This paper explores the possibility of identifying the rheology of a fluid by monitoring how the free surface velocity field is affected by a perturbation in the flow. The dam-break problem is considered which results from the release of a gate initially separating two fluid pools of different depth. The flow velocity is measured by seeding the free surface with buoyant particles and using Particle Tracking Velocimetry. In parallel, a mathematical model based on the lubrication approximation for fluids with a power-law rheology is developed. The model is validated against a similarity solution which is obtained for the spreading of a gravity current under its own weight and neglecting surface tension. Minimizing the difference between the free surface velocity fields obtained numerically and measured experimentally enables the identification of rheological parameters. The methodology is tested on ideal and noisy synthetic data sets and experimental data obtained with aqueous glycerol.