Accounting for Backwater Effects in Flow Routing by the Discrete Linear Cascade Model

Flow-routing at a tributary (Koros River) of the Tisza River in Hungary was achieved by relating the storage coefficient ($k$) of the state-space formulated discrete linear cascade model (DLCM) to the concurrent discharge rate of the Tisza. As a result, the root mean square error of the 1-day forecasts decreased from $25{\mathrm{m}}^3·{\mathrm{s}}^{-1}$ ($k=1.7{\mathrm{days}}^{-1}$ and the number of storage elements is 2) with the corresponding Nash-Sutcliffe-type performance value of $0.95\mathrm{to}11{\mathrm{m}}^3·{\mathrm{s}}^{-1}$ in the calibration period and to $15{\mathrm{m}}^3·{\mathrm{s}}^{-1}$ in the validation period (the corresponding Nash-Sutcliff-type performance values are 0.99 and 0.98, respectively). During floods of the Tisza, the $k$ value decreased to as little as $0.35{\mathrm{days}}^{-1}$, indicating a significant slowdown of the tributary flood-wave because of the resulting backwater effect. Subsequent stage-forecasts were aided by a coupled autoregressive moving-average (1,1) model of the DLCM error sequence and the application of the Jones formula in addition to a conveyance curve, the latter yielding the most accurate 1-day forecasts with a root mean square error of 28 cm and Nash-Sutcliff-type performance value of 0.99 for the combined (validation and calibration) time periods. The method requires no significant change in the mathematical structure of the original DLCM and thus is well-posed for inclusion of existing operational streamflow-forecasting schemes.