Hydrological flow routing covers a class of simple and computationally highly efficient techniques for steep river reaches without backwater effects. It is often applied as a routing component in semi-distributed and distributed hydrological models or as a stand-alone routing scheme in flow forecasting systems. If embedded into variational data assimilation (DA) or model predictive control (MPC), i.e. running the model in optimization mode, three main characteristics of the routing approach become essential: i) numerical robustness, ii) mass conservation and iii) the efficient computation of first-order sensitivities. We present a unified approach in which we reformulate various hydrological routing approaches as a cascade of non-linear reservoirs. This covers linear and nonlinear reservoir routing as well as Muskingum-type schemes. Whereas original variable-parameter versions of these schemes, e.g. Muskingum-Cunge, are not mass conservative, the reformulated version guarantees strict mass conservation. An iterative Newton-Raphson scheme integrates the implicit schematization of the reservoir equation in time. The first order sensitivities are derived by the implicit function theorem and the adjoint sensitivity equation at the computational costs of the time integration itself. The novel framework is applied to an academic test case and a routing network in the upper basin of Main River in Germany. Results show the performance of the routing scheme and verify the mass conservation properties of the approach. Furthermore, we give an outlook at the future use of the model within variational DA and MPC scenarios.
Montero, R. A., Schwanenberg, D., Krahe, P., & Helmke, P. (2016). Unified Hydrological Flow Routing for Variational Data Assimilation and Model Predictive Control. In Procedia Engineering (Vol. 154, pp. 1341–1348). Elsevier Ltd. https://doi.org/10.1016/j.proeng.2016.07.488