Abstract
Persistence is a crucial trait of many complex Earth systems. Although connecting this statistical concept to ecosystem physical properties is challenging, it reflects how long the system remains at a certain state before changing 1. Characterising persistence in the terrestrial biosphere is important to understanding intrinsic system properties, including legacy effects of extreme climate events 2. Such memory effects are often highly non-linear and, therefore, challenging to detect in observational records and poorly represented in Earth system models. This study estimates nonlinear persistence in remote sensing products over European forests and the corresponding hydrometeorological data using state-of-the-art machine learning methods. Characterising persistence in this way allows us to make inferences on the interaction between forest dynamics, drought-heat events, and ecosystem resilience 3.Classical statistical methods struggle with non-linear interactions and high-dimensional problems when characterising persistence 1. While state-of-the-art deep learning techniques have been used to indirectly measure persistence in forests 4, such models have limited potential memory due to gradient instability during backpropagation. Echo state networks (ESNs) provide a different perspective, keeping the weights fixed and training only the network's last layer using linear regression. This strategy circumvents classical training pitfalls such as gradient instability and allows them to maintain a memory of the input system 5. We exploit these networks to estimate non-linear persistence using the technique suggested in 6, where intuitively, the …
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