Method for retrieving particulate matter concentration from lidar data based on random forest algorithm

Abstract

The present application relates to the technical field of environmental monitoring, and particularly relates to a method for retrieving particulate matter concentration based on laser radar data using a random forest algorithm. The method comprises: collecting atmospheric backscatter signals using a particulate matter laser radar, and synchronously collecting surface particulate matter concentration data corresponding to a geographical location and time to construct a data set; after pre-processing the data of the data set, dividing the data set into a training set, a validation set and a test set; constructing a random forest model, training and validating the random forest model using the training set and the validation set to obtain a trained model; inputting the test set into the trained model to obtain particulate matter concentration. The present application can better utilize high-precision laser radar data, improve the utilization efficiency and retrieval accuracy of the data, and effectively extract key features such as the depolarization ratio and the extinction coefficient from the laser radar data, thereby providing a high-quality data basis for subsequent retrieval and prediction.

Description

Technical Field

[0001] This invention relates to the field of environmental monitoring technology, and in particular to a method for retrieving particulate matter concentration from lidar data based on a random forest algorithm. Background Technology

[0002] With the rapid pace of industrialization and urbanization, atmospheric particulate matter pollution has become increasingly severe, making PM10 a key parameter of concern for residents and governments. Traditional ground-based monitoring provides relatively accurate results, but its high cost and limited data volume make it difficult to reflect the distribution of particulate matter over a large area, and its low data update frequency fails to meet the needs of real-time monitoring. Lidar technology, due to its high spatial resolution and real-time monitoring capabilities, has been widely used for monitoring atmospheric particulate matter concentrations. In recent years, lidar technology has demonstrated enormous potential in atmospheric particulate matter concentration monitoring due to its high spatial resolution and real-time monitoring capabilities. Lidar emits laser pulses and receives their backscattered signals to obtain physical quantities such as the extinction coefficient and depolarization degree of atmospheric particulate matter, thereby retrieving the spatiotemporal distribution characteristics of particulate matter. However, despite the significant advantages of lidar technology, some technical challenges remain in practical applications, particularly the accuracy of particulate matter concentration retrieval.

[0003] Traditional algorithms for retrieving particulate matter concentrations, while providing a certain level of accuracy under ideal conditions, suffer a significant drop in accuracy in complex atmospheric environments, particularly during winter when particulate matter pollution requires close monitoring. Meteorological conditions such as temperature, relative humidity, and wind speed significantly influence the relationship between extinction coefficients and particulate matter concentrations. Although partial corrections can be made using multiple linear regression models, these models have limited effectiveness and cannot completely eliminate the interference of meteorological factors. Particularly in winter foggy conditions, the extinction coefficient increases significantly, leading to substantial deviations in lidar retrieval results. Fog increases atmospheric water vapor content, affecting the propagation and scattering characteristics of laser signals, thus distorting the retrieval results. Inaccurate particulate matter concentration retrieval not only affects the reliability of monitoring results but also limits the application scope of high-precision lidar data. Due to inaccurate retrieval results, a large amount of high-precision lidar data cannot be effectively utilized, wasting valuable monitoring resources. Environmental protection departments and research institutions rely on accurate particulate matter concentration data for environmental management and scientific research; inaccurate retrieval leads to inaccurate decision support information, affecting policy formulation and implementation effectiveness. Furthermore, accurate particulate matter concentration data is crucial for assessing public health risks. Inaccurate inversion can affect the accuracy of health risk assessments, thereby impacting the development and implementation of public health measures.

[0004] In recent years, artificial intelligence (AI) technology has been widely applied in fields such as weather forecasting, achieving remarkable results. These successful cases demonstrate AI's powerful capabilities in processing complex data and recognizing patterns. Therefore, how to combine high-precision lidar detection data with advanced AI algorithms to develop a method that can adapt to complex meteorological environments and achieve high-precision and high-reliability inversion of atmospheric particulate matter concentration is a pressing technical problem to be solved in the field of environmental monitoring. Summary of the Invention

[0005] Therefore, the purpose of this invention is to provide a method for retrieving particulate matter concentration from lidar data based on the random forest algorithm, so as to improve the accuracy and efficiency of the retrieval.

[0006] To achieve the above objectives, the present invention adopts the following technical solution:

[0007] This invention first provides a method for retrieving particulate matter concentration from lidar data based on the random forest algorithm, which includes the following steps:

[0008] Atmospheric echo signals were collected using particulate matter lidar, and surface particulate matter concentration data at corresponding geographical locations and times were collected simultaneously to construct a dataset;

[0009] After preprocessing, the dataset is divided into a training set, a validation set, and a test set.

[0010] Construct a random forest model, and use the training set and the validation set to train and validate the random forest model to obtain the trained model;

[0011] The test set is input into the trained model to obtain the particulate matter concentration.

[0012] As a further improvement to the above scheme, the preprocessing includes: calculating the signal-to-noise ratio of the atmospheric echo signal and removing outliers, then performing convolution sliding denoising and normalization; using the Fernald method to invert the normalized atmospheric echo signal to obtain the extinction coefficient of the aerosol, and calculating the depolarization ratio based on the vertical and horizontal components of the atmospheric echo signal; performing spatiotemporal matching of the extinction coefficient, depolarization ratio, and surface particulate matter concentration data of the aerosol, and removing outliers and records of rainfall and snowfall periods.

[0013] As a further improvement to the above scheme, the calculation of the signal-to-noise ratio of the atmospheric echo signal and the removal of outliers include:

[0014] The signal-to-noise ratio of the atmospheric echo signal is calculated using the following formula:

[0015]

[0016] In the formula, This represents the atmospheric echo signal value after removing the background signal. p i This represents the atmospheric echo signal value at the corresponding location. This represents the average value of the background signal, where m is the starting point for calculating the background baseline and n is the ending point of the background baseline.

[0017] Remove all atmospheric echo signals from the data after the first altitude SNR falls below the signal-to-noise ratio threshold.

[0018] As a further improvement to the above scheme, the convolution sliding denoising uses a 3×11 convolution window, and the convolution formula is:

[0019]

[0020] Where: y(p) represents the atmospheric echo signal value at spatial index p after denoising; x represents the atmospheric echo signal value after removing outliers; h(k) represents the convolution kernel; L represents the length of the convolution window; and k represents the local index of the element inside the convolution kernel.

[0021] As a further improvement to the above scheme, the normalization formula is:

[0022]

[0023] In the formula, x1 represents the atmospheric echo signal value after convolution sliding denoising, μ represents the mean value of the atmospheric echo signal value after convolution sliding denoising, and σ represents the standard deviation of the atmospheric echo signal value after convolution sliding denoising.

[0024] As a further improvement to the above scheme, the inversion calculation of the normalized atmospheric echo signal using the Fernald method to obtain the extinction coefficient includes:

[0025] The extinction coefficient of atmospheric molecules at the target altitude R is obtained based on the standard atmospheric model. Backscattering coefficient ;

[0026] The extinction coefficient of aerosol particles at target height R is calculated using the back integral form of the Fernald equation. Backscattering coefficient :

[0027]

[0028]

[0029] In the formula, Extinction coefficient representing aerosol particles at target height R Extinction coefficient of atmospheric molecules at target altitude R The sum of The backscattering coefficient of aerosol particles at target height R Backscattering coefficient of atmospheric molecules at target altitude R sum;

[0030] Define the extinction backscattering ratio S of an aerosol. a Extinction backscattering ratio S m They are respectively:

[0031]

[0032]

[0033] In the formula: S a S m All are constants. ;

[0034] Extinction coefficient of aerosol at target height R As shown below:

[0035]

[0036] Reference calibration height The above aerosol extinction coefficients As shown below:

[0037]

[0038] In the formula: r is the integral variable in the definite integral process, representing the intermediate distance between the target height R and the reference calibration height Rc; P(R) represents the extinction coefficient of atmospheric molecules at altitude r; P(R) represents the lidar echo signal at a distance R from the radar; exp(·) is the natural exponential function, R c This represents the reference calibration height.

[0039] As a further improvement to the above scheme, the formula for calculating the depolarization ratio is:

[0040]

[0041] In the formula: This represents the depolarization ratio at a distance z from the radar. This represents the vertical component of the atmospheric echo signal received by the radar. The horizontal component of the atmospheric echo signal. This is the polarization gain calibration constant for the radar system.

[0042] As a further improvement to the above scheme, the random forest model consists of a preset number of decision trees, which are trained in the following manner:

[0043] The training set is randomly resampled with replacement to generate a training subset;

[0044] When splitting at each node of the decision tree, a preset number of feature subsets are randomly selected from all features, and the optimal splitting feature and the best splitting point are found in the feature subsets with the minimum mean square error as the evaluation criterion.

[0045] The training subset is assigned to child nodes, and the splitting process is recursively executed until a preset stopping condition is met, thereby constructing a single decision tree.

[0046] Compared with the prior art, the present invention has the following beneficial effects:

[0047] This invention enables better utilization of high-precision lidar data, improving data utilization efficiency and inversion accuracy. Through improved signal processing techniques, this invention can effectively extract key features from lidar data, such as depolarization ratio and extinction coefficient, thus providing a high-quality data foundation for subsequent inversion prediction. Regarding outliers and dataset partitioning, the selected lidar data, PM10 concentration, and related environmental meteorological parameters are first inspected and deleted to remove outliers. Then, the inspected data undergoes preprocessing, including data normalization and spatiotemporal matching, to ensure data consistency and reliability.

[0048] This invention leverages the advantages of the random forest algorithm in handling nonlinear relationships, combined with the high precision of LiDAR data, to construct a particulate matter concentration inversion model. Specifically, by introducing the random forest algorithm, a subset of features is randomly selected from the original features for training, increasing model diversity and reducing the risk of overfitting. Simultaneously, a bootstrap sampling method is used to construct a training set, with each decision tree built based on the new training set, further improving the model's robustness and generalization ability. During the prediction process, the prediction results of each decision tree are integrated, typically using an average value to obtain the final predicted particulate matter concentration.

[0049] This invention combines depolarization bit and extinction coefficient characteristics with a random forest algorithm to better invert particulate matter concentration, especially under low visibility conditions such as heavy fog in winter. This method not only maintains high accuracy under complex weather conditions but also significantly improves the performance of lidar under these conditions. Efficient time-series data prediction is achieved through a lightweight model, significantly reducing computational resource consumption and costs.

[0050] This invention achieves efficient time-series data prediction using a lightweight model under limited computational resources, significantly reducing computational resource consumption and costs. By combining the random forest algorithm with the high-precision characteristics of lidar data, this invention not only improves the accuracy of particulate matter concentration retrieval but also enhances the model's practicality and robustness. These improvements make this invention widely applicable in environmental monitoring and pollution control, providing a new solution for atmospheric particulate matter monitoring. Compared with existing technologies, the method of this invention can more accurately retrieve particulate matter concentration, improving the real-time performance and accuracy of monitoring. It is suitable for urban environmental monitoring, air quality forecasting, and other fields, effectively improving the accuracy and efficiency of particulate matter concentration retrieval. Attached Figure Description

[0051] Figure 1 A flowchart of a method for retrieving PM10 concentration from lidar data using a random forest algorithm provided in an embodiment of the present invention;

[0052] Figure 2 This is a graph showing the prediction results of the random forest model constructed in this embodiment of the invention. Detailed Implementation

[0053] To facilitate understanding of the present invention, a more comprehensive description will be given below with reference to specific embodiments. However, the present invention can be implemented in many different forms and is not limited to the embodiments described herein. Rather, these embodiments are provided to provide a more thorough and complete understanding of the disclosure of the present invention.

[0054] Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention pertains. The terminology used herein in the description of the invention is for the purpose of describing particular embodiments only and is not intended to be limiting of the invention.

[0055] This embodiment proposes a method for retrieving PM10 concentration from lidar data using a random forest algorithm, which mainly includes the following four steps S1-S4.

[0056] S1. Use particulate matter lidar to collect atmospheric echo signals and simultaneously collect surface particulate matter concentration data at corresponding geographical locations and times to construct a dataset.

[0057] Data under different meteorological conditions (such as winter and spring) are classified and recorded to improve the model's generalization ability and adaptability.

[0058] S2. After preprocessing the dataset, it is divided into training set, validation set and test set.

[0059] Preprocessing includes:

[0060] (1) Calculate the signal-to-noise ratio of the atmospheric echo signal and remove outliers, then perform convolution sliding denoising and normalization;

[0061] The signal-to-noise ratio of the atmospheric echo signal is calculated using the following formula:

[0062]

[0063] In the formula, This represents the atmospheric echo signal value after removing the background signal. p i This represents the atmospheric echo signal value at the corresponding location. The value represents the average value of the background signal, m is the starting point for calculating the background baseline (m=3500 in this embodiment), and n is the ending point of the background baseline (n=4000 in this embodiment).

[0064] All atmospheric echo signals after the first altitude SNR falls below the signal-to-noise ratio threshold (3 in this embodiment) are removed from the data. Outliers in the data are identified and eliminated through statistical analysis. Outliers may be caused by equipment failure, environmental interference, or other external factors; removing these outliers can improve the quality and reliability of the data.

[0065] The convolution sliding noise reduction uses a 3×11 convolution window, and the convolution formula is:

[0066]

[0067] Where: y(p) represents the atmospheric echo signal value at spatial index p after denoising; x represents the atmospheric echo signal value after removing outliers; h(k) represents the convolution kernel; L represents the length of the convolution window; and k represents the local index of the element inside the convolution kernel.

[0068] To eliminate the impact of dimensional differences on subsequent analysis, data normalization is performed to transform data with different dimensions and scales to the same dimension and scale range. This invention uses the Z-Score normalization method, and the normalization formula is as follows:

[0069]

[0070] In the formula, x1 represents the atmospheric echo signal value after convolutional sliding denoising, μ represents the mean of the atmospheric echo signal value after convolutional sliding denoising, and σ represents the standard deviation of the atmospheric echo signal value after convolutional sliding denoising. Data normalization can improve the efficiency and accuracy of model training and ensure that the weights of each feature are reasonably allocated in the model.

[0071] (2) The extinction coefficient of the aerosol was obtained by inverting the denoised atmospheric echo signal using the Fernald method, and the depolarization ratio was calculated based on the vertical and horizontal components of the signal.

[0072] The formula for calculating the depolarization ratio is as follows:

[0073]

[0074] In the formula: This represents the depolarization ratio at a distance z from the radar. This represents the vertical component of the atmospheric echo signal received by the radar. The horizontal component of the atmospheric echo signal. This is the polarization gain calibration constant for the radar system.

[0075] The extinction coefficient of aerosols was obtained by inverting the normalized atmospheric echo signal using the Fernald method, including:

[0076] The extinction coefficient of atmospheric molecules at altitude R was obtained based on the American Standard Atmospheric Model. Backscattering coefficient ;

[0077] The extinction coefficient of aerosol particles at target height R is calculated using the back integral form of the Fernald equation. Backscattering coefficient :

[0078]

[0079]

[0080] In the formula, Extinction coefficient representing aerosol particles at target height R Extinction coefficient of atmospheric molecules at target altitude R The sum of The backscattering coefficient of aerosol particles at target height R Backscattering coefficient of atmospheric molecules at target altitude R sum;

[0081] Define the extinction backscattering ratio S of an aerosol. a Extinction backscattering ratio S m They are respectively:

[0082]

[0083]

[0084] In the formula: S aThe extinction backscattering ratio (i.e., radar ratio) of the aerosol is a preset empirical constant based on the main aerosol types in the local area, and is taken as 50 sr in this embodiment; S m It is a constant. ;

[0085] Because the Fernald method for inverting atmospheric aerosol particles requires prior acquisition of a reference calibration height R. c The extinction coefficient or backscattering coefficient of aerosols is typically chosen to be close to the altitude of a clean atmosphere without aerosols. Through differentiation, taking the natural logarithm, and integration of the lidar equations, calculations are performed from the reference calibration altitude. Solve for different heights continuously downwards. Extinction coefficient of aerosol at the location As shown below:

[0086]

[0087] Reference calibration height The above aerosol extinction coefficients As shown below:

[0088]

[0089] In the formula, r is the integral variable in the definite integral process, representing the intermediate distance between the target height R and the reference calibration height Rc; P(R) represents the extinction coefficient of atmospheric molecules at altitude r; P(R) represents the lidar echo signal at a distance R from the radar; exp(·) is the natural exponential function, R c This represents the reference calibration distance.

[0090] (3) The extinction coefficient, depolarization ratio and surface particulate matter concentration data of aerosols were spatiotemporally matched, and outliers and records of rainfall and snowfall periods were removed.

[0091] By comparing timestamps and geographic altitudes, the consistency of lidar data and particulate matter concentration monitoring data in time and space is ensured. Rainfall and snowfall data, as well as data that do not meet time or spatial matching requirements, are discarded to ensure the accuracy of subsequent analysis.

[0092] S3. Construct a random forest model, and use the training set and validation set to train and validate the random forest model to obtain the trained model.

[0093] Taking winter as an example, we define winter as the period from December of the current year to February of the following year, and randomly divide the winter data into training set, validation set and test set in a ratio of 70:20:10.

[0094] Assume the training samples are Where i is the sample index (1≤i≤Q); for the i-th sample, its feature vector is X. i = [ ],in Representing the extinction coefficient and depolarization ratio, respectively, y i and Represent the actual and predicted values ​​of particulate matter concentration, respectively; assuming the decision tree model is... .

[0095] The training process uses the extinction coefficient and depolarization ratio of aerosols as inputs and the concentration of collected particulate matter as output. The training process is as follows:

[0096] (1) Construct a random forest model consisting of M decision trees;

[0097] (2) Using a random sampling method with replacement (Bootstrap), Q samples are drawn from the original training set D each time to form a training subset, which is used to train a decision tree. Since it is sampling with replacement, about 36.8% of the samples in the original training set are not drawn into this training subset. These undrawn samples constitute the out-of-bag (OOB) data of the decision tree.

[0098] (3) When splitting at each node of the decision tree, since the input feature dimension of this model is two-dimensional (i.e., extinction coefficient and depolarization ratio), the algorithm evaluates and divides these two features to find the best splitting feature and the best splitting point.

[0099] (4) Repeat steps (2) to (3) above for a total of M times to complete the construction of M decision trees;

[0100] (5) Calculate the out-of-bag data error: For any specific sample in the original training set, find all decision trees (i.e., the set of out-of-bag trees corresponding to the sample) that were not extracted during the training process; input the sample into all the corresponding out-of-bag trees for prediction, calculate the arithmetic mean of the prediction results of all out-of-bag trees as the out-of-bag prediction value of the sample; calculate the mean square error (MSE) between the actual particulate matter concentration of the sample and the out-of-bag prediction value, and sum up the errors of all samples to obtain the out-of-bag data error of the overall model.

[0101] (6) The importance of feature w can be calculated using the out-of-bag (OOB) data errors obtained twice: The OOB importance ranking method is used. First, the original OOB error E1 is calculated; then, the order of a certain feature w in the out-of-bag data is randomly shuffled, and the OOB error E2 is recalculated. Feature importance = E2 - E1. The greater the increase in error, the more important the feature is for predicting particulate matter concentration.

[0102] (7) The model is tuned based on the evaluation results of the training set. The algorithm model is tuned by adjusting parameters such as the number of decision trees, maximum depth, and minimum number of leaf nodes. Grid search combined with K-fold cross-validation is used. By traversing the combination of parameters such as the number of decision trees, maximum depth, and minimum number of leaf nodes, the optimal hyperparameter combination is selected with the goal of minimizing the mean squared error (MSE) on the validation set, and the trained model is obtained.

[0103] S4. Input the test set into the trained model to obtain the predicted particulate matter concentration.

[0104] The test set data is input into the trained model, and the model outputs standardized prediction values. The predicted value is then destandardized using the following formula:

[0105]

[0106] In the formula, This represents the final predicted physical particulate matter concentration. and These represent the mean and standard deviation of the true values ​​of surface particulate matter concentration in the training set, respectively.

[0107] Error metrics and correlation coefficients are introduced to evaluate the prediction results. These include the root mean square error (RMSE) and the Pearson correlation coefficient. The calculation formulas are as follows:

[0108]

[0109]

[0110] In the formula, V is the total number of samples in the test set. This represents the true particulate matter concentration of the v-th test sample. For the corresponding predicted particulate matter concentration, and These represent the actual average concentration and the predicted average concentration, respectively.

[0111] Uncertainty analysis is performed on the prediction results to enhance their reliability. Specifically, this involves using the independent prediction results of M decision trees in a random forest for the same test sample. ( ), calculate its standard deviation As an indicator of the uncertainty of this forecast:

[0112]

[0113] In the formula, The smaller the value, the higher the predictive consistency of the decision trees in the forest, and the stronger the reliability of the inverted particulate matter concentration.

[0114] The technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0115] The embodiments described above are merely illustrative of several implementations of the present invention, and while the descriptions are relatively specific and detailed, they should not be construed as limiting the scope of the invention patent. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of the present invention, and these all fall within the protection scope of the present invention. Therefore, the protection scope of this invention patent should be determined by the appended claims.

Claims

1. A method for retrieving particulate matter concentration from lidar data based on the random forest algorithm, characterized in that, It includes the following steps: Atmospheric echo signals were collected using particulate matter lidar, and surface particulate matter concentration data at corresponding geographical locations and times were collected simultaneously to construct a dataset; After preprocessing, the dataset is divided into a training set, a validation set, and a test set. Construct a random forest model, and use the training set and the validation set to train and validate the random forest model to obtain the trained model; The test set is input into the trained model to obtain the particulate matter concentration.

2. The method for retrieving particulate matter concentration from lidar data based on the random forest algorithm according to claim 1, characterized in that, The preprocessing includes: calculating the signal-to-noise ratio of the atmospheric echo signal and removing outliers, followed by convolution sliding denoising and normalization; using the Fernald method to invert the normalized atmospheric echo signal to obtain the extinction coefficient of the aerosol, and calculating the depolarization ratio based on the vertical and horizontal components of the atmospheric echo signal; and performing spatiotemporal matching of the extinction coefficient, depolarization ratio, and surface particulate matter concentration data of the aerosol, removing outliers and records from periods of rainfall and snowfall.

3. The method for retrieving particulate matter concentration from lidar data based on the random forest algorithm according to claim 2, characterized in that, The calculation of the signal-to-noise ratio of the atmospheric echo signal and the removal of outliers include: The signal-to-noise ratio of the atmospheric echo signal is calculated using the following formula: In the formula, This represents the atmospheric echo signal value after removing the background signal. p i This represents the atmospheric echo signal value at the corresponding location. This represents the average value of the background signal, where m is the starting point for calculating the background baseline and n is the ending point of the background baseline. Remove all atmospheric echo signals from the data after the first altitude SNR falls below the signal-to-noise ratio threshold.

4. The method for retrieving particulate matter concentration from lidar data based on the random forest algorithm according to claim 2, characterized in that, The convolution sliding denoising uses a 3×11 convolution window, and the convolution formula is: Where: y(p) represents the atmospheric echo signal value at spatial index p after denoising; x represents the atmospheric echo signal value after removing outliers; h(k) represents the convolution kernel; L represents the length of the convolution window; and k represents the local index of the element inside the convolution kernel.

5. The method for retrieving particulate matter concentration from lidar data based on the random forest algorithm according to claim 2, characterized in that, The normalization formula is: In the formula, x1 represents the atmospheric echo signal value after convolution sliding denoising, μ represents the mean value of the atmospheric echo signal value after convolution sliding denoising, and σ represents the standard deviation of the atmospheric echo signal value after convolution sliding denoising.

6. The method for retrieving particulate matter concentration from lidar data based on the random forest algorithm according to claim 2, characterized in that, The extinction coefficient is obtained by inverting the normalized atmospheric echo signal using the Fernald method, including: The extinction coefficient of atmospheric molecules at the target altitude R is obtained based on the standard atmospheric model. Backscattering coefficient ; The extinction coefficient of aerosol particles at target height R is calculated using the back integral form of the Fernald equation. Backscattering coefficient : In the formula, Extinction coefficient representing aerosol particles at target height R Extinction coefficient of atmospheric molecules at target altitude R The sum of The backscattering coefficient of aerosol particles at target height R Backscattering coefficient of atmospheric molecules at target altitude R sum; Define the extinction backscattering ratio S of an aerosol. a Extinction backscattering ratio S m They are respectively: In the formula: S a S m All are constants. ; Extinction coefficient of aerosol at target height R As shown below: Reference calibration height The above aerosol extinction coefficients As shown below: In the formula, r is the integral variable in the definite integral process, representing the intermediate distance between the target height R and the reference calibration height Rc; P(R) represents the extinction coefficient of atmospheric molecules at altitude r; P(R) represents the lidar echo signal at a distance R from the radar; exp(·) is the natural exponential function, R c This represents the reference calibration height.

7. The method for retrieving particulate matter concentration from lidar data based on the random forest algorithm according to claim 2, characterized in that, The formula for calculating the depolarization ratio is: In the formula: This represents the depolarization ratio at a distance z from the radar. This represents the vertical component of the atmospheric echo signal received by the radar. The horizontal component of the atmospheric echo signal. This is the polarization gain calibration constant for the radar system.

8. The method for retrieving particulate matter concentration from lidar data based on the random forest algorithm according to claim 1, characterized in that, The random forest model consists of a preset number of decision trees, which are trained in the following manner: The training set is randomly resampled with replacement to generate a training subset; When splitting at each node of the decision tree, a preset number of feature subsets are randomly selected from all features, and the optimal splitting feature and the best splitting point are found in the feature subsets with the minimum mean square error as the evaluation criterion. The training subset is assigned to child nodes, and the splitting process is recursively executed until a preset stopping condition is met, thereby constructing a single decision tree.

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