Juan Pablo Rivera

Multiple Cost Functions and Regularization Options for Improved Retrieval of Leaf Chlorophyll Content and LAI through Inversion of the PROSAIL Model

Lookup-table (LUT)-based radiative transfer model inversion is considered a physically-sound and robust method to retrieve biophysical parameters from Earth observation data but regularization strategies are needed to mitigate the drawback of ill-posedness. We systematically evaluated various regularization options to improve leaf chlorophyll content (LCC) and leaf area index (LAI) retrievals over agricultural lands, including the role of (1) cost functions (CFs); (2) added noise; and (3) multiple solutions in LUT-based inversion. Three families of CFs were compared: information measures, M-estimates and minimum contrast methods. We have only selected CFs without additional parameters to be tuned, and thus they can be immediately implemented in processing chains. The coupled leaf/canopy model PROSAIL was inverted against simulated Sentinel-2 imagery at 20 m spatial resolution (8 bands) and validated against field data from the ESA-led SPARC (Barrax, Spain) campaign. For all 18 considered CFs with noise introduction and opting for the mean of multiple best solutions considerably improved retrievals; relative errors can be twice reduced as opposed to those without these regularization options. M-estimates were found most successful, but also data normalization influences the accuracy of the retrievals. Here, best LCC retrievals were obtained using a normalized “L1 -estimate” function with a relative error of 17.6% (r2 : 0.73), while best LAI retrievals were obtained through non-normalized “least-squares estimator” (LSE) with a relative error of 15.3% (r2 : 0.74).

On the Semi-Automatic Retrieval of Biophysical Parameters Based on Spectral Index Optimization

Regression models based on spectral indices are typically empirical formulae enabling the mapping of biophysical parameters derived from Earth Observation (EO) data. Due to its empirical nature, it remains nevertheless uncertain to what extent a selected regression model is the most appropriate one, until all band combinations and curve fitting functions are assessed. This paper describes the application of a Spectral Index (SI) assessment toolbox in the Automated Radiative Transfer Models Operator (ARTMO) package. ARTMO enables semi-automatic retrieval and mapping of biophysical parameters from optical remote sensing observations. The SI toolbox facilitates the assessment of biophysical parameter retrieval accuracy of established as well as new and generic SIs. For instance, based on the SI formulation used, all possible band combinations of formulations with up to ten bands can be defined and evaluated. Several options are available in the SI assessment: calibration/validation data partitioning, the addition of noise and the definition of curve fitting models. To illustrate its functioning, all two-band combinations according to simple ratio (SR) and normalized difference (ND) formulations as well as various fitting functions (linear, exponential, power, logarithmic, polynomial) have been assessed. HyMap imaging spectrometer (430–2490 nm) data obtained during the SPARC-2003 campaign in Barrax, Spain, have been used to extract leaf area index (LAI) and leaf chlorophyll content (LCC) estimates. For both SR and ND formulations the most sensitive regions have been identified for two-band combinations of green (539–570 nm) with longwave SWIR (2421–2453 nm) for LAI (r2: 0.83) and far-red (692 nm) with NIR (1340 nm) or shortwave SWIR (1661–1686 nm) for LCC (r2: 0.93). Polynomial, logarithmic and linear fitting functions led to similar best correlations, though spatial differences emerged when applying the functions to HyMap imagery. We suggest that a systematic SI assessment is a strong requirement in the quality assurance approach for accurate biophysical parameter retrieval.

Optimizing LUT-Based RTM Inversion for Semiautomatic Mapping of Crop Biophysical Parameters from Sentinel-2 and -3 Data: Role of Cost Functions

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. ESAs 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 ×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 %).

Gaussian processes retrieval of leaf parameters from a multi-species reflectance, absorbance and fluorescence dataset

Biochemical and structural leaf properties such as chlorophyll content (Chl), nitrogen content (N), leaf water content (LWC), and specific leaf area (SLA) have the benefit to be estimated through nondestructive spectral measurements. Current practices, however, mainly focus on a limited amount of wavelength bands while more information could be extracted from other wavelengths in the full range (400-2500nm) spectrum. In this research, leaf characteristics were estimated from a field-based multi-species dataset, covering a wide range in leaf structures and Chl concentrations. The dataset contains leaves with extremely high Chl concentrations (>100μgcm(-2)), which are seldom estimated. Parameter retrieval was conducted with the machine learning regression algorithm Gaussian Processes (GP), which is able to perform adaptive, nonlinear data fitting for complex datasets. Moreover, insight in relevant bands is provided during the development of a regression model. Consequently, the physical meaning of the model can be explored. Best estimates of SLA, LWC and Chl yielded a best obtained normalized root mean square error of 6.0%, 7.7%, 9.1%, respectively. Several distinct wavebands were chosen across the whole spectrum. A band in the red edge (710nm) appeared to be most important for the estimation of Chl. Interestingly, spectral features related to biochemicals with a structural or carbon storage function (e.g. 1090, 1550, 1670, 1730nm) were found important not only for estimation of SLA, but also for LWC, Chl or N estimation. Similar, Chl estimation was also helped by some wavebands related to water content (950, 1430nm) due to correlation between the parameters. It is shown that leaf parameter retrieval by GP regression is successful, and able to cope with large structural differences between leaves.

An Emulator Toolbox to Approximate Radiative Transfer Models with Statistical Learning

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

Emulation of leaf, canopy and atmosphere radiative transfer models for fast global sensitivity analysis

Physically-based radiative transfer models (RTMs) help understand the interactions of radiation with vegetation and atmosphere. However, advanced RTMs can be computationally burdensome, which makes them impractical in many real applications, especially when many state conditions and model couplings need to be studied. To overcome this problem, it is proposed to substitute RTMs through surrogate meta-models also named emulators. Emulators approximate the functioning of RTMs through statistical learning regression methods, and can open many new applications because of their computational efficiency and outstanding accuracy. Emulators allow fast global sensitivity analysis (GSA) studies on advanced, computationally expensive RTMs. As a proof-of-concept, three machine learning regression algorithms (MLRAs) were tested to function as emulators for the leaf RTM PROSPECT-4, the canopy RTM PROSAIL, and the computationally expensive atmospheric RTM MODTRAN5. Selected MLRAs were: kernel ridge regression (KRR), neural networks (NN) and Gaussian processes regression (GPR). For each RTM, 500 simulations were generated for training and validation. The majority of MLRAs were excellently validated to function as emulators with relative errors well below 0.2%. The emulators were then put into a GSA scheme and compared against GSA results as generated by original PROSPECT-4 and PROSAIL runs. NN and GPR emulators delivered identical GSA results, while processing speed compared to the original RTMs doubled for PROSPECT-4 and tripled for PROSAIL. Having the emulator-GSA concept successfully tested, for six MODTRAN5 atmospheric transfer functions (outputs), i.e., direct and diffuse at-surface solar irradiance ( E d i f , E d i r ), direct and diffuse upward transmittance ( T d i r , T d i f ), spherical albedo (S) and path radiance ( L 0 ), the most accurate MLRA’s were subsequently applied as emulator into the GSA scheme. The sensitivity analysis along the 400–2500 nm spectral range took no more than a few minutes on a contemporary computer—in comparison, the same analysis in the original MODTRAN5 would have taken over a month. Key atmospheric drivers were identified, which are on the one hand aerosol optical properties, i.e., aerosol optical thickness (AOT), Angstrom coefficient (AMS) and scattering asymmetry variable (G), mostly driving diffuse atmospheric components, E d i f and T d i f ; and those affected by atmospheric scattering, L 0 and S. On the other hand, as expected, AOT, AMS and columnar water vapor (CWV) in the absorption regions mostly drive E d i r and T d i r atmospheric functions. The presented emulation schemes showed very promising results in replacing costly RTMs, and we think they can contribute to the adoption of machine learning techniques in remote sensing and environmental applications.

FLEX End-to-End Mission Performance Simulator

The FLuorescence EXplorer (FLEX) mission, selected as the European Space Agencys 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 mW · m-2 · sr-1 · 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.

Active Learning Methods for Efficient Hybrid Biophysical Variable Retrieval

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.

Synthetic scene simulator for hyperspectral spaceborne passive optical sensors. Application to ESA's FLEX/sentinel-3 tandem mission

The simulation of synthetic images serve scientists and engineers to study the instrument configuration as well as to develop image processing and retrieval strategies for a sensor in development. Despite synthetic scene simulators have been developed in the past in the frame of satellite missions, their functionality and flexibility to create a user-defined scene is limited by their architecture, design and implementation. This paper introduces the design of a generic scene simulator with the flexibility to generate realistic synthetic scenes by configuration of the surface and atmosphere. Following this generic design, a scene simulator is being developed for the ESAs Earth Explorer 8th candidate mission FLEX in order to reproduce the high spectral resolution signal acquired by its hyperspectral instrument. The proposed design and architecture can be adapted to any other passive optical space and airborne instruments.

Retrieval of canopy water content of different crop types with two new hyperspectral indices: Water Absorption Area Index and Depth Water Index

Abstract Crop canopy water content (CWC) is an essential indicator of the crop’s physiological state. While a diverse range of vegetation indices have earlier been developed for the remote estimation of CWC, most of them are defined for specific crop types and areas, making them less universally applicable. We propose two new water content indices applicable to a wide variety of crop types, allowing to derive 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). This dataset consists of water content and other biophysical variables for five common crop types (lucerne, corn, potato, sugar beet and onion) and corresponding top-of-canopy (TOC) reflectance spectra acquired by the hyperspectral HyMap airborne sensor. First, commonly used water content index formulations were analysed and validated for the variety of crops, overall resulting in a R2 lower than 0.6. In an attempt to move towards more generically applicable indices, the two new CWC indices exploit the principal water absorption features in the near-infrared by using multiple bands sensitive to water content. We propose the Water Absorption Area Index (WAAI) as the difference between the area under the null water content of TOC reflectance (reference line) simulated with PROSAIL and the area under measured TOC reflectance between 911 and 1271 nm. We also propose the Depth Water Index (DWI), a simplified four-band index based on the spectral depths produced by the water absorption at 970 and 1200 nm and two reference bands. Both the WAAI and DWI outperform established indices in predicting CWC when applied to heterogeneous croplands, with a R2 of 0.8 and 0.7, respectively, using an exponential fit. However, these indices did not perform well for species with a low fractional vegetation cover (