Sinuosity of Finnish rivers

Introduction

Meandering of rivers. Fractal dimension. Sinuosity. Scale-specific sinuosity. Stream geometry.

Geomorphology.

Sinuosity is linked to eg terrain features.

Relationships between sinuosity and fractal dimension have been searched (e.g., Snow, 1989; Klinkenberg, 1992; Montgomery, 1996; Troutman and Karlinger, 1998). An empirical relationship indicates that sinuosity correlates with fractal dimension (Montgomery, 1996). It seems that a single fractal dimension value may not capture the true character of a line.

Methods

Spectral analysis

Fourier shape analysis

Wavelet transforms

Series of shape metric.

Scale-specific sinuosity (S3) metric. "The S3 plot can be interpreted as a histogram of bends of different sizes".

Scale-specific sinuosity

Stride length / length of a measure stick.

Incomplete paths where the final stride is too short of the end of the feature, thus we will have $F_{\text{extra}}$. That can be incorporated using eg

$\ell ={\frac {F}{F-F_{\text{extra}}}}ns$

where $F$ is the full length, $n$ is the number of full steps and $s$ is the stride length.

References

At what scales does a river meander? Scale-specific sinuosity (S3) metric for quantifying stream meander size distribution, Lawrence V. Stanislawski, Barry J. Kronenfeld, Barbara P. Buttenfield, Ethan J. Shavers. https://www.sciencedirect.com/science/article/pii/S0169555X2300154X

Fractal geometry to length, perimeter, area and volume: (Richardson, 1961; Mandelbrot, 1967, Mandelbrot, 1977, Mandelbrot, 1982; Lam and De Cola, 1993).