Runoff Hydrographs for Mathematical Watershed Model

by Roger E. Machmeier,
Curtis L. Larson,

Serial Information: Journal of the Hydraulics Division, 1968, Vol. 94, Issue 6, Pg. 1453-1474

Document Type: Journal Paper


A mathematical model of the channel system of a 21.35-sq mile watershed was developed. The partial-differential equations of momentum and continuity were expressed in finite difference form, and used to route the unsteady flow through the channel system, yielding outflow hydrographs. Rainfall excess in various rates and durations was used as the input to the model. All of the hydrologic time parameters which were evaluated from the model output varied with the supply rate. If the response of the watershed model can be considered representative of a natural watershed, none of the presently defined time parameters should be considered constants for a given watershed. The time to virtual (97% of) equilibrium varied inversely as the 0.23 power of the supply rate. The peak-flow rates showed a nonlinear relationship to runoff amount for a given duration. Peak discharges obtained with the model watershed do not support the unit-hydrograph principle but add to the existing evidence of runoff nonlinearity.

Subject Headings: Runoff | Hydrographs | Mathematics | Watersheds | Mathematical models | Hydrologic models | Channel flow | Parameters (statistics)

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