Earth observation involves the analysis of satellite and aerial imagery, social media data, in-situ observations, mathematical models, and other sources. Among the variety of data sources, geophysical methods have been employed to understand the underground soil characteristics. Particularly, in precision agriculture, electrical resistivity tomography (ERT) is one of the most popular methods due to its advantages in terms of non-destructiveness, data acquisition, processing facilities, and multiscale measurements. On the other hand, satellite imagery is a very popular tool to survey the use of soil across the agriculture territories, with the advantage of its wide field of view, relatively large temporal resolution, and ease to obtain data of surface observation. In this manuscript, a conceptual structure is presented with the general description of the most relevant building blocks of a machine learning system that combine earth observation data. Similarly, a proposal based on a mixture of experts strategy is described for ERT and satellite imagery combination in agriculture.

Statistical regression methods are widely used in remote sensing applications but tend to lack physical interpretability. In this paper, we introduce a methodological framework to improve model emulation and its understanding with machine learning feature selection. Our wrapper-forward feature selection method seamlessly integrates physics knowledge into model emulation, improving the trade-off between accuracy and interpretability. We illustrate our methodology by applying it to atmospheric radiative transfer models in the context of global sensitivity analysis (GSA) and emulation. Our approach consistently aligns with variance-based GSA, pinpointing the critical features of aerosol properties, solar zenith angle, and water vapor. While our physically-based emulators yield only a modest accuracy improvement of 0.2% over conventional Gaussian Processes emulators, its introduction signifies a step forward to physics-aware machine learning-based emulation. The emulator performance remains steadfast, unaffected by substantial changes, further underscoring the reliability of our approach.

Hyperspectral satellite images provide highly-resolved spectral information for large areas. However, spaceborne imaging spectrometers are expensive and currently only a few hyperspectral satellites are in operation. This is a strong limitation, since hyperspectral satellite data provide vital information for numerous fields of application. To overcome this, we developed an emulator using machine learning techniques to generate a synthetic hyperspectral satellite image based on the relationship of a Sentinel-2 (S2) scene and a hyperspectral HyPlant airborne image. The proposed approach was tested on data sets recorded from an agricultural region in western Germany and the results show that a reliable hyperspectral image with the spectral resolution of HyPlant and the spatial extent of the S2 scene can be generated. We systematically tested the approach for different spatial resolutions, including and excluding the S2 spectral bands B1 (coastal aerosol band) and B10 (cirrus band), different machine learning regression algorithms and different numbers of training samples. The best performing parameters were: excluding B1 and B10 bands, resample to 20m and train the emulator with a Neural Networks (NN) with 100'000 samples. That emulator was then applied to the L2A (bottom-of-atmosphere reflectance) S2 subset, and obtained hyperspectral reflectance data were then compared to a reference HyPlant reflectance image of the same region. The synthetic hyperspectral S2-like map was generated quickly and a good agreement with the reference reflectance was achieved. To evaluate the result image we selected the band located at 760 nm due to its importance for the retrieval of solar-induced fluorescence. Goodness-of-fit results (R2of 0.92 and NRMSE of 3.87%) suggest that hyperspectral S2-like reflectance scenes can be produced with high accuracy. The emulator was then applied to a full S2 tile to generate a hyperspectral S2-like reflectance scene (60 Gb), which took less than one hour.

Atmospheric radiative transfer models (RTMs) simulate the light propagation in the Earth's atmosphere. With the evolution of RTMs, their increase in complexity makes them impractical in routine processing such as atmospheric correction. To overcome their computational burden, standard practice is to interpolate a multidimensional lookup table (LUT) of prestored simulations. However, accurate interpolation relies on large LUTs, which still implies large computation times for their generation and interpolation. In recent years, emulation has been proposed as an alternative to LUT interpolation. Emulation approximates the RTM outputs by a statistical regression model trained with a low number of RTM runs. However, a concern is whether the emulator reaches sufficient accuracy for atmospheric correction. Therefore, we have performed a systematic assessment of key aspects that impact the precision of emulating MODTRAN: 1) regression algorithm; 2) training database size; 3) dimensionality reduction (DR) method and a number of components; and 4) spectral resolution. The Gaussian processes regression (GPR) was found the most accurate emulator. The principal component analysis remains a robust DR method and nearly 20 components reach sufficient precision. Based on a database of 1000 samples covering a broad range of atmospheric conditions, GPR emulators can reconstruct the simulated spectral data with relative errors below 1% for the 95th percentile. These emulators reduce the processing time from days to minutes, preserving sufficient accuracy for atmospheric correction and providing model uncertainties and derivatives. We provide a set of guidelines and tools to design and generate accurate emulators for satellite data processing applications.

Sugarcane is one of the most important crops in Mexico; but it is facing increasing issues in its productivity, making necessary implementing monitoring techniques to improve crop management. To contribute to solve the problem, a method to identify anomalies in sugarcane cultivations was proposed through image data obtained from MultiSpectral Instrument sensor (MSI) onboard Sentinel-2 satellites. Three main steps were defined in the methodology: (1) image preprocessing, (2) Index calculation, and (3) anomaly detection. Two study areas were defined. On one hand, an area with a thorough control of the crop was selected, of which a health profile was defined by using PVI and LAI indices. On the other hand, a test area was selected to detect possible anomalous zones in the crop. Results showed that test area of sugarcane crop showed anomalies from day 200. To conclude, determining areas presenting deficiencies in sugarcane crops was possible through the proposed method.

Acapulco coasts are occasionally contaminated by illegal discharges originated by temporary or permanent floods that disembogue to the pacific ocean. Plumes formed by contaminated water running through the ocean can be distinguished in satellite imagery, and their reflectance is related to the polluting elements. Although some spacial agencies provide data from diverse multispectral sensors, application-specific requirements are fulfilled by merging heterogeneous imagery (differences in spatial, temporal, and spectral resolutions). This paper proposes a continuous monitoring strategy to detect pollution in water discharges by combining data from Sentinel-2 and Sentinel-3 platforms. First, the region of interest to be monitored is detected using the bands with high spatial resolution. Then, distance-based supervised machine learning is employed to detect pixel-wise pollution in water. Finally, the historic detections over time are presented to detect recurrent discharges.

The retrieval of sun-induced fluorescence (SIF) from hyperspectral radiance data grew to maturity with research activities around the FLuorescence EXplorer satellite mission FLEX, yet the used methods are computationally expensive. To bypass this computational load, this work aims to approximate the currently used spectral fitting method (SFM) by means of statistical learning, i.e. emulation. To do so, we analyzed the possibility of approximating the SFM with an emulator without losing the precision of the original method. In order to enable emulating the hyperspectral radiance spectrum into the multispectral SIF output signal, a double principal component analysis (PCA) dimensionality reduction, i.e. in both input and output, has been implemented. We systematically tested different machine learning regression algorithms, number of principal components (PCs), number of training samples and quality of training samples. The best performing emulator was then applied to a HyPlant flight line containing at sensor radiance information, and the results were compared to the SFM SIF map of the same flight line, which was used as reference. The emulated SIF map was generated quasi-instantaneously and a good agreement with the SFM map could be achieved: R2 of 0.88 and NRMSE of 3.77%. Finally, to evaluate the robustness and transferability, the emulator was applied to other HyPlant flight lines, leading to R2 of 0.97 and NRMSE of 2.56%. Generated emulated SIF maps proved to be consistent while processing time was in the order of 3 minutes. In comparison, by using SFM the SIF processing took approximately 78 minutes.

Upcoming satellite imaging spectroscopy missions will deliver spatiotemporal explicit data streams to be exploited for mapping vegetation properties, such as nitrogen (N) content. Within retrieval workflows for real-time mapping over agricultural regions, such crop-specific information products need to be derived precisely and rapidly. To allow fast processing, intelligent sampling schemes for training databases should be incorporated to establish efficient machine learning (ML) models. In this study, we implemented active learning (AL) heuristics using kernel ridge regression (KRR) to minimize and optimize a training database for variational heteroscedastic Gaussian processes regression (VHGPR) to estimate aboveground N content. Several uncertainty and diversity criteria were applied on a lookup table (LUT) composed of aboveground N content and corresponding hyperspectral reflectance simulated by the PROSAIL-PRO model. The best-performing AL criteria were Euclidian distance-based diversity (EBD) resulting in a reduction of the LUT training data set by 81% (50 initial samples plus 141 samples selected from a pool of 1000 samples). This reduced LUT was used for training VHGPR, which is not only a competitive algorithm but also provides uncertainty estimates. Validation againstin situN reference data provided excellent results with a root-mean-square error (RMSE) of 1.84 g/m2and a coefficient of determination ($R^{2}$) of 0.92. Mapping aboveground N content over an agricultural region yielded reliable estimates and meaningful associated uncertainties. These promising results encourage the transfer of such hybrid workflows into space and time within the frame of future operational N monitoring from satellite imaging spectroscopy data.

While the mapping of LAI green (LAIG) is well established, current operational products are not calibrated for LAI brown (LAIB), i.e. LAI estimation over senescent vegetation. With Sentinel-2 (S2) new opportunities are opened to estimate LAI brown. An explicit distinction between LAIGand LAIBcan be achieved thanks to the S2 bands in the red edge (B5: 705 nm and B6: 740 nm) and in the shortwave infrared (B11: 1610 nm). By using LAI ground measurements data from multiple campaigns together with available S2 data, independent LAIGand LAIBmodels were optimized using Gaussian processes regression (LAIG: R2= 0.89, NRMSE= 7.1%; LAIB: R2= 0.75, NRMSE= 13.7%). These models can then be combined into LAIGBcomposite maps. The uncertainty estimates were used to map only those LAI estimated values that fall within a 50% uncertainty threshold. As only the vegetated areas fall within that threshold there is no need to apply additional masks. For multiple European core test sites, LAIGBcomposite maps were generated from S2 images, enabling to quantify when crops start senescing across the European regions.

A diverse range of vegetation indices have earlier been developed for the remote estimation of canopy water content (CWC), but most of them are not universally applicable. The aim of this study is to define new indices valid for a wide variety of crop types, that allow to obtain CWC maps at a large spatial scale. These indices were developed based on PROSAIL simulations and then optimized with an experimental dataset (SPARC03; Barrax, Spain), which consists of field data including water content and other biophysical parameters collected for 6 different crops (lucerne, corn, potato, sugar beet, garlic and onion) and associated TOC reflectance spectra acquired by the HyMap airborne sensor. Specifically, Water Absorption Area Index (WAAI) has been defined as the area between the spectrum with null water content, i.e. a straight line whose slope depends only on the reflectance at 800 nm, and the spectrum between 911 and 1271 nm. On the other hand, it is proposed the Depth Water Index (DWI), which is a simple index, applicable to those sensors with lower spectral resolution, based on the spectral depths estimation produced by the water absorption at 970 and 1200 nm. These algorithms outperform commonly used indices in predicting CWC, being applicable to heterogeneous zones, with a R2of 0.8 and 0.7, respectively, using an exponential fit.

An End-to-end simulator (E2ES) is a tool to evaluate the performance of a satellite mission. Once a mission is approved for operation, E2ES evolves during Phase C/D to become a supporting tool for the development and validation of the ground data processor, as well as for simulating data sets to test the Prototype and Operational Processors. FLEX-E is the E2ES of the FLEX/Sentinel-3 tandem mission, which was selected in 2015 as ESA's eighth Earth Explorer. The FLEX-E evolution implies the consolidation of all the retrieval algorithms (e.g. fluorescence, reflectance, biophysical variables), the implementation of new scientific developments, as well the improvement of the co-registration process, the atmospheric correction, and the retrieval of the Level-2 products. The high-level modular design of the improved Level-2 retrieval module will permit a detailed analysis of the errors propagating through the processing chain.

Physical radiative transfer models (RTMs) of leaf and canopies with sufficient realism enable the retrieval of biophysical variables from imaging spectroscopy through numerical inversion. However, advanced RTMs are computationally intensive, which hampers practical applicability of inversion schemes against remote sensing images. To bypass the computational load such RTMs, it has been proposed to approximate these models by means of statistical learning, i.e. emulation. Here we tested three machine learning regression algorithms, i.e. neural networks, kernel ridge regression and Gaussian processes regression, on their ability to emulate the advanced RTM SCOPE (Soil-Canopy-Observation of Photosynthesis and the Energy balance) for limited set of input variables. The best performing emulator was implemented into a numerical inversion scheme to process a subset of an hyperspectral image into a multitude of vegetation properties. Obtained maps are not only consistent, but also processing time was in the order of minutes - in comparison, by using SCOPE the processing would have taken days.

The collection of field data (biophysical variables with associated spectral data) are an essential part of the development and validation of imaging spectroscopy vegetation products. Yet, their quality can only be assessed in the subsequent analysis, and often it appears that there is a wish for extra data to fill up gaps. In an attempt to generate such additional data, we propose to exploit emulation, i.e. variables-based reconstruction of spectral data through statistical learning. We evaluated emulation against classical interpolation techniques using an experimental field dataset with associated airborne hyperspectral HyMap reflectance spectra to produce HyMap-like spectra for any combination of input variables. Results indicate that: (1) emulation produces reflectance spectra more accurately than interpolation when validating against a split part of the field dataset (8% vs 12% errors), (2) emulation produces spectral data multiple times (tens to hundreds) faster than interpolation, and (3) emulation enables meaningful extrapolation outputs. Consequently, this technique opens various new analysis opportunities, e.g., emulators not only allow to produce large experimental-like datasets in a fraction of a second, but they also can be implemented into computationally intensive processing routines to speed up processing, such as global sensitivity analysis or inversion schemes.

End-to-end mission performance simulators (E2ES) are suitable tools to accelerate satellite mission development from concet to deployment. One core element of these E2ES is the generation of synthetic scenes that are observed by the various instruments of an Earth Observation mission. The generation of these scenes rely on Radiative Transfer Models (RTM) for the simulation of light interaction with the Earth surface and atmosphere. However, the execution of advanced RTMs is impractical due to their large computation burden. Classical interpolation and statistical emulation methods of pre-computed Look-Up Tables (LUT) are therefore common practice to generate synthetic scenes in a reasonable time. This work evaluates the accuracy and computation cost of interpolation and emulation methods to sample the input LUT variable space. The results on MONDTRAN-based top-of-atmosphere radiance data show that Gaussian Process emulators produced more accurate output spectra than linear interpolation at a fraction of its time. It is concluded that emulation can function as a fast and more accurate alternative to interpolation for LUT parameter space sampling.

During the design phase of a satellite mission, end-to-end mission performance simulator (E2ES) tools allow scientists and engineers evaluating the mission concept, consolidating system technical requirements and analyzing the suitability of the implemented technical solutions and data processing algorithms. The generation of synthetic scenes is one of the core parts of an E2ES, providing scenes (ground truth) as would be observed by satellite instruments and used as reference against simulated retrieved mission products. An appropriate generation of the scene also allows assessing the performance of the ground data processing chain replacing real instrument data before the mission is in orbit, for which the fidelity of the scene generation is critical. This paper describes the design of a generic scene generator (GSG) with capabilities to generate complex 3-D synthetic scenes that combine the effects of surface, heterogeneity, topography and atmosphere, and viewing/illumination geometry. The proposed design allows generating consistent high spatial and spectral resolution top-of-atmosphere radiance scenes for multiple instruments based on the use of thematic maps, radiative transfer models, and reflectance databases. The described GSG was implemented within the FLuorescence EXplorer (FLEX) E2ES software tool and showed its capabilities to generate compatible scenes for the fluorescence imaging spectrometer, ocean and land color instrument, and sea and land surface temperature radiometer instruments of ESA’s FLEX/Sentinel-3 tandem mission and to validate the fulfillment of the FLEX mission requirements.

Kernel-based machine learning regression algorithms (MLRAs) are potentially powerful methods for being implemented into operational biophysical variable retrieval schemes. However, they face difficulties in coping with large training data sets. With the increasing amount of optical remote sensing data made available for analysis and the possibility of using a large amount of simulated data from radiative transfer models (RTMs) to train kernel MLRAs, efficient data reduction techniques will need to be implemented. Active learning (AL) methods enable to select the most informative samples in a data set. This letter introduces six AL methods for achieving optimized biophysical variable estimation with a manageable training data set, and their implementation into a Matlab-based MLRA toolbox for semiautomatic use. The AL methods were analyzed on their efficiency of improving the estimation accuracy of the leaf area index and chlorophyll content based on PROSAIL simulations. Each of the implemented methods outperformed random sampling, improving retrieval accuracy with lower sampling rates. Practically, AL methods open opportunities to feed advanced MLRAs with RTM-generated training data for the development of operational retrieval models.

The FLuorescence EXplorer (FLEX) mission, selected as the European Space Agency's eighth Earth Explorer, aims to globally measure the sun-induced-chlorophyll-fluorescence spectral emission from terrestrial vegetation. In the frame of the FLEX mission, several industrial and scientific studies have analyzed the instrument design, image processing algorithms, or modeling aspects. At the same time, a common tool is needed to address the overall FLEX mission performance by combining all these features. For this reason, an end-to-end mission performance simulator has been developed for the FLEX mission (FLEX-E). This paper describes the FLEX-E software design, which combines the generation of complex synthetic scenes with an advanced modeling of the instrument behavior and the full processing scheme up to the final fluorescence product. The results derived from FLEX-E simulations indicate that the instrument and developed image processing algorithms are able to retrieve the sun-induced fluorescence with an accuracy below the 0.2$\text{mW}\cdot\text{m}^{-2}\cdot\text{sr}^{-1}\cdot \text{nm}^{-1}$mission requirement. It is expected that FLEX-E will not only optimize the FLEX retrieval algorithms and technical requirements, but also serve as the baseline for the ground processing implementation and testing of calibration/validation procedures.

Physically-based radiative transfer models (RTMs) help in understanding the processes occurring on the Earth's surface and their interactions with vegetation and atmosphere. 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. They are advantageous in real practice because of the computational efficiency and excellent accuracy and flexibility for extrapolation. We here present an `Emulator toolbox' that enables analyzing three multi-output machine learning regression algorithms (MO-MLRAs) on their ability to approximate an RTM. As a proof of concept, a case study on emulating sun-induced fluorescence (SIF) is presented. The 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.

Inversion of radiative transfer models (RTM) using a lookup-table (LUT) approach against satellite reflectance data can lead to concurrent retrievals of biophysical parameters such as leaf chlorophyll content$(Chl)$and leaf area index (LAI), but optimization strategies are not consolidated yet. ESA's upcoming satellites Sentinel-2 (S2) and Sentinel-3 (S3) aim to ensure continuity of old generation satellite sensors by providing superspectral images of high spatial and temporal resolution. This unprecedented data availability leads to an urgent need for developing robust, accurate, and operational retrieval methods. For three simulated Sentinel settings (S2-10 m: 4 bands, S2-20 m: 8 bands and S3-OLCI: 19 bands) various optimization strategies in LUT-based RTM inversion have been evaluated, being the role of i) added noise, ii) multiple best solutions, iii) combined parameters$(Chl \times \hbox{LAI})$, and iv) applied cost functions. By inverting the PROSAIL model and using data from the ESA-led field campaign SPARC (Barrax, Spain), it was demonstrated that introducing noise and opting for multiple best solutions in the inversion considerably improved retrievals. However, the widely used RMSE was not the best performing cost function. Three families of alternative cost functions were applied here: information measures, minimum contrast, and M-estimates. We found that so-called “Power divergence measure”, “Trigonometric”, and spectral measure with “Contrast function$K(x) = -\log(x) + x$”, yielded more accurate results, although this also depended on the biophysical parameter. Particularly, when simultaneous retrieval of multiple biophysical parameters is the objective then “Contrast function$K(x) = -\log(x) + x$” provided most consistent optimized estimates of leaf$Chl$, LAI and canopy$Chl$across the different Sentinel configurations (relative RMSE: 24–29$\%$).

The main objective of FLEX is the measurement of vegetation chlorophyll fluorescence (Fs) from space and the exploitation of this signal to better understand the carbon cycle. FLuORescence Imaging Spectrometer (FLORIS) is the main instrument of the FLEX mission concept. ESA's Earth Science Advisory Committee recommended the investigation of the FLEX concept as an in-orbit demonstrator to be flown as a tandem mission with Sentinel-3 (S-3). S-3 is amongst others equipped with the Ocean Land Colour Instrument (OLCI). When flown in tandem these instruments are expected to provide an accurate characterization of key atmospheric and surface parameters to facilitate Fs retrieval for FLORIS. In this work the performance of FLORIS and S3-OLCI sensors and their synergy was evaluated on their capability of retrieving relevant biophysical parameters using simulated top-of-atmosphere radiance data (LTOA). For both sensors, LTOAdata were simulated across a wide range of vegetation, atmospheric and geometry parameters by coupling leaf, canopy and atmospheric radiative transfer models. The pursued analysis was to train for each retrievable parameter (here: Chl, LAI, soil type and Ftotal) a regression model using the simulated datasets and then evaluate its performance. Two regression types were chosen, a conventional linear regressor and a more advanced nonlinear regressor, and two types of training/validation strategies were followed: a local strategy (at least 2 parameters fixed) and a generic strategy (uniform random subset of the complete dataset). The simulation study led to the following conclusions: 1) FLORIS is well equipped for accurate retrieval of biophysical parameters; 2) however, advanced nonlinear regressors may be needed to achieve robust results, and 3) the large number of bands can lead to redundancy in the nonlinear regressors which can be overcomed by band optimization strategies. Finally, 4) it was demonstrated that a synergy of both FLORIS and S3-OLCI datasets leads to improved biophysical parameter retrieval.

Inversion of radiative transfer models using a lookup-table (LUT) approach against hyperspectral data streams leads to retrievals of biophysical parameters such as chlorophyll content (Chl), but necessary optimization strategies are not consolidated yet. Here, various regularization options have been evaluated to the benefit of improved Chl retrieval from hyperspectral CHRIS data, being: i) the role of added noise, ii) the role of multiple best solutions, and iii) the role of applied cost functions in LUT-based inversion. By using data from the ESA-led field campaign SPARC (Barrax, Spain), it was found that introducing noise and opting for multiple best solutions in the inversion considerably improved retrievals. However, the widely used RMSE was not the best performing cost function. Three families of alternative cost functions were applied here: information measures, minimum contrast and M-estimates. We found that so-called ‘Power divergence measure’, ‘Trigonometric’ and spectral measure with ‘Contrast function K(x)=−log(x)+x’ outperformed RMSE. The whole inversion approach, including more than 60 different cost functions, has been implemented in the ARTMO (Automated Radiative Transfer Models Operator) GUI toolbox and can easily be applied to other kinds of multispectral or hyperspectral images.