Evaluating Forest Resilience in Europe with Deep Learning Persistence Analysis
Authors: Williams Tristan , Martinuzzi Francesco , Camps-Valls Gustau , D. Mahecha Miguel 
Published: March 2024

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 non-linear persistence in remote sensing products over European forests and the corresponding hydro-meteorological 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].&#160;Classical statistical methods struggle with non-linear interactions and high-dimensional problems when characterising persistence [1].&#160; 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 persistence of the system can be estimated by the model's response when the input fades abruptly. We apply this method to a 30-year archive of satellite derived greenness to generate maps of persistence across Europe and assess the forests' response to changing hydro-climatic conditions. Furthermore, we explore memory changes surrounding extreme events, focusing on recent drought-heat events in Europe. Thus providing an estimate of engineering resilience, an important metric to inform forest management strategies. Furthermore, this work provides insights into the ability of different models to capture ecological memory and, therefore give more reliable predictions.&#160;References&#160;[1]&#160; Salcedo-Sanz, S., et al. &#8220;Persistence in complex systems&#8221;. Physics Reports 957, 1-73, (2022).[2] Bastos, Ana, et al. &#8220;Direct and seasonal legacy effects of the 2018 heat wave and drought on European ecosystem productivity." Science Advances 6.24 (2020)[3] Scheffer, M., Carpenter, S. R., Dakos, V. &amp; van Nes, E. H. Generic indicators of ecological resilience: inferring the chance of a critical transition. Annu. Rev. Ecol. Evol. Syst. 46, 145&#8211;167 (2015).[4] Besnard S, Carvalhais N, Arain MA, Black A, Brede B, Buchmann N, et al. (2019) Memory effects of climate and vegetation affecting net ecosystem CO2 fluxes in global forests. PLoS ONE 14(2): e0211510.&#160;[5] Hart, Allen, James Hook, and Jonathan Dawes. "Embedding and approximation theorems for echo state networks." Neural Networks 128 (2020): 234-247.[6] Barredo Arrieta, A., Gil-Lopez, S., La&#241;a, I. et al. On the post-hoc explainability of deep echo state networks for time series forecasting, image and video classification. Neural Comput &amp; Applic 34, 10257&#8211;10277 (2022).