Small streams often underwent engineering works conducted without special care for the hydromorphological and ecosystemic consequences. To allow small Walloon watercourses to comply with the European Water Framework Directive, renaturation is required. However, the cost of such projects is often prohibitive for small streams. Therefore, the Rivialis project aims at designing a methodology to support such works, based on a “small river quality index” that requires the collection of various data under the form of an “ID card” of the investigated river reach, allowing to obtain a synthetic overview of the key features of the study reach. Such an ID card, and ultimately the index, should include the most relevant components among existing morphological and biological indicators. To reduce the project costs, the number of field measurements to build this ID card should be limited; the data should be obtained from online and publicly available data sources or easily collected on site. In this paper, key metrics are identified from the literature. They are then determined along a reach of the Petit Bocq River with the aim of assessing those that can be obtained at a low cost from available databases and those that require more costly field investigations. The results show that combining available databases and numerical simulations allows determining a river reach ID card yielding a first set of valuable information at a low cost. Field surveys can then be limited to the verification of these values and to the collection of biological information.

When balanced truncation is used for model order reduction, one has to solve a pair of Lyapunov equations for two Gramians and uses them to construct a reduced-order model. Although advances in solving such equations have been made, it is still the most expensive step of this reduction method. Parametric model order reduction aims to determine reduced-order models for parameter-dependent systems. Popular techniques for parametric model order reduction rely on interpolation. Nevertheless, the interpolation of Gramians is rarely mentioned, most probably due to the fact that Gramians are symmetric positive semidefinite matrices, a property that should be preserved by the interpolation method. In this contribution, we propose and compare two approaches for Gramian interpolation. In the first approach, the interpolated Gramian is computed as a linear combination of the data Gramians with positive coefficients. Even though positive semidefiniteness is guaranteed in this method, the rank of the interpolated Gramian can be significantly larger than that of the data Gramians. The second approach aims to tackle this issue by performing the interpolation on the manifold of fixed-rank positive semidefinite matrices. The results of the interpolation step are then used to construct parametric reduced-order models, which are compared numerically on two benchmark problems.