Effective Rainfall Given as the Answer to an Inverse Problem using the Kinematic Wave Model

The retrospective reasoning for getting the time series of effective rainfall from a direct runoff discharge using the kinematic wave model was discussed as an inverse problem. The procedure for getting effective rainfall was proposed, and the one-to-one correspondence of the series of discharge to the series of effective rainfall as an answer was discussed. This reasoning was examined using the data given in a small field as a basin.<BR>The main procedure for getting these answers is calculating the water depth from the lower end of the slope to the upper end along the characteristic curve. At the lower end of the slope, the water depth is given from a measured direct runoff discharge using an equation involving the roughness coefficient. From boundary condition, the effective rainfall was attempted on the condition that the distance of water depth zero to converge to the upper end of the slope.<BR>It was clarified that no more than one series of rainfall do not exist, because the distance of water depth zero on the characteristic curve is getting large as the numerical order of rainfall at the lower end of the slope on the same characteristic curve.<BR>In the example, not only the plus rainfall but also the minus rainfall were given. The minus rainfall is presumed to be the main reason for no convergence of the distance at the water depth zero. In the case of no convergence, the distance of water depth zero was confirmed changing minus to plus uncontinously for a continuous change in rainfall.<BR>The time series of rainfall including the cases that the boundary condition had not been satisfied exactly was given for some roughness coefficient. These kinds of calculation seem to be effective for the runoff analysis of the field for a small amount of data.