A simple Lagrangian water quality model was designed to investigate the hypothesis of sporadic silica limitations of diatom growth in the lower Elbe River in Germany. For each fluid parcel a limited reservoir of silica was specified to be consumed by diatoms. The model's simplicity notwithstanding, a set of six selected model parameters could not be fully identified from existing observations at one station. After the introduction of prior knowledge of the ranges of meaningful parameter values, calibration of the over-parameterised model manifested itself primarily in the generation of posterior parameter covariances. Estimations of the covariance matrix based on (a) second order partial derivatives of a quadratic cost function at its optimum and (b) Monte Carlo simulations exploring the whole space of parameter values gave consistent results. Diagonalisation of the covariance matrix yielded two linear parameter combinations that were most effectively controlled by data from periods with and without lack of silica, respectively. The two parameter combinations were identified as the essential inputs that govern the successful simulation of intermittently decreasing chlorophyll a concentrations in summer. A satisfactory simulation of the pronounced chlorophyll a minimum in spring, by contrast, was found to be beyond the means of the simple model.