A systematic approach and software for the analysis of point patterns on river networks

Abstract

Many geomorphic phenomena such as bank failures, landslide dams, riffle-pool sequences and knickpoints can be modelled as spatial point processes. However, as the locations of these phenomena are constrained to lie on or alongside rivers, their analysis must account for the geometry and topology of river networks. Here, we introduce a new numeric class in TopoToolbox called Point Pattern on Stream networks (PPS), which supports exploratory analysis, statistical modelling, simulation and visualization of point processes. We present three case studies that aim at inferring processes and factors that control the spatial density of geomorphic phenomena along river networks: analysis of a synthetic dataset of points on a stream network, the analysis of knickpoints in river profiles, and modelling spatial locations of beaver dams based on topographic metrics. The case studies rely on exploratory analysis and statistical inference using inhomogeneous Poisson point processes. Thereby, statistical and probabilistic procedures implemented in PPS provide a systematic approach for treating and quantifying uncertainties. PPS offers a consistent numeric framework for modelling point processes on river networks with a wide range of applications in fluvial geomorphology, but also other disciplines such as ecology.