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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.

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.

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.

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.

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.

The development of foundation models has revolutionized our ability to interpret the Earth's surface using satellite observational data. Traditional models have been siloed, tailored to specific sensors or data types like optical, radar, and hyperspectral, each with its own unique characteristics. This specialization hinders the potential for a holistic analysis that could benefit from the combined strengths of these diverse data sources. Our novel approach introduces the Dynamic One-For-All (DOFA) model, leveraging the concept of neural plasticity in brain science to integrate various data modalities into a single framework adaptively. This dynamic hypernetwork, adjusting to different wavelengths, enables a single versatile Transformer jointly trained on data from five sensors to excel across 12 distinct Earth observation tasks, including sensors never seen during pretraining. DOFA's innovative design offers a promising leap towards more accurate, efficient, and unified Earth observation analysis, showcasing remarkable adaptability and performance in harnessing the potential of multimodal Earth observation data., Comment: 36 pages, 7 figures

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.

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., Comment: Accepted by ICLR 2024 Machine Learning for Remote Sensing (ML4RS) Workshop

We introduce a causal regularisation extension to anchor regression (AR) for improved out-of-distribution (OOD) generalisation. We present anchor-compatible losses, aligning with the anchor framework to ensure robustness against distribution shifts. Various multivariate analysis (MVA) algorithms, such as (Orthonormalized) PLS, RRR, and MLR, fall within the anchor framework. We observe that simple regularisation enhances robustness in OOD settings. 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 MVA approaches and its role in enhancing replicability while guarding against distribution shifts. The extended AR framework advances causal inference methodologies, addressing the need for reliable OOD generalisation., Comment: 21 pages, 15 figures

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.

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.

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., Comment: Accepted at NeurIPS 2023 Workshop on Tackling Climate Change with Machine Learning: Blending New and Existing Knowledge Systems

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., Comment: Accepted for publication and presentation at the International Geoscience and Remote Sensing Symposium (IGARSS) 2024

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., Comment: 4 pages, 2 figures, 3 tables, CausalStats23: When Causal Inference meets Statistical Analysis, April 17-21, 2023, Paris, France

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., Comment: Accepted at the ICCV 2023 workshop on Artificial Intelligence for Humanitarian Assistance and Disaster Response

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., Comment: Accepted at the 37th Conference on Neural Information Processing Systems (NeurIPS 2023) Track on Datasets and Benchmarks (oral presentation)

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., Comment: 137 pages

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.

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., Comment: Presented at Climate Informatics 2023 in Cambridge; Submitted to Environmental Data Science Journal Updates Version: New version of dataset is linked. Please use that version: https://zenodo.org/record/7965381

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., Comment: Accepted at the Norwegian Artificial Intelligence Symposium 2022. Code available at: https://github.com/Wickstrom/KernelizedTaylorDiagram

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.

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., Comment: Mach Learn (2021)

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.

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., Comment: This is an accepted version of work to be published in the IEEE Transactions on Geoscience and Remote Sensing. 11 pages

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., Comment: Accepted to the workshop on Artificial Intelligence for Humanitarian Assistance and Disaster Response at the 35th Conference on Neural Information Processing Systems (NeurIPS 2021)

In many inference problems, the evaluation of complex and costly models is often required. In this context, Bayesian methods have become very popular in several fields over the last years, in order to obtain parameter inversion, model selection or uncertainty quantification. Bayesian inference requires the approximation of complicated integrals involving (often costly) posterior distributions. Generally, this approximation is obtained by means of Monte Carlo (MC) methods. In order to reduce the computational cost of the corresponding technique, surrogate models (also called emulators) are often employed. Another alternative approach is the so-called Approximate Bayesian Computation (ABC) scheme. ABC does not require the evaluation of the costly model but the ability to simulate artificial data according to that model. Moreover, in ABC, the choice of a suitable distance between real and artificial data is also required. In this work, we introduce a novel approach where the expensive model is evaluated only in some well-chosen samples. The selection of these nodes is based on the so-called compressed Monte Carlo (CMC) scheme. We provide theoretical results supporting the novel algorithms and give empirical evidence of the performance of the proposed method in several numerical experiments. Two of them are real-world applications in astronomy and satellite remote sensing., Comment: published in IEEE Transactions on Aerospace and Electronic Systems

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.

The modelling of Earth observation data is a challenging problem, typically approached by either purely mechanistic or purely data-driven methods. Mechanistic models encode the domain knowledge and physical rules governing the system. Such models, however, need the correct specification of all interactions between variables in the problem and the appropriate parameterization is a challenge in itself. On the other hand, machine learning approaches are flexible data-driven tools, able to approximate arbitrarily complex functions, but lack interpretability and struggle when data is scarce or in extrapolation regimes. In this paper, we argue that hybrid learning schemes that combine both approaches can address all these issues efficiently. We introduce Gaussian process (GP) convolution models for hybrid modelling in Earth observation (EO) problems. We specifically propose the use of a class of GP convolution models called latent force models (LFMs) for EO time series modelling, analysis and understanding. LFMs are hybrid models that incorporate physical knowledge encoded in differential equations into a multioutput GP model. LFMs can transfer information across time-series, cope with missing observations, infer explicit latent functions forcing the system, and learn parameterizations which are very helpful for system analysis and interpretability. We consider time series of soil moisture from active (ASCAT) and passive (SMOS, AMSR2) microwave satellites. We show how assuming a first order differential equation as governing equation, the model automatically estimates the e-folding time or decay rate related to soil moisture persistence and discovers latent forces related to precipitation. The proposed hybrid methodology reconciles the two main approaches in remote sensing parameter estimation by blending statistical learning and mechanistic modeling.

We introduce a method for manifold alignment of different modalities (or domains) of remote sensing images. The problem is recurrent when a set of multitemporal, multisource, multisensor and multiangular images is available. In these situations, images should ideally be spatially coregistred, corrected and compensated for differences in the image domains. Such procedures require the interaction of the user, involve tuning of many parameters and heuristics, and are usually applied separately. Changes of sensors and acquisition conditions translate into shifts, twists, warps and foldings of the image distributions (or manifolds). The proposed semisupervised manifold alignment (SS-MA) method aligns the images working directly on their manifolds, and is thus not restricted to images of the same resolutions, either spectral or spatial. SS-MA pulls close together samples of the same class while pushing those of different classes apart. At the same time, it preserves the geometry of each manifold along the transformation. The method builds a linear invertible transformation to a latent space where all images are alike, and reduces to solving a generalized eigenproblem of moderate size. We study the performance of SS-MA in toy examples and in real multiangular, multitemporal, and multisource image classification problems. The method performs well for strong deformations and leads to accurate classification for all domains.

In the last years we have witnessed the fields of geosciences and remote sensing and artificial intelligence to become closer. Thanks to both the massive availability of observational data, improved simulations, and algorithmic advances, these disciplines have found common objectives and challenges to advance the modeling and understanding of the Earth system. Despite such great opportunities, we also observed a worrying tendency to remain in disciplinary comfort zones applying recent advances from artificial intelligence on well resolved remote sensing problems. Here we take a position on research directions where we think the interface between these fields will have the most impact and become potential game changers. In our declared agenda for AI on Earth sciences, we aim to inspire researchers, especially the younger generations, to tackle these challenges for a real advance of remote sensing and the geosciences., Comment: In press at IEEE Geoscience and Remote Sensing Magazine

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., Comment: 7 pages, 4 figures

Gaussian Processes (GPs) has experienced tremendous success in geoscience in general and for bio-geophysical parameter retrieval in the last years. GPs constitute a solid Bayesian framework to formulate many function approximation problems consistently. This paper reviews the main theoretical GP developments in the field. We review new algorithms that respect the signal and noise characteristics, that provide feature rankings automatically, and that allow applicability of associated uncertainty intervals to transport GP models in space and time. All these developments are illustrated in the field of geoscience and remote sensing at a local and global scales through a set of illustrative examples.

Products derived from a single multispectral sensor are hampered by a limited spatial, spectral or temporal resolutions. Image fusion in general and downscaling/blending in particular allow to combine different multiresolution datasets. We present here an optimal interpolation approach to generate smoothed and gap-free time series of Landsat reflectance data. We fuse MODIS (moderate-resolution imaging spectroradiometer) and Landsat data globally using the Google Earth Engine (GEE) platform. The optimal interpolator exploits GEE ability to ingest large amounts of data (Landsat climatologies) and uses simple linear operations that scale easily in the cloud. The approach shows very good results in practice, as tested over five sites with different vegetation types and climatic characteristics in the contiguous US.

This paper introduces a modular processing chain to derive global high-resolution maps of leaf traits. In particular, we present global maps at 500 m resolution of specific leaf area, leaf dry matter content, leaf nitrogen and phosphorus content per dry mass, and leaf nitrogen/phosphorus ratio. The processing chain exploits machine learning techniques along with optical remote sensing data (MODIS/Landsat) and climate data for gap filling and up-scaling of in-situ measured leaf traits. The chain first uses random forests regression with surrogates to fill gaps in the database ($> 45 \% $ of missing entries) and maximize the global representativeness of the trait dataset. Along with the estimated global maps of leaf traits, we provide associated uncertainty estimates derived from the regression models. The process chain is modular, and can easily accommodate new traits, data streams (traits databases and remote sensing data), and methods. The machine learning techniques applied allow attribution of information gain to data input and thus provide the opportunity to understand trait-environment relationships at the plant and ecosystem scales.

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., Comment: 4 pages, 3 figures

Developing accurate models of crop stress, phenology and productivity is of paramount importance, given the increasing need of food. Earth observation remote sensing data provides a unique source of information to monitor crops in a temporally resolved and spatially explicit way. In this study, we propose the combination of multisensor (optical and microwave) remote sensing data for crop yield estimation and forecasting using two novel approaches. We first propose the lag between Enhanced Vegetation Index derived from MODIS and Vegetation Optical Depth derived from SMAP as a new joint metric combining the information from the two satellite sensors in a unique feature or descriptor. Our second approach avoids summarizing statistics and uses machine learning to combine full time series of EVI and VOD. This study considers two statistical methods, a regularized linear regression and its nonlinear extension called kernel ridge regression to directly estimate the county-level surveyed total production, as well as individual yields of the major crops grown in the region: corn, soybean and wheat. The study area includes the US Corn Belt, and we use agricultural survey data from the National Agricultural Statistics Service (USDA-NASS) for year 2015 for quantitative assessment., Comment: 53 pages, 8 figures, 3 tables

Spatially and temporally explicit canopy water content (CWC) data are important for monitoring vegetation status, and constitute essential information for studying ecosystem-climate interactions. Despite many efforts there is currently no operational CWC product available to users. In the context of the Satellite Application Facility for Land Surface Analysis (LSA-SAF), we have developed an algorithm to produce a global dataset of CWC based on data from the Advanced Very High Resolution Radiometer (AVHRR) sensor on board Meteorological Operational (MetOp) satellites forming the EUMETSAT Polar System (EPS). CWC reflects the water conditions at the leaf level and information related to canopy structure. An accuracy assessment of the EPS/AVHRR CWC indicated a close agreement with multi-temporal ground data from SMAPVEX16 in Canada and Dahra in Senegal. The present study further evaluates the consistency of the LSA-SAF product with respect to the Simplified Level 2 Product Prototype Processor (SL2P) product, and demonstrates its applicability at different spatio-temporal resolutions using optical data from MSI/Sentinel-2 and MODIS/Terra and Aqua. We conclude that the EPS/AVHRR CWC product is a promising tool for monitoring vegetation water status at regional and global scales.

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.

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., Comment: Preprint corresponding to the paper published in 2017 IEEE International Geoscience and Remote Sensing Symposium (IGARSS), Fort Worth, TX, USA, pp. 2255-2258

Soil moisture (SM) is a key state variable of the hydrological cycle, needed to monitor the effects of a changing climate on natural resources. Soil moisture is highly variable in space and time, presenting seasonalities, anomalies and long-term trends, but also, and important nonlinear behaviours. Here, we introduce a novel fast and nonlinear complex PCA method to analyze the spatio-temporal patterns of the Earth's surface SM. We use global SM estimates acquired during the period 2010-2017 by ESA's SMOS mission. Our approach unveils both time and space modes, trends and periodicities unlike standard PCA decompositions. Results show the distribution of the total SM variance among its different components, and indicate the dominant modes of temporal variability in surface soil moisture for different regions. The relationship of the derived SM spatio-temporal patterns with El Ni{\~n}o Southern Oscillation (ENSO) conditions is also explored.

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., Comment: arXiv admin note: text overlap with arXiv:2005.09907

Anomalous change detection (ACD) is an important problem in remote sensing image processing. Detecting not only pervasive but also anomalous or extreme changes has many applications for which methodologies are available. This paper introduces a nonlinear extension of a full family of anomalous change detectors. In particular, we focus on algorithms that utilize Gaussian and elliptically contoured (EC) distribution and extend them to their nonlinear counterparts based on the theory of reproducing kernels' Hilbert space. We illustrate the performance of the kernel methods introduced in both pervasive and ACD problems with real and simulated changes in multispectral and hyperspectral imagery with different resolutions (AVIRIS, Sentinel-2, WorldView-2, and Quickbird). A wide range of situations is studied in real examples, including droughts, wildfires, and urbanization. Excellent performance in terms of detection accuracy compared to linear formulations is achieved, resulting in improved detection accuracy and reduced false-alarm rates. Results also reveal that the EC assumption may be still valid in Hilbert spaces. We provide an implementation of the algorithms as well as a database of natural anomalous changes in real scenarios http://isp.uv.es/kacd.html.

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., Comment: arXiv admin note: substantial text overlap with arXiv:1710.05578