Estimating evapotranspiration (ET) has been one of the most critical research areas in agriculture because of water scarcity, the growing population, and climate change. The accurate estimation and mapping of ET are necessary for crop water management. Traditionally, researchers use water balance, soil moisture, weighing lysimeters, or an energy balance approach, such as Bowen ratio or eddy covariance towers to estimate ET. However, these ET methods are point-specific or area-weighted measurements and cannot be extended to a large scale. With the advent of satellite technology, remote sensing images became able to provide spatially distributed measurements. However, the spatial resolution of multispectral satellite images is in the range of meters, tens of meters, or hundreds of meters, which is often not enough for crops with clumped canopy structures, such as trees and vines. Unmanned aerial vehicles (UAVs) can mitigate these spatial and temporal limitations. Lightweight cameras and sensors can be mounted on the UAVs and take high-resolution images. Unlike satellite imagery, the spatial resolution of the UAV images can be at the centimeter-level. UAVs can also fly on-demand, which provides high temporal imagery. In this study, the authors examined different UAV-based approaches of ET estimation at first. Models and algorithms, such as mapping evapotranspiration at high resolution with internalized calibration (METRIC), the two-source energy balance (TSEB) model, and machine learning (ML) are analyzed and discussed herein. Second, challenges and opportunities for UAVs in ET estimation are also discussed, such as uncooled thermal camera calibration, UAV image collection, and image processing. Then, the authors share views on ET estimation with UAVs for future research and draw conclusive remarks.

Accurate cotton yield prediction is essential for optimizing agricultural practices, improving storage management, and efficiently utilizing resources like fertilizers and water, ultimately benefiting farmers economically. Traditional yield estimation methods, such as field sampling and cotton weighing, are time-consuming and labor intensive. Emerging technologies provide a solution by offering farmers advanced forecasting tools that can significantly enhance production efficiency. In this study, the authors employ segmentation techniques on cotton crops collected using unmanned aerial vehicles (UAVs) to predict yield. The authors apply Segment Anything Model (SAM) for semantic segmentation, combined with You Only Look Once (YOLO) object detection, to enhance the cotton yield prediction model performance. By correlating segmentation outputs with yield data, we implement a linear regression model to predict yield, achieving an R² value of 0.913, indicating the model’s reliability. This approach offers a robust framework for cotton yield prediction, significantly improving accuracy and supporting more informed decision-making in agriculture.

Fractional-order calculus is about the differentiation and integration of non-integer orders. Fractional calculus (FC) is based on fractional-order thinking (FOT) and has been shown to help us to understand complex systems better, improve the processing of complex signals, enhance the control of complex systems, increase the performance of optimization, and even extend the enabling of the potential for creativity. In this article, the authors discuss the fractional dynamics, FOT and rich fractional stochastic models. First, the use of fractional dynamics in big data analytics for quantifying big data variability stemming from the generation of complex systems is justified. Second, we show why fractional dynamics is needed in machine learning and optimal randomness when asking: “is there a more optimal way to optimize?”. Third, an optimal randomness case study for a stochastic configuration network (SCN) machine-learning method with heavy-tailed distributions is discussed. Finally, views on big data and (physics-informed) machine learning with fractional dynamics for future research are presented with concluding remarks.

Stochastic Configuration Network (SCN) has a powerful capability for regression and classification analysis. Traditionally, it is quite challenging to correctly determine an appropriate architecture for a neural network so that the trained model can achieve excellent performance for both learning and generalization. Compared with the known randomized learning algorithms for single hidden layer feed-forward neural networks, such as Randomized Radial Basis Function (RBF) Networks and Random Vector Functional-link (RVFL), the SCN randomly assigns the input weights and biases of the hidden nodes in a supervisory mechanism. Since the parameters in the hidden layers are randomly generated in uniform distribution, hypothetically, there is optimal randomness. Heavy-tailed distribution has shown optimal randomness in an unknown environment for finding some targets. Therefore, in this research, the authors used heavy-tailed distributions to randomly initialize weights and biases to see if the new SCN models can achieve better performance than the original SCN. Heavy-tailed distributions, such as Lévy distribution, Cauchy distribution, and Weibull distribution, have been used. Since some mixed distributions show heavy-tailed properties, the mixed Gaussian and Laplace distributions were also studied in this research work. Experimental results showed improved performance for SCN with heavy-tailed distributions. For the regression model, SCN-Lévy, SCN-Mixture, SCN-Cauchy, and SCN-Weibull used less hidden nodes to achieve similar performance with SCN. For the classification model, SCN-Mixture, SCN-Lévy, and SCN-Cauchy have higher test accuracy of 91.5%, 91.7% and 92.4%, respectively. Both are higher than the test accuracy of the original SCN.

Estimating evapotranspiration (ET) has been one of the most important research in agriculture recently because of water scarcity, growing population, and climate change. ET is the sum of evaporation from the soil and transpiration from the crops to the atmosphere. The accurate estimation and mapping of ET are necessary for crop water management. Traditionally, people use weighing lysimeters, Bowen ratio, eddy covariance and many other methods to estimate ET. However, these ET methods are points or location-specific measurements and cannot be extended to a large scale of ET estimation. With the advent of satellites technology, remote sensing images can provide spatially distributed measurements. The satellites multispectral images spatial resolution, however, is in the range of meters, which is often not enough for crops with clumped canopy structure such as trees and vines. And, the timing or frequency of satellites overpass is not always enough to meet the research or water management needs. The Unmanned Aerial Vehicles (UAVs), commonly referred to as drones, can help solve these spatial and temporal challenges. Lightweight cameras and sensors can be mounted on drones and take high-resolution images on a large scale of field. Compared with satellites images, the spatial resolution of UAVs’ images can be as high as 1 cm per pixel. And, people can fly a drone at any time if the weather condition is good. Cloud cover is less of a concern than satellite remote sensing. Both temporal and spatial resolution is highly improved by drones. In this paper, a review of different UAVs based approaches of ET estimations are presented. Different modified models used by UAVs, such as Mapping Evapotranspiration at high Resolution with Internalized Calibration (METRIC), Two-source energy balance (TSEB) model, etc, are also discussed.