Space−Time Cube and Cluster Representation of Evolving Landforms at Local and Regional Scales Using Lidar Time Series Data

Repeated light detection and ranging (lidar) observations (3D x,y,z point cloud data) acquired from terrestrial and aerial perspective are utilized to study evolving landforms at local and regional scales. To do so, space-time cube representation and unsupervised clustering are applied to analyze patterns in spatial-temporal surface evolution captured in the lidar time series data. Two cases studies will be presented.

In the first case study, terrestrial lidar, more commonly referred to as terrestrial laser scanning (TLS), is applied to monitor bank erosion along an inland stream in North Carolina USA that has incised through historic millpond (legacy) sediment. Differencing of digital terrain models (DTMs) derived from the TLS point cloud time series revealed that volume change was highly variable both in space and time across the survey epochs. Computation of contributing sediment loss by sedimentary layer (legacy vs non-legacy) revealed that the majority of loss occurred within legacy sediment during the 3^rd survey epoch. This epoch corresponded to the highest rainfall intensities recorded during the study period and indicates groundwater seepage as the main mechanism for bank failure. To fully capture patterns in surface change in both space and time, the DTM time series was stacked into a voxel model to form a space-time cube (STC). The STC provides a compact representation for extracting unique visualizations of landform evolution, such as 3D temporal slices and contour isosurfaces. Continuous STC further extends this approach by generating a voxel model directly from the time series of point cloud data using trivariate interpolation. A uniform time resolution STC was generated in this manner and used to derive spatiotemporal gradients (vectors of fastest surface change) to further explore connections between surface change and the underlying physical processes. Furthermore, k-means clustering was implemented to explore patterns in surface behavior. The surface was clustered into k distinct groups based on rate of surface elevation change and acceleration derived from the STC. Clustering revealed distinct differences in how the surface evolved within legacy and non-legacy sediment layers indicating different controlling processes, such as seepage and fluvial erosion.

In the second case study, a time series of airborne lidar surveys are used to examine Hurricane Ike beach and foredune recovery along the upper Texas coast. Hurricane Ike made landfall on the northern end of Galveston Island, Texas, at approximately 0700 UTC on September 13, 2008, with a minimum barometric pressure of 950 mbar (28 inHg) and sustained winds of 110 mph (180 km/h), making Ike a Category 2 hurricane. The lidar surveys were acquired in 2008 (post-impact), 2010, 2011, and 2012. Bare-earth digital elevation models (DEMs) derived from the lidar data are used to examine volumetric sediment loss and recovery alongshore. First, we apply STC representation to examine the range of landform change alongshore. Next, we seek to identify different regions of beach and foredune recovery alongshore. To do so, an unsupervised clustering approach is applied using the k-means algorithm. Clustering is performed on the grid cell difference between two consecutive DEMs. In so doing, we are clustering based on how elevation is changing spatially (per grid cell) and temporally alongshore (beach and foredune). The objective is to identify regions of the coast exhibiting different behavior (e.g. eroding, accreting, stable). Inherent to k-means is the need to determine the optimal number of clusters “k” that best represents the multi-dimensional input space of the data. A method is developed to derive the k number of clusters based on a modified information criterion. The output from the cluster analysis is a segmentation of the beach and foredune system into k distinct regions (clusters). Results reveal interesting patterns in post-Ike beach and foredune recovery behavior along the coast. This discussion will present an interpretation of those results including connections to geomorphology and physical processes in the region.