Geomorphic trajectory and landform analysis using graph theory

A big chunk of my research has focused on studying emergent sandbars in large sand-bedded rivers like the Missouri River. I first got involved with the work through a short-term contract with the USACE Hydrologic Engineering Center. Stanford Gibson was collaborating with the USACE Omaha District and the Missouri River Recovery Program to provide some additional sediment transport and geomorphology expertise. Part of his work involved generating some maps and statistics of sandbar change based on classified satellite imagery (classified as in Object-Based Image Analysis, not as in top-secret). I was already looking for an excuse to get involved with HEC, and my background in GIS made me a pretty good fit for the task.

I completed the project without much trouble, building Stan a GIS toolbox for processing the imagery and generating statistics on sandbar area. The work was tricky because the imagery captured sandbars at a wide range of river conditions. Some images captured the river at low-flow conditions, showing a river with huge sandbars and large swathes of bare sand; others captured the river at high-flow conditions, when most of the sandbars were drowned and only the vegetated high ground of the largest bars remained above water. To make matters worse, each image captured only a fraction of the study area; getting a complete snapshot of the system required a lot of effort chopping and splicing images at similar flows to get a complete picture. I was proud of the work I did, but I had this nagging feeling that there had to be a better way.

That better way turned into a chapter of my dissertation and my latest manuscript, published to Progress in Physical Geography (the accepted version is also available here). In the paper, I describe a novel method for generating time series of landforms from sets of fully- or partially-overlapping snapshots of a system. The method automatically links observations of individual landforms across images—even in cases where landforms fragment, merge, migrate, or become temporarily obstructed from view—and generates time series for individual landforms. The method is powered by graph theory, which I use to create a data structure that represents connections between features across snapshots.

This is a methods paper, so I focus on how the procedure compares to current practices of analyzing spatial data. I do some fairly basic demonstrations of analyzing the panel datasets the method generates, and explore the potential for applying some of the more advanced aspects of graph theory for an alternative approach to analyzing spatial data. But I’m not done yet! I’ve been applying the method to an analysis of the imagery that started this whole thing, and—at the risk of sounding immodest—the results are powerful. On top of that, I’m also pursuing an entirely new analysis that uses the datasets I developed for the NOAA Habitat Blueprint for the Russian River to demonstrate the method’s utility in ecological studies. In this new work, I also extend the method to capture not just connections between features between snapshots, but also how relationships between features in the same layer (e.g., feature adjacency) change through time.

I’m looking forward to sharing my analysis of the emergent sandbars of the Missouri River later this year. I think the method is a powerful new tool that can be applied to almost any field interested in tracking landscape features through time—whether they are actual landforms, habitat patches, or even more abstract spatial structures. If I haven’t convinced you to feel the same way, try reading the paper!