Flux-exchange between stream and aquifer is assessed on a 85.9 km stretch of the Danube River in Hungary. Streamflow is modeled with a spatially and temporally discretized version of the linear kinematic wave equation written in a state-space form which allows for an easy inversion of flow routing. By knowing in- and outflow of the reach, lateral flux exchange between stream and groundwater can be assessed. Continuous baseflow separation, in terms of groundwater gained by the river between the two gaging stations, is made possible at the downstream station by routing groundwater discharged to the stream reach, separately from streamflow measured at the upstream gaging station.