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Example of how to perform wavelet analysis on a sequence of directional data, using the example of the flow direction of the Colorado river, USA. Supplementary code relating to the paper "Scale-Dependent Flow Directions of Rivers and the Importance of Subplate Support"
DEM preprocessing was written for Generic Mapping Tools v6 but is compatible with some older versions.
The python scripts require python version 3.6.9 and a modified version of the mlpy package. Generic scientific computing pacakges are also used (e.g. numpy, pandas, matplotlib etc...)
This repository contains 5 files.
preprocessing.sh indicates how to resample a river stored as a sequence of longitudes and latitudes into a sequence of azimuth as a function of downstream distance. This bash script calls a python script,
find_near.py is an auxilliary script called from within preprocessing.sh which finds the nearest adjacent point for a given river.
azimuths_wavelets_colorado.py performs wavelet transformation on the Colorado river flow-direction as a function of distance downstream by transforming azimuth into the complex plane. The script transforms the bearing into a function of distance and wavenumber, and subsequently displays the results. The script then performs the inverse wavelet transformation to reconstruct the original signal, as well as reconstructing filtered versions of the signal by removing variation contained on small wavelengths. Finally, the script shows that performing wavelet analysis on azimuths by splitting it into 'eastings' and 'northings' produces identical results to the method in the complex plane.
colorado.dat is a text file containing the longitude, latitude, distance downstream and flow direction of the Colorado river.
continuous.py is a modified source code of the mlpy package. These modifications can be implemented by simply replacing the original continuous.py (found where your python implementation is stored) with the one in this repository. Alternatively, the modifications are minor and are detailed in continuous.py.