Limitations of satellite radar altimetry for operational hydrology include its spatial and temporal sampling as well as measurement problems caused by local topography and heterogeneity of the reflecting surface. In this study, we develop an approach that eliminates most of these limitations to produce an approximately 3-day-temporal resolution water-level time series from the original typically (sub-)monthly datasets for the Po River in detail, and for Congo, Mississippi and Danube rivers. We follow a geodetic approach by which, after estimating and removing inter-satellite biases, all virtual stations of several satellite altimeters are connected hydraulically and statistically to produce water-level time series at any location along the river. We test different data-selection strategies and validate our method against the extensive available in situ data over the Po River, resulting in an average correlation of 0.7, Root Mean Square Error of 0.8m, bias of -0.4m and Nash-Sutcliffe efficiency coefficient of 0.5. We validate the transferability of our method by applying it to the Congo, Mississippi and Danube rivers, which have very different geomorphological and climatic conditions. The methodology yields correlations above 0.75 and Nash-Sutcliffe coefficients of 0.84 (Congo), 0.34 (Mississippi), and 0.35 (Danube).