Classification of channel network geometry using the width function and classification trees

Channel networks can have different geometries due to the variety of geophysical and climatic processes that take place across the different regions where they are located. Many river networks can be classified into dendritic, parallel, pinnate, rectangular and trellis. Quantitative methods have been proposed to perform this classification, but they can be difficult to implement. A simpler objective classification method could lead to better identification of networks, more widespread use, and improved construction of rainfall-runoff models due to the strong linkage between the basin morphology and the hydrologic response. In this work, we propose and explore several classification methods based on the distribution of flowpath lengths within the basin. In particular, we represent this distribution both in the space domain through the width function (WF) and the frequency domain through the power spectrum density (PSD) of the WF. Several classification trees are proposed using the following parameters: (1) PSD slope and breakpoint at which high frequencies do not contribute significantly, (2) the lowest frequency component's phase angle of the PSD, (3) the first four moments of the WF, (4) the parameters of a Beta function fitted to the WF, and (5) the standard deviation of the errors between the WF and the Beta function. Ten basins of each network type (previously identified) were used to construct and test the classification trees. Several trees based on 2 to 4 parameters are able to attain overall efficiencies between 88% to 92%. These trees also have efficiencies of 60% to 65% when cross validation tests were performed. Overall, the classification trees perform quite well, given the high efficiency values, the reduced number of parameters, and the fact that only one well-known and easy-to-compute function, the width function, is needed for the classification.