Open Access
Add to BibSonomy
Abstract
Lidar is an effective remote sensing method to obtain the vertical distribution of aerosols, and how to select the aerosol extinction-backscattering ratio (AE-BR) during the inversion process is a key step to guarantee the accuracy of the lidar inversion of aerosol optical thickness (AOD) and aerosol extinction coefficient profile (AECP). In this paper, an inversion algorithm for AOD and AECP based on a genetic BP (GA-BP) neural network is proposed. Simultaneous measurements are carried out using CE318 sun photometer and lidar, and the mapping relationship between the lidar echo signal and AOD is established based on the genetic BP (GA-BP) neural network method, which achieves the accurate inversion of AOD with an absolute error mean value of 0.0156. Based on the AOD output from the GA-BP neural network, the real-time best AE- BR to improve the inversion accuracy of AECP. Finally, practical tests show that the method achieves accurate inversion of AOD, determines the range of AE-BR from 20-50sr, realizes real-time dynamic correction of AECP, and has strong generalization ability and applicability in practical situations.
© 2024 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Fine detection of the vertical distribution of atmospheric aerosols, which directly affect the balance of the Earth's atmospheric system by absorbing and scattering solar radiation, is of great importance in climate change studies [1,2]. At present, there are various remote sensing methods to detect and characterize the vertical distribution of aerosols, and the remote sensing detection of aerosol optical properties can be subdivided into passive remote sensing detection and active remote sensing detection [3–5]. Lidar has the advantages of simple setup, high spatial and temporal resolution, and long-term continuous high-precision measurements, and has become an active remote sensing tool to effectively obtain the vertical distribution of aerosols [6]. For example, the European Aerosol Lidar Research Network (EARLINET), the Asian Dust and Aerosol Lidar Observation Network (AD-Net), and the NASA Micropulse Lidar Network (MPLNET) explore the vertical distribution of aerosols through advanced laser remote sensing techniques. Lidar inversion of aerosol extinction coefficients is mostly based on the method proposed by Fernald in 1986. The Fernald lidar equation contains two unknown variables: the backscattering coefficient and aerosol extinction coefficient, if we want to compute the AECP value and AOD from the lidar equation, we have to know the boundary value of aerosol extinction coefficients and the AE-BR with a high degree of accuracy [7,8].AE-BR characterizes the size and absorption capacity of aerosol particles to a certain extent and is closely related to the scale spectral distribution and composition of aerosol particles, with values generally in the range of 10-100sr [9,10]. The aerosol particle properties have a great influence on the AE-BR, and the inversion of the aerosol extinction coefficients will produce a large error if a fixed AE-BR is used in the process of using Fernald's method [11,12]. The AOD, as a measure of the most basic optical properties of the aerosol, is one of the most important parameters describing the extinction properties of the aerosol, which characterizes the attenuation properties of the aerosol to light [13]. Conventional lidar calculation of AOD requires the calculation of the integral of the aerosol extinction coefficient over the vertical path, and if the calculated aerosol extinction coefficient is in error, it will lead to the distortion of the inverted AOD. Pavel and Mollner used lidar scanning to obtain AOD by assuming that the integral of the path of the aerosol extinction coefficient is invariant to the pointing angle of the lidar [14]. He et al. obtained AOD values from lidar signals reflected from the sea surface, but they need to take into account the effect of uncertainty due to reflection patterns at the surface [15]. The sun photometer is a passive remote sensing detection tool for obtaining AOD, and the measured AOD is often used as a calibration value for other instruments [16]. Parameter calibration of lidar can be achieved using AOD measured by the sun photometer [13,17]. If we detach from the sun photometer, the selection of the optimal AE-BR cannot be achieved. From the above analysis, it is clear that it is still challenging to improve the accuracy and efficiency of lidar data retrieval in real time.
To find an inversion method that can improve the accuracy of AOD and AECP, this paper proposes a new method based on the GA-BP neural network to realize lidar AOD inversion and AECP correction. Firstly, the network is trained by the lidar data and the AOD value of the sun photometer, and the mapping relationship between the lidar data and the AOD is established to achieve the accurate inversion of the AOD. Then the optimal AE-BR is selected iteratively by the AOD values output from the BP neural network, and the accuracy of the AECP inversion can be improved by using the real-time dynamic AE-BR.
2. Method principle analysis
The lidar AOD inversion and extinction contour correction method based on the GA-BP neural network mainly contains BP neural network connection structure determination, genetic algorithm optimization of BP neural network thresholds and connection weights, BP neural network training output AOD values, output AOD values for real-time optimal AE-BR selection, and correction of AECP in five parts. The specific process is shown in Fig. 1.
Firstly, the determination of neural network topology is carried out, and the global search ability of the genetic algorithm is used to determine the optimal range of BP neural network weights and thresholds, and then the BP neural network is used to search for the local optimal solution. When the BP neural network training converges slowly or even does not converge, the thresholds and weights of each hidden layer node and output layer node of the BP neural network are used as the input information of the genetic algorithm. Using the selection operator, crossover operator, and variation operator of the genetic algorithm, the optimal solution of the BP neural network was obtained. The neural network was continued to be trained and this step was repeated until the desired AOD error accuracy was achieved [18,19]. The AOD values output from the network are then used for iterative selection of the optimal AE-BR and real-time dynamic correction of the AECP.
2.1 BP neural network structure determination
The underlying structure of BP neural networks consists of nonlinear units that can theoretically approximate any function with strong nonlinear mapping capabilities. This enables BP neural networks to learn and model various complex relationships between inputs and outputs, including nonlinear, highly abstract patterns. The gradient descent law is used to continuously adjust the network weights and thresholds through the forward propagation of the signal and the backpropagation of the error. Minimize the error between the network's output and the desired output. Through repeated iterative training, the network can automatically learn and adjust its parameters, gradually improving the accuracy of the network model output. It consists of input, hidden, and output layers. Define the network in this paper contains ${x_1},{x_2}\ldots ,{x_n}(n = 667)$ as the input variables, which represent the distance squared correction signals of the lidar at different heights; $y$ is the output variable, which represents the AOD output from the network; and ${y_d}$ is the desired output, which represents the AOD measured by the sun photometer, as the target value for network training. Considering the network running time and the accuracy of the training results, the final network hidden layer is set to 8 layers, using the activation function for the Tansig function, the specific structure of the network is shown in Fig. 2. In the first stage, the forward propagation of the signal is processed through the input layer and hidden layer to obtain the actual output of each unit. The output ${\mu _j}$ of the implicit layer is expressed as:
Where f represents the mapping relationship of neurons, which is called the activation function. ${v_{ij}}$ represents the weight of the i-th input variable and the j-th neuron and ${x_i}$ represents the input variable. Where ${\omega _j}$ represents the weight connecting the j-th neuron to the output value y.
Fig. 2. BP network model and AECP correction diagram, the top of the picture shows the topology of the BP neural network, and the bottom shows the selection flow chart of the optimal AE-BR.
Fig. 4. Lidar signal processing result diagram. As shown in Fig. 4(a), The abscissa represents the number of laser radar echo photons, and the ordinate represents the detection height. the green line represents the number of lidar echo photons corrected by the geometric overlap factor, and the red line indicates the signal after noise. The curve of Fig. 4(b) represents the signal of the laser radar from the square correction.
Fig. 5. Schematic diagram of AOD center wavelength conversion of solar photometer. The blue line represents the AOD value at 440nm, the red line represents the AOD value measured at 870nm, and the green line represents the calculated AOD value at 532 nm.
Fig. 6. Fig. 6(a) shows the correlation analysis between the predicted value and the target value in the testing process. Fig. 6(b) shows the correlation analysis between the predicted value and the target value in the training process, with the horizontal coordinates representing the AOD measured by the sun photometer and the vertical coordinates representing the AOD output from the GA-BP neural network.
The second stage is the back-propagation of error, if the output layer is not able to get the desired value, then a layer-by-layer recursive calculation of the error, the difference between the actual output and the desired value, using the error to adjust the weight of each level, the error between the output value and the desired value is expressed as:
The weight change from the hidden layer to the output layer $\Delta {\omega _{ij}}$ is:
The weight change from the input layer to the hidden layer $\Delta {\nu _{ij}}$ is:
Where $\eta$ called learning rate.2.2 Genetic algorithm design
The role of the genetic algorithm is to determine the optimal thresholds and weights for all levels of the network and can make the BP neural network error function value, so the inverse of the error function of the BP neural network is selected as the fitness function of the genetic algorithm [20].
The weights and thresholds between each level of the BP neural network were flattened into a chromosome as input to the genetic algorithm. The parameters of the genetic algorithm were determined using the control variable method with multiple training and testing. The genetic algorithm chooses the roulette selection method as the selection operator, the population size is 50, the number of genetic generations is determined to be 600, the crossover probability is determined to be 0.25, the mutation probability is determined to be 0.001, and the evaluation parameter is 0.01. When the training of the BP neural network is slow to converge or even does not converge, the genetic algorithm is used to optimize the thresholds and the weights of the network, and finally, the network's desired error value is reached. The trained network model can perform an accurate prediction of AOD.
2.3 Basic principle of AOD countermeasures
In 1984, Fernald proposed a method that was based on the laser radar equations against the air-soluble lighting coefficient. Although this model was defective, it is still the most used model [21]. This paper uses the form of inverse integration to calculate the aerosol extinction coefficient profile value ${\alpha _a}(R)$:
The lidar inversion AOD can be expressed as:
Where ${\tau _{lidar}}(\lambda )$ the AOD is obtained by the lidar calculation.Because the central wavelength used in the lidar is 532 nm, it does not correspond to the wavelength of the CE318 Solar Photometer used in the experiment, so the AOD obtained by the solar optical meter is calculated. Angstrom pointed out that AOD can be expressed as two atmospheric turbidity parameters [22]:
Where ${\tau _\textrm{a}}(\lambda )$ represents the AOD measured by the sun photometer. $\beta$ represents the atmospheric turbidity coefficient, and $\alpha$ represents the atmospheric wavelength index. Assuming that ${\lambda _1}$, ${\lambda _2}$ are wavelengths that are not affected by water vapor, then:Based on formulas (10) and (11) if the two central wavelengths and their corresponding AOD values are known, the atmospheric wavelength index $\alpha$ and the atmospheric turbidity index $\beta$ are calculated, which in turn leads to the AOD values for any wavelength range under the same conditions.
2.4 Real-time dynamic solution of optimal AE-BR value
By continuously optimizing the GA-BP neural network model, the error between the AOD value output by it and the AOD value output by the sun photometer is minimized. The optimal AE-BR is found iteratively using the AOD output from the GA-BP neural network as shown in Fig. 2. The range of AE-BR is set to 10-100sr, the initial value of AE-BR is set to 10sr, and the step length of each cycle is set to 5sr. If the result of the difference between the AOD value calculated by the Fernald method and the AOD value output from the BP neural network continues to decrease, the step length is kept unchanged, and if the result of the difference between the AOD calculated by the Fernald and the AOD output from the network compared to the previous time appears to increase, then return to the AE-BR value of the previous iteration, while switching the AE-BR step size to 1sr. The iteration of the above steps is carried out continuously until the difference between the two reaches the minimum and then the iteration process is terminated, the AE-BR value is output at this time, and the AECP value under this AE-BR value is calculated. By this method, the determination of the optimal AE-BR can be carried out dynamically in real time, which makes the inverted AECP value more accurate and real.
3. Experimental results and discussion
3.1 Observation areas and instruments
The data measurement site of this paper is located in Changchun City, Jilin Province, China (43°47′N, 125°22′E), and the data collection was carried out during the daytime from 20 December 2023 to 15 January 2024. The lidar is controlled to work vertically upward, with a distance resolution of 15 m and a time resolution of 3 min. The sun photometer worked in AOTORUN mode to synchronize the AOD measurements. Since aerosols are mostly distributed at high altitudes below 10km, the data collected by the lidar are selected to be below 10km; the solar photometer uses AOD data with a data quality level of Level 1.5 (cloud screening and quality control). A total of 1224 valid data sets were retained after screening and data process matching. Field data collection experiment as shown in Fig. 3.
To fully test the inversion algorithm for AOD using the GA-BP neural network, this study uses a meter-scattering lidar with a polarisation channel for the measurement of aerosol optical properties, and the specific parameters of the lidar are shown in Table 1 below:
Table 1. Lidar parameter table
The solar photometer is a CE318 automatic tracking and scanning photometer manufactured by CIMEL, France, with a total of 8 channels and center wavelengths of 340, 380, 440, 500, 670, 870, 1020, and 1640 nm. The solar radiation data measured by the CE318 can be used to invert and calculate the corresponding wavelengths of the AOD. The solar photometer is calibrated by professional staff once every six months, and the accuracy of the solar photometer can be maintained at a high level, so the AOD measured by the solar photometer can be used as the target value of the training network.
3.2 Experimental data processing
When the lidar system is performing aerosol detection, the density of the near-surface aerosol distribution is large, and it is necessary to correct the geometric overlap factor of the lidar echo data to correctly use it to study AOD. In order to reduce the random effects of subsequent network training due to noise, noise is removed from the lidar echo signal. This paper uses a wavelet denoising method based on soft thresholds to reduce the noise of lidar echo signals and improve the system signal-to-noise ratio [23]. The attenuation rate of laser transmission in the atmosphere is inversely proportional to the square of the detection distance, so distance-squared correction is required for the lidar signal. The signal after lidar signal denoising and distance correction is shown in Fig. 4.
Since the center wavelength used by the lidar is 532 nm, the AOD values measured by the sun photometer need to be corrected according to Eq. (10) and Eq. (11), and the AOD values of 440nm and 870nm of the sun photometer are used to correct the AOD values corresponding to the center wavelength of the lidar of 532 nm. The AOD values corresponding to the center wavelength of the lidar of 532 nm are obtained, as the sun photometer only works during the daytime, which leads to the lack of nighttime data, making the AOD values have no continuity. The AOD results after wavelength correction are shown in Fig. 5.
3.3 Network training and parameter optimization
The lidar distance squared corrected signal and the sun photometer corrected 532 nm AOD value are input into the network for training, to avoid the phenomenon of overfitting and unstable with training in the process of network training, the dataset is randomly disrupted, so that the trained network has a better generalization ability and convergence ability. Constant adjustment and optimization of the network parameters are carried out, and finally, the number of training times is determined to be 1500, the learning rate is 0.001, and the dataset is partitioned using the ratio of 7:2:1, respectively, for the training set, the test set, and the overfitting validation set, to achieve the optimal output AOD value.
The correlation R between the two in the training set reaches 0.9863, and the correlation R between the two in the test set reaches 0.9840. The red and blue lines indicate the regression lines fitted to the training and the test data, respectively, and the degree of fit and correlation between the model's training and the test is high, which achieves the accurate prediction of AOD.
As can be obtained from Fig. 7, the calculation results of AOD using GA-BP neural network and the optical thickness values measured by the sun photometer have an absolute value of error below 0.06, and the mean absolute error and root mean square error are used to evaluate and analyze the prediction of AOD. The average absolute error MAE is only 0.0156, and the root mean square error RMSE is only 0.0214, which indicates that the established model has a higher prediction accuracy for AOD, a better fitting effect, and a lower sensitivity to the occurrence of outliers, and can achieve accurate prediction of AOD.
Fig. 7. Comparison of GA-BP network predicted AOD with sun photometer AOD The purple line indicates the 532 nm AOD measured by the sun photometer, and the red line indicates the AOD predicted by the GA-BP neural network, and the bar graph indicates the error value between AOD BP and AOD SUN.
The diurnal aerosol vertical distribution observation was carried out from 7 January 2024 to 10 January 2024 at noon using lidar and a sun photometer, and 429 sets of valid data (Level 1.5) were extracted from the sun photometer during the test time, which was 137 sets in total for 7 January from 9:13 to 16:03, and 134 sets in total for 8 January from 8:57 to 16:50, respectively. 158 groups, respectively, and a total of 134 groups from 9:22 to 16:01 on 9 January. The lidar measured a total of 1673 groups of data, including 477 groups of data on 7 January, 478 groups of data on 8 January, 477 groups of data on 9 January, and 241 groups of data on 10 January. The inversion of AOD was performed using the trained network model inputting the lidar distance squared correction signal, and the inversion results are shown in Fig. 8:
Fig. 8. The GA-BP neural network continuously observes the AOD, the horizontal axis represents the time in hours, and the vertical axis represents the output AOD value of the GA-BP.
From Fig. 8, The triangles represent the output values of AOD from GA-BP, and the pentagrams represent the AOD values when the sun photometer is operating. The middle bar represents the error value of AOD-BP versus AOD-SUN, and the different colored fills indicate the period when the sun photometer was working on different dates. The mean absolute error (MAE) between the AOD output from the GA-BP neural network and the AOD measured by the solar photometer is only 0.0126, and the trend of the measured AOD is the same. Lidar can still observe and invert the AOD when the sun photometer stops observing. The AOD is more stable in the early morning and night and fluctuates and rises in the morning and midday, which is probably due to the increase of aerosol particle concentration caused by people's work and life, and the heating of the ground by the solar radiation, which leads to the unstable structure of the atmosphere and the formation of turbulence transport, so that the aerosol particles on the ground enter into the atmosphere.
3.4 Real-time dynamic optimal AE-BR
The optimal AE-BR is selected by the AOD value output from the GA-BP neural network, and the data at 11:02 on 7 January 2024 (group 221) is selected. At this time, the AOD output from the sun photometer is 0.1631 and the output from the GA-BP neural network is 0.1639. The following figure demonstrates the AECP values of some nodes in the iterative process of the optimal AE-BR.
From Fig. 9, it is obvious that the AE-BR has a large influence on the inversion of the extinction coefficient to the near-surface, and the corresponding AODs are 0.327, 0.223, 0.151, 0.121, 0.095, and 0.072 when the AE-BR is AEBR_50, AEBR_40, AEBR_30, AEBR_25, AEBR_20, and AEBR_15, respectively, The final iteration of the optimal AE-BR solved by the algorithm is 32sr, at which time the AOD obtained by integrating the AECP using the Fernald method is 0.1637, which is negligible with the error value of AOD measured by the sun photometer of only 0.0006. By the method proposed in this paper, the determination of the optimal AE-BR can be achieved and the realism of the inversion of the AECP values can be enhanced.
Fig. 9. AECP output from Fernald's method at different AE-BRs, with horizontal coordinates indicating AECP values and vertical coordinates indicating heights.
The 1673 sets of data from 7 January 2024 to 12:00 on 10 January 2024 were used for the selection of the optimal AE-BR, and the real-time dynamic optimal AE-BR selection was carried out by inputting the AOD values output from the GA-BP network into the model, and the output of the optimal AE-BR values is shown in Fig. 10. At this time, the real-time AE-BR is inputted, and the pseudo-color map drawn from the 1673 sets of AECP values inverted using the Fernald method is shown in Fig. 11.
Fig. 10. The optimal AE-BR is calculated based on the AOD output by the GA-BP neural network. The abscissa represents time in hours, and the ordinate represents the optimal AE-BR.
Fig. 11. The calculated optimal AE-BR is put into Fernald to calculate. 1673 groups of AECP are obtained. The abscissa represents time, the unit is hours, and the ordinate represents altitude. Colors are used to represent the results of the AECP calculation.
From Fig. 10, it can be seen that AE-BR is a real-time dynamically changing parameter, roughly ranging between 20-50sr, and the average value of AE-BR calculated using the method of this paper is 31.4sr. In this paper, the accurate inversion of AOD is achieved by using the GA-BP neural network to determine the optimal value of dynamically changing AE-BR and achieve a more accurate and real AECP value.
4. Conclusions
In this paper, we propose a model for AOD prediction using a GA-BP neural network, and at the same time, we are able to determine the optimal AE-BR for each set of AECP in real-time, which improves the accuracy of lidar inversion of AECP. The average absolute error of AOD inversion by the GA-BP neural network is only 0.0156, the root-mean-square error is 0.0214, and the experimental results of the practical experiments show that the method can obtain AOD accuracy with comparable accuracy to the sun photometer. The robustness and accuracy of AOD inversion using lidar data are improved. At the same time, the AOD values from the BP neural network inversion can be used to correct the AE-BR in the inversion process of the Fernald method in real time, which can obtain more realistic AECP data. This method provides an effective way to observe the vertical distribution of urban aerosols continuously and accurately.
Funding
Jilin Provincial Key Research and Development Plan Project.
Acknowledgments
We thank the Department of Science and Technology of Jilin Province for providing financial support for this study and establishing the Jilin Province Key R&D Program Project (20180201002SF), and we are very grateful to the anonymous reviewers for their comments.
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
References
1. C. W. Zhang, J. Wu, W. X. Fan, et al., “A Method of Inversing Dynamic Aerosol Extinction-to-Backscattering Ratio Based on Lidar Echo Signal and Ground Aerosol Extinction Coefficient or Aerosol Optical Depth,” IEEE Trans. Geosci. Remote Sensing 60, 1–15 (2022). [CrossRef]
2. S. Zhang, Z. W. Huang, M. S. Li, et al., “Vertical Structure of Dust Aerosols Observed by a Ground-Based Raman Lidar with Polarization Capabilities in the Center of the Taklimakan Desert,” Remote Sens. 14(10), 2461 (2022). [CrossRef]
3. Q. Q. Dong, Z. W. Huang, W. R. Li, et al., “Polarization Lidar Measurements of Dust Optical Properties at the Junction of the Taklimakan Desert–Tibetan Plateau,” Remote Sens. 14(3), 558 (2022). [CrossRef]
4. Z. W. Huang, X. T. Shen, S. H. Tang, et al., “Simulated depolarization ratios for dust and smoke at laser wavelengths: implications for lidar application,” Opt. Express 31(6), 10541–10553 (2023). [CrossRef]
5. Y. Bian, W. Xu, Y. Hu, et al., “Method to retrieve aerosol extinction profiles and aerosol scattering phase functions with a modified CCD laser atmospheric detection system,” Opt. Express 28(5), 6631–6647 (2020). [CrossRef]
6. G. Fiocco and L. D. Smullin, “Detection of Scattering Layers in the Upper Atmosphere (60-140 km) by Optical Radar,” Nature 199(4900), 1275–1276 (1963). [CrossRef]
7. J. D. Klett, “Lidar inversion with variable backscatter extinction ratios,” Appl. Opt. 24(11), 1638–1643 (1985). [CrossRef]
8. H. G. Hughes, J. A. Ferguson, and D. H. Stephens, “Sensitivity of a lidar inversion algorithm to parameters relating atmospheric backscatter and extinction,” Appl. Opt. 24(11), 1609–1613 (1985). [CrossRef]
9. Y. Sasano, E. V. Browell, and S. Ismail, “Error caused by using a constant extinction/backscattering ratio in the lidar solution,” Appl. Opt. 24(22), 3929–3932 (1985). [CrossRef]
10. F. G. Fernald, B. M. Herman, and J. A. Reagan, “Determination of Aerosol Height Distributions by Lidar,” J. Appl. Meteor. 11(3), 482–489 (1972). [CrossRef]
11. N. W. Cao, S. P. Yang, S. J. Cao, et al., “Accuracy calculation for lidar ratio and aerosol size distribution by dual-wavelength lidar,” Appl. Phys. A 125(9), 590 (2019). [CrossRef]
12. T. Q. Liu, Q. S. He, Y. H. Chen, et al., “Long-term variation in aerosol lidar ratio in Shanghai based on Raman lidar measurements,” Atmos. Chem. Phys. 21(7), 5377–5391 (2021). [CrossRef]
13. Q. Q. Xu, X. L. Chen, S. B. Yang, et al., “Spatiotemporal relationship between Himawari-8 hourly columnar aerosol optical depth (AOD) and ground-level PM2.5 mass concentration in mainland China,” Sci. Total Environ. 765, 144241 (2021). [CrossRef]
14. I. I. Pavel and A. K. Mollner, “Aerosol Optical Thickness Measurement with Elevation-Scanning Lidar,” J Atmos Ocean Technol 32(7), 1364–1371 (2015). [CrossRef]
15. M. He, Y. X. Hu, J. P. Huang, et al., “Aerosol optical depth under “clear” sky conditions derived from sea surface reflection of lidar signals,” Opt. Express 24(26), A1618–A1614 (2016). [CrossRef]
16. H. Zhao, J. D. Mao, C. Y. Zhou, et al., “A method of determining multi-wavelength lidar ratios combining aerodynamic particle sizer spectrometer and sun-photometer,” J. Quant. Spectrosc. Radiat. Transfer 217, 224–228 (2018). [CrossRef]
17. H. X. Li, J. H. Chang, F. Xu, et al., “An RBF neural network approach for retrieving atmospheric extinction coefficients based on lidar measurements,” Appl. Phys. B 124(9), 184 (2018). [CrossRef]
18. S. X. Li, “Evaluation Model of Innovation and Entrepreneurship Ability of Colleges and Universities Based on Improved BP Neural Network,” Comput. Intell. Neurosci 2022, 1–11 (2022). [CrossRef]
19. W. Y. Feng and F. Feng, “Research on the Multimodal Digital Teaching Quality Data Evaluation Model Based on Fuzzy BP Neural Network,” Comput. Intell. Neurosci 2022, 1–12 (2022). [CrossRef]
20. Z. Wang, J. Wu, H. Wang, et al., “Optimal Underwater Acoustic Warfare Strategy Based on a Three-Layer GA-BP Neural Network,” Sensors 22(24), 9701 (2022). [CrossRef]
21. F. G. Fernald, “Analysis of atmospheric lidar observations: some comments,” Appl. Opt. 23(5), 652–653 (1984). [CrossRef]
22. A. Angström, “The parameters of atmospheric turbidity,” Tellus 16(1), 64–75 (1964). [CrossRef]
23. Z. R. Zhou, D. X. Hua, Y. F. Wang, et al., “Improvement of the signal to noise ratio of Lidar echo signal based on wavelet de-noising technique,” Opt Lasers Eng 51(8), 961–966 (2013). [CrossRef]
