HR: 08:30h
AN: H41A-03    [Abstracts]
TI: Flow Rate Estimation via Inverse Flood Routing and Spectral Error Control
AU: * Aldama, A
EM: alvaro.aldama@gmail.com
AF: Mexican Institute of Water Technology, Paseo Cuauhnahuac 8532, Jiutepec, MOR 62550, Mexico
AU: Aguilar, E
EM: eaguilar@tlaloc.imta.mx
AF: Mexican Institute of Water Technology, Paseo Cuauhnahuac 8532, Jiutepec, MOR 62550, Mexico
AB: Flow rate gauging stations along river channels are located at topographical constrictions where a hydraulic control is likely to exist. Dams are also located at topographic constrictions and, particularly in developing countries, the operation of flow rate gauging stations is discontinued once a dam has been built at the same or nearly the same site where the station was located. Thereafter, to keep the flow rate record up to date, the dam reservoir is used as a measurement device; i.e., inflow rates are estimated by employing the observed time evolution of the reservoir water levels and solving the continuity equation in an inverse fashion, a procedure known as "inverse flood routing". The inverse numerical solution of such equation entails dividing stored volume differences in a given time interval by the time step. Numerical procedures such as the popular trapezoidal rule, perform very poorly in the solution of the inverse problem. This is due to the fact that small errors in water levels are amplified when stored volumes are estimated, and amplified once again when stored volume differences are divided by small time steps. A theoretical analysis of the problem is presented and the performance of the trapezoidal rule (Crank-Nicolson), the second order Adams-Bashforth scheme, and the central difference scheme, is evaluated. By employing an analytical solution of the reservoir flood routing problem and an error propagation analysis, it is shown that the third scheme outperforms the other two, since it is the only one that does not propagate the error in a given time level to succeeding time levels. Now, some times the use of the central difference scheme is not enough to counteract the influence of errors in water levels, since these may contain a large level of high frequency components. Hence, water level and stored volume spectra are estimated, in order to identify spurious Fourier components, which may be eliminated via filtering. The application of the combined central difference-spectral error control methodology to various rivers and dams in Mexico produces excellent results.
DE: 1821 Floods
DE: 1847 Modeling
DE: 1849 Numerical approximations and analysis
DE: 1872 Time series analysis (3270, 4277, 4475)
SC: Hydrology [H]
MN: 2007 Joint Assembly