Miguel D. Mahecha

Francesco Martinuzzi, Chris Rackauckas, Anas Abdelrehim et al.

We introduce ReservoirComputing.jl, an open source Julia library for reservoir computing models. The software offers a great number of algorithms presented in the literature, and allows to expand on them with both internal and external tools in a simple way. The implementation is highly modular, fast and comes with a comprehensive documentation, which includes reproduced experiments from literature. The code and documentation are hosted on Github under an MIT license https://github.com/SciML/ReservoirComputing.jl.

David Montero, Guido Kraemer, Anca Anghelea et al.

Recent advancements in Earth system science have been marked by the exponential increase in the availability of diverse, multivariate datasets characterised by moderate to high spatio-temporal resolutions. Earth System Data Cubes (ESDCs) have emerged as one suitable solution for transforming this flood of data into a simple yet robust data structure. ESDCs achieve this by organising data into an analysis-ready format aligned with a spatio-temporal grid, facilitating user-friendly analysis and diminishing the need for extensive technical data processing knowledge. Despite these significant benefits, the completion of the entire ESDC life cycle remains a challenging task. Obstacles are not only of a technical nature but also relate to domain-specific problems in Earth system research. There exist barriers to realising the full potential of data collections in light of novel cloud-based technologies, particularly in curating data tailored for specific application domains. These include transforming data to conform to a spatio-temporal grid with minimum distortions and managing complexities such as spatio-temporal autocorrelation issues. Addressing these challenges is pivotal for the effective application of Artificial Intelligence (AI) approaches. Furthermore, adhering to open science principles for data dissemination, reproducibility, visualisation, and reuse is crucial for fostering sustainable research. Overcoming these challenges offers a substantial opportunity to advance data-driven Earth system research, unlocking the full potential of an integrated, multidimensional view of Earth system processes. This is particularly true when such research is coupled with innovative research paradigms and technological progress.

Leonard Schulz, Jürgen Vollmer, Miguel D. Mahecha et al.

Understanding the dynamics of the land-atmosphere exchange of CO$_2$ is key to advance our predictive capacities of the coupled climate-carbon feedback system. In essence, the net vegetation flux is the difference of the uptake of CO$_2$ via photosynthesis and the release of CO$_2$ via respiration, while the system is driven by periodic processes at different time-scales. The complexity of the underlying dynamics poses challenges to classical decomposition methods focused on maximizing data variance, such as singular spectrum analysis. Here, we explore whether nonlinear data-driven methods can better separate periodic patterns and their harmonics from noise and stochastic variability. We find that Nonlinear Laplacian Spectral Analysis (NLSA) outperforms the linear method and detects multiple relevant harmonics. However, these harmonics are not detected in the presence of substantial measurement irregularities. In summary, the NLSA approach can be used to both extract the seasonal cycle more accurately than linear methods, but likewise detect irregular signals resulting from irregular land-atmosphere interactions or measurement failures. Improving the detection capabilities of time-series decomposition is essential for improving land-atmosphere interactions models that should operate accurately on any time scale.

David Montero, Miguel D. Mahecha, Francesco Martinuzzi et al.

Monitoring the spatiotemporal dynamics of forest CO$_2$ uptake (Gross Primary Production, GPP), remains a central challenge in terrestrial ecosystem research. While Eddy Covariance (EC) towers provide high-frequency estimates, their limited spatial coverage constrains large-scale assessments. Remote sensing offers a scalable alternative, yet most approaches rely on single-sensor spectral indices and statistical models that are often unable to capture the complex temporal dynamics of GPP. Recent advances in deep learning (DL) and data fusion offer new opportunities to better represent the temporal dynamics of vegetation processes, but comparative evaluations of state-of-the-art DL models for multimodal GPP prediction remain scarce. Here, we explore the performance of two representative models for predicting GPP: 1) GPT-2, a transformer architecture, and 2) Long Short-Term Memory (LSTM), a recurrent neural network, using multivariate inputs. Overall, both achieve similar accuracy. But, while LSTM performs better overall, GPT-2 excels during extreme events. Analysis of temporal context length further reveals that LSTM attains similar accuracy using substantially shorter input windows than GPT-2, highlighting an accuracy-efficiency trade-off between the two architectures. Feature importance analysis reveals radiation as the dominant predictor, followed by Sentinel-2, MODIS land surface temperature, and Sentinel-1 contributions. Our results demonstrate how model architecture, context length, and multimodal inputs jointly determine performance in GPP prediction, guiding future developments of DL frameworks for monitoring terrestrial carbon dynamics.

Julia Peters, Karin Mora, Miguel D. Mahecha et al.

Earth observation (EO) foundation models have emerged as an effective approach to derive latent representations of the Earth system from various remote sensing sensors. These models produce embeddings that can be used as analysis-ready datasets, enabling the modelling of ecosystem dynamics without extensive sensor-specific preprocessing. However, existing models typically operate at fixed spatial or temporal scales, limiting their use for ecological analyses that require both fine spatial detail and high temporal fidelity. To overcome these limitations, we propose a representation learning framework that integrates different EO modalities into a unified feature space at high spatio-temporal resolution. We introduce the framework using Sentinel-1 and Sentinel-2 data as representative modalities. Our approach produces a latent space at native 10 m resolution and the temporal frequency of cloud-free Sentinel-2 acquisitions. Each sensor is first modeled independently to capture its sensor-specific characteristics. Their representations are then combined into a shared model. This two-stage design enables modality-specific optimisation and easy extension to new sensors, retaining pretrained encoders while retraining only fusion layers. This enables the model to capture complementary remote sensing data and to preserve coherence across space and time. Qualitative analyses reveal that the learned embeddings exhibit high spatial and semantic consistency across heterogeneous landscapes. Quantitative evaluation in modelling Gross Primary Production reveals that they encode ecologically meaningful patterns and retain sufficient temporal fidelity to support fine-scale analyses. Overall, the proposed framework provides a flexible, analysis-ready representation learning approach for environmental applications requiring diverse spatial and temporal resolutions.

David Montero, César Aybar, Chaonan Ji et al.

Advancements in Earth system science have seen a surge in diverse datasets. Earth System Data Cubes (ESDCs) have been introduced to efficiently handle this influx of high-dimensional data. ESDCs offer a structured, intuitive framework for data analysis, organising information within spatio-temporal grids. The structured nature of ESDCs unlocks significant opportunities for Artificial Intelligence (AI) applications. By providing well-organised data, ESDCs are ideally suited for a wide range of sophisticated AI-driven tasks. An automated framework for creating AI-focused ESDCs with minimal user input could significantly accelerate the generation of task-specific training data. Here we introduce cubo, an open-source Python tool designed for easy generation of AI-focused ESDCs. Utilising collections in SpatioTemporal Asset Catalogs (STAC) that are stored as Cloud Optimised GeoTIFFs (COGs), cubo efficiently creates ESDCs, requiring only central coordinates, spatial resolution, edge size, and time range.

David Montero, Miguel D. Mahecha, César Aybar et al.

The Sentinel-2 (S2) mission from the European Space Agency's Copernicus program provides essential data for Earth surface analysis. Its Level-2A products deliver high-to-medium resolution (10-60 m) surface reflectance (SR) data through the MultiSpectral Instrument (MSI). To enhance the accuracy and comparability of SR data, adjustments simulating a nadir viewing perspective are essential. These corrections address the anisotropic nature of SR and the variability in sun and observation angles, ensuring consistent image comparisons over time and under different conditions. The $c$-factor method, a simple yet effective algorithm, adjusts observed S2 SR by using the MODIS BRDF model to achieve Nadir BRDF Adjusted Reflectance (NBAR). Despite the straightforward application of the $c$-factor to individual images, a cohesive Python framework for its application across multiple S2 images and Earth System Data Cubes (ESDCs) from cloud-stored data has been lacking. Here we introduce sen2nbar, a Python package crafted to convert S2 SR data to NBAR, supporting both individual images and ESDCs derived from cloud-stored data. This package simplifies the conversion of S2 SR data to NBAR via a single function, organized into modules for efficient process management. By facilitating NBAR conversion for both SAFE files and ESDCs from SpatioTemporal Asset Catalogs (STAC), sen2nbar is developed as a flexible tool that can handle diverse data format requirements. We anticipate that sen2nbar will considerably contribute to the standardization and harmonization of S2 data, offering a robust solution for a diverse range of users across various applications. sen2nbar is an open-source tool available at https://github.com/ESDS-Leipzig/sen2nbar.

David Montero, Miguel D. Mahecha, Francesco Martinuzzi et al.

Accurate quantification of Gross Primary Production (GPP) is crucial for understanding terrestrial carbon dynamics. It represents the largest atmosphere-to-land CO$_2$ flux, especially significant for forests. Eddy Covariance (EC) measurements are widely used for ecosystem-scale GPP quantification but are globally sparse. In areas lacking local EC measurements, remote sensing (RS) data are typically utilised to estimate GPP after statistically relating them to in-situ data. Deep learning offers novel perspectives, and the potential of recurrent neural network architectures for estimating daily GPP remains underexplored. This study presents a comparative analysis of three architectures: Recurrent Neural Networks (RNNs), Gated Recurrent Units (GRUs), and Long-Short Term Memory (LSTMs). Our findings reveal comparable performance across all models for full-year and growing season predictions. Notably, LSTMs outperform in predicting climate-induced GPP extremes. Furthermore, our analysis highlights the importance of incorporating radiation and RS inputs (optical, temperature, and radar) for accurate GPP predictions, particularly during climate extremes.

Chaonan Ji, Tonio Fincke, Vitus Benson et al.

With climate extremes' rising frequency and intensity, robust analytical tools are crucial to predict their impacts on terrestrial ecosystems. Machine learning techniques show promise but require well-structured, high-quality, and curated analysis-ready datasets. Earth observation datasets comprehensively monitor ecosystem dynamics and responses to climatic extremes, yet the data complexity can challenge the effectiveness of machine learning models. Despite recent progress in deep learning to ecosystem monitoring, there is a need for datasets specifically designed to analyse compound heatwave and drought extreme impact. Here, we introduce the DeepExtremeCubes database, tailored to map around these extremes, focusing on persistent natural vegetation. It comprises over 40,000 spatially sampled small data cubes (i.e. minicubes) globally, with a spatial coverage of 2.5 by 2.5 km. Each minicube includes (i) Sentinel-2 L2A images, (ii) ERA5-Land variables and generated extreme event cube covering 2016 to 2022, and (iii) ancillary land cover and topography maps. The paper aims to (1) streamline data accessibility, structuring, pre-processing, and enhance scientific reproducibility, and (2) facilitate biosphere dynamics forecasting in response to compound extremes.

J. Emmanuel Johnson, Valero Laparra, Adrián Pérez-Suay et al.

Kernel methods are powerful machine learning techniques which implement generic non-linear functions to solve complex tasks in a simple way. They Have a solid mathematical background and exhibit excellent performance in practice. However, kernel machines are still considered black-box models as the feature mapping is not directly accessible and difficult to interpret.The aim of this work is to show that it is indeed possible to interpret the functions learned by various kernel methods is intuitive despite their complexity. Specifically, we show that derivatives of these functions have a simple mathematical formulation, are easy to compute, and can be applied to many different problems. We note that model function derivatives in kernel machines is proportional to the kernel function derivative. We provide the explicit analytic form of the first and second derivatives of the most common kernel functions with regard to the inputs as well as generic formulas to compute higher order derivatives. We use them to analyze the most used supervised and unsupervised kernel learning methods: Gaussian Processes for regression, Support Vector Machines for classification, Kernel Entropy Component Analysis for density estimation, and the Hilbert-Schmidt Independence Criterion for estimating the dependency between random variables. For all cases we expressed the derivative of the learned function as a linear combination of the kernel function derivative. Moreover we provide intuitive explanations through illustrative toy examples and show how to improve the interpretation of real applications in the context of spatiotemporal Earth system data cubes. This work reflects on the observation that function derivatives may play a crucial role in kernel methods analysis and understanding.