This study presents a new approach to quantify multi-year hydrological memory, using exclusively streamflow and climate data. The rainfall-runoff relationship is analysed through the concept of elasticity. The anomaly in runoff yield is predicted using the anomaly in humidity index of the same year and, if adding value, those of previous years. To describe the rate at which the impact of these climate anomalies fades with time, we define Catchment Forgetting Curves (CFCs), which we parameterise using a Gamma distribution. We identify the CFCs of two OZCAR observatories, and we compare them to those of a set of 500 French catchments. As expected, catchments with significant multi-year memory are groundwater-dominated in France. Interestingly, the aridity index appears to be one of the main drivers of catchment memory, with longer memory generally observed in dry hydroclimatic regions. Catchment area, often pointed out as a driver of catchment memory in the literature, does not seem to play a first-order role. Additionally, we show that the reliability of the assessment of elasticity indices is improved when accounting for catchment memory with a much more spatially coherent organisation of the elasticity indices. The elasticity indices were also well related to aridity, with humid catchments showing lower elasticity.