Flood routing on small streams: A review of Muskingum-Cunge, cascading reservoirs, and full dynamic solutions

Flood wave routing methods are adapted for small, naturally meandering streams. A simplified derivation of the Muskingum-Cunge equation is presented, based on Perumal and Kalinin-Milyukov's "characteristic reach length" concept. The derivation was extended to meandering streams, using the "parallel channels" analogy. "Cascading reservoirs", a second approximate method, is shown to be a special case of Muskingum-Cunge when properly formulated. Both approximate methods were evaluated against two "fully dynamic" solutions: the UNET-based solver in HEC-RAS and the National Weather Service's FLDWAV program.;The four models were tested on four natural streams in northeastern Kansas. Detailed procedures for creating "equivalent reaches" were developed. The sensitivity of model stability was tested against variations in distance step size and other controls. HEC-RAS and FLDWAV gave nearly identical results for all the test reaches. The two approximate methods also performed well, but with deviations which are discussed. Recommendations were given for setting distance steps in fully dynamic solutions.