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Food security is at stake, with climate change heavily impacting agriculture and food production. In the present context of extreme events and changing conditions, developing advanced crop yield models can learn from all available information, and providing interpretable predictions for decision-making is of paramount relevance. This work explores the potential and limitations of developing interpretable crop yield models using long short-term memory (LSTM) neural networks, which typically excel at extracting information from time series. LSTMs were designed and trained with multisource satellite and meteorological time series over Continental US (CONUS) and corn, soybean, and wheat yield data from the US Department of Agriculture. Two recent attribution methods are used to interpret and extract knowledge from the developed models: integrated gradients (IG), based on back-propagation, and Shapley (SHAP) values, based on perturbations. Our results show that: 1) LSTM models achieved high accuracy ($\text {R}^{2}>0.56$); 2) multisource combinations outperformed single-variable models in all crop models; 3) both attribution methods were equivalent in detecting essential drivers and their contribution; 4) satellite estimates of enhanced vegetation index (EVI) and vegetation optical depth (VOD) together with meteorological estimates of maximum temperature (TMX) were the most relevant input features for crop yield estimations; and finally and 5) we discovered critical periods of the crop growth cycle for the corn, soybean, and wheat models. The suggested strategy constitutes an important step toward modeling and understanding crop production systems and advancing in automatic data-driven and accountable field management. [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]

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]

Gaussian processes (GPs) are a class of Kernel methods that have shown to be very useful in geoscience and remote sensing applications for parameter retrieval, model inversion, and emulation. They are widely used because they are simple, flexible, and provide accurate estimates. GPs are based on a Bayesian statistical framework which provides a posterior probability function for each estimation. Therefore, besides the usual prediction (given in this case by the mean function), GPs come equipped with the possibility to obtain a predictive variance (i.e., error bars, confidence intervals) for each prediction. Unfortunately, the GP formulation usually assumes that there is no noise in the inputs, only in the observations. However, this is often not the case in earth observation problems where an accurate assessment of the measuring instrument error is typically available, and where there is huge interest in characterizing the error propagation through the processing pipeline. In this letter, we demonstrate how one can account for input noise estimates using a GP model formulation which propagates the error terms using the derivative of the predictive mean function. We analyze the resulting predictive variance term and show how they more accurately represent the model error in a temperature prediction problem from infrared sounding data. [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]

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]

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]

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]

Interannual variations in ecosystem primary productivity are dominated by water availability. Until recently, characterizing the photosynthetic response of different ecosystems to soil moisture anomalies was hampered by observational limitations. Here, we use a number of satellite‐based proxies for productivity, including spectral indices, sun‐induced chlorophyll fluorescence, and data‐driven estimates of gross primary production, to reevaluate the relationship between terrestrial photosynthesis and water. In contrast to nonwoody vegetation, we find a resilience of forested ecosystems to reduced soil moisture. Sun‐induced chlorophyll fluorescence and data‐driven gross primary production indicate an increase in photosynthesis as a result of the accompanying higher amounts of light and temperature despite lowered light‐use‐efficiency. Conversely, remote sensing indicators of greenness reach their detection limit and largely remain stable. Our study thus highlights the differential responses of ecosystems along a tree cover gradient and illustrates the importance of differentiating photosynthesis indicators from those of greenness for the monitoring and understanding of ecosystems. Plain Language Summary: The capacity of vegetation to thrive and to sequester carbon depends on how much water they can have access to. In this work, we evaluate how different types of satellite observations can describe the response of vegetation to changes in soil moisture over the entire planet. The first source of observation measures only the greenness of the land surface, the second measures light that is emitted by pigments in plants which are photosynthetically active (chlorophyll fluorescence), and the third are simulations of gross carbon uptake derived from machine learning techniques. For periods of water shortage all three indicate a reduction of growth in ecosystems with few trees. However, in cold boreal forests, when soil moisture is particularly low, we still detect an increase in photosynthesis due to higher light and temperature conditions, but this is not reflected in the greenness indicator. This work illustrates how lack of water is not necessarily harmful for catching carbon through photosynthesis, but to monitor this effect, we need remote sensing indicators that measure more than just how green the plants are, and fluorescence is likely a good candidate. Key Points: Satellite‐based plant greenness, chlorophyll fluorescence, and gross photosynthesis are evaluated with respect to soil moisture fluctuationsEcosystem responses to water availability change sign along a tree cover gradientWe show spaceborne observations of light‐ and temperature‐enhanced forest photosynthesis in times of reduced soil moisture at constant greenness [ABSTRACT FROM AUTHOR]

Physically based radiative transfer models (RTMs) are widely used in Earth observation to understand the radiation processes occurring on the Earth’s surface and their interactions with water, vegetation, and atmosphere. Through continuous improvements, RTMs have increased in accuracy and representativity of complex scenes at expenses of an increase in complexity and computation time, making them impractical in various remote sensing applications. To overcome this limitation, the common practice is to precompute large lookup tables (LUTs) for their later interpolation. To further reduce the RTM computation burden and the error in LUT interpolation, we have developed a method to automatically select the minimum and optimal set of input–output points (nodes) to be included in an LUT. We present the gradient-based automatic LUT generator algorithm (GALGA), which relies on the notion of an acquisition function that incorporates: 1) the Jacobian evaluation of an RTM and 2) the information about the multivariate distribution of the current nodes. We illustrate the capabilities of GALGA in the automatic construction and optimization of MODTRAN-based LUTs of different dimensions of the input variables space. Our results indicate that when compared with a pseudorandom homogeneous distribution of the LUT nodes, GALGA reduces: 1) the LUT size by >24%; 2) the computation time by ~27%; and 3) the maximum interpolation relative errors by at least 10%. It is concluded that an automatic LUT design might benefit from the methodology proposed in GALGA to reduce interpolation errors and computation time in computationally expensive RTMs. [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]

Computationally expensive radiative transfer models (RTMs) are widely used to realistically reproduce the light interaction with the earth surface and atmosphere. Because these models take long processing time, the common practice is to first generate a sparse look-up table (LUT) and then make use of interpolation methods to sample the multidimensional LUT input variable space. However, the question arise whether common interpolation methodsperform most accurate. As an alternative to interpolation, this paper proposes to use emulation, i.e., approximating the RTM output by means of the statistical learning. Two experiments were conducted to assess the accuracy in delivering spectral outputs using interpolation and emulation: at canopy level, using PROSAIL; and at top-of-atmosphere level, using MODTRAN. Various interpolation (nearest-neighbor, inverse distance weighting, and piece-wice linear) and emulation [Gaussian process regression (GPR), kernel ridge regression, and neural networks] methods were evaluated against a dense reference LUT. In all experiments, the emulation methods clearly produced more accurate output spectra than classical interpolation methods. The GPR emulation performed up to ten times more accurately than the best performing interpolation method, and this with a speed that is competitive with the faster interpolation methods. It is concluded that emulation can function as a fast and more accurate alternative to commonly used interpolation methods for reconstructing RTM spectral data. [ABSTRACT FROM AUTHOR]

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

Earth observation from satellite sensory data poses challenging problems, where machine learning is currently a key player. In recent years, Gaussian Process (GP) regression has excelled in biophysical parameter estimation tasks from airborne and satellite observations. GP regression is based on solid Bayesian statistics, and generally yields efficient and accurate parameter estimates. However, GPs are typically used for inverse modeling based on concurrent observations and in situ measurements only. Very often a forward model encoding the well-understood physical relations between the state vector and the radiance observations is available though and could be useful to improve predictions and understanding. In this work, we review three GP models that respect and learn the physics of the underlying processes in the context of both forward and inverse modeling . After reviewing the traditional application of GPs for parameter retrieval, we introduce a Joint GP (JGP) model that combines in situ measurements and simulated data in a single GP model. Then, we present a latent force model (LFM) for GP modeling that encodes ordinary differential equations to blend data-driven modeling and physical constraints of the system governing equations. The LFM performs multi-output regression, adapts to the signal characteristics, is able to cope with missing data in the time series, and provides explicit latent functions that allow system analysis and evaluation. Finally, we present an Automatic Gaussian Process Emulator (AGAPE) that approximates the forward physical model using concepts from Bayesian optimization and at the same time builds an optimally compact look-up-table for inversion. We give empirical evidence of the performance of these models through illustrative examples of vegetation monitoring and atmospheric modeling. [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]

Automatic land cover classification from satellite image time series is of paramount relevance to assess vegetation and crop status, with important implications in agriculture, biofuels, and food. However, due to the high cost and human resources needed to characterize and classify land cover through field campaigns, a recurrent limiting factor is the lack of available labeled data. On top of this, the biophysical–geophysical variables exhibit particular temporal structures that need to be exploited. Land cover classification based on image time series is very complex because of the data manifold distortions through time. We propose the use of the kernel manifold alignment (KEMA) method for domain adaptation of remote sensing time series before classification. KEMA is nonlinear and semisupervised and reduces to solve a simple generalized eigenproblem. We give empirical evidence of performance through classification of biophysical (leaf area index, fraction of absorbed photosynthetically active radiation, fractional vegetation cover, and normalized difference vegetation index) time series on a global scale. [ABSTRACT FROM PUBLISHER]

In this paper, we discuss the scientific outcomes of the 2015 data fusion contest organized by the Image Analysis and Data Fusion Technical Committee (IADF TC) of the IEEE Geoscience and Remote Sensing Society (IEEE GRSS). As for previous years, the IADF TC organized a data fusion contest aiming at fostering new ideas and solutions for multisource studies. The 2015 edition of the contest proposed a multiresolution and multisensorial challenge involving extremely high-resolution RGB images and a three-dimensional (3-D) LiDAR point cloud. The competition was framed in two parallel tracks, considering 2-D and 3-D products, respectively. In this paper, we discuss the scientific results obtained by the winners of the 2-D contest, which studied either the complementarity of RGB and LiDAR with deep neural networks (winning team) or provided a comprehensive benchmarking evaluation of new classification strategies for extremely high-resolution multimodal data (runner-up team). The data and the previously undisclosed ground truth will remain available for the community and can be obtained at http://www.grss-ieee.org/community/technical-committees/data-fusion/2015-ieee-grss-data-fusion-contest/. The 3-D part of the contest is discussed in the Part-B paper [1]. [ABSTRACT FROM PUBLISHER]

Physically-based radiative transfer models (RTMs) help understand the interactions of radiation with vegetation and atmosphere. However, advanced RTMs can be computationally burdensome, which makes them impractical in many real applications, especially when many state conditions and model couplings need to be studied. To overcome this problem, it is proposed to substitute RTMs through surrogate meta-models also named emulators. Emulators approximate the functioning of RTMs through statistical learning regression methods, and can open many new applications because of their computational efficiency and outstanding accuracy. Emulators allow fast global sensitivity analysis (GSA) studies on advanced, computationally expensive RTMs. As a proof-of-concept, three machine learning regression algorithms (MLRAs) were tested to function as emulators for the leaf RTM PROSPECT-4, the canopy RTM PROSAIL, and the computationally expensive atmospheric RTM MODTRAN5. Selected MLRAs were: kernel ridge regression (KRR), neural networks (NN) and Gaussian processes regression (GPR). For each RTM, 500 simulations were generated for training and validation. The majority of MLRAs were excellently validated to function as emulators with relative errors well below 0.2%. The emulators were then put into a GSA scheme and compared against GSA results as generated by original PROSPECT-4 and PROSAIL runs. NN and GPR emulators delivered identical GSA results, while processing speed compared to the original RTMs doubled for PROSPECT-4 and tripled for PROSAIL. Having the emulator-GSA concept successfully tested, for six MODTRAN5 atmospheric transfer functions (outputs), i.e., direct and diffuse at-surface solar irradiance (Edif, Edir), direct and diffuse upward transmittance (Tdir, Tdif), spherical albedo (S) and path radiance (LO), the most accurate MLRA's were subsequently applied as emulator into the GSA scheme. The sensitivity analysis along the 400-2500 nm spectral range took no more than a few minutes on a contemporary computer-in comparison, the same analysis in the original MODTRAN5 would have taken over a month. Key atmospheric drivers were identified, which are on the one hand aerosol optical properties, i.e., aerosol optical thickness (AOT), Angstrom coefficient (AMS) and scattering asymmetry variable (G), mostly driving diffuse atmospheric components, Edifand Tdif; and those affected by atmospheric scattering, LO and S. On the other hand, as expected, AOT, AMS and columnar water vapor (CWV) in the absorption regions mostly drive Edir and Tdir atmospheric functions. The presented emulation schemes showed very promising results in replacing costly RTMs, and we think they can contribute to the adoption of machine learning techniques in remote sensing and environmental applications. [ABSTRACT FROM AUTHOR]

Spatial-temporal fields of land-atmosphere fluxes derived from data-driven models can complement simulations by process-based Land Surface Models. While a number of strategies for empirical models with eddy covariance flux data have been applied, a systematic intercomparison of these methods has been missing so far. In this study, we perform a cross validation experiment for predicting carbon dioxide (CO2), latent heat, sensible heat and net radiation fluxes, in different ecosystem types with eleven machine learning (ML) methods from four different classes (kernel methods, neural network, tree methods, and regression splines). We employ two complementary setups: (1) eight days average fluxes based on remotely sensed data, and (2) daily mean fluxes based on meteorological data and mean seasonal cycle of remotely sensed variables. The pattern of predictions from different ML and setups were very consistent. There were systematic differences variables. The pattern of predictions from different ML and setups were very consistent. There were systematic differences respiration (R2>0.6), gross primary production (R2>0.7), latent heat (R2>0.7), sensible heat (R2>0.7), net radiation (R2>0.8). ML methods predicted very well the across sites variability and the seasonal cycle (R2> 0.7) of the observed fluxes, while the eight days deviations from the mean seasonal cycle were not well predicted (R2< 0.5). Fluxes were better predicted at forested and temperate climate sites than at ones growing in extreme climates or less representated in training data (e.g. the tropics). The large ensemble of ML based models evaluated will be the basis of new global flux products. [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]

Leaf area index (LAI) is a key biophysical parameter used to determine foliage cover and crop growth in environmental studies. Smartphones are nowadays ubiquitous sensor devices with high computational power, moderate cost, and high-quality sensors. A smartphone app, which is called PocketLAI, was recently presented and tested for acquiring ground LAI estimates. In this letter, we explore the use of state-of-the-art nonlinear Gaussian process regression (GPR) to derive spatially explicit LAI estimates over rice using ground data from PocketLAI and Landsat 8 imagery. GPR has gained popularity in recent years because of its solid Bayesian foundations that offer not only high accuracy but also confidence intervals for the retrievals. We show the first LAI maps obtained with ground data from a smartphone combined with advanced machine learning. This letter compares LAI predictions and confidence intervals of the retrievals obtained with PocketLAI with those obtained with classical instruments, such as digital hemispheric photography (DHP) and LI-COR LAI-2000. This letter shows that all three instruments obtained comparable results, but PocketLAI is far cheaper. The proposed methodology hence opens a wide range of possible applications at moderate cost. [ABSTRACT FROM PUBLISHER]

Earth observation through remote sensing images allows the accurate characterization and identification of materials on the surface from space and airborne platforms. Multiple and heterogeneous image sources can be available for the same geographical region: multispectral, hyperspectral, radar, multitemporal, and multiangular images can today be acquired over a given scene. These sources can be combined/fused to improve classification of the materials on the surface. Even if this type of systems is generally accurate, the field is about to face new challenges: the upcoming constellations of satellite sensors will acquire large amounts of images of different spatial, spectral, angular, and temporal resolutions. In this scenario, multimodal image fusion stands out as the appropriate framework to address these problems. In this paper, we provide a taxonomical view of the field and review the current methodologies for multimodal classification of remote sensing images. We also highlight the most recent advances, which exploit synergies with machine learning and signal processing: sparse methods, kernel-based fusion, Markov modeling, and manifold alignment. Then, we illustrate the different approaches in seven challenging remote sensing applications: 1) multiresolution fusion for multispectral image classification; 2) image downscaling as a form of multitemporal image fusion and multidimensional interpolation among sensors of different spatial, spectral, and temporal resolutions; 3) multiangular image classification; 4) multisensor image fusion exploiting physically-based feature extractions; 5) multitemporal image classification of land covers in incomplete, inconsistent, and vague image sources; 6) spatiospectral multisensor fusion of optical and radar images for change detection; and 7) cross-sensor adaptation of classifiers. The adoption of these techniques in operational settings will help to monitor our planet from space in the very near future. [ABSTRACT FROM PUBLISHER]

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 coregistered, corrected, and compensated for differences in the image domains. Such procedures require massive 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 (typically nonlinear) manifolds where images lie. 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. A MATLAB implementation of the proposed method is provided at http://isp. uv.es/code/ssma.htm. [ABSTRACT FROM PUBLISHER]

Solar irradiation prediction is an important problem in geosciences with direct applications in renewable energy. Recently, a high number of machine learning techniques have been introduced to tackle this problem, mostly based on neural networks and support vector machines. Gaussian process regression (GPR) is an alternative nonparametric method that provided excellent results in other biogeophysical parameter estimation. In this letter, we evaluate GPR for the estimation of solar irradiation. Noting the nonstationary temporal behavior of the signal, we develop a particular time-based composite covariance to account for the relevant seasonal signal variations. We use a unique meteorological data set acquired at a radiometric station that includes both measurements and radiosondes, as well as numerical weather prediction models. We show that the so-called temporal GPR outperforms ten state-of-the-art statistical regression algorithms (even when including time information) in terms of accuracy and bias, and it is more robust to the number of predictions used. [ABSTRACT FROM PUBLISHER]

The use of deep learning (DL) approaches for the analysis of remote sensing (RS) data is rapidly increasing. DL techniques have provided excellent results in applications ranging from parameter estimation to image classification and anomaly detection. Although the vast majority of studies report precision indicators, there is a lack of studies dealing with the interpretability of the predictions. This shortcoming hampers a wider adoption of DL approaches by a wider users community, as model's decisions are not accountable. In applications that involve the management of public budgets or policy compliance, a better interpretability of predictions is strictly required. This work aims to deepen the understanding of a recurrent neural network for land use classification based on Sentinel-2 time series in the context of the European Common Agricultural Policy (CAP). This permits to address the relevance of predictors in the classification process leading to an improved understanding of the behaviour of the network. The conducted analysis demonstrates that the red and near infrared Sentinel-2 bands convey the most useful information. With respect to the temporal information, the features derived from summer acquisitions were the most influential. These results contribute to the understanding of models used for decision making in the CAP to accomplish the European Green Deal (EGD) designed in order to counteract climate change, to protect biodiversity and ecosystems, and to ensure a fair economic return for farmers. [ABSTRACT FROM AUTHOR]

Although a key driver of Earth's climate system, global land-atmosphere energy fluxes are poorly constrained. Here we use machine learning to merge energy flux measurements from FLUXNET eddy covariance towers with remote sensing and meteorological data to estimate global gridded net radiation, latent and sensible heat and their uncertainties. The resulting FLUXCOM database comprises 147 products in two setups: (1) 0.0833° resolution using MODIS remote sensing data (RS) and (2) 0.5° resolution using remote sensing and meteorological data (RS + METEO). Within each setup we use a full factorial design across machine learning methods, forcing datasets and energy balance closure corrections. For RS and RS + METEO setups respectively, we estimate 2001–2013 global (±1 s.d.) net radiation as 75.49 ± 1.39 W m−2 and 77.52 ± 2.43 W m−2, sensible heat as 32.39 ± 4.17 W m−2 and 35.58 ± 4.75 W m−2, and latent heat flux as 39.14 ± 6.60 W m−2 and 39.49 ± 4.51 W m−2 (as evapotranspiration, 75.6 ± 9.8 × 103 km3 yr−1 and 76 ± 6.8 × 103 km3 yr−1). FLUXCOM products are suitable to quantify global land-atmosphere interactions and benchmark land surface model simulations. Design Type(s) modeling and simulation objective • factorial design Measurement Type(s) energy Technology Type(s) machine learning Factor Type(s) machine learning • Energy Balance • temporal_interval • geographic location Sample Characteristic(s) Earth (Planet) • land • vegetation layer • climate system Machine-accessible metadata file describing the reported data (ISA-Tab format) [ABSTRACT FROM AUTHOR]

The colored dissolved organic matter (CDOM) variable is the standard measure of humic substance in waters optics. CDOM is optically characterized by its spectral absorption coefficient, a C D O M at at reference wavelength (e.g., ≈ 440 nm). Retrieval of CDOM is traditionally done using bio-optical models. As an alternative, this paper presents a comparison of five machine learning methods applied to Sentinel-2 and Sentinel-3 simulated reflectance ( R r s ) data for the retrieval of CDOM: regularized linear regression (RLR), random forest regression (RFR), kernel ridge regression (KRR), Gaussian process regression (GPR) and support vector machines (SVR). Two different datasets of radiative transfer simulations are used for the development and training of the machine learning regression approaches. Statistics comparison with well-established polynomial regression algorithms shows optimistic results for all models and band combinations, highlighting the good performance of the methods, especially the GPR approach, when all bands are used as input. Application to an atmospheric corrected OLCI image using the reflectance derived form the alternative neural network (Case 2 Regional) is also shown. Python scripts and notebooks are provided to interested users. [ABSTRACT FROM AUTHOR]

Leaf area index (LAI) is a key biophysical variable fundamental in natural vegetation and agricultural land monitoring and modelling studies. This paper is aimed at comparing, validating and discussing different LAI satellite products from operational services and customized solution based on innovative Earth Observation (EO) data such as Landsat-7/8 and Sentinel-2A. The comparison was performed to assess overall quality of LAI estimates for rice, as a fundamental input of different scale (regional to local) operational crop monitoring systems such as the ones developed during the “An Earth obseRvation Model based RicE information Service” (ERMES) project. We adopted a multiscale approach following international recognized protocols of the Committee on Earth Observation Satellites (CEOS) Land Product Validation (LPV) guidelines in different steps: (1) acquisition of representative field sample measurements, (2) validation of decametric satellite product (10–30 m spatial resolution), and (3) exploitation of such data to assess quality of medium-resolution operational products (~1000 m). The study areas were located in the main European rice areas in Spain, Italy and Greece. Field campaigns were conducted during three entire rice seasons (2014, 2015 and 2016—from sowing to full-flowering) to acquire multi-temporal ground LAI measurements and to assess Landsat-7/8 LAI estimates. Results highlighted good correspondence between Landsat-7/8 LAI estimates and ground measurements revealing high correlations (R2 ≥ 0.89) and low root mean squared errors (RMSE ≤ 0.75) in all seasons. Landsat-7/8 as well as Sentinel-2A high-resolution LAI retrievals, were compared with satellite LAI products operationally derived from MODIS (MOD15A2), Copernicus PROBA-V (GEOV1), and the recent EUMETSAT Polar System (EPS) LAI product. Good agreement was observed between high- and medium-resolution LAI estimates. In particular, the EPS LAI product was the most correlated product with both Landsat/7-8 and Sentinel-2A estimates, revealing R2 ≥ 0.93 and RMSE ≤ 0.53 m2/m2. In addition, a comparison exercise of EPS, GEOV1 and MODIS revealed high correlations (R2 ≥ 0.90) and RMSE ≤ 0.80 m2/m2 in all cases and years. The temporal assessment shows that the three satellite products capture well the seasonality during the crop phenological cycle. Discrepancies are observed mainly in absolute values retrieved for the peak of rice season. This is the first study that provides a quantitative assessment on the quality of available operational LAI product for rice monitoring to both the scientific community and users of agro-monitoring operational services. [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]

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]

• 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]

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]

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]

The estimation of biophysical variables is at the core of remote sensing science, allowing a close monitoring of crops and forests. Deriving temporally resolved and spatially explicit maps of parameters of interest has been the subject of intense research. However, deriving products from optical sensors is typically hampered by cloud contamination and the trade-off between spatial and temporal resolutions. In this work we rely on the HIghly Scalable Temporal Adaptive Reflectance Fusion Model (HISTARFM) algorithm to generate long gap-free time series of Landsat surface reflectance data by fusing MODIS and Landsat reflectances. An artificial neural network is trained on PROSAIL inversion to predict monthly biophysical variables at 30 m spatial resolution with associated, realistic uncertainty bars. We emphasize the need for a more thorough analysis of uncertainty, and propose a general and scalable approach to combine both epistemic and aleatoric uncertainties by exploiting Monte Carlo (MC) dropout techniques from the trained artificial network and the propagation of HISTARFM uncertainties through the model, respectively. A model recalibration was performed in order to provide reliable uncertainties. We provide new high resolution products of several key variables to quantify the terrestrial biosphere: Leaf Area Index (LAI), Fraction of Absorbed Photosynthetically Active Radiation (FAPAR), Canopy Water Content (CWC) and Fractional Vegetation Cover (FVC) are at 30 m Landsat spatial resolution and over large continental areas. Two study areas are considered: the large heterogeneous but moderately cloud covered contiguous United States, and the homogeneous but largely cloud covered Amazonia. The produced vegetation products largely agree with the test dataset (R = 0.90, RMSE = 0.80 m 2/ m 2 and ME = 0.12 m 2/ m 2 for LAI, and R = 0.98, RMSE = 0.07 and ME = 0.01 for FAPAR) providing low error and high accuracy. Additionally, the validation considers a thorough comparison with operational and largely validated medium resolution products, such as the Moderate-Resolution Imaging Spectroradiometer (MODIS) and Copernicus Global Land Service. Our products presented a good agreement and consistency with both MODIS (R = 0.84 and R = 0.85 for LAI and FAPAR, respectively) and Copernicus (R = 0.92 and R = 0.91 for LAI and FAPAR, respectively). To foster a wider adoption and reproducibility of the methodology we provide an application in GEE and source code at: https://github.com/IPL-UV/ee_BioNet/ • Proposed a methodology based on RTM inversion with NN for biophysical parameter estimation. • Uncertainty quantification considering model and data uncertainties. • Biophysical parameters and realistic uncertainties gap-free maps at high resolution (30 m). • Implications for high resolution carbon fluxes and phenologies applications. [ABSTRACT FROM AUTHOR]

Increasing evidence points towards soil moisture availability as the single most important factorfor variations of vegetation productivity between years [1,2] with substantial effects on fluctuations in the atmospheric CO 2 growth rate [3]. Forests sequester about half of the global annual biospheric carbon uptake, yet, there are still gaps in our understanding of how short-term environmental fluctuations affect their metabolism and photosynthetic activity. Current observational capabilities are limited as the trees do not show immediate visible signs of stress or health. In our study, we re-evaluate how plant productivity varies globally with changing soil moisture along a tree cover gradient. For that, we use three different types of remote sensing proxies for vegetation productivity (16 day temporal and 1degree spatial resolution) : 1) traditional vegetation indices sensitive to greenness (EVI, NDVI, NIRv based on MODIS surface reflectances MCD43C4), 2) sun-induced chlorophyll fluorescence as a proxy for photosynthesis (based on GOME2), and 3) data-driven estimates of gross primary productivity based on machine learning upscaling of flux-tower data (FLUXCOM,http://www.fluxcom.org/). We find that, when soil water content is reduced, both fluorescence and the modelled gross photosynthesis reflect a consistent pattern of enhanced photosynthesis for high tree cover and reduced photosynthesis in regions with low tree cover. In contrast, the traditional satellite-based greenness indices do barely show this pattern of increased forest productivity during below average soil moisture. Our work therefore represents an important incentive to reconsider the differential responses of ecosystems along a tree cover gradient and it illustrates the importance of differentiating indicators of plant greenness from those of photosynthesis for the monitoring and understanding of ecosystems. Moreover, by evaluating the variability in proxies of absorbed light energy and of the efficiency of using it in C-fixation or reemission as fluorescence we can explain that the effects of higher illumination (and temperature) concurrently to and despite of reduced soil water content on photosynthesis actually overcompensate opposed changes in light-use-efficiency in forests on average (and vice versa for wetter than normal conditions). [1] Ahlström et al. 2015, Science, doi: 10.1126/science.aaa1668; [2] Jung et al. 2017, Nature, doi:10.1038/nature20780)[3] Poulter et al. 2014, Nature, doi:10.1038/nature13376 [ABSTRACT FROM AUTHOR]

Earth observation (EO) remote sensing data provide a unique source of information to monitor crops in a temporally resolved and spatially explicit manner. This is of paramount relevance given the ever-growing demand of biofuels and food. Traditional remote sensing applications have exploited vegetation indices (VIs) to monitor crop phenology cycles, and have vastly relied on summarizing the time series in a set of spatial and/or temporal descriptors. It is customary to summarize EO time series with temporal metrics like the maximum peak or the start/end of season, as well as to summarize all pixel-based observations within a region with the spatial average. We posit here that summarizing is not a good idea, and propose two nonlinear regression methods to account for all time and space observations that allows blending multisensor (e.g. optical and microwave) observations too. We illustrate the performance of the methods in two scenarios. First, we combine synergistically optical (MODIS-EVI) and microwave (SMAP-VOD) data using full time series stacked at county level. Such data are then fed into a standard linear and nonlinear (kernel-based) machine learning regression to obtain county-based crop yield estimates over the U.S. corn belt. It is shown that the kernel regression outperforms the linear counterpart, and that the use of full time series from multisensor data improves the results obtained with standard metrics and single sensors. The second experiment takes into account all goals simultaneously. In this case, we follow a distribution regression strategy that does not need to summarize the behavior of a county in an averaged time series. This novel machine learning method exploits higher-order relations between all time series in a county, allows working with the native spatial resolution of each sensor, improves accuracy and bias over previous methods. Results confirm the validity of the multisensor fusion and the advantage of using distribution regression models with full time series for crop yield estimation. [ABSTRACT FROM AUTHOR]