Gustau Camps‐Valls

Ioannis Prapas, Nikolaos Ioannis Bountos, Spyros Kondylatos et al.

Wildfires are increasingly exacerbated as a result of climate change, necessitating advanced proactive measures for effective mitigation. It is important to forecast wildfires weeks and months in advance to plan forest fuel management, resource procurement and allocation. To achieve such accurate long-term forecasts at a global scale, it is crucial to employ models that account for the Earth system's inherent spatio-temporal interactions, such as memory effects and teleconnections. We propose a teleconnection-driven vision transformer (TeleViT), capable of treating the Earth as one interconnected system, integrating fine-grained local-scale inputs with global-scale inputs, such as climate indices and coarse-grained global variables. Through comprehensive experimentation, we demonstrate the superiority of TeleViT in accurately predicting global burned area patterns for various forecasting windows, up to four months in advance. The gain is especially pronounced in larger forecasting windows, demonstrating the improved ability of deep learning models that exploit teleconnections to capture Earth system dynamics. Code available at https://github.com/Orion-Ai-Lab/TeleViT.

Spyros Kondylatos, Ioannis Prapas, Gustau Camps-Valls et al.

We introduce Mesogeos, a large-scale multi-purpose dataset for wildfire modeling in the Mediterranean. Mesogeos integrates variables representing wildfire drivers (meteorology, vegetation, human activity) and historical records of wildfire ignitions and burned areas for 17 years (2006-2022). It is designed as a cloud-friendly spatio-temporal dataset, namely a datacube, harmonizing all variables in a grid of 1km x 1km x 1-day resolution. The datacube structure offers opportunities to assess machine learning (ML) usage in various wildfire modeling tasks. We extract two ML-ready datasets that establish distinct tracks to demonstrate this potential: (1) short-term wildfire danger forecasting and (2) final burned area estimation given the point of ignition. We define appropriate metrics and baselines to evaluate the performance of models in each track. By publishing the datacube, along with the code to create the ML datasets and models, we encourage the community to foster the implementation of additional tracks for mitigating the increasing threat of wildfires in the Mediterranean.

José A. Padrón-Hidalgo, Valero Laparra, Gustau Camps-Valls

Anomaly detection is a field of intense research. Identifying low probability events in data/images is a challenging problem given the high-dimensionality of the data, especially when no (or little) information about the anomaly is available a priori. While plenty of methods are available, the vast majority of them do not scale well to large datasets and require the choice of some (very often critical) hyperparameters. Therefore, unsupervised and computationally efficient detection methods become strictly necessary. We propose an unsupervised method for detecting anomalies and changes in remote sensing images by means of a multivariate Gaussianization methodology that allows to estimate multivariate densities accurately, a long-standing problem in statistics and machine learning. The methodology transforms arbitrarily complex multivariate data into a multivariate Gaussian distribution. Since the transformation is differentiable, by applying the change of variables formula one can estimate the probability at any point of the original domain. The assumption is straightforward: pixels with low estimated probability are considered anomalies. Our method can describe any multivariate distribution, makes an efficient use of memory and computational resources, and is parameter-free. We show the efficiency of the method in experiments involving both anomaly detection and change detection in different remote sensing image sets. Results show that our approach outperforms other linear and nonlinear methods in terms of detection power in both anomaly and change detection scenarios, showing robustness and scalability to dimensionality and sample sizes.

Daniel Heestermans Svendsen, Daniel Hernández-Lobato, Luca Martino et al.

Earth observation from satellites offers the possibility to monitor our planet with unprecedented accuracy. Radiative transfer models (RTMs) encode the energy transfer through the atmosphere, and are used to model and understand the Earth system, as well as to estimate the parameters that describe the status of the Earth from satellite observations by inverse modeling. However, performing inference over such simulators is a challenging problem. RTMs are nonlinear, non-differentiable and computationally costly codes, which adds a high level of difficulty in inference. In this paper, we introduce two computational techniques to infer not only point estimates of biophysical parameters but also their joint distribution. One of them is based on a variational autoencoder approach and the second one is based on a Monte Carlo Expectation Maximization (MCEM) scheme. We compare and discuss benefits and drawbacks of each approach. We also provide numerical comparisons in synthetic simulations and the real PROSAIL model, a popular RTM that combines land vegetation leaf and canopy modeling. We analyze the performance of the two approaches for modeling and inferring the distribution of three key biophysical parameters for quantifying the terrestrial biosphere.

Kristoffer Wickstrøm, J. Emmanuel Johnson, Sigurd Løkse et al.

This paper presents the kernelized Taylor diagram, a graphical framework for visualizing similarities between data populations. The kernelized Taylor diagram builds on the widely used Taylor diagram, which is used to visualize similarities between populations. However, the Taylor diagram has several limitations such as not capturing non-linear relationships and sensitivity to outliers. To address such limitations, we propose the kernelized Taylor diagram. Our proposed kernelized Taylor diagram is capable of visualizing similarities between populations with minimal assumptions of the data distributions. The kernelized Taylor diagram relates the maximum mean discrepancy and the kernel mean embedding in a single diagram, a construction that, to the best of our knowledge, have not been devised prior to this work. We believe that the kernelized Taylor diagram can be a valuable tool in data visualization.

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.

Víctor Elvira, Émilie Chouzenoux, Jordi Cerdà et al.

Granger causality (GC) is often considered not an actual form of causality. Still, it is arguably the most widely used method to assess the predictability of a time series from another one. Granger causality has been widely used in many applied disciplines, from neuroscience and econometrics to Earth sciences. We revisit GC under a graphical perspective of state-space models. For that, we use GraphEM, a recently presented expectation-maximisation algorithm for estimating the linear matrix operator in the state equation of a linear-Gaussian state-space model. Lasso regularisation is included in the M-step, which is solved using a proximal splitting Douglas-Rachford algorithm. Experiments in toy examples and challenging climate problems illustrate the benefits of the proposed model and inference technique over standard Granger causality methods.

Vasileios Sitokonstantinou, Emiliano Díaz Salas Porras, Jordi Cerdà Bautista et al.

In a changing climate, sustainable agriculture is essential for food security and environmental health. However, it is challenging to understand the complex interactions among its biophysical, social, and economic components. Predictive machine learning (ML), with its capacity to learn from data, is leveraged in sustainable agriculture for applications like yield prediction and weather forecasting. Nevertheless, it cannot explain causal mechanisms and remains descriptive rather than prescriptive. To address this gap, we propose causal ML, which merges ML's data processing with causality's ability to reason about change. This facilitates quantifying intervention impacts for evidence-based decision-making and enhances predictive model robustness. We showcase causal ML through eight diverse applications that benefit stakeholders across the agri-food chain, including farmers, policymakers, and researchers.

Jordi Cerdà-Bautista, José María Tárraga, Vasileios Sitokonstantinou et al.

In the face of climate change-induced droughts, vulnerable regions encounter severe threats to food security, demanding urgent humanitarian assistance. This paper introduces a causal inference framework for the Horn of Africa, aiming to assess the impact of cash-based interventions on food crises. Our contributions include identifying causal relationships within the food security system, harmonizing a comprehensive database including socio-economic, weather and remote sensing data, and estimating the causal effect of humanitarian interventions on malnutrition. On a country level, our results revealed no significant effects, likely due to limited sample size, suboptimal data quality, and an imperfect causal graph resulting from our limited understanding of multidisciplinary systems like food security. Instead, on a district level, results revealed significant effects, further implying the context-specific nature of the system. This underscores the need to enhance data collection and refine causal models with domain experts for more effective future interventions and policies, improving transparency and accountability in humanitarian aid.

Zhitong Xiong, Yi Wang, Fahong Zhang et al.

Earth observation (EO) in open-world settings presents a unique challenge: different applications rely on diverse sensor modalities, each with varying ground sampling distances, spectral ranges, and numbers of spectral bands. However, existing EO foundation models are typically tailored to specific sensor types, making them inflexible when generalizing across the heterogeneous landscape of EO data. To address this, we propose the Dynamic One-For-All (DOFA) model, a unified, multimodal foundation framework designed for diverse vision tasks in EO. Inspired by neural plasticity, DOFA utilizes a wavelength-conditioned dynamic hypernetwork to process inputs from five distinct satellite sensors flexibly. By continually pretraining on five EO modalities, DOFA achieves state-of-the-art performance across multiple downstream tasks and generalizes well to unseen modalities. Enhanced with hybrid continual pretraining, DOFA+ requires significantly fewer computational resources while outperforming counterparts trained with extensive GPU budgets. Experiments on diverse datasets highlight DOFA's potential as a foundation for general-purpose vision models in the sensor-diverse EO domain. The code and pre-trained weights are publicly available at https://github.com/zhu-xlab/DOFA.

Oscar J. Pellicer-Valero, Cesar Aybar, Gustau Camps Valls

Large-scale Earth system datasets, from high-resolution remote sensing imagery to spatiotemporal climate model outputs, exhibit characteristics analogous to those of standard videos. Their inherent spatial, temporal, and spectral redundancies can thus be readily exploited by established video compression techniques. Here, we present xarrayvideo, a Python library for compressing multichannel spatiotemporal datasets by encoding them as videos. Our approach achieves compression ratios of up to 250x while maintaining high fidelity by leveraging standard, well-optimized video codecs through ffmpeg. We demonstrate the library's effectiveness on four real-world multichannel spatiotemporal datasets: DynamicEarthNet (very high resolution Planet images), DeepExtremeCubes (high resolution Sentinel-2 images), ERA5 (weather reanalysis data), and the SimpleS2 dataset (high resolution multichannel Sentinel-2 images), achieving Peak Signal-to-Noise Ratios (PSNRs) of 55.86, 40.60, 46.58, and 43.23 dB at 0.1 bits per pixel per band (bpppb) and 65.91, 54.28, 62.90, and 55.04 dB at 1 bpppb. We are redistributing two of these datasets, DeepExtremeCubes (2.3 Tb) and DynamicEarthNet (525 Gb), in the machine-learning-ready and cloud-ready TACO format through HuggingFace at significantly reduced sizes (270 Gb and 8.5 Gb, respectively) without compromising quality (PSNR 55.77-56.65 and 60.15). No performance loss is observed when the compressed versions of these datasets are used in their respective deep learning-based downstream tasks (next step reflectance prediction and landcover segmentation). In conclusion, xarrayvideo presents an efficient solution for handling the rapidly growing size of Earth observation datasets, making advanced compression techniques accessible and practical to the Earth science community. The library is available for use at https://github.com/IPL-UV/xarrayvideo

Nathan Mankovich, Homer Durand, Emiliano Diaz et al.

Detecting latent confounders from proxy variables is an essential problem in causal effect estimation. Previous approaches are limited to low-dimensional proxies, sorted proxies, and binary treatments. We remove these assumptions and present a novel Proxy Confounder Factorization (PCF) framework for continuous treatment effect estimation when latent confounders manifest through high-dimensional, mixed proxy variables. For specific sample sizes, our two-step PCF implementation, using Independent Component Analysis (ICA-PCF), and the end-to-end implementation, using Gradient Descent (GD-PCF), achieve high correlation with the latent confounder and low absolute error in causal effect estimation with synthetic datasets in the high sample size regime. Even when faced with climate data, ICA-PCF recovers four components that explain $75.9\%$ of the variance in the North Atlantic Oscillation, a known confounder of precipitation patterns in Europe. Code for our PCF implementations and experiments can be found here: https://github.com/IPL-UV/confound_it. The proposed methodology constitutes a stepping stone towards discovering latent confounders and can be applied to many problems in disciplines dealing with high-dimensional observed proxies, e.g., spatiotemporal fields.

Claudio Persello, Jan Dirk Wegner, Ronny Hänsch et al. · mila

The synergistic combination of deep learning models and Earth observation promises significant advances to support the sustainable development goals (SDGs). New developments and a plethora of applications are already changing the way humanity will face the living planet challenges. This paper reviews current deep learning approaches for Earth observation data, along with their application towards monitoring and achieving the SDGs most impacted by the rapid development of deep learning in Earth observation. We systematically review case studies to 1) achieve zero hunger, 2) sustainable cities, 3) deliver tenure security, 4) mitigate and adapt to climate change, and 5) preserve biodiversity. Important societal, economic and environmental implications are concerned. Exciting times ahead are coming where algorithms and Earth data can help in our endeavor to address the climate crisis and support more sustainable development.

Kai-Hendrik Cohrs, Gherardo Varando, Nuno Carvalhais et al.

Hybrid modeling integrates machine learning with scientific knowledge to enhance interpretability, generalization, and adherence to natural laws. Nevertheless, equifinality and regularization biases pose challenges in hybrid modeling to achieve these purposes. This paper introduces a novel approach to estimating hybrid models via a causal inference framework, specifically employing Double Machine Learning (DML) to estimate causal effects. We showcase its use for the Earth sciences on two problems related to carbon dioxide fluxes. In the $Q_{10}$ model, we demonstrate that DML-based hybrid modeling is superior in estimating causal parameters over end-to-end deep neural network (DNN) approaches, proving efficiency, robustness to bias from regularization methods, and circumventing equifinality. Our approach, applied to carbon flux partitioning, exhibits flexibility in accommodating heterogeneous causal effects. The study emphasizes the necessity of explicitly defining causal graphs and relationships, advocating for this as a general best practice. We encourage the continued exploration of causality in hybrid models for more interpretable and trustworthy results in knowledge-guided machine learning.

Shan Zhao, Ioannis Prapas, Ilektra Karasante et al.

Wildfire forecasting is notoriously hard due to the complex interplay of different factors such as weather conditions, vegetation types and human activities. Deep learning models show promise in dealing with this complexity by learning directly from data. However, to inform critical decision making, we argue that we need models that are right for the right reasons; that is, the implicit rules learned should be grounded by the underlying processes driving wildfires. In that direction, we propose integrating causality with Graph Neural Networks (GNNs) that explicitly model the causal mechanism among complex variables via graph learning. The causal adjacency matrix considers the synergistic effect among variables and removes the spurious links from highly correlated impacts. Our methodology's effectiveness is demonstrated through superior performance forecasting wildfire patterns in the European boreal and mediterranean biome. The gain is especially prominent in a highly imbalanced dataset, showcasing an enhanced robustness of the model to adapt to regime shifts in functional relationships. Furthermore, SHAP values from our trained model further enhance our understanding of the model's inner workings.

Nathan Mankovich, Gustau Camps-Valls, Tolga Birdal

Principal component analysis (PCA), along with its extensions to manifolds and outlier contaminated data, have been indispensable in computer vision and machine learning. In this work, we present a unifying formalism for PCA and its variants, and introduce a framework based on the flags of linear subspaces, ie a hierarchy of nested linear subspaces of increasing dimension, which not only allows for a common implementation but also yields novel variants, not explored previously. We begin by generalizing traditional PCA methods that either maximize variance or minimize reconstruction error. We expand these interpretations to develop a wide array of new dimensionality reduction algorithms by accounting for outliers and the data manifold. To devise a common computational approach, we recast robust and dual forms of PCA as optimization problems on flag manifolds. We then integrate tangent space approximations of principal geodesic analysis (tangent-PCA) into this flag-based framework, creating novel robust and dual geodesic PCA variations. The remarkable flexibility offered by the 'flagification' introduced here enables even more algorithmic variants identified by specific flag types. Last but not least, we propose an effective convergent solver for these flag-formulations employing the Stiefel manifold. Our empirical results on both real-world and synthetic scenarios, demonstrate the superiority of our novel algorithms, especially in terms of robustness to outliers on manifolds.

Ilias Tsoumas, Vasileios Sitokonstantinou, Georgios Giannarakis et al.

Pesticides serve as a common tool in agricultural pest control but significantly contribute to the climate crisis. To combat this, Integrated Pest Management (IPM) stands as a climate-smart alternative. Despite its potential, IPM faces low adoption rates due to farmers' skepticism about its effectiveness. To address this challenge, we introduce an advanced data analysis framework tailored to enhance IPM adoption. Our framework provides i) robust pest population predictions across diverse environments with invariant and causal learning, ii) interpretable pest presence predictions using transparent models, iii) actionable advice through counterfactual explanations for in-season IPM interventions, iv) field-specific treatment effect estimations, and v) assessments of the effectiveness of our advice using causal inference. By incorporating these features, our framework aims to alleviate skepticism and encourage wider adoption of IPM practices among farmers.

Nathan Mankovich, Ignacio Santamaria, Gustau Camps-Valls et al.

Flag manifolds encode nested sequences of subspaces and serve as powerful structures for various computer vision and machine learning applications. Despite their utility in tasks such as dimensionality reduction, motion averaging, and subspace clustering, current applications are often restricted to extracting flags using common matrix decomposition methods like the singular value decomposition. Here, we address the need for a general algorithm to factorize and work with hierarchical datasets. In particular, we propose a novel, flag-based method that decomposes arbitrary hierarchical real-valued data into a hierarchy-preserving flag representation in Stiefel coordinates. Our work harnesses the potential of flag manifolds in applications including denoising, clustering, and few-shot learning.

Spyros Kondylatos, Nikolaos Ioannis Bountos, Ioannis Prapas et al.

Label noise poses a significant challenge in Earth Observation (EO), often degrading the performance and reliability of supervised Machine Learning (ML) models. Yet, given the critical nature of several EO applications, developing robust and trustworthy ML solutions is essential. In this study, we take a step in this direction by leveraging probabilistic ML to model input-dependent label noise and quantify data uncertainty in EO tasks, accounting for the unique noise sources inherent in the domain. We train uncertainty-aware probabilistic models across a broad range of high-impact EO applications-spanning diverse noise sources, input modalities, and ML configurations-and introduce a dedicated pipeline to assess their accuracy and reliability. Our experimental results show that the uncertainty-aware models consistently outperform the standard deterministic approaches across most datasets and evaluation metrics. Moreover, through rigorous uncertainty evaluation, we validate the reliability of the predicted uncertainty estimates, enhancing the interpretability of model predictions. Our findings emphasize the importance of modeling label noise and incorporating uncertainty quantification in EO, paving the way for more accurate, reliable, and trustworthy ML solutions in the field.

Ioannis Prapas, Nikolaos Papadopoulos, Nikolaos-Ioannis Bountos et al.

Forecasting wildfires weeks to months in advance is difficult, yet crucial for planning fuel treatments and allocating resources. While short-term predictions typically rely on local weather conditions, long-term forecasting requires accounting for the Earth's interconnectedness, including global patterns and teleconnections. We introduce TeleViT, a Teleconnection-aware Vision Transformer that integrates (i) fine-scale local fire drivers, (ii) coarsened global fields, and (iii) teleconnection indices. This multi-scale fusion is achieved through an asymmetric tokenization strategy that produces heterogeneous tokens processed jointly by a transformer encoder, followed by a decoder that preserves spatial structure by mapping local tokens to their corresponding prediction patches. Using the global SeasFire dataset (2001-2021, 8-day resolution), TeleViT improves AUPRC performance over U-Net++, ViT, and climatology across all lead times, including horizons up to four months. At zero lead, TeleViT with indices and global inputs reaches AUPRC 0.630 (ViT 0.617, U-Net 0.620), at 16x8day lead (around 4 months), TeleViT variants using global input maintain 0.601-0.603 (ViT 0.582, U-Net 0.578), while surpassing the climatology (0.572) at all lead times. Regional results show the highest skill in seasonally consistent fire regimes, such as African savannas, and lower skill in boreal and arid regions. Attention and attribution analyses indicate that predictions rely mainly on local tokens, with global fields and indices contributing coarse contextual information. These findings suggest that architectures explicitly encoding large-scale Earth-system context can extend wildfire predictability on subseasonal-to-seasonal timescales.

Nathan Mankovich, Kai-Hendrik Cohrs, Homer Durand et al.

Earth observation involves collecting, analyzing, and processing an ever-growing mass of data. Automatically harvesting information is crucial for addressing significant societal, economic, and environmental challenges, ranging from environmental monitoring to urban planning and disaster management. However, the high dimensionality of these data poses challenges in terms of sparsity, inefficiency, and the curse of dimensionality, which limits the effectiveness of machine learning models. Dimensionality reduction (DR) techniques, specifically feature extraction, address these challenges by preserving essential data properties while reducing complexity and enhancing tasks such as data compression, cleaning, fusion, visualization, anomaly detection, and prediction. This review provides a handbook for leveraging DR across the RS data value chain and identifies opportunities for under-explored DR algorithms and their application in future research.

Spyros Kondylatos, Gustau Camps-Valls, Ioannis Papoutsis

Wildfires are among the most severe natural hazards, posing a significant threat to both humans and natural ecosystems. The growing risk of wildfires increases the demand for forecasting models that are not only accurate but also reliable. Deep Learning (DL) has shown promise in predicting wildfire danger; however, its adoption is hindered by concerns over the reliability of its predictions, some of which stem from the lack of uncertainty quantification. To address this challenge, we present an uncertainty-aware DL framework that jointly captures epistemic (model) and aleatoric (data) uncertainty to enhance short-term wildfire danger forecasting. In the next-day forecasting, our best-performing model improves the F1 Score by 2.3% and reduces the Expected Calibration Error by 2.1% compared to a deterministic baseline, enhancing both predictive skill and calibration. Our experiments confirm the reliability of the uncertainty estimates and illustrate their practical utility for decision support, including the identification of uncertainty thresholds for rejecting low-confidence predictions and the generation of well-calibrated wildfire danger maps with accompanying uncertainty layers. Extending the forecast horizon up to ten days, we observe that aleatoric uncertainty increases with time, showing greater variability in environmental conditions, while epistemic uncertainty remains stable. Finally, we show that although the two uncertainty types may be redundant in low-uncertainty cases, they provide complementary insights under more challenging conditions, underscoring the value of their joint modeling for robust wildfire danger prediction. In summary, our approach significantly improves the accuracy and reliability of wildfire danger forecasting, advancing the development of trustworthy wildfire DL systems.

Homer Durand, Gherardo Varando, Gustau Camps-Valls

We propose a novel approach for learning causal response representations. Our method aims to extract directions in which a multidimensional outcome is most directly caused by a treatment variable. By bridging conditional independence testing with causal representation learning, we formulate an optimisation problem that maximises the evidence against conditional independence between the treatment and outcome, given a conditioning set. This formulation employs flexible regression models tailored to specific applications, creating a versatile framework. The problem is addressed through a generalised eigenvalue decomposition. We show that, under mild assumptions, the distribution of the largest eigenvalue can be bounded by a known $F$-distribution, enabling testable conditional independence. We also provide theoretical guarantees for the optimality of the learned representation in terms of signal-to-noise ratio and Fisher information maximisation. Finally, we demonstrate the empirical effectiveness of our approach in simulation and real-world experiments. Our results underscore the utility of this framework in uncovering direct causal effects within complex, multivariate settings.

Gustau Camps-Valls, Miguel-Ángel Fernández-Torres, Kai-Hendrik Cohrs et al.

In recent years, artificial intelligence (AI) has deeply impacted various fields, including Earth system sciences. Here, AI improved weather forecasting, model emulation, parameter estimation, and the prediction of extreme events. However, the latter comes with specific challenges, such as developing accurate predictors from noisy, heterogeneous and limited annotated data. This paper reviews how AI is being used to analyze extreme events (like floods, droughts, wildfires and heatwaves), highlighting the importance of creating accurate, transparent, and reliable AI models. We discuss the hurdles of dealing with limited data, integrating information in real-time, deploying models, and making them understandable, all crucial for gaining the trust of stakeholders and meeting regulatory needs. We provide an overview of how AI can help identify and explain extreme events more effectively, improving disaster response and communication. We emphasize the need for collaboration across different fields to create AI solutions that are practical, understandable, and trustworthy for analyzing and predicting extreme events. Such collaborative efforts aim to enhance disaster readiness and disaster risk reduction.

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.

Kai-Hendrik Cohrs, Gherardo Varando, Emiliano Diaz et al.

Causality is essential for understanding complex systems, such as the economy, the brain, and the climate. Constructing causal graphs often relies on either data-driven or expert-driven approaches, both fraught with challenges. The former methods, like the celebrated PC algorithm, face issues with data requirements and assumptions of causal sufficiency, while the latter demand substantial time and domain knowledge. This work explores the capabilities of Large Language Models (LLMs) as an alternative to domain experts for causal graph generation. We frame conditional independence queries as prompts to LLMs and employ the PC algorithm with the answers. The performance of the LLM-based conditional independence oracle on systems with known causal graphs shows a high degree of variability. We improve the performance through a proposed statistical-inspired voting schema that allows some control over false-positive and false-negative rates. Inspecting the chain-of-thought argumentation, we find causal reasoning to justify its answer to a probabilistic query. We show evidence that knowledge-based CIT could eventually become a complementary tool for data-driven causal discovery.

Homer Durand, Gherardo Varando, Nathan Mankovich et al.

We propose a regularisation strategy of classical machine learning algorithms rooted in causality that ensures robustness against distribution shifts. Building upon the anchor regression framework, we demonstrate how incorporating a straightforward regularisation term into the loss function of classical multivariate analysis algorithms, such as (orthonormalized) partial least squares, reduced-rank regression, and multiple linear regression, enables out-of-distribution generalisation. Our framework allows users to efficiently verify the compatibility of a loss function with the regularisation strategy. Estimators for selected algorithms are provided, showcasing consistency and efficacy in synthetic and real-world climate science problems. The empirical validation highlights the versatility of anchor regularisation, emphasizing its compatibility with multivariate analysis approaches and its role in enhancing replicability while guarding against distribution shifts. The extended anchor framework advances causal inference methodologies, addressing the need for reliable out-of-distribution generalisation.

Gustau Camps-Valls, Andreas Gerhardus, Urmi Ninad et al.

Physics is a field of science that has traditionally used the scientific method to answer questions about why natural phenomena occur and to make testable models that explain the phenomena. Discovering equations, laws and principles that are invariant, robust and causal explanations of the world has been fundamental in physical sciences throughout the centuries. Discoveries emerge from observing the world and, when possible, performing interventional studies in the system under study. With the advent of big data and the use of data-driven methods, causal and equation discovery fields have grown and made progress in computer science, physics, statistics, philosophy, and many applied fields. All these domains are intertwined and can be used to discover causal relations, physical laws, and equations from observational data. This paper reviews the concepts, methods, and relevant works on causal and equation discovery in the broad field of Physics and outlines the most important challenges and promising future lines of research. We also provide a taxonomy for observational causal and equation discovery, point out connections, and showcase a complete set of case studies in Earth and climate sciences, fluid dynamics and mechanics, and the neurosciences. This review demonstrates that discovering fundamental laws and causal relations by observing natural phenomena is being revolutionised with the efficient exploitation of observational data, modern machine learning algorithms and the interaction with domain knowledge. Exciting times are ahead with many challenges and opportunities to improve our understanding of complex systems.

Devis Tuia, Konrad Schindler, Begüm Demir et al.

Earth observation (EO) is a prime instrument for monitoring land and ocean processes, studying the dynamics at work, and taking the pulse of our planet. This article gives a bird's eye view of the essential scientific tools and approaches informing and supporting the transition from raw EO data to usable EO-based information. The promises, as well as the current challenges of these developments, are highlighted under dedicated sections. Specifically, we cover the impact of (i) Computer vision; (ii) Machine learning; (iii) Advanced processing and computing; (iv) Knowledge-based AI; (v) Explainable AI and causal inference; (vi) Physics-aware models; (vii) User-centric approaches; and (viii) the much-needed discussion of ethical and societal issues related to the massive use of ML technologies in EO.

Kai Jeggle, David Neubauer, Gustau Camps-Valls et al.

Cirrus clouds are key modulators of Earth's climate. Their dependencies on meteorological and aerosol conditions are among the largest uncertainties in global climate models. This work uses three years of satellite and reanalysis data to study the link between cirrus drivers and cloud properties. We use a gradient-boosted machine learning model and a Long Short-Term Memory (LSTM) network with an attention layer to predict the ice water content and ice crystal number concentration. The models show that meteorological and aerosol conditions can predict cirrus properties with $R^2 = 0.49$. Feature attributions are calculated with SHapley Additive exPlanations (SHAP) to quantify the link between meteorological and aerosol conditions and cirrus properties. For instance, the minimum concentration of supermicron-sized dust particles required to cause a decrease in ice crystal number concentration predictions is $2 \times 10^{-4}$ mg m\textsuperscript{-3}. The last 15 hours before the observation predict all cirrus properties.

Gulsen Taskin, Gustau Camps-Valls

Learning the manifold structure of remote sensing images is of paramount relevance for modeling and understanding processes, as well as to encapsulate the high dimensionality in a reduced set of informative features for subsequent classification, regression, or unmixing. Manifold learning methods have shown excellent performance to deal with hyperspectral image (HSI) analysis but, unless specifically designed, they cannot provide an explicit embedding map readily applicable to out-of-sample data. A common assumption to deal with the problem is that the transformation between the high-dimensional input space and the (typically low) latent space is linear. This is a particularly strong assumption, especially when dealing with hyperspectral images due to the well-known nonlinear nature of the data. To address this problem, a manifold learning method based on High Dimensional Model Representation (HDMR) is proposed, which enables to present a nonlinear embedding function to project out-of-sample samples into the latent space. The proposed method is compared to manifold learning methods along with its linear counterparts and achieves promising performance in terms of classification accuracy of a representative set of hyperspectral images.

Ioannis Prapas, Spyros Kondylatos, Ioannis Papoutsis et al.

Wildfire forecasting is of paramount importance for disaster risk reduction and environmental sustainability. We approach daily fire danger prediction as a machine learning task, using historical Earth observation data from the last decade to predict next-day's fire danger. To that end, we collect, pre-process and harmonize an open-access datacube, featuring a set of covariates that jointly affect the fire occurrence and spread, such as weather conditions, satellite-derived products, topography features and variables related to human activity. We implement a variety of Deep Learning (DL) models to capture the spatial, temporal or spatio-temporal context and compare them against a Random Forest (RF) baseline. We find that either spatial or temporal context is enough to surpass the RF, while a ConvLSTM that exploits the spatio-temporal context performs best with a test Area Under the Receiver Operating Characteristic of 0.926. Our DL-based proof-of-concept provides national-scale daily fire danger maps at a much higher spatial resolution than existing operational solutions.

Daniel Heestermans Svendsen, Pablo Morales-Alvarez, Ana Belen Ruescas et al.

Parameter retrieval and model inversion are key problems in remote sensing and Earth observation. Currently, different approximations exist: a direct, yet costly, inversion of radiative transfer models (RTMs); the statistical inversion with in situ data that often results in problems with extrapolation outside the study area; and the most widely adopted hybrid modeling by which statistical models, mostly nonlinear and non-parametric machine learning algorithms, are applied to invert RTM simulations. We will focus on the latter. Among the different existing algorithms, in the last decade kernel based methods, and Gaussian Processes (GPs) in particular, have provided useful and informative solutions to such RTM inversion problems. This is in large part due to the confidence intervals they provide, and their predictive accuracy. However, RTMs are very complex, highly nonlinear, and typically hierarchical models, so that often a shallow GP model cannot capture complex feature relations for inversion. This motivates the use of deeper hierarchical architectures, while still preserving the desirable properties of GPs. This paper introduces the use of deep Gaussian Processes (DGPs) for bio-geo-physical model inversion. Unlike shallow GP models, DGPs account for complicated (modular, hierarchical) processes, provide an efficient solution that scales well to big datasets, and improve prediction accuracy over their single layer counterpart. In the experimental section, we provide empirical evidence of performance for the estimation of surface temperature and dew point temperature from infrared sounding data, as well as for the prediction of chlorophyll content, inorganic suspended matter, and coloured dissolved matter from multispectral data acquired by the Sentinel-3 OLCI sensor. The presented methodology allows for more expressive forms of GPs in remote sensing model inversion problems.

Ana B. Ruescas, Martin Hieronymi, Sampsa Koponen et al.

The coloured dissolved organic matter (CDOM) concentration is the standard measure of humic substance in natural waters. CDOM measurements by remote sensing is calculated using the absorption coefficient (a) at a certain wavelength (e.g. 440nm). This paper presents a comparison of four machine learning methods for the retrieval of CDOM from remote sensing signals: regularized linear regression (RLR), random forest (RF), kernel ridge regression (KRR) and Gaussian process regression (GPR). Results are compared with the established polynomial regression algorithms. RLR is revealed as the simplest and most efficient method, followed closely by its nonlinear counterpart KRR.

Anna Mateo-Sanchis, Jordi Munoz-Mari, Manuel Campos-Taberner et al.

In this work we evaluate multi-output (MO) Gaussian Process (GP) models based on the linear model of coregionalization (LMC) for estimation of biophysical parameter variables under a gap filling setup. In particular, we focus on LAI and fAPAR over rice areas. We show how this problem cannot be solved with standard single-output (SO) GP models, and how the proposed MO-GP models are able to successfully predict these variables even in high missing data regimes, by implicitly performing an across-domain information transfer.

Gonzalo Mateo-García, Luis Gómez-Chova, Gustau Camps-Valls

Convolutional neural networks (CNN) have proven to be state of the art methods for many image classification tasks and their use is rapidly increasing in remote sensing problems. One of their major strengths is that, when enough data is available, CNN perform an end-to-end learning without the need of custom feature extraction methods. In this work, we study the use of different CNN architectures for cloud masking of Proba-V multispectral images. We compare such methods with the more classical machine learning approach based on feature extraction plus supervised classification. Experimental results suggest that CNN are a promising alternative for solving cloud masking problems.

Luis Gómez-Chova, Gonzalo Mateo-García, Jordi Muñoz-Marí et al.

This paper presents the development and implementation of a cloud detection algorithm for Proba-V. Accurate and automatic detection of clouds in satellite scenes is a key issue for a wide range of remote sensing applications. With no accurate cloud masking, undetected clouds are one of the most significant sources of error in both sea and land cover biophysical parameter retrieval. The objective of the algorithms presented in this paper is to detect clouds accurately providing a cloud flag per pixel. For this purpose, the method exploits the information of Proba-V using statistical machine learning techniques to identify the clouds present in Proba-V products. The effectiveness of the proposed method is successfully illustrated using a large number of real Proba-V images.

Juan Emmanuel Johnson, Valero Laparra, Gustau Camps-Valls

Gaussian Processes (GPs) are a class of kernel methods that have shown to be very useful in geoscience applications. They are widely used because they are simple, flexible and provide very accurate estimates for nonlinear problems, especially in parameter retrieval. An addition to a predictive mean function, GPs come equipped with a useful property: the predictive variance function which provides confidence intervals for the predictions. The GP formulation usually assumes that there is no input noise in the training and testing points, only in the observations. However, this is often not the case in Earth observation problems where an accurate assessment of the instrument error is usually available. In this paper, we showcase how the derivative of a GP model can be used to provide an analytical error propagation formulation and we analyze the predictive variance and the propagated error terms in a temperature prediction problem from infrared sounding data.

David Malmgren-Hansen, Allan Aasbjerg Nielsen, Valero Laparra et al.

The Infrared Atmospheric Sounding Interferometer (IASI) on board the MetOp satellite series provides important measurements for Numerical Weather Prediction (NWP). Retrieving accurate atmospheric parameters from the raw data provided by IASI is a large challenge, but necessary in order to use the data in NWP models. Statistical models performance is compromised because of the extremely high spectral dimensionality and the high number of variables to be predicted simultaneously across the atmospheric column. All this poses a challenge for selecting and studying optimal models and processing schemes. Earlier work has shown non-linear models such as kernel methods and neural networks perform well on this task, but both schemes are computationally heavy on large quantities of data. Kernel methods do not scale well with the number of training data, and neural networks require setting critical hyperparameters. In this work we follow an alternative pathway: we study transfer learning in convolutional neural nets (CNN s) to alleviate the retraining cost by departing from proxy solutions (either features or networks) obtained from previously trained models for related variables. We show how features extracted from the IASI data by a CNN trained to predict a physical variable can be used as inputs to another statistical method designed to predict a different physical variable at low altitude. In addition, the learned parameters can be transferred to another CNN model and obtain results equivalent to those obtained when using a CNN trained from scratch requiring only fine tuning.

Anna Mateo-Sanchis, Jordi Muñoz-Marí, Adrián Pérez-Suay et al.

This paper introduces warped Gaussian processes (WGP) regression in remote sensing applications. WGP models output observations as a parametric nonlinear transformation of a GP. The parameters of such prior model are then learned via standard maximum likelihood. We show the good performance of the proposed model for the estimation of oceanic chlorophyll content from multispectral data, vegetation parameters (chlorophyll, leaf area index, and fractional vegetation cover) from hyperspectral data, and in the detection of the causal direction in a collection of 28 bivariate geoscience and remote sensing causal problems. The model consistently performs better than the standard GP and the more advanced heteroscedastic GP model, both in terms of accuracy and more sensible confidence intervals.

Emiliano Díaz, Adrián Pérez-Suay, Valero Laparra et al.

This paper introduces a novel statistical regression framework that allows the incorporation of consistency constraints. A linear and nonlinear (kernel-based) formulation are introduced, and both imply closed-form analytical solutions. The models exploit all the information from a set of drivers while being maximally independent of a set of auxiliary, protected variables. We successfully illustrate the performance in the estimation of chlorophyll content.

Devis Tuia, Benjamin Kellenberger, Adrian Pérez-Suay et al.

We present a deep learning model with temporal memory to detect clouds in image time series acquired by the Seviri imager mounted on the Meteosat Second Generation (MSG) satellite. The model provides pixel-level cloud maps with related confidence and propagates information in time via a recurrent neural network structure. With a single model, we are able to outline clouds along all year and during day and night with high accuracy.

David Malmgren-Hansen, Valero Laparra, Allan Aasbjerg Nielsen et al.

In this paper we present a combined strategy for the retrieval of atmospheric profiles from infrared sounders. The approach considers the spatial information and a noise-dependent dimensionality reduction approach. The extracted features are fed into a canonical linear regression. We compare Principal Component Analysis (PCA) and Minimum Noise Fraction (MNF) for dimensionality reduction, and study the compactness and information content of the extracted features. Assessment of the results is done on a big dataset covering many spatial and temporal situations. PCA is widely used for these purposes but our analysis shows that one can gain significant improvements of the error rates when using MNF instead. In our analysis we also investigate the relationship between error rate improvements when including more spectral and spatial components in the regression model, aiming to uncover the trade-off between model complexity and error rates.

Fatih Nar, Adrián Pérez-Suay, José Antonio Padrón et al.

This work tackles the target detection problem through the well-known global RX method. The RX method models the clutter as a multivariate Gaussian distribution, and has been extended to nonlinear distributions using kernel methods. While the kernel RX can cope with complex clutters, it requires a considerable amount of computational resources as the number of clutter pixels gets larger. Here we propose random Fourier features to approximate the Gaussian kernel in kernel RX and consequently our development keep the accuracy of the nonlinearity while reducing the computational cost which is now controlled by an hyperparameter. Results over both synthetic and real-world image target detection problems show space and time efficiency of the proposed method while providing high detection performance.

Ana B. Ruescas, Gonzalo Mateo-Garcia, Gustau Camps-Valls et al.

Water quality parameters are derived applying several machine learning regression methods on the Case2eXtreme dataset (C2X). The used data are based on Hydrolight in-water radiative transfer simulations at Sentinel-3 OLCI wavebands, and the application is done exclusively for absorbing waters with high concentrations of coloured dissolved organic matter (CDOM). The regression approaches are: regularized linear, random forest, Kernel ridge, Gaussian process and support vector regressors. The validation is made with and an independent simulation dataset. A comparison with the OLCI Neural Network Swarm (ONSS) is made as well. The best approached is applied to a sample scene and compared with the standard OLCI product delivered by EUMETSAT/ESA

José A. Padrón Hidalgo, Adrián Pérez-Suay, Fatih Nar et al.

In this work we propose a method to find anomalous changes in remote sensing images based on the chronochrome approach. A regressor between images is used to discover the most {\em influential points} in the observed data. Typically, the pixels with largest residuals are decided to be anomalous changes. In order to find the anomalous pixels we consider the Cook distance and propose its nonlinear extension using random Fourier features as an efficient nonlinear measure of impact. Good empirical performance is shown over different multispectral images both visually and quantitatively evaluated with ROC curves.

Adrián Pérez-Suay, Julia Amorós-López, Luis Gómez-Chova et al.

Landmark recognition and matching is a critical step in many Image Navigation and Registration (INR) models for geostationary satellite services, as well as to maintain the geometric quality assessment (GQA) in the instrument data processing chain of Earth observation satellites. Matching the landmark accurately is of paramount relevance, and the process can be strongly impacted by the cloud contamination of a given landmark. This paper introduces a complete pattern recognition methodology able to detect the presence of clouds over landmarks using Meteosat Second Generation (MSG) data. The methodology is based on the ensemble combination of dedicated support vector machines (SVMs) dependent on the particular landmark and illumination conditions. This divide-and-conquer strategy is motivated by the data complexity and follows a physically-based strategy that considers variability both in seasonality and illumination conditions along the day to split observations. In addition, it allows training the classification scheme with millions of samples at an affordable computational costs. The image archive was composed of 200 landmark test sites with near 7 million multispectral images that correspond to MSG acquisitions during 2010. Results are analyzed in terms of cloud detection accuracy and computational cost. We provide illustrative source code and a portion of the huge training data to the community.

Adrián Pérez-Suay, Gustau Camps-Valls

Establishing causal relations between random variables from observational data is perhaps the most important challenge in today's \blue{science}. In remote sensing and geosciences this is of special relevance to better understand the Earth's system and the complex interactions between the governing processes. In this paper, we focus on observational causal inference, thus we try to estimate the correct direction of causation using a finite set of empirical data. In addition, we focus on the more complex bivariate scenario that requires strong assumptions and no conditional independence tests can be used. In particular, we explore the framework of (non-deterministic) additive noise models, which relies on the principle of independence between the cause and the generating mechanism. A practical algorithmic instantiation of such principle only requires 1) two regression models in the forward and backward directions, and 2) the estimation of {\em statistical independence} between the obtained residuals and the observations. The direction leading to more independent residuals is decided to be the cause. We instead propose a criterion that uses the {\em sensitivity} (derivative) of the dependence estimator, the sensitivity criterion allows to identify samples most affecting the dependence measure, and hence the criterion is robust to spurious detections. We illustrate performance in a collection of 28 geoscience causal inference problems, in a database of radiative transfer models simulations and machine learning emulators in vegetation parameter modeling involving 182 problems, and in assessing the impact of different regression models in a carbon cycle problem. The criterion achieves state-of-the-art detection rates in all cases, it is generally robust to noise sources and distortions.

Jose E. Adsuara, Adrián Pérez-Suay, Jordi Muñoz-Marí et al.

In many remote sensing applications one wants to estimate variables or parameters of interest from observations. When the target variable is available at a resolution that matches the remote sensing observations, standard algorithms such as neural networks, random forests or Gaussian processes are readily available to relate the two. However, we often encounter situations where the target variable is only available at the group level, i.e. collectively associated to a number of remotely sensed observations. This problem setting is known in statistics and machine learning as {\em multiple instance learning} or {\em distribution regression}. This paper introduces a nonlinear (kernel-based) method for distribution regression that solves the previous problems without making any assumption on the statistics of the grouped data. The presented formulation considers distribution embeddings in reproducing kernel Hilbert spaces, and performs standard least squares regression with the empirical means therein. A flexible version to deal with multisource data of different dimensionality and sample sizes is also presented and evaluated. It allows working with the native spatial resolution of each sensor, avoiding the need of match-up procedures. Noting the large computational cost of the approach, we introduce an efficient version via random Fourier features to cope with millions of points and groups.

José A. Padrón Hidalgo, Adrián Pérez-Suay, Fatih Nar et al.

Current anomaly detection algorithms are typically challenged by either accuracy or efficiency. More accurate nonlinear detectors are typically slow and not scalable. In this letter, we propose two families of techniques to improve the efficiency of the standard kernel Reed-Xiaoli (RX) method for anomaly detection by approximating the kernel function with either {\em data-independent} random Fourier features or {\em data-dependent} basis with the Nyström approach. We compare all methods for both real multi- and hyperspectral images. We show that the proposed efficient methods have a lower computational cost and they perform similar (or outperform) the standard kernel RX algorithm thanks to their implicit regularization effect. Last but not least, the Nyström approach has an improved power of detection.