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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., Competing Interests: The authors have declared that no competing interests exist.

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.

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]

Existing methods for fine-scale air quality assessment have significant gaps in their reliability. Purely data-driven methods lack any physically-based mechanisms to simulate the interactive process of air pollution, potentially leading to physically inconsistent or implausible results. Here, we report a hybrid multilevel graph neural network that encodes fluid physics to capture spatial and temporal dynamic characteristics of air pollutants. On a multi-air pollutant test in China, our method consistently improved extrapolation accuracy by an average of 11–22% compared to several baseline machine learning methods, and generated physically consistent spatiotemporal trends of air pollutants at fine spatial and temporal scales. [ABSTRACT FROM AUTHOR]

Cirrus clouds are key modulators of Earth’s climate. Their dependencies on meteorological and aerosol conditions are among the largest uncertainties in global climate models. This work uses 3 years of satellite and reanalysis data to study the link between cirrus drivers and cloud properties. We use a gradient-boosted machine learning model and a long short-term memory network with an attention layer to predict the ice water content and ice crystal number concentration. The models show that meteorological and aerosol conditions can predict cirrus properties with R² = 0.49. Feature attributions are calculated with SHapley Additive exPlanations to quantify the link between meteorological and aerosol conditions and cirrus properties. For instance, the minimum concentration of supermicron-sized dust particles required to cause a decrease in ice crystal number concentration predictions is 2 × 10-4 mg/m³. The last 15 hr before the observation predict all cirrus properties. [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]

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]

Bivariate causal discovery amounts to inferring the causal association between two random variables, usually from observational data. This task is the simplest and most fundamental causal discovery problem from which more complex discovery methods can be envisioned and developed. Classical bivariate causal discovery methods exploit a combination of specific sets of assumptions and data to obtain identifiability of the causal direction. Data-driven supervised approaches train machine learning models over large sets of causally-labeled bivariate datasets to learn the task of inferring the causal relationship from data. In this work, an ensemble algorithm based on support measure machines is proposed with the aim of combining the strength of different classical approaches (base methods) with data-driven decisions. In particular, support measure machine classifiers are trained to estimate the performance of each base method. Their decision functions are then used as data-dependent weights of a weighted voting scheme to estimate the causal direction in a bivariate causal discovery problem. This work demonstrates that the proposed algorithm, denoted as Causal Ensemble Measure Machine, performs equal to or better than state-of-the-art methods on a wide range of synthetic and real-world bivariate problems. Perhaps more importantly, this method enables a closer examination of the assumption dependence of existing algorithms on observational data. • New methodology for pairwise causal discovery based on kernel mean embeddings. • Optimized ensemble method combining base causal discovery approaches. • State-of-the-art performance and interpretable results in many bench- mark datasets. [ABSTRACT FROM AUTHOR]

Forest disturbance regimes are expected to intensify as Earth's climate changes. Quantifying forest vulnerability to disturbances and understanding the underlying mechanisms is crucial to develop mitigation and adaptation strategies. However, observational evidence is largely missing at regional to continental scales. Here, we quantify the vulnerability of European forests to fires, windthrows and insect outbreaks during the period 1979–2018 by integrating machine learning with disturbance data and satellite products. We show that about 33.4 billion tonnes of forest biomass could be seriously affected by these disturbances, with higher relative losses when exposed to windthrows (40%) and fires (34%) compared to insect outbreaks (26%). The spatial pattern in vulnerability is strongly controlled by the interplay between forest characteristics and background climate. Hotspot regions for vulnerability are located at the borders of the climate envelope, in both southern and northern Europe. There is a clear trend in overall forest vulnerability that is driven by a warming-induced reduction in plant defence mechanisms to insect outbreaks, especially at high latitudes. Natural disturbances imperil healthy and productive forests, but quantifying their effects at large scales is challenging. Here the authors apply machine learning to disturbance records and satellite data to quantify and map European forest vulnerability to fires, windthrows, and insect outbreaks through 1979-2018. [ABSTRACT FROM AUTHOR]

The terrestrial biosphere is currently slowing down global warming by absorbing about 30% of human emissions of carbon dioxide (CO2). The largest flux of the terrestrial carbon uptake is gross primary production (GPP) defined as the production of carbohydrates by photosynthesis. Elevated atmospheric CO2 concentration is expected to increase GPP ("CO2 fertilization effect"). However, Earth system models (ESMs) exhibit a large range in simulated GPP projections. In this study, we combine an existing emergent constraint on CO2 fertilization with a machine learning approach to constrain the spatial variations of multimodel GPP projections. In a first step, we use observed changes in the CO2 seasonal cycle at Cape Kumukahi to constrain the global mean GPP at the end of the 21st century (2091–2100) in Representative Concentration Pathway 8.5 simulations with ESMs participating in the Coupled Model Intercomparison Project Phase 5 (CMIP5) to 171 ± 12 Gt C yr−1, compared to the unconstrained model range of 156–247 Gt C yr−1. In a second step, we use a machine learning model to constrain gridded future absolute GPP and gridded fractional GPP change in two independent approaches. For this, observational data are fed into the machine learning algorithm that has been trained on CMIP5 data to learn relationships between present‐day physically relevant diagnostics and the target variable. In a leave‐one‐model‐out cross‐validation approach, the machine learning model shows superior performance to the CMIP5 ensemble mean. Our approach predicts an increased GPP change in northern high latitudes compared to regions closer to the equator. Plain Language Summary: About a quarter of human emissions of carbon dioxide (CO2) is absorbed by vegetation and soil on the Earth's surface and hence does not contribute to global warming caused by CO2 in the atmosphere. Thus, in order to better define the remaining carbon budgets left to meet particular warming targets like the 1.5°C of the Paris Agreement, it is important to accurately quantify the carbon uptake by plants in the future. Currently, this is modeled by Earth system models yet with great uncertainties. In this work, we present an alternative machine learning approach to reduce spatial uncertainties of vegetation carbon uptake in future climate projections using observations of today's conditions. Key Points: An emergent constraint on CO2 seasonal cycle amplitude changes reduces uncertainties in global mean gross primary production projectionsA machine learning model with multiple predictors can further constrain the spatial distribution of gross primary productionHigh‐latitude ecosystems show higher gross primary production increase over the 21st century compared to regions closer to the equator [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]

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]

Current remote sensing image classification problems have to deal with an unprecedented amount of heterogeneous and complex data sources. Upcoming missions will soon provide large data streams that will make land cover/use classification difficult. Machine-learning classifiers can help at this, and many methods are currently available. A popular kernel classifier is the Gaussian process classifier (GPC), since it approaches the classification problem with a solid probabilistic treatment, thus yielding confidence intervals for the predictions as well as very competitive results to the state-of-theart neural networks and support vector machines. However, its computational cost is prohibitive for large-scale applications, and constitutes the main obstacle precluding wide adoption. This paper tackles this problem by introducing two novel efficient methodologies for GP classification. We first include the standard random Fourier features approximation into GPC, which largely decreases its computational cost and permits large-scale remote sensing image classification. In addition, we propose a model which avoids randomly sampling a number of Fourier frequencies and alternatively learns the optimal ones within a variational Bayes approach. The performance of the proposed methods is illustrated in complex problems of cloud detection from multispectral imagery and infrared sounding data. Excellent empirical results support the proposal in both computational cost and accuracy. [ABSTRACT FROM AUTHOR]

Progress in advanced radiative transfer models (RTMs) led to an improved understanding of reflectance (R) and sun-induced chlorophyll fluorescence (SIF) emission throughout the leaf and canopy. Among advanced canopy RTMs that have been recently modified to deliver SIF spectral outputs are the energy balance model SCOPE and the 3D models DART and FLIGHT. The downside of these RTMs is that they are computationally expensive, which makes them impractical in routine processing, such as scene generation and retrieval applications. To bypass their computational burden, a computationally effective technique has been proposed by only using a limited number of model runs, called emulation. The idea of emulation is approximating the original RTM by a surrogate machine learning model with low computation time. However, a concern is whether the emulator reaches sufficient accuracy. To this end, we analyzed key aspects of emulator development that may impact the precision of emulating SCOPE-like R and SIF spectra, being: (1) type of machine learning, (2) type of dimensionality reduction (DR) method, and (3) number of components and lookup table (LUT) size. The machine learning family of Gaussian processes regression and neural networks were found best suited to function as emulators. The classical principal component analysis (PCA) remains a robust DR method, but the number of components needs to be optimized depending on the complexity of the spectral data. Based on a small Latin hypercube sampling LUT of 500 samples (70% used for training) covering a selection of SCOPE input variables, the best-performing emulators can reconstruct any combination for the selected SCOPE input variables with relative errors along the spectral range below 2% for R and 4% for SIF. That is sufficient for a precise reconstruction for the large majority of possible combinations, and errors can be further reduced when increasing LUT size for training. As a proof of concept, we imported the best-performing emulators into a newly developed Automated Scene Generator Module (A-SGM) to generate a R and SIF synthetic scene of a vegetated surface. Using emulators as alternative of SCOPE reduced the processing time from the order of days to the order of minutes while preserving sufficient accuracy. [ABSTRACT FROM AUTHOR]

With current and upcoming imaging spectrometers, automated band analysis techniques are needed to enable efficient identification of most informative bands to facilitate optimized processing of spectral data into estimates of biophysical variables. This paper introduces an automated spectral band analysis tool (BAT) based on Gaussian processes regression (GPR) for the spectral analysis of vegetation properties. The GPR-BAT procedure sequentially backwards removes the least contributing band in the regression model for a given variable until only one band is kept. GPR-BAT is implemented within the framework of the free ARTMO's MLRA (machine learning regression algorithms) toolbox, which is dedicated to the transforming of optical remote sensing images into biophysical products. GPR-BAT allows (1) to identify the most informative bands in relating spectral data to a biophysical variable, and (2) to find the least number of bands that preserve optimized accurate predictions. To illustrate its utility, two hyperspectral datasets were analyzed for most informative bands: (1) a field hyperspectral dataset (400–1100 nm at 2 nm resolution: 301 bands) with leaf chlorophyll content (LCC) and green leaf area index (gLAI) collected for maize and soybean (Nebraska, US); and (2) an airborne HyMap dataset (430–2490 nm: 125 bands) with LAI and canopy water content (CWC) collected for a variety of crops (Barrax, Spain). For each of these biophysical variables, optimized retrieval accuracies can be achieved with just 4 to 9 well-identified bands, and performance was largely improved over using all bands. A PROSAIL global sensitivity analysis was run to interpret the validity of these bands. Cross-validated R CV 2 (NRMSE CV ) accuracies for optimized GPR models were 0.79 (12.9%) for LCC, 0.94 (7.2%) for gLAI, 0.95 (6.5%) for LAI and 0.95 (7.2%) for CWC. This study concludes that a wise band selection of hyperspectral data is strictly required for optimal vegetation properties mapping. [ABSTRACT FROM AUTHOR]

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]

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]

Physically-based radiative transfer models (RTMs) help in understanding the processes occurring on the Earth's surface and their interactions with vegetation and atmosphere. When it comes to studying vegetation properties, RTMs allows us to study light interception by plant canopies and are used in the retrieval of biophysical variables through model inversion. However, advanced RTMs can take a long computational time, which makes them unfeasible in many real applications. To overcome this problem, it has been proposed to substitute RTMs through so-called emulators. Emulators are statistical models that approximate the functioning of RTMs. Emulators are advantageous in real practice because of the computational efficiency and excellent accuracy and flexibility for extrapolation. We hereby present an "Emulator toolbox" that enables analysing multi-output machine learning regression algorithms (MO-MLRAs) on their ability to approximate an RTM. The toolbox is included in the free-access ARTMO's MATLAB suite for parameter retrieval and model inversion and currently contains both linear and non-linear MO-MLRAs, namely partial least squares regression (PLSR), kernel ridge regression (KRR) and neural networks (NN). These MO-MLRAs have been evaluated on their precision and speed to approximate the soil vegetation atmosphere transfer model SCOPE (Soil Canopy Observation, Photochemistry and Energy balance). SCOPE generates, amongst others, sun-induced chlorophyll fluorescence as the output signal. KRR and NN were evaluated as capable of reconstructing fluorescence spectra with great precision. Relative errors fell below 0.5% when trained with 500 or more samples using cross-validation and principal component analysis to alleviate the underdetermination problem. Moreover, NN reconstructed fluorescence spectra about 50-times faster and KRR about 800-times faster than SCOPE. The Emulator toolbox is foreseen to open new opportunities in the use of advanced RTMs, in which both consistent physical assumptions and data-driven machine learning algorithms live together. [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]

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]

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]

• 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]

This paper presents the algorithm developed in LSA-SAF (Satellite Application Facility for Land Surface Analysis) for the derivation of global vegetation parameters from the AVHRR (Advanced Very High Resolution Radiometer) sensor on board MetOp (Meteorological–Operational) satellites forming the EUMETSAT (European Organization for the Exploitation of Meteorological Satellites) Polar System (EPS). The suite of LSA-SAF EPS vegetation products includes the leaf area index (LAI), the fractional vegetation cover (FVC), and the fraction of absorbed photosynthetically active radiation (FAPAR). LAI, FAPAR, and FVC characterize the structure and the functioning of vegetation and are key parameters for a wide range of land–biosphere applications. The algorithm is based on a hybrid approach that blends the generalization capabilities offered by physical radiative transfer models with the accuracy and computational efficiency of machine learning methods. One major feature is the implementation of multi-output retrieval methods able to jointly and more consistently estimate all the biophysical parameters at the same time. We propose a multi-output Gaussian process regression (GPR multi ), which outperforms other considered methods over PROSAIL (coupling of PROSPECT and SAIL (Scattering by Arbitrary Inclined Leaves) radiative transfer models) EPS simulations. The global EPS products include uncertainty estimates taking into account the uncertainty captured by the retrieval method and input errors propagation. A sensitivity analysis is performed to assess several sources of uncertainties in retrievals and maximize the positive impact of modeling the noise in training simulations. The paper discusses initial validation studies and provides details about the characteristics and overall quality of the products, which can be of interest to assist the successful use of the data by a broad user’s community. The consistent generation and distribution of the EPS vegetation products will constitute a valuable tool for monitoring of earth surface dynamic processes. [ABSTRACT FROM AUTHOR]

Current and upcoming airborne and spaceborne imaging spectrometers lead to vast hyperspectral data streams. This scenario calls for automated and optimized spectral dimensionality reduction techniques to enable fast and efficient hyperspectral data processing, such as inferring vegetation properties. In preparation of next generation biophysical variable retrieval methods applicable to hyperspectral data, we present the evaluation of 11 dimensionality reduction (DR) methods in combination with advanced machine learning regression algorithms (MLRAs) for statistical variable retrieval. Two unique hyperspectral datasets were analyzed on the predictive power of DR + MLRA methods to retrieve leaf area index (LAI): (1) a simulated PROSAIL reflectance data (2101 bands), and (2) a field dataset from airborne HyMap data (125 bands). For the majority of MLRAs, applying first a DR method leads to superior retrieval accuracies and substantial gains in processing speed as opposed to using all bands into the regression algorithm. This was especially noticeable for the PROSAIL dataset: in the most extreme case, using the classical linear regression (LR), validation results R CV 2 (RMSE CV ) improved from 0.06 (12.23) without a DR method to 0.93 (0.53) when combining it with a best performing DR method (i.e., CCA or OPLS). However, these DR methods no longer excelled when applied to noisy or real sensor data such as HyMap. Then the combination of kernel CCA (KCCA) with LR, or a classical PCA and PLS with a MLRA showed more robust performances ( R CV 2 of 0.93). Gaussian processes regression (GPR) uncertainty estimates revealed that LAI maps as trained in combination with a DR method can lead to lower uncertainties, as opposed to using all HyMap bands. The obtained results demonstrated that, in general, biophysical variable retrieval from hyperspectral data can largely benefit from dimensionality reduction in both accuracy and computational efficiency. [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]

Given the forthcoming availability of Sentinel-2 (S2) images, this paper provides a systematic comparison of retrieval accuracy and processing speed of a multitude of parametric, non-parametric and physically-based retrieval methods using simulated S2 data. An experimental field dataset (SPARC), collected at the agricultural site of Barrax (Spain), was used to evaluate different retrieval methods on their ability to estimate leaf area index (LAI). With regard to parametric methods, all possible band combinations for several two-band and three-band index formulations and a linear regression fitting function have been evaluated. From a set of over ten thousand indices evaluated, the best performing one was an optimized three-band combination according to ( ρ 560 - ρ 1610 - ρ 2190 ) / ( ρ 560 + ρ 1610 + ρ 2190 ) with a 10-fold cross-validation R CV 2 of 0.82 ( RMSE CV : 0.62). This family of methods excel for their fast processing speed, e.g., 0.05 s to calibrate and validate the regression function, and 3.8 s to map a simulated S2 image. With regard to non-parametric methods, 11 machine learning regression algorithms (MLRAs) have been evaluated. This methodological family has the advantage of making use of the full optical spectrum as well as flexible, nonlinear fitting. Particularly kernel-based MLRAs lead to excellent results, with variational heteroscedastic (VH) Gaussian Processes regression (GPR) as the best performing method, with a R CV 2 of 0.90 ( RMSE CV : 0.44). Additionally, the model is trained and validated relatively fast (1.70 s) and the processed image (taking 73.88 s) includes associated uncertainty estimates. More challenging is the inversion of a PROSAIL based radiative transfer model (RTM). After the generation of a look-up table (LUT), a multitude of cost functions and regularization options were evaluated. The best performing cost function is Pearson’s χ -square. It led to a R 2 of 0.74 ( RMSE : 0.80) against the validation dataset. While its validation went fast (0.33 s), due to a per-pixel LUT solving using a cost function, image processing took considerably more time (01:01:47). Summarizing, when it comes to accurate and sufficiently fast processing of imagery to generate vegetation attributes, this paper concludes that the family of kernel-based MLRAs (e.g. GPR) is the most promising processing approach. [ABSTRACT FROM AUTHOR]

The availability of satellite optical information is often hampered by the natural presence of clouds, which can be problematic for many applications. Persistent clouds over agricultural fields can mask key stages of crop growth, leading to unreliable yield predictions. Synthetic Aperture Radar (SAR) provides all-weather imagery which can potentially overcome this limitation, but given its high and distinct sensitivity to different surface properties, the fusion of SAR and optical data still remains an open challenge. In this work, we propose the use of Multi-Output Gaussian Process (MOGP) regression, a machine learning technique that learns automatically the statistical relationships among multisensor time series, to detect vegetated areas over which the synergy between SAR-optical imageries is profitable. For this purpose, we use the Sentinel-1 Radar Vegetation Index (RVI) and Sentinel-2 Leaf Area Index (LAI) time series over a study area in north west of the Iberian peninsula. Through a physical interpretation of MOGP trained models, we show its ability to provide estimations of LAI even over cloudy periods using the information shared with RVI, which guarantees the solution keeps always tied to real measurements. Results demonstrate the advantage of MOGP especially for long data gaps, where optical-based methods notoriously fail. The leave-one-image-out assessment technique applied to the whole vegetation cover shows MOGP predictions improve standard GP estimations over short-time gaps (R2 of 74% vs 68%, RMSE of 0.4 vs 0.44 [ m 2 m − 2 ]) and especially over long-time gaps (R2 of 33% vs 12%, RMSE of 0.5 vs 1.09 [ m 2 m − 2 ]). A second assessment is focused on crop-specific regions, clustering pixels fulfilling specific model conditions where the synergy is profitable. Results reveal the MOGP performance is crop type and crop stage dependent. For long time gaps, best R2 are obtained over maize, ranging from 0.1 (tillering) to 0.36 (development) up to 0.81 (maturity); for moderate time gap, R2 = 0.93 (maturity) is obtained. Crops such as wheat, oats, rye and barley, can profit from the LAI-RVI synergy, with R2 varying between 0.4 and 0.6. For beet or potatoes, MOGP provides poorer results, but alternative descriptors to RVI should be tested for these specific crops in the future before discarding synergy real benefits. In conclusion, active-passive sensor fusion with MOGP represents a novel and promising approach to cope with crop monitoring over cloud-dominated areas. [ABSTRACT FROM AUTHOR]

Developing accurate models of crop stress, phenology and productivity is of paramount importance, given the increasing need of food. Earth observation (EO) remote sensing data provides a unique source of information to monitor crops in a temporally resolved and spatially explicit way. In this study, we propose the combination of multisensor (optical and microwave) remote sensing data for crop yield estimation and forecasting using two novel approaches. We first propose the lag between Enhanced Vegetation Index (EVI) derived from MODIS and Vegetation Optical Depth (VOD) derived from SMAP as a new joint metric combining the information from the two satellite sensors in a unique feature or descriptor. Our second approach avoids summarizing statistics and uses machine learning to combine full time series of EVI and VOD. This study considers two statistical methods, a regularized linear regression and its nonlinear extension called kernel ridge regression to directly estimate the county-level surveyed total production, as well as individual yields of the major crops grown in the region: corn, soybean and wheat. The study area includes the US Corn Belt, and we use agricultural survey data from the National Agricultural Statistics Service (USDA-NASS) for year 2015 for quantitative assessment. Results show that (1) the proposed EVI-VOD lag metric correlates well with crop yield and outperforms common single-sensor metrics for crop yield estimation; (2) the statistical (machine learning) models working directly with the time series largely improve results compared to previously reported estimations; (3) the combined exploitation of information from the optical and microwave data leads to improved predictions over the use of single sensor approaches with coefficient of determination R ≥ 2 0.76 ; (4) when models are used for within-season forecasting with limited time information, crop yield prediction is feasible up to four months before harvest (models reach a plateau in accuracy); and (5) the robustness of the approach is confirmed in a multi-year setting, reaching similar performances than when using single-year data. In conclusion, results confirm the value of using both EVI and VOD at the same time, and the advantage of using automatic machine learning models for crop yield/production estimation. • 1. Optical and passive microwave data are complementary and useful to estimate crop yield. • 2. The time lag between EVI and VOD is proposed as a new metric for crop assessment. • 3. The EVI/VOD lag outperforms common single-sensor metrics for crop yield estimation. • 4. Machine learning further improves results by directly blending multisensor time series. • 5. Crop yield prediction is feasible up to four months before harvest. [ABSTRACT FROM AUTHOR]

Eddy covariance (EC) technique is largely applied for monitoring carbon dioxide (CO2), water (H2O) and energy exchanges between land ecosystems and atmosphere. The use of EC is currently increasing and now more than 700 globally distributed sites are monitored. Additionally, the monitored study sites are often grouped in network (e.g. FLUXNET). EC allows the continuously monitoring of fluxes at fine (subdaily) time resolution over the growing season. However, only net fluxes can be directly measured, while the source signals must be retrieved by models. In the case of CO2, EC measured the net ecosystem exchange (NEE), that is the net balance between two gross CO2 fluxes: the CO2 uptake from atmosphere by (ecosystem level) photosynthesis or gross primary production (GPP) and the CO2 released in the atmosphere by ecosystem respiration (RECO). The partitioning methods applied in FLUXNET dataset allow to retrieve RECO and GPP from NEE and they made use of non-linear relationships and few meteorological drivers. In fact, the Lloyd & Taylor equation and air temperature are used for estimating RECO; GPP is retrieved by the Michaelis & Menten equation making use of the incoming radiation and vapor pressure deficit as drivers. These approaches are based on strong knowledge assumption and allow a large applicability; however there are limitations in particular when additional drivers have important effects on fluxes variability or when functional relationships deviate from the prescribed ones. In this experiment we investigated the feasibility to use a customized neural network algorithm (NNcust) for CO2 fluxes partitioning. NNcust have been designed for estimating NEE by simultaneously retrieving GPP and RECO. The two gross CO2 fluxes have been retrieved by two subnetworks each one using specific and comprehensive micrometeorological drivers from soil and atmosphere. We investigated many features of the partitioned fluxes and the comparison with FLUXNET standard methods have been carried out. The results showed high consistency between magnitude of partitioned fluxes by NNcust and standard methods implemented in FLUXNET such as in the seasonal, daily, subdaily variability and in the functional relationships between inputs and outputs. However, small (in magnitude) but consistent differences emerged by the comparison of the diurnal cycle of gross CO2 fluxes that could be linked to deviation in modeled functions, the interaction of drivers or to the inhibition of leaf respiration in daytime condition, differently accounted in the modeled output. [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]