APPLICABILITY AND LIMITATION OF A PREVIOUSLY PROPOSED EMPIRICAL EQUATION ESTIMATING WATERFALL RECESSION RATE

A waterfall is a prominent geomorphological feature in bedrock rivers, and its recession rate is often crucial to understand the development of fluvial landscapes. Our previous examinations of waterfall recession rates in several field sites in Japan, Taiwan and USA revealed that the waterfall recession rate is related to some physically-relevant parameters. Waterfall recession rate, D/T (m/y), is a distance (D) divided by time (T) of the recession, estimated from geomorphological and geological evidences. Factors relevant to the rate is modeled as below (Hayakawa and Matsukura, 2003, Earth Surf. Proc. Landf.): Supposing that waterfall recession rate is a function of erosive force of streams and resisting bedrock strength, a force/resistance index (FR) is derived from dimensional analysis using relevant parameters to be: FR = AP·(WH)^-1·r^0.5·S_c^-0.5, where A is upstream drainage area (km²), P is annual precipitation (mm y^-1), W is width of waterfall (m), H is height of waterfall (m), r is water density (kg m^-3), S_c is unconfined compressive strength of bedrock (MPa). Relationship between the dimensionless index FR and the estimated recession rates for waterfalls in the Boso district, eastern Japan, is shown as D/T = 99.7 FR^0.73. Case studies applying this empirical equation for various waterfalls suggest that the equation is basically applicable to waterfalls in rivers without much sediment load, while it is not with abundant sediment load, and the actual recession rates of the waterfalls are considerably higher than the equation-derived rates. This suggests that the transported sediments, acting as abrasion tool, can enhance the rate of erosion of waterfalls, and further data collection for waterfalls in rivers with abundant sediments is necessary. Other possible factors, such as scale, temporal changes in shape and environments, should also be examined.