An Automated System of Knickpoint Definition and Extraction from a Digital Elevation Model (DEM): Implications for Efficient Large-Scale Mapping and Statistical Analyses of Knickpoint Distributions in Fluvial Networks

Abstract:

Knickpoints, or convexities in a stream’s longitudinal profile, often delineate boundaries in stream networks that separate reaches eroding at different rates resulting from sharp temporal or spatial changes in uplift rate, contributing drainage area, precipitation, or bedrock lithology. We explicitly defined the geometry of a knickpoint in a manner that can be identified using an algorithm which operates in accordance with the stream power incision model, using a chi-plot analysis approach. This method allows for comparison between the real stream profile extracted from a DEM, and a linear best-fit line profile in chi-elevation space, representing a steady state theoretical stream functioning in accordance to uniform temporal and spatial conditions listed above. Assessing where the stream of interest is “under-steepened” and “over-steepened” with respect to a theoretical linear profile reveals knickpoints as certain points of slope inflection, extractable by our algorithm. 

We tested our algorithm on a 1m resolution LiDAR DEM of Santa Cruz Island (SCI), a tectonically active island 25km south of Santa Barbara, CA with an estimated uplift rate between 0.5 and 1.2mm/yr calculated from uplifted paleoshorelines. We have identified 1025 knickpoints using our algorithm and compared the position of these knickpoints to a similarly-sized dataset of knickpoints manually selected from distance-elevation longitudinal stream profiles for the same region. Our algorithm reduced mapping time by 99.3% and agreed with knickpoint positions from the manually selected knickpoint map for 85% of the 1025 knickpoints. Discrepancies can arise from inconsistencies in manual knickpoint selection that are not present in an automated computation. Additionally, the algorithm measures useful characteristics for each knickpoint allowing for quick statistical analyses. Histograms of knickpoint elevation and chi coordinate have a 3 peaked distribution, possibly expressing 3 levels of uplifted marine terrace platforms on SCI. Few knickpoints exist with a contributing drainage area >200,000m², demonstrating a cutoff drainage area where knickpoint migration has stalled. We intend to use this tool to further explore the significance, evolution, and dynamics of knickpoint features on SCI.