Quantifying the influence of asymmetric uplift, base level elevation, and erodibility on cross-divide χ difference

It is generally accepted that a river long profile contains both temporal and spatial signals on uplift rate. The uplift history (temporal variation) inferred from the channel profile will be substantially affected by spatial variation of the uplift rate. Therefore, knowing the spatial variation in uplift rate is the premise of obtaining a reliable uplift history. The χ-plot approach is widely used as a substitute for a channel profile when extracting tectonic information from topography. Theoretically, when a drainage divide is at a steady-state, the cross-divide difference in χ values is controlled by the uplift rate and erosion coefficient of bedrock. However, how the spatial variation in uplift rate and lithology influence the cross-divide difference in χ values is still unclear. In this study, we derive an analytical solution to quantify the influence of spatially variable rock uplift rate, erosion coefficient, outlet elevation, and drainage-basin morphology on cross-divide χ difference. We then use numerical landscape evolution models with different uplift rate ratios, erosion coefficients, and base level elevations, across drainage divides, to test the equation. The cross-divide χ ratios in the numerical models are broadly consistent with theoretical prediction, confirming reliability of the formula. We further apply the formula to two natural examples, showing its applications. In the Wula Shan case, the uplift rate ratio of its two boundary faults is ~0.20, and in the Xizhou Shan case, the main drainage divide is migrating southward according to the equation. The new equation improves the reconstruction of tectonics from channel profiles. Moreover, it extends the cross-divide comparison of χ values to more complex geological conditions for measuring the stability of drainage divides.