2.2.3. Attribute Augmentation by Incorporating External Factors

Generally, the dynamic movement of a landslide is subject to internal geological conditions and external triggering factors [4,21]. As for landslides on the reservoir bank of TGR, the fluctuation of the reservoir water level and varying precipitation are two main external factors influencing landslide behaviours [22,23]. However, the studies using GCN to learn spatial dependencies often adhere to a single measure (e.g., distance) to represent the weights in the adjacency matrix [24,25] without considering the effects of the external trigging factors, which inevitably hampers the model performance given the complexity of landslide deformation patterns.

In this study, we apply attribute-augmented graph convolution operations on GNSS observations. The attribute-augmented unit integrates features of the displacements time series, the synchronous precipitation and the water level fluctuation to represent the contribution of the external dynamic triggering factors. The augmented matrix with weighted adjacency matrices is incorporated into the forecast model to enhance the extraction of realistic spatiotemporal dependency.

An attribute matrix *<sup>D</sup>* ∈ *RN*×(*k*∗*t*) stands for *<sup>k</sup>* external factors at time *<sup>t</sup>*. It considers that the effects of the triggering factors on the landslide displacements show significant time lags. We use an extended time window *m* + 1 to express the attribute information instead of the original one at time t; that is, the attribute matrix *D<sup>k</sup>* is denoted by

*Dk <sup>t</sup>*−*m*,*<sup>t</sup>* = [*D<sup>k</sup> <sup>t</sup>*−*m*, *<sup>D</sup><sup>k</sup> <sup>t</sup>*−*m*−1, ... , *<sup>D</sup><sup>k</sup> <sup>t</sup>* ]. Then, the attribute-augmented matrix *S* can be inferred by combining the feature matrix *X* and the attribute matrix *D*:

$$S\_t = [X\_{t'}D\_{t-m,t'}^1D\_{t-m,t'}^2 \dots, D\_{t-m,t}^k] \tag{3}$$

Thus, the displacement prediction task can be regarded as learning the function *f* to predict the displacements, as shown in Equation (4):

$$f(G, X | D) = [X\_{t+1}, \dots, X\_{t+T}] \tag{4}$$
