We investigate the response of a laboratory aquifer submitted to artificial rainfall, with an emphasis on the early stage of a rain event. In this almost two-dimensional experiment, the infiltrating rainwater forms a groundwater reservoir which exits the aquifer through one side. The resulting outflow resembles a typical stream hydrograph: the water discharge increases rapidly during rainfall and decays slowly after the rain has stopped. The Dupuit–Boussinesq theory, based on Darcy’s law and the shallow-water approximation, quantifies these two asymptotic regimes. At the early stage of a rainfall event, the discharge increases linearly with time, at a rate proportional to the rainfall rate to the power of
. Long after the rain has stopped, it decreases as the squared inverse of time (Boussinesq, C. R. Acad. Sci., vol. 137, 1903, pp. 5–11). We compare these predictions with our experimental data.