How do lowered sea levels cause rivers to erode their beds more strongly?

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When sea levels drop, rivers are rejuvenated because their baselevel—the lowest point to which a stream can erode its bed—is lowered.12

Because sea level serves as the ultimate baselevel for most rivers, a decline in sea level increases the vertical distance between the river's source and its mouth. This change enhances the river's potential energy, which is then transformed into the kinetic energy of river flow. Consequently, the river gains greater power to incise and erode its bed as it cuts across the newly exposed continental shelf to reach the new, lower coastline. This process of entrenchment continues until the river adjusts to the new baselevel.1234