Geomorphic trajectory and landform analysis using graph theory: A panel data approach to quantitative geomorphology

Comparing successive datasets of GIS polygons derived from remote-sensing data is a common approach to quantify morphological change. GIS-derived datasets capture instantaneous observations or “snapshots” of the state of a system at a given time but do not explicitly capture the temporal sequences needed to characterize system processes. Comparisons between these “temporally-naive” datasets can be used to infer properties and trends of the landscape as a whole, but tracking changes in the characteristics of individual landforms (e.g. sandbars, dunes, or other surface features of interest) across snapshots is labor-intensive and infeasible for large or irregular datasets. Using traditional computer-based procedural methods to compare sequences of datasets without knowledge of temporal trajectories introduces several challenges and data artifacts that complicate analysis. We propose a graph-theory approach for processing sequential spatial data to automatically identify and track distinct groups of related landforms or “geomorphic units” across fully or partially overlapping snapshots. This approach allows tracking even in cases where landforms fragment, merge, migrate, or become temporarily obstructed from view. The method promotes new panel data analysis opportunities and overcomes three critical limitations of traditional procedural methods of assessing landscape change from spatial data: (1) it can generate landscape metrics based on geomorphic units, rather than the arbitrary geographic units of the underlying spatial datasets, (2) it distinguishes missing or obstructed observations from changes in the characterization of landforms due to environmental conditions, and (3) it automatically generates panel datasets and discriminates between within-landform change and across-landform variation. The panel datasets can be used to upscale feature-level information to system-level metrics and analysis. Furthermore, a graph-theory approach can yield insight on geomorphic change through analysis of the graph structure, and offers a promising approach for geomorphological analyses which retain information on the spatial configuration of geomorphic units. We demonstrate the method with examples from emergent sandbars on the Missouri River