Allometric scaling of retrogressive thaw slumps
Authors: van der Sluijs Jurjen , Kokelj Steven V. , Tunnicliffe Jon F. 
Published: October 2023

Abstract. In the warming Arctic, retrogressive thaw slumping (RTS) has emerged as the primary thermokarst modifier of ice-rich permafrost slopes, raising urgency to investigate the distribution and intensification of disturbances and the cascade of effects. Tracking RTS is challenging due to the constraints of remote sensing products and a narrow understanding of complex, thaw-driven landforms; however, high-resolution elevation models provide new insights into geomorphic change. Structural traits, such as RTS depth of thaw or volume, can be obtained through allometric scaling. To address fundamental knowledge gaps related to area–volume scaling of RTS, a suitable surface interpolation technique was first needed to model pre-disturbance topography upon which volume estimates could be based. Among eight methods with 32 parameterizations, natural neighbour surface interpolation achieved the best precision in reconstructing pre-disturbed slope topography (90th percentile root mean square difference ±1.0 m). An inverse association between RTS volume and relative volumetric error was observed, with uncertainties < 10 % for large slumps and < 20 % for small to medium slumps. Second, a multisource slump inventory (MSI) for two study areas in the Beaufort Delta (Canada) region was developed to characterize the diverse range of disturbance morphologies and activity levels, which provided consistent characterization of thaw-slump-affected slopes between regions and through time. The MSI delineation of high-resolution hillshade digital elevation models (DEMs) for three time periods (airborne stereo-imagery, lidar, ArcticDEM) revealed temporal and spatial trends in these chronic mass-wasting features. For example, in the Tuktoyaktuk Coastlands, a +38 % increase in active RTS counts and +69 % increase in total active surface area were observed between 2004 and 2016. However, the total disturbance area of RTS-affected terrain did not change considerably (+3.5 %) because the vast majority of active thaw slumping processes occurred in association with past disturbances. Interpretation of thaw-driven change is thus dependent on how active RTS is defined to support disturbance inventories. Our results highlight that active RTS is tightly linked to past disturbances, underscoring the importance of inventorying inactive scar areas. Third, the pre-disturbance topographies, MSI digitizations, and DEMs were integrated to explore allometric scaling relationships between RTS area and eroded volume. The power-law model indicated non-linearity in the rates of RTS expansion and intensification across scales (adj-R2 of 0.85, n= 1522) but also revealed that elongated, shoreline RTS reflects outliers poorly represented by the modelling. These results indicate that variation in the allometric scaling of RTS populations is based on morphometry, terrain position, and complexity of the disturbance area, as well as the method and ontology by which slumps are inventoried. This study highlights the importance of linking field-based knowledge to feature identification and the utility of high-resolution DEMs in quantifying rates of RTS erosion beyond tracking changes in the planimetric area.