In this study, we use a two-dimensional high-order ice flow model named as PoLIM (Polythermal Land Ice Model) . PoLIM is developed according to the hydrostatic approximation, where the horizontal gradient of the vertical velocity is neglected in the viscous rheology and momentum equation . The momentum conservation equation of PoLIM is given by: 1∂∂x(2τxx+τyy)+∂τxy∂y+∂τxz∂z=ρig∂s∂x, where x represents the streamline direction, y represents the transverse direction, and both x and y axes lie in the horizontal plane, while z represents the vertical direction, and s represents the surface elevation of the glacier. In addition, ρi represents the ice density (set as a constant), and g represents the acceleration due to gravity. Finally, τij is the component of the deviatoric stress tensor, which can be calculated from the strain rate 2τij=2ηϵ˙ij, where ϵ˙ij(i,j=1,2,3) are the corresponding strain-rate components, and η is the effective viscosity, calculated as: 3η=12A-1/nϵ˙e(1-n)/n, where n is the flow law exponent and the effective strain rate ϵ˙e is defined as 4ϵ˙e2≃∂u∂x2+∂v∂y2+∂u∂x∂v∂y+14∂u∂y2+14∂u∂z2. Then the effective stress (σe) can be calculated by 5σe=2ηϵ˙e. Sedongpu Glacier is a typical maritime glacier in southeastern Tibet. In this study, we assume Sedongpu Glacier is temperate and set A as a constant for ice temperature close to 0 °C (Table 1), i.e., we do not include a temperature solver in our model. At the glacier surface, we use a stress-free boundary condition, and at the glacier base, we apply a linear friction law prior to the occurrence of glacier detachment, 6τb=-βub, where τb is the basal stress, ub is the basal sliding speed, and β is the basal friction parameter. β is hold constant in time before detachment. The glacier evolution is described by the mass continuity equation, 7∂H∂t=-∂(u‾H)∂x+ms, where H is ice thickness, t is model time, u‾ is depth-averaged velocity, and ms is surface mass balance.

The model applies a finite difference discretization method. We set model time step to 0.5 s, and set ms to 0 given a very short model time span (25 min) in this study. We use a Δx=48 m in x and 20 vertical layers in z with a terrain-following coordinate. By these numerical settings, our model can satisfy the Courant–Friedrichs–Lewy (CFL) condition and keep numerical stability during forward runs. All model constants and parameters can be found in Table 1. Note that the values of critical strain and intact strength are from .

From the model descriptions above, we can see that glacier movement consists of two components: internal deformation and basal sliding. Internal deformation is influenced by ice viscosity. Decreased viscosity lead to increased ice flow. The basal sliding is controlled by the friction at ice-bed interface. Factors such as soft sediments and basal meltwater lubrication will reduce the basal friction, consequently accelerating ice flow, which are not considered separately but taken as a result of changing basal frictions in the sliding law in this study.

Before simulating the Sedongpu detachment processes, we need to initialize the ice flow model using observed ice surface velocity data. Following and , we solve the basal friction coefficient using the Robin inversion algorithm by iteratively minimizing the cost function J across the basal domain 8J=∫ΓbβuD-uN2dS, where uD is the observed ice surface velocity and uN is the ice surface velocity solved in the model by applying a stress-free surface boundary condition. This cost function represents the mismatch between the Neumann and Dirichlet velocity fields. Following , the basal friction coefficient was updated as follows, 9βi+1(x,y)=βi(x,y)+αβubN2-ubD2, where βi is the basal friction at the ith iteration step, ubN and ubD are basal velocity for Neumann and Dirichlet iterations, αβ is a positive parameter that determines the step size, given as 10αβ=βnubDpubNp-ubDpubN2-ubD2, where p is a positive parameter, as given in Table 1.

The overall model framework can be seen in Fig. . In order to simulate the tipping mechanism of Sedongpu detachment, we implement a numerical scheme that couples basal slip and ice stiffness, following the approach in , which integrates the continuum and discrete processes of ice flow. In this scheme, the new ice viscosity is calculated as 11ηnew=ηmin⁡+1η+1ηdiff+1ηplas-1, where η is the viscosity for Glen's power law creep flow (Eq. ), ηdiff and ηplas are the viscosity for diffusion creep and plastic deformation when ice failure occurs (see the supplementary materials in ), respectively. ηmin⁡ is a tunable minimum viscosity for numerical stability. The inclusion of the viscosity ηplas in the fracture process indicates that stress does not increase with increasing strain when the ice mass reaches the yield stress.

The presence of a “plastic” viscosity results in a low stiffness value and high velocity, as the ice viscosity remains relatively low. This phase corresponds to the development of ice crevasses and prevalent ice failure in reality. Additionally, the yield strength is not stable and constant; it decreases with the acceleration of ice flow, resulting in an unstable ice flow pattern , 12τy=max⁡τc-(τc-τmin⁡)ϵpϵc,τmin⁡, where τy is the yield strength of ice, τc is the intact strength (see Table 1), τmin⁡ is a tunable, prescribed minimum yield stress, ϵc is the critical strain, and ϵp is the plastic strain accumulated in faults and fractures which can be calculated during the model run. For the basal sliding law, we also consider the impact of yield strength of basal ice, similar to , 13τb=-1β+ubτy-1ub, where τb and ub are basal stress and speed, respectively, and β is the basal friction we use before the detachment. Here τy is the ice yield stress at the bed, representing interactions between basal ice and soft till, i.e., basal ice stress will continue to decrease if it exceeds yield strength. With this improvement, basal slip is enhanced as ice failure increases and basal ice strength decreases. Therefore, this mechanism can better capture the dynamics of the soft and thick till layer underneath Sedongpu glacier, which could deform significantly during detachment .

In Fig. , we present a diagram of our numerical modeling processes. In traditional ice flow models (e.g., Glen's flow law), increased stress enhances viscosity during the elastic deformation phase, promoting slow and stable ice motion. However, basal sliding formulations (e.g., the Weertman sliding law) relate basal friction to velocity and stress while neglecting ice stiffness. This limitation hinders the simulation of ice detachment processes.

The proposed model framework incorporates the plastic phase of ice flow by introducing a yield stress tipping point, establishing two positive feedback mechanisms: (1) within internal ice deformation and (2) at the ice-bed interface. We first initialize the ice flow model and compute stresses during forward simulations. These stresses are then compared to the ice yield strength. When stress reaches this threshold, ice stiffness and yield strength decrease, triggering further yielding and increasing glacier vulnerability. Then, reduced basal ice stiffness lowers basal friction, facilitating accelerated sliding. This dual process creates a positive feedback mechanism coupling ice stiffness and basal slip.

As shown in Fig. , we inverted for the basal sliding coefficient of Sedongpu Glacier. The 2018 Sedongpu Glacier detachment occurred on 17 October. Prior to this event, several ice-rock avalanches in the glacier's upper region between June 2014 and October 2017 increased flow velocity from around 0.3 m d⁻¹ in 2017 to 25 m d⁻¹ by September 2018 . Due to insufficient high-resolution observations, it is difficult to accurately simulate the glacier's acceleration during this period. Therefore, to model the 2018 detachment, we initialize our simulation using the 2015–2018 mean observed ice velocity preceding the event. The results show faster flow in upstream regions with lower basal friction (likely due to steeper slopes), while downstream regions exhibit slower motion where greater ice thickness corresponds to higher basal friction.

Environmental forcings may have acted as external triggers for the 2018 Sedongpu detachment. From January to October 2018, the region experienced a historical mean temperature increase rate of 0.039 K yr⁻¹ . Although precipitation during this period was below historical observations, intense rainfall occurred 2–4 d before the detachment event. This rainfall likely softened basal ice and accelerated flow, altering internal ice dynamics and ultimately triggering the abrupt collapse.

As shown in Fig. , our simulation successfully reproduces the decrease in ice thickness and increase in ice velocity associated with a glacier detachment. We activated the yield strength and stiffness-slip coupling mechanism at t0=5 min after confirming model stability pre-detachment, then ran the simulation for 25 min. Within several time steps, the bulk viscosity of the glacier decreased to its minimum (ηmin⁡), significantly enhancing ice fluidity. Consequently, ice velocity surged from less than 1 m h⁻¹ to around 90 000 m h⁻¹, with a mean speed of approximately 34 000 m h⁻¹ over the 25 min simulation period. As the glacier rapidly thinned due to mass loss, velocity stabilized at lower values, reaching a new steady state.

The mean effective stress in Sedongpu Glacier increased drastically from 200 kPa pre-detachment to around 1000 kPa during detachment acceleration. Generally, higher ice flow velocities result in greater englacial stresses, increasing the vulnerability of ice regions to detachment instability. During the simulation, rapid mass transfer from upstream to downstream reduced glacier thickness by ∼80 % within 6.3 min and 90 % within 11 min after t0 (Fig. ). Post-collapse oscillations in velocity and stress arise from our prescribed minimum ice thickness (1 m) and the internal numerical instability, an artificial constraint that creates non-smooth thickness distributions and corresponding fluctuations. Our modeled detachment duration (6.7 min) and mean velocity (approximately 20 m s⁻¹, i.e., 72 000 m h⁻¹) align closely with estimates for the 17 October 2018 event from a previous study . This validation is further strengthened by seismic data indicating a 5 min detachment duration .

In this study, we assume a spatially uniform yield strength at model initialization (hereafter defined as “initial yield strength”) across Sedongpu Glacier. The initial yield strength is a crucial parameter that determines abrupt glacier detachment. As it typically varies between 100–1000 kPa , we conducted sensitivity experiments to assess its impact on glacier dynamics. This allows us to estimate the destabilizing threshold (tipping point) for Sedongpu Glacier. Figure a shows cases with initial yield strengths between 300 and 500 kPa. Detachment occurs only when the initial yield strength is set below 440 kPa, indicating that the mechanical properties of glacier ice control sudden collapse when failure exceeds critical thresholds. While subglacial hydrology-ice dynamics coupling can explain glacier surge mechanisms , it cannot reproduce extreme detachment instability without accounting for dramatic ice weakening. This is demonstrated by cases with initial yield strengths above 450 kPa in Fig. a, where glacier ice remains intact throughout the simulation.

Additionally, the rate of ice loss can be significantly influenced by two tuning parameters, τmin⁡ (prescribed minimum yield stress) and ηmin⁡ (prescibed minimum viscosity) (Eqs. and ), the choice of model parameters, in our model. These parameters determine the maximum ice flow fluidity and thus can greatly impact the rate of mass loss during detachment. As shown in Fig. b, for the same initial yield stress value (300 kPa), a combination of lower minimum stress (τmin⁡) and minimum viscosity (ηmin⁡) values leads to a greater reduction in glacier mass. However, this does not change the tipping point of glacier collapse, which is determined by ice flow dynamics and mechanical properties. Once some ice regions yield, the yield strength further decreases, making the glacier even more vulnerable to fracturing. Consequently, this plastic, accelerating ice flow quickly affects the entire glacier, leading to drastic detachment.

We should note that the yield strength of glacier ice is generally an unknown parameter and is highly heterogeneous in space. In this study, we approximate this tipping threshold value as a spatially uniform constant for the convenience of explaining the critical role ice strength plays in glacier detachment. The positive feedback between the weakening of ice stress beyond yield strength and the rate-weakening basal friction likely contributed together to the collapse of the Sedongpu Glacier in 2018.

We can gain further insight into the detachment mechanism from Fig. , which shows the dynamic changes of Sedongpu Glacier at three subsequent time steps after activating the stiffness-slip coupling mechanism at time t0. When the initial yield strength is set to 300 kPa, the ice stress exceeds the yield strength near the glacier's head, terminus, and around km 1.3 at t0. By the next time step, the ice stress across the entire glacier surpasses the yield strength, resulting in whole plastic deformation and a significant acceleration of ice flow.

However, when the initial yield strength is increased to 430 and 500 kPa, the plastic deformation regions near the head and terminus disappear after updating the velocity and ice thickness in the following two time steps. At 430 kPa, the entire glacier is in plastic deformation by the third time step, and the ice velocity surges dramatically to nearly 100 000 m h⁻¹, indicating glacier detachment. In contrast, at 500 kPa, the glacier remains stable over the next three time steps.

Previous studies by and conducted in-depth analyses of the 2016 Aru Glacier collapse, revealing that the catastrophic event was controlled by multiple factors, including a deformable substrate, increased driving stress, temperate ice conditions, and connections to subglacial water. The transition from slow ice movement to catastrophic instability may have developed over months or even years before the collapse. In this study, we focus on the dynamic instability during abrupt glacier detachment – a process that can occur within minutes. We argue that the transition from elastic to plastic ice deformation likely plays a non-negligible role in this rapid phase. Once ice stress exceeds the yield strength, a tipping point is reached, triggering localized acceleration that abruptly propagates across the entire glacier. This leads to highly fractured ice geometry within seconds to minutes. Such a mechanism creates a positive feedback mechanism of accelerating ice flow and strength reduction – a process traditionally not fully considered in numerical glacier flow simulations.

This glacier detachment tipping mechanism may also apply to other high-risk glaciers surrounding the Sedongpu Valley. For example, the Zelongnong Glacier (Fig. a) represents a potential candidate for future detachment events. By assuming dynamic characteristics similar to Sedongpu (e.g., comparable initial yield strength), we could assess Zelongnong's detachment risk through surface velocity monitoring and numerical simulations of its internal stress regime. Implementing such an approach would require detailed investigations of glacier geometry to establish a reliable ice flow model and develop an effective early warning system.

Similar to , our modeling approach is still based on the Glen’s flow law framework but incorporates a novel stiffness-basal slip coupling scheme. While we assume constant ice density during detachment, this simplification may limit the model’s ability to fully capture the dynamics of Sedongpu Glacier's highly fractured detachment. The continuum modeling scheme we employ simultaneously accounts for ice flow and failure, though it cannot fully replicate discrete methods in simulating ice collapse processes. In addition, our bed elevation extraction – based on pre- and post-detachment geometry comparisons – introduces potential uncertainties. These arise from the soft basal sediment characteristics of Sedongpu Glacier and possible subglacial geometry alterations during detachment.

Furthermore, our model does not incorporate thermal coupling or basal hydrology schemes, potentially neglecting key physical mechanisms involved in glacier detachment. For instance, identified a velocity-strengthening-weakening transition that governs surge initiation, though their framework assumes intact ice and slow movement–conditions that may not adequately capture rapid detachment dynamics. While we acknowledge the importance of ice-bed interactions with basal hydrology , our current implementation employs a simplified sliding law (Eq. ) to couple basal till strength with ice flow. This approach, though computationally efficient, could be enhanced in future work to better represent these complex processes.

analyzed the force balance of simplified, slab geometries and marked Sedongpu Glacier as instable. In fact, for stable glaciers with basal cavities, basal drag is constrained by an upper limit known as Iken's bound , 14τb/N⩽mmax, where τb is the basal shear stress, N is the effective pressure and mmax is the maximum value of the up-glacier-facing slopes of obstacles. Here we assume N is the overburden ice pressure (no basal water pressure) and set mmax to the maximum bed slope. Figure  shows that once the detachment instability mechanism is triggered at t0, the ratio τb/(Nmmax) in the upstream region of Sedongpu Glacier rapidly exceeds 1 (violating Iken's bound), which aligns closely well with the timing of the detachment event.