Mangroves play pivotal roles in ecosystem services, but anthropogenic pressures contribute to their alarming degradation. Precise quantification of vital vegetation characteristics, particularly leaf area index (LAI), is crucial for effective monitoring. LAI serves as a key biophysical parameter in assessing vegetation structure, eco-physiological processes, and overall health. This study pioneers the exploration of a hybrid model (combining radiative transfer with machine learning) for LAI estimation in mangroves. Employing (INvertible FOrest Reflectance Model) INFORM and support vector regression in Bhitarkanika Wildlife Sanctuary, India, we utilized digital hemispherical photographs and Sentinel-2 optical data. Results reveal INFORM's superior retrieval capacity (RMSE = 2.56 m2.m−2) over the PROSAIL model (RMSE = 0.73 m2.m−2). The study underscores the efficacy of physical-based models, particularly INFORM, in accurate LAI estimation, particularly in challenging environments like mangrove ecosystems where in-situ data collection is constrained.

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.

Atmospheric radiative transfer models (RTMs) are widely used in satellite data processing to correct for the scattering and absorption effects caused by aerosols and gas molecules in the Earth’s atmosphere. As the complexity of RTMs grows and the requirements for future Earth Observation missions become more demanding, the conventional lookup-table (LUT) interpolation approach faces important challenges. Emulators have been suggested as an alternative to LUT interpolation, but they are still too slow for operational satellite data processing. Our research introduces a solution that harnesses the power of multifidelity methods to improve the accuracy and runtime of Gaussian process (GP) emulators. We investigate the impact of the number of fidelity layers, dimensionality reduction, and training dataset size on the performance of multifidelity GP emulators. We find that an optimal multifidelity emulator can achieve relative errors in surface reflectance below 0.5% and performs atmospheric correction of hyperspectral PRISMA satellite data (one million pixels) in a few minutes. Additionally, we provide a suite of functions and tools for automating the creation and generation of atmospheric RTM emulators.

Recent advancements in unmanned aerial vehicle (UAV) technologies made it possible to monitor agricultural fields at higher spatial and temporal resolution than commonly possible by aerial and satellite surveys. Mapping crop variables such as leaf area index (LAI) and leaf chlorophyll content (LCC) from low-cost UAV-based multispectral cameras can deliver vital information about crop status to farmers and plant breeders. Retrieval of these variables using radiative transfer models (RTMs) has been widely studied in the satellite remote sensing community but is still not well explored in the UAV remote sensing community. This study aims to investigate the advantages of high spatial resolution UAV image data for retrieving LAI and LCC using RTM inversion. A breeding experiment consisting of soybean plots has shown that high-resolution imagery (0.015m) delivers better retrieval accuracy compared to coarser resampled image data. Particularly, biochemical parameters, such as LCC, benefit from high spatial resolution.

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.

Remote sensing observations of variables related to vegetation at microwave and optical/infrared wavelengths are presented over three regions in Europe in the Iberian peninsula, northern Finland and central Europe. They include the instrumented sites of Las Majadas, Sodankyla and Reusel. The final goal is to better constrain land carbon cycle models using the complementarities of vegetation optical depth derived at different frequencies from active and passive instruments (related to vegetation water content and biomass) as well as optical data of the fraction of absorbed photosynthetically active radiation or solar induced fluorescence, closely linked to photosynthesis. The first results confirm this complementarity. For instance, time series of different variables exhibit positive correlations in some areas and negative correlations in other areas.

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.

Monitoring crop phenology significantly assists agricultural managing practices and plays an important role in crop yield predictions. Multi-temporal satellite-based observations allow analyzing vegetation seasonal dynamics over large areas by using vegetation indices or deriving biophysical variables. This study presents a framework for automatic corn phenology characterization based on high spatial and temporal resolution time series. By using the Difference Vegetation Index (DVI) estimated from Sentinel-2 data over Iowa (US), independent phenological models were optimized using Gaussian Processes regression. Their respective performances were assessed based on simulated phenological indicators estimated with double logistic approach. The results showed good model performances for the estimation of different phenological phases such as Start-of-Season and End-of-Season, with a mean RMSE and$R^{2}$values of about 3.50 days and 0.86, respectively, and this with a gain in runtime of about 380 times faster than the double logistic method. To the benefit of crop monitoring community, all these findings will be implemented into the freely downloadable GUI toolbox DATimeS (Decomposition and Analysis of Time Series Software - https://artmotoolbox.com/).

Non-photosynthetic vegetation (NPV) has been identified as priority variable in the context of new spaceborne imaging spectroscopy missions. In this study we provide a first attempt to quantify NPV biomass from these unprecedented data streams to be provided by multiple recently launched or planned instruments. A hybrid workflow is proposed including Gaussian process regression (GPR) trained over radiative transfer model (RTM) simulations and applying active learning strategies. A soybean field data set including two dates with NPV measurements on yellow and senescent (brown) plant organs was used for model validation, resulting in relative errors of 13.4%. This prototype retrieval model was then applied over a resampled Copernicus Hyperspectral Imaging Mission for the Environment (CHIME) scene, resulting in trustful estimates of NPV biomass for some areas with crop residue cover and senescent vegetation. In view of these results, the proposed workflow may show a promising path towards operational delivery of next-generation global NPV products.

End-To-End mission performance simulators (E2Es) are software tools developed to support satellite mission preparatory activities. For passive remote sensing missions, E2Es generate synthetic scenes simulating the interaction of the solar radiation between the atmosphere and the surface; therefore allowing the estimation of the mission performance before its launch. In this paper, we present the CHIME Scene Generator Module (SGM) as part of CHIME E2Es, with state-of-the-art parallelization and optimization that give a performance allowing to obtain a whole year of daily worldwide Top-Of-Atmosphere radiance images in a matter of hours. The CHIME SGM generates 100x200km hyperspectral scenes with elevation effects, shadow projecting clouds, and detailed surface definition in less than an hour. This high performance is due to the producer-consumer design and clever use of the Intel Threading Building Blocks library. The design paves the way to integrate a sensor definition as a library in the part of the convolution of the SGM algorithm, giving an even better performance in the processing chain of the CHIME E2Es.

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.

Along with the unprecedented availability of satellite data acquisition and technological facilities, monitoring of the Biosphere became priority during last years. At the same time, machine learning (ML) solutions evolved into standard practice to solve prediction problems and speed up processing tasks. With the ambition to overcome limitations related to technical resources in satellite image processing, in this work we implemented the ML algorithm Gaussian process regression (GPR) into Google Earth Engine (GEE) to enable spatiotemporal mapping of vegetation traits at European scale. Also, associated uncertainty is provided, allowing to evaluate robustness of the models. In the case of LAI, deviations lower than 1.2 m2/m2are observed. The used imagery collection came from the Sentinel-3 (S3) OLCI (Ocean and Land Colour Instrument) top-of-atmosphere (TOA) radiance (L1C) starting from April 2016 until the present date. The generated products were then further used to analyze phenology. A demonstration case is provided over the Iberian peninsula. We observed annual patterns with peaks during spring close to 20 µg/cm2for LCC (Leaf Clorophyl Content), 1.5 m2/m2for LAI (Leaf Area Index) and 0.5 for FAPAR (Fraction of Absorbed Photosyntheticaly Active Radiation) and FVC (Fractional Vegetation Cover), calculated as average over the targeted area. Eventually, the developed S3 vegetation products are aimed to support of the FLEX fluorescence mission that is dedicated to monitor vegetation photosynthetic activity.

The Copernicus Hyperspectral Imaging Mission for the Environment (CHIME) is in preparation to carry a unique visible to shortwave infrared spectrometer. CHIME will globally provide routine hyperspectral observations to support new and enhanced services for, among others, sustainable agricultural and biodiversity management. The mission shall provide Level 1B, 1C and 2A products, as well a set of downstream products related to the different environmental applications, such as the quantification of vegetation traits. In this context, this work presents the first hybrid retrieval models for the operational delivery of vegetation properties products. Within ESA's CHIME end-to-end (E2E) simulator study, 13 leaf and canopy trait models were developed as part of the L2B vegetation (L2BV) module. The E2E framework functions as a simulated reality that enabled to test and improve the algorithms. The models were further tuned and validated against campaign data using active learning methods. As a proof of concept, the prototype retrieval models were applied to both hyperspectral airborne (HyPlant) and spaceborne (PRISMA) imagery that were first resampled to CHIME band settings. Among the provided vegetation products, it led to a first space-based canopy nitrogen content map over a heterogeneous landscape. The obtained CHIME-like L2BV traits maps demonstrate the feasibility to routinely deliver a collection of next-generation vegetation products across the globe.

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.

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

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.

Since oxygen (O2) absorption of light becomes more pronounced at higher pressure levels, even a few meters distance between the target and the sensor can strongly affect canopy-leaving Solar-Induced chlorophyll Fluorescence (SIF) retrievals. This study was conducted to quantify the consequent error propagation and the impact of ignoring oxygen absorption effects on proximal sensing SIF measurements based on the O2-A absorption band with field-acquired and simulated data. It was demonstrated that the uncorrected oxygen transmittance between target and sensor distance of 10 m can lead to SIF relative errors ranging from 66% to higher than 100% when using a Spectral Fitting (SF) technique or the 3FLD retrieval method, respectively. A proposed strategy to include oxygen transmittance effects on the well-known 3FLD and SF techniques is presented here and applied to the NASA-GSFC multi-angular spectral system known as FUSION over a field of corn plants (Zea mays L.) during the second half of the 2014 growing season. Daily averages of oxygen-corrected SIF measurements from FUSION were related to daily averages of heat and energy fluxes obtained from a nearby Eddy-Covariance (EC) flux tower, and showed a consistent behaviour with similar experiments performed at leaf level.

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.

This paper focuses on biophysical parameter retrieval based on Gaussian Processes (GPs). Very often an arbitrary transformation is applied to the observed variable (e.g. chlorophyll content) to better pose the problem. This standard practice essentially tries to linearize/uniformize the distribution by applying non-linear link functions like the logarithmic, the exponential or the logistic functions. In this paper, we propose to use a GP model that automatically learns the optimal transformation directly from the data. The so-called warped GP regression (WGPR) presented in [1] models output observations as a parametric nonlinear transformation of a GP. The parameters of such 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, which outperforms the regular GPR and a more advanced heteroscedastic GPR model.

A new fluorescence retrieval method is proposed to support ESA's 8th Earth Explorer FLuorescence EXplorer/Sentinel-3 (FLEX-S3) candidate tandem mission. FLEX is the first mission specially dedicated to measure the Sun-Induced vegetation chlorophyll fluorescence (SIF) strongly related with the vegetation photosynthetic activity. Most hyperspectral fluorescence retrieval algorithms available in the literature are very sensitive to true reflectance modelization and/or they assume the atmospheric status as known. The proposed algorithm delivers the retrieval of full fluorescence spectrum at canopy level by using only Top Of Atmosphere (TOA) radiances from S3 and FLEX as input. Once the spatial co-registration and cross-calibration of S3 and FLEX images have been performed, the proposed method starts with (1) the atmospheric correction of TOA radiances, characterizing the state of the atmosphere, (2) performing a first estimation of fluorescence values in main oxygen absorption bands without any approximation of true reflectance spectrum, and using this fluorescence estimation to initialize a Spectral Fitting Method (SFM) to finally retrieving a full fluorescence spectrum. This proposed fluorescence retrieval method is currently being implemented at the Level-2 Retrieval Module (L2RM) of the FLEX/End-To-End Simulator (E2ES).

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.

An accurate estimation of biophysical variables is the key to monitor our Planet. Leaf chlorophyll content helps in interpreting the chlorophyll fluorescence signal from space, whereas oceanic chlorophyll concentration allows us to quantify the healthiness of the oceans. Recently, the family of Bayesian nonparametric methods has provided excellent results in these situations. A particularly useful method in this framework is the Gaussian process regression (GPR). However, standard GPR assumes that the variance of the noise process is independent of the signal, which does not hold in most of the problems. In this letter, we propose a nonstandard variational approximation that allows accurate inference in signal-dependent noise scenarios. We show that the so-called variational heteroscedastic GPR (VHGPR) is an excellent alternative to standard GPR in two relevant Earth observation examples, namely, Chl vegetation retrieval from hyperspectral images and oceanic Chl concentration estimation from in situ measured reflectances. The proposed VHGPR outperforms the tested empirical approaches, as well as statistical linear regression (both least squares and least absolute shrinkage and selection operator), neural nets, and kernel ridge regression, and the homoscedastic GPR, in terms of accuracy and bias, and proves more robust when a low number of examples is available.

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$\%$).

Accurate estimation of biophysical variables is the key to monitor our Planet. In particular, leaf chlorophyll content helps in interpreting the chlorophyll fluorescence signal from space, which is an accurate indicator of the actual state of the vegetation beyond greenness. Recently, the family of Bayesian nonparametric methods has provided excellent results in these situations. A particularly useful method in this framework is the Gaussian Processes regression (GP). However, standard GP assumes that the variance of the noise process is independent of the signal, which does not hold in most of the problems. In this paper, we propose a non-standard variational approximation that allows accurate inference in signal-dependent noise scenarios. We show that the so-called Variational Heteroscedastic Gaussian Process (VHGP) regression is an excellent alternative to standard GP for the retrieval of vegetation chlorophyll content from hyperspectral images. In general VHGP outperforms GP (and many other empirical and machine learning techniques) in accuracy and bias, and reveals more robust when a low number of examples is available.

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.

This paper evaluates state-of-the-art parametric and nonparametric approaches for the estimation of leaf chlorophyll content$(Chl)$, leaf area index, and fractional vegetation cover from space. The parametric approach involves comparison of established and generic narrowband vegetation indices (VIs) and the Normalized Area Over reflectance Curve method, which calculates the continuum spectral region sensitive to$Chl$. However, as not all available bands take part in these spectral algorithms, it remains unclear whether optimal estimations are achieved. Alternatively, the nonparametric approach is based on Gaussian process (GP) techniques and allows inclusion of all bands. GP builds a nonlinear regression as a linear combination of spectra mapped to a high-dimensional space. Moreover, GP provides an indication of the most contributing bands for each parameter, a weight for the most relevant spectra contained in the training data set, and a confidence estimate of the retrieval. GP has previously demonstrated to be competitive in accuracy with support vector regression and neural networks. Results from hyperspectral Compact High Resolution Imaging Spectrometer data over the Spanish Barrax test site show that GP outperformed the VIs in assessing the vegetation properties when using at least four out of the 62 bands. GP identified most contributing bands in the red and red edge and, to a lower extent, in the blue and NIR parts of the spectrum. Since the proposed GP method is able to build robust relationships between the parameter of interest and only a few bands, it is a promising approach for multispectral data as well.

This letter proposes a multioutput support vector regression (M-SVR) method for the simultaneous estimation of different biophysical parameters from remote sensing images. General retrieval problems require multioutput (and potentially nonlinear) regression methods. M-SVR extends the single-output SVR to multiple outputs maintaining the advantages of a sparse and compact solution by using an$\varepsilon$-insensitive cost function. The proposed M-SVR is evaluated in the estimation of chlorophyll content, leaf area index and fractional vegetation cover from a hyperspectral compact high-resolution imaging spectrometer images. The achieved improvement with respect to the single-output regression approach suggests that M-SVR can be considered a convenient alternative for nonparametric biophysical parameter estimation and model inversion.

The Compact High Resolution Imaging Spectrometer (CHRIS) mounted onboard the Project for Onboard Autonomy (PROBA) spacecraft is capable of sampling reflected radiation at five viewing angles over the visible and near-infrared regions of the solar spectrum with high spatial resolution. We combined the spectral domain with the angular domain of CHRIS data in order to map the surface heterogeneity of an Alpine coniferous forest during winter. In the spectral domain, linear spectral unmixing of the nadir image resulted in a canopy cover map. In the angular domain, pixelwise inversion of the Rahman-Pinty-Verstraete (RPV) model at a single wavelength at the red edge (722 nm) yielded a map of the Minnaert-k parameter that provided information on surface heterogeneity at a subpixel scale. However, the interpretation of the Minnaert-k parameter is not always straightforward because fully vegetated targets typically produce the same type of reflectance anisotropy as non-vegetated targets. Merging both maps resulted in a forest cover heterogeneity map, which contains more detailed information on canopy heterogeneity at the CHRIS subpixel scale than is possible to realize from a single-source optical data set.