Runout Distance Research Articles

Rainfall-Triggered Landslides and Numerical Modeling of Subsequent Debris Flows at Kalli Village of Suntar Formation in the Lesser Himalayas in Nepal

Hazardous debris flows are common in the tectonically active young Himalayas. The present study is focused on the recurrent, almost seasonal, landslides and debris flows initiated from Kalli village in Achham District of Nepal, located in the Lesser Himalayas. Such geological hazards pose a significant threat to the neighboring communities. The field survey reveals vulnerable engineering geological conditions and adverse environmental factors in the study area. It is found that a typical complete debris transport process may consist of two stages depending on the rainfall intensity. In the first stage, debris flows mobilized from a landslide have low mobility and their runout distance is quite modest; in the second stage, with an increase in water content they are able to travel a longer distance. Numerical simulations based on a multi-phase flow model are conducted to analyze the characteristics of the debris flows in motion, including the debris deposition profiles and runout distances in both stages. Overall, the numerical results are reasonably consistent with relevant field observations. Future debris flows may likely occur again in this area due to the presence of large soil blocks separated by tension cracks, rampant in the field; numerical simulations predict that these potential debris flows may exhibit similar characteristics to past events.

Heat Transfer in Pyroclastic Density Current‐Ice Interactions: Insights From Experimental and Numerical Simulations

AbstractStratovolcanoes are common globally, with high‐altitude summit regions that are often glacier‐clad and intersect the seasonal and perennial snow line. During an eruption, interaction between snow/ice and hot, pyroclastic deposits will potentially lead to extensive melt and steam production. This is particularly pertinent when pyroclastic density currents (PDCs) are emplaced onto and propagate over glacierised substrates. Generated melt and steam are incorporated into the flow, which can cause a transformation from a hot, dry granular flow, to a water‐saturated, sediment‐laden flow, termed a lahar. Both PDCs and ice‐melt lahars are highly hazardous due to their high energy during flow and long runout distances. Knowledge of the physics that underpin these interactions and the transformation to ice‐melt lahar is extremely limited, preventing accurate descriptions within hazard models. To physically constrain the thermal interactions we conduct static melting experiments, where a hot granular layer was emplaced onto an ice substrate. The rate of heat transfer through the particle layer, melt and steam generation were quantified. Experiments revealed systematic increases in melt and steam with increasing particle layer thicknesses and temperatures. We also present a one‐dimensional numerical model for heat transfer, calibrated against experimental data, capable of accurately predicting temperature and associated melting. Furthermore, similarity solutions are presented for early‐time melting which are used to benchmark our numerical scheme, and to provide rapid estimates for meltwater flux hydrographs. These data are vital for predicting melt volume and incorporation into PDCs required to facilitate the transformation to and evolution of ice‐melt lahars.

Air drag controls the runout of small laboratory landslides.

Laboratory granular landslides are smaller-scale, simplified, yet well-controlled versions of larger and often tragic natural landslides. Using systematic experiments and scaling analysis, we quantify the influence of grain size, fall height, and landslide volume on runout distance. We also determine the minimum landslide size required to observe this scaling, which we find is set by a combination of air drag, grain size, and fall height.

Density Stratification and Buoyancy Evolution in Pyroclastic Density Currents

AbstractPyroclastic density currents (PDCs) are density‐stratified along their vertical axis, with the near‐bed portion being denser than the upper portion, resulting from particle settling and ambient air entrainment at current margins. Whereas vertical density stratification likely influences mixing, sedimentation, and buoyancy of PDCs, many depth‐averaged models of PDC dynamics assume currents are well‐mixed. We investigated this discrepancy by performing sub‐aqueous laboratory experiments and conducted complementary numerical simulations to interrogate current dynamics at finer scales. Currents with small temperature difference with the ambient fluid become density‐stratified during propagation. The dynamics of such currents resemble two‐phase flows, in which particles move freely and particle concentration becomes stratified, but fluid density remains constant. Currents with large temperature difference with the ambient fluid, however, do not develop density stratification during propagation, due to current dynamics becoming dominated by the fluid phase and the lessening importance of particles. Currents that develop density stratification do not lift off from the bed within the domain of the setup, whereas poorly stratified currents do lift off, forming a rising plume. Strong density stratification within currents inhibits turbulence production, preventing entrained ambient fluid on current edges from mixing into current interiors. Poorly stratified currents are highly turbulent, have vigorous internal mixing, thereby achieving lift‐off. The strongly stratified currents are analogous to PDCs that result from eruption column collapse, maintaining fast velocity, low internal mixing, and high temperature over long distances. The poorly stratified currents are analogous to dilute ash‐cloud surges that develop atop basal avalanches, having short runout distances.

Multi-source remote sensing-based landslide investigation: the case of the August 7, 2020, Gokseong landslide in South Korea

Landslides pose a growing concern worldwide, emphasizing the need for accurate prediction and assessment to mitigate their impact. Recent advancements in remote sensing technology offer unprecedented datasets at various scales, yet practical applications demand further case studies to fully integrate these technologies into landslide analysis. This study presents a case study approach to fully leverage variety of multi-source remote sensing technologies for analyzing the characteristics of a landslide. The selected case is a landslide with a long runout debris flow that occurred in Gokseong County, South Korea, on August 7, 2020. The chosen multi-source technologies encompass digital photogrammetry using RGB and multi-spectral imageries, 3D point clouds acquired by light detection and ranging (LiDAR) mounted on an unmanned aerial vehicle (UAV), and satellite interferometric synthetic aperture radar (InSAR). The satellite InSAR analysis identifies the initial displacement, triggered by rainfall and later transforming into a debris flow. The utilization of digital photogrammetry, employing UAV-RGB and multi-spectral image data, precisely delineates the extent affected by the landslide. The landslide encompassed a runout distance of 678 m, featuring an initiation zone characterized by an average slope of 35°. Notably, the eroded and deposited areas measured 2.55 × 104 m2 and 1.72 × 104 m2, respectively. The acquired UAV-LiDAR data further reveal the eroded and deposited landslide volumes approximately measuring 5.60 × 104 m3 and 1.58 × 104 m3, respectively. This study contributes a valuable dataset on a rainfall-induced landslide with a long runout debris flow, underscoring the effectiveness of multi-source remote sensing technology in monitoring and comprehending complex landslide events.

Identifying rheological regimes within pyroclastic density currents

Pyroclastic density currents (PDCs) are the most lethal of all volcanic hazards. An ongoing challenge is to accurately forecast their run-out distance such that effective mitigation strategies can be implemented. Central to this goal is an understanding of the flow mobility—a quantitative rheological model detailing how the high temperature gas-pyroclast mixtures propagate. This is currently unknown, yet critical to accurately forecast the run-out distance. Here, we use a laboratory apparatus to perform rheological measurements on real gas-pyroclast mixtures at dynamic conditions found in concentrated to intermediate pumice-rich PDCs. We find their rheology to be non-Newtonian featuring (i) a yield stress where deposition occurs; (ii) shear-thinning behavior that promotes channel formation and local increases in velocity and (iii) shear-thickening behavior that promotes decoupling and potential co-PDC plume formation. We provide a universal regime diagram delineating these behaviors and illustrating how flow can transition between them during transport.

Inverse analysis of granular flows using differentiable graph neural network simulator

Inverse problems in granular flows, such as landslides and debris flows, involve estimating material parameters or boundary conditions based on a target runout profile. Traditional high-fidelity simulators for these inverse problems are computationally expensive, restricting the number of possible simulations. These simulators are also non-differentiable, making efficient gradient-based optimization methods for high-dimensional spaces inapplicable. Machine learning-based surrogate models offer computational efficiency and differentiability. However, they often struggle to generalize beyond their training data due to relying on low-dimensional input–output mappings that fail to capture the complete physics of granular flows. We propose a novel differentiable graph neural network simulator (GNS) that combines reverse mode automatic differentiation of graph neural networks with gradient-based optimization for solving inverse problems. GNS learns the dynamics of granular flow by representing the system as a graph and predicts the evolution of the graph at the next timestep, given the current state. The differentiable GNS demonstrates optimization capabilities beyond the training data. We demonstrate the effectiveness of our method for inverse estimation across single and multi-parameter optimization problems, including evaluating material properties and boundary conditions for a target runout distance and designing baffle locations to limit a landslide runout. Our proposed differentiable GNS framework solves inverse problems with orders of magnitude faster convergence than the conventional gradient-based optimization approach using finite difference.

A Hydrodynamic‐Based Physical Unified Modeling for Simulating Shallow Landslide Local Failures, Mass Release and Debris Flow Run‐Out Extent Behavior

AbstractAccurate prediction of shallow landslide occurrence and the subsequent motion range after transformation into debris flows is crucial for reducing disaster‐induced losses. The use of Cellular Automata‐based (CA) hydrodynamic models has seen increasing application in predicting landslides, debris flows, and other related hazards. However, previous CA‐based models have primarily focused on the motion and evolution process of debris flows, lacking detailed description about the dynamic instability associated with shallow landslides. In this study, we propose a comprehensive CA‐based model that is based on existing theories and improved models for simulating hydrological processes, sliding surface identification algorithms, threshold‐based mechanical interactions, material entrainment, and deposition. The model was applied to the Yindongzi (YDZ) landslides in Sichuan, China. The accuracy of the model was validated through comparisons with field investigation results and calculations based on shallow water equations. This model enables efficient and rapid prediction of shallow landslide occurrence time, volume, spatial distribution, and runout distance. Evaluation of the model’s predictive performance reveals an error range of −23.12% to +44.26% for YDZ landslides. Moreover, the influence of different shallow landslide failure patterns on the deposition and erosion of debris flows was analyzed. The results indicate that the failure patterns of shallow landslides significantly affect the deposition and entrainment capacity of debris flows. This study provides a novel approach for predicting the occurrence of shallow landslides and the subsequent motion, entrainment, and deposition after transformation into debris flows.

Analysis of landslide susceptibility and potential impacts on infrastructures and settlement areas (a case from the southeastern region of Türkiye)

Landslides have harmful effects not only on buildings but also on infrastructure and the natural environment. While they are typically triggered by natural events, such as heavy rainfalls and earthquakes, landslides can also be induced by anthropogenic activities, such as excavation and blasting. In certain regions, gigantic paleo-landslides exist, but triggering them is extremely difficult. However, triggering secondary landslides in gigantic paleo-landslides is relatively easy compared to the main corpus. The main purpose of this study was to produce a susceptibility map in a region in southeastern Türkiye and to discuss the impact of petroleum seismological investigation concerning the trigger of the landslides. For this purpose, a landslide inventory was compiled using geospatial data sets and field observations and used for landslide susceptibility mapping with the Random Forest algorithm. The accelerations sourced from blasting were also measured and the run-out distances were determined. A run-out distance map was produced using inverse distance weights. The study presents comprehensive insights by integrating a landslide susceptibility map and run-out distance map. It evaluates the impact of blasting on landslides through in-situ measurements and slope stability analyses. Findings indicate that no triggering effect on landslides was observed if the dynamite quantity remains below 4 kg and the blasting distance exceeds 10 m from the landslide.

Effects of slope topography on rock avalanche mobility and deposition: A 2-D discrete element method investigation

The impact of rock avalanches is a major concern in mountain areas. However, fundamental understanding and reliable prediction of the depositional area of rock avalanches remains inadequate. Here, an idealized numerical study of granular materials flowing down a slope is carried out using two-dimensional (2-D) discrete element method simulations. The effects of the slope geometry on the mobility and deposit morphology of the granular flow are studied in detail. It is found that the granular flow mobility increases with the curvature radius of the circular ramp, leading to a longer runout distance, which is explained from the viewpoint of energy transfer and dissipation. The results are expected to enhance understanding of the travel and deposition mechanisms of rock avalanches and other related geophysical flows.

Uncertainty Analysis of Post-Failure Behavior in Landslides Based on SPH Method and Generalized Geotechnical Random Field Theory

In slope stability analysis, the inherent heterogeneity and spatial variability of soil significantly influence the aftermath of landslides, including critical aspects like runout distance, influence distance, and volume. This research integrates Smoothed Particle Hydrodynamics (SPH) with random field theory to precisely model the large deformation events in slopes with anisotropic shear parameters, while leveraging Graphics Processing Unit (GPU) parallel computing to expedite the generation of random field samples and SPH simulations. This approach meticulously examines how spatial heterogeneity of soil affects slope instability, simulating soil parameters across varied geological settings. It considers the fluctuation scale of anisotropy, the cross-correlation of cohesion and the angle of internal friction, along with their coefficient of variation (CV), to elucidate their impact on landslide magnitude and severity. This study furnishes a robust tool for a holistic assessment of slope impacts and landslide volumes. Additionally, by delineating the computational efficiency disparities between GPUs and Central processing units (CPUs), it underscores the pronounced efficiency benefits of GPU computing. The insights garnered offer fresh perspectives and methodologies in slope stability analysis and disaster risk evaluation, contributing to the finer prediction and management of this prevalent and grave geological hazard.

Damage assessment of Siverek Castle during the Kahramanmaraş Earthquakes (Mw 7.7 and Mw 7.6) on 06 February 2023: Remediation and strengthening proposals

On February 6, 2023, two significant earthquakes with magnitudes (Mw) of 7.7 and 7.6 struck Turkey, occurring nine hours apart. In addition to the tragic loss of over 50,000 lives in the earthquakes centered in Kahramanmaraş, hundreds of thousands of engineering structures, such as residences, schools, hospitals, historical landmarks, highways, and more, were severely damaged. This study assesses the damages and risk scenario following the Kahramanmaraş earthquakes concerning Siverek Castle. In addition, remediation and strengthening proposals, required to eliminate the damage and the possible risk, have been developed. The initial stage involved observational damage assessments on the castle and surrounding slopes as part of field studies, identifying five different types of damage and potential risks. Subsequently, a precise 3D digital model of the damaged castle and its slopes was generated using the digital photogrammetry method. Additionally, geological and geophysical studies were conducted in the field to determine the characteristics of the mound structure, historical castle walls, soil and rock on the slope. Non-destructive, geophysical methods consisting Vertical Electrical Sounding (VES), Seismic Refraction Method (SRM) and Multichannel Analysis of Surface Waves (MASW) measurements were specifically employed in the area with historical remnants. To verify the obtained data, five boreholes were drilled in the lower parts of the slope, and experimental studies were conducted to determine the soil and rock material properties of the slope. In the numerical studies, a total of 54 2D stability analyses were performed under static, long-term static, and dynamic conditions. Additionally, 1000 different probabilistic rockfall analyses were conducted, both in 2D and 3D, to calculate the run-out distance, bounce height, velocity, and kinetic energies of the blocks that fell or were about to fall during the earthquake. In the final stage of the study, remediation and strengthening recommendations were prepared for the strengthening of the fortification walls and slopes where failures occurred, and stability analyses were conducted. Consequently, a design proposal recommending five distinct approaches to remediate and strengthen the castle and slopes impacted by the Kahramanmaraş earthquakes was endorsed by the relevant authorities, and construction has commenced. When the remediation and strengthening works are completed, the security of the cultural heritage will be ensured, and it is planned to be opened to visitors.

A mass transfer-based LES modelling methodology for analyzing the movement of submarine sediment flows with extensive shear behavior

This study employs the large-eddy simulation (LES) method to investigate the interaction of submarine sediment flows with extensive shear behavior and ambient water. This method is validated with good accuracy by simulating the head velocity and evolution geometries of a submarine mud flow with non-Newtonian fluid characteristics and a submarine turbidity current with Newtonian fluid characteristics in inclined and regular lock-exchange flume experiments. This study finds that the violent mass transfer at the interface of the submarine sediment flow and seawater is caused by numerous eddies, which significantly alter the submarine sediment flow's geometry, resulting in varying degrees of undulation, including the deposition pattern of the submarine sediment flow tail. The acceleration zone, where the velocity of the submarine sediment flow increases significantly at this undulation, propels the sediment flow forward, supporting its long-distance transport. Furthermore, the turbulence and mass transport characteristics of submarine turbidity currents with low dynamic viscosity Newtonian fluid characteristics are stronger than those of submarine mud flows with high dynamic viscosity non-Newtonian fluid characteristics. Therefore, when submarine landslides develop into later stages, such as submarine turbidity currents with high velocity, large volume, and long run-out distance characteristics, more attention must be given to the mass transport process.

Spatial heterogeneity and temporal tendency of channeled snow avalanche activity retrieved from Landsat images in the maritime snow climate of the Parlung Tsangpo catchment, southeastern Tibet

The spatial heterogeneity and temporal tendency of snow avalanche (hereafter called avalanche) activities are responses to variations in the inducing environment under climate warming and epitomize the repercussions of the global cryosphere on climate warming. This paper focuses on channeled avalanches in the marine snow climate region of the Parlung Tsangpo catchment in southeast Tibet as an example. Through field investigations, we identify the spatial extents of avalanche paths, while historical avalanche flow paths from the past 35 years (1986/1987–2021/2022) within these paths are interpreted using Landsat optical images. Statistical analysis is then employed to derive spatial heterogeneity and temporal tendencies within and between years. The results indicate that the runout altitudes of historical avalanches primarily range from 3468 m to 4051 m, with average flow directions predominantly following the northwest, north and northeast directions. Avalanche activity peaks between February and April, with longer runout distances observed during this period. Regarding interannual regularity, the evolution of the runout distance, runout altitude, and height difference of avalanche flow paths over the past 35 years demonstrates a cyclic evolution akin to a sine function. Additionally, a moderate correlation between the interannual variation in historical avalanche activity intensity and the Southern Oscillation Index was observed. These findings strengthen the understanding of the temporal evolutionary pattern of avalanches in response to climate warming, providing valuable insights into the channeled avalanche occurrences in the maritime snow climate of southeastern Tibet.

Forest damage and its braking effect on the extreme snow avalanche on Mt. Nodanishoji, Japan, in 2021

ABSTRACT An extreme snow avalanche occurred on Mt. Nodanishoji, Japan, in 2021. This avalanche was the second largest ever documented in Japan and destroyed many trees and structures. Despite the increasing interest in avalanche disaster mitigation effects of forests, there are limited opportunities to obtain actual data sets on avalanches and forests. In this study, we reconstructed the avalanche velocity based on the cedar forest damage and simulated the avalanche flow using the dynamical run-out model Titan2D to reveal the avalanche movement and ascertain the braking effect of the forest on the avalanche. We successfully simulated the whole movement of the extreme avalanche with a horizontal runout distance of 2,800 m from the starting zone at an altitude of 1,700 m to the run-out zone considering the effect of the forest by increasing the frictional parameters in the model. Whereas in the case of no forest, the avalanche spread beyond its actual reach, considering the forest, the run-out distance decreased and was consistent with the observed reach. Comparing the results with and without forests, we ascertained the distinct braking effect of the forest on the extreme avalanche and quantify it in terms of a locally increased friction angle.

Modeling Shallow Landslide Runout Distance in Eocene Flysch Facies Using Empirical–Statistical Models (Western Black Sea Region of Türkiye)

Uncertainties related to runout distances in shallow landslide analyses may not only affect lives but may also result in economic losses. Owing to the increase in shallow landslides, which are especially triggered by heavy rainfall, runout distances have been investigated to decipher whether applications of a functional runout distance are feasible. This paper aims to give insights into the modeling of the shallow landslide runout probability in Eocene flysch facies in the Western Black Sea region of Türkiye. There are two main stages in this study—which are dominated by empirical models, the detection of initiation points, and propagation—which help us to understand and visualize the possible runout distances in the study area. Shallow landslide initiation point determination using machine learning has a critical role in the ordered tasks in this study. Modified Holmgren and simplified friction-limited model (SFLM) parameters were applied to provide a good approximation of runout distances during the propagation stage using Flow-R software. The empirical model parameters suggested for debris flows and shallow landslides were investigated comparatively. The runout distance models had approximately the same performance depending on the debris flow and shallow landslide parameters. While the impacted total runout areas for the debris flow parameters were predicted to amount to approximately 146 km2, the impacted total runout areas for the shallow landslide parameters were estimated to be about 101 km2. Considering the inclusion of the RCP 4.5 and RCP 8.5 precipitation scenarios in the analyses, this also shows that the shallow landslide and debris flow runout distance impact areas will decrease. The investigation of runout distance analyses and the inclusion of the RCP scenarios in the runout analyses are highly intriguing for landslide researchers.

A Mechanistic Model and Experiments on Bedrock Incision and Channelization by Rockfall

AbstractRockfall and rock avalanches are common in steep terrain on Earth and potentially on other planetary bodies such as the Moon and Mars. Since impacting rocks can damage exposed bedrock as they roll and bounce downhill, rockfall might be an important erosive agent in steep landscapes, even in the absence of water. We developed a new theory for rockfall‐driven bedrock abrasion using the ballistic trajectories of rocks transported under gravity. We calibrated this theory using laboratory experiments of rockfall over an inclined bedrock simulant. Both the experiments and the model demonstrate that bedrock hillslopes can be abraded by dry rockfall, even at gradients below the angle of repose, depending on the bedrock roughness. Feedback between abrasion and topographic steering of rockfall can produce channel‐like forms, such as bedrock chutes, in the absence of water. Particle size has a dominant influence on abrasion rates and runout distances, while the hillslope angle has a comparatively minor influence. Rockfall transport is sensitive to bedrock roughness; terrain with high friction angles can trap rocks creating patches of rock cover that affect subsequent rockfall pathways. Our results suggest that dry rockfall can play an important role in eroding and channelizing steep, rocky terrain on Earth and other planets, such as crater degradation on the Moon and Mars.

Investigation of granular flow run-out behavior under dilative and compressive Coriolis conditions using DEM simulation

Centrifuge modeling allows granular flows to be simulated under stresses characteristic of full-scale flows, while maintaining repeatability. However, the impact of the Coriolis effect on the run-out behavior of dry granular flows is not fully understood. In this study, using the discrete element method (DEM), we conducted simulations of dry granular flow both with and without Coriolis (dilative and compressive) conditions to analyze the impact of the Coriolis effect on granular run-out mobility, flow structure, and granular interaction. For unsteady flows, the dilative Coriolis force increased the moving distance of the flow centroid by 60%–70% and increased the maximum kinetic energy by 5%–17%, whereas those parameters were reduced by 30% and 2%–9%, respectively, under compressive Coriolis conditions. Results showed that selecting a lower centrifugal acceleration by reducing the rotational angular velocity in physical modeling is ineffective for realizing a weaker Coriolis effect. This study established that using a larger centrifuge could mitigate the Coriolis effect, but that this outcome became less notable as the centrifugal radius increased. Additionally, we suggest a preliminary relation that could be used to correct the results of experimental granular flow final run-out distance obtained using a geotechnical centrifuge.

Granular-fluid avalanches: the role of vertical structure and velocity shear

Field observations of debris flows often show that a deep dry granular front is followed by a progressively thinner and increasingly watery tail. These features have been captured in recent laboratory flume experiments (Taylor-Noonan et al., J. Geophys. Res.: Earth Surf., vol. 127, 2022, e2022JF006622). In these experiments different initial release volumes were used to investigate the dynamics of an undersaturated monodisperse grain–water mixture as it flowed downslope onto a horizontal run-out pad. Corresponding dry granular flows, with the same particle release volumes, were also studied to show the effect of the interstitial fluid. The inclusion of water makes debris flows much more mobile than equivalent volumes of dry grains. In the wet flows, the formation of a dry front is crucially dependent on the heterogeneous vertical structure of the flow and the velocity shear. These effects are included in the depth-averaged theory of Meng et al. (J. Fluid Mech., vol. 943, 2022, A19), which is used in this paper to quantitatively simulate both the wet and dry experimental flows using a high-resolution shock-capturing scheme. The results show that velocity shear causes dry grains (located near the free surface) to migrate forwards to create a dry front. The front is more resistant to motion than the more watery material behind, which reduces the overall computed run-out distance compared with debris-flow models that assume plug flow and develop only small dry snouts. Velocity shear also implies that there is a net transport of water to the back of the flow. This creates a thin oversaturated tail that is unstable to roll waves in agreement with experimental observations.

Submarine pyroclastic deposits from 7.3 ka caldera-forming Kikai-Akahoya eruption

Extensive submarine pyroclastic deposits were discovered around the Kikai caldera, Southwest Japan, which originated from the caldera-forming Kikai-Akahoya (K-Ah) eruption that occurred at 7.3 ka. This submarine pyroclastic unit originated from a pyroclastic density current (PDC) that entered the sea and was transformed into a subaqueous density current. Our high-resolution marine seismic reflection surveys reveal that the uppermost unit exhibiting prominent seismic facies thins radially away from the caldera and covers >4500 km2 of the seafloor. The estimated volume of the submarine deposits is >71 km3 based on the isopach map. Seismic sequence stratigraphic analyses and correlation of shard glass compositions from the piston core and remotely operated vehicle samples with those from subaerial outcrops identified the unit as pyroclastic deposits produced by the K-Ah eruption. The geomorphological features of the unit indicate a long runout distance (i.e., 40 km), exponential thinning with increasing distance from the source, and a depression-filling nature of the deposits suggesting that the unit was formed predominantly by a density current that entered the water. The quantitative comparisons of geometric shape and its thinning rate, including that for non-volcanic density currents, indicate that the subaerial PDC entering into the water was transported as a dilute density current in the water. We propose that the formation of these dilute density currents transformed by PDCs probably requires sufficient water depth, as inferred also from previous analog experiments. Adding on-land ignimbrite of 5 km3 and widespread tephra of 249–374 km3, our estimate of submarine pyroclastic deposits of >71 km3 leads to a total bulk volume of the K-Ah eruption of 332–457 km3 (133–183 km3 in DRE), making it probably the largest eruption of the Holocene.