A distributed surface flow model for watersheds with large water bodies and channel loops

SummaryLarge water bodies (25 and 172 km2) and channel loops exist in the study watershed, the Tone River basin, Japan. In order to overcome the difficulties in routing the two-dimensional surface flows in the water bodies and channel loops, the Large-scale, Unified, and Optimization Model has been developed. In the model, the ordering scheme based on the freely-seriate-tree structure is adopted to order the stream network with channel loops. The diffusive wave approximation of the two-dimensional free surface flow equations are employed as the governing equations for the surface flows including both overland and channel flows. Both overland and channel flows are placed in the same physical domain, in which a channel grid cell exchanges mass and momentum with the eight adjacent grid cells of overland, channels and water bodies, and consequently it is simple and easy to incorporate water bodies and channel loops into the model. The finite difference method based on the staggered grid scheme is utilized to discretize the governing equations and the optimization numerical scheme, SIMPLE, is employed to solve the finite difference equations using a tri-diagonal matrix. This paper focuses primarily on the formulation of the model. Limited model calibration and validation using point streamflow data in the Tone River basin are presented, and more complete evaluation of the distributed outputs is left for future work.