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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 has been fundamental in physical sciences throughout the centuries. Discoveries emerge from observing the world and, when possible, performing interventions on the system under study. With the advent of big data and data-driven methods, the fields of causal and equation discovery have developed and accelerated progress in computer science, physics, statistics, philosophy, and many applied fields. 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 data-driven causal and equation discovery, point out connections, and showcase comprehensive 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 revolutionised with the efficient exploitation of observational data and simulations, modern machine learning algorithms and the combination with domain knowledge. Exciting times are ahead with many challenges and opportunities to improve our understanding of complex systems. [ABSTRACT FROM AUTHOR]

Learning the manifold structure of remote sensing images is of paramount relevance for modeling and understanding processes, as well as encapsulating the high dimensionality in a reduced set of informative features for subsequent classification, regression, or unmixing. Manifold learning methods have shown excellent performance when dealing with hyperspectral image (HSI) analysis, but, unless specifically designed, they cannot provide an explicit embedding map readily applicable to out-of-sample (OOS) data. A common assumption to deal with the problem is that the transformation between the high-dimensional input space and the latent space (typically low) is linear. This is a particularly strong assumption, especially when dealing with HSIs 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 a nonlinear embedding function to project OOS samples into the latent space. The proposed method is compared to manifold learning methods along with their linear counterparts and achieves promising performance in terms of classification accuracy for a representative set of HSIs. [ABSTRACT FROM AUTHOR]

The article offers information on unified vegetation index for quantifying the terrestrial biosphere. It mentions that generalize the broad family of commonly used vegetation indices by exploiting all higher-order relations between the spectral channels involved. It discusses that dynamics and potentials for stabilizing atmospheric carbon dioxide and mitigating global climate change.

Despite their success deep neural networks still lack interpretability and are regarded as black boxes. This hampers a wider adoption in applications with societal, environmental or economical implications, and motivated a variety of techniques for explaining their outputs. Such explanations are however typically produced after model training so there is no guarantee that models learn faithful attributions, a goal they were not trained for. We evaluate the impact of different penalty terms in the loss function that promote explainable feature attributions, and that can be learned during training in an unsupervised way. We show that explainability-constrained models produce better saliency maps based on multiple metrics and tests. Regularizers imposing locality , fidelity and symmetry properties lead to the best performances in terms of MoRF and ROAR scores. • Novel attribution priors enforcing formal axioms and properties are introduced. • Explanations can be optimized at training time in an unsupervised way. • Locality, fidelity and symmetry constraints produce more reliable saliency maps. • Constrained models outperform baselines according to metrics such as ROAR. [ABSTRACT FROM AUTHOR]

Satellite remote sensing has been widely used in the last decades for agricultural applications, both for assessing vegetation condition and for subsequent yield prediction. Existing remote sensing-based methods to estimate gross primary productivity (GPP), which is an important variable to indicate crop photosynthetic function and stress, typically rely on empirical or semi-empirical approaches, which tend to over-simplify photosynthetic mechanisms. In this work, we take advantage of all parallel developments in mechanistic photosynthesis modeling and satellite data availability for an advanced monitoring of crop productivity. In particular, we combine process-based modeling with the soil-canopy energy balance radiative transfer model (SCOPE) with Sentinel-2 and Landsat 8 optical remote sensing data and machine learning methods in order to estimate crop GPP. With this approach, we by-pass the need for an intermediate step to retrieve the set of vegetation biophysical parameters needed to accurately model photosynthesis, while still accounting for the complex processes of the original physically-based model. Several implementations of the machine learning models are tested and validated using simulated and flux tower-based GPP data. Our final neural network model is able to estimate GPP at the tested flux tower sites with r 2 of 0.92 and RMSE of 1.38 gC d−1 m−2, which outperforms empirical models based on vegetation indices. The first test of applicability of this model to Landsat 8 data showed good results (r 2 of 0.82 and RMSE of 1.97 gC d−1 m−2), which suggests that our approach can be further applied to other sensors. Modeling and testing is restricted to C3 crops in this study, but can be extended to C4 crops by producing a new training dataset with SCOPE that accounts for the different photosynthetic pathways. Our model successfully estimates GPP across a variety of C3 crop types and environmental conditions even though it does not use any local information from the corresponding sites. This highlights its potential to map crop productivity from new satellite sensors at a global scale with the help of current Earth observation cloud computing platforms. • Sentinel-2 offers a great potential for the monitoring of agricultural productivity. • Machine learning applied to a process-based model to estimate GPP from satellite data. • Our hybrid approach accurately estimates GPP without any local information. • The use of red edge bands of Sentinel-2 improves GPP modeling. • Global application to multiple satellites using on the same model [ABSTRACT FROM AUTHOR]

Establishing causal relations between random variables from observational data is perhaps the most important challenge in today’s 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 an observational causal inference, and 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 (nondeterministic) 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 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 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 the performance in a collection of 28 geoscience causal inference problems, a database of radiative transfer models simulations and machine learning emulators in vegetation parameter modeling involving 182 problems, and assessing the impact of different regression models in a carbon cycle problem. The criterion achieves the state-of-the-art detection rates in all cases, and it is generally robust to noise sources and distortions. The presented approach confirms the validity in observational bivariate problems in the earth sciences. [ABSTRACT FROM AUTHOR]

Abstract 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 maximizes the global representativeness of the trait dataset. Plant species are then aggregated to Plant Functional Types (PFTs). Next, the spatial abundance of PFTs at MODIS resolution (500 m) is calculated using Landsat data (30 m). Based on these PFT abundances, representative trait values are calculated for MODIS pixels with nearby trait data. Finally, different regression algorithms are applied to globally predict trait estimates from these MODIS pixels using remote sensing and climate data. The methods were compared in terms of precision, robustness and efficiency. The best model (random forests regression) shows good precision (normalized RMSE≤ 20 %) and goodness of fit (averaged Pearson's correlation R = 0.78) in any considered trait. 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. The new data products – the gap-filled trait matrix, a global map of PFT abundance per MODIS gridcells and the high-resolution global leaf trait maps – are complementary to existing large-scale observations of the land surface and we therefore anticipate substantial contributions to advances in quantifying, understanding and prediction of the Earth system. Highlights • Presented a modular process chain for plant trait mapping including local effects • High-resolution global maps of leaf traits by fusing measured trait data, LANDSAT and MODIS • Scope for testing and parameterizing trait-enabled Earth System models • Implications for land management and Earth system science applications [ABSTRACT FROM AUTHOR]

The wealth of sensory data coming from different modalities has opened numerous opportunities for data analysis. The data are of increasing volume, complexity and dimensionality, thus calling for new methodological innovations towards multimodal data processing. However, multimodal architectures must rely on models able to adapt to changes in the data distribution. Differences in the density functions can be due to changes in acquisition conditions (pose, illumination), sensors characteristics (number of channels, resolution) or different views (e.g. street level vs. aerial views of a same building). We call these different acquisition modes domains, and refer to the adaptation problem as domain adaptation. In this paper, instead of adapting the trained models themselves, we alternatively focus on finding mappings of the data sources into a common, semantically meaningful, representation domain. This field of manifold alignment extends traditional techniques in statistics such as canonical correlation analysis (CCA) to deal with nonlinear adaptation and possibly non-corresponding data pairs between the domains. We introduce a kernel method for manifold alignment (KEMA) that can match an arbitrary number of data sources without needing corresponding pairs, just few labeled examples in all domains. KEMA has interesting properties: 1) it generalizes other manifold alignment methods, 2) it can align manifolds of very different complexities, performing a discriminative alignment preserving each manifold inner structure, 3) it can define a domain-specific metric to cope with multimodal specificities, 4) it can align data spaces of different dimensionality, 5) it is robust to strong nonlinear feature deformations, and 6) it is closed-form invertible, which allows transfer across-domains and data synthesis. To authors’ knowledge this is the first method addressing all these important issues at once. We also present a reduced-rank version of KEMA for computational efficiency, and discuss the generalization performance of KEMA under Rademacher principles of stability. Aligning multimodal data with KEMA reports outstanding benefits when used as a data pre-conditioner step in the standard data analysis processing chain. KEMA exhibits very good performance over competing methods in synthetic controlled examples, visual object recognition and recognition of facial expressions tasks. KEMA is especially well-suited to deal with high-dimensional problems, such as images and videos, and under complicated distortions, twists and warpings of the data manifolds. A fully functional toolbox is available at . [ABSTRACT FROM AUTHOR]

Forthcoming superspectral satellite missions dedicated to land monitoring, as well as planned imaging spectrometers, will unleash an unprecedented data stream. The processing requirements for such large data streams involve processing techniques enabling the spatio-temporally explicit quantification of vegetation properties. Typically retrieval must be accurate, robust and fast. Hence, there is a strict requirement to identify next-generation bio-geophysical variable retrieval algorithms which can be molded into an operational processing chain. This paper offers a review of state-of-the-art retrieval methods for quantitative terrestrial bio-geophysical variable extraction using optical remote sensing imagery. We can categorize these methods into (1) parametric regression , (2) non-parametric regression , (3) physically-based and (4) hybrid methods . Hybrid methods combine generic capabilities of physically-based methods with flexible and computationally efficient methods, typically non-parametric regression methods. A review of the theoretical basis of all these methods is given first and followed by published applications. This paper focusses on: (1) retrievability of bio-geophysical variables, (2) ability to generate multiple outputs, (3) possibilities for model transparency description, (4) mapping speed, and (5) possibilities for uncertainty retrieval. Finally, the prospects of implementing these methods into future processing chains for operational retrieval of vegetation properties are presented and discussed. [ABSTRACT FROM AUTHOR]

In this paper we present an approach to perform relative spectral alignment between optical cross-sensor acquisitions. The proposed method aims at projecting the images from two different and possibly disjoint input spaces into a common latent space, in which standard change detection algorithms can be applied. The system relies on the regularized kernel canonical correlation analysis transformation (kCCA), which can accommodate nonlinear dependencies between pixels by means of kernel functions. To learn the projections, the method employs a subset of samples belonging to the unchanged areas or to uninteresting radiometric differences. Since the availability of ground truth information to perform model selection is limited, we propose a completely automatic strategy to select the hyperparameters of the system as well as the dimensionality of the transformed (latent) space. The proposed scheme is fully automatic and allows the use of any change detection algorithm in the transformed latent space. A synthetic problem built from real images and a case study involving a real cross-sensor change detection problem illustrate the capabilities of the proposed method. Results show that the proposed system outperforms the linear baseline and provides accuracies close the ones obtained with a fully supervised strategy. We provide a MATLAB implementation of the proposed method as well as the real cross-sensor data we prepared and employed at https://sites.google.com/site/michelevolpiresearch/codes/cross-sensor . [ABSTRACT FROM AUTHOR]

The terrestrial component of the Earth system has witnessed considerable changes in the past decades due to anthropogenic action. Throughout this period, the NASA Terra mission has been constantly monitoring the surface with the Moderate Resolution Imaging Spectroradiometer (MODIS) instrument. When combined with the MODIS instrument on-board of the Aqua platform, we obtain a hyper-frequent revisit capability providing sub-daily observations globally at a moderate resolution of ~250 m, but with a strong multi-angular variation of the observation footprint. Here we propose to exploit this particular configuration provided by the combined Terra + Aqua constellation to infer spatial homogeneity from the temporal stability of the observation time series. We thus designed a Temporal Coherence Index (TCI) based on the concept of information entropy. We test it on both synthetic and real landscapes showing its capacity to isolate which time series correspond to homogeneous targets based only on the MODIS measurements themselves. The index is calculated annually for the entirety of emerged surfaces for the period 2003–2020 by leveraging on the scaling capacity of the cloud computing Google Earth Engine (GEE). We foresee multiple practical applications for this index as a novel information layer that should foster the integration of surface data with satellite records, a practice that is increasingly necessary in Earth System Science. • We propose a new Temporal Coherence Index (TCI) from MODIS • TCI is an effective proxy from spatial homogeneity directly from MODIS observations • TCI should foster finer integration of surface data with satellite records [ABSTRACT FROM AUTHOR]

In the context of climate change, droughts, increasingly frequent and severe, necessitate effective monitoring. Existing methods, such as drought indices and data-driven models, face important limitations. Drought indices are built on prior expert knowledge but lack calibration based on actual drought events, while data-driven models prioritize goodness of fit over real event identification, undermining their credibility and generalization, and also struggling to generalize from regional to large-scale contexts. To address these challenges, here we introduce a hybrid machine learning framework for time series that combines domain knowledge and observational data in a variational recurrent neural network. The network models the joint distribution of total precipitation, air temperature, and real drought events, providing accurate predictions and uncertainty estimates. Extensive experiments focusing on a wide range of European drought events from 2011 to 2018 consistently show that our hybrid model surpasses both drought indices and data-driven models in terms of accuracy in drought detection, underlining its effectiveness, robustness, and stability. Our model achieves the best ROC-AUC (%) results in Afghanistan (79.7 ± 0.5), Italy (84.3 ± 0.6), Russia (89.4 ± 0.2), Europe-0 (84.3 ± 0.1), and Europe-1 (82.8 ± 0.4), effectively capturing the starting and ending times of drought events with lower uncertainty, and also generalizing better for unseen locations. • We propose DK-VRN, a novel hybrid framework for drought monitoring. • DK-VRN takes ECVs as input and integrates multi-scalar SPEI as domain knowledge prior. • DK-VRN is end-to-end supervised by historical drought events. • DK-VRN can detect droughts over diverse timeframes and across continental scales. • Experiments on European events from 2011 to 2018 show the effectiveness of DK-VRN. [ABSTRACT FROM AUTHOR]

Remote sensing observations, products and simulations are fundamental sources of information to monitor our planet. Uncovering the main modes of spatial and temporal variability in Earth data is essential to analyze and understand the underlying physical dynamics and processes driving the Earth System. Dimensionality reduction methods can work with spatio-temporal datasets and decompose the information efficiently. Principal Component Analysis (PCA), also known as Empirical Orthogonal Functions (EOF) in geophysics, has been traditionally used to analyze climatic data. However, when nonlinear feature relations are present, PCA/EOF fails. We propose a nonlinear PCA method to deal with spatio-temporal Earth data. The proposed method, called Rotated Complex Kernel PCA (ROCK-PCA for short), works in reproducing kernel Hilbert spaces to account for nonlinear processes, operates in the complex kernel domain to account for both space and time features, and adds an extra rotation for improved flexibility. The result is a spatially-explicit and temporally-resolved decomposition of the Earth data cube. The method is unsupervised and computationally very efficient. We illustrate its ability to uncover spatio-temporal patterns using synthetic experiments and real data. Results of the decomposition of three essential climate variables are shown: satellite-based global Gross Primary Productivity (GPP) and Soil Moisture (SM), and reanalysis Sea Surface Temperature (SST) data. The ROCK-PCA method allows identifying their annual and seasonal oscillations, as well as their non-seasonal trends and spatial variability patterns. The main modes of GPP and SM match expected distributions of land-cover and eco-hydrological zones, respectively; the inter-annual component of SM is shown to be highly correlated with El Niño Southern Oscillation (ENSO) phenomenon; and the SST annual oscillation is perfectly uncoupled in magnitude and phase from the global warming trend and ENSO anomalies, as well as from their mutual interactions. [ABSTRACT FROM AUTHOR]

All ocean basins have been experiencing significant warming and rising sea levels in recent decades. There are, however, important regional differences, resulting from distinct processes at different timescales (temperature-driven changes being a major contributor on multi-year timescales). In view of this complexity, it deems essential to move towards more sophisticated data-driven techniques as well as diagnostic and prognostic prediction models to interpret observations of ocean warming and sea level variations at local or regional sea basins. In this context, we present a machine learning approach that exploits key ocean temperature estimates (as proxies for the regional thermosteric sea level component) to model coastal sea level variability and associated uncertainty across a range of timescales (from months to several years). Our findings also demonstrate the utility of machine learning to estimate the possible tendency of near-future regional sea levels. When compared to actual sea-level records, our models perform particularly well in the coastal areas most influenced by internal climate variability. Yet, the models are widely applicable to evaluate the patterns of rising and falling sea levels across many places around the globe. Thus, our approach is a promising tool to model and anticipate sea level changes in the coming (1–3) years, which is crucial for near-term decision making and strategic planning about coastal protection measures. [ABSTRACT FROM AUTHOR]

As deep learning (DL) gains popularity for its ability to make accurate predictions in various fields, its applications in geosciences are also on the rise. Many studies focus on achieving high accuracy in DL models by selecting models, developing more complex architectures, and tuning hyperparameters. However, the interpretability of these models, or the ability to understand how they make their predictions, is less frequently discussed. To address the challenge of high accuracy but low interpretability of DL models in geosciences, we study rock classification from thin-section photomicrographs of six types of sedimentary rocks, including quartz arenite, feldspathic arenite, lithic arenite, siltstone, oolitic packstone, and dolomite. These rocks' characteristic framework grains and grain textures are their distinguishing features, such as the rounded or oval ooids in oolitic packstone. We first train regular DL models, such as ResNet-50, on these photomicrographs and achieve an accuracy of over 0.94. However, these models make classifications based on features like cracks, cements, and scale bars, which are irrelevant for distinguishing sedimentary rocks in real-world applications. We then propose an attention-based dual network incorporating both global (overall photomicrograph) and local (distinguishing framework grains) features to address this issue. Our proposed model achieves not only high accuracy (0.99) but also provides interpretable feature extractions. Our study highlights the need to consider interpretability and geological knowledge in developing DL models, in addition to aiming for high accuracy. [Display omitted] • Proposed dual network achieves high accuracy (0.99) and interpretable feature extractions for sedimentary rock classification. • Regular DL models achieved high accuracy (>0.94), but relied on irrelevant features for classification. • This study emphasizes importance of interpretability and geological knowledge in developing DL models for geosciences. [ABSTRACT FROM AUTHOR]

Remote sensing observations, products, and simulations are fundamental sources of information to monitor our planet and its climate variability. Uncovering the main modes of spatial and temporal variability in Earth data is essential to analyze and understand the underlying physical dynamics and processes driving the Earth System. Dimensionality reduction methods can work with spatio-temporal data sets and decompose the information efficiently. Principal component analysis (PCA), also known as empirical orthogonal functions (EOFs) in geophysics, has been traditionally used to analyze climatic data. However, when nonlinear feature relations are present, PCA/EOF fails. In this article, we propose a nonlinear PCA method to deal with spatio-temporal Earth system data. The proposed method, called rotated complex kernel PCA (ROCK-PCA for short), works in reproducing kernel Hilbert spaces to account for nonlinear processes, operates in the complex kernel domain to account for both space and time features, and adds an extra rotation for improved flexibility. The result is an explicitly resolved spatio-temporal decomposition of the Earth data cube. The method is unsupervised and computationally very efficient. We illustrate its ability to uncover spatio-temporal patterns using synthetic experiments and real data. Results of the decomposition of three essential climate variables are shown: satellite-based global gross primary productivity (GPP), soil moisture (SM), and reanalysis sea surface temperature (SST) data. The ROCK-PCA method allows identifying their annual and seasonal oscillations, as well as their nonseasonal trends and spatial variability patterns. The main modes of variability of GPP and SM match expected distributions of land-cover and eco-hydrological zones, respectively; the interannual component of SM is shown to be highly correlated with El Niño Southern Oscillation (ENSO) phenomenon; and the SST annual oscillation is perfectly uncoupled in magnitude and phase from the global warming trend and ENSO anomalies, as well as from their mutual interactions. We provide the working source code of the presented method for the interested reader in https://github.com/DiegoBueso/ROCK-PCA. [ABSTRACT FROM AUTHOR]

The World Bank routinely publishes over 1500 "World Development Indicators" to track the socioeconomic development at the country level. A range of indices has been proposed to interpret this information. For instance, the "Human Development Index" was designed to specifically capture development in terms of life expectancy, education, and standard of living. However, the general question which independent dimensions are essential to capture all aspects of development still remains open. Using a nonlinear dimensionality reduction approach we aim to extract the core dimensions of development in a highly efficient way. We find that more than 90% of variance in the WDIs can be represented by solely five uncorrelated dimensions. The first dimension, explaining 74% of variance, represents the state of education, health, income, infrastructure, trade, population, and pollution. Although this dimension resembles the HDI, it explains much more variance. The second dimension (explaining 10% of variance) differentiates countries by gender ratios, labor market, and energy production patterns. Here, we differentiate societal structures when comparing e.g. countries from the Middle-East to the Post-Soviet area. Our analysis confirms that most countries show rather consistent temporal trends towards wealthier and aging societies. We can also find deviations from the long-term trajectories during warfare, environmental disasters, or fundamental political changes. The data-driven nature of the extracted dimensions complements classical indicator approaches, allowing a broader exploration of global development space. The extracted independent dimensions represent different aspects of development that need to be considered when proposing new metric indices. [ABSTRACT FROM AUTHOR]

Global estimation of Gross Primary Production (GPP) - the uptake of atmospheric carbon dioxide by plants through photosynthesis - is commonly based on optical satellite remote sensing data. This presents a source-driven approach since it uses the amount of absorbed light, the main driver of photosynthesis, as a proxy for GPP. Vegetation Optical Depth (VOD) estimates obtained from microwave sensors provide an alternative and independent data source to estimate GPP on a global scale, which may complement existing GPP products. Recent studies have shown that VOD is related to aboveground biomass, and that both VOD and temporal changes in VOD relate to GPP. In this study, we build upon this concept and propose a model for estimating GPP from VOD. Since the model is driven by vegetation biomass, as observed through VOD, it presents a carbon sink-driven approach to quantify GPP and, therefore, is conceptually different from common source-driven approaches. The model developed in this study uses single frequencies from active or passive microwave VOD retrievals from C-, X- and Ku-band (Advanced Scatterometer (ASCAT) and Advanced Microwave Scanning Radiometer for Earth Observation (AMSR-E)) to estimate GPP at the global scale. We assessed the ability for temporal and spatial extrapolation of the model using global GPP from FLUXCOM and in situ GPP from FLUXNET. We further performed upscaling of in situ GPP based on different VOD data sets and compared these estimates with the FLUXCOM and MODerate-resolution Imaging Spectroradiometer (MODIS) GPP products. Our results show that the model developed for individual grid cells using VOD and change in VOD as input performs well in predicting temporal patterns in GPP for all VOD data sets. For spatial extrapolation of the model, however, additional input variables are needed to represent the spatial variability of the VOD-GPP relationship due to differences in vegetation type. As additional input variable, we included the grid cell median VOD (as a proxy for vegetation cover), which increased the model performance during cross validation. Mean annual GPP obtained for AMSR-E X-band data tends to overestimate mean annual GPP for FLUXCOM and MODIS but shows comparable latitudinal patterns. Overall, our findings demonstrate the potential of VOD for estimating GPP. The sink-driven approach provides additional information about GPP independent of optical data, which may contribute to our knowledge about the carbon source-sink balance in different ecosystems. • Estimating Gross Primary Production (GPP) based on Vegetation Optical Depth (VOD) • Relationship between VOD and GPP can be described through a differential equation. • Further, we use Generalized Additive Models for estimating GPP from VOD. [ABSTRACT FROM AUTHOR]

Highlights • Kernel signal-to-noise ratio presented for some of the most relevant tasks in machine learning. • kSNR seeks to maximize the signal variance while minimizing the estimated noise variance explicitly in a rkHs. • kSNR provides a regularizer that successfully deals with non-linear signal-to-noise relations. • Noise estimation is evaluated for both implicit and explicit formulations. • Theoretical properties are analyzed to reduce the computational cost and to ensure the stability. Abstract This paper introduces the kernel signal-to-noise ratio (kSNR) for different machine learning and signal processing applications. The kSNR seeks to maximize the signal variance while minimizing the estimated noise variance explicitly in a reproducing kernel Hilbert space (rkHs). The kSNR gives rise to considering complex signal-to-noise relations beyond additive noise models, and can be seen as a useful regularizer for feature extraction and dimensionality reduction. We show that the kSNR generalizes kernel PCA (and other spectral dimensionality reduction methods), least squares SVM, and kernel ridge regression to deal with cases where signal and noise cannot be assumed independent. We give computationally efficient alternatives based on reduced-rank Nyström and projection on random Fourier features approximations, and analyze the bounds of performance and its stability. We illustrate the method through different examples, including nonlinear regression, nonlinear classification in channel equalization, nonlinear feature extraction from high-dimensional spectral satellite images, and bivariate causal inference. Experimental results show that the proposed kSNR yields more accurate solutions and extracts more noise-free features when compared to standard approaches. [ABSTRACT FROM AUTHOR]

Solving inverse problems is central in geosciences and remote sensing. The radiative transfer models (RTMs) represent mathematically the physical laws that rule the phenomena in remote sensing applications (forward models). The numerical inversion of the RTM equations is a challenging and computationally demanding problem. For this reason, often the application of a simpler statistical regression is preferred. In general, the regression models predict the biophysical parameter of interest from the corresponding received radiance, learning a mapping from in situ data. However, this approach does not employ the physical information encoded in the RTMs. An alternative strategy, which attempts to include the physical knowledge, consists in learning a regression model trained using simulated data by an RTM code. In this paper, we introduce a nonlinear nonparametric regression model that combines the benefits of the two aforementioned approaches. The inversion is performed considering jointly both real observations and RTMsimulated data. The proposed joint Gaussian process (JGP) provides a solid framework for exploiting the regularities between the two types of data, in order to perform inverse modeling. The JGP automatically detects the relative quality of the simulated and real data, and combines them properly. This occurs by learning an additional hyperparameter with respect to a standard Gaussian process model, so that the novel scheme is at the same time simple and robust, i.e., capable of adapting to different scenarios. The advantages of the JGP method compared with benchmark strategies are shown considering synthetic and real data in different experiments. Specifically, we consider leaf area index retrieval from Landsat data combined with simulated data generated by the PROSAIL model. [ABSTRACT FROM AUTHOR]

Environmental change is a consequence of many interrelated factors. How vegetation responds to natural and human activity still needs to be well established, quantified and understood. Recent satellite missions providing hydrologic and ecological indicators enable better monitoring of Earth system changes, yet there is no automatic way to address this issue directly from observations. Here, we develop an observation-based methodology to capture evidence of changes in global terrestrial ecosystems and attribute these changes to natural or anthropogenic activity. We use the longest time record of global microwave L-band soil moisture and vegetation optical depth as satellite data and build spatially explicit maps of change in soil and vegetation water content and biomass reflecting large ecosystem changes during the last decade, 2010–20. Regions of prominent trends (from $-8\%$ to 9% per year) are observed, especially in humid and semi-arid climates. We further combine such trends with land cover change maps, vegetation greenness and precipitation variability to assess their relationship with major documented ecosystem changes. Several regions emerge from our results. They cluster changes according to human activity drivers, including deforestation (Amazon, Central Africa) and wildfires (East Australia), artificial reforestation (South-East China), abandonment of farm fields (Central Russia) and climate shifts related to changes in precipitation variability (East Africa, North America and Central Argentina). Using the high sensitivity of soil and vegetation water content to ecosystem changes, microwave satellite observations enable us to quantify and attribute global vegetation responses to climate or anthropogenic activities as a direct measure of environmental changes and the mechanisms driving them. This work identifies and quantifies the main large ecosystem changes during 2010-2020. Regions with prominent joint SM and VOD trends stand out, and can be semantically attributed to climate or anthropogenic activities, from reforestation and deforestation to irrigation changes and wildfires. [ABSTRACT FROM AUTHOR]

This paper presents and evaluates multitemporal LAI estimates derived from Sentinel-2A data on rice cultivated area identified using time series of Sentinel-1A images over the main European rice districts for the 2016 crop season. This study combines the information conveyed by Sentinel-1A and Sentinel-2A into a high-resolution LAI retrieval chain. Rice crop was detected using an operational multi-temporal rule-based algorithm, and LAI estimates were obtained by inverting the PROSAIL radiative transfer model with Gaussian process regression. Direct validation was performed with in situ LAI measurements acquired in coordinated field campaigns in three countries (Italy, Spain and Greece). Results showed high consistency between estimates and ground measurements, revealing high correlations (R2 > 0.93) and good accuracies (RMSE < 0.83, rRMSEm < 23.6% and rRMSEr < 16.6%) in all cases. Sentinel-2A estimates were compared with Landsat-8 showing high spatial consistency between estimates over the three areas. The possibility to exploit seasonally-updated crop mask exploiting Sentinel-1A data and the temporal consistency between Sentinel-2A and Landsat-7/8 LAI time series demonstrates the feasibility of deriving operationally high spatial-temporal decametric multi-sensor LAI time series useful for crop monitoring. [ABSTRACT FROM AUTHOR]

This paper presents an operational chain for high-resolution leaf area index (LAI) retrieval from multiresolution satellite data specifically developed for Mediterranean rice areas. The proposed methodology is based on the inversion of the PROSAIL radiative transfer model through the state-of-the-art nonlinear Gaussian process regression (GPR) method. Landsat and SPOT5 data were used for multitemporal LAI retrievals at high-resolution. LAI estimates were validated using time series of in situ LAI measurements collected during the rice season in Spain and Italy. Ground LAI data were collected with smartphones using PocketLAI, a specific phone application for LAI estimation. Temporal evolution of the LAI estimates using Landsat and SPOT5 data followed consistently the temporal evolution of the in situ LAI measurements acquired on several Mediterranean rice varieties. The estimates had a root-mean-square-error (RMSE) of 0.39 and 0.51 m 2 /m 2 in Spain and 0.38 and 0.47 m 2 /m 2 in Italy for Landsat and SPOT5 respectively, with a strong correlation (R 2 > 0.92) for both cases. Spatial-temporal assessment of the estimated LAI from Landsat and SPOT5 data confirmed the robustness and consistency of the retrieval chain. This paper demonstrates the importance of an adequate characterization of the underlying rice background in order to address changes in background condition related to water management. Results highlight the potential of the proposed chain for deriving multitemporal near real-time decametric LAI maps fundamental for operational rice crop monitoring, and demonstrate the readiness of the proposed method for the processing of data such as the recently launched Sentinel-2. [ABSTRACT FROM AUTHOR]

Remote sensing image classification exploiting multiple sensors is a very challenging problem: data from different modalities are affected by spectral distortions and mis-alignments of all kinds, and this hampers re-using models built for one image to be used successfully in other scenes. In order to adapt and transfer models across image acquisitions, one must be able to cope with datasets that are not co-registered, acquired under different illumination and atmospheric conditions, by different sensors, and with scarce ground references. Traditionally, methods based on histogram matching have been used. However, they fail when densities have very different shapes or when there is no corresponding band to be matched between the images. An alternative builds upon manifold alignment . Manifold alignment performs a multidimensional relative normalization of the data prior to product generation that can cope with data of different dimensionality (e.g. different number of bands) and possibly unpaired examples. Aligning data distributions is an appealing strategy, since it allows to provide data spaces that are more similar to each other, regardless of the subsequent use of the transformed data. In this paper, we study a methodology that aligns data from different domains in a nonlinear way through kernelization . We introduce the Kernel Manifold Alignment (KEMA) method, which provides a flexible and discriminative projection map, exploits only a few labeled samples (or semantic ties) in each domain, and reduces to solving a generalized eigenvalue problem. We successfully test KEMA in multi-temporal and multi-source very high resolution classification tasks, as well as on the task of making a model invariant to shadowing for hyperspectral imaging. [ABSTRACT FROM AUTHOR]

Land use (LU) monitoring and mapping from remote sensing (RS) data are relevant topics in Earth observation (EO). LU monitoring requires powerful/robust classification approaches able to provide reliable identifications in decision-making applications, even over challenging areas. The European Common Agricultural Policy (CAP) promotes the use of remote sensing for LU monitoring in Europe useful in the compliance control of the subsidy payments. In this context, the present study proposes a novel classification chain to identify ten land uses, namely: forest (FOR), pasture with trees (TRE), pasture with shrubs (SHR), pastureland (PAS), vineyard (VIN), arable land (ARL), fruit trees (FRU), nut trees (NUT), citrus (CIT), and olive grove (OLI), over three areas in the Valencian Autonomous Region (Spain) where smallholding farming predominates. The approach exploits the multitemporal information provided by Sentinel-2 data using a novel spatial strategy specifically designed to deal with heterogeneous agricultural areas. More precisely, we implemented a deep learning algorithm based on bidirectional recurrent neural networks to account for complex temporal dynamics. The classification results over the three areas showed accuracies higher than 95.5% over validation sets composed of in-situ checks never used during the training process. The proposed methodology outperformed standard approaches that not consider the spatial variability of the training samples, and revealed very good agreement concerning the Land Parcel Identification System (LPIS) of Spain. In addition, the developed chain proposes the novelty of using the kernel normalized difference vegetation index (kNDVI) as a predictor in a LU classification processing chain. Including the kNDVI instead of the traditional NDVI outperformed the classification accuracy in all metrics and classes. Ultimately, the obtained classifications were used for assessing the 2020 farmers' declarations in the three study areas. The declarations showed a level of agreement concerning the proposed approach near 99%. [ABSTRACT FROM AUTHOR]

Vegetation indices computed from spectral signatures are vastly used for monitoring the terrestrial biosphere. Indices are convenient proxies for canopy structure, and leaf pigment content, and consequently to estimate the photosynthetic activity of vegetation. Owing to its simplicity, the celebrated Normalized Difference Vegetation Index (NDVI) has been used as a proxy for greenness and canopy structure. Unfortunately, NDVI can only capture linear relationships of the near infrared (NIR) - red difference with the parameter of interest. To account for higher-order relations between the spectral channels, kernel NDVI (kNDVI) was proposed in (Camps-Valls et al., 2021). In this work, we give useful prescriptions for its proper use and show its good performance in a wider set of applications. We discuss the good characteristics of the index like boundedness, low error propagation. Furthermore, we give empirical evidence of performance in estimating in-situ vegetation parameters (leaf area index (LAI), gross primary productivity (GPP), leaf, and canopy chlorophyll content, green and total LAI and fraction of absorbed photosynthetically active radiation (fAPAR)) as well as the estimation of latent heat at flux tower level. We confirm the generally good performance of the index (correlation coefficient of kNDVI and canopy chlorophyll content is 0.919 and 0.933 for maize over two sites, as well as the correlation coefficient between kNDVI and carotenoid, is 0.816, 0.520 and 0.579 for three forest sites) and highlight its convenience in monitoring terrestrial ecosystems. To foster wider adoption of the new family of the index, we provide source code in 6 programming languages as well as efficient implementations in the Google Earth Engine (GEE) platform at https://github.com/IPL-UV/kNDVI. • The nonlinear kNDVI generalizes standard vegetation indices. • kNDVI propagates lower uncertainty and addresses saturation issues. • Prescriptions for the correct use of the index are given. • kNDVI yields improved performance to estimate in-situ vegetation parameters. • kNDVI improves estimation of latent heat at flux tower level. [ABSTRACT FROM AUTHOR]

• A general framework of empirical risk minimization with fairness regularizers and an analysis of its risk and fairness statistical consistency results are presented. • A Gaussian Process (GP) formulation of the fairness regularization framework is derived, which allows uncertainty quantification and principled hyperparameter selection. • A normalized version of the fairness regularizer which makes it less sensitive to the choice of kernel parameters is derived. Current adoption of machine learning in industrial, societal and economical activities has raised concerns about the fairness, equity and ethics of automated decisions. Predictive models are often developed using biased datasets and thus retain or even exacerbate biases in their decisions and recommendations. Removing the sensitive covariates, such as gender or race, is insufficient to remedy this issue since the biases may be retained due to other related covariates. We present a regularization approach to this problem that trades off predictive accuracy of the learned models (with respect to biased labels) for the fairness in terms of statistical parity, i.e. independence of the decisions from the sensitive covariates. In particular, we consider a general framework of regularized empirical risk minimization over reproducing kernel Hilbert spaces and impose an additional regularizer of dependence between predictors and sensitive covariates using kernel-based measures of dependence, namely the Hilbert-Schmidt Independence Criterion (HSIC) and its normalized version. This approach leads to a closed-form solution in the case of squared loss, i.e. ridge regression. We also provide statistical consistency results for both risk and fairness bound for our approach. Moreover, we show that the dependence regularizer has an interpretation as modifying the corresponding Gaussian process (GP) prior. As a consequence, a GP model with a prior that encourages fairness to sensitive variables can be derived, allowing principled hyperparameter selection and studying of the relative relevance of covariates under fairness constraints. Experimental results in synthetic examples and in real problems of income and crime prediction illustrate the potential of the approach to improve fairness of automated decisions. [ABSTRACT FROM AUTHOR]

This paper introduces the use of single-layer and deep convolutional networks for remote sensing data analysis. Direct application to multi- and hyperspectral imagery of supervised (shallow or deep) convolutional networks is very challenging given the high input data dimensionality and the relatively small amount of available labeled data. Therefore, we propose the use of greedy layerwise unsupervised pretraining coupled with a highly efficient algorithm for unsupervised learning of sparse features. The algorithm is rooted on sparse representations and enforces both population and lifetime sparsity of the extracted features, simultaneously. We successfully illustrate the expressive power of the extracted representations in several scenarios: classification of aerial scenes, as well as land-use classification in very high resolution or land-cover classification from multi- and hyperspectral images. The proposed algorithm clearly outperforms standard principal component analysis (PCA) and its kernel counterpart (kPCA), as well as current state-of-the-art algorithms of aerial classification, while being extremely computationally efficient at learning representations of data. Results show that single-layer convolutional networks can extract powerful discriminative features only when the receptive field accounts for neighboring pixels and are preferred when the classification requires high resolution and detailed results. However, deep architectures significantly outperform single-layer variants, capturing increasing levels of abstraction and complexity throughout the feature hierarchy. [ABSTRACT FROM PUBLISHER]

The accurate quantification of carbon fluxes at continental spatial scale is important for future policy decisions in the context of global climate change. However, many elements contribute to the uncertainty of such estimate. In this study, the uncertainties of eight days gross primary production (GPP) predicted by Random Forest (RF) machine learning models were analysed at the site, ecosystem and European spatial scales. At the site level, the uncertainties caused by the missing of key drivers were evaluated. The most accurate predictions of eight days GPP were obtained when all available drivers were used (Pearson's correlation coefficient, ρ ~ 0.84; Root Mean Square Error (RMSE) ~ 1.8 g C m −2 d −1 ). However, when predictions were based on only remotely sensed data the accuracy was close to the optimum (ρ ~ 0.8; RMSE ~ 1.9 g C m −2 d −1 ) and to a commonly used light use efficiency model (MOD17) with parameters optimised for the applied study sites (the MOD17 +, ρ ~ 0.79; RMSE ~ 2.04 g C m −2 d −1 ). Remotely sensed data were key drivers for the accurate prediction of GPP in ecosystems with high variability of green biomass over the phenological cycle (e.g., deciduous broad-leaved forests) or highly affected by the human management (e.g. croplands). In contrast, in the ecosystems with low variability of greenness (e.g., evergreen broad-leaved forests), the predictions were poor when meteorological information were not used. At a European spatial scale, when modelled grids of meteorological, land cover and fPAR data were used as inputs, the propagation of their uncertainty, not accounted in the models training, had significant effects on the uncertainty of the mean annual GPP. At this scale, the effects of meteorological uncertainty were higher than the misclassification error. These findings suggested that a strategy based on satellite-measured data could be a favourable improvement for the spatial upscaling of GPP, because avoiding the propagation of the uncertainties of the modelled grids. [ABSTRACT FROM AUTHOR]

Climate change exacerbates the occurrence of extreme droughts and heatwaves, increasing the frequency and intensity of large wildfires across the globe. Forecasting wildfire danger and uncovering the drivers behind fire events become central for understanding relevant climate‐land surface feedback and aiding wildfire management. In this work, we leverage Deep Learning (DL) to predict the next day's wildfire danger in a fire‐prone part of the Eastern Mediterranean and explainable Artificial Intelligence (xAI) to diagnose model attributions. We implement DL models that capture the temporal and spatio‐temporal context, generalize well for extreme wildfires, and demonstrate improved performance over the traditional Fire Weather Index. Leveraging xAI, we identify the substantial contribution of wetness‐related variables and unveil the temporal focus of the models. The variability of the contribution of the input variables across wildfire events hints into different wildfire mechanisms. The presented methodology paves the way to more robust, accurate, and trustworthy data‐driven anticipation of wildfires. Plain Language Summary: Climate change drives the aggravation of wildfires globally. In this context, it is crucial to better predict and understand wildfires. Our work proposes methods to accurately forecast wildfire danger and hints into the mechanisms that drive it. We use Machine Learning (ML) to predict next‐day wildfire danger, using meteorological, vegetation, and human‐related data, improving the results of the widely used Fire Weather Index, which is based only on meteorological forecasts. We then look to understand what the models have learned and how the different conditioning factors contribute to the final prediction. We find that ML models focus more on soil moisture and relative humidity for their predictions. They also take into account the cumulative temperature and precipitation, as well as the last day's wind speed and the relative humidity in the 2 days preceding fire ignition. These associations lead to new, data‐driven ways to anticipate wildfires. Key Points: When forecasting fires that lead to large burned areas, Deep Learning models indicate higher predictive skill than the Fire Weather IndexSoil moisture, Normalized Difference Vegetation Index, and weather are the most important predictors; changes in their importance across events reveal diverse wildfire typesModels' explainability uncovers physically‐consistent associations and temporal dynamics of the fire drivers [ABSTRACT FROM AUTHOR]

Land, atmosphere and climate interact constantly and at different spatial and temporal scales. In this paper we rely on causal discovery methods to infer spatial patterns of causal relations between several key variables of the carbon and water cycles: gross primary productivity, latent heat energy flux for evaporation, surface air temperature, precipitation, soil moisture and radiation. We introduce a methodology based on the convergent cross-mapping (CCM) technique. Despite its good performance in general, CCM is sensitive to (even moderate) noise levels and hyper-parameter selection. We present a robust CCM (RCCM) that relies on temporal bootstrapping decision scores and the derivation of more stringent cross-map skill scores. The RCCM method is combined with the information-geometric causal inference (IGCI) method to address the problem of strong and instantaneous variable coupling, another important and long-standing issue of CCM. The proposed methodology allows to derive spatially explicit global maps of causal relations between the involved variables and retrieve the underlying complexity of the interactions. Results are generally consistent with reported patterns and process understanding, and constitute a new way to quantify and understand carbon and water fluxes interactions. [ABSTRACT FROM AUTHOR]

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 MC 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. (Corresponding author: Luca Martino.) [ABSTRACT FROM AUTHOR]

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

• Introduction of methodology for active multi-output Gaussian process emulators. • Gaussian processes allow the construction of accurate, compact and interpretable emulators. • Adaptive sequential construction of both the emulator and look-up-table. • New acquisition function combines function geometry and predictive uncertainty. • Application to complex codes used on remote sensing leads to considerable computational savings. Many fields of science and engineering rely on running simulations with complex and computationally expensive models to understand the involved processes in the system of interest. Nevertheless, the high cost involved hamper reliable and exhaustive simulations. Very often such codes incorporate heuristics that ironically make them less tractable and transparent. This paper introduces an active learning methodology for adaptively constructing surrogate models, i.e. emulators , of such costly computer codes in a multi-output setting. The proposed technique is sequential and adaptive, and is based on the optimization of a suitable acquisition function. It aims to achieve accurate approximations, model tractability, as well as compact and expressive simulated datasets. In order to achieve this, the proposed Active Multi-Output Gaussian Process Emulator (AMOGAPE) combines the predictive capacity of Gaussian Processes (GPs) with the design of an acquisition function that favors sampling in low density and fluctuating regions of the approximation functions. Comparing different acquisition functions, we illustrate the promising performance of the method for the construction of emulators with toy examples, as well as for a widely used remote sensing transfer code. [ABSTRACT FROM AUTHOR]

Retrieval of vegetation properties from satellite and airborne optical data usually takes place after atmospheric correction, yet it is also possible to develop retrieval algorithms directly from top-of-atmosphere (TOA) radiance data. One of the key vegetation variables that can be retrieved from at-sensor TOA radiance data is leaf area index (LAI) if algorithms account for variability in atmosphere. We demonstrate the feasibility of LAI retrieval from Sentinel-2 (S2) TOA radiance data (L1C product) in a hybrid machine learning framework. To achieve this, the coupled leaf-canopy-atmosphere radiative transfer models PROSAIL-6SV were used to simulate a look-up table (LUT) of TOA radiance data and associated input variables. This LUT was then used to train the Bayesian machine learning algorithms Gaussian processes regression (GPR) and variational heteroscedastic GPR (VHGPR). PROSAIL simulations were also used to train GPR and VHGPR models for LAI retrieval from S2 images at bottom-of-atmosphere (BOA) level (L2A product) for comparison purposes. The BOA and TOA LAI products were consistently validated against a field dataset with GPR ( R 2 of 0.78) and with VHGPR ( R 2 of 0.80) and for both cases a slightly lower RMSE for the TOA LAI product (about 10% reduction). Because of delivering superior accuracies and lower uncertainties, the VHGPR models were further applied for LAI mapping using S2 acquisitions over the agricultural sites Marchfeld (Austria) and Barrax (Spain). The models led to consistent LAI maps at BOA and TOA scale. The LAI maps were also compared against LAI maps as generated by the SNAP toolbox, which is based on a neural network (NN). Maps were again consistent, however the SNAP NN model tends to overestimate over dense vegetation cover. Overall, this study demonstrated that hybrid LAI retrieval algorithms can be developed from TOA radiance data given a cloud-free sky, thus without the need of atmospheric correction. To the benefit of the community, the development of such hybrid models for the retrieval vegetation properties from BOA or TOA images has been streamlined in the freely downloadable ALG-ARTMO software framework. [ABSTRACT FROM AUTHOR]

The eddy covariance (EC) technique is used to measure the net ecosystem exchange (NEE) of CO2 between ecosystems and the atmosphere, offering a unique opportunity to study ecosystem responses to climate change. NEE is the difference between the total CO2 release due to all respiration processes (RECO), and the gross carbon uptake by photosynthesis (GPP). These two gross CO2 fluxes are derived from EC measurements by applying partitioning methods that rely on physiologically based functional relationships with a limited number of environmental drivers. However, the partitioning methods applied in the global FLUXNET network of EC observations do not account for the multiple co‐acting factors that modulate GPP and RECO flux dynamics. To overcome this limitation, we developed a hybrid data‐driven approach based on combined neural networks (NNC‐part). NNC‐part incorporates process knowledge by introducing a photosynthetic response based on the light‐use efficiency (LUE) concept, and uses a comprehensive dataset of soil and micrometeorological variables as fluxes drivers. We applied the method to 36 sites from the FLUXNET2015 dataset and found a high consistency in the results with those derived from other standard partitioning methods for both GPP (R2 >.94) and RECO (R2 >.8). High consistency was also found for (a) the diurnal and seasonal patterns of fluxes and (b) the ecosystem functional responses. NNC‐part performed more realistic than the traditional methods for predicting additional patterns of gross CO2 fluxes, such as: (a) the GPP response to VPD, (b) direct effects of air temperature on GPP dynamics, (c) hysteresis in the diel cycle of gross CO2 fluxes, (d) the sensitivity of LUE to the diffuse to direct radiation ratio, and (e) the post rain respiration pulse after a long dry period. In conclusion, NNC‐part is a valid data‐driven approach to provide GPP and RECO estimates and complementary to the existing partitioning methods. [ABSTRACT FROM AUTHOR]

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 very often a single (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 big remote sensing model inversion problems. [ABSTRACT FROM AUTHOR]

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, with RMSE of 0.19 kg m−2 and 0.078 kg m−2 respectively. Particularly, when the Normalized Difference Infrared Index (NDII) was included the algorithm was better constrained in semi-arid regions and saturation effects were mitigated in dense canopies. An analysis of spatial scale effects shows the mean bias error in CWC retrievals remains below 0.001 kg m−2 when spatial resolutions ranging from 20 m to 1 km are considered. 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 & Aqua. Results suggest that the LSA-SAF EPS/AVHRR algorithm is robust, agrees with the CWC dynamics observed in available ground data, and is also applicable to data from other sensors. We conclude that the EPS/AVHRR CWC product is a promising tool for monitoring vegetation water status at regional and global scales. [ABSTRACT FROM AUTHOR]

Understanding Earth system dynamics in light of ongoing human intervention and dependency remains a major scientific challenge. The unprecedented availability of data streams describing different facets of the Earth now offers fundamentally new avenues to address this quest. However, several practical hurdles, especially the lack of data interoperability, limit the joint potential of these data streams. Today, many initiatives within and beyond the Earth system sciences are exploring new approaches to overcome these hurdles and meet the growing interdisciplinary need for data-intensive research; using data cubes is one promising avenue. Here, we introduce the concept of Earth system data cubes and how to operate on them in a formal way. The idea is that treating multiple data dimensions, such as spatial, temporal, variable, frequency, and other grids alike, allows effective application of user-defined functions to co-interpret Earth observations and/or model–data integration. An implementation of this concept combines analysis-ready data cubes with a suitable analytic interface. In three case studies, we demonstrate how the concept and its implementation facilitate the execution of complex workflows for research across multiple variables, and spatial and temporal scales: (1) summary statistics for ecosystem and climate dynamics; (2) intrinsic dimensionality analysis on multiple timescales; and (3) model–data integration. We discuss the emerging perspectives for investigating global interacting and coupled phenomena in observed or simulated data. In particular, we see many emerging perspectives of this approach for interpreting large-scale model ensembles. The latest developments in machine learning, causal inference, and model–data integration can be seamlessly implemented in the proposed framework, supporting rapid progress in data-intensive research across disciplinary boundaries. [ABSTRACT FROM AUTHOR]

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 the 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 with a number of remotely sensed observations. This problem setting is known in statistics and machine learning as multiple instance learning (MIL) or distribution regression (DR). This article introduces a nonlinear (kernel-based) method for DR 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 for matchup 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. Real experiments involve the Soil Moisture Active Passive (SMAP) vegetation optical depth (VOD) data for the estimation of crop production in the U.S. Corn Belt and the Moderate Resolution Imaging Spectroradiometer (MODIS) and Multi-angle Imaging SpectroRadiometer (MISR) reflectances for the estimation of aerosol optical depth (AOD). An exhaustive empirical evaluation of the method is done against naive (linear and nonlinear) approaches based on input-space means as well as previously presented methods for MIL. We provide source code of our methods in http://isp.uv.es/code/dr.html. [ABSTRACT FROM AUTHOR]

Infrared atmospheric sounders, such as IASI, provide an unprecedented source of information for atmosphere monitoring and weather forecasting. Sensors provide rich spectral information that allows retrieval of temperature and moisture profiles. From a statistical point of view, the challenge is immense: on the one hand, "underdetermination" is common place as regression needs to work on high dimensional input and output spaces; on the other hand, redundancy is present in all dimensions (spatial, spectral and temporal). On top of this, several noise sources are encountered in the data. In this paper, we present for the first time the use of convolutional neural networks for the retrieval of atmospheric profiles from IASI sounding data. The first step of the proposed pipeline performs spectral dimensionality reduction taking into account the signal to noise characteristics. The second step encodes spatial and spectral information, and finally prediction of multidimensional profiles is done with deep convolutional networks. We give empirical evidence of the performance in a wide range of situations. Networks were trained on orbits of IASI radiances and tested out of sample with great accuracy over competing approximations, such as linear regression (+32%). We also observed an improvement in accuracy when predicting over clouds, thus increasing the yield by 34% over linear regression. The proposed scheme allows us to predict related variables from an already trained model, performing transfer learning in a very easy manner. We conclude that deep learning is an appropriate learning paradigm for statistical retrieval of atmospheric profiles. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Microwave satellite observations are increasingly being used for describing large-scale vegetation properties. Due to its all-weather capabilities, microwave vegetation optical depth (VOD) represents an alternative data source of vegetation information upon traditional optical-based retrievals. A recent study by Teubner et al. (2018, http://dx.doi.org/10.1016/j.jag.2017.10.006) has indicated that VOD can be linked to gross primary production (GPP) by a combination of the original VOD values and temporal changes therein. Building upon this concept, here we present a model for estimating GPP from microwave VOD. The model was applied at local to global scale using active (Advanced Scatterometer – ASCAT) and passive (Advanced Microwave Scanning Radiometer for Earth Observation – AMSR-E) microwave VOD observations from C-, X- and Ku-band. We assessed the model's ability to extrapolate temporally and spatially in situ measurements of GPP from FLUXNET, which we compared with GPP from FLUXCOM and the Moderate-resolution Imaging Spectroradiometer (MODIS). The model performs well at extrapolating GPP temporally based on VOD information, while it requires additional information related to vegetation type for performing accurate spatial extrapolation of in situ GPP observations. The VOD-based upscaling of GPP tends to overestimate mean annual GPP compared to FLUXCOM and MODIS but exhibits similar latitudinal patterns. Overall, our findings underpin the potential of VOD as an alternative to diagnose GPP globally from space. Since the approach provides additional information about GPP independent of optical data, our approach may create the basis for analysing ecosystem properties such as carbon allocation and may further contribute to improved GPP estimations especially in cloud-prone regions. [ABSTRACT FROM AUTHOR]

Agriculture monitoring and yield estimation are important for food security, both regionally and globally. Understanding the year-to-year variability in crop yield and its relationship to meteorological conditions is particularly important for several regions where yield is highly dependent on changing environmental factors. For example, wheat yields in India have been steadily increasing since the 1960s and 1970s due to benefits of the Green Revolution, but in recent years the wheat yield has been unstable as major crop yield losses were attributed to unfavorable meteorological conditions. Modeling the effects of various environmental variables can be challenging, as their impact on the final yield is complex and varies depending on their intensity and the crop growth stage at which they occur (e.g., moderate rainfall is beneficial for crops, but extensive and untimely rainfalls can lead to huge yield losses).In this work, we exploit interconnections between meteorological conditions and satellite data on vegetation during the whole growing season, and their simultaneous impact on wheat yield in the Wheat Belt in India. We use GLDAS 2.1 data as the meteorological input and MODIS data for the vegetation remote sensing input. Adding satellite information on crop is crucial for yield estimation, as it carries information on both crop phenology, as well as the crop response to the meteorological conditions. We apply machine learning algorithms (e.g., convolutional neural networks, CNNs) that can model non-linear processes and can extract important features in the multivariate time series automatically from data, without prior knowledge or human effort in feature design. By doing so, we do not force assumptions on which time is the most important for the final crop yield and we can include in the analysis the whole time series of multiple input variables at a high temporal resolution. Furthermore, we analyze the CNNs in terms of important features and crucial time windows for yield estimation, which shows that they the vary across space and time. By combining meteorological and satellite vegetation data with CNNs this work may help to disentangle the complex interactions between the features in the time series of the input data and the wheat yield. [ABSTRACT FROM AUTHOR]

In this paper, we analyze the effect of spatial and spectral compression on the performance of statistically based retrieval. Although the quality of the information is not completely preserved during the coding process, experiments reveal that a certain amount of compression may yield a positive impact on the accuracy of retrievals. We unveil two strategies, both with interesting benefits: either to apply a very high compression, which still maintains the same retrieval performance as that obtained for uncompressed data; or to apply a moderate to high compression, which improves the performance. As a second contribution of this paper, we focus on the origins of these benefits. On the one hand, we show that a certain amount of noise is removed during the compression stage, which benefits the retrievals performance. On the other hand, we analyze the effect of compression on spectral/spatial regularization (smoothing). We quantify the amount of information shared among the spatial neighbors for the different methods and compression ratios. We also propose a simple strategy to specifically exploit spectral and spatial relations and find that, when these relations are taken into account beforehand, the benefits of compression are reduced. These experiments suggest that compression can be understood as an indirect way to regularize the data and exploit spatial neighbors information, which improves the performance of pixelwise statistics-based retrieval algorithms. [ABSTRACT FROM AUTHOR]