the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 09 Mar 2023
Coupling physics-informed neuronal networks with 3D scanning pulsed Doppler lidar
Abstract. Physics-Informed neuronal networks (PINN) is a research field where a neuronal network is trained to solve an incorporated partial differential equation that describes some physical phenomenon. This work describes the coupling of the Navier Stokes (NS) equation with data from a 3D scanning pulsed Doppler lidar to reconstruct blanked sectors with radial velocities in a plan position indicator (PPI) scan. For the reconstruction, only the adjacent line of sight (LOS) measurements were used as input data for the neuronal network. Almost one year of collected lidar data were used to analyze the wind field sector reconstruction algorithm. The results show that the reconstruction of 35° azimuth sectors feature mean square errors of less than 1 m2/s2 and absolute errors of less than 2 m/s in 99 % and 98 %, respectively, of all cases. The runtime is about 0.1 minutes on average with commercial off-the-shelve CPU hardware. The reconstructed wind field of radial velocities can be used either to fill in sectors where the lidar is blocked e.g. by an obstacle or to extend the maximum operational range by measuring only a few lines-of-sight with increased pulse accumulation time. An example of a range extension PPI provided here demonstrates that the range can be extended to 25 km while maintaining the total recording time of 30 s as for the reference PPI scan featuring only a maximum range of approximately 12 km.
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Interactive discussion
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RC1: 'Comment on amt-2023-39', Jincheng Zhang, 17 Mar 2023
Comments on the manuscript entitled “Coupling physics-informed neuronal networks with 3D scanning pulsed Doppler lidar”
In this work, the authors focus on reconstructing the wind field based on physics-informed neural networks and lidar measurements. The employed approach follows the recently published work (i.e. Zhang & Zhao 2021) which focused on reconstructing and forecasting wind field in front of a wind turbine based on turbine-mounted short-range wind lidar. Different from the published work, this paper investigates the problem of reconstructing wind fields using long-range wind Lidar in the context of wind monitoring at an airport. The study includes mainly two user scenarios: the reconstruction of empty PPI section and the extension of the maximum operational range, which are both very interesting and of great applied value. The results presented in the paper show that successful reconstruction of the wind field can be achieved for both empty PPI section reconstruction and range extension. It is thus useful for providing further insight into the development of wind monitoring technology combining physics and data. However, there are still some major issues that need to be addressed before I can suggest it to be accepted for publication.
(1) In the paper, the results are mainly presented by the example cases and the overall error metrics. More results are needed to quantify the performance of wind field reconstruction more clearly. For example, it is suggested to add figures/plots in a similar style as Figure 2 but showing the error distributions for the example cases and more importantly for the mean value of the reconstruction errors averaged over all the cases covering the whole year. In addition, figures/plots similar to Figure 5 and Figure 6 but showing the error distributions averaged over many cases need to be added, so that the reconstruction accuracy and range extension performance can be clearly quantified statistically. If the ground truth (i.e. the lidar measurements) is not available for the extended area in the scenario of range extension (as shown in Figure 5), the error distribution for the smaller area is at least needed.
(2) From the reviewer’s understanding, the characteristic velocity (i.e. 10 m/s) is set according to the typical wind speed of the measurement site. However, why is the characteristic length L set as 200 m? It seems that the default choice for L should be something around several kilometers if there are no other typical length scales for the considered problem. Such a length scale will make sure that the neural network output is ~1 which is beneficial for the NN training.
(3) For each case, the PINN is trained from scratch as described in the paper. The author also discussed several ways to achieve real-time performance such as using more computational power. It is suggested to try out transfer learning approaches / pre-training of the PINNs to accelerate the training process.
(4) The paper focuses solely on wind field reconstruction. Is wind forecasting also of interest for the investigated scenarios? If so, it will be interesting to see the forecasting performance as well.
(5) The paper mentioned, in a lot of places, the 3D scanning lidar. However, it seems that the PINN model, the NS equations, and the reconstructed flow fields in this paper, are all 2D in space. Is the lidar data used for training the model actually 3D or 2D? Please clarify.
(6) In the Discussion part, the sentence “the NS equations are solved numerically based on some assumptions and simplifications” seems to indicate that the PINN approach is somehow more accurate than CFD approaches in terms of solving the NS equations, which is very much debatable. Instead, it is suggested to focus more on the PINN’s advantage in handling inverse problems.
(7) There are also some minor editorial issues, and the manuscript needs further proofreading. For example, ‘neuronal networks’ should be ‘neural network’; ‘feature’ in line 11 should be ‘features’; the sentence in Line 25 (i.e. ‘Neuronal networks represent a new capability to approximate a possible solution of these equations by training a neuronal network) needs to be reorganized; ‘rangegate’ should be ‘range gates’ in Line 88.
Overall, the paper is very interesting and the method is sound. Please carefully consider the above suggestions for improvements.
Citation: https://doi.org/10.5194/amt-2023-39-RC1 -
AC1: 'Reply on RC1', Christian Schiefer, 23 Mar 2023
We thank Dr. Zhang for his thorough review of our contribution and we are happy to respond to his comments
(1) We interpret your comment in the following manner: we should show the error distribution spatially resolved to make a correlation between error and range, is that correct? If so, we think that this is a good point that we would like to add in further plots to show this. Fig5 only shows a use case of how to use the algorithm to reconstruct a full PPI with extended range. As Mr. Zhang remarks, for the extended range we do not have a reference measurement to quantify the error. This could only be achieved with an additional source (sensor). Since the "smaller range PPI" is only a juxtaposition of individual sector reconstructions, where the error analysis is already shown over the entire measurement campaign data set in Fig. 3 and the new plot mentioned above, this information would be redundant. We will, however, add a note that independent validation of the extended range will be the subject of future work. For example, this could be achieved with a collocated Doppler weather radar in light rain, since the radar easily measures to the ranges required. Furthermore, the use case example in Fig6 is intended to illustrate the problem that the number of LOS must be chosen very carefully so that all dangerous wind phenomena are captured. We also emphasize that these are only 2 use cases and are not necessarily representative.
(2) We have estimated our characteristic length L according to the assumptions of meteorological scale analysis. We choose the L according to the Rosby number which has to be significantly larger than one for non geostrophical wind (boundary layer phenomena) for which the Coriolis forces can be neglected. Additionally, we did some trial and error analysis over several lengths in order to optimize our choice based on the results. The best results in terms of accuracy have been achieved for L=200m. We will consider this in an additional sentence.
(3) Thank you for providing a further possibility to accelerate the calculation time. If you like a could consider this in an additional sentence.
(4) Yes, Wind forecasting using PINN is also very interesting but out of scope of this paper. We will consider this for future work on the subject.
(5) We mentioned that we use the NS equations in polar coordinates (i.e. 2D), but the lidar is a remote sensing device that is equipped with an azimuth-elevation scanner and performs volume scans. Of these, only the lowest elevation angle of 1.5° is used here. NS in 3D should be definitely used for larger elevation angles and we will add a comment on this.
(6). We will remove the suggestive part of this sentence. It is not the scope of this contribution to make any comparison with classical CFD.
(7) Thank you for pointing that out.
Citation: https://doi.org/10.5194/amt-2023-39-AC1
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AC1: 'Reply on RC1', Christian Schiefer, 23 Mar 2023
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RC2: 'Comment on amt-2023-39', Anonymous Referee #2, 20 Mar 2023
The comment was uploaded in the form of a supplement: https://amt.copernicus.org/preprints/amt-2023-39/amt-2023-39-RC2-supplement.pdf
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AC2: 'Reply on RC2', Christian Schiefer, 25 Mar 2023
Dear reviewer, thank you for taking the time to provide your input. Please find our detailed responses (in blue) to your comments in the attachment.
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EC1: 'Reply on AC2: Considering comparing with a simple interpolation.', Jorge Luis Chau, 30 Mar 2023
Regarding the comment number (6), i.e., "Multiple times while reading the paper, I wanted to ask how does this PINN method compare to simply interpolating between adjacent lidar profiles? Does PINN give a meaningfully better result than simple interpolation?" could you address this point with a simple interpolation scheme between lidar measurements? I understand that different interpolation schemes could be investigated, but using at least one can help answering the reviewer's question without too much effort. After all one of the aims of the work is to "fill gaps" between measurements.
Citation: https://doi.org/10.5194/amt-2023-39-EC1 -
AC3: 'Reply on EC1', Christian Schiefer, 24 Apr 2023
Dear Mr Chau, thank you for your comment. We will consider it in the final version of the manuscript.
Citation: https://doi.org/10.5194/amt-2023-39-AC3
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AC3: 'Reply on EC1', Christian Schiefer, 24 Apr 2023
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EC1: 'Reply on AC2: Considering comparing with a simple interpolation.', Jorge Luis Chau, 30 Mar 2023
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AC2: 'Reply on RC2', Christian Schiefer, 25 Mar 2023
Interactive discussion
Status: closed
-
RC1: 'Comment on amt-2023-39', Jincheng Zhang, 17 Mar 2023
Comments on the manuscript entitled “Coupling physics-informed neuronal networks with 3D scanning pulsed Doppler lidar”
In this work, the authors focus on reconstructing the wind field based on physics-informed neural networks and lidar measurements. The employed approach follows the recently published work (i.e. Zhang & Zhao 2021) which focused on reconstructing and forecasting wind field in front of a wind turbine based on turbine-mounted short-range wind lidar. Different from the published work, this paper investigates the problem of reconstructing wind fields using long-range wind Lidar in the context of wind monitoring at an airport. The study includes mainly two user scenarios: the reconstruction of empty PPI section and the extension of the maximum operational range, which are both very interesting and of great applied value. The results presented in the paper show that successful reconstruction of the wind field can be achieved for both empty PPI section reconstruction and range extension. It is thus useful for providing further insight into the development of wind monitoring technology combining physics and data. However, there are still some major issues that need to be addressed before I can suggest it to be accepted for publication.
(1) In the paper, the results are mainly presented by the example cases and the overall error metrics. More results are needed to quantify the performance of wind field reconstruction more clearly. For example, it is suggested to add figures/plots in a similar style as Figure 2 but showing the error distributions for the example cases and more importantly for the mean value of the reconstruction errors averaged over all the cases covering the whole year. In addition, figures/plots similar to Figure 5 and Figure 6 but showing the error distributions averaged over many cases need to be added, so that the reconstruction accuracy and range extension performance can be clearly quantified statistically. If the ground truth (i.e. the lidar measurements) is not available for the extended area in the scenario of range extension (as shown in Figure 5), the error distribution for the smaller area is at least needed.
(2) From the reviewer’s understanding, the characteristic velocity (i.e. 10 m/s) is set according to the typical wind speed of the measurement site. However, why is the characteristic length L set as 200 m? It seems that the default choice for L should be something around several kilometers if there are no other typical length scales for the considered problem. Such a length scale will make sure that the neural network output is ~1 which is beneficial for the NN training.
(3) For each case, the PINN is trained from scratch as described in the paper. The author also discussed several ways to achieve real-time performance such as using more computational power. It is suggested to try out transfer learning approaches / pre-training of the PINNs to accelerate the training process.
(4) The paper focuses solely on wind field reconstruction. Is wind forecasting also of interest for the investigated scenarios? If so, it will be interesting to see the forecasting performance as well.
(5) The paper mentioned, in a lot of places, the 3D scanning lidar. However, it seems that the PINN model, the NS equations, and the reconstructed flow fields in this paper, are all 2D in space. Is the lidar data used for training the model actually 3D or 2D? Please clarify.
(6) In the Discussion part, the sentence “the NS equations are solved numerically based on some assumptions and simplifications” seems to indicate that the PINN approach is somehow more accurate than CFD approaches in terms of solving the NS equations, which is very much debatable. Instead, it is suggested to focus more on the PINN’s advantage in handling inverse problems.
(7) There are also some minor editorial issues, and the manuscript needs further proofreading. For example, ‘neuronal networks’ should be ‘neural network’; ‘feature’ in line 11 should be ‘features’; the sentence in Line 25 (i.e. ‘Neuronal networks represent a new capability to approximate a possible solution of these equations by training a neuronal network) needs to be reorganized; ‘rangegate’ should be ‘range gates’ in Line 88.
Overall, the paper is very interesting and the method is sound. Please carefully consider the above suggestions for improvements.
Citation: https://doi.org/10.5194/amt-2023-39-RC1 -
AC1: 'Reply on RC1', Christian Schiefer, 23 Mar 2023
We thank Dr. Zhang for his thorough review of our contribution and we are happy to respond to his comments
(1) We interpret your comment in the following manner: we should show the error distribution spatially resolved to make a correlation between error and range, is that correct? If so, we think that this is a good point that we would like to add in further plots to show this. Fig5 only shows a use case of how to use the algorithm to reconstruct a full PPI with extended range. As Mr. Zhang remarks, for the extended range we do not have a reference measurement to quantify the error. This could only be achieved with an additional source (sensor). Since the "smaller range PPI" is only a juxtaposition of individual sector reconstructions, where the error analysis is already shown over the entire measurement campaign data set in Fig. 3 and the new plot mentioned above, this information would be redundant. We will, however, add a note that independent validation of the extended range will be the subject of future work. For example, this could be achieved with a collocated Doppler weather radar in light rain, since the radar easily measures to the ranges required. Furthermore, the use case example in Fig6 is intended to illustrate the problem that the number of LOS must be chosen very carefully so that all dangerous wind phenomena are captured. We also emphasize that these are only 2 use cases and are not necessarily representative.
(2) We have estimated our characteristic length L according to the assumptions of meteorological scale analysis. We choose the L according to the Rosby number which has to be significantly larger than one for non geostrophical wind (boundary layer phenomena) for which the Coriolis forces can be neglected. Additionally, we did some trial and error analysis over several lengths in order to optimize our choice based on the results. The best results in terms of accuracy have been achieved for L=200m. We will consider this in an additional sentence.
(3) Thank you for providing a further possibility to accelerate the calculation time. If you like a could consider this in an additional sentence.
(4) Yes, Wind forecasting using PINN is also very interesting but out of scope of this paper. We will consider this for future work on the subject.
(5) We mentioned that we use the NS equations in polar coordinates (i.e. 2D), but the lidar is a remote sensing device that is equipped with an azimuth-elevation scanner and performs volume scans. Of these, only the lowest elevation angle of 1.5° is used here. NS in 3D should be definitely used for larger elevation angles and we will add a comment on this.
(6). We will remove the suggestive part of this sentence. It is not the scope of this contribution to make any comparison with classical CFD.
(7) Thank you for pointing that out.
Citation: https://doi.org/10.5194/amt-2023-39-AC1
-
AC1: 'Reply on RC1', Christian Schiefer, 23 Mar 2023
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RC2: 'Comment on amt-2023-39', Anonymous Referee #2, 20 Mar 2023
The comment was uploaded in the form of a supplement: https://amt.copernicus.org/preprints/amt-2023-39/amt-2023-39-RC2-supplement.pdf
-
AC2: 'Reply on RC2', Christian Schiefer, 25 Mar 2023
Dear reviewer, thank you for taking the time to provide your input. Please find our detailed responses (in blue) to your comments in the attachment.
-
EC1: 'Reply on AC2: Considering comparing with a simple interpolation.', Jorge Luis Chau, 30 Mar 2023
Regarding the comment number (6), i.e., "Multiple times while reading the paper, I wanted to ask how does this PINN method compare to simply interpolating between adjacent lidar profiles? Does PINN give a meaningfully better result than simple interpolation?" could you address this point with a simple interpolation scheme between lidar measurements? I understand that different interpolation schemes could be investigated, but using at least one can help answering the reviewer's question without too much effort. After all one of the aims of the work is to "fill gaps" between measurements.
Citation: https://doi.org/10.5194/amt-2023-39-EC1 -
AC3: 'Reply on EC1', Christian Schiefer, 24 Apr 2023
Dear Mr Chau, thank you for your comment. We will consider it in the final version of the manuscript.
Citation: https://doi.org/10.5194/amt-2023-39-AC3
-
AC3: 'Reply on EC1', Christian Schiefer, 24 Apr 2023
-
EC1: 'Reply on AC2: Considering comparing with a simple interpolation.', Jorge Luis Chau, 30 Mar 2023
-
AC2: 'Reply on RC2', Christian Schiefer, 25 Mar 2023
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