At what scales does a river meander? Scale-specific sinuosity (S3) metric for quantifying stream meander size distribution

Stream bend geometry is linked to terrain features, hydrologic and ecologic conditions, and anthropogenic forces. Knowledge of the distributions of geometric properties of streams advances understanding of changing landscape conditions and associated processes that operate over a range of spatial scales. Statistical decomposition of sinuosity in natural linear features has proven a longstanding challenge and a particular impediment to automated analysis. This paper demonstrates that sinuosity can vary with the magnitude of units at which it is measured (measurement scales). The paper derives a scale-specific sinuosity (S3) metric intended to measure stream bend geometry across a range of measurement scales. The metric is warranted for analysis and modeling at measurement scales equal or similar to the spatial process and landscape conditions under investigation. Derived from the Richardson (1961) plot, the S3 metric quantifies a frequency signature of planform bend sizes spanning a range of measurement units, enabling visual and quantitative analysis of bend geometry in linear stream features. Derivation of the metric makes evident a systematic relationship between stream bend size, sinuosity, and measurement scale, formalizing a relationship between sinuosity and fractal dimension. The paper shows the utility of the S3 metric in examining bend patterns for synthetic and real-world linear stream data.