Relation between bank erosion and bed incision in the braided reach of the Lower Yellow River undergoing channel degradation

A general increase in the bankfull width and depth is found in downstream reaches because of upstream damming, especially in the braided reach of the Lower Yellow River (LYR), but the magnitude of bank erosion and its relation with bed incision remain little explored. Here based on long-term measured cross-sectional profiles (1999–2020), a quantitative method is proposed to estimate the bank erosion volume in the braided reach of the Lower Yellow River, with the contribution of bank erosion to the channel scour volume further determined. A quantitative relation was developed and calibrated between bank erosion width and bed incision depth, using the sediment continuity equation and measured data. The results indicate that: (i) significant bank erosion and bed incision processes are prevalent in the braided reach and its sub-reaches, with the bankfull widths increasing by 317–511 m and the bankfull depths increasing by 1.9–2.4 m in these reaches after the operation of the Xiaolangdi (XLD) Reservoir in 1999. Bank erosion has been dominant over bank accretion at more than 71% of the sections in the braided reach, with the most active bank deformation detected in the middle sub-reach. (ii) The cumulative bank erosion volumes temporally increased and spatially decreased, with the value of 1.80×10⁸ m³ in the upper sub-reach (R1), 1.52×10⁸ m³ in the middle sub-reach (R2), 1.08×10⁸ m³ in the lower sub-reach (R3), and 4.40×10⁸ m³ in the whole braided reach during the period of 1999–2020. Bank erosion contributed 33% of the cumulative channel scour volume in the braided reach, with a close relation developed between cumulative bank erosion volume and the previous 5-year average incoming sediment coefficient during flood seasons. (iii) A close inverse relation exists between bank erosion and bed incision in the whole braided reach and its sub-reaches, with the coefficients of determination greater than 0.90, which indicated that bank erosion hindered the process of bed incision. If there was no bank erosion after 1999, the cumulative bed incision depth would increase by at least 0.7 m in each reach. Furthermore, a similar quantitative relation was also applied to calculate the cumulative bed incision depth and bank erosion width in the braided reach during the period of 1960–1964 (the first stage after operation of the Sanmenxia Reservoir). Quite high accuracy was achieved in this analysis, with the coefficient of determination being equal to 0.96.