Search

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]

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

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]

Gaussian process regression (GPR) has experienced tremendous success in biophysical parameter retrieval in the past years. The GPR provides a full posterior predictive distribution so one can derive mean and variance predictive estimates, i.e., point-wise predictions and associated confidence intervals. GPR typically uses translation invariant covariances that make the prediction function very flexible and nonlinear. This, however, makes the relative relevance of the input features hardly accessible, unlike in linear prediction models. In this paper, we introduce the sensitivity analysis of the GPR predictive mean and variance functions to derive feature rankings and spectral spacings, respectively. The methodology can be used to uncover knowledge in any kernel-based regression method, it is fast to compute, and it is expressed in closed-form. The methodology is evaluated on GPR for global ocean chlorophyll prediction, revealing the most important spectral bands and their spectral spacings. We illustrate the (successful) methodology in several datasets and sensors. [ABSTRACT FROM PUBLISHER]

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]

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

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

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

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

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]

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]

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]