Our model (RTSEvo v1.0) simulates RTS evolution by discretizing the landscape into a grid of cells (pixels). Unlike LUCC models that often manage transitions among multiple land cover types, our model simplifies the system to a binary classification. Each cell exists in one of two states: non-RTS (value = 0) or RTS (value = 1). This focus allows the framework to concentrate on the irreversible transition of cells from a non-RTS to an RTS state over annual time steps. This state transition is governed by a modular framework designed to integrate regional-scale trends with local-scale drivers (Fig. 1).

The framework consists of three core, interlinked modules. (1) RTS areal demand forecasting module: This module projects the total RTS area for the target year, establishing a top-down, macro-scale constraint on overall RTS expansion. (2) Base occurrence probability mapping module: This module uses machine learning to calculate the baseline probability of RTS initiation for each individual pixel based on its unique environmental characteristics (e.g., topography, climate, geology). (3) Constrained spatial allocation module: This module serves as the dynamic engine of the model. It iteratively allocates new RTS cells on the landscape by combining the base occurrence probability with spatial interaction rules (neighborhood and retrogressive erosion effects) until the estimated total area demand is met.

The model is calibrated using a historical RTS distribution map from a reference year. The optimal model parameters are determined by systematically tuning them to maximize the agreement between the simulated and observed RTS patterns from that reference year.

A key constraint for the simulation is the total new area of RTS to be allocated in a given year. To prevent uncontrolled expansion, we first forecast this regional demand. We employed Holt's linear trend method, an exponential smoothing technique well-suited for time-series data exhibiting a clear trend (Holt, 2004), which has been observed for RTS growth on the QTP since 2011 (Maier et al., 2025b). The method uses a level equation (current magnitude), a trend equation (rate of change), and a forecast equation: 1Levelequation:lt=ayt+(1-a)lt-1+bt-1Trendequation:bt=β*lt-lt-1+1-β*bt-1Forecastequation:y^(t+h|t)=lt+hbt where lt is the estimated level (baseline area) at time t, bt is the estimated trend (growth rate), yt is the observed area at time t, and y^(t+h|t) is the forecasted area for h time steps into the future. The smoothing parameters for level (α) and trend (β*) range from 0 to 1 and control the weighting of recent versus past observations.

This module quantifies the intrinsic suitability of each pixel for RTS formation based on a suite of environmental driving factors, independent of its spatial context. We tested two widely used machine learning algorithms for this task: Logistic Regression (LR) and Random Forest (RF).

LR is a generalized linear model that calculates the probability of an outcome using the sigmoid function, providing a clear, interpretable relationship between the drivers and RTS occurrence (Cramer, 2003). The probability Pi for pixel i is given by: 2PiXi=11+e(-z) where Xi represents the feature vector for a single pixel i, containing the values of all environmental driving factors for that specific pixel, and z=w1x1i+w2x2i+…+wnxni+b, is the linear combination of weighted predictor variables. w represents the weights associated with each predictor variable, and b is the bias term.

RF is an ensemble learning algorithm that builds a multitude of decision trees and aggregates their outputs. It is robust to non-linear relationships and interactions between variables. The probability is calculated as the proportion of trees in the forest that classify the pixel as an RTS (Breiman, 2001; Sun et al., 2021): 3PiXi=∑n=1Treetotal1TreenXi=1Treetotal where 1(⋅) is the indicator function and Tree_total is the total number of trees in the forest. Treen(Xi) refers to the prediction from a single decision tree within the RF, i.e., the output of the nth tree when it is given the feature vector Xi as input.

The performance of machine learning models is highly dependent on the selection of their hyperparameters, which are settings that control the learning process itself (Probst et al., 2019). To find the optimal configuration for both the RF and LR models, we implemented a systematic tuning process. While traditional methods like Grid Search and Randomized Grid Search are common, they can be computationally inefficient, especially with many parameters. Therefore, we employed Latin Hypercube Sampling (LHS), a more advanced statistical method for parameter optimization. LHS is superior because it explores the parameter space more efficiently by dividing each parameter's range into equal intervals and sampling exactly one value from each interval, ensuring a more uniform and representative coverage with fewer trials (McKay et al., 1979). We first defined a plausible search range for each key hyperparameter in the RF and LR models (Table 1). For RF, this included parameters like the number of trees (n_estimators) and maximum tree depth (max_depth); for LR, it included regularization strength (C) and the optimization algorithm (solver). LHS was used to generate 100 unique combinations of hyperparameters from these ranges. Then each parameter combination was evaluated using 10-fold cross-validation accuracy as the objective function. The hyperparameter combination that resulted in the highest average cross-validation accuracy was selected as the optimal configuration for the final model used for base occurrence probability mapping.

This module transforms the static probability map from Module 2 into a dynamic RTS distribution that adheres to the area demand from Module 1. This is achieved through an iterative process within a cellular automata framework (Wolfram, 1983; Toffoli and Margolus, 1987). At each iteration k, a total transition probability (PTotal,ik) is calculated for every non-RTS cell, integrating the base probability with four dynamic factors: 4PTotal,ik=Pi×Uik×Erosionik×RAik×Inertiaik where Pi is the base occurrence probability representing the intrinsic suitability of pixel i, as calculated in Module 2; Uik represents the neighborhood effect that accounts for spatial autocorrelation, based on the principle that a new RTS is more likely to form near existing ones; Erosionik is a retrogressive erosion factor, a novel component designed to mimic the characteristic upslope (headward) retreat of RTS; RAik is a stochastic factor designed to simulate the inherent randomness and unmodeled variables in natural systems; and Inertiaik denotes an adaptive inertia coefficient serving as a dynamic regulator that accelerates or decelerates the overall rate of new RTS allocation to ensure the final simulated area matches the target area demand from Module 1.

The neighborhood effect factor is calculated as the density of RTS cells within a defined neighborhood window: 5Uik=∑N×N1sik-1=1N×N-1×w where the numerator counts RTS cells in an N×N window at the previous iteration (k-1) and w is a weight factor. 1(sik-1=1) is an indicator function that counts how many neighboring cells are already in the RTS state (s=1).

The retrogressive erosion factor assigns a higher probability weight to cells located in the direction opposite to the local slope aspect (Luo et al., 2024a), thereby promoting directional growth. The directional weight (wmn) is calculated based on the angular difference (Δθ) between the potential growth direction and the theoretical erosion direction (θerosion), which is 180° from the slope aspect, representing how closely its direction aligns with the ideal erosion path. The equations are given as follows: 6θerosion=θaspect+180°mod360°θmn→ij=arctan⁡2(i-m,n-j)mod360°Δθ=min|θmn→ij-θerosion|,360°-|θmn→ij-θerosion|wmn=cos⁡(Δθ/2)Erosionik=∑N×Nwmn×1smnk=1∑N×Nwmn where θaspect is the standard slope aspect for the cell calculated from the digital elevation model (DEM), and θmn→ij is the azimuth angle from a central cell at coordinates (i, j) to each of its neighbors at coordinates (mn). 1(smn=1) is an indicator function (where state s=1). Erosionik is thus calculated as a proportion of a numerator term that sums the directional weights (wmn) of all neighboring cells that are currently in the RTS state, over a denominator that is the sum of the directional weights of all neighbors, regardless of their state.

The stochastic factor (RAit) is based on an extreme value distribution (Coles, 2001; Davison and Huser, 2015): 7RAik=1+βstoch×(-log⁡R)αstoch-0.5 where R is a random value between 0 and 1, and αstoch and βstoch control the shape and magnitude of the perturbation. The search range of αstoch was set to (0.01, 0.5) for practical purposes, as this range ensures the introduction of moderate, plausible fluctuations without destabilizing the model. The range of βstoch was set to (0.1, 1) which aims to balance the influence of randomness in the model.

The inertia coefficient is calculated by a piecewise function (Eq. 8). The core variable is Dk, which represents the difference between the number of simulated RTS cells and the required number (the demand) at iteration k. 8Inertiak=Inertiak-1ifDk-1≤Dk-2Inertiak-1×Dk-2Dk-1ifDk-1<Dk-2<0Inertiak-1×Dk-1Dk-2if0<Dk-2<Dk-1 Once the total transition probability (PTotal,ik) is calculated for each non-RTS cell, a probability threshold method is used to determine if a state change occurs. If PTotal,ik>PThresholdk, the cell's state transitions from non-RTS (0) to RTS (1). Crucially, this state transition is assumed to be irreversible; once a pixel converts to the RTS state, it remains in that state for all subsequent time steps of the simulation. This entire allocation process continues iteratively. The simulation for a given year concludes when the total area of simulated RTS cells meets the target demand projected by Module 1.

The Constrained Spatial Allocation module contains several key parameters (e.g., neighborhood size N, neighborhood weight w, stochastic shape parameters αstoch and proportional coefficient βstoch) that require calibration (Table 2). We implemented a systematic calibration procedure using LHS to efficiently sample the multi-dimensional parameter space. For each parameter set generated by LHS, the model was run to simulate the RTS distribution for a historical reference year. The performance of each run was evaluated by comparing the simulated map to the actual observed map using the Figure of Merit (FoM) metric, which measures the accuracy of change detection. The parameter set that yielded the highest FoM was selected as the optimal configuration for future simulations.

We designed four experiments to systematically evaluate the performance of both the individual model components and the integrated framework, as well as its cross-regional generalizability.

Experiment 1: Areal Demand Forecasting. To test the capability of this time series forecasting module, we trained the Holt's linear trend model using the observed total RTS area in the Beiluhe Basin for each year from 2016 to 2020. The trained model was then used to predict the total regional RTS area within the basin for 2021 and 2022. The performance was evaluated using the coefficient of determination (R2) and the Mean Absolute Percentage Error (MAPE).

First, the κ coefficient (Eq. 9) and F1 Score (Eq. 10) were used to measure overall spatial accuracy. This metric quantifies the level of agreement between the simulated and observed maps, correcting for agreement that could have occurred by chance (Cohen, 1960). It ranges from -1 to 1, with values closer to 1 indicating higher consistency between the simulated and actual data. 9κ=p0-pe1-pe×100% where p0 is the proportion of correctly classified cells and pe is the expected agreement by chance. 10F1=2⋅precision⋅recallprecision+recall where “precision” is the proportion of predicted RTS that are actually RTS, and “recall” is the proportion of actual RTS that are correctly predicted.

Second, FoM (Eq. 11) was used to specifically assess the model's change detection capability (Pontius et al., 2008). FoM is a highly stringent metric that focuses exclusively on the model's ability to correctly simulate new RTS growth. It ranges from 0 to 1, with higher values indicating a more accurate capture of the evolution process. 11FoM=HitMiss+Hit+Falsealarm×100% where “Hit” is the number of pixels that were correctly simulated as new RTS growth, “Miss” is the number of pixels that were actual new RTS growth but were not identified by the model, and “False alarm” is the number of pixels that the model incorrectly simulated as new RTS growth, but in reality, did not change.

Finally, the global Moran's I index (Eq. 12) was used to evaluate the model's ability to reproduce the observed spatial pattern (Moran, 1950). This metric assesses the degree of spatial autocorrelation in the simulated RTS distribution. It ranges from -1 to 1, where positive values indicate spatial clustering, negative values indicate dispersion, and values near 0 suggest a random spatial pattern. 12I=nS0×∑i=1n∑j=1nwijyij-y‾yj-y‾∑i=1nyi-y‾2 where n is the total number of spatial units in the study area, yi and yj are attribute values for pixel i and j, respectively, y‾ is the mean of the attribute values across all spatial units, wij is a spatial weight defines the relationship between pixel i and pixel j, and S0 is the sum of all the spatial weights in the map.

The Holt's linear trend model was trained using RTS area data from 2016 to 2020 to forecast the total area demand for the Beiluhe Basin in 2021 and 2022 (Experiment 1). The model's performance was evaluated against the observed RTS areas derived from the RTS distribution maps, yielding R2=0.545 and MAPE = 11.3 %. The model fit was noted to be strong for the 2017–2020 period, with the lower overall R2 value influenced by a relatively large discrepancy in the initial year of 2016.

An analysis of the optimal model parameters was revealing: a level smoothing coefficient (α) of 0.6650 indicated that the forecast is highly sensitive to recent observations, reflecting the strong influence of short-term factors like extreme precipitation events on the RTS area within the basin. A trend smoothing coefficient (β*) of 0.6650 suggested that while the long-term growth trend maintains strong inertia consistent with geological processes, it remains responsive to rapid environmental changes. The model's initial trend value of 3 484 800 m² a⁻¹ confirmed a substantial expansion rate within the Beiluhe Basin at the onset of the study period. This rapid expansion aligns with the broader central QTP's observed warming rate of 0.4 °C per decade (Yao et al., 2022), which is a primary driver of widespread permafrost degradation.

The predictive performance of the RF and LR models, which form the basis of the probability mapping module, was evaluated using the testing dataset for the Beiluhe Basin (Experiment 2). The hyperparameter optimization process yielded significant improvements for both models. The AUC for the RF model increased from an initial 0.9434 to 0.9903, and the AUC for the LR model increased from 0.8573 to 0.8777 (Fig. 3c and g). Both optimized models demonstrated excellent discriminative performance (AUC > 0.85), with the RF model achieving the highest accuracy. The rolling time-window validation confirmed that the models effectively captured spatiotemporal dynamics, maintaining high performance across different annual periods. The RF model was particularly stable, with AUC values consistently above 0.91 for all validation windows. The LR model also remained stable with AUC values mostly above 0.85, though it showed a performance dip to 0.7771 for the 2019–2020 test set (Fig. 3d and h). While the near-perfect AUC of the RF model might initially suggest potential overfitting, its excellent performance on unseen future years during the rolling time-window validation (AUC > 0.91) indicates that the highly tuned model still generalizes well. In contrast, the smaller gap between the LR model's main AUC (0.8777) and its temporal validation scores (mostly >0.85) suggests the simpler model was less prone to overfitting.

Based on the hyperparameter-optimized models, occurrence probability maps were predicted for the Beiluhe Basin for the 2020–2021 and 2021–2022 periods (Fig. 3a, b, e and f). A visual analysis reveals significant similarities between the predictions of both the RF and LR models. In both years, the models agreed on the general spatial pattern, identifying the highest RTS occurrence probabilities in the central regions of the basin while assigning lower probabilities to the peripheral areas. This overall pattern is consistent with the known distribution of existing RTSs. Despite this broad agreement, the models produced distinct spatial textures. The RF model's output is characterized by discrete, scattered patches of high probability (Fig. 3a for 2021, Fig. 3b for 2022), whereas the LR model yields continuous, ribbon-like zones with more gradual transitions between high- and low-risk areas, revealing finer spatial details (Fig. 3e for 2021, Fig. 3f for 2022). The LR model consistently identified a larger proportion of high-probability pixels (probability > 0.9) than the RF model in both 2021 (2.67 % vs. 2.07 %) and 2022 (1.12 % vs. 0.22 %). These high-risk zones from the LR model demonstrate a higher degree of spatial consistency with the observed clusters of actual RTSs. Comparing the predictions between the two years reveals subtle inter-annual variations that reflect the models' sensitivity to the different climate inputs. For instance, in the LR model's predictions, the peak probabilities appear slightly less intense and widespread in the 2022 map (Fig. 3f) compared to the 2021 map (Fig. 3e).

In Experiment 3, the integrated Logistic Regression Evolution Model (LR-EM) and Random Forest Evolution Model (RF-EM) were first calibrated using the observed 2020 RTS distribution in the Beiluhe Basin as the reference target, with optimized parametric values presented in Table 2. In this calibration step, both models achieved a strong fit to the data (Table 3). While both models demonstrated high overall spatial accuracy with κ coefficients and F1 Scores exceeding 88 %, these global metrics are inevitably inflated by the massive class imbalance inherent to regional geohazard modeling, where the vast majority of the landscape remains stable. A more stringent and realistic evaluation metric is the FoM, which evaluates only correctly predicted changes and excludes stable areas. In this regard, the LR-EM exhibited a superior ability to capture new growth, achieving a FoM of 20.05 %, which surpassed the RF-EM's 17.36 %. In comparable land-use and land-cover change (LUCC) simulation studies, FoM values commonly range between approximately 2 % and 25 %, particularly for rare or spatially clustered change processes (Pontius et al., 2008). Within this context, the FoM values obtained by RTSEvo are highly competitive and indicate a highly effective capture of the underlying expansion mechanisms. Furthermore, the model demonstrates a substantial relative improvement compared to baseline probability-only simulations, with FoM increases exceeding 29 % when our dynamic allocation process-based rules are included. Both calibrated models also effectively reproduced the observed spatial clustering; the Moran's I of the simulated results for both the LR-EM (0.603) and RF-EM (0.599) closely matched the Moran's I of the actual 2020 RTS distribution (0.596).

Following calibration, the models with their optimized parameters were used for a predictive simulation of RTS evolution for the subsequent years, 2021 and 2022, which served as an independent validation. The LR-EM model consistently outperformed the RF-EM in both validation years in terms of absolute accuracy (Table 3). In 2021, the LR-EM achieved a FoM of 12.00 % compared to 10.77 % for the RF-EM. However, the accuracy of both models notably declined in 2022. Rather than a structural failure of the model, this drop is likely linked to a severe, anomalous summer heatwave occurred that year (Zhu et al., 2024), which introduced extreme non-linear thermal forcing that deviates from the baseline conditions used for calibration. This extreme climatic event highlighted differences in model robustness; while the RF-EM's performance declined less sharply, the LR-EM still maintained higher overall accuracy scores (FoM, κ, and F1 Score) in both validation years. A spatial analysis of the simulation errors (Fig. 4) provides further insight. It reveals that while the models correctly identify the active margins of existing slumps as the primary zones for new growth, they struggle to pinpoint the precise, pixel-by-pixel location of that expansion. Most errors, both observed growth that the model missed (Misses) and areas incorrectly simulated as growth (False Alarms), are concentrated along these active boundaries. Visually, the LR-EM tended to produce larger, more contiguous clusters of correctly predicted pixels (Hits), which is consistent with its higher FoM score (Fig. 4c and d).

Despite variations in pixel-level accuracy, both models demonstrated excellent performance in reproducing the overall spatial patterns of RTS development. The average relative error of the Moran's I index was controlled within 1.5 % for both models, validating the effectiveness of the spatial allocation rules in capturing the characteristic regional clustering of RTSs. Furthermore, a qualitative comparison of slump morphology in the validation areas (Fig. 4) shows that the simulations successfully captured the general shape, size, and orientation of observed RTS expansion. The simulated slump boundaries, however, were generally smoother and less intricate than their real-world counterparts, indicating that while the model excels at capturing the macro-scale physical process, it tends to simplify complex, fine-scale topographic boundary details.

Evaluating the model's cross-regional generalizability revealed the physical limitations of direct parameter transfer across heterogeneous permafrost environments (Experiment 4). Baseline parameters derived from the highly concentrated RTS samples in the Beiluhe Basin proved strictly optimized for that region's specific climate forcing. When testing the Holt's linear trend model in the Haiding Nuo'er Subregion, an independent test area, the module achieved strong areal demand forecasting performance (R2=0.913, MAPE = 13.75 %). However, this regional forecast required a higher smoothing coefficient (α=0.8401) and a lower trend smoothing coefficient (β*=0.4330) relative to the Beiluhe Basin. These parameter differences indicate that the temporal dynamics and climatic responsiveness of RTS expansion differ meaningfully between the two regions.

During the spatial allocation phase, the base occurrence probability maps generated by the LR module for the Haiding Nuo'er Subregion (Fig. S3) revealed that high probability zones are predominantly distributed in elongated, ribbon-like patterns adjacent to existing RTS features. Applying the direct transfer of Beiluhe Basin spatial allocation parameters to the Haiding Nuo'er Subregion yielded baseline FoM values of 15.81 %, 5.27 %, and 6.10 % for 2020, 2021, and 2022, respectively. Conversely, locally recalibrating the parameters based on the 2020 RTS distribution of the secondary site produced notable performance improvements, increasing the FoM to 18.15 % in 2020 and 6.25 % in 2021, although a modest decrease to 4.29 % was observed in 2022 (Fig. 5).

These performance outcomes demonstrate that the RTSEvo architecture remains fully operational and capable of simulating RTS evolution when deployed in a different permafrost region. At the same time, the consistent accuracy gains achieved through local recalibration prove that spatial allocation parameters exhibit limited cross-regional generalizability. This finding highlights a reality of permafrost geomorphology: local topography, soil composition, and thermal forcing heavily modulate RTS expansion, necessitating region-specific optimization to achieve maximum predictive accuracy.

While traditional RTS research has heavily relied on static susceptibility mapping, which successfully identifies high-risk spatial zones, these approaches inherently fail to capture the temporal evolution and physical propagation of these dynamic features. Our framework represents a paradigm shift in permafrost geohazard modeling by introducing a dynamic spatial allocation module constrained by a macro-scale area demand. This approach offers three key scientific advantages: (1) it ensures that simulated local spatial patterns are strictly anchored to observed regional expansion trends; (2) its rigorous calibration yields higher predictive accuracy in reproducing the realistic morphologic extent and clustering of RTS development; and (3) it provides a true predictive capability that is essential for forecasting RTS response under future climate scenarios.

From a scientific and practical standpoint, this predictive power is invaluable for engineering and environmental planning. It provides a more robust tool for assessing short- and long-term risks to critical infrastructure in permafrost regions and offers a quantitative method for understanding the cascading impacts of permafrost degradation, such as the mobilization of previously frozen carbon. However, this dynamic approach also introduces modeling challenges. A key issue is the potential for error propagation, where small inaccuracies in early simulation steps can accumulate over time, leading to deviations in long-term predictions. Furthermore, the base probability models showed some sensitivity to non-stationary environmental conditions. This was particularly evident in 2022, when a severe summer heatwave altered permafrost stability and led to a decline in simulation accuracy. This highlights a vulnerability of pure data-driven models when extrapolating to extreme, anomalous climatic events that are not well-represented in their historical training data.

While the RTSEvo model adopts its core top-down demand and bottom-up allocation structure from established LUCC modeling framework, it is technically specialized for geohazard simulation in two fundamental ways. First, and most critically, unlike many LUCC models where transition rules are set empirically based on expert knowledge, RTSEvo integrates mechanistic, process-based rules by embedding a direct physical understanding of terrain failure into the allocation rules. Second, the model implements a systematic optimization routine driven by maximizing FoM, ensuring the algorithm explicitly learns the behavior of new slump growth rather than just static background features.

A central innovation of RTSEvo is the explicit integration of physical geomorphic processes, particularly the retrogressive erosion factor, into a data-driven framework. Our comparative experiments in the Beiluhe Basin definitively quantify the value of this approach. When comparing baseline models (using only statistical occurrence probability) against the full evolution models for the 2020 calibration year, the results were obvious: the FoM for the LR-based model increased from 6.67 % (baseline) to 20.05 % (full model), while the RF-based model's FoM jumped from a mere 0.42 % to 17.36 %. This massive discrepancy demonstrates that spatial allocation rules are absolutely essential for accurately capturing RTS evolution.

To specifically isolate the contribution of the retrogressive erosion factor, we conducted a sensitivity analysis comparing the full evolution models with and without this single factor across 50 randomized trials (Fig. 6). The results confirm that excluding this physical rule led to a statistically significant (p<0.01) reduction in simulation accuracy. In the 2021 validation, its inclusion improved the FoM from 9.99 % to 11.94 % for the LR-EM, and from 8.41 % to 11.15 % for the RF-EM. The stabilizing power of this physical constraint was even more pronounced during the anomalous 2022 heatwave, where its inclusion drove massive relative FoM improvements of 29.3 % for the LR-EM and 22.3 % for the RF-EM.

The theoretical importance of this factor stems from its ability to encode fundamental geomorphic feedbacks that are otherwise absent in purely statistical frameworks. In natural RTS evolution, headwall retreat is governed by thermally driven ice melt and subsequent slope failure, which cause a highly directional growth pattern. By introducing a directional weighting term aligned with upslope retreat, the model effectively reduces spatial randomness in cell transitions and enhances spatial autocorrelation that is strictly consistent with observed morphodynamics. The larger relative improvement observed in 2022 highlights a modeling reality. Because extreme thermal forcing diminished the predictive reliability of the purely statistical components during that specific year, the physical rule provided by the erosion factor acted as a critical anchor. It guided the simulation toward a physically plausible outcome even when the statistical relationships temporarily broke down.

To further understand the underlying environmental drivers of RTS initiation, a SHapley Additive exPlanations (SHAP) analysis was performed (Fig. A4). The results identified maximum summer temperature (mean SHAP value: 0.09) and ground ice content (0.087) as the two most influential factors, representing the key energy input and material basis for RTS development. Factors of moderate importance, such as land cover and geology, reflect the synergistic control of surface conditions. In contrast, precipitation parameters exhibited relatively weaker impacts. This temperature-dominance strongly aligns with the known mechanisms of permafrost degradation on the QTP, corroborating field observations that link RTS events to anomalously high thermal energy inputs (Lewkowicz and Way, 2019; Luo et al., 2022a).

A practical challenge in regional permafrost modeling is the scale mismatch between local geomorphological features and the coarse resolution of continuous satellite-derived environmental predictors. In the Beiluhe Basin, individual RTS features have a mean area of 2.61 ha, corresponding to an approximate diameter of 160 m. When predictors like MODIS NDVI (250 m) or reanalysis climate forcing are resampled to 10 m modeling grid, sub-pixel spatial heterogeneity is not explicitly represented. In traditional susceptibility mapping, this scale gap typically results in overly smooth, unrealistic hazard zones that fail to capture the sharp boundaries of actual terrain failure.

RTSEvo is designed to mitigate this scale gap through its two-stage modeling structure, which mathematically isolates the smoothing effect. In the first stage, the probability estimation module uses regional-scale predictors merely to identify permissive bioclimatic areas where RTS expansion is environmentally plausible. In the second stage, the constrained spatial allocation module determines how RTS expansion is actually expressed at high spatial resolution. This allocation process is controlled by neighborhood interactions and RTS expansion rules, allowing fine-scale spatial patterns to emerge even when the background predictors are spatially smooth.

To rigorously validate this structural merit, we focused our sensitivity testing on vegetation (NDVI). Vegetation is a critical modulator of ground thermal regimes and was confirmed as a meaningful predictor in our SHAP analysis (Fig. A4). We tested whether its coarse representation was bottlenecking our simulation. Upgrading the vegetation input from 250 m MODIS to a reconstructed 30 m Landsat 8 NDVI dataset for the 2021 independent simulation in the Beiluhe Basin yielded only marginal performance gains (<1.2 % FoM increase) (Figs. S4 and S5). This counterintuitive finding reveals that while finer-resolution vegetation data naturally enhances local contrast, vegetation density only indicates general environmental susceptibility. Because RTSEvo explicitly delegates physical constraints to the high-resolution spatial allocation module, it prevents the smoothing effect of coarse predictors from destabilizing the final simulation.

This finding carries significant operational implications for permafrost geohazard forecasting. High-resolution imagery (e.g., 30 m or finer) on the QTP frequently suffers from severe temporal limitations, including frequent cloud contamination and irregular acquisition intervals. Our results demonstrate that regional simulation efforts do not need to be bottlenecked by the absence of high-resolution datasets. By combining coarse but temporally consistent environmental data with strict, physically based allocation rules, researchers can generate highly realistic, fine-scale evolutionary projections.

The parametric sensitivity observed during our cross-regional validation is not a structural limitation of the RTSEvo algorithm, but rather a direct reflection of the profound spatial heterogeneity inherent to permafrost landscapes. Because RTS expansion is fundamentally a phase-change driven geomorphic process, regional variations in subsurface thermal regimes, active layer thickness, and ground ice distribution physically alter how a slump propagates. Consequently, a parameter set highly optimized for the specific ice-rich, high-elevation environment of the Beiluhe Basin naturally misaligns with the distinct climatic and topographic boundary conditions of the Haiding Nuo'er Subregion. This confirms that while the universal physical rules encoded in the model (such as retrogressive erosion) remain valid across all environments, the statistical weights governing their local spatial expression cannot be universally transferred.

This physical reality exposes a critical vulnerability in the growing trend of applying monolithic, “one-size-fits-all” machine learning frameworks to pan-Tibetan or pan-Arctic permafrost simulations. Purely data-driven models trained on concentrated regional inventories risk severe spatial uncertainty and catastrophic predictive failure when extrapolated to novel environments because they conflate universal failure mechanisms with local environmental sensitivities. Our results prove that by mathematically separating universal physical mechanisms (the spatial allocation rules) from local environmental sensitivities (the occurrence probability weights), dynamic models developed a structural resistance to this deterioration and can be successfully ported across regions. However, to achieve reliable continental-scale projections, the permafrost modeling community still have to adopt a “regionalized” parameterization paradigm.

Although the proposed evolution model demonstrates strong predictive capabilities for simulating RTS dynamics, several limitations remain. These primarily stem from inherent uncertainties in input data and necessary simplifying modeling assumptions.

A first source of uncertainty arises from the RTS inventory datasets used for model calibration and validation. While high-resolution imagery and field surveys minimize mapping errors, the delineation of slump boundaries remain subject to interpreter bias, seasonal visibility constraints, and the time gaps between observations .(Xia et al., 2024b; Nitze et al., 2025). These uncertainties inevitably propagate into the training samples and affect the model's reliability. The driving factor datasets also exhibit inherent limitations. While prepared at a high spatial resolution, they may not adequately capture highly localized or short-duration extreme events, such as acute heatwaves, intense precipitation, or seismic disturbances, that are known to play a key role in triggering or accelerating RTS activity (Yin et al., 2023; Chen et al., 2024; Nesterova et al., 2024; Luo et al., 2025). This omission likely contributed to the decline in model accuracy observed under the anomalous conditions of the 2022 extreme heatwave.

Beyond data-related issues, the modeling framework also embeds several theoretical assumptions that require careful consideration. The model assumes synchronicity between RTS mapping and environmental drivers by using annual snapshots of both. In reality, RTS initiation and expansion is likely to exhibit a time-lagged geomorphic response to climate and geomorphic forcing (Dai et al., 2025), suggesting that an annual resolution may oversimplify complex thermal-mechanical delays. Furthermore, the framework assumes that once a pixel converts to an RTS, it irreversibly remains in that state. This assumption is physically justified over short- to medium-term simulations. Field observations and remote-sensing studies consistently indicate that the processes of RTS stabilization, revegetation, and surface recovery typically operate over multi-decadal timescales, often exceeding 20 years, and are strongly modulated by local climate, sediment availability, and hydrological conditions (Burn and Friele, 1989; Leibman et al., 2014; Nesterova et al., 2024; Krautblatter et al., 2024). However, for extended temporal horizons (e.g., >30–50 years), neglecting stabilization and recovery processes may lead to a systematic overestimation of active RTS extent. Future iterations of the model must incorporate multi-class state transitions to simulate the recovery state of the RTS.

Therefore, future improvements should focus on integrating multi-source uncertainty quantification, incorporating event-based drivers such as extreme climate anomalies and seismic activity, and relaxing the irreversibility assumption to account for possible slump stabilization processes. These enhancements will improve the evolution model's robustness and generalizability across diverse permafrost environments.