Dimensionless hydrographs and equations for the time of equilibrium were developed for sections of nonuniform width. In order to determine the dimensionless hydrographs the equations of momentum and continuity were solved implicitly. This method was chosen because it is unconditionally stable independent of the time and distance increment. Using Manning's Equation for the frictional slope, a time increment of one-twelfth of the time of equilibrium, and boundary conditions of upstream depth and velocity equal to zero the dimensionless hydrograph for uniform sections matched that of the kinematic wave to nearly 60 percent of the equilibrium discharge. It also corresponded well with Morgali's results and Izzard's measured hydrograph. When the model was applied to sections of nonuniform width it was found only the end ratio, defined as the downstream width over the upstream width, affected the shape of the dimensionless hydrograph and the time of equilibrium. Equations were developed to find the time of equilibrium for ranges of end ratios. Corrections to find the hydrographs for sections of nonuniform width were determined to be applied to the kinematic wave discharge equation. For storms of duration less than the time of equilibrium the recession limb coincides with the recession limb from total equilibrium some time T after the rain ends. The time T was found to be independent of the end ratio and only affected by the discharge when the storm ended. / Master of Science

The HYDROPAC model was developed to improve the technology transfer from the science of hydrology to environmental planning disciplines by initiating advanced spatial analysis techniques for predicting rainfall-runoff relationships. This model integrates the Soil Conservation Service (SCS) equations for calculating runoff and a Geographic Information System (Map Analysis Package) in a framework that allows the simulation of runoff processes over a digital elevation model. The simulations are done in discrete time steps allowing the generation of a hydrograph at any desired point in the watershed and the overland flow patterns are displayed in maps. This framework addresses some of the current limitations of hydrologic model for stormwater management planning in terms of capabilities for analysis and communication of results. This manuscript describes the methods used to develop the framework of the HYDROPAC model and its usefulness for analyzing potential runoff problems during the planning process.

Project Completion Report, OWRT Project No. A-049-ARIZ / Agreement No. 14-31-0001-4003 / Project Dates: July 1, 1973 - June 30, 1974. / Acknowledgement: The work upon which this report is based was supported by funds provided by the United States Department of the Interior, Office of Water Research and Technology, as authorized under the Water Resources Research Act of 1964. / A non-linear reservoir model is used to represent the rainfall-runoff relationships for thunderstorms on the urban watersheds of Tucson, Arizona. Two types of computer programs are developed: a calibration program to obtain a best -fit calculated hydrograph; and a verification program to generate storm hydrographs given the watershed characteristics and a hyetograph. Calibration reveals the relationship of the model parameters, namely, (f) the inflow coefficient, (a) the constant coefficient, and (TL) the time lag, to the total rainfall, drainage area, channel length, and infiltration capacity of the watershed. The average discrepancy between the predicted hydrograph and the actual hydrograph for Tucson urban watersheds is 20 -25 percent.