A statistical test for drainage network recognition using MeanStreamDrop analysis

This paper provides a new statistical test to evaluate the threshold of validity for the Mean Stream Drop analysis. In the case of a constant area threshold, the method aims to provide a unique threshold value to extract the drainage network through a statistical test more efficient than those widely used. The proposal starts from the assumption that a minimum threshold value exists suitable for drainage network extraction. Then, the method proceeds with Horton–Strahler ordering of the network and statistically analysing the network geometry. This procedure is repeated for all the threshold values in the set under investigation, using a statistical permutation test, called APTDTM (Adjusted Permutation Test based on the Difference between Trimmed Means). Statistical significance is evaluated by p-values adjusted to account for multiple comparisons. As a final result of the statistical analysis, the right threshold value for the specific basin is identified. Classical procedures are based on a set of two sample t-tests. However, this method relies on the assumptions of normality and homogeneity of variance, which are unlikely to hold in practice. The APTDTM test presented here provides accurate p-values even when the sampling distribution is not close to normal, or there is heteroskedasticity in the data.