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Transient river profiles with slope-break knickpoints record past and present tectonic information. The channel upstream of a knickpoint represents a relict profile in equilibrium with previous tectonic forcing, while the downstream segment reflects current uplift rates. Relict profile reconstruction projects the paleo-channel across the knickpoint to estimate the minimum incision depth. Traditional methods, such as slope-area analysis and the integral approach, can introduce errors due to data smoothing, resampling, and residual autocorrelation in chi-elevation regressions. To address these limitations, we propose an improved integral approach equipped with generalized least squares to eliminate autocorrelated residuals and provide accurate estimates of channel concavity and steepness indices. These indices are then used to reconstruct the relict profile and estimate incision depth. We validate our method using a synthetic transient river profile generated by 1D numerical modeling and further apply it to rivers crossing the mountain ranges bounding the Taiyuan Basin in northern China. Our results identify slope-break knickpoints, reconstruct relict profiles, and estimate incision depths, which provide lower limits of fault throw since the late Miocene to early Pliocene. This improved method offers a robust approach to analyzing transient river profiles and quantifying tectonic deformation.

Equipping the integral approach with generalized least squares to reconstruct relict channel profile and its usage in the Shanxi Rift, northern China