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Abstract Rates of land surface processes provide insights into climatic and tectonic influences on topography. Bedrock incision rates are estimated by dating perched landforms such as strath terraces, assuming a constant bedrock incision rate from terrace abandonment to the next terrace level or present river level. These estimates express biases from the stochastic nature of sediment and water discharge in controlling river incision as well as from using a mobile channel elevation as a reference frame, leading to different incision rates when calculated over different timeframes. We introduce a 1‐D model incorporating fluvial mechanics, tectonics, sediment, and climate variability to predict these biases and assess their sensitivity to climate and tectonics. Findings suggest biases intensify under highly variable climates and slow rock uplift, with climate periodicity being a primary control for our modeled scenarios. Our model provides a mechanism to improve river incision measurement uncertainty, impacting paleoclimate and tectonic geomorphology reconstructions.