Progress in Emulation For Radiative Transfer Modeling And Mapping

The current exponential increase of spatiotemporally explicit data streams from satellitebased Earth observation missions offers promising opportunities for global vegetation monitoring. Intelligent sampling through active learning (AL) heuristics provides a pathway for fast inference of essential vegetation variables by means of hybrid retrieval approaches, i.e., machine learning regression algorithms trained by radiative transfer model (RTM) simulations. In this study we summarize AL theory and perform a brief systematic literature survey about AL heuristics used in the context of Earth observation regression problems over terrestrial targets. Across all relevant studies it appeared that: (i) retrieval accuracy of AL-optimized training data sets outperformed models trained over large randomly sampled data sets, and (ii) Euclidean distance-based (EBD) diversity method tends to be the most efficient AL technique in terms of accuracy and computational demand. Additionally, a case study is presented based on experimental data employing both uncertainty and diversity AL criteria. Hereby, a a simulated training data base by the PROSAIL-PRO canopy RTM is used to demonstrate the benefit of AL techniques for the estimation of total leaf carotenoid content (Cxc) and leaf water content (Cw). Gaussian process regression (GPR) was incorporated to minimize and optimize the training data set with AL. Training the GPR algorithm on optimally AL-based sampled data sets led to improved variable retrievals compared to training on full data pools, which is further demonstrated on a mapping example. From these findings we can recommend the use of AL-based sub-sampling procedures to select the most informative samples out of large training data pools. This will not only optimize regression accuracy due to exclusion of redundant information, but also speed up processing time and reduce final model size of kernel-based machine learning regression algorithms, such as GPR. With this study we want to encourage further testing and implementation of AL sampling methods for hybrid retrieval workflows. AL can contribute to the solution of regression problems within the framework of operational vegetation monitoring using satellite imaging spectroscopy data, and may strongly facilitate data processing for cloud-computing platforms.

<p>Optical Earth observation satellites provide spatially-explicit data that are necessary to study trends in vegetation dynamics. However, more of often than not optical data are discontinuous in time, due to persistent cloud cover and instrumental noises. Hence, the operating constraints of these data require several essential pre-processing steps, especially when aiming to reach towards monitoring of vegetation seasonal trends.  To facilitate this task, here we present an end-to-end processing software framework applied to Sentinel-2 images.</p><p>To do so, first biophysical retrieval models were generated by means of a trained machine learning regression algorithm (MLRA) using simulated data coming from radiative transfer models. Among various tested MLRAs, the variational heteroscedastic Gaussian process regression (VHGPR) was evaluated as best performing. to train the retrieval model.  The training and retrieval were conducted in the Automated Radiative Transfer Models Operator (ARTMO) software framework.</p><p>Subsequently, in view of retrieving the phenological parameters from the obtained vegetation products, a novel times series toolbox as part of the ARTMO framework was used, called:  Decomposition and Analysis of Time Series software (DATimeS). DATimeS provides temporal interpolation among other functionalities with several advanced MLRAs for gap filling, smoothing functions and subsequent calculation of phenology indicators. Various MLRAs were tested for gap filling to reconstruct cloud-free maps of biophysical variables at a step of 10 days.</p><p>A demonstration case is presented involving the retrieval of Leaf area index (LAI), fraction of Absorbed Photosynthetically Active Radiation (FAPAR) from sentinel-2 time series.  A large agricultural Algerian site of 143, 75 km² including Oued Rhiou, Ouarizane, Djidioua (1,345,075 pixels) was chosen for this study.  A reference image was excluded from the time series in order to evaluate the reconstruction accuracy over a 40-day artificial gap.</p><p>  The reference vs.  Reconstructed maps produced by the gap-filling methods were compared with statistical goodness-of-fit metrics.  Considering both accuracy and processing speed, the fitting algorithms Gaussian process regression (GPR) and Next neighbour interpolation (R²= 0.90 / 0.081 sec per pixel and R²=0.88 / 0.001 sec per pixel respectively) interpolations proved to reconstruct the vegetation products the most efficient, with GPR as more accurate but Next faster by a factor of 70.</p><p>Finally, we evaluated of the phenology indicators such as start-of-season and end-of-season based on LAI and FAPAR. The obtained maps provide valid information of the vegetation dynamics.  Altogether, the ARTMO-DATimeS software framework enabled seamless processing of all essential steps:  (1) from L2A sentinel-2 images converted to vegetation products, (2) to cloud-free composite products, and finally (3) converted into vegetation phenology indicators.</p><p> </p>

In this study, we reviewed methods, sensors and study areas in estimation of vegetation biophysical (VBph) and biochemical (VBch) parameters using satellite optical remote sensing, in terms of (1) their performance and (2) extent of their use. Performance of parametric regression methods is dependent on the type of sensor, vegetation parameter, vegetation cover and biome of study area. Artificial neural network, partial least-squares regression, random forest, support vector machine and Gaussian process regression (GPR) had acceptable performances in the estimations. Performance of physically based methods depends on selecting appropriate radiative transfer model, inversion method and cost function, optimal solution (e.g. mean of some of the best lookup-table solutions) and adding appropriate Gaussian noise. In recent years, the use of active learning techniques (especially Euclidean distance-based diversity), to optimize training datasets against field datasets, with machine learning regression algorithms (MLRAs) (especially GPR) has led to acceptable performances by hybrid methods in estimation of VBph and VBch parameters using real and/or simulated (Re/Si) satellite hyperspectral (and multispectral) data with dimensionality reduction techniques in the spectral domain (especially principal component analysis with 20 principal components). In overall, Re/Si satellite optical sensors data containing red-edge (mostly for VBch parameters) and/or short-wave infrared (mostly for VBph parameters) spectral band(s) performed well. Emerging trend observed in recent years in the estimations by using Re/Si medium spatial resolution sensors data with relatively good spectral resolutions (e.g. precursore iperspettrale della missione applicativa, environmental mapping and analysis program and Sentinel-2 multispectral instrument) and non-parametric regression (especially MLRAs) and hybrid methods.

Estimation of canopy water content for wheat through combining radiative transfer model and machine learning

The leaf chlorophyll content (LCC) is a critical index to characterize crop growth conditions, photosynthetic capacity, and physiological status. Its dynamic change characteristics are of great significance for monitoring crop growth conditions and understanding the process of material and energy exchange between crops and the environment. Extensive research has focused on LCC retrieval with hyperspectral data onboard various sensor platforms. Nevertheless, limited attention has been paid to LCC inversion from multispectral data, such as the data from Landsat-8, and the potentials and capabilities of the data for crop LCC estimation have not been fully explored. The present study made use of Landsat-8 Operational Land Imager (OLI) imagery and the corresponding field experimental data to evaluate their capabilities and potentials for LCC modeling using four different retrieval methods: vegetation indices (VIs), machine learning regression algorithms (MLRAs), lookup-table (LUT)-based inversion, and hybrid regression approaches. The results showed that the modified triangular vegetation index (MTVI2) exhibited the best estimate accuracy for LCC retrieval with a root mean square error (RMSE) of 5.99 μg/cm2 and a relative RMSE (RRMSE) of 10.49%. Several other vegetation indices that were established from red and near-infrared (NIR) bands also exhibited good accuracy. Models established from Gaussian process regression (GPR) achieved the highest accuracy for LCC retrieval (RMSE = 5.50 μg/cm2, RRMSE = 9.62%) compared with other MLRAs. Moreover, red and NIR bands outweighed other bands in terms of GPR modelling. LUT-based inversion methods with the “K(x) = −log (x) + x” cost function that belongs to the “minimum contrast estimates” family showed the best estimation results (RMSE = 8.08 μg/cm2, RRMSE = 14.14%), and the addition of multiple solution regularization strategies effectively improved the inversion accuracy. For hybrid regression methods, the use of active learning (AL) techniques together with GPR for LCC modelling significantly increased the estimation accuracy, and the combination of entropy query by bagging (EQB) AL and GPR had the best accuracy for LCC estimation (RMSE = 12.43 μg/cm2, RRMSE = 21.77%). Overall, our study suggest that Landsat-8 OLI data are suitable for crop LCC retrieval and could provide a basis for LCC estimation with similar multispectral datasets.

Radiative transfer models (RTMs) are often used to retrieve biophysical parameters from earth observation data. RTMs with multi-temporal and realistic forest representations enable radiative transfer (RT) modeling for real-world dynamic processes. To achieve more realistic RT modeling for dynamic forest processes, this study presents the 3D-explicit reconstruction of a typical temperate deciduous forest in 2015 and 2022. We demonstrate for the first time the potential use of bitemporal 3D-explicit RT modeling from terrestrial laser scanning on the forward modeling and quantitative interpretation of: (1) remote sensing (RS) observations of leaf area index (LAI), fraction of absorbed photosynthetically active radiation (FAPAR), and canopy light extinction, and (2) the impact of canopy gap dynamics on light availability of explicit locations. Results showed that, compared to the 2015 scene, the hemispherical-directional reflectance factor (HDRF) of the 2022 forest scene relatively decreased by 3.8% and the leaf FAPAR relatively increased by 5.4%. At explicit locations where canopy gaps significantly changed between the 2015 scene and the 2022 scene, only under diffuse light did the branch damage and closing gap significantly impact ground light availability. This study provides the first bitemporal RT comparison based on the 3D RT modeling, which uses one of the most realistic bitemporal forest scenes as the structural input. This bitemporal 3D-explicit forest RT modeling allows spatially explicit modeling over time under fully controlled experimental conditions in one of the most realistic virtual environments, thus delivering a powerful tool for studying canopy light regimes as impacted by dynamics in forest structure and developing RS inversion schemes on forest structural changes.

We proposed a framework to generate high spatio-temporal resolution leaf area index (LAI) and uncertainty maps based on the integration of LAINet observation system, Consistent Adjustment of the Climatology to Actual Observations (CACAO) method and Gaussian process regression (GPR). LAINet, which is a wireless sensor network based automatic LAI observation instrument, was used to provide temporally continuous field measurements; CACAO, a data blending method, was used to blend the high and low spatial resolution remote sensing observations to obtain high spatio-temporal resolution remote sensing observations synchronous with the field measurements. GPR, a machine learning regression algorithm, was used to upscale the spatially discrete field measurements to spatially explicit LAI maps, and get the concomitant uncertainty maps. The performance of the proposed method was evaluated over a crop site, where seven LAI maps and their accompanying uncertainty maps all with 30 m and 8 days resolutions were generated. Results show that the framework can provide accurate LAI retrievals. In addition, the concomitant uncertainty maps provide insight into the reliability of the LAI retrievals. This paper contributes to precision agriculture and validation activities for coarse resolution LAI products.

The growth of rice is a sequence of three different phenological phases. This sequence of change in rice phenology implies that the condition of the plant during the vegetative phase relates directly to the health of leaves functioning during the reproductive and ripening phases. As such, accurate monitoring is important towards understanding rice growth dynamics. Leaf Area Index (LAI) is an important indicator of rice yields and the availability of this information during key phenological phases can support more informed farming decisions. Satellite remote sensing has been adopted as a proxy to field measurements of LAI and with the launch of freely available high resolution Satellite images such as Sentinel-2, it is imperative that accurate retrieval methods are adopted towards monitoring LAI at irrigated rice fields. Here, we evaluate the potential of a hybrid radiative transfer model (i.e., PROSAIL - Gaussian Process Regression (GPR), for estimating the phenological dynamics of irrigated rice LAI using imager derived from the Sentinel-2 multispectral instrument. LAI field measurements were obtained from an experimental rice field in Nasarawa state, Nigeria during the dry season. We used the PROSAIL radiative transfer model to create a look up table (LUT) that was subsequently used to train a GPR model. Afterwards, we evaluated the potential of the hybrid modelling approach by assessing the overall model accuracy and the extent to which LAI was able to accurately predict LAI during key rice phenological phases. We compared the predicted hybrid GPR LAI values with LAI values generated from the SNAP toolbox, based on a hybrid Artificial Neural Network (ANN) modelling approach. Our results show that the overall predictive accuracy of the hybrid GPR model (R2 = 0.82, RMSE = 1.65) was more accurate than that of the hybrid ANN model (R2 = 0.66, RMSE = 3.89) for retrieving LAI values from Sentinel-2 imagery. Both models underestimated LAI values during the reproductive and ripening phases . However, the accuracy during the phenological phases were more significant when using the hybrid GPR model (P < 0.05). During the different phenological phases, the hybrid GPR model predicted LAI more accurately during the reproductive (R2 = 0.7) and ripening (R2 = 0.59) phases compared to the hybrid ANN reproductive and ripening phases. When monitoring LAI phenological profiles of both hybrid models, the hybrid GPR and ANN models underestimated LAI during the reproductive and ripening phases. However, the ANN model underestimations were statistically significantly greater than those for the hybrid GPR model (P < 0.05). Our results highlight the potential of hybrid GPR models for estimating the phenological dynamics of irrigated rice LAI from Sentinel-2 data. They provided more accurate estimation of LAI patterns from varying nitrogen and water applications than hybrid ANN models.

The unprecedented availability of optical satellite data in cloud-based computing platforms, such as Google Earth Engine (GEE), opens new possibilities to develop crop trait retrieval models from the local to the planetary scale. Hybrid retrieval models are of interest to run in these platforms as they combine the advantages of physically-based radiative transfer models (RTM) with the flexibility of machine learning regression algorithms. Previous research with GEE primarily relied on processing bottom-of-atmosphere (BOA) reflectance data, which requires atmospheric correction. In the present study, we implemented hybrid models directly into GEE for processing Sentinel-2 (S2) Level-1C (L1C) top-of-atmosphere (TOA) reflectance data into crop traits. To achieve this, a training dataset was generated using the leaf-canopy RTM PROSAIL in combination with the atmospheric model 6SV. Gaussian process regression (GPR) retrieval models were then established for eight essential crop traits namely leaf chlorophyll content, leaf water content, leaf dry matter content, fractional vegetation cover, leaf area index (LAI), and upscaled leaf variables (i.e., canopy chlorophyll content, canopy water content and canopy dry matter content). An important pre-requisite for implementation into GEE is that the models are sufficiently light in order to facilitate efficient and fast processing. Successful reduction of the training dataset by 78% was achieved using the active learning technique Euclidean distance-based diversity (EBD). With the EBD-GPR models, highly accurate validation results of LAI and upscaled leaf variables were obtained against in situ field data from the validation study site Munich-North-Isar (MNI), with normalized root mean square errors (NRMSE) from 6% to 13%. Using an independent validation dataset of similar crop types (Italian Grosseto test site), the retrieval models showed moderate to good performances for canopy-level variables, with NRMSE ranging from 14% to 50%, but failed for the leaf-level estimates. Obtained maps over the MNI site were further compared against Sentinel-2 Level 2 Prototype Processor (SL2P) vegetation estimates generated from the ESA Sentinels' Application Platform (SNAP) Biophysical Processor, proving high consistency of both retrievals (R2 from 0.80 to 0.94). Finally, thanks to the seamless GEE processing capability, the TOA-based mapping was applied over the entirety of Germany at 20 m spatial resolution including information about prediction uncertainty. The obtained maps provided confidence of the developed EBD-GPR retrieval models for integration in the GEE framework and national scale mapping from S2-L1C imagery. In summary, the proposed retrieval workflow demonstrates the possibility of routine processing of S2 TOA data into crop traits maps at any place on Earth as required for operational agricultural applications.

Energy-based seismic design is being rapidly developed and suggests that the seismic demands are met by the energy dissipation capacity of the structural members. Equivalent damping ratio is a measure of energy dissipation in structural members that accounts for the post-elastic behavior of the member and provides insight regarding the dynamic response reduction during a seismic event. The present study implements a machine learning algorithm to estimate the equivalent damping ratio in reinforced concrete shear walls at displacements corresponding to a 1.0% lateral drift ratio. Five different machine learning models, namely, Robust Linear Regression, K-Nearest Neighbor Regression, Kernel Ridge Regression, Support Vector Regression, and Gaussian process regression were evaluated in order to choose the model with the highest accuracy. Among all models, Gaussian process regression, a machine learning method with successful implementation experiences in civil/structural engineering related problems, is selected to identify the equivalent damping ratio. The developed GPR-based algorithm uses a database of 161 rectangular shear walls subjected to quasi-static reversed cyclic loading with geometry and mechanical properties commonly found in building stocks of many earthquake-prone countries. The proposed algorithm estimates the equivalent damping ratio for each specimen by predicting the cyclic dissipated energy and lateral force values as two dependent variables. The model validation results show a mean coefficient of determination (R2) of about 0.89; a relative root mean square error of about 0.14 and a mean absolute percentage error of 10.44%, which is considered a substantially accurate prediction for such a complex problem. An open-source model and the entire database are provided which can be used by researchers and also design engineers. The proposed predictive model enables comparing the damping capacity of shear walls and the outcomes of this study are believed to contribute to the energy-based design or performance evaluation procedures in terms of predicting the energy capacity of shear walls.

Earth observation offers an unprecedented opportunity to monitor intensively cultivated areas providing key support to assess fertilizer needs and crop water uptake. Routinely, vegetation traits mapping can help farmers to monitor plant development along the crop’s phenological cycle, which is particularly relevant for irrigated agricultural areas. The high spatial and temporal resolution of the Sentinel-2 (S2) multispectral instrument leverages the possibility to estimate leaf area index (LAI), canopy chlorophyll content (CCC), and vegetation water content (VWC) from space. Therefore, our study presents a hybrid retrieval workflow combining a physically-based strategy with a machine learning regression algorithm, i.e., Gaussian processes regression, and an active learning technique to estimate LAI, CCC and VWC of irrigated winter wheat. The established hybrid models of the three traits were validated against in-situ data of a wheat campaign in the Bonaerense valley, South of the Buenos Aires Province, Argentina, in the year 2020. We obtained good to highly accurate validation results with LAI: R2 = 0.92, RMSE = 0.43 m2 m−2, CCC: R2 = 0.80, RMSE = 0.27 g m−2 and VWC: R2 = 0.75, RMSE = 416 g m−2. The retrieval models were also applied to a series of S2 images, producing time series along the seasonal cycle, which reflected the effects of fertilizer and irrigation on crop growth. The associated uncertainties along with the obtained maps underlined the robustness of the hybrid retrieval workflow. We conclude that processing S2 imagery with optimised hybrid models allows accurate space-based crop traits mapping over large irrigated areas and thus can support agricultural management decisions.

Retrieval schemes often use two important components: 1) a radiative transfer model (RTM) inside the retrieval procedure or to construct the learning dataset for the training of the statistical retrieval algorithms and 2) a numerical weather prediction (NWP) model to provide a first guess or, again, to construct a learning dataset. This is particularly true in operational centers. As a consequence, any physical retrieval or similar method is limited by inaccuracies in the RTM and NWP models on which it is based. In this paper, a method for partially compensating for these errors as part of the sensor calibration is presented and evaluated. In general, RTM/NWP errors are minimized as best as possible prior to the training of the retrieval method, and then tolerated. The proposed method reduces these unknown and generally nonlinear residual errors by training a separate preprocessing neural network (NN) to produce calibrated radiances from real satellite data that approximate those radiances produced by the “flawed” NWP and RTM models. The final “compensated/flawed” retrieval assures better internal consistency of the retrieval procedure and then produces more accurate results. To the authors’ knowledge, this type of NN model has not been used yet for this purpose. The calibration approach is illustrated here on one particular application: the retrieval of atmospheric water vapor from the Advanced Microwave Scanning Radiometer for Earth Observing System (AMSR-E) and the Humidity Sounder for Brazil (HSB) measurements for nonprecipitating scenes, over land and ocean. Before being inverted, the real observations are “projected” into the space of the RTM simulation space from which the retrieval is designed. Validation of results is performed with radiosonde measurements and NWP analysis departures. This study shows that the NN calibration of the AMSR-E/HSB observations improves water vapor inversion, over ocean and land, for both clear and cloudy situations. The NN calibration is efficient and very general, being applicable to a large variety of problems. The nonlinearity of the NN allows for the calibration procedure to be state dependent and adaptable to specific cases (e.g., the same correction will not be applied to medium-range measurement and to extreme conditions). Its multivariate nature allows for a full exploitation of the complex correlation structure among the instrument channels, making the calibration of each single channel more robust. The procedure would make it possible to project the satellite observations in a reference observational space defined by radiosonde measurements, RTM simulations, or other instrument observational space.

A stock price index measures the change in several share prices, which can describe the market and assist investors in deciding on a specific investment. Thus, foreseeing the stock price index benefits investors in creating a better investment strategy. However, forecasting the stock price index can be challenging due to its non-linearity, non-stationary and high uncertainty. Gaussian process regression (GPR) is an attractive and powerful approach for prediction, especially when the data fluctuates over time with fewer restrictions. Besides, the GPR gains advantages over other forecasting techniques as it can offer predictions with uncertainty to provide margin errors. In this study, we evaluate the use of GPR to predict the stock price of Thailand (SET). The SET data are divided into 2 datasets; the data in the year 2015 - 2020 and the data in the year 2020 due to the massive change during the COVID-19 pandemic. The prediction results from the GPR are then compared to the machine learning approaches, artificial neural network (ANN) and recurrent neural network (RNN) using evaluation scores; the root mean square error (RMSE), the mean absolute error (MAE), the mean absolute percentage error (MAPE) and the Nash-Sutcliffe efficiency (NSE). The results indicate that the GPR is superior to the ANN and RNN for both datasets as it provides a high prediction accuracy. Moreover, the results suggest that the GPR is less sensitive to the number of input lags in the model. Therefore, the GPR is more favorable for the prediction of SET than the ANN and RNN.&#x0D; HIGHLIGHTS&#x0D; &#x0D; The Gaussian process regression (GPR) was applied to predict the stock price index of Thailand (SET)&#x0D; The predictive performance of the GPR was compared to artificial neural networks (ANNs) and recurrent neural networks (RNNs)&#x0D; The results indicate that GPR outperformed the other methods as it provided a high prediction accuracy along with prediction intervals&#x0D; &#x0D; GRAPHICAL ABSTRACT

Radiative transfer models (RTM) provide universally applicable, highly accurate prospects for plant parameter retrieval. Due to the ill-posed nature of radiative transfer theory, however, the retrieval of plant parameters requires sophisticated strategies for model inversion. We argue that object-based image analysis (OBIA) works as an effective regularization measure to cope with this ill-posedness. Despite similar findings reported in the literature, OBIA and RTM are rarely used in a combined manner. Additionally, there is a clear lack of software solutions ready for operational usage. Therefore, we propose OBIA4RTM as an approach to combine OBIA and RTM using Python and PostgreSQL/PostGIS spatial databases in a fully Open Geospatial Consortium (OGC) compliant way. First results obtained in agricultural regions in southern Germany and Austria using Sentinel-2 data during the 2017 and 2018 growing season show root mean squared errors (RMSE) in the leaf area index (LAI) of 1.47 m²/m² in the case of silage maize and 1.31 m²/m² in the case of winter cereals. Issues of integrating space and time as well as defining appropriate validation strategies, however, require further research.

Aligned with the prevailing sustainability paradigm, the imperative adoption of bio‐based substitutes for constituents within petroleum‐derived epoxy resin becomes evident. Blending bio‐based and petroleum‐based epoxy resins and curing agents, establishes a synergistic compromise addressing both sustainability imperatives and the mechanical efficacy of thermosets. The conventional approach to discovering optimal compositions for multi‐component mixtures under specific boundary conditions includes empirical trial and error and is seen as a protracted and inefficient endeavor. Conversely, leveraging machine learning might afford a streamlined and confident resolution to this challenge. This investigation elucidates the requisite strategies for maximizing the efficiency of material property optimization through the application of Bayesian optimization and active learning. Illustratively, the study demonstrates the proficient optimization of the glass transition temperature within a four‐component epoxy resin system. This optimization is conducted across varying ranges of bio‐content and cost considerations. The study underscores the utility of machine learning in achieving this task with notable efficiency. The efficacy of least squares, kernel ridge regression, Gaussian process regression, and artificial neural networks, is meticulously evaluated through comprehensive seven‐fold cross‐validation and validated against experimental data.