Alluvial fans are the most prominent landscape features in the semi-arid and arid regions of the world. This geographic feature is often observed in the American Southwest. From the viewpoint of engineering practices, the hydraulic behavior of overland flows on alluvial fans is very different from open channel flows. Alluvial fan flows are subject to high roughness effects due to wide and shallow surface flow. In current practices, many floodplain studies on alluvial fans rely on qualitative approaches to provide general approximations of flow depth, width and velocity. Since 1980s, the Federal Emergency Management Agency (FEMA) has recommended a stochastic approach for assessing flood risks and hazards on alluvial fans. The method applies a conditional probability based on the risk level of the selected flood event, and the site location on the fan area. This probabilistic approach has been accepted as a reasonable approximation for alluvial floodplain studies, according to FEMA regulations. From a regulatory standpoint, this approach provides a conservative assessment to delineate the boundaries of flood hazard areas. But, it has been long recognized that the rainfall-runoff process should be included as primary input parameters to determine the flood flows on an alluvial fan. As urban areas continued to expand and invaded into alluvial fans in the recent years, it is critically important to quantitatively determine the flood flow characteristics with a higher accuracy and consistency. By understandings the hydrologic processes on alluvial fans, it will definitely assist engineers to better manage the risks and uncertainties in land use planning and mitigate flood hazard when conducting a regional master drainage plan for alluvial fan areas.;In this study, the Kinematic Wave (KW) overland flow approach on a rectangular plane was reviewed, and then expended into converging and diverging planes to simulate overland flow hydraulics on fan shape geometry. The continuity principle was applied to balance the runoff volumes among excess rainfall amount, runoff inflow and outflow and surface detention volume. New governing equations were derived to describe the accumulations of overland flows, according to the geometry of the KW plane -- rectangular, converging, or diverging. These equations were also expanded to provide analytical and numerical solutions to present overland flows on diverging or converging planes. The results of the numerical simulations are well agreed with several reported laboratory studies and field observations. It is believed that the method presented in this study can improve the current FEMA flood flow study procedure and minimize the environmental impacts as the urbanization process encroaches into alluvial fans in the southwest States of the US.
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