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The sea surface wind field is an important physical parameter in oceanography and meteorology. With the continuous refinement of numerical weather prediction, air-sea interface materials, energy exchange, and other studies, three-dimensional (3D) wind field distribution at local locations on the sea surface must be measured accurately. The current in-situ observation of sea surface wind parameters is mainly achieved through the installation of wind sensors on ocean data buoys. However, the results obtained from this single-point measurement method cannot reflect wind field distribution in a vertical direction above the sea surface. Thus, the present paper proposes a theoretical framework for the optimal inversion of the 3D wind field structure variation in the area where the buoy is located. The variation analysis method is first used to reconstruct the wind field distribution at different heights of the buoy, after which theoretical analysis verification and numerical simulation experiments are conducted. The results indicate that the use of variational methods to reconstruct 3D wind fields is significantly effective in eliminating disturbance errors in observations, which also verifies the correctness of the theoretical analysis of this method. The findings of this article can provide a reference for the layout optimization design of wind measuring instruments in buoy observation systems and also provide theoretical guidance for the design of new observation buoys in the future. [ABSTRACT FROM AUTHOR]

In the present work, a methodology for wind field reconstruction based on the Meteo Particle model (MPM) from numerical weather prediction (NWP) data is presented. The development of specific wind forecast services is a challenging research topic, in particular for what concerns the availability of accurate local weather forecasts in highly populated areas. Currently, even if NWP limited area models (LAMs) are run at a spatial resolution of about 1 km, this level of information is not sufficient for many applications; for example, to support drone operation in urban contexts. The coupling of the MPM with the NWP limited area model COSMO has been implemented in such a way that the MPM reads the NWP output over a selected area and provides wind values for the generic point considered for the investigation. The numerical results obtained reveal the good behavior of the method in reproducing the general trend of the wind speed, as also confirmed by the power spectra analysis. The MPM is able to step over the intrinsic limitations of the NWP model in terms of the spatial and temporal resolution, even if the MPM inherits the bias that inevitably affects the COSMO output. [ABSTRACT FROM AUTHOR]

In the present work, a methodology for wind field reconstruction based on the Meteo Particle model (MPM) from numerical weather prediction (NWP) data is presented. The development of specific wind forecast services is a challenging research topic, in particular for what concerns the availability of accurate local weather forecasts in highly populated areas. Currently, even if NWP limited area models (LAMs) are run at a spatial resolution of about 1 km, this level of information is not sufficient for many applications; for example, to support drone operation in urban contexts. The coupling of the MPM with the NWP limited area model COSMO has been implemented in such a way that the MPM reads the NWP output over a selected area and provides wind values for the generic point considered for the investigation. The numerical results obtained reveal the good behavior of the method in reproducing the general trend of the wind speed, as also confirmed by the power spectra analysis. The MPM is able to step over the intrinsic limitations of the NWP model in terms of the spatial and temporal resolution, even if the MPM inherits the bias that inevitably affects the COSMO output.

In the present work, the main methodologies used to reconstruct wind fields in the U-SPACE have been analyzed. The SESAR U-SPACE program aims to develop an Unmanned Traffic Management system with a progressive introduction of procedures and services designed to support secure access to the air space for a large number of drones. Some of these techniques were originally developed for reconstruction at high altitudes, but successively adapted to treat different heights. A common approach to all techniques is to approximate the probabilistic distribution of wind speed over time with some parametric models, apply spatial interpolation to the parameters and then read the predicted value. The approaches are based on the fact that modern aircraft are equipped with automatic systems. Moreover, the proposed concepts demonstrated the possibility of using drones as a large network to complement the current network of sensors. The methods can serve the micro-scale weather forecasts and the collection of information necessary for the definition of the flight plan of drones in urban contexts. Existing limitations in the applications of wind field reconstruction, related to the fact that estimations can be produced only if a sufficient number of drones are already flying, could be mitigated using data provided by Numerical Weather Prediction models (NWPs). The coupling of methodologies used to reconstruct wind fields with an NWP will ensure that estimations can be produced in any geographical area. [ABSTRACT FROM AUTHOR]

Short-term wind power forecasting is crucial for updating the wind power trading strategy, equipment protection and control regulation. To solve the difficulty surrounding the instability of the statistical model and the time-consuming nature of the physical model in short-term wind power forecasting, two innovative wind field reconstruction methods combining CFD and a reduced-order model were developed. In this study, POD and Tucker decomposition were employed to obtain the spatial–temporal information correlation of 2D and 3D wind fields, and their inverse processes were combined with sparse sensing to reconstruct multi-dimensional unsteady wind fields. Simulation and detailed discussion were performed to verify the practicability of the proposed algorithms. The simulation results indicate that the wind speed distributions could be reconstructed with reasonably high accuracy (where the absolute velocity relative error was less than 0.8%) using 20 sensors (which only accounted for 0.04% of the total data in the 3D wind field) based on the proposed algorithms. The factors influencing the results of reconstruction were systematically analyzed, including all-time steps, the number of basis vectors and 4-mode dimensions, the diversity of CFD databases, and the reconstruction time. The results indicated that the reconstruction time could be shortened to the time interval of data acquisition to synchronize data acquisition with wind field reconstruction, which is of great significance in the reconstruction of unsteady wind fields. Although there are still many studies to be carried out to achieve short-term predictions, both unsteady reconstruction methods proposed in this paper enable a new direction for short-term wind field prediction. [ABSTRACT FROM AUTHOR]

Various types of measurement techniques, such as Light Detection and Ranging (LiDAR) devices, anemometers, and wind vanes, are extensively utilized in wind energy to characterize the inflow. However, these methods typically gather data at limited points within local wind fields, capturing only a fraction of the wind field's characteristics at wind turbine sites, thus hindering detailed wind field analysis. This study introduces a framework using Physics-informed Neural Networks (PINNs) to assimilate diverse sensor data types. This includes line-of-sight (LoS) wind speed, velocity magnitude and direction, velocity components, and pressure. Moreover, the parameterized Navier–Stokes (N–S) equations are integrated as physical constraints, ensuring that the neural networks accurately represent atmospheric flow dynamics. The framework accounts for the turbulent nature of atmospheric boundary layer flow by including artificial eddy viscosity in the network outputs, enhancing the model's ability to learn and accurately depict large-scale flow structures. The reconstructed flow field and the effective wind speed are in good agreement with the actual data. Furthermore, a transfer learning strategy is employed for the online deployment of pre-trained PINN, which requires less time than that of the actual physical flow. This capability allows the framework to reconstruct wind flow fields in real time based on live data. In the demo cases, the maximum error between the effective wind speed reconstructed online and the actual value at the wind turbine site is only 3.7%. The proposed data assimilation framework provides a universal tool for reconstructing spatiotemporal wind flow fields using various measurement data. Additionally, it presents a viable approach for the online assimilation of real-time measurements. To facilitate the utilization of wind energy, our framework's source code is openly accessible. • A framework was proposed to assimilate wind flow fields from diverse data. • Line-of-sight speed, velocity vector/component, and pressure data are supported. • The parameterized N-S equations are integrated as physical constraints of PINN. • A transfer learning strategy is employed for the online deployment. [ABSTRACT FROM AUTHOR]

In the present work, the main methodologies used to reconstruct wind fields in the U-SPACE have been analyzed. The SESAR U-SPACE program aims to develop an Unmanned Traffic Management system with a progressive introduction of procedures and services designed to support secure access to the air space for a large number of drones. Some of these techniques were originally developed for reconstruction at high altitudes, but successively adapted to treat different heights. A common approach to all techniques is to approximate the probabilistic distribution of wind speed over time with some parametric models, apply spatial interpolation to the parameters and then read the predicted value. The approaches are based on the fact that modern aircraft are equipped with automatic systems. Moreover, the proposed concepts demonstrated the possibility of using drones as a large network to complement the current network of sensors. The methods can serve the micro-scale weather forecasts and the collection of information necessary for the definition of the flight plan of drones in urban contexts. Existing limitations in the applications of wind field reconstruction, related to the fact that estimations can be produced only if a sufficient number of drones are already flying, could be mitigated using data provided by Numerical Weather Prediction models (NWPs). The coupling of methodologies used to reconstruct wind fields with an NWP will ensure that estimations can be produced in any geographical area.

Accurate information on tropical cyclone position, intensity, and structure is critical for storm surge prediction. Atmospheric reanalysis datasets can provide gridded, full coverage, long-term and multi-parameter atmospheric fields for the research on the impact of tropical cyclones on the upper ocean, which effectively makes up for the uneven temporal and spatial distribution of satellite remote sensing and in situ data. However, the reanalysis data cannot accurately describe characteristic parameters of tropical cyclones, especially in high wind conditions. In this paper, the performance of the tropical cyclone representation in ERA5 (European Centre for Medium-Range Weather Forecasts Reanalysis 5th Generation) is investigated and analyzed with respect to IBTrACS (International Best Track Archive for Climate Stewardship) during the period 2018–2020. Comparisons demonstrate that ERA5 winds significantly underestimate the maximum wind speed during the tropical cyclones (>30 m/s) compared to those provided by IBTrACS. An effective wind reconstruction method is examined to enhance tropical cyclone intensity representation in reanalysis data in 94 cases of 31 tropical cyclones 2018–2020. The reconstructed wind speeds are in good agreement with the SFMR (Stepped Frequency Microwave Radiometer) measured data and SMAP (Soil Moisture Active Passive) L-band radiometer remotely sensed measurements. The proposed wind reconstruction method can effectively improve the accuracy of the tropical cyclone representation in ERA5, and will benefit from the establishment of remote sensing satellite retrieval model and the forcing fields of the ocean model. [ABSTRACT FROM AUTHOR]

In this numerical study, we use a multi-scale version of physics-informed neural network (PINN) for wind field reconstruction from LiDAR measurements. The reference velocity field is obtained from high-fidelity large-eddy simulation of neutral atmospheric boundary layer, and the LiDAR measurement strategy is restricted to that of a real LiDAR. The multi-scale PINN reconstructs the velocity field by minimizing a combination of the L2-error with respect to the LiDAR measurements and residuals of the governing equations. Our most significant finding is that adding a multi-scale layer to PINN enables us to: (i) capture wider range of scales, (ii) reconstruct the flow field outside the LiDAR scanning area, and (iii) reach faster convergence. We also find that for volumetric flow reconstruction and to deal with uncertainty in the wind direction, the reconstruction accuracy can be greatly improved by employing multiple LiDAR devices. Overall, our results show that the normalized errors in the reconstructed wind field are lower than 5% for all the experiments conducted in this study and that the errors do not increase even in the presence of measurement noise levels of typical LiDAR. These findings show the feasibility of three-dimensional dynamic wind field reconstruction across large wind farms using LiDAR devices. • Successful wind field reconstruction using a multi-scale PINN from LiDAR data. • Multi-scale layer allows for capturing wider scales and faster convergence. • The neural network requires no prior training data for wind field reconstruction. • The study paves the way for real-time wind field reconstruction. [ABSTRACT FROM AUTHOR]

Short-term wind power forecasting is crucial for updating the wind power trading strategy, equipment protection and control regulation. To solve the difficulty surrounding the instability of the statistical model and the time-consuming nature of the physical model in short-term wind power forecasting, two innovative wind field reconstruction methods combining CFD and a reduced-order model were developed. In this study, POD and Tucker decomposition were employed to obtain the spatial–temporal information correlation of 2D and 3D wind fields, and their inverse processes were combined with sparse sensing to reconstruct multi-dimensional unsteady wind fields. Simulation and detailed discussion were performed to verify the practicability of the proposed algorithms. The simulation results indicate that the wind speed distributions could be reconstructed with reasonably high accuracy (where the absolute velocity relative error was less than 0.8%) using 20 sensors (which only accounted for 0.04% of the total data in the 3D wind field) based on the proposed algorithms. The factors influencing the results of reconstruction were systematically analyzed, including all-time steps, the number of basis vectors and 4-mode dimensions, the diversity of CFD databases, and the reconstruction time. The results indicated that the reconstruction time could be shortened to the time interval of data acquisition to synchronize data acquisition with wind field reconstruction, which is of great significance in the reconstruction of unsteady wind fields. Although there are still many studies to be carried out to achieve short-term predictions, both unsteady reconstruction methods proposed in this paper enable a new direction for short-term wind field prediction.

Accurate and reliable wind forecasts for urban blocks play a pivotal role in the construction of zero-energy communities by guiding the selection and placement of wind turbines and the aerodynamic design optimization of ducted openings. While relatively accurate wind fields are available based on numerical methods, their heavy computational cost and discontinuity make it necessary to explore an interactive and end-to-end method. In this study, we develop a physics-inspired and data-driven two-stage deep learning approach that can reconstruct complex wind fields precisely. The proposed method integrates a physical feature extraction model of the flow field with a sparse measurement data-driven error correction approach. In particular, a well-designed and well-trained flow field feature extraction model (original model) can preserve salient features of CFD modelling, while data-driven error correction techniques may harvest the uncertainty features and fill the remaining gaps between the original model predictions and the measured data. The proposed method is verified by a measured dataset from a community in Beijing. Experimental validation illustrates that the proposed algorithm successfully accomplishes wind field reconstruction in complex terrains using sparse datasets. We show that the proposed two-stage strategy exhibits significantly improved prediction results over the purely original method, with an average accuracy improvement of 47.17% and a maximum accuracy improvement of 72.59%. Overall, the proposed method delivers the potential in accurate wind field construction and urban wind energy forecasting. [Display omitted] • A physics-inspired and data-driven two-stage deep learning approach for wind field reconstruction is proposed. • A well-designed and well-trained flow field feature extraction model is developed. • An error correction method is proposed by considering the uncertainties present in real conditions. • Effectiveness of the proposed approach is verified via full-scale experiment. • The proposed algorithm exhibits good performance in simulating high wind speed field with significant fluctuations. [ABSTRACT FROM AUTHOR]

For long span bridges located in coastal areas, a limited number of anemometers are often installed on the bridge to monitor wind conditions and wind effects. To make best use of wind information from limited anemometers, this paper proposes a wind field reconstruction method, based on wind conditional simulation method with the iteration of coherence function along the bridge deck, for providing a complete wind field for the bridge. In terms of wind field reconstruction method, this paper further investigates the optimal anemometer placement for obtaining the best wind field reconstruction with the least number of anemometers. The proposed two methods are finally applied to a real long suspension bridge equipped with three anemometers on one side of the bridge to demonstrate the feasibility and accuracy of the methods. The results show that the reconstructed wind field not only matches with the measured wind speed histories and spectrums but also provides the best wind coherence function, wind speed histories, and wind spectrums for the entire bridge deck. The results also show that with the limited number of anemometers installed at appropriate positions relative to the bridge deck, the wind field can be reconstructed satisfactorily. [ABSTRACT FROM AUTHOR]

Physics-informed neural network (PINN)-based methods have recently been applied to reconstruct the spatiotemporal wind field based on LIDAR measurements. However, the accuracy of this reconstruction considerably degrades when LIDAR measurement noise exists. Unfortunately, LIDAR measurement noise is inevitable in the real world. To address this limitation, this paper proposes a novel anti-noise method to reconstruct the wind field based on real-world noisy LIDAR measurements. To this end, we first address the gradient vanishing problem in PINN's automatic differentiation process, which prevents the Navier-Stokes (NS) equations from being fully leveraged in wind field reconstruction. This problem is addressed by proposing a residual-connected PINN (RC-PINN) framework. Its advantage in solving the gradient vanishing problem is mathematically proven. Subsequently, by incorporating the NS equations into the RC-PINN, an anti-noise wind field reconstruction method is established. The key feature of this method is that, by employing the RC-PINN, the NS equations are more effectively utilized in the training process, thus improving its anti-noise capability. The numerical results show that, at a wide range of noise levels, the proposed method can achieve a significant improvement in reconstruction performance. Especially, at the noise level of commercially available LIDAR, the reconstruction results are quite satisfactory. Moreover, the proposed method can converge faster. • A residual-connected physics-informed neural network (RC-PINN) is proposed. • The advantage of the RC-PINN is proven mathematically. • An anti-noise wind field reconstruction method is established based on the RC-PINN. • The anti-noise mechanism behind the proposed method is demonstrated. [ABSTRACT FROM AUTHOR]

Accurate information on tropical cyclone position, intensity, and structure is critical for storm surge prediction. Atmospheric reanalysis datasets can provide gridded, full coverage, long-term and multi-parameter atmospheric fields for the research on the impact of tropical cyclones on the upper ocean, which effectively makes up for the uneven temporal and spatial distribution of satellite remote sensing and in situ data. However, the reanalysis data cannot accurately describe characteristic parameters of tropical cyclones, especially in high wind conditions. In this paper, the performance of the tropical cyclone representation in ERA5 (European Centre for Medium-Range Weather Forecasts Reanalysis 5th Generation) is investigated and analyzed with respect to IBTrACS (International Best Track Archive for Climate Stewardship) during the period 2018–2020. Comparisons demonstrate that ERA5 winds significantly underestimate the maximum wind speed during the tropical cyclones (>30 m/s) compared to those provided by IBTrACS. An effective wind reconstruction method is examined to enhance tropical cyclone intensity representation in reanalysis data in 94 cases of 31 tropical cyclones 2018–2020. The reconstructed wind speeds are in good agreement with the SFMR (Stepped Frequency Microwave Radiometer) measured data and SMAP (Soil Moisture Active Passive) L-band radiometer remotely sensed measurements. The proposed wind reconstruction method can effectively improve the accuracy of the tropical cyclone representation in ERA5, and will benefit from the establishment of remote sensing satellite retrieval model and the forcing fields of the ocean model.

In a real wind farm, complex airflow conditions result in complexities of wind speed and direction, with possibly significant intermittency and fluctuations. This problem can be alleviated if the wind speed distribution over a wind farm is known in advance. In this article, a new method is proposed for real-time wind field reconstruction for large areas, based on the idea of a “virtual time”, i.e., a time span needed for an object to travel across a certain distance. The distribution of wind speed and direction can be acquired prior to its occurrence in the wind farm with refined spatial resolutions. A procedure is also developed to stabilize the solution process, and this stabilization leads to an optimal allocation of the wind speed sensors; this allocation is necessary for the efficient use of a limited number of sensors. The reconstruction algorithm has been substantially studied, and a mathematical quantity was correlated to the reconstruction error. This correlation enables us to obtain good reconstruction results by using the greedy algorithm we proposed in this study. Simulation and experimental results demonstrated the strong feasibility of successful reconstructions by our proposed algorithm. Moreover, the sensor optimization scheme not only reduces the error significantly but also improves the efficiency of sensor applications; this improvement should apply to a wide range of conditions. [ABSTRACT FROM AUTHOR]

Physical and data-based approach for wind forecast has been under rapid development recently. Yet challenges remain when high spatial resolutions of the velocity distributions are desired for a wind farm. One of the major causes is the huge computation load that cannot be accomplished in time for a large area. In this study, a method for rapid wind field reconstruction is developed that can provide refined spatial resolution. The method first generates a large number of numerical wind fields using computational fluid dynamics, and extracts the basis vectors of dramatically reduced dimensions by means of proper orthogonal decomposition. With the basis vectors, a wind field can be rapidly reconstructed in an inverse process based on limited measurement data by the sensors. A procedure is proposed to optimize the solution process, which effectively leads to optimal sensor placement. Both simulations and experiments are carried out to evaluate the methods. The results are compared and good agreements are observed. [ABSTRACT FROM AUTHOR]

Short-term wind forecasting is important in updating wind electricity trading strategies, facility protection and more effective operation control. Physical based models, particularly those using computational fluid dynamics (CFD), are able to provide ever more detailed wind speed data. However, such methods involve handling a huge amount of CFD data, which is prohibitively time consuming for a short-term wind forecast in real situations. To solve this problem, Singular Value Decomposition (SVD) and Principal Component Analysis (PCA) algorithms are applied in this study to reduce the dimensions of wind speed data and the proposed method is applied to reconstruct the wind field. Wind fields have successfully been reconstructed with good accuracy for the wind direction angles ranging from 0° to 90°. This method is validated by experimental data from a wind tunnel experiment. The accuracy of the proposed reconstruction algorithm increases with the sampling rate of the measurement and the locations of the sensors do not significantly affect the accuracy of the results. Gaussian noise introduced into the input signal does not significantly deteriorate the reconstruction quality. Results show that the proposed method can adequately be used to reconstruct the wind field for the models tested with a high degree of confidence. [ABSTRACT FROM AUTHOR]

Dual-Doppler lidar is a powerful remote sensing technique that can accurately measure horizontal wind speeds and enable the reconstruction of two-dimensional wind fields based on measurements from two separate lidars. Previous research has provided a framework of dual-Doppler algorithms for processing both radar and lidar measurements, but their application to wake measurements has not been addressed in detail yet. The objective of this paper is to reconstruct two-dimensional wind fields of wind turbine wakes and assess the performance of dual-Doppler lidar scanning strategies, using the newly developed Multiple-Lidar Wind Field Evaluation Algorithm (MuLiWEA). This processes non-synchronous dual-Doppler lidar measurements and solves the horizontal wind field with a set of linear equations, also considering the mass continuity equation. MuLiWEA was applied on simulated measurements of a simulated wind turbine wake, with two typical dual-Doppler lidar measurement scenarios. The results showed inaccuracies caused by the inhomogeneous spatial distribution of the measurements in all directions, related to the ground-based scanning of a wind field at wind turbine hub height. Additionally, MuLiWEA was applied on a real dual-Doppler lidar measurement scenario in the German offshore wind farm “alpha ventus”. It was concluded that the performance of both simulated and real lidar measurement scenarios in combination with MuLiWEA is promising. Although the accuracy of the reconstructed wind fields is compromised by the practical limitations of an offshore dual-Doppler lidar measurement setup, the performance shows sufficient accuracy to serve as a basis for 10 min average steady wake model validation. [ABSTRACT FROM AUTHOR]

Dual-Doppler lidar is a powerful remote sensing technique that can accurately measure horizontal wind speeds and enable the reconstruction of two-dimensional wind fields based on measurements from two separate lidars. Previous research has provided a framework of dual-Doppler algorithms for processing both radar and lidar measurements, but their application to wake measurements has not been addressed in detail yet. The objective of this paper is to reconstruct two-dimensional wind fields of wind turbine wakes and assess the performance of dual-Doppler lidar scanning strategies, using the newly developed Multiple-Lidar Wind Field Evaluation Algorithm (MuLiWEA). This processes non-synchronous dual-Doppler lidar measurements and solves the horizontal wind field with a set of linear equations, also considering the mass continuity equation. MuLiWEA was applied on simulated measurements of a simulated wind turbine wake, with two typical dual-Doppler lidar measurement scenarios. The results showed inaccuracies caused by the inhomogeneous spatial distribution of the measurements in all directions, related to the ground-based scanning of a wind field at wind turbine hub height. Additionally, MuLiWEA was applied on a real dual-Doppler lidar measurement scenario in the German offshore wind farm “alpha ventus”. It was concluded that the performance of both simulated and real lidar measurement scenarios in combination with MuLiWEA is promising. Although the accuracy of the reconstructed wind fields is compromised by the practical limitations of an offshore dual-Doppler lidar measurement setup, the performance shows sufficient accuracy to serve as a basis for 10 min average steady wake model validation.

We investigate the use of spatial interpolation methods for reconstructing the horizontal near-surface wind field given a sparse set of measurements. In particular, random Fourier features is compared with a set of benchmark methods including kriging and inverse distance weighting. Random Fourier features is a linear model β ( x ) = ∑ k = 1 K β k   e i ω k x approximating the velocity field, with randomly sampled frequencies ω k and amplitudes β k trained to minimize a loss function. We include a physically motivated divergence penalty | ∇ ⋅ β ( x ) | 2 , as well as a penalty on the Sobolev norm of β . We derive a bound on the generalization error and a sampling density that minimizes the bound. We then devise an adaptive Metropolis-Hastings algorithm for sampling the frequencies of the optimal distribution. In our experiments, our random Fourier features model outperforms the benchmark models., (© 2021 The Authors.)