A hydrologic flood routing method that predicts a river reach's outflow hydrograph from its inflow, using a storage equation with two parameters, K and x.
Muskingum routing is a hydrologic method for moving a flood wave down a river reach. Given the inflow hydrograph at the top of a reach, it predicts the outflow at the bottom, showing how the peak is delayed and flattened. It was developed in the 1930s for flood control work on the Muskingum River basin in Ohio, USA, and is still used in models such as HEC-HMS. The method assumes the water stored in the reach depends on both inflow I and outflow O: S = K[xI + (1 - x)O]. K is roughly the travel time of the flood wave through the reach. x is a weighting factor from 0 to 0.5. With x = 0 the reach acts like a reservoir and flattens the peak most. Natural rivers often have x of about 0.1 to 0.3. With the continuity equation this gives a routing step, O₂ = C₀I₂ + C₁I₁ + C₂O₁, where the three coefficients add up to 1. For example, take K = 12 h, x = 0.2 and a time step of 6 h. The denominator is 2K(1 - x) + Δt = 19.2 + 6 = 25.2, giving C₀ = (6 - 4.8) / 25.2 = 0.0476, C₁ = (6 + 4.8) / 25.2 = 0.4286 and C₂ = (19.2 - 6) / 25.2 = 0.5238. If inflow rises from 50 to 80 m³/s while outflow is 50 m³/s, the next outflow is (1.2 × 80 + 10.8 × 50 + 13.2 × 50) / 25.2 = 51.4 m³/s. K and x are usually fitted from observed inflow and outflow hydrographs. The time step should lie between 2Kx and 2K(1 - x), or the coefficients can turn negative and give odd results. The method cannot handle backwater, tides or flow reversal. The Muskingum-Cunge variant links K and x to channel shape and slope, so they can be estimated without flow records.