHA. GDs characteristic of geomorphic disturbance—abrupt growth suppressions (GS), compression wood (CW), and injuries (I)—were identified, with GS/CW intensity categorized (weak/medium/strong). Juvenile rings (first 30) were excluded. Events were inferred from medium/strong injuries, GS, and CW. Event detection and completeness: The study area was zoned into sectors (SI–SIV) and transects (T1–T4). Event detection in each sector used thresholds adapting to sample size (ss): for ss<50, GDs ≥2 and It ≥6; for 50<ss≤99, GDs ≥3 and It ≥4; for ss≥100, GDs ≥4 and It ≥2. Events were assigned confidence levels based on GD intensity. Years with incoherent spatial GD patterns (e.g., climatic/insect signals), documented avalanche years, or high P. mugo mortality (tree-ring index <1.5) were excluded. Completeness analyses to assess bias on the early part of the chronology employed Negative Binomial and non-parametric change-point approaches (R np package), yielding unbiased start dates of 1687 or 1750 depending on method. Spatial extent and magnitude classification: The fan was divided into 16 units by crossing four sectors (SI–SIV) with four transects (T1–T4). For a given year, a unit was marked affected if an event was reconstructed in its sector and at least one tree on the corresponding transect showed a GD. Event magnitude classes were defined by the fraction of affected units: XS (1–10%), S (10–20%), M (20–30%), L (30–40%), XL (40–50%), XXL (>50%). Recurrence intervals were computed as record length divided by the number of events per area. Trend and repose-time analyses: Decadal frequencies were tested for trends using nonparametric Mann–Kendall, Wald–Wolfowitz, and Theil–Sen slope estimators over 1687–2020 and 1750–2020. Cumulative event series were tested for breakpoints. Repose times (inter-event intervals) were modeled with exponential (random Poisson process), Weibull (regular/dependent), and log-logistic (clustered) distributions. Suitability was evaluated by Monte Carlo Kolmogorov–Smirnov p-values (>0.05) and Akaike Information Criterion (AIC); hazard functions provided the conditional probability of an event as a function of elapsed time since the previous event.

• Tree-ring analyses of 478 Swiss mountain pines yielded 1427 growth disturbances and identified 56 event years with debris-flow activity since 1626 CE.
• Completeness analyses indicate the unbiased reconstruction starts in 1687 (by one approach) or 1750 (by another).
• From 1687 (n=55 events) and 1750 (n=44 events), long-term average occurrence is 0.16 and 0.20 debris flows per year, respectively.
• Decadal variability includes inactive periods (1750–1769, 1790–1799, 1850–1859, 1940–1950, 2010–2019) and peaks of ~0.4 events year⁻¹ in the 1860s, 1890s, and 1910s.
• No significant long-term trend in frequency or magnitude: Theil–Sen slope is zero; Mann–Kendall, Bartels, and Wald–Wolfowitz tests yield p-values > 0.05; no breakpoint detected in cumulative events.
• Size distribution since 1687: XS 7% (4 events), S 55% (30), M 16% (9), L 7% (4), XL 4% (2), XXL 11% (6).
• Spatial patterns show shorter recurrence at fan margins (10–20 yr) vs center (40–70 yr). XXL events in 1816 and 1849 reconfigured fan morphology and shifted activity westward through the late 19th–early 20th centuries.
• No L, XL, or XXL events recorded since 1990, and no evidence for increased activity during recent warming.
• Repose-time distributions are best fit by the Weibull distribution (p>0.05; lowest AIC) for both 1687–2020 and 1750–2020, indicating regular, dependent occurrence characteristic of supply-limited systems; the conditional probability slightly increases with time since the last event.
• Despite >2 °C local warming since the late 19th century and plausible changes in freeze–thaw cycles, there is no detectable signal of increased sediment availability affecting debris-flow activity at Multetta.

The reconstruction shows that in a supply-limited system like Multetta, debris-flow activity over multi-centennial scales is governed predominantly by sediment recharge and availability rather than directly by climate warming. The regular, Weibull-type repose-time pattern and absence of long-term frequency/magnitude trends indicate dependency on cut-and-fill cycles and the time needed to replenish limited sediment sources in bedrock-dominated headwaters. While decadal peaks coincide with wetter summers and early fall periods, sustained increases attributable to warming are absent. This contrasts with transport-limited, permafrost-influenced catchments (e.g., Ritigraben), where increased precipitation and warming can translate into more frequent and larger debris flows due to abundant unconsolidated sediment. The findings suggest that climate impacts on debris-flow hazards are strongly mediated by basin sediment dynamics and connectivity, and that hazard assessments and mitigation must account for whether systems are sediment-supply-limited or transport-limited.

This study provides the longest continuous dendrogeomorphic reconstruction of debris-flow activity in the Eastern Swiss Alps (1626–2020) and demonstrates that a supply-limited torrent (Multetta) exhibits no long-term increase in debris-flow frequency or magnitude despite pronounced recent climate warming. Event occurrence is regular and dependent, with repose times best described by a Weibull distribution, underscoring control by sediment availability and recharge cycles. The clear behavioral contrast with transport-limited systems has practical implications: climate-proof torrent management should prioritize understanding sediment budgets, recharge times, and avulsion dynamics, informing hazard zoning and the design of defense structures. Future research should integrate direct sediment budget monitoring, higher-resolution event dating to resolve multiple events within a year, and coupled hydro-geomorphic modeling to project sediment-supply-sensitive responses under evolving precipitation regimes and cryospheric changes.

Tree-ring reconstructions have annual resolution, limiting the ability to distinguish multiple debris flows within the same year. The apparent spatial extent of older events is biased low due to fewer surviving old trees and overprinting or erosion of older deposits. Sample depth decreases back in time, necessitating completeness analyses; the unbiased period likely begins only after 1687 or 1750 depending on method. Event detection thresholds and exclusions (e.g., years with incoherent GD patterns, avalanche years, or elevated tree mortality) may omit some true debris-flow signals. Spatial magnitude classification relies on a schematic 16-unit approach rather than direct areal inundation mapping. The study infers sediment-supply dynamics indirectly from geomorphic mapping and event patterns without direct, continuous sediment flux measurements. Climatic drivers (precipitation intensity, freeze–thaw cycles, permafrost state) are not explicitly modeled at event scale, limiting attribution precision.