Spatial prediction of InSAR-derived hillslope velocities via deep learning

Spatiotemporal patterns of earth surface deformation are influenced by a combination of static and dynamic environmental characteristics specific to any landscape of interest. Nowadays, these patterns can be captured for larger areas using Interferometric Synthetic-Aperture Radar (InSAR) technologies and yet, their spatial prediction has been poorly investigated so far. Here, we initially compute the InSAR-derived line-of-sight hillslope velocities (V_LOS) and calculate their mean (ranging from 0 to ~ 30 mm/y) and maximum (ranging from 0 to ~ 60 mm/y) values per Slope Units (SUs). These separately constitute the response variables to be modelled through a series of deep learning routines: i) a basic neural network (Multi-Layer Perceptron), ii) a Graph Convolutional Network implemented to capture spatial dependence among neighbouring SUs, and iii) an Edge-Featured Graph Attention Network sensitive not only to the interdependence brought by the SU positions in space but also to reciprocal terrain characteristics. We assessed the model performance for both models via Mean Absolute Error (MAE), r-squared (R²), and Pearson Correlation Coefficient (PCC). The Edge-Featured Graph Attention Network model produced the best performance. The result for the first model targeting the mean V_LOS are 4.75 mm/y, 0.63, and 0.79 for MAE, R², and PCC, respectively. As for the second model, targeting the maximum V_LOS, these are 19.52 mm/y, 0.55 and 0.75. We also showcased interpretable multivariate models, where the contribution of each predictor to the InSAR velocities is summarized and interpreted. This represent a clear example where InSAR-derived hillslope velocities are accurately estimated at regional scales, thus setting up the scene for further advances towards space-time regional deformation modelling.