Persistence is an important characteristic of many complex systems in nature and of the Earth system in particular. The concept is rather elusive but related to how long the system remains at a certain state before changing to a different one. Characterising persistence in the terrestrial biosphere is very relevant to understand intrinsic properties of the system and thus the legacy effects of extreme events, such as droughts and heatwaves. Such memory effects are challenging to detect in observational records and poorly represented in Earth system models. We use a number of statistical and machine learning methods to extract long and short term persistence in remotely sensed data.