A unit hydrograph rainfall-runoff model using Mathematica

Many of the most commonly used rainfall-runoff computer programs involve runoff generation and hood hydrograph routing algorithms that reduce into Toeplitz matrix systems (see Hromadka II and Whitley, 2000, ASCE Journal of Hydrolic Engineering, submitted for publication). A link-node model representation of the watershed is constructed by subdividing the watershed into numerous subareas, and connecting the subareas by a network of hydrologic routing links (using Muskingum, convex, convolution, or pure translation methods). The U.S. Army Corps of Engineers Hydrologic Engineering Center's computer program HEC-1, or related programs, is used to implement the details of the link-node modeling. In contrast, the single-area unit hydrograph model approach represents a watershed as a single subarea, and utilizes a single unit hydrograph to represent all the effects being modeled by a link-node model representation. The system of Toeplitz matrices developed in Hromadka II and Whitley (2000) precisely describes the single-area and link-node model structures as they are actually applied; namely, in discretized timestep unit period additions and multiplications. It was shown that the single-area unit hydrograph model structure similar to the link-node unit hydrograph model structure; namely, both structures are Toeplitz matrix systems of the same dimension. It was also shown that the calibrated single-area unit hydrograph model Toeplitz matrices which are developed by direct calibration to gauged data achieves the minimum variance between the model structure and the available rainfall-runoff data. In this paper, a computer program is presented that implements the procedures presented in Hromadka II and Whitley (2000) for optimizing the unit hydrograph method. (C) 2000 Elsevier Science Ltd. All rights reserved.