Forecasting landslides using community detection on geophysical satellite data

As a result of extreme weather conditions, such as heavy precipitation, natural hillslopes can fail dramatically; these slope failures can occur on a dry day, due to time lags between rainfall and pore-water pressure change at depth, or even after days to years of slow motion. While the prefailure deformation is sometimes apparent in retrospect, it remains challenging to predict the sudden transition from gradual deformation (creep) to runaway failure. We use a network science method—multilayer modularity optimization—to investigate the spatiotemporal patterns of deformation in a region near the 2017 Mud Creek, California landslide. We transform satellite radar data from the study site into a spatially embedded network in which the nodes are patches of ground and the edges connect the nearest neighbors, with a series of layers representing consecutive transits of the satellite. Each edge is weighted by the product of the local slope (susceptibility to failure) measured from a digital elevation model and ground surface deformation (current rheological state) from interferometric synthetic aperture radar (InSAR). We use multilayer modularity optimization to identify strongly connected clusters of nodes (communities) and are able to identify both the location of Mud Creek and nearby creeping landslides which have not yet failed. We develop a metric, i.e., community persistence, to quantify patterns of ground deformation leading up to failure, and find that this metric increased from a baseline value in the weeks leading up to Mud Creek's failure. These methods hold promise as a technique for highlighting regions at risk of catastrophic failure.

Figure 1

The root mean square (rms) of the line-of-sight (LOS) velocity (black circles) for the entire study area leading up to the day of failure ($T=0$); data from Handwerger et al. [27]. Blue bars are the total weekly precipitation, from PRISM [40]. The wet seasons roughly correspond to December to May each year.

Figure 2

(a) The root mean square (rms) of the line-of-sight (LOS) velocity, for each of the four regions. The wet seasons shown in Fig. 1 are shaded in blue. Inset: bare earth hillshade map from light detection and ranging (LIDAR) showing the four regions within the study area. (b) Maps of the LOS velocity for each of the four regions at two times: $-32$ and $-176$ days before failure. Data is from [27].

Figure 3

Schematic of the construction and analysis of our multilayer network. We sample the digital elevation model (DEM) and a series of velocity maps on a disordered mesh to create a multilayer network weighted by both. Using this network, we selected the spatial coupling parameter $\gamma$ and the temporal coupling parameter $\omega$ to detect communities of interest.

Figure 4

(a) Network flexibility $\mathrm{\Xi }$ [Eq. (4)] and (b) network stationarity $\zeta$ [Eq. (5)] as a function of the choice of a particular temporal coupling parameter $\omega$, for fixed spatial coupling $\gamma =1$. Each data point is for one of the 10 meshes, distinguished by color.

Figure 5

Results of community detection using $\gamma =1, \omega =1$, shown for six representative layers prior to failure at $T=0$ days. Nodes that are members of the same community have the same (arbitrary) color, corresponding to a single community ID number. Black nodes represent singleton communities. The black outline is Mud Creek.

Figure 6

Strip-chart showing the evolution of the community structures detected for parameters $\gamma =1$ and $\omega =1$, separately highlighting location, duration, and significance ${\mathrm{\Psi }}_c$. Each detected community that is found has an ID number that is arbitrary (but corresponds to the order of detection) and is plotted as a line with three properties: color specifies its location (see inset map), the extent along the horizontal axis specifies its duration, and the thickness of the line measures the size and strength of that community at layer $\ell$, according to Eq. (6). The outlines of the creeping landslides found within the area are shown in the inset map.

Figure 7

Community persistence ${\mathrm{\Pi }}_{\ell }$ [Eq. (7)] as a function of time before failure, averaged over 10 meshes, (a) for different choices of spatial coupling parameter $\gamma$ at fixed $\omega =1$ and (b) for different choices of temporal coupling parameter $\omega$ at fixed $\gamma =1.0$). (c) The mean community persistence ${\mathrm{\Pi }}_{\ell }$ over 10 meshes using $\gamma =1,\omega =1$. The standard error, measured across the ensemble of 10 meshes, is smaller than the symbol size; the horizontal black line shows the temporal mean. The dashed lines represent the six snapshots of the community structures that are shown in Fig. 5. The blue shaded area represents the wet seasons shown in Fig. 1. The red shaded area highlights where ${\mathrm{\Pi }}_{\ell }$ starts to significantly rise above the mean. The black line shows the maximum cumulative displacement within the Mud Creek polygon.