Rates of River Level Rise: Observations and Theory

ABSTRACT Rapidly rising water levels are the most dangerous attribute of flash floods. Stream gauges quantify the rates of river rise, and their analysis reveals the governing factors. Progressively larger rivers show greater total rise, but slower rates of rise than smaller streams. The theoretical diffusion hydrograph usefully predicts the progressive rise of water depth H and rise rate dH / dt for rainfall delivered steadily at rate R for any gauged basin of area A and quantifiable time constant b . This theory predicts that the rise rate depends on the rainfall intensity and the basin response velocity A 0.5 / b , which is borne out by examples. It also successfully predicts that rise rates are greatest when the channel begins to fill but progressively decrease with increasing water depth. Over time, for steady rain, the water depth asymptotically increases until the volumetric outflow matches the inflow of delivered precipitation.