A recursion model to calculate the original widths of narrow terraces and their backwearing rates in a coastal area subjected to regular uplift during the late Holocene

- A new recursion model for flights of narrow terraces is proposed.
- Widths of narrow terraces are reconstructed and backwearing rates calculated.
- Estimated backwearing rates may have value for comparison with numerical simulations.

This paper presents a new and simple recursion model to calculate the erosion rates of flights of narrow, late Holocene terraces under conditions of regular uplift. The general equations developed are: Δxn = Δx′n + Δxn − 1 − Δzn − 1 / tanθn − 1, and εn = Δxn / (tn − tn + 1), where n is the number of narrow terraces, Δxn is the original width of narrow terrace n, Δx′n is the observed width of narrow terrace n, Δxn − 1 is the original width of narrow terrace n - 1 (one step below terrace n), Δz is the height of the narrow terrace, θ is the gradient of the slope, and ε is the backwearing (i.e., horizontal erosion) rate. The model can be used to calculate the backwearing rate if the widths of the present shore platform and of the emerged narrow terraces can be obtained, and where chronological control is available. Backwearing rates on the Ashizuri, Boso and Kii peninsulas in Japan were calculated using the model to be approximately 0.001, 0.2-1.0, and 0.009 m/yr, respectively. These calculated values are in agreement with the rates of backwearing directly measured in previous studies.