# Spatiotemporal Mechanism-Based Spacetimeformer Network for InSAR Deformation Prediction and Identification of Retrogressive Thaw Slumps in the Chumar River Basin

^{1}

^{2}

^{3}

^{4}

^{*}

## Abstract

**:**

## 1. Introduction

^{6}km

^{2}(with temperatures lower than −2 °C) [1], and it is particularly sensitive and vulnerable to global warming and human activities [2]. Currently, the central region of the QTP is undergoing rapid and substantial permafrost degradation, marked by rising ground temperatures, an expanding active layer, contracting extent, decreasing thickness, and an ascending lower boundary [3]. Retrogressive thaw slumps (RTSs), among the most dynamic geomorphological features in the QTP’s permafrost zones, are experiencing accelerated melting and erosion from the warming of global permafrost, particularly due to extensive melting of ice-rich permafrost. This not only alters the landscape and ecosystem of the Qinghai–Tibet Plateau but also potentially accelerates the release of soil organic carbon, which could undermine infrastructure stability and impact the global carbon cycle and climate change [4,5,6]. Understanding the surface deformation characteristics and future trends of these thaw slumps across spatial and temporal dimensions is crucial. Additionally, conducting comprehensive studies on the spatiotemporal patterns of surface deformation, exploring large-scale deformation mapping possibilities, and assessing future trends, remain equally essential. [7]. Therefore, deformation monitoring and mid-short-term prediction techniques for RTSs are significant in assessing the deformation trends of thaw slumps and the stability of infrastructure in cold regions. In recent decades, interferometric synthetic aperture radar (InSAR) technology, capable of measuring surface deformation with centimeter to subcentimeter precision and offering high spatial resolution and wide coverage in all weathers, has provided a powerful method for monitoring ground deformation in permafrost areas [8]. Additionally, the open data policy of the Sentinel-1 satellite has facilitated the application of InSAR technology for large-scale deformation measurement in permafrost areas. Alternatively, multi-temporal InSAR techniques (MT-InSAR) such as permanent scatterer interferometry (PSI) [9] and small baseline subset (SBAS) [10] have been successfully used to monitor seasonal changes and interannual surface elevation changes in permafrost areas of the QTP [11,12,13,14]. These studies have effectively monitored the freeze–thaw cycles of permafrost on the QTP, including combining seasonal deformation data with the Stefan model to invert the thickness of the active layer [15,16].

## 2. Study Area and Datasets

#### 2.1. Study Area

#### 2.2. Datasets

#### 2.2.1. Satellite Data

#### 2.2.2. Auxiliary Data

## 3. Methodology

#### 3.1. MT-InSAR Processing

#### 3.2. Mapping of Retrogressive Thaw Slump Boundaries

#### 3.3. Time Series Deformation Prediction of Spacetimeformer Models

#### 3.3.1. Dataset Preprocessing and Holt–Winters Time-Series Decomposition

#### 3.3.2. Deformation Prediction of Spacetimeformer Model

#### 3.3.3. Experimental Design

^{−10}, and the base learning rate was set to 5 × 10

^{−4}. During inference, the trained Spacetimeformer model was used for estimating the time-series deformation prediction values for each pixel. Finally, the predicted time-series deformations for each category were geocoded, resulting in the generation of post-prediction time-series deformation maps.

## 4. Results and Analysis

#### 4.1. InSAR Deformation Results

#### 4.2. Extraction Results of Retrogressive Thaw Slumps

^{2}in 2023, and the number of such slumps had risen by 19. Notably, B and C were newly added retrogressive thaw slumps, while the areas of thaw slumps in regions A and D expanded by 49.29% and 51.40%, respectively. The InSAR observation results align with the aforementioned increase in thaw slump area and quantity, indicating that the Chumar River area is undergoing dynamic evolution of RTSs.

#### 4.3. Time-Series Deformation Prediction Results

^{2}was 0.95, confirming the validity of the predicted results.

## 5. Discussion

#### 5.1. Discussion of Spacetimeformer Method in InSAR Time Series Deformation Prediction

#### 5.2. Comparing the Predictive Performance of the Spacetimeformer Model with Other Methods

#### 5.3. Combining InSAR Deformation RTSs for Detailed Explanation

## 6. Conclusions

^{2}in 2023, and the number of such slumps rose by 19.

^{2}of 0.95. Compared with other deep learning methods, the Spacetimeformer model with its spatiotemporal concept demonstrated better deformation prediction performance than the transformer and LSTM models. The Spacetimeformer model can continuously capture important trend changes in deformation prediction and provide relatively stable prediction results.

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

- Zou, D.; Zhao, L.; Sheng, Y.; Chen, J.; Hu, G.; Wu, T.; Wu, J.; Xie, C.; Wu, X.; Pang, Q.; et al. A New Map of Permafrost Distribution on the Tibetan Plateau. Cryosphere
**2017**, 11, 2527–2542. [Google Scholar] [CrossRef] - Ran, Y.; Li, X.; Cheng, G. Climate Warming Has Led to the Degradation of Permafrost Stability in the Past Half Century over the Qinghai-Tibet Plateau; Frozen Ground. Cryosphere Discuss.
**2017**, 12, 1–30. [Google Scholar] [CrossRef] - Yang, M.; Nelson, F.E.; Shiklomanov, N.I.; Guo, D.; Wan, G. Permafrost Degradation and Its Environmental Effects on the Tibetan Plateau: A Review of Recent Research. Earth-Sci. Rev.
**2010**, 103, 31–44. [Google Scholar] [CrossRef] - Luo, J.; Niu, F.; Lin, Z.; Liu, M.; Yin, G. Recent Acceleration of Thaw Slumping in Permafrost Terrain of Qinghai-Tibet Plateau: An Example from the Beiluhe Region. Geomorphology
**2019**, 341, 79–85. [Google Scholar] [CrossRef] - Olefeldt, D.; Goswami, S.; Grosse, G.; Hayes, D.; Hugelius, G.; Kuhry, P.; McGuire, A.D.; Romanovsky, V.E.; Sannel, A.B.K.; Schuur, E.A.G.; et al. Circumpolar Distribution and Carbon Storage of Thermokarst Landscapes. Nat. Commun.
**2016**, 7, 13043. [Google Scholar] [CrossRef] - Turetsky, M.R.; Abbott, B.W.; Jones, M.C.; Walter Anthony, K.; Olefeldt, D.; Schuur, E.A.G.; Koven, C.; McGuire, A.D.; Grosse, G.; Kuhry, P.; et al. Permafrost Collapse Is Accelerating Carbon Release. Nature
**2019**, 569, 32–34. [Google Scholar] [CrossRef] - Jiao, Z.; Xu, Z.; Guo, R.; Zhou, Z.; Jiang, L. Potential of Multi-Temporal InSAR for Detecting Retrogressive Thaw Slumps: A Case of the Beiluhe Region of the Tibetan Plateau. Int. J. Disaster Risk Sci.
**2023**, 14, 523–538. [Google Scholar] [CrossRef] - Zhang, Z.; Lin, H.; Wang, M.; Liu, X.; Chen, Q.; Wang, C.; Zhang, H. A Review of Satellite Synthetic Aperture Radar Interferometry Applications in Permafrost Regions: Current Status, Challenges, and Trends. IEEE Geosci. Remote Sens. Mag.
**2022**, 10, 93–114. [Google Scholar] [CrossRef] - Ferretti, A.; Prati, C.; Rocca, F. Permanent Scatterers in SAR Interferometry. IEEE Trans. Geosci. Remote Sens.
**2001**, 39, 8–20. [Google Scholar] [CrossRef] - Berardino, P.; Fornaro, G.; Lanari, R.; Sansosti, E. A New Algorithm for Surface Deformation Monitoring Based on Small Baseline Differential SAR Interferograms. IEEE Trans. Geosci. Remote Sens.
**2002**, 40, 2375–2383. [Google Scholar] [CrossRef] - Zhang, X.; Zhang, H.; Wang, C.; Tang, Y.; Zhang, B.; Wu, F.; Wang, J.; Zhang, Z. Time-Series InSAR Monitoring of Permafrost Freeze-Thaw Seasonal Displacement over Qinghai–Tibetan Plateau Using Sentinel-1 Data. Remote Sens.
**2019**, 11, 1000. [Google Scholar] [CrossRef] - Wang, L.; Marzahn, P.; Bernier, M.; Ludwig, R. Sentinel-1 InSAR Measurements of Deformation over Discontinuous Permafrost Terrain, Northern Quebec, Canada. Remote Sens. Environ.
**2020**, 248, 111965. [Google Scholar] [CrossRef] - Wang, J.; Wang, C.; Zhang, H.; Tang, Y.; Duan, W.; Dong, L. Freeze-Thaw Deformation Cycles and Temporal-Spatial Distribution of Permafrost along the Qinghai-Tibet Railway Using Multitrack InSAR Processing. Remote Sens.
**2021**, 13, 4744. [Google Scholar] [CrossRef] - Lu, P.; Han, J.; Yi, Y.; Hao, T.; Zhou, F.; Meng, X.; Zhang, Y.; Li, R. MT-InSAR Unveils Dynamic Permafrost Disturbances in Hoh Xil (Kekexili) on the Tibetan Plateau Hinterland. IEEE Trans. Geosci. Remote Sens.
**2023**, 61, 1–16. [Google Scholar] [CrossRef] - Wang, Y.; Sun, Z.; Sun, Y. Effects of a Thaw Slump on Active Layer in Permafrost Regions with the Comparison of Effects of Thermokarst Lakes on the Qinghai–Tibet Plateau, China. Geoderma
**2018**, 314, 47–57. [Google Scholar] [CrossRef] - Zhang, X.; Zhang, H.; Wang, C.; Tang, Y.; Zhang, B.; Wu, F.; Wang, J.; Zhang, Z. Active Layer Thickness Retrieval Over the Qinghai-Tibet Plateau Using Sentinel-1 Multitemporal InSAR Monitored Permafrost Subsidence and Temporal-Spatial Multilayer Soil Moisture Data. IEEE Access
**2020**, 8, 84336–84351. [Google Scholar] [CrossRef] - Mudelsee, M. Trend Analysis of Climate Time Series: A Review of Methods. Earth-Sci. Rev.
**2019**, 190, 310–322. [Google Scholar] [CrossRef] - Stoffer, D.S.; Ombao, H. Editorial: Special Issue on Time Series Analysis in the Biological Sciences. J. Time Ser. Anal.
**2012**, 33, 701–703. [Google Scholar] [CrossRef] - Topol, E.J. High-Performance Medicine: The Convergence of Human and Artificial Intelligence. Nat. Med.
**2019**, 25, 44–56. [Google Scholar] [CrossRef] - Lim, B.; Zohren, S. Time Series Forecasting with Deep Learning: A Survey. Philos. Trans. R. Soc. A
**2020**, 379, 20200209. [Google Scholar] [CrossRef] - Adhikari, R.; Agrawal, R.K. An Introductory Study on Time Series Modeling and Forecasting. arXiv
**2013**, arXiv:1302.6613. [Google Scholar] - Bartholomew, D.J.; Box, G.E.P.; Jenkins, G.M. Time Series Analysis Forecasting and Control. Oper. Res. Q.
**1971**, 22, 199. [Google Scholar] [CrossRef] - Winters, P.R. Forecasting Sales by Exponentially Weighted Moving Averages. Manag. Sci.
**1960**, 6, 324–342. [Google Scholar] [CrossRef] - Harvey, A.C. Forecasting, Structural Time Series Models and the Kalman Filter; Cambridge University Press: Cambridge, UK, 1990. [Google Scholar]
- Deng, Z.; Ke, Y.; Gong, H.; Li, X.; Li, Z. Land Subsidence Prediction in Beijing Based on PS-InSAR Technique and Improved Grey-Markov Model. GIScience Remote Sens.
**2017**, 54, 797–818. [Google Scholar] [CrossRef] - Kim, S.; Wdowinski, S.; Dixon, T.H.; Amelung, F.; Kim, J.W.; Won, J. Measurements and Predictions of Subsidence Induced by Soil Consolidation Using Persistent Scatterer InSAR and a Hyperbolic Model. Geophys. Res. Lett.
**2010**, 37, 2009GL041644. [Google Scholar] [CrossRef] - Aoqing, G.U.O.; Jun, H.U.; Wanji, Z.; Rong, G.U.I.; Zhigui, D.U.; Wu, Z.H.U.; Lehe, H.E. N-BEATS Deep Learning Method for Landslide Deformation Monitoring and Prediction Based on InSAR: A Case Study of Xinpu Landslide. Acta Geod. Et Cartogr. Sin.
**2022**, 51, 2171. [Google Scholar] [CrossRef] - Ding, Q.; Shao, Z.; Huang, X.; Altan, O.; Zhuang, Q.; Hu, B. Monitoring, Analyzing and Predicting Urban Surface Subsidence: A Case Study of Wuhan City, China. Int. J. Appl. Earth Obs. Geoinf.
**2021**, 102, 102422. [Google Scholar] [CrossRef] - Ahmed, N.K.; Atiya, A.F.; Gayar, N.E.; El-Shishiny, H. An Empirical Comparison of Machine Learning Models for Time Series Forecasting. Econom. Rev.
**2010**, 29, 594–621. [Google Scholar] [CrossRef] - Antonova, S.; Sudhaus, H.; Strozzi, T.; Zwieback, S.; Kääb, A.; Heim, B.; Langer, M.; Bornemann, N.; Boike, J. Thaw Subsidence of a Yedoma Landscape in Northern Siberia, Measured In Situ and Estimated from TerraSAR-X Interferometry. Remote Sens.
**2018**, 10, 494. [Google Scholar] [CrossRef] - Ma, P.; Zhang, F.; Lin, H. Prediction of InSAR Time-Series Deformation Using Deep Convolutional Neural Networks. Remote Sens. Lett.
**2020**, 11, 137–145. [Google Scholar] [CrossRef] - Nukala, V.H.; Nayak, M.; Gubbi, J.; Purushothaman, B. Multi-Scale Attention Guided Recurrent Neural Network for Deformation Map Forecasting. In Proceedings of the Image and Signal Processing for Remote Sensing XXVII, Online, 13–17 September 2021; SPIE: Bellingham, WI, USA, 2021; Volume 11862, pp. 154–159. [Google Scholar]
- Chen, Y.; He, Y.; Zhang, L.; Chen, Y.; Pu, H.; Chen, B.; Gao, L. Prediction of InSAR Deformation Time-Series Using a Long Short-Term Memory Neural Network. Int. J. Remote Sens.
**2021**, 42, 6919–6942. [Google Scholar] [CrossRef] - Hill, P.; Biggs, J.; Ponce-López, V.; Bull, D. Time-Series Prediction Approaches to Forecasting Deformation in Sentinel-1 InSAR Data. JGR Solid Earth
**2021**, 126, e2020JB020176. [Google Scholar] [CrossRef] - Bao, X.; Zhang, R.; Shama, A.; Li, S.; Xie, L.; Lv, J.; Fu, Y.; Wu, R.; Liu, G. Ground Deformation Pattern Analysis and Evolution Prediction of Shanghai Pudong International Airport Based on PSI Long Time Series Observations. Remote Sens.
**2022**, 14, 610. [Google Scholar] [CrossRef] - Wang, J.; Li, C.; Li, L.; Huang, Z.; Wang, C.; Zhang, H.; Zhang, Z. InSAR Time-Series Deformation Forecasting Surrounding Salt Lake Using Deep Transformer Models. Sci. Total Environ.
**2023**, 858, 159744. [Google Scholar] [CrossRef] [PubMed] - Yao, S.; He, Y.; Zhang, L.; Yang, W.; Chen, Y.; Sun, Q.; Zhao, Z.; Cao, S. A ConvLSTM Neural Network Model for Spatiotemporal Prediction of Mining Area Surface Deformation Based on SBAS-InSAR Monitoring Data. IEEE Trans. Geosci. Remote Sens.
**2023**, 61, 1–22. [Google Scholar] [CrossRef] - He, Y.; Yao, S.; Chen, Y.; Yan, H.; Zhang, L. Spatio-temporal prediction of time-series InSAR Land subsidence based on ConvLSTM neural network. Geomat. Inf. Sci. Wuhan Univ.
**2023**, 1–21. [Google Scholar] [CrossRef] - Xia, L.; Yang, Q.; Li, Z.; Wu, Y.; Feng, Z. The Effect of the Qinghai-Tibet Railway on the Migration of Tibetan Antelope Pantholops Hodgsonii in Hoh-Xil National Nature Reserve, China. Oryx
**2007**, 41, 352–357. [Google Scholar] [CrossRef] - Yao, X.; Li, L.; Zhao, J.; Sun, M.; Li, J.; Gong, P.; An, L. Spatial-Temporal Variations of Lake Ice Phenology in the Hoh Xil Region from 2000 to 2011. J. Geogr. Sci.
**2016**, 26, 70–82. [Google Scholar] [CrossRef] - Yang, Y.; Wu, Q.; Zhang, P.; Jiang, G. Stable Isotopic Evolutions of Ground Ice in Permafrost of the Hoh Xil Regions on the Qinghai-Tibet Plateau. Quat. Int.
**2017**, 444, 182–190. [Google Scholar] [CrossRef] - Zhao, L.; Zou, D.; Hu, G.; Du, E.; Pang, Q.; Xiao, Y.; Li, R.; Sheng, Y.; Wu, X.; Sun, Z.; et al. Changing Climate and the Permafrost Environment on the Qinghai–Tibet (Xizang) Plateau. Permafr. Periglac. Process.
**2020**, 31, 396–405. [Google Scholar] [CrossRef] - Lanari, R.; Casu, F.; Manzo, M.; Zeni, G.; Berardino, P.; Manunta, M.; Pepe, A. An Overview of the Small BAseline Subset Algorithm: A DInSAR Technique for Surface Deformation Analysis. In Deformation and Gravity Change: Indicators of Isostasy, Tectonics, Volcanism, and Climate Change; Wolf, D., Fernández, J., Eds.; Pageoph Topical Volumes; Birkhäuser Basel: Basel, Switzerland, 2007; pp. 637–661. ISBN 978-3-7643-8416-6. [Google Scholar]
- Hersbach, H.; Bell, B.; Berrisford, P.; Hirahara, S.; Horányi, A.; Muñoz-Sabater, J.; Nicolas, J.; Peubey, C.; Radu, R.; Schepers, D.; et al. The ERA5 Global Reanalysis. Quart. J. R. Meteoro. Soc.
**2020**, 146, 1999–2049. [Google Scholar] [CrossRef] - Savitzky, A.; Golay, M.J.E. Smoothing and Differentiation of Data by Simplified Least Squares Procedures. Available online: https://0-pubs-acs-org.brum.beds.ac.uk/doi/pdf/10.1021/ac60214a047 (accessed on 21 December 2023).
- Ahmed, M.; Seraj, R.; Islam, S.M.S. The K-Means Algorithm: A Comprehensive Survey and Performance Evaluation. Electronics
**2020**, 9, 1295. [Google Scholar] [CrossRef] - Chatfield, C. The Holt-Winters Forecasting Procedure. J. R. Stat. Soc. Ser. C (Appl. Stat.)
**1978**, 27, 264–279. [Google Scholar] [CrossRef] - Prats-Iraola, P.; Scheiber, R.; Marotti, L.; Wollstadt, S.; Reigber, A. TOPS Interferometry with TerraSAR-X. IEEE Trans. Geosci. Remote Sens.
**2012**, 50, 3179–3188. [Google Scholar] [CrossRef] - Yague-Martinez, N.; Prats-Iraola, P.; Rodriguez Gonzalez, F.; Brcic, R.; Shau, R.; Geudtner, D.; Eineder, M.; Bamler, R. Interferometric Processing of Sentinel-1 TOPS Data. IEEE Trans. Geosci. Remote Sens.
**2016**, 54, 2220–2234. [Google Scholar] [CrossRef] - Xu, X.; Sandwell, D.T.; Tymofyeyeva, E.; Gonzalez-Ortega, A.; Tong, X. Tectonic and Anthropogenic Deformation at the Cerro Prieto Geothermal Step-over Revealed by Sentinel-1A InSAR. IEEE Trans. Geosci. Remote Sens.
**2017**, 55, 5284–5292. [Google Scholar] [CrossRef] - Goldstein, R.M.; Werner, C.L. Radar Interferogram Filtering for Geophysical Applications. Geophys. Res. Lett.
**1998**, 25, 4035–4038. [Google Scholar] [CrossRef] - Pepe, A.; Lanari, R. On the Extension of the Minimum Cost Flow Algorithm for Phase Unwrapping of Multitemporal Differential SAR Interferograms. IEEE Trans. Geosci. Remote Sens.
**2006**, 44, 2374–2383. [Google Scholar] [CrossRef] - Chen, J.; Liu, L.; Zhang, T.; Cao, B.; Lin, H. Using Persistent Scatterer Interferometry to Map and Quantify Permafrost Thaw Subsidence: A Case Study of Eboling Mountain on the Qinghai-Tibet Plateau. JGR Earth Surf.
**2018**, 123, 2663–2676. [Google Scholar] [CrossRef] - Agram, P.S.; Jolivet, R.; Riel, B.; Lin, Y.N.; Simons, M.; Hetland, E.; Doin, M.-P.; Lasserre, C. New Radar Interferometric Time Series Analysis Toolbox Released. EoS Trans.
**2013**, 94, 69–70. [Google Scholar] [CrossRef] - Kang, Y.; Lu, Z.; Zhao, C.; Qu, W. Inferring Slip-Surface Geometry and Volume of Creeping Landslides Based on InSAR: A Case Study in Jinsha River Basin. Remote Sens. Environ.
**2023**, 294, 113620. [Google Scholar] [CrossRef] - Krishna, K.; Murty, M.N. Genetic K-Means Algorithm. IEEE Trans. Syst. Man Cybern. Part B (Cybern.)
**1999**, 29, 433–439. [Google Scholar] [CrossRef] [PubMed] - Grigsby, J.; Wang, Z.; Nguyen, N.; Qi, Y. Long-Range Transformers for Dynamic Spatiotemporal Forecasting. arXiv
**2021**, arXiv:2109.12218. [Google Scholar] [CrossRef] - Kingma, D.P.; Adam, B.J. A Method for Stochastic. Optimization 3rd International Conference for Learning Representations. San Diego. arXiv
**2015**, arXiv:1412.6980. [Google Scholar] - Chen, J.; Wu, T.; Zou, D.; Liu, L.; Wu, X.; Gong, W.; Zhu, X.; Li, R.; Hao, J.; Hu, G. Magnitudes and Patterns of Large-Scale Permafrost Ground Deformation Revealed by Sentinel-1 InSAR on the Central Qinghai-Tibet Plateau. Remote Sens. Environ.
**2022**, 268, 112778. [Google Scholar] [CrossRef] - Lewkowicz, A.G.; Way, R.G. Extremes of Summer Climate Trigger Thousands of Thermokarst Landslides in a High Arctic Environment. Nat. Commun.
**2019**, 10, 1329. [Google Scholar] [CrossRef] - Patton, A.I.; Rathburn, S.L.; Capps, D.M.; McGrath, D.; Brown, R.A. Ongoing Landslide Deformation in Thawing Permafrost. Geophys. Res. Lett.
**2021**, 48, e2021GL092959. [Google Scholar] [CrossRef]

**Figure 1.**Geographic location of the study area and coverage of Sentinel-1 data. (

**a**) Sentinel-1 images and the study area superimposed on a color map of China; (

**b**) the Chumar River area superimposed on Shuttle Radar Topography Mission (SRTM) digital elevation model (DEM) shaded topography map.

**Figure 2.**Processing flow of Spacetimeformer time-series deformation prediction method. This figure depicts content related to Section 3.1, Section 3.2 and Section 3.3 in the text.

**Figure 4.**The Spacetimeformer architecture for RTS deformation prediction. (

**a**) Holt–Winters time-series decomposition; (

**b**) model architecture.

**Figure 5.**Deformation time-series decomposition feature diagram. (

**a**) InSAR time-series deformation; (

**b**) trend component of displacement; (

**c**) seasonal component of displacement; (

**d**) residual component of displacement.

**Figure 6.**Deformation results in the study area. (

**a**) LOS deformation rate; (

**b**) amplitude of seasonal deformation.

**Figure 7.**Retrogressive thaw slumps in the Chumar River area. (

**a**) InSAR-derived LOS velocity; (

**b**) the retrogressive thaw slump areas mapped in 2019 and 2023.

**Figure 8.**Retrogressive thaw slump boundaries in 2019 (blue) and 2023 (red), manually extracted from Sentinel-2B images. (

**a**,

**c**) LOS velocity of Points A–D, (

**b**,

**d**) Sentinel-2B images of the areas of Points A–D.

**Figure 9.**Time-series deformation smoothed via the SG filter. (

**a**) Point A; (

**b**) Point B; (

**c**) Point C; (

**d**) Point D.

**Figure 11.**The comparison of time-series displacement between the Spacetimeformer model and the SBAS method, as well as the residual map between the two methods, from 5 August 2023 to 4 October 2023. The first column displays the time-series deformation maps predicted with the model, the second column shows the time-series deformation map derived through the SBAS method, and the third column presents the difference maps of the time-series deformation between the two methods.

**Figure 12.**Statistical results of the cumulative deformation on 4 October 2023. (

**a**) Histograms of the cumulative deformation; (

**b**) density distribution map of two results.

**Figure 13.**The predicted InSAR time-series deformations at Point A (

**a**), Point B (

**b**), Point C (

**c**), Point D (

**d**).

**Figure 14.**The predicted InSAR time-series deformations at Point E (

**a**), Point F (

**b**), Point G (

**c**), Point H (

**d**).

**Figure 15.**InSAR time-series deformation curves based on LSTM, transformer, and Spacetimeformer models at Point A (

**a**), Point B (

**b**), Point C (

**c**), Point D (

**d**).

Satellite Data | Number of Images | Time | Spatial Resolution (m) | Spectral Bands | Wavelength |
---|---|---|---|---|---|

Sentinel-1 | 158 | 2018/05/03~2023/10/04 | 2.7 × 22.5 (rg × az) | C | 5.6 cm |

Sentinel-2 | 2 | 2019/08/15 2023/09/13 | 10 | B2 Blue B3 Green B4 Red B8 Near-infrared (NIR) | 492.1 nm 559 nm 665 nm 833 nm |

**Table 2.**LOS velocity, periodic amplitude, and coherence calculated from the InSAR results for retrogressive thaw slumps in four sampled areas.

RTS Area | LOS Velocity (mm/yr) | Periodic Amplitude (mm) | Cumulative Subsidence (mm) | Standard Deviation (mm) | Coherence Values |
---|---|---|---|---|---|

Point A | −27.35 | 36.08 | 70.38 | 2.10 | 0.70 |

Point B | −11.36 | 14.54 | 24.17 | 5.18 | 0.66 |

Point C | −28.03 | 27.89 | 50.02 | 4.14 | 0.69 |

Point D | −11.80 | 29.02 | 49.04 | 3.13 | 0.67 |

**Table 3.**Comparison of accuracy evaluation indexes of the Spacetimeformer model during training and testing at point scale.

Training Dataset | Validation Dataset | Test Dataset | |||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|

Evaluation Index | RMSE (mm) | MAE (mm) | MAPE (%) | SMAPE (%) | RMSE (mm) | MAE (mm) | MAPE (%) | SMAPE (%) | RMSE (mm) | MAE (mm) | MAPE (%) | SMAPE (%) | Loss (mm) |

Point A | 3.151 | 2.343 | 2.144 | 0.667 | 1.575 | 1.112 | 0.963 | 0.321 | 1.358 | 0.985 | 0.547 | 0.240 | 0.038 |

Point B | 2.154 | 1.502 | 12.419 | 0.389 | 2.181 | 1.587 | 1.320 | 0.446 | 2.262 | 1.654 | 2.192 | 0.452 | 0.091 |

Point C | 2.637 | 1.894 | 1.375 | 0.494 | 1.655 | 1.219 | 0.870 | 0.355 | 1.639 | 1.200 | 0.906 | 0.356 | 0.051 |

Point D | 1.914 | 1.394 | 0.878 | 0.385 | 1.379 | 1.024 | 0.946 | 0.348 | 1.249 | 0.898 | 0.408 | 0.223 | 0.043 |

Point E | 3.036 | 2.288 | 1.783 | 0.596 | 2.282 | 1.390 | 1.150 | 0.433 | 2.471 | 2.458 | 1.385 | 0.476 | 0.537 |

Point F | 2.448 | 1.691 | 3.388 | 0.482 | 1.877 | 1.278 | 1.244 | 0.383 | 1.743 | 1.217 | 1.439 | 0.285 | 0.048 |

Point G | 1.861 | 0.607 | 0.590 | 0.259 | 2.029 | 0.626 | 0.449 | 0.225 | 1.751 | 0.727 | 0.277 | 0.338 | 0.064 |

Point H | 3.073 | 3.863 | 1.450 | 0.498 | 2.662 | 1.783 | 0.879 | 0.374 | 1.816 | 1.994 | 0.462 | 0.674 | 0.082 |

Point Index | Evaluation Index | LSTM | Transformer | Spacetimeformer |
---|---|---|---|---|

Point A | RMSE (mm) | 5.012 | 7.036 | 1.358 |

MAE (mm) | 4.809 | 6.525 | 1.865 | |

MAPE (%) | 7.165 | 9.668 | 0.754 | |

SMAPE (%) | 7.450 | 10.234 | 1.844 | |

Point B | RMSE (mm) | 0.589 | 2.899 | 2.262 |

MAE (mm) | 0.379 | 2.870 | 1.654 | |

MAPE (%) | 1.603 | 12.276 | 2.192 | |

SMAPE (%) | 1.634 | 13.098 | 0.452 | |

Point C | RMSE (mm) | 1.820 | 1.481 | 1.639 |

MAE (mm) | 1.645 | 1.226 | 1.200 | |

MAPE (%) | 4.353 | 3.291 | 0.906 | |

SMAPE (%) | 4.312 | 3.343 | 0.356 | |

Point D | RMSE (mm) | 3.097 | 2.360 | 1.249 |

MAE (mm) | 2.753 | 1.620 | 0.898 | |

MAPE (%) | 6.527 | 4.259 | 0.408 | |

SMAPE (%) | 6.273 | 4.070 | 0.223 |

Disclaimer/Publisher’s Note: The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content. |

© 2024 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Wang, J.; Fan, X.; Zhang, Z.; Zhang, X.; Nie, W.; Qi, Y.; Zhang, N.
Spatiotemporal Mechanism-Based Spacetimeformer Network for InSAR Deformation Prediction and Identification of Retrogressive Thaw Slumps in the Chumar River Basin. *Remote Sens.* **2024**, *16*, 1891.
https://0-doi-org.brum.beds.ac.uk/10.3390/rs16111891

**AMA Style**

Wang J, Fan X, Zhang Z, Zhang X, Nie W, Qi Y, Zhang N.
Spatiotemporal Mechanism-Based Spacetimeformer Network for InSAR Deformation Prediction and Identification of Retrogressive Thaw Slumps in the Chumar River Basin. *Remote Sensing*. 2024; 16(11):1891.
https://0-doi-org.brum.beds.ac.uk/10.3390/rs16111891

**Chicago/Turabian Style**

Wang, Jing, Xiwei Fan, Zhijie Zhang, Xuefei Zhang, Wenyu Nie, Yuanmeng Qi, and Nan Zhang.
2024. "Spatiotemporal Mechanism-Based Spacetimeformer Network for InSAR Deformation Prediction and Identification of Retrogressive Thaw Slumps in the Chumar River Basin" *Remote Sensing* 16, no. 11: 1891.
https://0-doi-org.brum.beds.ac.uk/10.3390/rs16111891