Algorithm for inverting distance resolution CO2 concentration from laser radar column integral signal

Abstract

The invention provides an algorithm for inverting distance resolution CO2 concentration from laser radar column integral signals. The algorithm comprises the following steps: acquiring echo signals corresponding to a plurality of groups of detection laser with distance resolution emitted to target atmosphere by a laser radar; the detection laser comprises first laser and second laser, and the absorption coefficient of the first laser to carbon dioxide is higher than that of the second laser to carbon dioxide; de-noising processing is carried out on the echo signal to obtain a de-noised signal; inverting an atmospheric carbon dioxide column concentration profile distributed along with the distance based on the de-noised signal; performing smooth fitting processing on the atmospheric carbon dioxide column concentration profile to obtain an optimized column concentration profile; and performing differential operation on the optimized column concentration profile to determine the distance-resolved concentration of the atmospheric carbon dioxide. The detection method can give consideration to both high range resolution and long detection range.

Description

Technical Field

[0001] This invention relates to the field of lidar detection technology, and specifically to an algorithm for retrieving CO2 concentration from lidar column integral signals to distinguish distance. Background Technology

[0002] Detecting atmospheric carbon dioxide concentration at a distance using differential absorption lidar is a conventional method. To obtain a fine profile of carbon dioxide variation with distance, range-resolved detection (RR-DIAL) technology is typically employed. However, to achieve long-range detection, this technology usually requires selecting weak absorption lines with small absorption cross-sections to prevent excessively rapid attenuation of laser energy during transmission. However, weak absorption results in minimal difference between the echo signals from the online and offline wavelengths, making the differential signal extremely weak. In subsequent data processing, retrieving the range-resolved concentration typically requires differentiating the signal. Differentiation, essentially a high-pass filter, significantly amplifies random noise during the measurement process. This forces existing RR-DIAL systems, under weak signal conditions, to often sacrifice range resolution drastically (e.g., reducing it to over 300 meters), making it impossible to discern the true fine structures within the atmosphere. Summary of the Invention

[0003] The purpose of this invention is to overcome the above-mentioned defects or problems in the prior art and to provide an algorithm for retrieving CO2 concentration from the linear integral signal of a lidar laser. This detection method can achieve both high distance resolution and long detection range.

[0004] To achieve the above objectives, the present invention adopts the following technical solution: Technical Solution 1: An algorithm for retrieving range-resolved CO2 concentration from lidar column integral signals, comprising: acquiring echo signals corresponding to multiple sets of range-resolved detection lasers emitted by the lidar towards the target atmosphere; the detection lasers include a first laser and a second laser, wherein the absorption coefficient of the first laser for carbon dioxide is higher than that of the second laser for carbon dioxide; denoising the echo signals to obtain a denoised signal; retrieving a range-distributed atmospheric carbon dioxide column concentration profile based on the denoised signal; performing smooth fitting on the atmospheric carbon dioxide column concentration profile to obtain an optimized column concentration profile; and performing differential operations on the optimized column concentration profile to determine the range-resolved concentration of atmospheric carbon dioxide. Technical Solution 2 based on Technical Solution 1: The denoising process is based on the wavelet transform principle, which includes: performing wavelet decomposition on the echo signal to obtain wavelet coefficients of different scales; calculating a threshold according to a preset threshold determination rule, and adjusting the wavelet coefficients using a threshold processing function to suppress the coefficients corresponding to noise; and performing wavelet reconstruction using the adjusted wavelet coefficients to obtain the denoised signal. Technical Solution 3 based on Technical Solution 2: The wavelet basis functions are selected from the Daubechies series, Symlets series, or Coiflets series; the threshold determination rule is selected from the general threshold method, Stein unbiased risk estimation method, or threshold estimation method based on median absolute deviation; the threshold processing function is selected from the soft threshold function, hard threshold function, or improved function thereof.

[0005] Technical Solution 4 based on Technical Solution 3: The wavelet decomposition has 5 decomposition layers; the noise estimation in the threshold determination rule adopts a single-level noise estimation mode, and the noise standard deviation is estimated using the first-level decomposition coefficients. Technical Solution Five, based on Technical Solution One: The inversion of the atmospheric carbon dioxide column concentration profile is based on the difference in absorption coefficients caused by the calculated gases. Achieve the difference in absorption coefficients Calculated using the following formula: ; In this context, the subscript "on" indicates the first laser, and the subscript "off" indicates the second laser. It is the number of photons received; It is the number of photons emitted; Laser wavenumber, in cm. -1 ; The distance is in meters (m). It is a system constant; The telescope area is expressed in meters (m²). 2 ; Distance Geometric overlap factor at the location; The Mie volume backscattering coefficient is expressed in m. -1 ; It is a transmittance function; This is the aerosol extinction coefficient, in m. -1 ; The molecular extinction coefficient is expressed as... ,in The absorption coefficient of carbon dioxide is denoted as . The extinction coefficient of other molecules in the target atmosphere; Indicates the emission point of the distance detection laser. Place; Distance Optical depth at that location. Technical Solution Six Based on Technical Solution Five: The Atmospheric Carbon Dioxide Concentration Profile Based on the difference in absorption coefficients It is determined using the following formula: ; in, and These represent the number densities of carbon dioxide and water molecules, respectively. Indicates the absorption cross section; Atmospheric pressure, measured in Pa; The number of moles of gas; T is the ambient temperature, in K. Here, is the Boltzmann constant, with a value of 1.380649 × 10⁻⁶. -23 J.K. -1 . Technical Solution Seven based on Technical Solution One: In the detection laser, the first laser and the second laser have the same absorption coefficient for H2O in the target atmosphere, and the number density of carbon dioxide molecules is: . Technical solution eight based on technical solution one: The smoothing fitting process is performed using a filter based on the principle of local polynomial least squares fitting. Technical Solution Nine based on Technical Solution Eight: The filter is a Savitzky-Golay filter; during the smooth fitting process, the sliding window width of the filter is dynamically adjusted according to the signal-to-noise ratio characteristics of the column concentration profile as a function of distance: a first window width is used in the near-distance region where the signal-to-noise ratio is higher than a preset value, and a second window width is used in the far-distance region where the signal-to-noise ratio is lower than a preset value, wherein the second window width is greater than the first window width. Technical Solution Ten based on Technical Solution One: The distance-resolved concentration of atmospheric carbon dioxide Calculated using the following formula: . As can be seen from the above description of the present invention, compared with the prior art, the present invention has the following beneficial effects: This invention provides an algorithm for retrieving range-resolved CO2 concentration from lidar column integral signals. Compared to conventional detection techniques, this method offers advantages in both long-range detection and high spatial resolution. Unlike traditional methods that directly solve for local concentration in the differential domain, this method utilizes denoised echo signals to first derive the atmospheric column concentration profile distributed with distance based on the differential absorption principle. Atmospheric column concentration, as a path integral, represents the cumulative effect from the detection starting point to various distance points. Leveraging the inherent low-pass filtering characteristics of integral operations, this step initially suppresses random noise during the construction of the intermediate data model. Compared to directly calculated local differential components, the column concentration profile exhibits a higher signal-to-noise ratio and robustness. Furthermore, this invention performs smoothing fitting on the obtained atmospheric column concentration profile. Since the processing object is a relatively robust integral curve, rather than a noisy instantaneous differential signal, smoothing fitting can effectively eliminate residual random disturbances while accurately preserving the macroscopic trend and inflection point characteristics of column concentration variation with distance. Subsequently, differential operations are performed on the optimized column concentration profile to resolve the range-resolved concentration. Since the continuity and smoothness of the input data are guaranteed in the integral domain, the noise amplification effect caused by differential operations is significantly suppressed. Through the aforementioned progressive processing chain of "denoising-integral inversion-integral domain smoothing-differential analysis," this invention avoids the error divergence problem caused by directly performing differential operations in the low signal-to-noise ratio stage. This allows the system to perform long-distance detection using weak absorption spectral lines without sacrificing a huge distance for signal averaging, thereby achieving high-precision range resolution over a long detection range and clearly resolving the fine stratification structure of carbon dioxide concentration in the atmosphere.

[0006] This invention employs a wavelet transform-based denoising scheme. Compared to traditional Fourier transform or low-pass filtering, this scheme utilizes the multi-resolution characteristics of wavelets in the time-frequency domain to separate the effective components of the signal from random noise at different scales. While removing high-frequency noise, this scheme avoids the signal edge blurring problem caused by traditional filtering, effectively preserving the transient characteristics of atmospheric echo signals reflecting concentration changes or stratification structures, thus providing high-fidelity basic data for subsequent inversion.

[0007] This invention limits the number of decomposition layers to 5 and adopts a single-level noise estimation mode based on the coefficients of the first layer. It uses the first-layer decomposition coefficients, which contain most of the high-frequency noise, to estimate the standard deviation, which can more accurately reflect the current background noise level. It avoids the problem of the threshold setting being too high (loss of effective signal) or too low (residual noise) due to noise estimation deviation, and ensures the stability of the denoising effect under different signal-to-noise ratio conditions.

[0008] This invention limits the absorption coefficients of the first and second lasers in the detection laser to the same level for H2O in the target atmosphere. When processing and analyzing the echo signal, the influence of H2O in the target atmosphere on the detection results can be ignored, reducing the computational difficulty and improving the detection accuracy.

[0009] This invention employs a smoothing process based on the principle of local polynomial least squares fitting. Compared to conventional moving average filtering, this scheme can better preserve the peak height, width, and higher-order moment characteristics of the curve when denoising column concentration profiles by utilizing the fitting ability of polynomials to local trends in the data.

[0010] This invention applies a Savitzky-Golay filter and introduces an adaptive window width configuration strategy. In the near-range high signal-to-noise ratio region, a small window is used to maximize the preservation of high-frequency spatial details and achieve high range resolution. In the far-range low signal-to-noise ratio region, it automatically switches to a large window, which enhances the ability to suppress divergent noise and effectively expands the usable detection range. Attached Figure Description

[0011] To more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings used in the following description of the embodiments are briefly introduced. Obviously, the drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0012] Figure 1 This is a schematic flowchart of the atmospheric carbon dioxide range-resolved concentration detection method based on lidar according to an embodiment of the present invention. Figure 2 This is a schematic diagram showing the comparison and relative error of lidar echo signals before and after wavelet denoising processing in an embodiment of the present invention; Figure 3 This is a schematic diagram of the spatiotemporal distribution of atmospheric carbon dioxide column concentration after smoothing and fitting in an embodiment of the present invention; Figure 4 This is a schematic diagram of the spatiotemporal distribution of atmospheric carbon dioxide distance-resolved concentration obtained in the final inversion embodiment of the present invention; Figure 5 This is a schematic diagram comparing the inversion results of the detection method provided in this embodiment of the invention, the inversion results of the traditional inversion method, and the measured results of the ground in-situ instrument. Detailed Implementation

[0013] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are preferred embodiments of the present invention and should not be considered as excluding other embodiments. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without creative effort are within the scope of protection of the present invention.

[0014] Unless otherwise expressly defined, the use of terms such as "first," "second," or "third" in the claims, description, and accompanying drawings of this invention is for distinguishing different objects and not for describing a specific order.

[0015] Unless otherwise expressly defined, in the claims, description, and accompanying drawings of this invention, the use of directional terms such as "center," "lateral," "longitudinal," "horizontal," "vertical," "top," "bottom," "inner," "outer," "upper," "lower," "front," "rear," "left," "right," "clockwise," and "counterclockwise" to indicate orientation or positional relationships is based on the orientation and positional relationships shown in the accompanying drawings and is only for the convenience of describing the invention and simplifying the description, and is not intended to indicate or imply that the device or element referred to must have a specific orientation or be constructed and operated in a specific orientation, and therefore should not be construed as limiting the specific scope of protection of this invention.

[0016] Unless otherwise expressly defined, the terms "fixed connection" or "fixed connection" used in the claims, description and drawings of this invention should be interpreted broadly to refer to any connection in which there is no displacement or relative rotation relationship between the two parties, including non-removable fixed connection, detachable fixed connection, integral connection and fixed connection by other means or components.

[0017] In the claims, description and accompanying drawings of this invention, the terms "comprising," "having," and variations thereof are used to mean "including but not limited to."

[0018] Example This invention relates to an algorithm for retrieving range-resolved CO2 concentration from a lidar column integral signal. This detection method is used to detect the range-resolved concentration of carbon dioxide in the target atmosphere using lidar. The lidar used is a differential absorption lidar, which can simultaneously emit two laser beams to detect the target atmosphere.

[0019] Reference Figure 1 This document illustrates the flowchart of the distance-resolved atmospheric carbon dioxide concentration detection method based on lidar provided in this embodiment. Specifically, the detection method includes the following steps: S100: Acquire the echo signals corresponding to multiple sets of detection lasers with range resolution emitted by the lidar into the target atmosphere; S200: Perform noise reduction processing on the echo signal to obtain a noise-reduced signal; S300: The atmospheric carbon dioxide column concentration profile distributed with distance is retrieved based on the denoised signal; S400: Perform smooth fitting on the atmospheric carbon dioxide column concentration profile to obtain an optimized column concentration profile; S500: Perform differential calculations on the optimized column concentration profile to determine the distance-resolved concentration of atmospheric carbon dioxide.

[0020] In step S100, the detection laser includes a first laser and a second laser, with the first laser having a higher absorption coefficient for carbon dioxide than the second laser. Furthermore, the first and second lasers selected for detection have the same absorption coefficient for H2O in the target atmosphere. During detection, multiple sets of detection lasers are emitted into the target atmosphere via a lidar system, each set having a different detection distance, thereby forming an echo signal with range resolution.

[0021] In step S200, the denoising process is based on the wavelet transform principle, which includes: performing wavelet decomposition on the echo signal to obtain wavelet coefficients at different scales; calculating a threshold according to a preset threshold determination rule, and adjusting the wavelet coefficients using a threshold processing function to suppress coefficients corresponding to noise; and performing wavelet reconstruction using the adjusted wavelet coefficients to obtain the denoised signal. The wavelet basis functions are selected from the Daubechies series, Symlets series, or Coiflets series; the threshold determination rule is selected from the general threshold method, the Stein unbiased risk estimation method, or the threshold estimation method based on the absolute deviation of the median; and the threshold processing function is selected from the soft threshold function, the hard threshold function, or an improved function thereof. The wavelet decomposition has 5 levels; the noise estimation in the threshold determination rule adopts a single-level noise estimation mode, using the first-level decomposition coefficients to estimate the noise standard deviation. Specifically, in this embodiment, in order to preserve the edge and detail features of the signal to the greatest extent possible under strong noise background, the wavelet basis function preferably uses the sym5 wavelet basis from the Symlets series, and the original echo signal is decomposed into 5 levels of wavelets. Regarding threshold selection, an adaptive threshold selection rule (i.e., the rigrsure rule) based on the Stein Unbiased Risk Estimation (SURE) principle is adopted. This rule automatically finds the threshold that minimizes the risk function based on the statistical characteristics of the current signal. Simultaneously, a soft thresholding function is used to shrink the wavelet coefficients. Compared to a hard thresholding function, soft thresholding avoids artifacts (i.e., ringing effects) during signal reconstruction, resulting in a smoother and more natural denoised waveform. Furthermore, for noise estimation, a single-level noise estimation (Sln) mode is employed, utilizing the high-frequency detail coefficients obtained from the first-level decomposition to estimate the standard deviation of the background noise. Through this specific parameter combination, the system effectively separates and suppresses random noise while fully preserving the key information reflecting abrupt changes in atmospheric concentration in the echo signal.

[0022] In step S300, the inversion of the atmospheric carbon dioxide column concentration profile is based on the calculation of the difference in absorption coefficients caused by the gas. Achieve the difference in absorption coefficients Calculated using the following formula: ; In this context, the subscript "on" indicates the first laser, and the subscript "off" indicates the second laser. It is the number of photons received; It is the number of photons emitted; Laser wavenumber, in cm. -1 ; The distance is in meters (m). It is a system constant; The telescope area is expressed in meters (m²).2 ; Distance Geometric overlap factor at the location; The Mie volume backscattering coefficient is expressed in m. -1 ; It is a transmittance function; This is the aerosol extinction coefficient, in m. -1 ; The molecular extinction coefficient is expressed as... ,in The absorption coefficient of carbon dioxide is denoted as . The extinction coefficient of other molecules in the target atmosphere; Indicates the emission point of the distance detection laser. Place; Distance Optical depth at that location.

[0023] Atmospheric carbon dioxide column concentration profile Based on the difference in absorption coefficients It is determined using the following formula: ; in, and These represent the number densities of carbon dioxide and water molecules, respectively. Indicates the absorption cross section; Atmospheric pressure, measured in Pa; The number of moles of gas; T is the ambient temperature, in K. Here, is the Boltzmann constant, with a value of 1.380649 × 10⁻⁶. -23 J.K. -1 .

[0024] Since the first and second lasers in the detection laser have the same absorption coefficient for H2O in the target atmosphere, the number density of carbon dioxide molecules is: Preferably, to minimize the interference of atmospheric water vapor on the carbon dioxide concentration inversion and ensure measurement accuracy, the center wavelength of the first laser (online wavelength) is set to 1572.335 nm, which is located at the strong absorption peak of carbon dioxide; the center wavelength of the second laser (offline wavelength) is set to 1572.45 nm, which is located in the weak absorption region of carbon dioxide. Under this specific wavelength combination, the absorption cross-section of water vapor at the first and second lasers is almost equal, therefore the absorption contribution term of water vapor in the above calculation formula can be ignored. At this time, the measured absorption coefficient difference... The molecular number density of carbon dioxide can be directly simplified in calculations, depending primarily on the absorption contribution of carbon dioxide. Furthermore, the required absorption cross section is calculated... Atmospheric pressure can be obtained by querying the HITRAN database. The ambient temperature T can be obtained in real time by ground weather stations that are paired with lidar, and then substituted into the above formula to accurately invert the atmospheric carbon dioxide column concentration profile distributed with distance.

[0025] In step S400, the smoothing fitting process employs a filter based on the principle of local polynomial least squares fitting. Specifically, the filter is a Savitzky-Golay filter. During the smoothing fitting process, the sliding window width of the filter is dynamically adjusted according to the signal-to-noise ratio (SNR) characteristics of the column concentration profile as a function of distance: a first window width is used in the near-distance region where the SNR is higher than a preset value, and a second window width is used in the far-distance region where the SNR is lower than a preset value, wherein the second window width is greater than the first window width. Specifically, this embodiment uses a Savitzky-Golay filter. Unlike traditional moving average filters, the SG filter performs least squares fitting of low-order polynomials (e.g., second- or third-order polynomials) on the data points within the moving window. This effectively filters out high-frequency random noise while preserving the signal peaks, widths, and higher-order moment characteristics (such as abrupt gradient changes), avoiding over-smoothing or distortion of the true concentration change trend. Furthermore, considering that the lidar echo signal intensity decreases inversely with the square of the detection distance, resulting in a significantly lower SNR at far distances compared to near distances, this process is further optimized. To address this contradiction, the system employs an adaptive strategy based on a signal-to-noise ratio (SNR) threshold: in near-range detection areas with high SNR (e.g., 0-2 km), a smaller sliding window width (i.e., the first window width, such as 5-11 data points) is selected to ensure high range resolution; while in far-range detection areas with low SNR (e.g., beyond 2 km), a larger sliding window width (i.e., the second window width, such as 21-31 data points) is automatically switched to enhance the smoothing effect by increasing the number of fitted points.

[0026] In step S500, the distance-resolved concentration of atmospheric carbon dioxide is... Calculated using the following formula: .

[0027] Specifically, the optimized column concentration profile obtained in step S400 physically represents the average concentration along the entire path from the lidar detection starting point (usually at distance 0) to a distance R. To obtain the local concentration with range resolution (i.e., the specific concentration value at a specific distance), this integral needs to be converted back to a differential component. The above formula calculates the difference between the product of the column concentration and the distance at two adjacent distance points and divides it by the distance interval between the two points, thereby accurately determining the average local concentration within that distance interval. Since the input column concentration profile has undergone wavelet denoising and smoothing fitting processing in the aforementioned steps, effectively suppressing data fluctuations, this differential operation can ultimately stably calculate an atmospheric carbon dioxide distribution profile with high spatial resolution.

[0028] The detection method described in this embodiment offers advantages over conventional detection techniques, combining long-range detection with high spatial resolution. Unlike traditional methods that directly solve for local concentrations in the differential domain, this method utilizes the denoised echo signal to first invert the atmospheric column concentration profile distributed with distance based on the differential absorption principle. Atmospheric column concentration, as a path integral, represents the cumulative effect from the detection starting point to various distance points. Leveraging the inherent low-pass filtering characteristics of integral operations, this step initially suppresses random noise when constructing the intermediate data model. Compared to directly calculated local differential components, the column concentration profile exhibits a higher signal-to-noise ratio and robustness. Furthermore, this embodiment performs smoothing fitting on the obtained atmospheric column concentration profile. Since the processing object is a relatively robust integral curve, rather than a noisy instantaneous differential signal, smoothing fitting can effectively eliminate residual random disturbances while accurately preserving the macroscopic trend and inflection point characteristics of column concentration changes with distance. Subsequently, differential operations are performed on the optimized column concentration profile to resolve the distance-resolved concentration. Since the continuity and smoothness of the input data are guaranteed in the integral domain, the noise amplification effect caused by differential operations is significantly suppressed. Through the aforementioned progressive processing chain of "denoising-integral inversion-integral domain smoothing-differential analysis," this embodiment avoids the error divergence problem caused by directly performing differential operations in the low signal-to-noise ratio stage. This allows the system to perform long-distance detection using weak absorption lines without sacrificing a huge distance for signal averaging, thereby achieving high-precision range resolution over a long detection range and clearly resolving the fine stratification structure of carbon dioxide concentration in the atmosphere.

[0029] This embodiment employs a wavelet transform-based denoising scheme. Compared to traditional Fourier transform or low-pass filtering, this scheme utilizes the multi-resolution characteristics of wavelets in the time-frequency domain to separate the effective components of the signal from random noise at different scales. While removing high-frequency noise, this scheme avoids the signal edge blurring problem caused by traditional filtering, effectively preserving the transient characteristics of atmospheric echo signals reflecting concentration changes or stratification structures, thus providing high-fidelity basic data for subsequent inversion.

[0030] This embodiment limits the number of decomposition layers to 5 and adopts a single-level noise estimation mode based on the first-layer coefficients. It uses the first-layer decomposition coefficients, which contain most of the high-frequency noise, to estimate the standard deviation, which can more accurately reflect the current background noise level. This avoids the problem of the threshold being set too high (loss of effective signal) or too low (residual noise) due to noise estimation deviation, and ensures the stability of the denoising effect under different signal-to-noise ratio conditions.

[0031] In this embodiment, the first and second lasers in the detection laser have the same absorption coefficient for H2O in the target atmosphere. When processing and analyzing the echo signal, the influence of H2O in the target atmosphere on the detection results can be ignored, reducing the calculation difficulty and improving the detection accuracy.

[0032] This embodiment employs a smoothing process based on the principle of local polynomial least squares fitting. Compared to conventional moving average filtering, this scheme can better preserve the peak height, width, and higher-order moment characteristics of the curve when denoising column concentration profiles by utilizing the fitting ability of polynomials to local trends in the data.

[0033] This embodiment applies a Savitzky-Golay filter and introduces an adaptive window width configuration strategy. A small window is used in the near-range high signal-to-noise ratio region to maximize the preservation of high-frequency spatial details and achieve high range resolution. In the far-range low signal-to-noise ratio region, it automatically switches to a large window, which enhances the ability to suppress divergent noise and effectively expands the available detection range.

[0034] The following provides a further explanation of the specific detection process of the detection method provided in this embodiment. In this description, a specific experiment verifies the effectiveness of the above-mentioned detection method. This experiment was conducted from September 5th to 8th, 2025, in a location in Xiamen, involving three consecutive nights of field observation. The observation path pointed southeast, covering an open coastal area.

[0035] In this embodiment, a differential absorption lidar is used to detect the target atmosphere. The emitted detection laser includes an online laser and an offline laser, namely the first laser and the second laser mentioned above. The lidar equations are expressed by the following equations (1) and (2): (1); (2); The meanings of the symbols in equations (1) and (2) have been explained above and will not be repeated here.

[0036] In this embodiment, the wavelength of the first laser is selected as 1572.335 nm, and the wavelength of the second laser is selected as 1572.45 nm. Both laser wavelengths have the same absorption coefficient for H2O in the target atmosphere, therefore the influence of water vapor on the CO2 detection results can be ignored. Furthermore, the differential absorption lidar system acquires raw echo signals with a time resolution of 20 s, a range resolution of 1.5 m, and a detection profile extending to nearly 10 km.

[0037] After receiving the echo signals, both the first and second laser echo signals are denoised. In this embodiment, wavelet transform is used for denoising, which can be implemented using the `wden` function in MATLAB. Specifically, the function is called to perform automatic one-dimensional denoising on the original echo signals of the first and second lasers. In terms of parameter configuration, the sym5 wavelet from the Symlets series is selected as the basis function, and the decomposition level is set to 5 levels to achieve multi-scale decomposition of the signal in the time-frequency domain. The rigrsure rule (based on Stein's unbiased risk estimation) is used as the threshold selection strategy to adaptively determine the optimal threshold based on signal characteristics. A soft thresholding function (parameter 's') is used to shrink the wavelet coefficients to avoid artifacts that may be introduced by hard thresholding. The sln (single-level noise estimation) mode is used, which readjusts the noise standard deviation using the high-frequency detail coefficients from the first-level decomposition. During execution, the algorithm first performs a 5-level wavelet decomposition on the echo signal based on the above parameters to obtain wavelet coefficients at each scale; then, it calculates the wavelet coefficients corresponding to the threshold noise removal or shrinkage based on the SURE principle; finally, it uses the processed coefficients to perform inverse wavelet transform reconstruction, thereby outputting a denoised signal that retains the signal edge features and significantly improves the signal-to-noise ratio.

[0038] Reference Figure 2 This diagram illustrates the comparison and relative error of the lidar echo signals before and after wavelet denoising. As can be seen from the diagram, the signal-to-noise ratio of the echo signal is significantly improved after this denoising process.

[0039] Meanwhile, since the wavelengths of the first and second lasers are very similar, when the emission energies of the online and offline lasers are the same, it can be considered that... , and It is not sensitive to wavelength, therefore it can be obtained from the lidar equation: (3); The absorption optical depth can be obtained according to equation (3). : (4); Therefore, the absorption difference caused by the gas It can be represented as: (5); Difference in absorption coefficient This can be further expressed as the sum of the contributions from carbon dioxide and water: (6).

[0040] Due to the selection of wavelengths for the first and second lasers, the absorption of water in the atmosphere can be ignored, thus yielding equation (7): (7); Therefore, the formula for the atmospheric carbon dioxide column concentration profile is obtained: (8).

[0041] Next, the atmospheric carbon dioxide column concentration profile was smoothed and fitted, as described above in the section on smoothing and fitting. Figure 3 It shows a schematic diagram of the spatiotemporal distribution of atmospheric carbon dioxide column concentration after Savitzky-Golay filtering. It can be seen that the column concentration profile after processing exhibits a continuous and stable distribution characteristic.

[0042] Then, differential calculations were performed on the optimized column concentration profile to resolve the distance-resolved atmospheric carbon dioxide concentration, as shown in equation (9): (9).

[0043] Reference Figure 4 This diagram illustrates the spatiotemporal distribution of the final retrieved atmospheric carbon dioxide distance-resolved concentration in this embodiment. The spatial resolution of the retrieval result is set to 30 m, and the temporal resolution to 5 min. Figure 4 The spatiotemporal distribution results show that atmospheric carbon dioxide concentration exhibits a continuous and clear stratification over three consecutive nights of observation. Specifically, The elevation increases at horizontal distances of approximately 2–4 km and 6–8 km. These enhancements may be related to nearby coastal industrial areas and high-traffic zones, while a stable nighttime boundary layer suppresses vertical mixing, leading to localized emissions buildup. This demonstrates the ability of the method in this embodiment to capture the evolution of atmospheric fine structure.

[0044] Reference Figure 5This diagram illustrates a comparison between the proposed method for retrieving range-resolved carbon dioxide concentration from lidar column integral signals and the results obtained from ground-based in-situ measurement instruments (Picarro). The diagram details the time-series comparison and statistical analysis of differences over three observation nights, including a time-series comparison and difference analysis of the carbon dioxide range-resolved concentration (30 m) obtained by the method in this embodiment and the ground-based Picarro measurement; a trend comparison and analysis of the 10 km path integral column concentration along the detection path and the ground-based Picarro measurement; and a comparison and difference analysis of the carbon dioxide range-resolved concentration (300 m) obtained using the traditional inversion method (direct differential smoothing) and the ground-based Picarro measurement. Through the above multi-dimensional comparative analysis, it can be found that the method proposed in this invention, while maintaining a high range resolution (30 m), achieves significantly better consistency between its inversion results and the results obtained by ground-based in-situ high-precision instruments (Picarro) than the results obtained using the traditional inversion method, even when the resolution is reduced to 300 m. The results show that the systematic bias and discrete error of the detection method provided in this embodiment are effectively controlled, proving that the detection method can suppress noise while perfectly restoring the real concentration fluctuation.

[0045] The foregoing description of the specifications and embodiments is intended to explain the scope of protection of this invention, but does not constitute a limitation on the scope of protection of this invention. Modifications, equivalent substitutions, or other improvements to the embodiments of this invention or a portion thereof that can be obtained by those skilled in the art through logical analysis, reasoning, or limited experimentation, based on the teachings of this invention or the foregoing embodiments, in conjunction with common knowledge, general technical knowledge, and / or existing technology, should all be included within the scope of protection of this invention.

Claims

1. An algorithm for retrieving distance-resolved CO2 concentration from lidar column integral signals, characterized in that, include: Acquire the echo signals corresponding to multiple sets of detection lasers with range resolution emitted by the lidar into the target atmosphere; The detection laser includes a first laser and a second laser, and the absorption coefficient of the first laser for carbon dioxide is higher than that of the second laser for carbon dioxide. The echo signal is denoised to obtain a denoised signal; Based on the denoised signal, the atmospheric carbon dioxide column concentration profile distributed with distance was retrieved; The atmospheric carbon dioxide column concentration profile was smoothed and fitted to obtain an optimized column concentration profile. Differential calculations are performed on the optimized column concentration profile to determine the distance-resolved concentration of atmospheric carbon dioxide.

2. The algorithm for retrieving distance-resolved CO2 concentration from a lidar column integral signal as described in claim 1, characterized in that, The denoising process is based on the wavelet transform principle and includes: Wavelet decomposition was performed on the echo signal to obtain wavelet coefficients at different scales; The threshold is calculated according to the preset threshold determination rule, and the wavelet coefficients are adjusted using the threshold processing function to suppress the coefficients corresponding to noise. The denoised signal is obtained by wavelet reconstruction using the adjusted wavelet coefficients.

3. The algorithm for retrieving distance-resolved CO2 concentration from lidar column integral signals as described in claim 2, characterized in that, The wavelet basis functions are selected from the Daubechies series, Symlets series, or Coiflets series. The threshold determination rule is selected from the general threshold method, the Stein unbiased risk estimation method, or the threshold estimation method based on the absolute deviation of the median; The threshold processing function is selected from soft threshold function, hard threshold function or improved function of them.

4. The algorithm for retrieving distance-resolved CO2 concentration from lidar column integral signals as described in claim 3, characterized in that, The wavelet decomposition has 5 decomposition layers; the noise estimation in the threshold determination rule adopts a single-level noise estimation mode, which uses the first-level decomposition coefficients to estimate the noise standard deviation.

5. The algorithm for retrieving distance-resolved CO2 concentration from a lidar column integral signal as described in claim 1, characterized in that, The inversion of the atmospheric carbon dioxide column concentration profile is based on the calculation of the difference in absorption coefficients caused by the gas. Achieve the difference in absorption coefficients Calculated using the following formula: ； In this context, the subscript "on" indicates the first laser, and the subscript "off" indicates the second laser. It is the number of photons received; It is the number of photons emitted; Laser wavenumber, in cm. -1 ; The distance is in meters (m). It is a system constant; The telescope area is expressed in meters (m²). 2 ; Distance Geometric overlap factor at the location; The Mie volume backscattering coefficient is expressed in m. -1 ; It is a transmittance function; This is the aerosol extinction coefficient, in m. -1 ; The molecular extinction coefficient is expressed as... ,in The absorption coefficient of carbon dioxide is denoted as . The extinction coefficient of other molecules in the target atmosphere; Indicates the emission point of the distance detection laser. Place; Distance Optical depth at that location.

6. The algorithm for retrieving range-resolved CO2 concentration from a lidar column integral signal as described in claim 5, characterized in that, Atmospheric carbon dioxide column concentration profile Based on the difference in absorption coefficients It is determined using the following formula: ； in, and These represent the number densities of carbon dioxide and water molecules, respectively. Indicates the absorption cross section; Atmospheric pressure, measured in Pa; The number of moles of gas; T is the ambient temperature, in K. Here, is the Boltzmann constant, with a value of 1.380649 × 10⁻⁶. -23 J.K. -1 .

7. The algorithm for inverting range-resolved CO2 concentration from a lidar column integral signal as described in claim 6, characterized in that, In the detection laser, the first laser and the second laser have the same absorption coefficient for H2O in the target atmosphere. At this time, the number density of carbon dioxide molecules is: .

8. The algorithm for retrieving range-resolved CO2 concentration from a lidar column integral signal as described in claim 1, characterized in that, The smoothing fitting process is performed using a filter based on the principle of local polynomial least squares fitting.

9. The algorithm for inverting range-resolved CO2 concentration from lidar column integral signals as described in claim 8, characterized in that, The filter is a Savitzky-Golay filter; during the smoothing fitting process, the sliding window width of the filter is dynamically adjusted according to the signal-to-noise ratio characteristics of the column concentration profile as a function of distance: a first window width is used in the near-distance region where the signal-to-noise ratio is higher than a preset value, and a second window width is used in the far-distance region where the signal-to-noise ratio is lower than a preset value, wherein the second window width is greater than the first window width.

10. The algorithm for retrieving range-resolved CO2 concentration from a lidar column integral signal as described in claim 1, characterized in that, The distance-resolved concentration of atmospheric carbon dioxide Calculated using the following formula: 。

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