We present a five-year (1997-2001) numerical simulation of daily mean chlorophyll a concentrations at station Geesthacht Weir on the lower Elbe River (Germany) using an extremely simple Lagrangian model driven by (a) water discharge, global radiation, water temperature, and (b) silica observations at station Schmilka in the upper reach of the Elbe River. Notwithstanding the lack of many mechanistic details, the model is able to reproduce observed chlorophyll a variability surprisingly well, including a number of sharp valleys and ascents/descents in the observed time series. The model's success is based on the assumption of three key effects: prevailing light conditions, sporadic limitation of algal growth due to lack of silica and algae loss rates that increase above an empirically specified temperature threshold of 20 degrees C. Trimmed-down model versions are studied to analyse the model's success in terms of these mechanisms. In each of the five years the model consistently fails, however, to properly simulate characteristic steep increases of chlorophyll a concentrations after pronounced spring minima. Curing this model deficiency by global model re-calibration was found to be impossible. However, suspension of silica consumption by algae for up to 10 days in spring is shown to serve as a successful placeholder for processes that are disregarded in the model but apparently play an important role in the distinctly marked period of model failure. For the remainder of the year the very simple model was found to be adequate