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Synthetic aperture radar (SAR) data provides an appealing opportunity for all-weather day or night Earth surface monitoring. The European constellation Sentinel-1 (S1) consisting of S1-A and S1-B satellites offers a suitable revisit time and spatial resolution for the observation of croplands from space. The C-band radar backscatter is sensitive to vegetation structure changes and phenology as well as soil moisture and roughness. It also varies depending on the local incidence angle (LIA) of the SAR acquisition’s geometry. The LIA backscatter dependency could therefore be exploited to improve the retrieval of the crop biophysical variables. The availability of S1 radar time-series data at distinct observation angles holds the feasibility to retrieve leaf area index (LAI) evolution considering spatiotemporal coverage of intensively cultivated areas. Accordingly, this research presents a workflow merging multi-date S1 smoothed data acquired at distinct LIA with a Gaussian processes regression (GPR) and a cross-validation (CV) strategy to estimate cropland LAI of irrigated winter wheat. The GPR-S1-LAI model was tested against in situ data of the 2020 winter wheat campaign in the irrigated valley of Colorador river, South of Buenos Aires Province, Argentina. We achieved adequate validation results for LAI with RCV2 = 0.67 and RMSECV = 0.88 m2 m−2. The trained model was further applied to a series of S1 stacked images, generating temporal LAI maps that well reflect the crop growth cycle. The robustness of the retrieval workflow is supported by the associated uncertainties along with the obtained maps. We found that processing S1 smoothed imagery with distinct acquisition geometries permits accurate radar-based LAI modeling throughout large irrigated areas and in consequence can support agricultural management practices in cloud-prone agri-environments.

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.

The present paper deals with the applicability of the Meyer–Peter and Müller (MPM) bed load transport formula. The performance of the formula is examined on data collected in a particular location of Nestos River in Thrace, Greece, in comparison to a proposed Εnhanced MPM (EMPM) formula and to two typical machine learning methods, namely Random Forests (RF) and Gaussian Processes Regression (GPR). The EMPM contains new adjustment parameters allowing calibration. The EMPM clearly outperforms MPM and, also, it turns out to be quite competitive in comparison to the machine learning schemes. Calibrations are repeated with suitably smoothed measurement data and, in this case, EMPM outperforms MPM, RF and GPR. Data smoothing for the present problem is discussed in view of a special nearest neighbor smoothing process, which is introduced in combination with nonlinear regression.

In this study, the subject of investigation was the dynamic double pendulum crank mechanism used in a robotic arm. The arm is driven by a DC motor though the crank system and connected to a fixed side with a mount that includes a single spring and damping. Robotic arms are now widely used in industry, and the requirements for accuracy are stringent. There are many factors that can cause the induction of nonlinear or asymmetric behavior and even excite chaotic motion. In this study, bifurcation diagrams were used to analyze the dynamic response, including stable symmetric orbits and periodic and chaotic motions of the system under different damping and stiffness parameters. Behavior under different parameters was analyzed and verified by phase portraits, the maximum Lyapunov exponent, and Poincaré mapping. Firstly, to distinguish instability in the system, phase portraits and Poincaré maps were used for the identification of individual images, and the maximum Lyapunov exponents were used for prediction. GoogLeNet and ResNet-50 were used for image identification, and the results were compared using a convolutional neural network (CNN). This widens the convolutional layer and expands pooling to reduce network training time and thickening of the image; this deepens the network and strengthens performance. Secondly, the maximum Lyapunov exponent was used as the key index for the indication of chaos. Gaussian process regression (GPR) and the back propagation neural network (BPNN) were used with different amounts of data to quickly predict the maximum Lyapunov exponent under different parameters. The main finding of this study was that chaotic behavior occurs in the robotic arm system and can be more efficiently identified by ResNet-50 than by GoogLeNet; this was especially true for Poincaré map diagnosis. The results of GPR and BPNN model training on the three types of data show that GPR had a smaller error value, and the GPR-21 × 21 model was similar to the BPNN-51 × 51 model in terms of error and determination coefficient, showing that GPR prediction was better than that of BPNN. The results of this study allow the formation of a highly accurate prediction and identification model system for nonlinear and chaotic motion in robotic arms.

Predicting the crop nitrogen (N) nutrition status is critical for optimizing nitrogen fertilizer application. The present study examined the ability of multiple image features derived from unmanned aerial vehicle (UAV) RGB images for winter wheat N status estimation across multiple critical growth stages. The image features consisted of RGB-based vegetation indices (VIs), color parameters, and textures, which represented image features of different aspects and different types. To determine which N status indicators could be well-estimated, we considered two mass-based N status indicators (i.e., the leaf N concentration (LNC) and plant N concentration (PNC)) and two area-based N status indicators (i.e., the leaf N density (LND) and plant N density (PND)). Sixteen RGB-based VIs associated with crop growth were selected. Five color space models, including RGB, HSV, L*a*b*, L*c*h*, and L*u*v*, were used to quantify the winter wheat canopy color. The combination of Gaussian processes regression (GPR) and Gabor-based textures with four orientations and five scales was proposed to estimate the winter wheat N status. The gray level co-occurrence matrix (GLCM)-based textures with four orientations were extracted for comparison. The heterogeneity in the textures of different orientations was evaluated using the measures of mean and coefficient of variation (CV). The variable importance in projection (VIP) derived from partial least square regression (PLSR) and a band analysis tool based on Gaussian processes regression (GPR-BAT) were used to identify the best performing image features for the N status estimation. The results indicated that (1) the combination of RGB-based VIs or color parameters only could produce reliable estimates of PND and the GPR model based on the combination of color parameters yielded a higher accuracy for the estimation of PND (R2val = 0.571, RMSEval = 2.846 g/m2, and RPDval = 1.532), compared to that based on the combination of RGB-based VIs; (2) there was no significant heterogeneity in the textures of different orientations and the textures of 45 degrees were recommended in the winter wheat N status estimation; (3) compared with the RGB-based VIs and color parameters, the GPR model based on the Gabor-based textures produced a higher accuracy for the estimation of PND (R2val = 0.675, RMSEval = 2.493 g/m2, and RPDval = 1.748) and the PLSR model based on the GLCM-based textures produced a higher accuracy for the estimation of PNC (R2val = 0.612, RMSEval = 0.380%, and RPDval = 1.601); and (4) the combined use of RGB-based VIs, color parameters, and textures produced comparable estimation results to using textures alone. Both VIP-PLSR and GPR-BAT analyses confirmed that image textures contributed most to the estimation of winter wheat N status. The experimental results reveal the potential of image textures derived from high-definition UAV-based RGB images for the estimation of the winter wheat N status. They also suggest that a conventional low-cost digital camera mounted on a UAV could be well-suited for winter wheat N status monitoring in a fast and non-destructive way.

Leaf area index (LAI) estimates can inform decision-making in crop management. The European Space Agency’s Sentinel-2 satellite, with observations in the red-edge spectral region, can monitor crops globally at sub-field spatial resolutions (10–20 m). However, satellite LAI estimates require calibration with ground measurements. Calibration is challenged by spatial heterogeneity and scale mismatches between field and satellite measurements. Unmanned Aerial Vehicles (UAVs), generating high-resolution (cm-scale) LAI estimates, provide intermediary observations that we use here to characterise uncertainty and reduce spatial scaling discrepancies between Sentinel-2 observations and field surveys. We use a novel UAV multispectral sensor that matches Sentinel-2 spectral bands, flown in conjunction with LAI ground measurements. UAV and field surveys were conducted on multiple dates—coinciding with different wheat growth stages—that corresponded to Sentinel-2 overpasses. We compared chlorophyll red-edge index (CIred-edge) maps, derived from the Sentinel-2 and UAV platforms. We used Gaussian processes regression machine learning to calibrate a UAV model for LAI, based on ground data. Using the UAV LAI, we evaluated a two-stage calibration approach for generating robust LAI estimates from Sentinel-2. The agreement between Sentinel-2 and UAV CIred-edge values increased with growth stage—R2 ranged from 0.32 (stem elongation) to 0.75 (milk development). The CIred-edge variance between the two platforms was more comparable later in the growing season due to a more homogeneous and closed wheat canopy. The single-stage Sentinel-2 LAI calibration (i.e., direct calibration from ground measurements) performed poorly (mean R2 = 0.29, mean NRMSE = 17%) when compared to the two-stage calibration using the UAV data (mean R2 = 0.88, mean NRMSE = 8%). The two-stage approach reduced both errors and biases by >50%. By upscaling ground measurements and providing more representative model training samples, UAV observations provide an effective and viable means of enhancing Sentinel-2 wheat LAI retrievals. We anticipate that our UAV calibration approach to resolving spatial heterogeneity would enhance the retrieval accuracy of LAI and additional biophysical variables for other arable crop types and a broader range of vegetation cover types.

Remote-sensing-based machine learning approaches for water quality parameters estimation, Secchi Disk Depth (SDD) and Turbidity, were developed for the Valle de Bravo reservoir in central Mexico. This waterbody is a multipurpose reservoir, which provides drinking water to the metropolitan area of Mexico City. To reveal the water quality status of inland waters in the last decade, evaluation of MERIS imagery is a substantial approach. This study incorporated in-situ collected measurements across the reservoir and remote sensing reflectance data from the Medium Resolution Imaging Spectrometer (MERIS). Machine learning approaches with varying complexities were tested, and the optimal model for SDD and Turbidity was determined. Cross-validation demonstrated that the satellite-based estimates are consistent with the in-situ measurements for both SDD and Turbidity, with R2 values of 0.81 to 0.86 and RMSE of 0.15 m and 0.95 nephelometric turbidity units (NTU). The best model was applied to time series of MERIS images to analyze the spatial and temporal variations of the reservoir’s water quality from 2002 to 2012. Derived analysis revealed yearly patterns caused by dry and rainy seasons and several disruptions were identified. The reservoir varied from trophic to intermittent hypertrophic status, while SDD ranged from 0–1.93 m and Turbidity up to 23.70 NTU. Results suggest the effects of drought events in the years 2006 and 2009 on water quality were correlated with water quality detriment. The water quality displayed slow recovery through 2011–2012. This study demonstrates the usefulness of satellite observations for supporting inland water quality monitoring and water management in this region.

Image processing entered the era of artificial intelligence, and machine learning algorithms emerged as attractive alternatives for time series data processing. Satellite image time series processing enables crop phenology monitoring, such as the calculation of start and end of season. Among the promising algorithms, Gaussian process regression (GPR) proved to be a competitive time series gap-filling algorithm with the advantage of, as developed within a Bayesian framework, providing associated uncertainty estimates. Nevertheless, the processing of time series images becomes computationally inefficient in its standard per-pixel usage, mainly for GPR training rather than the fitting step. To mitigate this computational burden, we propose to substitute the per-pixel optimization step with the creation of a cropland-based precalculations for the GPR hyperparameters θ . To demonstrate our approach hardly affects the accuracy in fitting, we used Sentinel-2 LAI time series over an agricultural region in Castile and Leon, North-West Spain. The performance of image reconstructions were compared against the standard per-pixel GPR time series processing. Results showed that accuracies were on the same order (RMSE 0.1767 vs. 0.1564 [ m 2 / m 2 ] , 12% RMSE degradation) whereas processing time accelerated about 90 times. We further evaluated the alternative option of using the same hyperparameters for all the pixels within the complete scene. It led to similar overall accuracies over crop areas and computational performance. Crop phenology indicators were also calculated for the three different approaches and compared. Results showed analogous crop temporal patterns, with differences in start and end of growing season of no more than five days. To the benefit of crop monitoring applications, all the gap-filling and phenology indicators retrieval techniques have been implemented into the freely downloadable GUI toolbox DATimeS.

Energy consumption issues are important factors concerning the achievement of sustainable social development and also have a significant impact on energy security, particularly for China whose energy structure is experiencing a transformation. Construction of an accurate and reliable prediction model for the volatility changes in energy consumption can provide valuable reference information for policy makers of the government and for the energy industry. In view of this, a novel improved model is developed in this article by integrating the modified state transition algorithm (MSTA) with the Gaussian processes regression (GPR) approach for non-fossil energy consumption predictions for China at the end of the 13th Five-Year Project, in which the MSTA is utilized for effective optimization of hyper-parameters in GPR. Aiming for validating the superiority of MSTA, several comparisons are conducted on two well-known functions and the optimization results show the effectiveness of modification in the state transition algorithm (STA). Then, based on the latest statistical renewable energy consumption data, the MSTA-GPR model is utilized to generate consumption predictions for overall renewable energy and each single renewable energy source, including hydropower, wind, solar, geothermal, biomass and other energies, respectively. The forecasting results reveal that the proposed improved GPR can promote the forecasting ability of basic GPR and obtain the best prediction effect among all the other comparison models. Finally, combined with the forecasting results, the trend of each renewable energy source is analyzed.

Leaf Area Index (LAI) and chlorophyll content are strongly related to plant development and productivity. Spatial and temporal estimates of these variables are essential for efficient and precise crop management. The availability of open-access data from the European Space Agency’s (ESA) Sentinel-2 satellite—delivering global coverage with an average 5-day revisit frequency at a spatial resolution of up to 10 metres—could provide estimates of these variables at unprecedented (i.e., sub-field) resolution. Using synthetic data, past research has demonstrated the potential of Sentinel-2 for estimating crop variables. Nonetheless, research involving a robust analysis of the Sentinel-2 bands for supporting agricultural applications is limited. We evaluated the potential of Sentinel-2 data for retrieving winter wheat LAI, leaf chlorophyll content (LCC) and canopy chlorophyll content (CCC). In coordination with destructive and non-destructive ground measurements, we acquired multispectral data from an Unmanned Aerial Vehicle (UAV)-mounted sensor measuring key Sentinel-2 spectral bands (443 to 865 nm). We applied Gaussian processes regression (GPR) machine learning to determine the most informative Sentinel-2 bands for retrieving each of the variables. We further evaluated the GPR model performance when propagating observation uncertainty. When applying the best-performing GPR models without propagating uncertainty, the retrievals had a high agreement with ground measurements—the mean R2 and normalised root-mean-square error (NRMSE) were 0.89 and 8.8%, respectively. When propagating uncertainty, the mean R2 and NRMSE were 0.82 and 11.9%, respectively. When accounting for measurement uncertainty in the estimation of LAI and CCC, the number of most informative Sentinel-2 bands was reduced from four to only two—the red-edge (705 nm) and near-infrared (865 nm) bands. This research demonstrates the value of the Sentinel-2 spectral characteristics for retrieving critical variables that can support more sustainable crop management practices.

Image processing entered the era of artificial intelligence, and machine learning algorithms emerged as attractive alternatives for time series data processing. Satellite image time series processing enables crop phenology monitoring, such as the calculation of start and end of season. Among the promising algorithms, Gaussian process regression (GPR) proved to be a competitive time series gap-filling algorithm with the advantage of, as developed within a Bayesian framework, providing associated uncertainty estimates. Nevertheless, the processing of time series images becomes computationally inefficient in its standard per-pixel usage, mainly for GPR training rather than the fitting step. To mitigate this computational burden, we propose to substitute the per-pixel optimization step with the creation of a cropland-based precalculations for the GPR hyperparameters θ . To demonstrate our approach hardly affects the accuracy in fitting, we used Sentinel-2 LAI time series over an agricultural region in Castile and Leon, North-West Spain. The performance of image reconstructions were compared against the standard per-pixel GPR time series processing. Results showed that accuracies were on the same order (RMSE 0.1767 vs. 0.1564 [m 2 /m 2 ], 12% RMSE degradation) whereas processing time accelerated about 90 times. We further evaluated the alternative option of using the same hyperparameters for all the pixels within the complete scene. It led to similar overall accuracies over crop areas and computational performance. Crop phenology indicators were also calculated for the three different approaches and compared. Results showed analogous crop temporal patterns, with differences in start and end of growing season of no more than five days. To the benefit of crop monitoring applications, all the gap-filling and phenology indicators retrieval techniques have been implemented into the freely downloadable GUI toolbox DATimeS., Competing Interests: Conflicts of Interest: The authors declare no conflict of interest. The funders had no role in the design of the study.