Flash Flood Runoff from Arid-land Watersheds
Investigators (most current known information)
The direct runoff hydrograph of a basin has complex interaction with geomorphologic formation. At the short time scales, hydrograph could be derived from the static geomorphologic information [e.g. Rodriguez-Iturbe and Valdes, 1979]. The importance of network geometry in determining the basic shape of travel time distribution has been widely emphasized [e.g. Rodriguez-Iturbe and Valdes, 1979; Rinaldo et al., 1991; Saco and Kumar, 2002]. However, network geometry is not sufficient to explain the observed nonlinear dependence of hydrograph on rainfall. Derivation and application of unit hydrographs for the experimental micro-watersheds in Israel revealed that the results are very sensitive to variations in rainfall intensity. This observation agrees well with other studies [e.g. Minshall, 1960] showing the significance of nonlinearity in runoff prediction. As an effort to explain this nonlinearity, we postulate that the observed nonlinear rainfall-runoff relationships may stem from the nonlinear hydraulic geometry relationships [Paik and Kumar, 2004]. This is based on the argument that different rainfall excess rates will produce different velocity fields in a basin due to the nonlinear relation between velocity and flow. In particular we show that if the mean velocity V varies with flow Q as V∝ Qm, then the time to peak tp and the peak flow f(tp) of the network instantaneous response function (IRF) vary as tp∝ ie-m and f(tp) ∝ ie+m where ie is the rainfall excess rate. At the longer time scales, geomorphologic formation dynamically evolves, in response to stream flow variability. Efforts to discover the possible natural laws which drive the fluvial landscape evolution, over last decades, have led to countless hypothesis and critiques. Theoretically, this law should be universal having unlimited applications including network formation, plan form, hydraulic geometry, downstream fining, bed profile, etc. Although each of hypotheses proposed can successfully explain some of these natural features, none of them can support these various natural observations as a single law. We question the necessity of the extremal hypotheses which pursue single objectives. With proposed new perspective, it is more physically sound that the nature seeks a certain range of stability constrained by multiple thresholds rather than extremal hypotheses.
Articles in Journals
Paik, K., C. Tsai and P. Kumar. 2004. "Hydrologic routing and risk evaluation for detention basins." Journal of Water Resources Planning and Management, ASCE (in review).
Paik, K. and P. Kumar. 2004. "Hydraulic geometry and the nonlinearity of the network instantaneous response." Water Researchers Research 40,W03602.