A method for inverting vertical profiles of sulfur dioxide from volcanoes based on the Lagrange diffusion model.

Abstract

This invention relates to the fields of atmospheric science and remote sensing, and particularly to a method for inverting the vertical profile of sulfur dioxide emissions from volcanoes based on a Lagrange diffusion model. This method acquires the total mass constraint of the volcanic eruption, satellite sulfur dioxide column concentration and effective pixels, three-dimensional meteorological driving data, and chemical scavenging parameters. It calculates the vertical weighting function using a radiative transfer model and generates an initial vertical distribution by combining column concentration stratification ratios. A diffusion model is constructed to simulate the backward trajectory of the gas mass and matches observed pixels to obtain the attributed gas mass distribution. The time series of vertical emissions of sulfur dioxide from volcanoes is optimized based on the attributed distribution and total mass constraint. The sequence is input into the diffusion model for forward simulation, and validation indicators are calculated by comparing with satellite observation data. The diffusion coefficient is corrected according to a threshold, and the target vertical emission profile time series is output. This invention significantly improves the accuracy of vertical distribution inversion of sulfur dioxide from volcanoes through closed-loop optimization of backward trajectory attribution and forward validation.

Description

Technical Field

[0001] This invention relates to the fields of atmospheric science and remote sensing technology, and in particular to a method for inverting vertical profiles of sulfur dioxide from volcanoes based on a Lagrange diffusion model. Background Technology

[0002] Volcanic eruptions release millions of tons of sulfur dioxide, which can be converted into sulfuric acid aerosols. In the troposphere, sulfuric acid aerosols are easily removed by precipitation, with a lifespan ranging from a few hours to one or two weeks. However, in the relatively dry and stable stratosphere, the lifespan of sulfuric acid aerosols can reach months to years, potentially being transported globally by stratospheric circulation. Stratospheric sulfates absorb infrared radiation, causing stratospheric warming, and reflect shortwave radiation, causing tropospheric cooling. Changes in radiation and temperature are just the beginning of a chain reaction, adjusting atmospheric circulation, precipitation, and other factors. Furthermore, stratospheric sulfate aerosols contribute to ozone depletion through direct or indirect chemical reactions, another indirect pathway affecting radiation and atmospheric circulation. Therefore, tracking sulfur dioxide from volcanic eruptions and its converted sulfuric acid aerosols is fundamental to studying the climate impacts of volcanic eruptions.

[0003] Since meteorological conditions during volcanic eruptions have a decisive influence on the formation and transport of sulfate aerosols, accurate temporal and spatial distribution of sulfur dioxide emissions from volcanic eruptions is fundamental to simulating subsequent chemical reactions, aerosol formation, and transport processes. However, existing passive remote sensing primarily provides sulfur dioxide column concentration or total column volume, and has long revisit times (once or twice a day), lacking specific, continuous-time three-dimensional distribution information for volcanic eruptions. In particular, it cannot obtain high spatiotemporal resolution vertical emission profiles of volcanic sulfur dioxide (lacking both vertical sub-layers and minute-level temporal resolution). Therefore, current methods struggle to characterize the evolution of injected sulfur dioxide levels and the temporal changes in intra-layer mass distribution over the eruption's duration (which can last for several days), limiting the accurate simulation and tracking of subsequent chemical transformations, sulfate aerosol formation, and long-range transport. Summary of the Invention

[0004] To address this, the present invention provides a method for inverting vertical profiles of sulfur dioxide from volcanoes based on a Lagrange diffusion model, thereby resolving the aforementioned problems in the prior art.

[0005] To achieve the above objectives, this invention provides a method for inverting vertical profiles of sulfur dioxide from volcanoes based on a Lagrange diffusion model, comprising:

[0006] Step S1: Obtain the total mass constraint of the volcanic eruption event, satellite observation data, three-dimensional meteorological driving data, and chemical scavenging parameters. The satellite observation data includes sulfur dioxide column concentration and effective pixels.

[0007] Step S2: For each effective pixel, calculate the vertical sensitivity profile of the pixel using the radiative transfer mode to obtain the sulfur dioxide vertical weighting function.

[0008] Step S3: Construct an air column at the center of the effective pixel, determine the number of air masses based on the sulfur dioxide column concentration, and perform vertical stratification and allocation of the air masses according to the vertical weighting function to obtain the initial vertical distribution of sulfur dioxide.

[0009] Step S4: Based on the three-dimensional meteorological driving data, the chemical scavenging parameters, and the initial vertical distribution, a diffusion model is used to simulate the backward trajectory of the air mass to obtain the trajectory endpoint position. The trajectory endpoint position is then matched with the spatiotemporal window of the volcanic eruption to obtain the attributable air mass distribution.

[0010] Step S5: Adjust the profile height and concentration distribution according to the attribution gas mass distribution and the total mass constraint to obtain the vertical emission profile time series;

[0011] Step S6: Use the vertical emission profile sequence as input to the diffusion model for forward simulation to obtain simulation results. Compare and verify the indicators based on the simulation results and the satellite observation data. Correct the diffusion coefficient based on the impact assessment indicators and preset indicator thresholds to obtain the target vertical emission profile time series.

[0012] Furthermore, the process of step S2 includes:

[0013] Based on the observed geometric parameters, cloud parameters, and surface albedo in the satellite observation data, effective pixels are selected; based on the effective pixels, a forward simulation is performed using the radiative transfer model to obtain the simulation results.

[0014] Based on the simulation results, the partial derivative of the top-of-atmosphere radiation with respect to the vertical layer concentration of sulfur dioxide is calculated using the radiative transfer model to generate the vertical sensitivity profile.

[0015] The vertical sensitivity profile is normalized to obtain the vertical weighting function.

[0016] Furthermore, the process of normalizing the vertical sensitivity profile to obtain the vertical weighting function includes:

[0017] The total sensitivity is calculated by integrating the vertical sensitivity profile within a preset height range.

[0018] The sensitivity of each height layer is normalized based on the total sensitivity to obtain the vertical weight function.

[0019] Furthermore, the process of step S3 includes:

[0020] An air column is constructed based on the latitude and longitude positions of the effective pixels, and the air column is uniformly divided into several layers at 0.2 km intervals in the vertical direction;

[0021] The number of air clusters in the air column at each pixel is determined based on the sulfur dioxide column concentration of all effective pixels. The number of air clusters at each pixel is proportional to the sulfur dioxide column concentration of that pixel, and the sum of the number of air clusters in all effective pixels is the preset total number of air clusters.

[0022] The air masses in the corresponding air column are vertically stratified and proportioned according to the vertical weight function at each effective pixel to obtain the initial vertical distribution of sulfur dioxide.

[0023] Further, the process of determining the number of air clusters in the air column at each pixel based on the sulfur dioxide column concentration of all effective pixels, wherein the number of air clusters at each pixel is proportional to the sulfur dioxide column concentration of that pixel, and the sum of the number of air clusters in all effective pixels is a preset total number of air clusters, includes:

[0024] Read the sulfur dioxide column concentration data for each valid pixel one by one;

[0025] Calculate the sum of sulfur dioxide column concentrations for all valid pixels;

[0026] Based on the preset total number of air masses, the number of air masses in the air column at each effective pixel is calculated according to the proportion of the sulfur dioxide column concentration of each effective pixel to the total.

[0027] The number of air clusters at each effective pixel is rounded down and adjusted so that the sum of the number of air clusters at all effective pixels equals the preset total number of air clusters.

[0028] Furthermore, the process of step S4 includes:

[0029] The diffusion model is initialized based on the three-dimensional meteorological driving data and chemical scavenging parameters;

[0030] The initial vertically distributed air mass is used as the input to the diffusion model to simulate the backward trajectory of the air mass and obtain the endpoint position of the trajectory.

[0031] A time window for volcanic eruption, a spatial near-field range, and a vertical height tolerance threshold are set. Gas masses that enter the spatial near-field range within the time window and whose height is within the vertical height tolerance threshold are selected to determine the distribution of the attributable gas masses.

[0032] Furthermore, the process of using the initially vertically distributed air mass as input to the diffusion model to simulate the backward trajectory of the air mass to obtain the endpoint position of the trajectory includes:

[0033] Based on the wind field in the three-dimensional meteorological driving data as the driving field, the air mass is back-time integrated through the diffusion model to generate the basic motion trajectory of the air mass within the time window.

[0034] Based on the basic motion trajectory, the random diffusion motion of the air mass is simulated through a subgrid turbulence parameterization process to obtain the real-time height and position of the air mass;

[0035] Based on the real-time altitude and location, the chemical conversion rate of sulfur dioxide is calculated using the ozone and hydroxyl concentrations in the chemical removal parameters.

[0036] Integrating along the timeline from the satellite observation time back to the volcanic eruption period, we can obtain the endpoint of the gas cloud's trajectory during the eruption period.

[0037] Furthermore, the process of step S5 includes:

[0038] Based on the attribution of air mass distribution, the mass percentage and spatial distribution density of air masses in each altitude layer are statistically analyzed to generate an initial altitude adjustment coefficient.

[0039] The initial height adjustment coefficient and the total mass constraint are optimized by iteratively minimizing the objective function to adjust the mass distribution ratio of each height layer. The objective function is defined as the sum of squares of the deviations between the attributable air mass mass ratio and the total mass constraint.

[0040] Based on the optimized mass distribution ratio, the air mass height in the initial vertical distribution is re-stratified to construct a corrected vertical emission profile.

[0041] Using the volcanic eruption period as the time axis, the corrected vertical emission profile is output at preset time intervals to form the vertical emission profile time series.

[0042] Furthermore, step S6 includes the following process:

[0043] The vertical emission profile time series was used as input to the diffusion model. Combined with three-dimensional meteorological driving data and chemical scavenging parameters, forward time integration was performed on the air mass to generate a simulated sulfur dioxide column concentration distribution.

[0044] The simulated sulfur dioxide column concentration distribution is compared pixel-by-pixel with the sulfur dioxide column concentration in satellite observation data to calculate the verification index.

[0045] Determine whether the verification index meets the preset index threshold to obtain the verification result;

[0046] The diffusion coefficient is optimized based on the verification results until the verification index meets the preset threshold or reaches the maximum number of iterations to obtain the target vertical emission profile time series.

[0047] Furthermore, the process of determining whether the verification indicator meets the preset indicator threshold to obtain the verification result includes:

[0048] If the verification index meets the preset index threshold, the current vertical emission profile time series is output as the target vertical emission profile time series.

[0049] If the verification index does not meet the preset index threshold, the horizontal diffusion coefficient and vertical diffusion coefficient in the diffusion model are dynamically adjusted according to the deviation ratio between the verification index and the preset threshold.

[0050] Compared with existing technologies, the advantages of this invention lie in its ability to acquire total mass constraints, satellite observation data, three-dimensional meteorological driving data, and chemical scavenging parameters of volcanic eruption events. It utilizes radiative transfer models to calculate the vertical sensitivity profile of pixels, obtaining a vertical weighting function. An air column is constructed at the center of effective pixels, determining the number and initial vertical distribution of air masses. A diffusion model is built to simulate the backward trajectory of air masses, yielding the attributable air mass distribution. Combining the attributable air mass distribution and total mass constraints, the profile height and concentration distribution are adjusted to obtain a vertical emission profile time series. Finally, the vertical emission profile series is used as input to the diffusion model for forward simulation, and the diffusion coefficient is corrected based on validation indicators to obtain the target vertical emission profile time series. This method can accurately simulate the transport and diffusion process of volcanic sulfur dioxide, improving the accuracy and reliability of the inversion results, providing strong support for the monitoring and early warning of volcanic eruptions, and also helping to better assess the impact of volcanic eruptions on the atmospheric environment and climate change.

[0051] In particular, by accurately simulating the atmospheric radiative transfer process and calculating partial derivatives, the influence of sulfur dioxide on the top-of-atmosphere radiation at different altitudes can be reflected more accurately, thereby improving the accuracy of subsequent inversion of the vertical distribution of sulfur dioxide. The normalized vertical weighting function highlights the relative importance of each altitude layer, making it easier to distinguish the distribution characteristics of sulfur dioxide at different altitudes during the inversion process and enhancing the vertical resolution.

[0052] In particular, high-resolution meteorological data ensures the accuracy of the driving field of the diffusion model, improving the accuracy of the simulation. Wind field driving and subgrid turbulence parameterization accurately simulate the trajectory of air masses, improving the accuracy of attribution analysis. Combining chemical conversion rate calculations comprehensively considers the chemical changes of sulfur dioxide during transport, enhancing the physical realism and applicability of the model. By setting temporal and spatial screening conditions, air masses potentially originating from volcanic eruptions are accurately identified, further improving the accuracy of attribution analysis.

[0053] In particular, by optimizing the algorithm, the mass allocation of the attributable gas mass is ensured to be highly consistent with the total mass constraint, improving the reliability of the inversion results. The resulting vertical emission profile time series reflects the dynamic changes in volcanic sulfur dioxide emissions, providing more accurate initial conditions for subsequent transport and conversion simulations. The corrected vertical emission profile more accurately reflects the actual distribution of sulfur dioxide during volcanic eruptions, enhancing the accuracy and reliability of the simulation results.

[0054] In particular, by combining three-dimensional meteorological data and chemical parameters, the transport, diffusion, and chemical transformation processes of sulfur dioxide gas masses are comprehensively simulated, improving the physical realism and reliability of the simulation results. By setting validation index thresholds, the output vertical emission profile time series is ensured to meet certain accuracy requirements, improving the credibility of the results. The diffusion coefficient is dynamically adjusted by the deviation ratio, enabling the model to adaptively optimize the simulation results and gradually improve consistency with observational data. Continuous adjustment of the diffusion coefficient makes the simulation results closer to actual observational data, enhancing the model's simulation accuracy and credibility. The thresholds and optimization strategies can be flexibly adjusted according to different validation indicators and research needs, demonstrating strong applicability and flexibility. Attached Figure Description

[0055] Figure 1 A schematic diagram of the process for inverting vertical profiles of sulfur dioxide from volcanoes based on the Lagrange diffusion model provided by this invention;

[0056] Figure 2 This is a flowchart illustrating step S2 in the vertical profile inversion method for volcanic sulfur dioxide based on the Lagrange diffusion model provided by the present invention.

[0057] Figure 3 This is a flowchart illustrating step S3 in the vertical profile inversion method for volcanic sulfur dioxide based on the Lagrange diffusion model provided by the present invention.

[0058] Figure 4 This is a flowchart illustrating step S4 in the vertical profile inversion method for volcanic sulfur dioxide based on the Lagrange diffusion model provided by the present invention.

[0059] Figure 5 This is a time series of sulfur dioxide vertical emission profiles corresponding to the Raecock volcano eruption case of this invention;

[0060] Figure 6 This is the critical success index for forward tracking of sulfur dioxide from the Raecock volcano eruption in this invention. Detailed Implementation

[0061] To make the objectives and advantages of the present invention clearer, the present invention will be further described below with reference to embodiments; it should be understood that the specific embodiments described herein are merely for explaining the present invention and are not intended to limit the present invention.

[0062] Preferred embodiments of the present invention will now be described with reference to the accompanying drawings. Those skilled in the art should understand that these embodiments are merely illustrative of the technical principles of the present invention and are not intended to limit the scope of protection of the present invention.

[0063] It should be noted that in the description of this invention, the terms "upper", "lower", "left", "right", "inner", "outer", etc., which indicate directions or positional relationships, are based on the directions or positional relationships shown in the accompanying drawings. This is only for the convenience of description and is not intended to indicate or imply that the device or element must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, it should not be construed as a limitation of this invention.

[0064] Furthermore, it should be noted that, in the description of this invention, unless otherwise explicitly specified and limited, the terms "installation," "connection," and "linking" should be interpreted broadly. For example, they can refer to a fixed connection, a detachable connection, or an integral connection; they can refer to a mechanical connection or an electrical connection; they can refer to a direct connection or an indirect connection through an intermediate medium; and they can refer to the internal connection of two components. Those skilled in the art can understand the specific meaning of the above terms in this invention according to the specific circumstances.

[0065] Please see Figure 1 As shown, this invention provides a method for inverting vertical profiles of sulfur dioxide from volcanoes based on a Lagrange diffusion model, comprising:

[0066] Step S1: Obtain the total mass constraint of the volcanic eruption event, satellite observation data, three-dimensional meteorological driving data, and chemical scavenging parameters. The satellite observation data includes sulfur dioxide column concentration and effective pixels.

[0067] Specifically, the total sulfur dioxide mass or mass range of the target volcanic eruption event provided by the Global Volcanism Program (GVP) is obtained as a constraint for inversion calibration. Satellite observation data: The TROPOMI volcanic sulfur dioxide column concentration product and its retrieval inputs (observation geometry, cloud parameters, surface albedo, quality indicators, etc.) within 10 days after the eruption are obtained, and quality control screening is performed: pixels with cloud cover greater than the threshold (0.3), high albedo snow / ice cover, and unqualified quality indicators are removed, and the rest are considered valid pixels. Three-dimensional meteorological driving data: The European Centre for Medium-Range Weather Forecasts (ERA5) provides three-dimensional wind field, temperature, humidity, cloud water, precipitation, and ozone data, with a horizontal resolution of 0.25°×0.25° and a temporal resolution of 1 hour. Chemical scavenging parameters from near-surface to 1 hPa altitude are derived from the simulation results of chemical transport models (such as the Lagrange chemical transport model CLaMS). These parameters include ozone and hydroxyl (OH) concentrations, which are used to describe the chemical transformation process of sulfur dioxide.

[0068] Step S2: Calculate the vertical sensitivity profile of each effective pixel using the radiative transfer mode to obtain the vertical weighting function;

[0069] Specifically, such as Figure 2 As shown, the process of step S2 includes:

[0070] Step S21: Based on the observation geometric parameters, cloud parameters and surface albedo in the satellite observation data, select effective pixels; based on the effective pixels, call the radiative transfer mode to perform forward simulation to obtain simulation results;

[0071] Specifically, the temperature, humidity, and pressure profiles in the three-dimensional meteorological driving data are coupled with the initial sulfur dioxide concentration field to the radiative transfer model; the shortwave radiation is calculated using the four-stream spherical harmonic function accumulation algorithm, and the bidirectional reflectivity is corrected by truncated multiple scattering (TMS), while simultaneously considering the cloud scattering effect; the top of the atmosphere (TOA) radiance value or brightness temperature value is generated and compared with the actual satellite observation data to form a benchmark.

[0072] Step S22: Based on the simulation results, calculate the partial derivative of the top atmospheric radiation with respect to the vertical layer concentration of sulfur dioxide using the radiative transfer mode to generate the vertical sensitivity profile.

[0073] Specifically, based on the simulation results, the partial derivative of the top-of-atmosphere radiation with respect to the vertical concentration of sulfur dioxide is calculated using a radiative transfer model to generate a vertical sensitivity profile: a unit concentration of sulfur dioxide disturbance (ΔSO2=1 DU) is sequentially injected at preset altitude layers (e.g., 0~25 km, 1 km intervals); the radiative transfer model is run for each disturbance layer to obtain the change in top-of-atmosphere radiation ΔR, and the partial derivative ∂R / ∂SO2 is calculated; the partial derivatives of each altitude layer are sorted by altitude to form a vertical sensitivity profile, which characterizes the response intensity of satellite observations to sulfur dioxide concentrations at different altitude layers.

[0074] Step S23: Normalize the vertical sensitivity profile to obtain the vertical weight function.

[0075] Specifically, the process of normalizing the vertical sensitivity profile to obtain the vertical weight function includes:

[0076] The total sensitivity is calculated by integrating the vertical sensitivity profile within a preset height range.

[0077] Specifically, numerical integration is performed on the vertical sensitivity profile within a preset altitude range (e.g., the troposphere and stratosphere, 0–25 km) to calculate the total sensitivity over the entire altitude range. A numerical integration method, such as the trapezoidal rule or Simpson's rule, is chosen; these methods are suitable for integration calculations of discrete data points. In the trapezoidal rule, the altitude range is divided into multiple small intervals, and the area of ​​each interval is approximately equal to the average height of two adjacent points multiplied by the interval width. The total sensitivity is obtained by summing the areas of all intervals.

[0078] The sensitivity of each height layer is normalized based on the total sensitivity to obtain the vertical weight function.

[0079] Specifically, the sensitivity value of each height layer is divided by the total sensitivity to obtain the normalized vertical weighting function w(z). This weighting function represents the relative contribution of each height layer to the total sensitivity, reflecting the relative importance of that height layer in the observation. The formula is:

[0080]

[0081] Where s(z) is the sensitivity at height z, and the integration range starts from the lowest height. to the highest altitude .

[0082] Specifically, by accurately simulating the atmospheric radiative transfer process and calculating partial derivatives, the influence of sulfur dioxide on the top-of-atmosphere radiation at different altitudes can be reflected more precisely, thereby improving the accuracy of subsequent inversion of the vertical distribution of sulfur dioxide. The normalized vertical weighting function highlights the relative importance of each altitude layer, enabling a clearer distinction of the distribution characteristics of sulfur dioxide at different altitudes during the inversion process, thus enhancing the vertical resolution.

[0083] Step S3: Construct an air column at the center of the effective pixel, determine the number of air masses based on the sulfur dioxide column concentration, and perform stratification and proportioning of the air masses according to the vertical weighting function to obtain an initial vertical distribution.

[0084] Specifically, such as Figure 3 As shown, the process of step S3 includes:

[0085] Step S31: Construct an air column based on the latitude and longitude positions of the effective pixels, and divide the air column into several layers at 0.2 km intervals in the vertical direction.

[0086] Specifically, an air column with a height range of 0–25 km is constructed at the latitude and longitude location of each effective pixel. The location of this air column corresponds to the geographical location of the effective pixel and is used for subsequent air mass allocation and vertical distribution calculations. The constructed air column is uniformly divided into several layers vertically at intervals of 0.2 km. Specifically, starting from the ground (0 km), each 0.2 km layer is considered a height layer, up to 25 km. Thus, the air column is divided into 126 uniform height layers. This uniform stratification method is independent of the vertical resolution of the meteorological driving data, ensuring that the vertical stratification of the air column has a uniform high resolution.

[0087] Step S32: Determine the number of air clusters in the air column at each pixel based on the sulfur dioxide column concentration of all effective pixels. The number of air clusters at each pixel is proportional to the sulfur dioxide column concentration of that pixel, and the sum of the number of air clusters of all effective pixels is the preset total number of air clusters.

[0088] Specifically, the process of determining the number of air clusters in the air column at each pixel based on the sulfur dioxide column concentration of all effective pixels, wherein the number of air clusters at each pixel is proportional to the sulfur dioxide column concentration of that pixel, and the sum of the number of air clusters in all effective pixels is a preset total number of air clusters, includes:

[0089] Read the sulfur dioxide column concentration data for each valid pixel one by one;

[0090] Specifically, sulfur dioxide column concentration information for effective pixels is extracted from satellite observation data. This data is typically stored as a two-dimensional array, with each element corresponding to the sulfur dioxide column concentration value of one pixel.

[0091] Calculate the sum of sulfur dioxide column concentrations for all valid pixels;

[0092] Specifically, the sulfur dioxide column concentration values ​​of all valid pixels are summed to obtain a total. This total will serve as the baseline value for subsequent scaling calculations.

[0093] Based on the preset total number of air masses, the number of air masses in the air column at each effective pixel is calculated according to the proportion of the sulfur dioxide column concentration of each effective pixel to the total.

[0094] Specifically, the preset total number of air masses N is determined, and the value of N is preferably 10. 6 , range 10 5 ~10 6 Adjustable. For each effective pixel, calculate the proportion of its sulfur dioxide column concentration to the total. Based on this proportion, calculate the number of gas clusters to be allocated at that effective pixel. The calculation formula is: Number of gas clusters for that pixel = Preset total number of gas clusters × (Sulfur dioxide column concentration for that pixel / Total sulfur dioxide column concentration).

[0095] The number of air clusters at each effective pixel is rounded down and adjusted so that the sum of the number of air clusters at all effective pixels equals the preset total number of air clusters.

[0096] Specifically, since the calculated number of air clusters may not be an integer, a rounding operation is required. This can be done by rounding to the nearest integer or by directly rounding to the nearest integer. After rounding, there may be a slight deviation between the sum of the number of air clusters in all pixels and the preset total number of air clusters. In this case, the number of air clusters needs to be adjusted, for example, by increasing or decreasing the number of air clusters in certain pixels according to the magnitude of the error, until the sum equals the preset total number of air clusters.

[0097] Step S33: Based on the vertical weighting function at each effective pixel, the air masses in the corresponding air column are vertically layered and proportioned to obtain the initial vertical distribution of sulfur dioxide.

[0098] Specifically, each effective pixel has a normalized vertical weighting function that provides weight values ​​for different height layers. Based on these weight values, the vertical distribution ratio of air masses is determined. Height layers with higher weight values ​​receive a larger proportion of air masses. According to this determined ratio, air masses at each effective pixel are allocated to different height layers. Specifically, each air mass is treated as a unit with the same sulfur dioxide mass and placed into the corresponding height layer according to the allocation ratio, ensuring that the number of air masses in each height layer is proportional to the weight value of that height layer. This process constructs the initial vertical distribution of sulfur dioxide, where the mass of sulfur dioxide is determined by the number of air masses in each height layer; the more air masses, the greater the mass of sulfur dioxide.

[0099] Step S4: Construct a diffusion model based on the three-dimensional meteorological driving data, the chemical scavenging parameters, and the initial vertical distribution to simulate the backward trajectory of the air mass and obtain the trajectory endpoint position. Match the trajectory endpoint position with the observed pixels to obtain the attributed air mass distribution.

[0100] Specifically, such as Figure 4 As shown, the process of step S4 includes:

[0101] Step S41: Initialize the diffusion model based on the three-dimensional meteorological driving data and chemical scavenging parameters;

[0102] Specifically, the process involves acquiring three-dimensional meteorological driving data, including information on three-dimensional wind field, temperature, humidity, cloud water, precipitation, and ozone concentration. Meteorological data for the target area and time range are extracted and interpolated onto the temporal and spatial grids required by the diffusion model. Chemical scavenging parameters, including ozone and hydroxyl (OH) concentrations, are obtained. These parameters are typically provided by chemical transport models (such as the CLaMS model). The chemical scavenging parameters are then interpolated onto the temporal and spatial grids required by the diffusion model. A suitable Lagrange particle diffusion model (such as MPTRAC) is selected. The meteorological data and chemical scavenging parameters are input into the diffusion model to initialize the model's driving field and parameterization scheme.

[0103] Step S42: Use the initially vertically distributed air mass as input to the diffusion model to simulate the backward trajectory of the air mass to obtain the endpoint position of the trajectory;

[0104] Specifically, the process of using the initially vertically distributed air mass as input to the diffusion model and simulating the backward trajectory of the air mass to obtain the endpoint of the trajectory includes:

[0105] Based on the wind field in the three-dimensional meteorological driving data as the driving field, the air mass is back-time integrated through the diffusion model to generate the basic motion trajectory of the air mass within the time window.

[0106] Specifically, the initial vertical distribution of air masses (including location, mass, and initial time) is input into the diffusion model. Based on the wind field information in the 3D meteorological driving data, the wind field data is interpolated according to the time series and spatial grid to match the time resolution (usually hourly) and spatial resolution (matching the meteorological data grid) required by the diffusion model. For each air mass, within each time step, based on the wind speed and direction at its location, the diffusion model is used for backward time integration to calculate the basic trajectory of the air mass driven by the wind field, simulating the macroscopic trend of the air mass moving with the wind.

[0107] Based on the basic motion trajectory, the random diffusion motion of the air mass is simulated through a subgrid turbulence parameterization process to obtain the real-time height and position of the air mass;

[0108] Specifically, horizontal and vertical diffusion coefficients are set according to the differences in atmospheric turbulence characteristics in the troposphere and stratosphere. In the troposphere, where turbulence is stronger, a larger diffusion coefficient is set; in the stratosphere, where turbulence is relatively weaker, a smaller diffusion coefficient is set. For each air mass, within each time step, random displacements conforming to a probability distribution are generated based on the diffusion coefficient and a random number generator. These displacements are superimposed on the wind-driven basic motion trajectory, thus obtaining the real-time height and position of the air mass after considering the influence of turbulence, simulating the random diffusion motion of the air mass at a microscale.

[0109] Based on the real-time altitude and location, the chemical conversion rate of sulfur dioxide is calculated using the ozone and hydroxyl concentrations in the chemical removal parameters.

[0110] Specifically, along the movement trajectory of the air mass, the chemical removal parameters (ozone and hydroxyl concentrations) at the air mass's location are acquired in real time. These parameters are then matched with the air mass trajectory points using an interpolation method. Based on the chemical reaction mechanism and in conjunction with the ozone and hydroxyl concentrations, the chemical conversion rate of sulfur dioxide is calculated. The formula for calculating the chemical conversion rate is:

[0111]

[0112] in, It is the rate of chemical transformation; It is the basic conversion rate constant, determined based on experimental and empirical data; and These are the concentrations of ozone and hydroxyl groups, respectively, reflecting the activity of oxidation reactions in the atmosphere.

[0113] Integrating along the timeline from the satellite observation time back to the volcanic eruption period, we can obtain the endpoint of the gas cloud's trajectory during the eruption period.

[0114] Specifically, starting from the satellite observation time, the process traces back along the timeline of the volcanic eruption, performing integral calculations step-by-step at set time steps (e.g., 2 minutes). Within each time step, the effects of wind driving, turbulent diffusion, and chemical transformation are comprehensively considered to update the position and state parameters of the air mass. When tracing back to the volcanic eruption period, the endpoint of the air mass's trajectory is recorded, including longitude, latitude, altitude, and the corresponding time, providing crucial data for subsequent attribution analysis.

[0115] Step S43: Set the time window, spatial near-field range, and vertical height tolerance threshold for volcanic eruptions, and filter out air masses that enter the spatial near-field range within the time window and whose height is within the vertical height tolerance threshold to determine the distribution of the attributable air masses.

[0116] Specifically, a time window for volcanic eruptions is defined (e.g., from 1 hour before the eruption to 10 days after the eruption). A near-field spatial range is defined (e.g., a 50 km radius around the crater). A vertical height tolerance threshold is defined (e.g., a range of 0–25 km). All simulated air mass trajectories are filtered to identify those that enter the near-field spatial range within the time window and whose altitude is within the vertical height tolerance threshold. The endpoint locations of these air mass trajectories are recorded (including longitude, latitude, altitude, and time). The selected air masses are statistically analyzed into attributable air mass distributions, and their three-dimensional positions and times of entry into the near-field are recorded.

[0117] Specifically, high-resolution meteorological data ensures the accuracy of the driving field in the diffusion model, improving simulation accuracy. Wind field driving and subgrid turbulence parameterization accurately simulate the trajectory of air masses, enhancing the accuracy of attribution analysis. Chemical conversion rate calculations comprehensively consider the chemical changes of sulfur dioxide during transport, strengthening the model's physical realism and applicability. By setting temporal and spatial screening conditions, air masses potentially originating from volcanic eruptions are accurately identified, further improving the accuracy of attribution analysis.

[0118] Step S5: Adjust the profile height and concentration distribution according to the attribution gas mass distribution and the total mass constraint to obtain the vertical emission profile time series;

[0119] Specifically, step S5 includes the following process:

[0120] Based on the attribution of air mass distribution, the mass percentage and spatial distribution density of air masses in each altitude layer are statistically analyzed to generate an initial altitude adjustment coefficient.

[0121] Specifically, based on the height layer division of the air column, the total mass of the attributable air mass is statistically analyzed according to the height layer, and the mass proportion of the air mass in each height layer is calculated using the following formula:

[0122]

[0123] in, , For height layer The number of air masses, For the mass of air mass j, For height layer quality This is the total mass of the attributable air mass.

[0124] The spatial distribution density at each altitude level is statistically analyzed to reflect the degree of air mass aggregation in the horizontal direction. Based on the mass proportion and spatial distribution density, and taking into account the relative importance of each altitude level, an initial altitude adjustment factor is generated.

[0125] The initial height adjustment coefficient and the total mass constraint are optimized by iteratively minimizing the objective function to adjust the mass distribution ratio of each height layer. The objective function is defined as the sum of squares of the deviations between the attributable air mass mass ratio and the total mass constraint.

[0126] Specifically, the objective function is defined as the sum of squared deviations between the attributable air mass mass percentage and the total mass constraint, as shown in the formula:

[0127]

[0128] in, For height layer The quality.

[0129] An iterative optimization algorithm (such as gradient descent or trust region algorithm) is used to adjust the mass allocation ratio of each height layer to minimize the objective function J. In each iteration, the adjustment coefficients are updated based on the initial height, the mass allocation ratio of each height layer is updated, and the new objective function value is calculated. The iterative process continues until the objective function value converges or the set number of iterations is met.

[0130] Based on the optimized mass distribution ratio, the air mass height in the initial vertical distribution is re-stratified to construct a corrected vertical emission profile.

[0131] Specifically, based on the optimized mass allocation ratio, the air mass height in the initial vertical distribution is redistributed to ensure that the mass at each height level is consistent with the optimized ratio. At each height level, the concentration distribution of sulfur dioxide is calculated based on the redistributed air mass mass, and a corrected vertical emission profile is constructed.

[0132] Using the volcanic eruption period as the time axis, the corrected vertical emission profile is output at preset time intervals to form the vertical emission profile time series.

[0133] Specifically, the timeline is based on the volcanic eruption period, with time points divided at preset time intervals (e.g., 15 minutes). At each time point, a corrected vertical emission profile is output, including the sulfur dioxide concentration and mass distribution at each altitude level. The vertical emission profiles from all time points are arranged in chronological order to form a vertical emission profile time series.

[0134] Specifically, by optimizing the algorithm, the mass allocation of the attributable gas mass is ensured to be highly consistent with the total mass constraint, improving the reliability of the inversion results. The resulting vertical emission profile time series reflects the dynamic changes in volcanic sulfur dioxide emissions, providing more accurate initial conditions for subsequent transport and conversion simulations. The corrected vertical emission profile more accurately reflects the actual distribution of sulfur dioxide during volcanic eruptions, enhancing the accuracy and reliability of the simulation results.

[0135] Step S6: Use the vertical emission profile sequence as input to the diffusion model for forward simulation to obtain simulation results. Compare and verify the indicators based on the simulation results and the satellite observation data. Correct the diffusion coefficient based on the impact assessment indicators and preset indicator thresholds to obtain the target vertical emission profile time series.

[0136] Specifically, step S6 includes the following process:

[0137] The vertical emission profile time series was used as input to the diffusion model. Combined with three-dimensional meteorological driving data and chemical scavenging parameters, forward time integration was performed on the air mass to generate a simulated sulfur dioxide column concentration distribution.

[0138] Specifically, the time series of vertical emission profiles is used as the input source term for the diffusion model, with each time step corresponding to a vertical emission profile. Forward time integration is performed using the diffusion model to simulate the transport process of the air mass from the volcanic eruption source to the satellite observation time. During the simulation, physicochemical processes such as wind-driven processes, subgrid turbulent diffusion, and chemical transformation are considered to calculate the trajectory of the air mass and the changes in sulfur dioxide concentration. The simulation results show the sulfur dioxide column concentration distribution at each pixel location.

[0139] The simulated sulfur dioxide column concentration distribution is compared pixel-by-pixel with the sulfur dioxide column concentration in satellite observation data to calculate the verification index.

[0140] Specifically, the Critical Success Index (CSI) is used to assess the consistency between simulation results and observed data. The formula is:

[0141]

[0142] CSI is used to measure spatial detection consistency in high sulfur dioxide areas (the closer the value is to 100%, the better the consistency).

[0143] Determine whether the verification index meets the preset index threshold to obtain the verification result;

[0144] Specifically, the process of determining whether the verification indicator meets the preset indicator threshold to obtain the verification result includes:

[0145] If the verification index meets the preset index threshold, the current vertical emission profile time series is output as the target vertical emission profile time series.

[0146] Specifically, for each verification metric, it is determined whether it meets a preset threshold. For example, if CSI ≥ 0.7, the spatial detection consistency of the simulation results at that pixel is considered good.

[0147] If the verification indicator does not meet the preset indicator threshold, then the deviation ratio between the verification indicator and the preset threshold is used as the basis for the calculation. The horizontal and vertical diffusion coefficients in the diffusion model are dynamically adjusted.

[0148] Specifically, for each verification metric, calculate the percentage deviation from a preset threshold. For example, the percentage deviation is:

[0149] Specifically, This represents the preset CSI threshold, indicating the minimum level of spatial detection consistency expected to be achieved. This represents the CSI value obtained from actual calculations, indicating the consistency between the simulation results and the observed data in spatial detection. This indicates the degree to which the actual CSI value is insufficient relative to the threshold. A positive value indicates that the actual CSI is below the threshold and needs adjustment; a negative value or zero indicates that the actual CSI meets or exceeds the threshold.

[0150] The diffusion coefficient is optimized based on the verification results until the verification index meets the preset threshold or reaches the maximum number of iterations to obtain the target vertical emission profile time series.

[0151] Specifically, the horizontal and vertical diffusion coefficients in the diffusion model are dynamically adjusted based on the deviation ratio between the verification index and the preset threshold. The adjustment formula is as follows:

[0152]

[0153] in, The new diffusion coefficient after adjustment. The old diffusion coefficient before adjustment. Adjustment coefficient (set based on experience, such as 0.1 or 0.2). To verify the relative difference between the metric and the threshold, the forward simulation and metric calculation are re-performed to assess whether the adjusted diffusion coefficient meets the threshold requirement. The diffusion coefficient adjustment and simulation verification are iteratively performed until the metric meets the preset threshold or the maximum number of iterations (e.g., 10 or 20) is reached. If the metric meets the threshold requirement, the current vertical emission profile time series is output as the final target vertical emission profile time series.

[0154] Specifically, by combining three-dimensional meteorological data and chemical parameters, the transport, diffusion, and chemical transformation processes of sulfur dioxide gas masses are comprehensively simulated, improving the physical realism and reliability of the simulation results. By setting validation index thresholds, the output vertical emission profile time series is ensured to meet certain accuracy requirements, enhancing the reliability of the results. The diffusion coefficient is dynamically adjusted by the deviation ratio, enabling the model to adaptively optimize the simulation results and gradually improve consistency with observational data. Continuous adjustment of the diffusion coefficient makes the simulation results closer to actual observational data, enhancing the model's simulation accuracy and reliability. The thresholds and optimization strategies can be flexibly adjusted according to different validation indicators and research needs, demonstrating strong applicability and flexibility.

[0155] In this embodiment, the sulfur dioxide from the June 2019 eruption of the Raikok volcano is used as an example to invert the vertical profile of sulfur dioxide.

[0156] The target event is the June 2019 eruption of the Rekok volcano. The Rekok eruption was one of the larger volcanic eruptions globally in the past decade, releasing large amounts of sulfur dioxide and volcanic ash, making it a representative case study for studying the transport and diffusion of sulfur dioxide from volcanic eruptions. The Rekok volcano is located in the Kuril Islands of Russia (48.29°N, 153.25°E, elevation 551 meters). Starting around 22 UTC on June 21, 2019, the Rekok volcano experienced a violent eruption that lasted approximately 24 hours, releasing a large amount of sulfur dioxide. The eruption column reached a height of approximately 15 km, entering the stratosphere. Total sulfur dioxide mass data for the 2019 Rekok eruption event were obtained from the Global Volcanism Program (GVP) and determined to be 1.40 Tg, which was used as a constraint for the total sulfur dioxide mass.

[0157] Step S1, Data Acquisition and Quality Control:

[0158] The satellite observation data source was the TROPOMI sulfur dioxide column concentration observation product, covering data within 10 days after the eruption (i.e., June 21, 2019 to July 1, 2019), along with solar / observed zenith angle and relative azimuth angle, cloud parameters (cloud cover, effective cloud height), surface albedo, and quality flag data. Pixels with cloud cover <0.3, albedo <0.3, and a qualified quality flag were selected as valid pixels through quality control.

[0159] Download ERA5 reanalysis data for 10 days before and after the volcanic eruption, including 3D wind field, temperature, humidity, precipitation, cloud water, and ozone concentration, with a horizontal resolution of 0.25° × 0.25° and a temporal resolution of 1 hour, with isobaric surfaces from near the ground to 1 hPa. Hydroxyl concentration was provided by the CLaMS model.

[0160] Step S2, Calculation of vertical weight function:

[0161] For each valid Tropomi pixel from the time of the eruption to 10 days afterward, the average factor (AMF) of sulfur dioxide at discrete height levels was calculated using the JURASSIC radiative transfer model. The discrete AMF was resampled to an equally spaced vertical grid using linear interpolation / spline interpolation. The resampled vertical sensitivity profile was normalized to obtain the vertical weighting function w(z) distributed with height. In the case of the Raikok eruption, the typical Tropomi pixel vertical weighting function showed relatively high sensitivity to sulfur dioxide above approximately 5 km in altitude.

[0162] Step S3: Obtain the vertical distribution of sulfur dioxide:

[0163] An air column ranging from 0 to 25 km was constructed at the center of each effective pixel, with a vertical spacing ΔZ of 0.2 km, for a total of 126 layers. The number of air clusters, Ni, was assigned to each pixel location based on the sulfur dioxide concentration in the air column. The total number of air clusters, N, was set to 1 × 10⁻⁶. 6 The specific allocation method is as follows: ,in, The column concentration of sulfur dioxide is given for pixel i. The pixel with the highest column concentration (>100 DU) is assigned to approximately 5000 gas clusters, and the pixel with the lowest effective concentration (>1 DU) is assigned to approximately 50 gas clusters.

[0164] The w(z) obtained in step S2 is used as the stratification weight to allocate the initial heights of the Ni air masses, ensuring that the samples meet the observation sensitivity characteristics in the vertical direction. For example, if the integral value of the vertical weight function of a pixel in the 10-12 km height range is 0.4, then 40% of the initial heights of the air masses in that pixel will fall within this height range. A uniform initial sulfur dioxide mass is assigned to each air mass particle, ensuring that the sum of the weights of the air mass particles within the pixel is consistent with the total mass of the column in that pixel. In the Raecock case, a single air mass represents approximately 1400 kg of sulfur dioxide.

[0165] Step S4: Obtain the distribution of attributable air masses:

[0166] The Lagrange particle diffusion model (MPTRAC) was used to perform backward integration on all air masses from the observation time to the eruption time (22:00 UTC on June 21, 2019). The time window ΔT for the volcanic eruption was set from 22:00 UTC on June 21, 2019 to 00:00 UTC on June 23, 2019, with a spatial near-field radius R of 50 km and a vertical height tolerance threshold of 0–25 km. Air masses that entered the volcanic near-field within ΔT along the tracking path were marked as "attributable air masses," and their three-dimensional position and time of entry into the near-field were recorded. In the Raecock case, approximately 65% ​​of the air masses were successfully attributable to the volcanic source.

[0167] Step S5: Inversion and calibration of the vertical discharge profile:

[0168] Based on the attribution of air mass distribution, the mass proportion and spatial distribution density of air masses in each altitude layer are statistically analyzed to generate initial altitude adjustment coefficients. These initial altitude adjustment coefficients are then combined with the total mass constraint, and the mass distribution ratio of each altitude layer is adjusted by iteratively minimizing the objective function. The objective function is defined as the sum of squared deviations between the attribution of air mass mass proportion and the total mass constraint. Based on the optimized mass distribution ratio, the air mass altitudes in the initial vertical distribution are re-stratified to construct a corrected vertical emission profile.

[0169] Using the volcanic eruption period as the time axis, the corrected vertical emission profile is output at preset time intervals (e.g., 15 minutes), forming a vertical emission profile time series E(t,z) (e.g., Figure 5 (As shown). E(t,z) shows that the main injection layer is located above the tropopause, and its height and thickness evolve with the eruption process. The main eruption phase occurred between 00 and 12 UTC on June 22, 2019, with the injection height concentrated at 8–14 km. Subsequently, the eruption intensity weakened, and the height concentrated at 10–12 km. During the entire eruption, approximately 67.37% of the sulfur dioxide was injected into the stratosphere (>9 km).

[0170] Step S6, Forward Simulation and Verification:

[0171] Using E(t,z) as the initial 3D source term for the eruption, a Lagrange particle diffusion model was driven for 10 days of forward tracking to simulate the sulfur dioxide column concentration field of the volcano. The simulated sulfur dioxide column concentration field was output every 30 minutes and interpolated to the TROPOMI observation grid. Data grids with sulfur dioxide column concentrations greater than 5 DU were selected for spatial comparison of column concentrations between TROPOMI observations and forward simulations. The Critical Success Index (CSI) was calculated: CSI = number of hits / (number of hits + number of false alarms + number of missed alarms), and the daily CSI curves for 10 days were given (e.g., Figure 6 (As shown).

[0172] Compared with the fixed injection height scheme, the E(t,z) obtained by inversion in this embodiment significantly improves the authenticity of the vertical profile of sulfur dioxide in volcanoes. The profile time series can also provide the upper and lower boundaries of the main injection layer and the percentage of layer mass. The forward simulation and satellite observation achieve higher CSI in terms of spatial consistency.

[0173] Specifically, by acquiring the total mass constraint of a volcanic eruption event, satellite observation data, three-dimensional meteorological driving data, and chemical scavenging parameters, the vertical sensitivity profile of pixels is calculated using a radiative transfer model to obtain the vertical weighting function. An air column is constructed at the center of effective pixels to determine the number and initial vertical distribution of air masses. A diffusion model is built to simulate the backward trajectory of air masses to obtain the attributable air mass distribution. Combining the attributable air mass distribution and the total mass constraint, the profile height and concentration distribution are adjusted to obtain the vertical emission profile time series. Finally, the vertical emission profile series is used as input to the diffusion model for forward simulation, and the diffusion coefficient is corrected according to the validation index to obtain the target vertical emission profile time series. This method can accurately simulate the transport and diffusion process of volcanic sulfur dioxide, improve the accuracy and reliability of the inversion results, provide strong support for the monitoring and early warning of volcanic eruptions, and also help to better assess the impact of volcanic eruptions on the atmospheric environment and climate change.

[0174] The technical solution of the present invention has been described above with reference to the preferred embodiments shown in the accompanying drawings. However, it will be readily understood by those skilled in the art that the scope of protection of the present invention is obviously not limited to these specific embodiments. Without departing from the principles of the present invention, those skilled in the art can make equivalent changes or substitutions to the relevant technical features, and the technical solutions after these changes or substitutions will all fall within the scope of protection of the present invention.

[0175] The above description is merely a preferred embodiment of the present invention and is not intended to limit the invention. Various modifications and variations can be made to the present invention by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for inverting vertical profiles of sulfur dioxide from volcanoes based on a Lagrange diffusion model, characterized in that, include: Step S1: Obtain the total mass constraint of the volcanic eruption event, satellite observation data, three-dimensional meteorological driving data, and chemical scavenging parameters. The satellite observation data includes sulfur dioxide column concentration and effective pixels. Step S2: For each effective pixel, calculate the vertical sensitivity profile of the pixel using the radiative transfer mode to obtain the sulfur dioxide vertical weighting function. Step S3: Construct an air column at the center of the effective pixel, determine the number of air masses based on the sulfur dioxide column concentration, and perform vertical stratification and allocation of the air masses according to the vertical weighting function to obtain the initial vertical distribution of sulfur dioxide. Step S4: Based on the three-dimensional meteorological driving data, the chemical scavenging parameters, and the initial vertical distribution of sulfur dioxide, a diffusion model is used to simulate the backward trajectory of the air mass to obtain the trajectory endpoint position. The trajectory endpoint position is then matched with the spatiotemporal window of the volcanic eruption to obtain the attributable air mass distribution. Step S5 involves adjusting the profile height and concentration distribution based on the attributable gas mass distribution and the total mass constraint to obtain a vertical emission profile time series. Specifically, Step S5 involves: calculating the mass percentage and spatial distribution density of gas masses in each height layer based on the attributable gas mass distribution to generate an initial height adjustment coefficient; optimizing the initial height adjustment coefficient with the total mass constraint by iteratively minimizing the objective function to adjust the mass allocation ratio of each height layer, where the objective function is defined as the sum of squares of the deviations between the attributable gas mass percentage and the total mass constraint; re-stratifying the gas mass height in the initial vertical distribution based on the optimized mass allocation ratio to construct a corrected vertical emission profile; and outputting the corrected vertical emission profile at preset time intervals, using the volcanic eruption period as the time axis to form a vertical emission profile time series. Step S6 involves using the vertical emission profile sequence as input to the diffusion model for forward simulation to obtain simulation results. The simulation results are then compared with the satellite observation data to calculate verification indicators. The diffusion coefficient is adjusted based on the verification indicators and a preset threshold to obtain the target vertical emission profile time series. Specifically, Step S6 involves: determining whether the verification indicators meet the preset threshold; if the verification indicators meet the preset threshold, the current vertical emission profile time series is output as the target vertical emission profile time series; if the verification indicators do not meet the preset threshold, the horizontal and vertical diffusion coefficients in the diffusion model are dynamically adjusted based on the deviation ratio between the verification indicators and the preset threshold, and forward simulation and verification indicator calculation are performed again until the verification indicators meet the preset threshold or the maximum number of iterations is reached to obtain the target vertical emission profile time series.

2. The method for inverting vertical profiles of volcanic sulfur dioxide based on the Lagrange diffusion model according to claim 1, characterized in that, The process of step S2 includes: Based on the observed geometric parameters, cloud parameters, and surface albedo in the satellite observation data, effective pixels are selected; based on the effective pixels, a forward simulation is performed using the radiative transfer model to obtain the simulation results. Based on the simulation results, the partial derivative of the top-of-atmosphere radiation with respect to the vertical layer concentration of sulfur dioxide is calculated using the radiative transfer model to generate the vertical sensitivity profile. The vertical sensitivity profile is normalized to obtain the vertical weighting function.

3. The method for inverting vertical profiles of volcanic sulfur dioxide based on the Lagrange diffusion model according to claim 2, characterized in that, The process of normalizing the vertical sensitivity profile to obtain the vertical weight function includes: The total sensitivity is calculated by integrating the vertical sensitivity profile within a preset height range. The sensitivity of each height layer is normalized based on the total sensitivity to obtain the vertical weight function.

4. The method for inverting vertical profiles of volcanic sulfur dioxide based on the Lagrange diffusion model according to claim 3, characterized in that, The process of step S3 includes: An air column is constructed based on the latitude and longitude positions of the effective pixels, and the air column is uniformly divided into several layers at 0.2 km intervals in the vertical direction; The number of air clusters in the air column at each pixel is determined based on the sulfur dioxide column concentration of all effective pixels. The number of air clusters at each pixel is proportional to the sulfur dioxide column concentration of that pixel, and the sum of the number of air clusters in all effective pixels is the preset total number of air clusters. The air masses in the corresponding air column are vertically stratified and proportioned according to the vertical weight function at each effective pixel to obtain the initial vertical distribution of sulfur dioxide.

5. The method for inverting vertical profiles of volcanic sulfur dioxide based on the Lagrange diffusion model according to claim 4, characterized in that, The process of determining the number of air clusters in the air column at each pixel based on the sulfur dioxide column concentration of all effective pixels, wherein the number of air clusters at each pixel is proportional to the sulfur dioxide column concentration of that pixel, and the sum of the number of air clusters in all effective pixels is a preset total number of air clusters, includes: Read the sulfur dioxide column concentration data for each valid pixel one by one; Calculate the sum of sulfur dioxide column concentrations for all valid pixels; Based on the preset total number of air masses, the number of air masses in the air column at each effective pixel is calculated according to the proportion of the sulfur dioxide column concentration of each effective pixel to the total. The number of air clusters at each effective pixel is rounded down and adjusted so that the sum of the number of air clusters at all effective pixels equals the preset total number of air clusters.

6. The method for inverting vertical profiles of volcanic sulfur dioxide based on the Lagrange diffusion model according to claim 5, characterized in that, The process of step S4 includes: The diffusion model is initialized based on the three-dimensional meteorological driving data and chemical scavenging parameters; The initial vertically distributed air mass is used as the input to the diffusion model to simulate the backward trajectory of the air mass and obtain the endpoint position of the trajectory. A time window for volcanic eruption, a spatial near-field range, and a vertical height tolerance threshold are set. Gas masses that enter the spatial near-field range within the time window and whose height is within the vertical height tolerance threshold are selected to determine the distribution of the attributable gas masses.

7. The method for inverting vertical profiles of volcanic sulfur dioxide based on the Lagrange diffusion model according to claim 6, characterized in that, The process of using the initially vertically distributed air mass as input to the diffusion model to simulate the backward trajectory of the air mass and obtain the endpoint position of the trajectory includes: Based on the wind field in the three-dimensional meteorological driving data as the driving field, the air mass is back-time integrated through the diffusion model to generate the basic motion trajectory of the air mass within the time window. Based on the basic motion trajectory, the random diffusion motion of the air mass is simulated through a subgrid turbulence parameterization process to obtain the real-time height and position of the air mass; Based on the real-time altitude and location, the chemical conversion rate of sulfur dioxide is calculated using the ozone and hydroxyl concentrations in the chemical removal parameters. Integrating along the timeline from the satellite observation time back to the volcanic eruption period, we can obtain the endpoint of the gas cloud's trajectory during the eruption period.

8. The method for inverting vertical profiles of volcanic sulfur dioxide based on the Lagrange diffusion model according to claim 1, characterized in that, The process of step S6 includes: The vertical emission profile time series was used as input to the diffusion model. Combined with three-dimensional meteorological driving data and chemical scavenging parameters, forward time integration was performed on the air mass to generate a simulated sulfur dioxide column concentration distribution. The simulated sulfur dioxide column concentration distribution is compared pixel-by-pixel with the sulfur dioxide column concentration in satellite observation data to calculate the verification index. Determine whether the verification index meets the preset index threshold to obtain the verification result; The diffusion coefficient is optimized based on the verification results until the verification index meets the preset threshold or reaches the maximum number of iterations to obtain the target vertical emission profile time series.

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