Parameter estimation of river incision models of soft sedimentary rocks – a case study on the Kamikita Coastal Plain, northeast Japan

Abstract. To predict long-term future landscape evolution, understanding of the river incision model, which is the main driver of continental erosion, is especially important. For the bedrock channel incision model (detachment-limited (DL) model: erosion rate E = KA^mSⁿ where A is drainage area, S is channel gradient, and K, m, n are parameters), parameters can be estimated by the slope-area analysis if E is known. Based on the worldwide basin-averaged denudation rates of ¹⁰Be concentrations, previous studies compiled the parameter values for variable lithology. However, the scarcity of data for the soft sedimentary rock limits the applicability of global scale compilation. In addition, measuring the ¹⁰Be concentration in sedimentary rock is difficult in humid and tectonically active regions like Japan. To address this, slope-area analysis was conducted in the Kamikita Coastal Plain, Japan, where bedrock lithology (sedimentary rocks of Miocene to Pleistocene) and uplift rate (~ 0.2 mm y⁻¹ for the past 300 ka) are assumed to be uniform. Parameter values were estimated based on river incision rates approximately derived from marine terraces (MIS 5e, 7, 9, and 11) which are widely distributed in the area. For six target rivers, DL-like behaviour was confirmed in the limited upstream and midstream areas located upstream of the alluvium distribution. Except for small rivers of A < 25 km², the concavity index m/n was between 0.35 and 0.6, which is the typical range for steady-state channels. The estimated exponent n was nonlinear, ranging between 1 and 2, which is consistent with the previous global compilations. This nonlinearity can be explained by past sea-level changes causing knickpoints at similar elevations. Finally, the erosion coefficient K was estimated to be 10^−5~−6 m^0.1 y⁻¹. For the main lithology of late Pliocene and early Pleistocene sedimentary rock, the estimated K almost agreed with the global relationship between K and unconfined compressive strength q_u (K ∝ 1/q_u²), supporting the significant influences of bedrock lithology on K.