Equivalent Horton’s ratios of channel network within the framework of variable source basin area

The Seolmacheon Experimental Basin, Korea. To estimate the equivalent Horton’s ratios for channel network which are independent of the magnitude of threshold area or source basin area This paper aims to estimate the equivalent Horton’s ratios for a small experimental river basin in Korea, which are independent of the magnitude of threshold area or source basin area. To this end, various pattern of channel networks is extracted with the correspondence to the variable source basin area. It turns out that the original Horton’s ratios are highly variable and sensitive to the scale of observation for channel networks. Nevertheless, the combination of those such as the logarithmic rate between bifurcation ratio and area ratio might have a relatively constant trend implying scale invariance, which could be considered as an avenue to Horton’s ratios independent of the source basin area. Thereby, the equivalent Horton’s ratios could be regarded as the representative values for the basin of interest, so that they can provide a reliable description of channel network regardless of the scale of observation. It is confirmed that the scale invariance of channel network closely related to Hortons’ ratios would be the result stemming from cooperation or competition between the elongation and expansion of channel network due to variable source basin area. [Display omitted] •Scale invariance of channel networks induced by variable source basin area.•Combination of Horton’s ratios has a relatively constant trend implying scale invariance.•Equivalent Horton’s ratios as the representative values against the scale of observation for channel networks.