Aerosol moisture absorption growth factor measurement method and device based on double OPS

Abstract

The invention discloses a method and a device for measuring an aerosol moisture absorption growth factor based on double OPS. A drying tube, a first optical particle spectrometer and a second optical particle spectrometer are adopted to obtain the particle size distribution of the dried aerosol and the particle size distribution of the non-dried aerosol, and the moisture absorption growth factor is obtained through inversion by means of the measured particle size spectrum distribution of the whole aerosol; the second total scattering intensity is obtained by directly adopting the scattering intensity distribution spectrum obtained by calculating the wet particle size aerosol, the first total scattering intensity is obtained by combining the dry particle size aerosol with the characteristics of the moisture-absorbed aerosol obtained by calculating the moisture absorption growth model, and the initial value of the moisture absorption growth factor is changed by utilizing a gradient descent method; performing inversion until the first total scattering intensity is equal to the second total scattering intensity to obtain an aerosol moisture absorption growth factor; the instrument cost is remarkably reduced, a humidifying unit is not needed to control the humidity of instrument equipment, and the maintenance difficulty is remarkably reduced; according to the method, the moisture absorption growth factor is obtained through inversion by using the measured particle size spectrum distribution of the whole aerosol, and the error is smaller.

Description

Technical Field

[0001] This invention relates to aerosol measurement technology, specifically to a method and apparatus for measuring the hygroscopic growth factor of aerosols based on dual OPS. Background Technology

[0002] Atmospheric aerosols directly affect the radiation balance of the Earth-atmosphere system by scattering and absorbing solar radiation. Furthermore, aerosols can act as cloud condensation nuclei or ice nuclei, altering the macroscopic and microscopic properties of clouds and thus indirectly influencing weather and climate. The direct and indirect effects of aerosols on climate are closely related to factors such as their particle size distribution and hygroscopicity, with hygroscopicity playing a particularly crucial role in these effects.

[0003] The hygroscopicity of aerosols describes their ability to interact with water vapor. Under high relative humidity conditions, the hygroscopic growth of aerosols alters their particle size distribution and complex refractive index, directly affecting radiation balance. Furthermore, the strength of aerosol hygroscopicity determines their ability to activate as cloud condensation nuclei, thus indirectly influencing radiation by altering cloud properties. Whether directly or indirectly, the hygroscopicity of aerosols is a core factor affecting radiation effects and is of great significance to weather, climate, and the environment.

[0004] The current method for quantifying the hygroscopic growth capacity of aerosols under different relative humidity conditions uses capacitive (κ-) Theoretically, the aerosol hygroscopic growth measurement device includes a separator, first and second differential electromigration analyzers (HTDMA), a humidification unit, and first and second optical particle counters. The particle size is selected by the first differential electromigration analyzer, humidified by the humidification unit, and then the particle size after hygroscopic growth is measured by the second differential electromigration analyzer. Finally, the particle counters are used to obtain the number of aerosol particles, and the particle size of the aerosol with the highest number of particles represents the particle size of the humidified aerosol. This method is time-consuming to measure the aerosol hygroscopic growth factor. When measuring the hygroscopic growth of a single-size aerosol online, it takes at least 5 minutes, making it unsuitable for high-temporal-resolution vertical observations. Furthermore, the measurement device is costly, and the humidification unit is difficult to maintain. Summary of the Invention

[0005] To address the problems existing in the prior art, this invention proposes a method and device for measuring the hygroscopic growth factor of aerosols based on dual OPS. This method reduces the use of differential electromigration analyzers, significantly lowering instrument costs; it eliminates the need for a humidification unit to control the humidity of the instrument, significantly reducing maintenance difficulty; and it uses the measured entire aerosol particle size distribution to invert the hygroscopic growth factor, resulting in smaller errors.

[0006] One object of the present invention is to provide a method for measuring the hygroscopic growth factor of aerosols based on dual OPS.

[0007] The method for measuring the hygroscopic growth factor of aerosols based on dual OPS of the present invention includes the following steps:

[0008] 1) Measuring device:

[0009] After sampling the environmental aerosols at the sampling port, they were divided into two paths. One path passed through a drying tube, and the particle size distribution PNSD1 of the dried aerosol was measured using the first optical particle spectrometer OPS1. The temperature T1 and relative humidity RH1 of the dried aerosol were measured using the first temperature and humidity probe. The other path was not dried, and the particle size distribution PNSD2 of the undried aerosol was directly measured using the second optical particle spectrometer OPS2. At the same time, the temperature T2 and relative humidity RH2 of the undried inlet of the gas path, as well as the temperature T3 and relative humidity RH3 of the undried outlet of the gas path, were measured using the second and third temperature and humidity probes before and after the second optical particle spectrometer OPS2, respectively.

[0010] 2) Calculate the equivalent relative humidity:

[0011] The second optical particle spectrum was calculated using the undried inlet temperature T2 and the undried inlet relative humidity RH2.

[0012] The water vapor content e2 at the inlet of instrument OPS2 is:

[0013]

[0014] The second optical particle spectrum was calculated using the undried outlet temperature T3 and the undried outlet relative humidity RH3.

[0015] The water vapor content e3 at the outlet of instrument OPS2 is:

[0016]

[0017] The equivalent water content e0 in the second optical particle spectrometer OPS2 is obtained as follows:

[0018]

[0019] The equivalent temperature T0 in the second optical particle spectrometer OPS2 is:

[0020]

[0021] Using the equivalent temperature T0 and equivalent water content e0 in the second optical particle spectrometer OPS2, the second optical particle spectrometer was calculated.

[0022] Equivalent relative humidity RH0 of aerosols in spectrometer OPS2:

[0023]

[0024] 3) Hygroscopic growth factor κ:

[0025] Based on the particle size distributions PNSD1 and PNSD2 of the dried aerosol, the equivalent relative humidity RH0 of the aerosol in the second optical particle spectrometer OPS2, and the commonly used complex refractive index RI0 of aerosol, the hygroscopic growth factor κ of the aerosol is calculated using the following method:

[0026] (1) The second total scattering intensity S2 is obtained by directly using the scattering intensity distribution spectrum calculated from wet particle size aerosol:

[0027] a. Particle size distribution of undried aerosols. PNSD2 represents different particle sizes Dp1, Dp2, ... Dp n The undried concentrations of the aerosols were N 21 N 22 …N 2n n is the number of different particle size types;

[0028] b. Using the Mie scattering model, the commonly used complex refractive index combinations for calculating particle size and aerosols are (Dp1,RI0), (Dp2,RI0)...(Dp... n The scattering intensities under RI0) are S 21 ,S 22 …S 2n The corresponding scattering intensity distribution spectrum S′ is obtained directly from wet particle size aerosol calculations. 2i for:

[0029] c. Based on the scattering intensity distribution spectrum obtained directly from wet particle size aerosols, the corresponding second total scattering intensity S2 is:

[0030]

[0031] (2) The first total scattering intensity S1 was obtained by calculating the scattering intensity distribution spectrum using a dry particle size aerosol combined with a hygroscopic growth model:

[0032] a. An initial value for the hygroscopic growth factor is arbitrarily set. The particle size distribution after aerosol drying, PNSD1, represents different particle sizes Dp1, Dp2, ... Dp. n The concentrations of the dried aerosols were N 11 N 12 …N 1n ;

[0033] b. Using Capacola Theoretical formula, under the conditions of relative humidity RH1 after drying to equivalent relative humidity RH0 and equivalent temperature T0, the particle size Dp of aerosol after hygroscopic growth from different particle sizes Dp1, Dp2, … Dpn is calculated n to the equivalent relative humidity 11 12 1n ;

[0034] c. Using the method of volume-weighted average, the complex refractive index RI of the aerosol corresponding to the particle size Dp of the i-th aerosol after hygroscopic growth is calculated 1i : 1i :

[0035] Where i = 1, 2 … n

[0036] Where RI is the complex refractive index of water; water

[0037] d. Using the Mie scattering model, the scattering intensity of the combination of particle size and complex refractive index of the aerosol after hygroscopic growth (Dp, RI), (Dp, RI) … (Dp, RI) is calculated respectively S, S … S; The corresponding scattering intensity distribution spectrum S′ calculated by the dry particle size aerosol combined with the hygroscopic growth model is: 11 11 12 12 1n 1n ; S′ 11 12 1n 1i

[0038] e. According to the scattering intensity distribution spectrum calculated by the dry particle size aerosol combined with the hygroscopic growth model, the corresponding first total scattering intensity S1 is:

[0039]

[0040] (3) The first total scattering intensity S1 and the second total scattering intensity S2 are essentially the same, both of which are the total scattering intensity of the wet particle size aerosol. The initial value of the hygroscopic growth factor is changed by using the gradient descent method until the first total scattering intensity S1 and the second total scattering intensity S2 are equal or the deviation between the two is less than a set threshold value. When this condition is met, the value κ0 of the hygroscopic growth factor is the last retrieved aerosol hygroscopic growth factor.

[0041] ​​​​​​​​​​​​Wherein, in (2) of step 3), the initial value of the optional hygroscopic growth factor is 0.01-1. n is 32 or 64, which is the number of particle sizes measured in the aerosol particle size spectrum distribution, and the number of particle sizes n is different for different OPS models.

[0042] Kappa (Kappa ) theory formula is:

[0043]

[0044] Wherein, Dp 1i is the particle size after hygroscopic growth at the i-th equivalent relative humidity, Dp i represents the i-th particle size, K is the hygroscopic growth factor of the aerosol, reflecting the hygroscopic growth ability of the aerosol itself, s s / a is the surface tension of the aerosol, which is usually taken as equal to the surface tension of water at high relative humidity, R is the Avogadro constant, M water is the molar mass of water, T0 is the equivalent temperature, and p w is the density of water.

[0045] In (3) of step 3), the threshold value is set to 10 -6 -10 -5 .

[0046] Another object of the present application is to provide a device for measuring the hygroscopic growth factor of aerosol based on double OPS.

[0047] The device for measuring the hygroscopic growth factor of aerosol based on double OPS of the present application comprises a drying tube, first and second optical particle spectrometers, and first to third temperature and humidity probes; wherein the inlet of the ambient aerosol is connected to the inlet of the drying tube and the gas inlet of the second optical particle spectrometer through pipelines respectively; the outlet of the drying tube is connected to the gas inlet of the first optical particle spectrometer; the first temperature and humidity probe is arranged at the outlet of the first optical particle spectrometer; the second and third temperature and humidity probes are arranged at the gas inlet and outlet of the second optical particle spectrometer respectively; after sampling, the ambient aerosol is divided into two paths, one of which passes through the drying tube, and the particle size distribution of the dried aerosol is measured by the first optical particle spectrometer, and the temperature and relative humidity of the dried aerosol are measured by the first temperature and humidity probe; the other path is not dried, and the particle size distribution of the undried aerosol is measured by the second optical particle spectrometer, and the inlet temperature and relative humidity of the undried aerosol and the outlet temperature and relative humidity of the undried aerosol are measured by the second and third temperature and humidity probes respectively before and after the second optical particle spectrometer; the equivalent relative humidity is calculated according to the temperature and humidity of the gas inlet and outlet of the second optical particle spectrometer; the Kappa (Kappa The theoretical formula calculates the particle size of aerosols after hygroscopic growth under equivalent relative humidity for each particle size. The scattering intensity distribution spectrum is obtained by combining dry particle size aerosols with the hygroscopic growth model to obtain the first total scattering intensity. The second total scattering intensity is obtained by directly using wet particle size aerosols. The initial value of the hygroscopic growth factor is changed by using the gradient descent method until the first total scattering intensity and the second total scattering intensity are equal or the deviation between them is less than a set threshold. When this condition is met, the value of the hygroscopic growth factor is the hygroscopic growth factor of the aerosol obtained by inversion.

[0048] Advantages of this invention:

[0049] This invention employs a drying tube and first and second optical particle spectrometers to obtain the particle size distribution of the aerosol after drying and before drying. The hygroscopic growth factor is obtained by inverting the measured particle size distribution of the entire aerosol. This invention does not use a differential electromigration analyzer, which significantly reduces instrument costs. Furthermore, it eliminates the need for a humidification unit to control the humidity of the instrument, significantly reducing maintenance difficulty. The inversion method of this invention uses the measured particle size distribution of the entire aerosol to invert the hygroscopic growth factor, resulting in smaller errors. Attached Figure Description

[0050] Figure 1 This is a schematic diagram of the aerosol hygroscopic growth factor measurement device based on dual OPS of the present invention;

[0051] Figure 2 This is a flowchart of the method for measuring the aerosol hygroscopic growth factor based on dual OPS according to the present invention. Detailed Implementation

[0052] The present invention will be further described below with reference to the accompanying drawings and specific embodiments.

[0053] The method for measuring the hygroscopic growth factor of aerosols based on dual OPS in this embodiment is as follows: Figure 2 As shown, it includes the following steps:

[0054] 1) Measuring device:

[0055] like Figure 1As shown, after sampling the environmental aerosol from the sampling port, it is divided into two paths. One path passes through a drying tube, and the particle size distribution PNSD1 of the dried aerosol is measured using the first optical particle spectrometer OPS1. The temperature T1 and relative humidity RH1 of the dried aerosol are measured using the first temperature and humidity probe. The other path is not dried, and the particle size distribution PNSD2 of the undried aerosol is directly measured using the second optical particle spectrometer OPS2. At the same time, before and after the second optical particle spectrometer OPS2, the temperature T2 and relative humidity RH2 of the undried inlet of the gas path, and the temperature T3 and relative humidity RH3 of the undried outlet of the gas path are measured using the second and third temperature and humidity probes, respectively.

[0056] 2) Calculate the equivalent relative humidity:

[0057] The second optical particle spectrum was calculated using the undried inlet temperature T2 and the undried inlet relative humidity RH2.

[0058] The water vapor content e2 at the inlet of instrument OPS2 is:

[0059]

[0060] Using the undried outlet temperature T3 and the undried outlet relative humidity RH3, the outlet water vapor content e3 of the second optical particle spectrometer OPS2 is calculated as follows:

[0061]

[0062] The equivalent water content e0 in the second optical particle spectrometer OPS2 is obtained as follows:

[0063]

[0064] The equivalent temperature T0 in the second optical particle spectrometer OPS2 is:

[0065]

[0066] Using the equivalent temperature T0 and equivalent water content e0 in the second optical particle spectrometer OPS2, calculate the equivalent relative humidity RH0 of the aerosol in the second optical particle spectrometer OPS2:

[0067]

[0068] 3) Hygroscopic growth factor κ:

[0069] (1) The second total scattering intensity S2 is obtained by directly using the scattering intensity distribution spectrum of wet particle size aerosol:

[0070] a. Particle size distribution of undried aerosols. PNSD2 represents different particle sizes Dp1, Dp2, ... Dpn The undried concentrations of the aerosols were N 21 N 22 …N 2n n is the number of different particle size types;

[0071] b. Using the Mie scattering model, the particle size and the commonly used complex refractive index combination for aerosols are calculated as follows (Dp) 11 ,RI0), (Dp2,RI0)…(Dp n The scattering intensities under RI0) are S 21 ,S 22 …S 2n RI0 = 1.46; the corresponding scattering intensity distribution spectrum S′ is obtained directly from wet particle size aerosol calculation. 2i for:

[0072] Based on the scattering intensity distribution spectrum obtained directly from wet particle size aerosols, the corresponding second total scattering intensity S2c is:

[0073]

[0074] (2) The first total scattering intensity S1 was obtained by calculating the scattering intensity distribution spectrum using a dry particle size aerosol combined with a hygroscopic growth model:

[0075] a. An initial value for the hygroscopic growth factor is arbitrarily set. The particle size distribution after aerosol drying, PNSD1, represents different particle sizes Dp1, Dp2, ... Dp. n The concentrations of the dried aerosols were N 11 N 12 …N 1n ;

[0076] b. Using Capacola The theoretical formula calculates the aerosol particle sizes Dp1, Dp2, ... Dp under the conditions of relative humidity RH1 to equivalent relative humidity RH0 and equivalent temperature T0 after drying. n Particle size Dp after hygroscopic growth at equivalent relative humidity 11 ,Dp 12 ,…Dp 1n :

[0077]

[0078] Among them, Dp 1i Let Dp be the particle size after hygroscopic growth at the i-th equivalent relative humidity. i Let σ represent the i-th particle size, κ be the hygroscopic growth factor of the aerosol, reflecting the hygroscopic growth capacity of the aerosol itself, and σ be the hygroscopic growth factor. s / aR is the surface tension of the aerosol. Under high relative humidity, this value is usually taken to be equal to the surface tension of water. R is Avogadro's constant, and M is... water Let ρ be the molar mass of water, T0 be the equivalent temperature, and ρ be the molar mass of water. w The density of water;

[0079] c. Calculate the particle size Dp of the corresponding aerosol after the i-th wet growth using the volume-weighted average method. 1i Complex refractive index RI of aerosols 1i :

[0080] Where i = 1, 2, ..., n

[0081] Among them, RI water is the complex refractive index of water;

[0082] d. Using the Mie scattering model, the combined complex refractive index of the wet-grown particle size and aerosol was calculated to be (Dp) 11 ,RI 11 ), (Dp 12 ,RI 12 ...(Dp) 1n ,RI 1n The scattering intensities under the following conditions are S 11 ,S 12 …S 1n The corresponding scattering intensity distribution spectrum S′ calculated using a dry particle size aerosol combined with a hygroscopic growth model. 1i for:

[0083] e. Based on the scattering intensity distribution spectrum calculated using the dry particle size aerosol combined with the hygroscopic growth model, the corresponding first total scattering intensity S1 is:

[0084]

[0085] (3) The first total scattering intensity S1 and the second total scattering intensity S2 are essentially the same, both being the total scattering intensity of wet particle size aerosols. The initial value of the hygroscopic growth factor is changed using the gradient descent method until the first total scattering intensity S1 and the second total scattering intensity S2 are equal or their deviation is less than 10. -5 The value of the hygroscopic growth factor κ0 when this condition is met is the final inversion hygroscopic growth factor of the aerosol.

[0086] Finally, it should be noted that the purpose of disclosing the embodiments is to help further understand the present invention. However, those skilled in the art will understand that various substitutions and modifications are possible without departing from the spirit and scope of the present invention and the appended claims. Therefore, the present invention should not be limited to the content disclosed in the embodiments, and the scope of protection of the present invention is defined by the claims.

Claims

1. A method for measuring the hygroscopic growth factor of aerosols based on dual OPS, characterized in that, The measurement method includes the following steps: 1) Measuring device: After sampling the environmental aerosols at the sampling port, they were divided into two paths. One path passed through a drying tube, and the particle size distribution PNSD1 of the dried aerosol was measured using a first optical particle spectrometer. The temperature T1 and relative humidity RH1 of the dried aerosol were also measured. The other path was not dried, and the particle size distribution PNSD2 of the undried aerosol was measured directly using a second optical particle spectrometer. At the same time, the temperature T2 and relative humidity RH2 of the undried inlet, the temperature T3 and relative humidity RH3 of the undried outlet were measured before and after the second optical particle spectrometer, respectively. 2) Calculate the equivalent relative humidity: Using the temperature and relative humidity of the undried inlet and outlet, the water vapor content of the inlet and outlet is calculated to obtain the equivalent water content and equivalent temperature in the second optical particle spectrometer, and then the equivalent relative humidity of the aerosol in the second optical particle spectrometer is calculated. 3) Hygroscopic growth factor κ: (1) The second total scattering intensity S2 is obtained by directly using the scattering intensity distribution spectrum calculated from wet particle size aerosol; (2) Obtain the particle size after hygroscopic growth under equivalent relative humidity, and obtain the first total scattering intensity S1 by calculating the scattering intensity distribution spectrum of dry particle size aerosol combined with hygroscopic growth model. (3) Use the gradient descent method to change the initial value of the hygroscopic growth factor until the first total scattering intensity S1 and the second total scattering intensity S2 are equal or the deviation between them is less than a set threshold. When this condition is met, the value of the hygroscopic growth factor is the aerosol hygroscopic growth factor obtained by the final inversion.

2. The measurement method as described in claim 1, characterized in that, In step 2), the equivalent relative humidity is calculated, including the following steps: Using the undried inlet temperature T2 and the undried inlet relative humidity RH2, the water vapor content e2 at the inlet of the second optical particle spectrometer is calculated as follows: Using the undried outlet temperature T3 and the undried outlet relative humidity RH3, the water vapor content e3 at the outlet of the second optical particle spectrometer is calculated as follows: The equivalent water content e0 obtained in the second optical particle spectrometer is: The equivalent temperature T0 in the second optical particle spectrometer is: Using the equivalent temperature T0 and equivalent water content e0 in the second optical particle spectrometer, calculate the equivalent relative humidity RH0 of the aerosol in the second optical particle spectrometer OPS2:

3. The measurement method as described in claim 1, characterized in that, In step 3), (1) the second total scattering intensity S2 is obtained directly from the scattering intensity distribution spectrum calculated using wet particle size aerosol, including the following steps: a. Particle size distribution of undried aerosols. PNSD2 represents different particle sizes Dp1, Dp2, ... Dp n The undried concentrations of the aerosols were N 21 N 22 …N 2n n is the number of different particle size types; b. Using the Mie scattering model, the commonly used complex refractive index combinations for particle size and aerosols are (Dp1,RI0), (Dp2,RI0)...(Dp... n The scattering intensities under RI0) are S 21 ,S 22 …S 2n The corresponding scattering intensity distribution spectrum S′ is obtained directly from wet particle size aerosol calculations. 2i for: c. Based on the scattering intensity distribution spectrum obtained directly from wet particle size aerosols, the corresponding second total scattering intensity S2 is:

4. The measurement method as described in claim 1, characterized in that, In step 3), (2) the first total scattering intensity S1 is obtained by calculating the scattering intensity distribution spectrum of dry particle size aerosol combined with the hygroscopic growth model, including the following steps: a. An initial value for the hygroscopic growth factor is arbitrarily set. The particle size distribution after aerosol drying, PNSD1, represents different particle sizes Dp1, Dp2, ... Dp. n The concentrations of the dried aerosols were N 11 N 12 …N 1n ; b. Using the Capacola theory, calculate the aerosol particle sizes Dp1, Dp2, ... Dp under conditions of relative humidity RH1 to equivalent relative humidity RH0 and equivalent temperature T0 after drying. n Particle size Dp after hygroscopic growth at equivalent relative humidity 11 ,Dp 12 ,…Dp 1n ; c. Calculate the particle size Dp of the corresponding aerosol after the i-th wet growth using the volume-weighted average method. 1i Complex refractive index RI of aerosols 1i : Where i = 1, 2, ..., n Among them, RI water is the complex refractive index of water; d. Using the Mie scattering model, the combined complex refractive index of the wet-grown particle size and aerosol is calculated to be (Dp) 11 ,RI 11 ), (Dp 12 ,RI 12 ...(Dp) 1n ,RI 1n The scattering intensities under the following conditions are S 11 ,S 12 …S 1n The corresponding scattering intensity distribution spectrum S′ calculated using a dry particle size aerosol combined with a hygroscopic growth model. 1i for: e. Based on the scattering intensity distribution spectrum calculated using the dry particle size aerosol combined with the hygroscopic growth model, the corresponding first total scattering intensity S1 is:

5. The measurement method as described in claim 1, characterized in that, In step 3), (2) the initial value of the hygroscopic growth factor is 0.01 to 1.

6. The measurement method as described in claim 1, characterized in that, In step 3), (3) the threshold is set to 10. -6 ~10 -5 .

7. A device for measuring the hygroscopic growth factor of aerosols based on dual OPS, characterized in that, The measuring device includes: a drying tube, first and second optical particle spectrometers, and first to third temperature and humidity probes; wherein, the inlet of the environmental aerosol is connected via pipes to the inlet of the drying tube and the air inlet of the second optical particle spectrometer; the outlet of the drying tube is connected to the air inlet of the first optical particle spectrometer; a first temperature and humidity probe is installed at the inlet of the first optical particle spectrometer; a second and a third temperature and humidity probe are installed at the air inlet and outlet of the second optical particle spectrometer, respectively; after sampling, the environmental aerosol is divided into two paths, one path passes through the drying tube, and the particle size distribution of the dried aerosol is measured using the first optical particle spectrometer, and the temperature and relative humidity of the dried aerosol are measured using the first temperature and humidity probe; the other path is not dried, and the particle size distribution of the undried aerosol is directly measured using the second optical particle spectrometer, and simultaneously, temperature and humidity probes are used before and after the second optical particle spectrometer. The second and third temperature and humidity probes measure the temperature and relative humidity of the undried inlet and outlet of the gas path. The equivalent relative humidity is calculated based on the inlet and outlet temperatures and humidity from the second optical particle spectrometer. The particle size after hygroscopic growth at the equivalent relative humidity is calculated using the Kappacolla theory formula. The scattering intensity distribution spectrum is calculated using a dry particle size aerosol combined with a hygroscopic growth model to obtain the first total scattering intensity. The second total scattering intensity is then directly calculated using wet particle size aerosols. The initial value of the hygroscopic growth factor is changed using the gradient descent method until the first and second total scattering intensities are equal or their deviation is less than a set threshold. The hygroscopic growth factor value, when this condition is met, is the final inverted aerosol hygroscopic growth factor.

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