As water drains toward oceans and seas, it slowly carves networks of valleys and channels such as the one shown in figure 1, a topographical map of a stream system that feeds the Apalachicola River near Bristol, Florida. Those so-called drainage networks form in part due to erosion by surface runoff, a process that involves a complex, hard-to-disentangle feedback: Runoff flows shape the topographical landscape, but that landscape also shapes the paths of runoff flow.

Drainage-network formation is also partly due to groundwater flows. Precipitation absorbed by the ground tends to settle into subsurface reservoirs, or aquifers. If an aquifer is pierced by a deep channel—one whose lowest point sits below the water table—then groundwater can seep into the channel and, in the process, erode the channel walls. Known as seepage erosion, that process causes low-lying streams to widen and lengthen over geologic time scales. Because the flow dynamics...

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