Modeling the Evolution of Incised Streams: I. Model Formulation and Validation of Flow and Streambed Evolution Components Eddy J. Langendoen, M.ASCE 1 ; and Carlos V. Alonso, M.ASCE 2 Abstract: A robust computational model for simulating the long-term evolution of incised and restored or rehabilitated stream corridors is presented. The physically based model simulates the three main processes that shape incised streams: hydraulics, sediment transport, and streambed and bank adjustments. A generalized implicit Preissmann scheme is used for the spatial and temporal discretization of the flow governing equations to accommodate large time steps and cross sections spaced at irregular intervals. The solution method introduces several enhancements that increase its robustness, specifically to simulate flashy flows. Transport of cohesive or cohesionless graded bed material is based on a total-load concept, and suspended and bed load transport modes are accounted for through nonequilibrium effects. The model simulates channel width adjustment by hydraulic erosion and gravitational mass failure of heterogeneous bank material. The present paper focuses mainly on the treatment of streamflow hydraulics and evolution of graded streambeds, and reports simulations of published experiments on degrading and aggrading channels with graded bed material. Description and validation of the model’s stream- bank erosion component and the application of the model to incised stream systems are presented elsewhere. DOI: 10.1061/ASCE0733-94292008134:6749 CE Database subject headings: Computer models; Channel morphology; Open channel flow; Bank erosion; Sediment transport; Streams. Introduction Channelization-induced stream incision is widespread in the mid- south and midwestern United States. The highly erodible soil is unable to halt the incision and subsequent widening of these channelized streams, leading to increased sediment production and yields as material is eroded from the bed and banks. In north- ern Mississippi incision has particularly been severe for those streams draining westwards from the Loess Hills into the Yazoo River Basin. Simon et al. 2004 show that the Mississippi Valley Loess Plains ecoregion experiences the second highest suspended sediment yields in the continental United States. Many of these streams have experienced severe instability since European settle- ment in the 1830s, leading to disruption of the fluvial system and severe impacts on local communities, farmers, and ecological habitats Watson et al. 1997. The Federal Interagency Demon- stration Erosion Control DEC project was established in 1984 and charged with planning, design, and construction of structural rehabilitation measures to stabilize the channels, restore habitat, and reduce sediment yield from the Yazoo River Basin Cooper et al. 1996. The DEC approach is largely based on geomorpho- logical concepts that depends on characterization of the rate and frequency at which water flows through a stream channel Dunne and Leopold 1978; Carling 1988. Determination of how much, how fast, how deep, and how often water flows is a critical step in predicting stream channel evolution and developing restoration initiatives FISRWG 1998. Similarly, accurate evaluation of how often and how much sediment is transported by a stream as a function of water discharge is an important step in establishing a scientifically defensible strategy to develop clean sediment total maximum daily loads TMDLs in incised streams and rivers USEPA 1999. The Federal Interagency Stream Restoration Working Group FISRWG recently reviewed eight computer models frequently used in simulations of alluvial streams FISRWG 1998. All these models exhibit in their present form one or more of the following limitations: 1 employ piecewise-steady inflow hydrographs and backwater computations that are not suitable for flashy stream- flows in upland areas; 2 channel width adjustment through mass wasting is either not considered or approximated through other than process-based algorithms; and 3 cannot simulate flow pro- cesses influenced by in-stream grade stabilization structures. Therefore, there is a definite need for a model that is free from any of these restrictions. In response to this need, the National Sedimentation Labora- tory of the U.S. Department of Agriculture-Agricultural Research Service developed the CONCEPTS CONservational Channel Evolution and Pollutant Transport System computer model to evaluate the long-term impact of DEC rehabilitation measures on sediment yield and TMDLs Langendoen 2000. CONCEPTS is a physically based computer model capable of simulating processes that shape degraded stream corridors over long periods of time. 1 Research Hydraulic Engineer, Agricultural Research Service, National Sedimentation Laboratory, U.S. Dept. of Agriculture, Oxford, MS 38655. E-mail: eddy.langendoen@ars.usda.gov 2 Research Hydraulic Engineer, Agricultural Research Service, National Sedimentation Laboratory, U.S. Dept. of Agriculture, Oxford, MS 38655 Note. Discussion open until November 1, 2008. Separate discussions must be submitted for individual papers. To extend the closing date by one month, a written request must be filed with the ASCE Managing Editor. The manuscript for this paper was submitted for review and pos- sible publication on January 12, 2006; approved on September 14, 2007. This paper is part of the Journal of Hydraulic Engineering, Vol. 134, No. 6, June 1, 2008. ©ASCE, ISSN 0733-9429/2008/6-749–762/$25.00. JOURNAL OF HYDRAULIC ENGINEERING © ASCE / JUNE 2008 / 749