River Meandering Calculator

Meandering rivers migrate sideways across their floodplain over time, and this calculator estimates both the geometry of those bends and how fast the banks are eroding. Meander wavelength, amplitude, and radius of curvature are all scaled directly off channel width using empirical ratios from classic fluvial geomorphology — most directly Leopold & Wolman's 1960 paper "River Meanders" in the Geological Society of America Bulletin, which found wavelength running roughly 7 to 15 times bankfull channel width, and Hickin & Nanson (1984) — roughly 11× width for wavelength and 2.7× width for amplitude. Sinuosity (channel length divided by valley length) is derived from that same geometry, and channel slope is simply valley slope divided by sinuosity, since a winding channel loses elevation more gradually than a straight one over the same ground distance. Be aware of what that derivation implies: because the wavelength and amplitude ratios are both fixed multiples of channel width, width cancels out of the sinuosity formula entirely and the model reports the same 1.386 for every river you enter — it is the sinuosity of the assumed meander shape, and the divisor that turns valley slope into channel slope, not a measurement of your reach. If you need your reach's real sinuosity, measure channel length against valley length on a map or aerial image.

The migration rate itself combines two things: a stream-power term (based on discharge, channel slope, and width, following ω = ρgQS/W) and a geometry factor that peaks when the radius-of-curvature-to-width ratio is near 2.5 — the classic Hickin & Nanson finding that bends which are neither too tight nor too gentle migrate fastest. Migration rate is then divided by a bank-resistance factor you supply, since cohesive clay or bedrock banks erode far slower than loose sand for the same stream power. Treat every output as an order-of-magnitude estimate rather than a site-specific prediction: real channels are affected by vegetation, bank armoring, ice, and flood history that this simplified model doesn't capture. The cutoff risk score is a rough heuristic based on how far the bank has migrated relative to the meander's amplitude, flagging when a neck might pinch off into an oxbow lake.