CN111048161B

CN111048161B - Aerosol extinction coefficient three-dimensional variation assimilation method based on IMPROVE equation

Info

Publication number: CN111048161B
Application number: CN201911003625.2A
Authority: CN
Inventors: 臧增亮; 梁延飞; 尤伟; 郝子龙; 胡译文; 刘斌; 汪代春; 潘晓滨
Original assignee: National University of Defense Technology
Current assignee: National University of Defense Technology
Priority date: 2019-10-22
Filing date: 2019-10-22
Publication date: 2022-09-13
Anticipated expiration: 2039-10-22
Also published as: CN111048161A

Abstract

A three-dimensional variation and assimilation method of aerosol extinction coefficients based on IMPROVE equation comprises the following steps: according to the three-dimensional variation theory and IMPROVE equation, writing a computer program for solving a three-dimensional variation target functional, and calling the computer program as an assimilation system; h is called an observation operator and is a matrix with dimension of M multiplied by N, wherein M is equal to the length of y, N is equal to the length of x, and the result Hx obtained by multiplying x by H is a vector with the same length as y; the role of H further includes interpolating the values of the grid points to the observed positions of the non-grid points; r is the covariance of the observation errors and is an M x M dimensional matrix; t represents the transpose of the vector. The calculation of Hx is performed according to the impulse equation, assuming that the observed position of y is exactly at the regular grid points of the pattern, the calculation of Hx does not involve an interpolation process.

Description

Aerosol extinction coefficient three-dimensional variation assimilation method based on IMPROVE equation

Technical Field

The invention relates to a method, belongs to the field of variable parameter data assimilation of atmospheric aerosol, and is mainly applied to data assimilation of aerosol extinction coefficients and air quality prediction research. In particular to a three-dimensional variation assimilation method of the extinction coefficient of the aerosol.

Background

The data of the aerosol extinction coefficient are uniformized, and the aim is to generate a three-dimensional analysis field which is closer to a real field and has more accurate aerosol mass concentration by utilizing the aerosol extinction coefficient data detected by a laser radar or a satellite on the basis of a background field (or a first guess value field, generally a three-dimensional grid field predicted by a numerical mode). One of the difficulties in assimilation for the extinction coefficients and other data reflecting the optical properties of aerosols is the method for implementing the conversion relationship between the mass concentration of multi-species aerosols and the extinction coefficients of aerosols in the computer numerical solver.

Currently, the assimilation method of aerosol extinction data is less researched, and in the existing consultable documents and methods, the conversion relation between the aerosol mass concentration and the aerosol extinction coefficient is mainly based on a rice scattering formula or a statistical regression equation (Wang et al, 2014) between PM2.5 (or PM10) and the extinction coefficient. The two methods have certain defects, wherein the calculation of the meter scattering formula is too complex and is sensitive to calculation parameters; the regression equation cannot reflect the contribution of different aerosol species to extinction coefficients, and the physical basis in the conversion relation is difficult to reflect due to the fact that the regression equation is based on statistical data, so that the applicable space-time range is limited.

The IMPROVE equation establishes a conversion relation which has a physical basis and can reflect the mass concentration of the multi-species aerosol to the extinction coefficient according to a meter scattering theory, a large number of mass concentrations of the multi-species aerosol and corresponding extinction coefficients, and the data assimilation of the extinction coefficients of the aerosol can be efficiently realized by introducing the IMPROVE equation into a data assimilation method. The form and parameters of the IMPROVE equation are referenced in the literature of Pitchford et al (2007) and Gordon et al (2018).

The reference:

[1]Wang Y,Sartelet K N,Bocquet M,et al.Assimilation of lidar signals:application to aerosol forecasting in the western Mediterranean basin[J].Atmospheric Chemistry and Physics,2014,14(22):134-138.

[2]Pitchford M,Maim W,Schichtel B,et al.Revised Algorithm for Estimating Light Extinction from IMPROVE Particle Speciation Data[J].Journal of the Air&Waste Management Association,2007,57(11):1326-1336.

[3]Gordon T D,Prenni A J,Renfro J R,et al.Open-path,closed-path and reconstructed aerosol extinction at a rural site[J].Journal of the Air&Waste Management Association,2018:10962247.2018.1452801.

disclosure of Invention

The invention aims to provide an IMPROVE equation-based three-dimensional variation assimilation method for aerosol extinction coefficients, which introduces a conversion method between aerosol mass concentration and aerosol extinction coefficients according to the IMPROVE equation into three-dimensional variation assimilation, and generates a more accurate three-dimensional analysis field of aerosol concentration by utilizing aerosol extinction coefficient data detected by radar or satellites on the basis of a numerical mode prediction result (background field). Compared with a background field, the analysis field can more accurately reflect the space-time distribution actual condition of the aerosol, can be used for researching the space-time evolution law of the aerosol and can also be used for improving the initial condition of a numerical mode, so that the aerosol forecasting effect of the numerical mode is improved, and more accurate air quality forecasting is made.

The invention discloses a technical scheme of a three-dimensional variation and assimilation method of an aerosol extinction coefficient based on an IMPROVE equation, which comprises the following steps:

according to the three-dimensional variation theory and IMPROVE equation, a computer program for solving the three-dimensional variation target functional is written and called an assimilation system. The form of the three-dimensional variation target functional is as follows:

wherein, x is called a control variable in an assimilation system, is a vector with the length of N, the element of the vector is the mass concentration value of a plurality of species aerosol variables at a three-dimensional grid point of a numerical mode, and the optimal solution x-x of the functional can be obtained by utilizing a numerical solving program of a computer ^a Then x ^a To solve the resulting analytical field;

x ^b called background field, is the first guess value of x, the vector structure is the same as x, and the forecast result of the numerical mode at the previous moment is generally taken as the background field. B is the background error covariance, which is a matrix of dimension NxN。

y is called an observation variable and is a vector of length M whose elements are observations of the aerosol extinction coefficients at a plurality of observation locations.

H, called the observer, is a matrix of dimensions M x N, where M is equal to the length of y, N is equal to the length of x, and the result of x left-multiplying H (Hx) is a vector of the same length as y. Its physical meaning includes two aspects: firstly, x is the mass concentration of multiple aerosol species, and y is an aerosol extinction coefficient, and the value of x needs to be converted into a corresponding aerosol extinction coefficient value by using H to subtract y, and secondly, because the observation position of y is not exactly at the regular grid point of the mode, the function of H also comprises the step of interpolating the value of the grid point to the observation position of a non-grid point.

R is the covariance of the observed error and is an M dimensional matrix. T represents the transpose of the vector.

The core content of the invention is to realize the calculation of Hx according to the impulse equation, and since the interpolation process is not the core content of the invention, the following technical solution is introduced assuming that the observation position of y is exactly at the regular grid point of the pattern, and the calculation of Hx does not involve the interpolation process.

1) Taking the WRF-Chem model (wherein the aerosol solution employs MOSAIC 4bin solution) as an example, the numerical model calculates the mass concentration of 8 types of aerosol species at any grid point, including Elemental Carbon (EC), Organic Carbon (OC), sulfate (SO4), nitrate (NO3), ammonium salt (NH4), Chloride (CL), sodium salt (NA), and other unclassified minerals (OIN), wherein each type of species is divided into 4 classes (4 bins) by particle size, including 0.039-0.1 μm, 0.1-1.0 μm, 1.0-2.5 μm, and 2.5-10 μm, respectively, and has 32 model variables.

In the assimilation system of the present example, the values of 1 to 3 th gear of each species are combined as one element of x, and the value of 4 th gear is taken as one element, so that 16 elements including x at any one grid point are respectively expressed as: EC (EC) _2.5 、EC _2.5-10 、OC _2.5 、OC _2.5-10 、NO3 _2.5 、NO3 _2.5-10 、SO4 _2.5 、SO4 _2.5-10 、CL _2.5 、CL _2.5-10 、NA _2.5 、NA _2.5-10 、NH4 _2.5 、NH4 _2.5-10 、OIN _2.5 、OIN _2.5-10 。

2) Collecting aerosol extinction coefficient data and a background field file of numerical mode simulation, and storing according to the format and position required by an assimilation system. Mainly 5 input files. The 1 st file is a background field file, and is typically a wrfout or wrfrst file at the assimilation time of the modal forecast output, and has a format of ncf. The 2 nd file is an observation file of the aerosol extinction coefficient data, the format is a text file, each line in the file represents an observation record, each observation record contains 4 lines of data, and the observed latitude, longitude, height from the ground and extinction coefficient values are respectively from left to right. The 3 rd file to the 5 th file are respectively a background error standard deviation file, a background error horizontal correlation coefficient file and a background error vertical correlation coefficient file, wherein the background error standard deviation file and the background error vertical correlation coefficient file are both in ncf format, and the background error horizontal correlation coefficient file is in a text file format.

3) Compiling and operating the assimilation system to obtain an assimilation analysis field. The assimilation system is compiled, installed and operated under a Linux operating system.

The system comprises 5 sub-directories, wherein the 1 st directory is an original program directory (source), a FORTRAN source code of a homogenization solving link is stored, and an executable file named da.exe is generated after the code is compiled. The 2 nd directory is an executive directory (bin) containing da.exe compiled from the 1 st directory. The 3 rd directory is a data directory (data) and is mainly used for storing various data files input and output by the assimilation system, and comprises the input file in the step (2) and the output file after operation. The 4 th directory is a control directory (control), an ASCII text file named da _ files.in is arranged below the control directory, and the content of the file is the full path of each input/output file. The batch processing script written according to the business operation requirement can also be stored in the control directory. The 5 th directory is an analysis directory (analysis) in which FORTRAN source code for generating analysis field files is stored, and the code is compiled to generate an executable file named dx2wrf.

In the first step, the program is compiled. The Makefile file is modified under the original program directory to give the correct netcdf library path, and then compiled using the make command at the command line. After the compilation is successful, an executable file da.exe is generated under the executive directory. The same method was used to compile dx2wrf.exe under the analysis catalog.

Second, the control file da _ files.in is modified. Each row of the file corresponds to a storage path of an input or output file, and is respectively a background field file path, a mode variable setting file path, an increment field file path, an observation file path, a background error standard deviation file path, a background error horizontal correlation coefficient file path, a background error vertical correlation coefficient file path and an observation background difference file path, wherein the increment field file and the observation background difference file are output files, and the rest are input files.

And thirdly, operating da.exe. The command format is "parameter 1 parameter 2", where parameter 1 is the path of da.exe and parameter 2 is the path of da _ files.in file. An analysis delta field may be generated after the run is complete.

And fourthly, generating an analysis field. In the analysis directory, dx2wrf.exe is operated, and the command format is 'parameter 1, parameter 2, parameter 3 and parameter 4', wherein parameter 1 is the path of dx2wrf.exe, parameter 2 is the path of a background field file, parameter 3 is the path of an analysis field file, and parameter 4 is the path of an increment field file. And obtaining a final analysis field after the operation is finished.

The invention has the beneficial effects that: according to the method, the three-dimensional analysis field of the aerosol concentration more accurate than the background field is generated by utilizing the aerosol extinction coefficient data detected by radar or satellite. Since the analysis field more accurately reflects the space-time distribution of the aerosol, the prediction effect of the numerical mode on the aerosol can be more accurate by using the analysis field as the initial condition of the numerical mode than by using the background field as the initial condition of the numerical mode. Compared with a background field, the three-dimensional analysis field for the aerosol concentration can more accurately reflect the space-time distribution actual condition of the aerosol, can be used for researching the space-time evolution rule of the aerosol and improving the initial condition of a numerical mode, so that the aerosol forecasting effect of the numerical mode is improved, and more accurate air quality forecasting is made.

Taking a forecast simulation test of a pollution process in Beijing area from 13 days to 14 days in 3 months to 3 months in 2018 as an example, an assimilation system assimilates aerosol extinction coefficient data detected by a radar hourly from 13 days 00 hours (world time, same below) to 13 days 12 hours in the Beijing area to generate an aerosol analysis field at 13 days 12, and the analysis field is used as a chemical initial field of a numerical mode to carry out PM analysis on the PM at 13 days 12 to 14 days 12 _2.5 And forecasting is carried out, and compared with a forecasting result which uses the background field as the chemical initial field, the comparison result shows that the forecasting effect after assimilation is obviously improved.

Drawings

FIG. 1 is a diagram showing the location distribution of a laser radar station and an air quality ground monitoring station in Beijing area. The laser radar data assimilated by the system come from 3 radar stations in Beijing area and are respectively positioned in Yanqing, suburb and mountain. The data for evaluating the data assimilation effect come from 12 air quality ground monitoring stations of China Ministry of environmental protection, and utilize hourly PM _2.5 The mass concentration data were evaluated. The starting time of the mode is 3 months, 13 days and 12 days, namely the time corresponding to the initial field of the mode.

FIG. 2 shows ground PM of the aerosol analytical field before (a) and after (b) assimilation _2.5 Mass concentration distribution and assimilation of PM _2.5 And (c) increasing. As can be seen from FIG. 2, after assimilating the radar data, the PM in Beijing area in the aerosol analysis field _2.5 The mass concentration is higher than that before assimilation and is closer to PM _2.5 The true distribution of (see fig. 4-fig. 7 for the contrast value at time 0, and the statistical results of fig. 8).

FIG. 3 is a comparison of the aerosol extinction coefficient profile and the observed profile at 3 radar stations (a, b, c in the figures, respectively) in the pre-and post-assimilation aerosol analytical fields. It can be found that the extinction coefficient profile of the post-assimilation aerosol is closer to the observation compared with that before assimilation, which shows that the data assimilation effectively improves the accuracy of the aerosol analysis field.

FIGS. 4-7 show the data assimilation vs. daling,PM of 4 sites in ancient city, east four and Shunqi New City _2.5 Analyzing and forecasting the influence. The distance between the four 3 stations of the tomb, the ancient city and the east is short, the direct influence of data assimilation is large, and the influence of the radar data assimilation on the areas around the radar stations can be represented; the paradoxical new city is far away from the radar station and is difficult to be directly influenced by data assimilation, but can be influenced by the advection and diffusion of aerosol in an upstream area along with the prediction time, so that the influence of radar data assimilation on areas without radar data is represented. In the figure, the horizontal axis is a time axis in units of hours, 0 represents the mode start time, namely 13 days and 12 days, a negative value represents the time before the start, and data assimilation is performed every hour within 12 hours before the start. Positive values represent the duration of the forecast, 24 hours total forecast. The longitudinal axis being PM _2.5 Mass concentration value of (2). The black line is the observed value, and the blue line is the simulated and predicted value without data assimilation mode (data assimilation vs. tomb station PM) _2.5 The impact of the forecast. Obs observed value, forecast value, increase value of increment), red line (lighter color) is PM in one assimilation process _2.5 The green line (slightly darker) is the predicted value of the post-assimilation mode. As can be seen from fig. 4-6, except for individual moments, radar data assimilation can bring the mode values closer to observation, as a red line approaches to a black line from the far end from the black line, indicating that assimilation has a better direct effect; compared with the prediction result of the mode before assimilation, the simulation and prediction result of the mode after assimilation are closer to the observation, and the result shows that a green line is closer to a black line than a blue line, which shows that the assimilation can improve the mode to PM _2.5 The effect of forecasting. As can be seen from FIG. 7, although assimilation has no great direct influence on the cis-new castle, and the red line of each assimilation is short, the PM of the cis-new castle after assimilation is smooth and diffused along with the advection and diffusion of the aerosol due to more accurate aerosol prediction in the upstream area after assimilation _2.5 The forecast is also closer to the observation. The radar data assimilation can not only improve the mode for PM in the surrounding area of the radar station _2.5 Can also improve the PM of downstream areas _2.5 The effect of forecasting.

FIG. 8 shows assimilationModel forecast PM of Beijing area after former assimilation _2.5 Root Mean Square Error (RMSE) of the measuring system as a function of the predicted time duration, PM used for the test _2.5 The observation data come from 12 air quality ground monitoring stations in Beijing area. The 0 th moment is the direct effect of assimilation, the later moments are the predicted effects. As can be seen from the figure, the RMS error before assimilation in the initial field of the pattern (i.e., initial time, time 0) is 126.9 μ gm ^-3 And after assimilation, the reduction was 35.2. mu.gm ^-3 And in the 24-hour forecasting period, the RMSE after assimilation is smaller than the unassimilated forecasting, which shows that the radar data assimilation can obviously improve the chemical initial condition of numerical forecasting and improve the forecasting effect of the mode.

Detailed Description

The three-dimensional variation assimilation method of the aerosol extinction coefficient based on the IMPROVE equation comprises the following steps:

1) according to the three-dimensional variation theory and the IMPROVE equation, a computer program for solving the three-dimensional variation target functional is written and called as an assimilation system. The form of the three-dimensional variation target functional is as follows:

wherein, x is called a control variable in an assimilation system, is a vector with the length of N, the element of the vector is the mass concentration value of a plurality of species aerosol variables at a three-dimensional grid point of a numerical mode, and the optimal solution x-x of the functional can be obtained by using a numerical solving program of a computer ^a Then x ^a To solve the resulting analytical field;

x ^b called background field, is the first guess value of x, the vector structure is the same as x, and the forecast result of the numerical mode at the previous moment is generally taken as the background field. B is the background error covariance, which is an N × N dimensional matrix.

Taking the WRF-Chem model (wherein the aerosol protocol employs MOSAIC 4bin protocol) as an example, the numerical model calculates the mass concentration of 8 types of aerosol species at any grid point, which are respectively Elemental Carbon (EC), Organic Carbon (OC), sulfate (SO4), nitrate (NO3), ammonium salt (NH4), Chloride (CL), sodium salt (NA), and other unclassified inorganic matter (OIN), and each type of species is further divided into 4 bins (4 bins) by particle size, which are respectively 0.039-0.1 μm, 0.1-1.0 μm, 1.0-2.5 μm, and 2.5-10 μm, for 32 mode variables.

Hx is used for obtaining the aerosol extinction coefficient value beta at the grid point by using the value conversion of the 16 elements _ext The conversion formula is as follows:

bet _ext ＝2.2×fs(RH)×[Small Sulfate]+4.8×fl(RH)×[Large Sulfate]+

2.4×fs(RH)×[Small Nitrate]+5.1×fl(RH)×[Large Nitrate]+

2.8×[Small Organic Mass]+6.1×[Large Organic Mass]+2

10×[Elemental Carbon]+1×[Fine Soil]+

1.7×fss(RH)×[Sea Salt]+0.6×[Coarse Mass]

in equation 2, the extinction coefficient value beta obtained by conversion is on the left _ext Unit 10 ^-6 m ^-1 The variables in parentheses in the right are obtained by combining 16 elements in units of μ gm ^-3 The variable coefficients fs (rh), fl (rh), fss (rh) reflect the influence of aerosol moisture absorption growth on luminous efficiency, the size is related to the relative humidity of air, and the specific parameters are shown in the attached tables 1, 2 and 3. The formula is obtained according to IMPROVE equation, the obtaining and discussion of the equation can refer to the literature of Pitchford et al (2007), and constant coefficients in the formula can also be adjusted to a certain extent according to new observation facts, and refer to the literature of Gordon et al (2018).

The method for combining 16 elements to obtain the variables in brackets is as follows:

wherein

The determination principle of (2) is as follows: mixing NH4 _2.5 Is preferentially allocated to SO4 _2.5 Excess NH4 _2.5 NO3 _2.5 。

Large Sulfate＝Sulfate-Small Sulfate

Large Nitrate＝Nitrate-Small Nitrate

Organic Mass＝OC _2.5

Large Organic Mass＝Organic Mass-Small Organic Mass

Elemental Carbon＝EC _2.5

Fine Soil＝OIN _2.5

Sea Salt＝CL _2.5 +NA _2.5

Coarse Mass＝SO4 _2.5-10 +NO3 _2.5-10 +NH4 _2.5-10 +OC _2.5-10 +EC _2.5-10 +CL _2.5-10 +NA _2.5-10 +OIN _2.5-10

The system comprises 5 sub-directories, wherein the 1 st directory is an original program directory (source), a FORTRAN source code of a homogenization solving link is stored, and an executable file named da.exe is generated after the code is compiled. The 2 nd directory is an executive directory (bin) and contains da.exe compiled from the 1 st directory. The 3 rd directory is a data directory (data) and is mainly used for storing various data files input and output by the assimilation system, and comprises the input file in the step (2) and the output file after operation. The 4 th directory is a control directory (control), an ASCII text file named da _ files.in is arranged below the control directory, and the content of the file is the full path of each input/output file. The batch processing script written according to the business operation requirement can also be stored in the control directory. The 5 th directory is an analysis directory (analysis) in which FORTRAN source code for generating analysis field files is stored, and the code is compiled to generate an executable file named dx2wrf.

And fourthly, generating an analysis field. And operating dx2wrf.exe under the analysis directory, wherein the command format is 'parameter 1, parameter 2, parameter 3 and parameter 4', the parameter 1 is a path of the dx2wrf.exe, the parameter 2 is a path of a background field file, the parameter 3 is a path of an analysis field file, and the parameter 4 is a path of an increment field file. And obtaining a final analysis field after the operation is finished.

TABLE 1 influence of Small Aerosol hygroscopic growth on luminous efficacy in IMPROVE equation fs (RH)

TABLE 2 influence of moisture absorption growth of Large Aerosol on luminous efficacy in IMPROVE equation, fl (RH)

Table 3 Effect of Seasalt Aerosol hygroscopic growth on luminous efficacy in IMPROVE equation, fss (RH)

Claims

1. An IMPROVE equation-based three-dimensional variation assimilation method for aerosol extinction coefficients is characterized by comprising the following steps:

according to the three-dimensional variation theory and IMPROVE equation, writing a computer program for solving a three-dimensional variation target functional, and calling the computer program as an assimilation system;

the form of the three-dimensional variation target functional is as follows:

wherein, x is called a control variable in an assimilation system, is a vector with the length of N, the element of the vector is the mass concentration value of a plurality of species aerosol variables at a three-dimensional grid point of a numerical mode, and the optimal solution x-x of the functional can be obtained by utilizing a numerical solving program of a computer ^a Then x is ^a To solve the resulting analytical field;

x ^b called the background field, is the first guess for x, and the vector structure is the same as x, and is generally numericalThe forecast result of the mode at the previous moment is used as a background field; b is the background error covariance, which is an N x N dimensional matrix;

y is called an observation variable and is a vector with the length of M, and the element of the vector is an observed value of the aerosol extinction coefficient at a plurality of observation positions;

h is called an observation operator and is a matrix of dimension M x N, wherein M is equal to the length of y, N is equal to the length of x, and the result (Hx) of left multiplication of x by H is a vector with the same length as y; its physical meaning includes two aspects: firstly, x is the mass concentration of multiple aerosol species, y is an aerosol extinction coefficient, and the value of x needs to be converted into a corresponding aerosol extinction coefficient value by using H to be subtracted from y, and secondly, because the observation position of y is not exactly at the regular grid point of the mode, the function of H also comprises the step of interpolating the value of the grid point to the observation position of a non-grid point;

r is the observation error covariance, which is a matrix of M dimensions, and T represents the transpose of the vector.

2. The method of claim 1, wherein the calculation of Hx is performed according to the impulse equation, and wherein the calculation of Hx does not involve an interpolation process assuming that the observed position of y is exactly at the regular grid points of the pattern.

3. The method of claim 1, wherein the WRF-Chem model is used, wherein the aerosol protocol uses the MOSAIC 4bin protocol, and the numerical model calculates the mass concentration of 8 types of aerosol species, namely, Elemental Carbon (EC), Organic Carbon (OC), sulfate (SO4), nitrate (NO3), ammonium salt (NH4), Chloride (CL), sodium salt (NA) and other unclassified inorganic matter (OIN), at any grid point, and each type of species is divided into 4 classes (4 bins) by particle size, namely, 0.039-0.1 μm, 0.1-1.0 μm, 1.0-2.5 μm and 2.5-10 μm, respectively, and has 32 model variables.

4. The method of claim 1, wherein the assimilation system combines the values of 1 to 3 of each species as an element of x, and the value of 4 th gear is used asIs one element, therefore, the 16 elements containing x at any one grid point are respectively noted as: EC (EC) _2.5 、EC _2.5-10 、OC _2.5 、OC _2.5-10 、NO3 _2.5 、NO3 _2.5-10 、SO4 _2.5 、SO4 _2.5-10 、CL _2.5 、CL _2.5-10 、NA _2.5 、NA _2.5-10 、NH4 _2.5 、NH4 _2.5-10 、OIN _2.5 、OIN _2.5-10 。

5. The method as set forth in claim 4,

bet _ext ＝2.2×fs(RH)×[Small Sulfate]+4.8×fl(RH)×[Large Sulfate]+2.4×fs(RH)×[Small Nitrate]+5.1×fl(RH)×[Large Nitrate]+2.8×[Small Organic Mass]+6.1×[Large Organic Mass]+210×[Elemental Carbon]+1×[Fine Soil]+1.7×fss(RH)×[Sea Salt]+0.6×[Coarse Mass]

in the above formula, the left side is the extinction coefficient value beta obtained by conversion _ext Unit 10 ^-6 m ^-1 The variables in parentheses in the right are derived from 16 element combinations in units of μ gm ^-3 The variable coefficients fs (RH), fl (RH), fss (RH) reflect the influence of the moisture absorption growth of the aerosol on the luminous efficiency, and the size of the variable coefficients is related to the relative humidity of air; the formula is obtained according to an IMPROVE equation; the method for combining 16 elements to obtain the variables in brackets is as follows: