Scale independence of basin hypsometry and steady state topography

Basin hypsometry has long been used as an indicator of stages in landscape evolution. It has also served as a tool for detecting tectonically active regions. Whether hypsometric curve and its integral are independent of differences in basin size and relief has been discussed in many recent studies. The Taiwan Mountain Range, the result of an oblique collision between the Phillipine Sea Plate and the Eurasian Plate, provides an excellent opportunity to study landscape evolution in relation to steady state conditions. Taking advantage of the space-for-time substitution concerning the building process of Taiwanese mountains, this study sampled major drainage basins for hypsometric analysis, from the southern tip of the island to the northern end. This study found that the area previously known as steady state topography is characterized by 1) the hypsometric integral (HI) close to 0.5, 2) S-shaped hypsometric curves, and 3) normally distributed elevations. The response time required for a drainage basin of various Strahler orders to evolve from exposure of sub-aerial erosion to steady state topography ranges from 0.5 to 2.0 My, and is longer for basins of a higher Strahler order. The HI value of 0.5 for a drainage basin seems critical in terms of landscape evolution. The scale dependence of basin hypsometry is manifested mainly by the fact that HI of basins increases as basin order and/or basin size decreases. This study also found that basin hypsometry is scale independent where topography is in a steady state; scale dependence occurs only when drainage basins are in a non-steady state. The basin hypsometry may therefore be useful to probe into the nature of steady-state topography.